2024-03-29T05:01:52Z
http://sdvcmr-prod-oai01:8080/oai/
oai:qucosa:de:qucosa:10829
2021-03-29T08:12:42Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
oai:qucosa:de:qucosa:11141
2021-03-29T08:16:31Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Fitness-based mating: A systematic analysis of a new preference model
Susanne
Schindler
510
510
Sympatrische Speziation
Paarungspraeferenz
Partnerwahl
fitness-basierte Partnerwahl
sympatric speciation
mate preference
mate choice
fitness-based mating
Natural populations exhibit a non-random mating behavior and it is assumed that mate preferences causing the non-random mating behavior play a role in sympatric speciation.
In my thesis, I have proposed a new model of a mate preference that is based on ecological performance and I have named it fitness-based mating. Individuals that express this mate preference choose primarily fit partners.
Fitness-based mating is modelled for haploid, diallelic populations. Individuals are distributed across two niches, and genomes are simplified to two loci. The first locus is subject to natural selection, and the second-locus genotype gives the strength of the mate preference. The population is separated into females and males, among which only females exhibit the mate preference. Ecological selection acts on both sexes alike.
With the model I have investigated how female choosiness based on direct advantages offered by their partners can cause and maintain a polymorphic population. Fitness-based mating is an evolutionary successful mating strategy. It spreads in a population due to its amplifying effect on the reproductive success and on the attractiveness of its carriers. A polymorphism arises naturally in the model. The emergence of a stable polymorphism of traits underlying ecological selection is of special interest, because a polymorphism can be a precursor of speciation.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Juergen
Jost
Prof. Dr.
Juergen
Jost
Prof. Dr.
Wolfgang
Banzhaf
Prof. Dr.
Joachim
Hermisson
Prof. Dr.
2010-06-28
2011-01-04
2011-03-22
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-66485
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
1
https://ul.qucosa.de/api/qucosa%3A11141/zip/
urn:nbn:de:bsz:15-qucosa-66485
oai:qucosa:de:qucosa:11754
2021-03-29T08:23:55Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:000
ddc:510
openaire
Hierarchische Integration und der Strahlungstransport in streuenden Medien
Peter
Meszmer
510
510
000
000
Strahlungstransport
numerische Integration
singuläres Integral
mehrdimensionales Integral
mehrfaches Integral
Finite-Elemente-Methode
schwachsinguläre Fredholm-Integralgleichung
Strahlungstransport in streuenden Medien
numerische Integration
singuläre Integrale
fredholmsche Integralgleichung zweiter Art
Radiative heat transfer in participating media
numerical integration
singular integrals
Fredholm integral equation of the second kind
Der Strahlungstransport stellt eine von drei Arten des Wärmetransports zwischen Gebieten unterschiedlicher Temperatur dar. Eine der einfachsten Formen bildet der Strahlungstransport im Vakuum, ein Vorgang, der im kosmischen Umfeld, beispielsweise bei der Energieübertragung von einem Stern auf seine Planeten, beobachtbar ist. Hierbei ist es hinreichend, sich auf die Betrachtung von Oberflächen zu beschränken. Strahlungstransport kann jedoch auch in semitransparenten Medien, wie biologischem Gewebe oder Glas, beobachtet werden. Das Medium, in dem der Strahlungstransport erfolgt, wirkt sich durch Vorgänge wie Absorption, Emission, Reflexion oder Streuung auf den Strahlungstransport aus. Für die Modellierung des Strahlungstransports in einem solchen Umfeld können verschiedene Modelle, darunter das Strahlenmodell, genutzt werden. Dieses Modell beschreibt den Wärmetransport anhand einer skalaren Größe, die Strahlungsintensität genannt wird. Betrachtet wird die Strahlungsintensität in diesem Modell entlang eines Strahls in eine vorgegebene Richtung. Die mathematische Darstellung des Strahlenmodells des Strahlungstransports in partizipierenden Medien führt auf eine richtungsabhängige Integro-Differentialgleichung. Ist die Richtungsabhängigkeit nicht von Interesse, so kann der Übergang zu einer winkelintegrierten Form erfolgen. Dieser Übergang führt schließlich auf ein System schwach singulärer fredholmscher Integralgleichungen zweiter Art. Dieses charakterisiert nun nicht mehr die erwähnte Strahlungsintensität, sondern beschreibt die sogenannte Einstrahlung sowie den Strahlungsfluss.
Das System singulärer Integralgleichungen kann mittels eines Galerkin-Ansatzes numerisch gelöst werden. Geht man von einer hinreichenden Glattheit des Randes aus, kann die Kompaktheit des Operators der Integralgleichungen gezeigt werden. Dies wiederum erlaubt Rückschlüsse auf die Existenz und Eindeutigkeit einer Lösung.
Ein Augenmerk bei der Ermittlung der Galerkin-Näherung ist auf die Bestimmung der singulären Integrale der Galerkin-Diskretisierung zu richten. Für die Bestimmung multidimensionaler, singulärer Integrale stellt die Arbeit das Verfahren der hierarchischen Integration vor. Basierend auf einer Zerlegung des Integrationsgebietes, erfolgt die Beschreibung singulärer Integrale durch ein Gleichungssystem, dessen rechte Seite nur von regulären Integralen abhängig ist. Können diese regulären Integrale sowie die Lösung des Gleichungssystems exakt bestimmt werden, so sind auch die singulären Integrale exakt bestimmt. Bei einer numerischen Bestimmung der regulären Integrale ist die Fehlerordnung ausschlaggebend für den Fehler der singulären Integrale. Als Integrationsgebiete werden Hyperwürfel beliebiger Dimension sowie Simplizes bis einschließlich Dimension 3 als Integrationsgebiete betrachtet. Als Voraussetzungen an den Kern des Doppelintegrals sind nur die Eigenschaften der Translationsinvarianz sowie der Homogenität zu richten. Kann ein nicht translationsinvarianter oder nicht homogener Kern eines Integrals in Summanden zerlegt werden, die selbst translationsinvariant und homogen sind, ist auch die Bestimmung solcher Integrale möglich. Darüber hinaus stellt die Arbeit Verbindungen zu dem Begriff des Hadamard partie finie her. Auf diese Weise lässt sich das Verfahren der hierarchischen Integration für beliebige Dimensionen und beliebige Singularitätsordnungen anwenden.
Die Strahlungstransportgleichung ist im Allgemeinen mittels eines Galerkin-Ansatzes lösbar, führt jedoch auf eine voll besetzte Systemmatrix. Numerische Beispiele beleuchten daher Methoden der Matrixkompression mittels hierarchischer Matrizen sowie der direkten Erzeugung schwach besetzter Matrizen über regulären Gittern und Gittern mit hängenden Knoten und skizziert Ansätze zur Parallelisierung auf entsprechenden Computersystemen.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Leipzig
Leipzig
Wolfgang
Hackbusch
Prof. Dr. Dr. h. c.
Wolfgang
Hackbusch
Prof. Dr. Dr. h. c.
Mario
Bebendorf
Prof. Dr.
2012-05-02
2012-10-10
2012-11-07
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-98584
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
Max-Planck-Institut für Mathematik in den Naturwissenschaften
Leipzig
1
https://ul.qucosa.de/api/qucosa%3A11754/zip/
urn:nbn:de:bsz:15-qucosa-98584
oai:qucosa:de:qucosa:11784
2021-03-29T08:24:16Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Relaxation oscillations in slow-fast systems beyond the standard form
Ilona
Kosiuk
510
510
Schnell - langsam Systeme
Relaxationsschwingungen
Blow-up Methode
slow-fast systems
relaxation oscillations
blow-up method
Relaxation oscillations are highly non-linear oscillations, which appear to
feature many important biological phenomena such as heartbeat,
neuronal activity, and population cycles of predator-prey type.
They are characterized by repeated switching of slow and fast motions and
occur naturally in singularly perturbed ordinary differential equations, which exhibit dynamics on different time scales.
Traditionally, slow-fast systems and the related oscillatory phenomena -- such as relaxation oscillations -- have been studied by the method of the matched asymptotic expansions, techniques from non-standard analysis, and recently a more qualitative approach known as geometric singular perturbation theory.
It turns out that relaxation oscillations can be found in a more general setting; in particular, in slow-fast systems, which are not written in the standard form. Systems in which separation into slow and fast variables is not given a priori, arise frequently in applications. Many of these systems include additionally various parameters of different orders of magnitude and complicated (non-polynomial) non-linearities. This poses several mathematical challenges, since the application of singular perturbation arguments is not at all straightforward. For that reason most of such systems have been studied only numerically guided by phase-space analysis arguments or analyzed in a rather non-rigorous way. It turns out that the main idea of singular perturbation approach can also be applied in such non-standard cases.
This thesis is concerned with the application of concepts from geometric singular perturbation theory and geometric desingularization based on the blow-up method to the study of relaxation oscillations in slow-fast systems beyond the standard form.
A detailed geometric analysis of oscillatory mechanisms in three mathematical models describing biochemical processes is presented. In all the three cases the aim is to detect the presence of an isolated periodic movement represented by a limit cycle.
By using geometric arguments from the perspective of dynamical systems theory and geometric desingularization based on the blow-up method analytic proofs of the existence of limit cycles in the models are provided.
This work shows -- in the context of non-trivial applications -- that the geometric approach, in particular the blow-up method, is valuable for the understanding of the dynamics of systems with no explicit splitting into slow and fast variables, and for systems depending singularly on several parameters.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Juergen
Jost
Prof. Dr.
Juergen
Jost
Prof. Dr.
Freddy
Dumortier
Prof. Dr.
2012-02-05
2012-11-14
2013-03-22
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-100566
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
1
https://ul.qucosa.de/api/qucosa%3A11784/zip/
urn:nbn:de:bsz:15-qucosa-100566
oai:qucosa:de:qucosa:13120
2021-03-29T08:40:42Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Numerical methods in Tensor Networks
Stefan
Handschuh
510
510
Tensor
Elementartensorsumme
Tensornetzwerk
Tensordarstellung
ALS
DMRG,
tensor
sum of elementary tensors
tensor network
tensor representation
ALS
DMRG
In many applications that deal with high dimensional data, it is important to not store the high dimensional object itself, but its representation in a data sparse way. This aims to reduce the storage and computational complexity.
There is a general scheme for representing tensors with the help of sums of elementary tensors, where the summation structure is defined by a graph/network. This scheme allows to generalize commonly used approaches in representing a large amount of numerical data (that can be interpreted as a high dimensional object) using sums of elementary tensors. The classification does not only distinguish between elementary tensors and non-elementary tensors, but also describes the number of terms that is needed to represent an object of the tensor space. This classification is referred to as tensor network (format).
This work uses the tensor network based approach and describes non-linear block Gauss-Seidel methods (ALS and DMRG) in the context of the general tensor network framework.
Another contribution of the thesis is the general conversion of different tensor formats. We are able to efficiently change the underlying graph topology of a given tensor representation while using the similarities (if present) of both the original and the desired structure. This is an important feature in case only minor structural changes are required.
In all approximation cases involving iterative methods, it is crucial to find and use a proper initial guess. For linear iteration schemes, a good initial guess helps to decrease the number of iteration steps that are needed to reach a certain accuracy, but it does not change the approximation result. For non-linear iteration schemes, the approximation result may depend on the initial guess. This work introduces a method to successively create an initial guess that improves some approximation results. This algorithm is based on successive rank 1 increments for the r-term format.
There are still open questions about how to find the optimal tensor format for a given general problem (e.g. storage, operations, etc.). For instance in the case where a physical background is given, it might be efficient to use this knowledge to create a good network structure. There is however, no guarantee that a better (with respect to the problem) representation structure does not exist.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Wolfgang
Hackbusch
Prof. Dr. Dr. h.c.
Wolfgang
Hackbusch
Prof. Dr. Dr. h.c.
Daniel
Kressner
Prof. Dr.
2014-10-06
2015-01-14
2015-01-28
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-159672
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
1
https://ul.qucosa.de/api/qucosa%3A13120/zip/
urn:nbn:de:bsz:15-qucosa-159672
oai:qucosa:de:qucosa:14611
2021-03-29T08:59:54Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Positivstellensätze for the Weyl Algebra
Konrad
Zimmermann
510
510
Positivstellensatz
Weylalgebra
reelle algebraische Geometrie
positivstellensatz
Weyl algebra
real algebraic geometry
We prove a strict positivstellensatz for Weyl algebra elements fulfilling an additional, asymptotic strict positivity condition. As a tool we develop a non-commutative analogue to the Newton polytope.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Konrad
Schmüdgen
Prof. Dr.
Konrad
Schmüdgen
Prof. Dr.
Tim
Netzer
Prof. Dr.
2015-10-12
2016-02-17
2016-04-01
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-199764
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
1
https://ul.qucosa.de/api/qucosa%3A14611/zip/
urn:nbn:de:bsz:15-qucosa-199764
oai:qucosa:de:qucosa:14915
2021-03-29T09:03:43Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Absorptionsphasenubergang für Irrfahrten mit Aktivierung und
stochastische Zelluläre Automaten
Absorptionsphasenubergang für Irrfahrten mit Aktivierung undstochastische Zelluläre Automaten
Lorenzo
Taggi
510
510
Interacting Particle System
Random Walks
This thesis studies two Markov processes describing the evolution of a system of many interacting random components. These processes undergo an absorbing-state phase transition, i.e., as one variates the parameter values, the process exhibits a transition from a convergence regime to one of the absorbing-states to an active regime. In Chapter 2 we study Activated Random Walk, which is an interacting particle system where the particles can be of two types and their number is conserved. Firstly, we
provide a new lower bound for the critical density on Z as a function of the jump distribution and of the sleeping rate and we prove that the critical density is not a constant function of the jump distribution. Secondly, we prove that on Zd in the case of biased jump distribution the critical density is strictly less than one, provided that the sleeping rate is small enough. This answers a question that has been asked by Dickman, Rolla, Sidoravicius [9, 28] in the case of biased jump distribution. Our results have been presented in [33].
In Chapter 3 we study a class of probabilistic cellular automata which are related by a natural coupling to a special type of oriented percolation model. Firstly, we consider the process on a finite torus of size n, which is ergodic for any parameter value. By employing dynamic-renormalization techniques, we prove that the average absorption time grows exponentially (resp. logarithmically) with n when the model on Z is in the active (resp. absorbing) regime. This answers a question that has been asked by Toom [37]. Secondly, we study how the neighbourhood of the model affects the critical probability for the process on Z. We provide a lower bound for the critical probability as
a function of the neighbourhood and we show that our estimates are sharp by comparing them with our numerical estimates. Our results have been presented in [34, 35].
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Artem
Sapozhnikov
Prof.
2015-04-15
2015-09-15
2016-08-16
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-208644
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Max Planck Institute for Mathematics in the Sciences
Leipzig
1
https://ul.qucosa.de/api/qucosa%3A14915/zip/
urn:nbn:de:bsz:15-qucosa-208644
oai:qucosa:de:qucosa:15149
2022-03-25T06:13:39Z
qucosa:ubl
doc-type:article
has-source-swb:false
open_access
ddc:510
status-type:publishedVersion
openaire
Two numerical solutions for the stochastic collection equation
Martin
Simmel
Gleichung für stochastisches Einsammeln
Lösung
stochastic collection equation
solution
551
551
510
510
Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic
moments. Therefore, the \'splitting factors\' (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Different bin resolutions and time steps are investigated. As expected, the results become better with increasing bin resolution. LDM and BSM do not show the anomalous dispersion which is a weakness of DM.
Es werden zwei verschiedene Methoden zur numerischen Lösung der \'Gleichung für stochastisches Einsammeln\' (stochastic collection equation, SCE) vorgestellt. Sie werden als Lineare Diskrete Methode (LDM) bzw. Bin Shift Methode (BSM) bezeichnet. Konzeptuell sind beide der bekannten Diskreten Methode (DM) von Kovetz und Olund ähnlich. Für LDM und BSM wird deren Konzept auf zwei prognostische Momente erweitert. Für LDM und BSM werden die\' Aufteil-Faktoren\' (die für DM zeitlich konstant sind) dadurch zeitabhängig. Es werden Simulationsrechnungen für die Koaleszenzfunktion nach Golovin (für die
eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach Hall gezeigt. Verschiedene Klassenauflösungen und Zeitschritte werden untersucht. Wie erwartet
werden die Ergebnisse mit zunehmender Auflösung besser. LDM und BSM zeigen nicht die anomale Dispersion, die eine Schwäche der DM ist.
Universität Leipzig
Leipzig
Leipzig
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
2000
2016-12-02
2022-03-25
article
publishedVersion
urn:nbn:de:bsz:15-qucosa-215378
Meteorologische Arbeiten aus Leipzig - 5.2000 = Wissenschaftliche Mitteilungen aus dem Institut für Meteorologie der Universität Leipzig und dem Institut für Troposphärenforschung e.V. Leipzig ; Bd. 17. 5,S. 61-73
http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-211410
eng
3092033-4
urn:nbn:de:bsz:15-qucosa-212214
info:eu-repo/semantics/openAccess
1
https://ul.qucosa.de/api/qucosa%3A15149/zip/
urn:nbn:de:bsz:15-qucosa-215378
oai:qucosa:de:qucosa:15260
2021-03-29T09:08:11Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen
Axel
Schüler
510
510
Quantengruppe
Differentialkalkül
äußere Algebra
Hodge-Zerlegung
quantum group
differential calculus
exterior algebra
Hodge decomposition
In dieser Arbeit wird die de-Rham-Kohomologie für die Quantengruppen zu den vier klassischen Serien von Lie-Gruppen bestimmt und es wird der Hodgeschen Zerlegungssatz gezeigt. Als entscheidendes Mittel wurde der Laplace-Beltrami-Operator L für Woronowicz’ äußere Algebren entwickelt. Für transzendente Werte von q und reguläre Kalkülparameter z ist L diagonalisierbar.
Für die obigen Quantengruppen bestimmen wir die Eigenwerte von L, die neben q und z von zwei integralen dominanten Gewichten abhängen.
Wie im klassischen Fall wird die de-Rham-Kohomologie durch harmonische Formen repräsentiert.
Jedoch entspricht nur im Fall der A-Serie jeder harmonischen Form auch eine de-Rham-Kohomologieklasse. Im Falle der B-, C- und D-Serien sind biinvariante Formen nicht notwendig geschlossen. Es gilt aber, dass jede biinvariante Form harmonisch ist.
Das zweite Hauptresultat ist die Hodge-Zerlegung für die Quantengruppen GLq(N) und SLq(N): Ist der Kalkülparameter z regulär, so lässt sich jede Form eindeutig zerlegen in die Summe aus einem Rand, einem Korand und einem Kohomologierepräsentanten. Ferner gilt, analog zum klassischen Fall, dass die folgenden drei Formenräume übereinstimmen: die biinvarianten Formen, die harmonischen Formen und die de-Rham-Kohomologie. Für die orthogonalen und symplektischen Quantengruppen gibt es keine vollständige Hodge-Zerlegung. Nur für die Elemente, die im Bild des Laplace-Beltrami-Operators liegen, gibt es eine eindeutige Zerlegung in Rand und Korand. Für die Standardkalküle auf den Quantengruppen GLq(N) und SLq(N) wird die Größe von Woronowicz’ äußerer Algebra bestimmt. Es wird gezeigt, dass der Raum der linksinvarianten k-Formen (N² über k)-dimensional ist. Die Algebra der biinvarianten Formen ist graduiert kommutativ. Ihre Poincaré-Reihe ist (1+t)(1+t³) ... (1+t^(2N-1)). Biinvariante Formen sind geschlossen.
Consider one of the standard bicovariant first order differential calculi for
the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a
transcendental complex number. It is shown that the de Rham cohomology
of Woronowicz'' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator.
As in the classical case all three spaces of differential forms coincide: bi-
invariant forms, harmonic forms and the de-Rham-cohomology. For orthog-
onal and symplectic quantum groups there is no complete Hodge decompo-
sition. In case of the standard calculi on the quantum groups GLq(N) and
SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Universität Leipzig
Konrad
Schmüdgen
Harald
Grosse
Alfons
van Dale
2000-09-15
2001-07-02
2017-01-30
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-218057
ger
info:eu-repo/semantics/openAccess
thesis.habilitation
Universität Leipzig
Fakultät für Mathematik und Informatik
1
https://ul.qucosa.de/api/qucosa%3A15260/zip/
urn:nbn:de:bsz:15-qucosa-218057
oai:qucosa:de:qucosa:15320
2021-03-29T09:08:58Z
qucosa:ubl
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Klassifikation von bikovarianten Differentialkalkülen auf Quantengruppen
Classification of bicovariant differential calculi on quantum groups
Axel
Schüler
510
510
bikovariante Differentialkalküle
Quantengruppe
Liesche Gruppe
Hecke-Algebra
bicovariant differential calculus
quantum group
Lie group
Hecke algebra
Unter der Voraussetzung, dass q keine Einheitswurzel ist und dass die Differentiale duij der Fundamentalmatrix den Linksmodul der 1-Formen erzeugen, werden die bikovarianten Differentialkalküle auf den Quantengruppen SLq(N), Oq(N) und Spq(N) klassifiziert. Es wird gezeigt, dass es auf den Quantengruppen SLq(N), N ≥ 3, abgesehen von eindimensionalen Kalkülen und endlich vielen Werten von q genau 2N bikovariante Differentialkalküle gibt. Diese Kalküle haben die Dimension N².
Für die Quantengruppen Oq(N) und Spq(N), N ≥ 3, gibt es unter den genannten Voraussetzungen bis auf endlich viele Werte von q genau zwei bikovariante Differentialkalküle der Dimension N². Die Bimodulstruktur der Kalküle sowie die zugeordneten ad-invarianten Rechtsideale werden explizit angegeben. Für die Quantengruppen SLq(N), N ≥ 3, wird gezeigt, dass es, sofern q keine Einheitwurzel ist, genau 2N² + 2N bikovariante Bimoduln vom Typ (u^c u; f) gibt.
If q is not a root of unity and under the assumption that the differentials duij of the fundamental matrix (uij) generate the left module of 1-forms, all bicovariant differential calculi on quantum groups SLq(N), Oq(N) and Spq(N) are classified. It is shown that on quantum groups SLq(N), N ≥ 3, except of 1-dimensional calculi and finitely many values of q, thre are exactly 2N bicovariant differential calculi. The space of invariant forms has dimension N².
For quantum groups Oq(N) and Spq(N), N ≥ 3, under the same assumptions and up to finitely many values of q, there are exactly two bicovariant differential calculi of dimension N². The bimodule structure of the calculi as well as the corresponding ad-invariant right ideals are explicitely described. For quantum groups SLq(N), N ≥ 3, there are exactly 2N² + 2N bicovariant
bimodules of type (u^c u; f) provided q is not a root of unity.
Universitätsbibliothek Leipzig
Leipzig
Beethovenstraße 6, 04107 Leipzig
Konrad
Schmüdgen
Konrad
Schmüdgen
Barnislav
Jurco
Jürgen
Stückrad
1994-05-31
1994-11-30
2017-02-09
2021-03-29
doctoralThesis
urn:nbn:de:bsz:15-qucosa-218907
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Universität Leipzig
Leipzig
Fakultät für Mathematik und Informatik
1
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urn:nbn:de:bsz:15-qucosa-218907
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Von geordneten Mengen bis zur Uranmaschine
Zu den Wechselbeziehungen zwischen Mathematik und Physik an der Universität Leipzig in der Zeit von 1905 bis 1945
Karl-Heinz
Schlote
Mathematik
Physik
Wissenschaftsgeschichte
Universitätsgeschichte
Leipzig
510
510
AL 54902
SG 580
UB 2380
NZ 15080
Universität Leipzig
Mathematik
Physik
Geschichte 1905-1945
Universität Leipzig
Sächsische Akademie der Wissenschaften zu Leipzig
Universität
Mathematik
Physik
Hochschullehrer
Vorlesung
Vorwort
1 Einleitung
2 Grundzüge der Entwicklung von Mathematik und Physik zu Beginn des 20. Jahrhunderts
2.1 Wichtige Trends in der Mathematik zu Beginn des 20. Jahrhunderts
2.2 Von der Quantenhypothese bis zur Quantenmechanik
2.3 Wandlungen im Wechselverhältnis von Mathematik und Physik
3 Die Veränderungen in der Personalstruktur bis zum Jahre 1914
3.1 Sachsen im Jahrzehnt vor dem Ersten Weltkrieg
3.2 Das neue Physikalische Institut und die Erweiterung des Lehrkörpers
3.3 Die Begründung einer Professur für Geschichte der Physik
3.4 Die Geophysik etabliert sich in Leipzig
3.5 Die Arbeit am Mathematischen Institut bis zum Jahre 1914
4 Der Erste Weltkrieg und die ersten Jahre der Weimarer Republik
4.1 Die Leipziger Physiker während und nach dem Ersten Weltkrieg
4.2 Die Hinwendung zur modernen theoretischen Physik
4.3 Die Neuprofilierung des Physikalischen Instituts
4.4 Die Veränderungen an den Lehrstühlen für Geophysik und Astronomie
4.5 Das Mathematische Institut in der Kriegs- und Nachkriegszeit
5 Die Vorlesungsaktivitäten zur mathematischen und theoretischen Physik in den Jahren 1905 – 1928
6 Das wissenschaftliche Leben auf den Gebieten der Mathematik und Physik sowie der angrenzenden Fächer
6.1 Wieners Ringen um einen einheitlichen Aufbau der Physik
6.2 Die Aktivitäten in den einzelnen Abteilungen des Physikalischen Instituts
6.3 Die Forschungen am Theoretisch-Physikalischen Institut
6.4 Neu und sogleich von Weltgeltung – die Geophysik in Leipzig
6.5 Von Neumann bis Lichtenstein – Kontinuität der mathematischen Physik?
6.6 Die Forschungen der außerordentlichen Professoren und Privatdozenten – Mengenlehre, Differentialgeometrie, Funktionentheorie, Zahlentheorie
6.7 Die fehlende Astrophysik – das Manko der Astronomie
6.8 Veränderungen in der Rolle der Sächsischen Akademie
7 Leipzigs Sternstunde in der theoretischen Physik und der bittere Niedergang
7.1 Veränderungen in den Wissenschaften
7.2 Die Profilierung des Physikalischen Instituts als Zentrum der theoretischen Physik
7.3 Das Geophysikalische Institut
7.4 Der mühsame Weg bei der Bewahrung der Tradition am Mathematischen Institut
7.5 Die Wiederbesetzung der Lichtenstein’schen Professur – die Rolle der angewandten Mathematik
7.6 Die Assistenten am Mathematischen Institut
7.7 Auseinandersetzungen um die Leitung des Mathematischen Instituts
7.8 Die Erneuerung des Instituts für Versicherungswissenschaft
7.9 Der schwere Stand der Astronomie
8 Das Lehrangebot in Mathematik und Physik in den Jahren 1928 – 1945
9 Mathematik und Physik in Leipzig – Vom sprudelnden Quell zum schwachen Rinnsal
9.1 Die Blüte der Leipziger theoretischen Physik
9.2 Die Aufklärung der Molekülstruktur – das zentrale Arbeitsthema von Debye und Hund
9.3 Die Erfolge der Abteilungen für technische Physik
9.4 Die Forschungen zur Kernspaltung und zur Uranmaschine
9.5 Die Forschungen am Geophysikalischen Institut
9.6 Kontinuität und Wandel in der Auseinandersetzung mit physikalischen Fragen – Lichtenstein und van der Waerden
9.7 Summenformeln, Uniformisierung Riemann’scher Mannigfaltigkeiten und Gruppentheorie – neue Resultate von O. Hölder bis Koebe
9.8 Die Beiträge der Leipziger Astronomen
9.9 Die Sächsische Akademie der Wissenschaften
10 Das Wechselverhältnis zwischen Mathematik und Physik im Überblick
Literatur und Quellen
Abbildungsverzeichnis
Personenverzeichnis
Es gibt wohl kaum Wissenschaftsgebiete, in denen die wechselseitige Beeinflussung stärker ist als zwischen Mathematik und Physik. Eine wichtige Frage ist dabei die nach der konkreten Ausgestaltung dieser Wechselbeziehungen, etwa an einer Universität, oder die nach prägenden Merkmalen in der Entwicklung dieser Beziehungen in einem historischen Zeitabschnitt.
Im Rahmen eines mehrjährigen Akademieprojekts wurden diese Beziehungen an den Universitäten in Leipzig, Halle und Jena für den Zeitraum vom Beginn des 19. bis zur Mitte des 20. Jahrhunderts untersucht und in fünf Bänden dargestellt. Der erste dieser Bände erschien in den Abhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, die nachfolgenden (u.a. der vorliegende) als eigenständige Reihe unter dem Titel “Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen“. Ein weiterer und abschließender Band dieser Reihe beinhaltet die Beiträge einer wissenschaftshistorischen Fachtagung im Jahr 2010, die das Thema in einem internationalen Kontext einbettet.
Der vorliegende Band behandelt den Zeitraum von 1905 bis 1945 an der Universität Leipzig. In diese Zeit fällt der fulminante Aufstieg der Leipziger theoretischen Physik nach einer längeren Stagnationsphase zu einem führenden Zentrum der quanten- und kernphysikalischen Forschungen durch das Wirken von Peter Debye und Werner Heisenberg sowie Friedrich Hund. Nahezu gleichzeitig erfuhren auch die Wechselbeziehungen zwischen Mathematik und Physik durch die Zusammenarbeit der theoretischen Physiker mit dem ebenfalls neu berufenen Mathematik-Ordinarius Bartel Leendert van der Waerden (1930) einen starken Entwicklungsschub. Zuvor hatten sich die Lehr- und Forschungsbedingungen der Mathematiker durch die Schaffung eines eigenen Institutsgebäudes (1905) spürbar verbessert. Diese erfolgreiche Entwicklung wurde nach der Machtergreifung der Nationalsozialisten jäh unterbrochen.
Wissenschaftlicher Verlag Harri Deutsch
Frankfurt am Main
Frankfurt am Main
Sächsische Akademie der Wissenschaften zu Leipzig
Leipzig
Leipzig
Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden
Dresden
Dresden
2008
2017-07-06
2021-03-27
book
publishedVersion
urn:nbn:de:bsz:14-qucosa2-158321
978-3-8171-1840-3
ger
Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen
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Funktechnik, Höhenstrahlung, Flüssigkristalle und algebraische Strukturen
Zu den Wechselbeziehungen zwischen Mathematik und Physik an der Universität Halle-Wittenberg in der Zeit von 1890 bis 1945
Karl-Heinz
Schlote
Martina
Schneider
Mathematik
Physik
Wissenschaftsgeschichte
Universitätsgeschichte
Halle (Saale)
500
500
510
510
530
530
AL 53202
SG 580
UB 2380
Martin-Luther-Universität Halle-Wittenberg
Mathematik
Physik
Geschichte 1890-1945
Vorwort
1 Einleitung
2 Historische Eckpunkte der Universitätsentwicklung
2.1 Regionale Strukturen: Deutschland – Sachsen-Anhalt – Halle
2.2 Einige Veränderungen in der Stellung der Universität
3 Die Entwicklung des Mathematischen Instituts
3.1 Die Schwierigkeiten beim Aufbau der Infrastruktur
3.2 Gutzmers Bemühungen zur Stärkung der angewandten Mathematik
3.3 Das vergebliche Ringen um die Erweiterung des mathematischen Lehrkörpers
3.4 Die relativ stabile Entwicklung und Attraktivität der Mathematik unter Hasse und Brandt
3.5 Das Schicksal der Astronomie als Nischenfach
4 Der Weg des Physikalischen Instituts in die Moderne
4.1 Das Physikalische Institut unter der Leitung von Ernst Dorn
4.2 Von der theoretischen zur technischen Physik und die schwierige Suche nach einem Nachfolger für G. Mie
4.3 Die Neuorientierung des Physikalischen Instituts
4.4 Die Abtrennung des Instituts für Theoretische Physik
4.5 Zwei physikalische Institute im Widerstreit
5 Das Lehrangebot in Mathematik und Physik
5.1 Überblick zur Lehre in Mathematik und Astronomie
5.2 Veranstaltungen zur mathematischen Physik
5.3 Zum Lehrangebot der Physik
5.4 Veranstaltungen zur theoretischen Physik
5.5 Vergleich mit anderen Universitäten
6 Die mathematische Forschung
6.1 Mengenlehre und Logik
6.2 Potentialtheorie und Analysis
6.3 Geometrie
6.4 Mechanik, Astronomie und angewandte Mathematik
6.4.1 Dynamische Probleme der Mechanik und Kreiseltheorie
6.4.2 Gyldén’sche Störungstheorie
6.4.3 Von der Aero- und Hydrodynamik über Optik bis zur Wärmeleitung
6.5 Algebra, Zahlentheorie und Topologie
6.5.1 Arithmetisierung der algebraischen Geometrie
6.5.2 Algebraische Zahlentheorie
6.5.3 Gruppoid und Arithmetik von Algebren
7 Mit stetem Blick auf Experiment und technische Anwendungen – die Forschungen am Physikalischen Institut
7.1 Elektrophysik
7.2 Hochfrequenzphysik und der rasche Aufschwung der Funktechnik
7.3 Physik der freien Atmosphäre
7.4 Atomphysik
7.4.1 Gasentladungs- und Strahlungsphysik
7.4.2 Kosmische Höhenstrahlung
7.4.3 Kernphysik
7.5 Materialwissenschaft
7.5.1 Flüssigkristalle – Dielektrika
7.5.2 Werkstoffkunde und Brucherscheinungen
7.6 Thermodynamik und Photochemie – zwei singuläre Punkte in den Hallenser Forschungen
7.7 Theorie der Materie – Relativitätstheorie
8 Hallenser Mathematiker und Physiker und die örtlichen Gelehrten Gesellschaften und Vereine
8.1 Naturforschende Gesellschaft zu Halle
8.2 Naturwissenschaftlicher Verein für Sachsen und Thüringen
8.3 Deutsche Akademie der Naturforscher Leopoldina
8.4 Fazit
9 Das Wechselverhältnis zwischen Mathematik und Physik an der Hallenser Universität im Spiegel der allgemeinen Entwicklung
9.1 Neue Aspekte in den Beziehungen zwischen Mathematik und Physik im Allgemeinen
9.2 Die Dominanz der Physiker – die spezielle Ausgestaltung des Wechselverhältnisses in Halle
Anhang: Verzeichnis der Vorlesungen zur mathematischen und theoretischen Physik (Wintersemester 1890/91 – Sommersemester 1945)
Literatur und Quellen
Abbildungsverzeichnis
Verzeichnis der Diagramme
Personenverzeichnis
Grafik: Vorlesungstätigkeit der Dozenten für Mathematik und Physik in Halle (1890-1945)
Es gibt wohl kaum Wissenschaftsgebiete, in denen die wechselseitige Beeinflussung stärker ist als zwischen Mathematik und Physik. Eine wichtige Frage ist dabei die nach der konkreten Ausgestaltung dieser Wechselbeziehungen, etwa an einer Universität, oder die nach prägenden Merkmalen in der Entwicklung dieser Beziehungen in einem historischen Zeitabschnitt.
Im Rahmen eines mehrjährigen Akademieprojekts wurden diese Beziehungen an den Universitäten in Leipzig, Halle und Jena für den Zeitraum vom Beginn des 19. bis zur Mitte des 20. Jahrhunderts untersucht und in fünf Bänden dargestellt. Der erste dieser Bände erschien in den Abhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, die nachfolgenden (u.a. der vorliegende) als eigenständige Reihe unter dem Titel “Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen“. Ein weiterer und abschließender Band dieser Reihe beinhaltet die Beiträge einer wissenschaftshistorischen Fachtagung im Jahr 2010, die das Thema in einem internationalen Kontext einbettet.
Der vorliegende Band behandelt den Zeitraum von 1890 bis 1945 an der Universität Halle-Wittenberg. Die Entwicklung der Hallenser Universität in dieser Zeit ist durch ein ständiges Bemühen gekennzeichnet, einen weiteren Bedeutungsverlust der Hallenser Alma Mater zu begrenzen. Gleichzeitig beeindrucken die Mathematiker und Physiker mit einer ganzen Reihe von bemerkenswerten Forschungsergebnissen, wie die Bestätigung der von Victor Hess entdeckten kosmischen Höhenstrahlung (Werner Kolhörster, 1914), die Studien zu Flüssigkristallen (Ernst Dorn und Wilhelm Kast, ab 1896 bzw. 1931), zu Elektronenstößen (Gustav Hertz, 1925), zur Bruchtheorie und zur Ionenleitung (Adolf Smekal, ab 1931), zur Atom-und Kernphysik (Gerhard Hoffmann und Heinz Pose, ab 1931), zur Anwendung der Laplace-Transformation (Gustav Doetsch, ab 1923) zur Klassenkörpertheorie (Helmut Hasse, 1926), zu Gruppoiden sowie zur Arithmetik von Algebren (Reinhold Baer bzw. Heinrich Brandt ab 1928) und zur Arithmetisierung der algebraischen Geometrie (Jung, ab 1925).
Wissenschaftlicher Verlag Harri Deutsch
Frankfurt am Main
Frankfurt am Main
Sächsische Akademie der Wissenschaften zu Leipzig
Leipzig
Leipzig
Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden
Dresden
Dresden
2009
2017-07-06
2021-03-27
book
publishedVersion
urn:nbn:de:bsz:14-qucosa2-158352
978-3-8171-1842-7
ger
Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa2-158337
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa2-158352
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Von Schweiggers erstem Galvanometer bis zu Cantors Mengenlehre
Zu den Wechselbeziehungen zwischen Mathematik und Physik an der Universität Halle-Wittenberg in der Zeit von 1817 bis 1890
Karl-Heinz
Schlote
Martina
Schneider
Mathematik
Physik
Wissenschaftsgeschichte
Universitätsgeschichte
Halle (Saale)
500
500
510
510
530
530
SG 575
Martin-Luther-Universität Halle-Wittenberg
Mathematik
Physik
Geschichte 1817-1890
Martin-Luther-Universität Halle-Wittenberg
Universität
Mathematik
Physik
Naturwissenschaften
Lehrstuhl
Lehrveranstaltung
Forschungsgegenstand
Mathematiker
Physiker
Vorwort
1 Einleitung
2 Die Anfänge der Vereinigten Friedrichs-Universität Halle-Wittenberg im Rahmen der neugestalteten Universitätenlandschaft Preußens ab 1817
3 Die Mathematik an der Vereinigten Friedrichs-Universität Halle-Wittenberg
3.1 Der Neubeginn und die ersten Lehrstuhlbesetzungen
3.2 Sohnckes Initiative zur Gründung eines mathematisch-physikalischen Seminars
3.3 Die Zeit der starken Fluktuation auf dem mathematischen Lehrstuhl und Heines Ringen um die Verbesserung der Ausbildung
3.4 Auf dem Weg zum mathematischen Institut
4 Die Astronomie – ein Hallenser Nischenfach
5 Die Einrichtung des Lehrstuhls für Physik und dessen Besetzung
5.1 Die Ära Schweigger
5.1.1 Die größere Repräsentanz der Physik durch Kaemtz und Weber
5.1.2 Auseinandersetzungen mit Schweigger und die Einrichtung des Ordinariats für Physik
5.1.3 Hankels Wechsel nach Leipzig und die Berufung Knoblauchs
5.2 Auf dem Weg zur Etablierung der theoretischen Physik
5.3 Der Bau des Physikalischen Instituts
6 Mathematik und Physik in der Lehre
6.1 Überblick
6.2 Vorlesungen zur Mechanik, mathematischen und theoretischen Physik
6.2.1 Erste Phase (1817 – 1842): relativ regelmäßiges Angebot
6.2.2 Zweite Phase (1843 – 1853): Einbruch
6.2.3 Dritte Phase (1854 – 1874): Wiederaufleben und Erstarken
6.2.4 Vierte Phase (1875 – 1890): Anstieg
6.3 Gesellschaften und Seminare als Vorläufer zur Etablierung von Übungen
7 Forschungsgebiete der Hallenser Mathematiker zwischen 1817 und 1890
7.1 Dynamik und Erdmagnetismus: F. Pfaff und J. G. Steinhäuser
7.1.1 Pfaffs Beitrag zur Integration der Bewegungsgleichungen
7.1.2 Steinhäusers Theorie zum Erdmagnetismus
7.1.3 Gartz’ Beiträge zur Mathematikgeschichte
7.2 Astronomische Berechnungen zur Kometenbahn: A. Rosenberger
7.3 Forschungsschwerpunkt Analysis: von J. J. Schoen bis E. Wiltheiß
7.3.1 Schoens Arbeiten
7.3.2 Scherks Beiträge
7.3.3 Sohnckes vielseitige Forschungsinteressen
7.3.4 Rochs Untersuchungen zu Abel’schen und elliptischen Integralen
7.3.5 Schwarz’ erste Arbeiten zu konformen Abbildungen
7.3.6 Thomaes Arbeiten zur Reihenentwicklung und Theorie der komplexen Funktionen
7.3.7 Jürgens’ Untersuchungen zu speziellen Funktionen und Differentialgleichungen
7.3.8 Wiltheiß’ Beiträge zu Abel’schen Funktionen und partiellen Differentialgleichungen
7.4 Beiträge zur Geometrie: von J. Plücker bis H. Wiener
7.4.1 Von der Theorie der algebraischen Kurven zur Optik: Julius Plücker
7.4.2 Algebraische projektive Geometrie: Ferdinand Joachimsthal und Otto Hesse
7.4.3 Untersuchungen zu den Grundlagen der Geometrie: Hermann Wiener
7.5 Die kurze Blütezeit der mathematischen Physik: E. Heine und C. Neumann
7.5.1 Ausbau der Potentialtheorie von mathematischer Seite: Eduard Heine
7.5.2 Von der Optik bis zur Kristallographie: Carl Neumanns vielfältige Beiträge zur mathematischen Physik
7.6 Die Begründung der Mengenlehre durch Georg Cantor
7.7 Zur Theorie der Newton’schen Ringe: A. Wangerin
8 Die physikalischen Forschungen an der Universität Halle-Wittenberg
8.1 Die stärkere Profilierung der Physik – Schweigger und seine Schüler
8.2 Knoblauch und die Erforschung der «strahlenden Wärme»
8.3 Die Vertretung der theoretischen Physik durch Cornelius, Oberbeck und Dorn
9 Hallenser Mathematiker und Physiker und die örtlichen Gelehrten Gesellschaften und Vereine
9.1 Die Naturforschende Gesellschaft zu Halle
9.2 Der Naturwissenschaftliche Verein
9.3 Die Deutsche Akademie der Naturforscher Leopoldina
10 Die Wechselbeziehungen zwischen Mathematik und Physik an der Hallenser Universität
10.1 Die grundlegenden Veränderungen in den Wechselbeziehungen
10.2 Die spezifische Hallenser Entwicklung der Wechselbeziehungen
Anhang: Verzeichnis der Vorlesungen zur mathematischen und theoretischen Physik (Wintersemester 1817/18 – Sommersemester 1891)
Literatur und Quellen
Abbildungsverzeichnis
Verzeichnis der Diagramme
Personenverzeichnis
Grafik: Vorlesungstätigkeit der Dozenten für Mathematik und Physik in Halle (1817-1890)
Es gibt wohl kaum Wissenschaftsgebiete, in denen die wechselseitige Beeinflussung stärker ist als zwischen Mathematik und Physik. Eine wichtige Frage ist dabei die nach der konkreten Ausgestaltung dieser Wechselbeziehungen, etwa an einer Universität, oder die nach prägenden Merkmalen in der Entwicklung dieser Beziehungen in einem historischen Zeitabschnitt.
Im Rahmen eines mehrjährigen Akademieprojekts wurden diese Beziehungen an den Universitäten in Leipzig, Halle und Jena für den Zeitraum vom Beginn des 19. bis zur Mitte des 20. Jahrhunderts untersucht und in fünf Bänden dargestellt. Der erste dieser Bände erschien in den Abhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig, die nachfolgenden (u.a. der vorliegende) als eigenständige Reihe unter dem Titel “Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen“. Ein weiterer und abschließender Band dieser Reihe beinhaltet die Beiträge einer wissenschaftshistorischen Fachtagung im Jahr 2010, die das Thema in einem internationalen Kontext einbettet.
Der vorliegende Band behandelt den Zeitraum von 1817 bis 1890 an der Universität Halle-Wittenberg. Recht deutlich fällt hier die meist nur mäßige Förderung der Hallenser Alma Mater auf, die sich aus ihrer Stellung in der Universitätslandschaft Preußens ergab. Trotz des daraus resultierenden engen Finanzbudgets gelang es der Philosophischen Fakultät, einige junge talentierte Dozenten sowie angesehene Fachvertreter (Gustav Roch, Hermann Amandus Schwarz, Wilhelm Hankel, Julius Plücker, Eduard Heine, Georg Cantor u.a.) zu gewinnen und, wenn auch oft nur für kurze Zeit, von deren Forschungsaktivitäten und -ideen zu profitieren. Gleichzeitig konnten Johann S. Chr. Schweigger und Hermann Knobloch mit der Einrichtung einer Professur für Physik bzw. dem Bau eines neuen Institutsgebäudes die Entwicklung der Physik voranbringen. Später trugen Ernst Dorn und Georg Cantor, die mehrere Jahrzehnte in Halle tätig waren, mit ihren Forschungen zum Ansehen der Hallenser Universität bei.
Wissenschaftlicher Verlag Harri Deutsch
Frankfurt am Main
Frankfurt am Main
Sächsische Akademie der Wissenschaften zu Leipzig
Leipzig
Leipzig
Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden
Dresden
Dresden
2009
2017-07-06
2021-03-27
book
publishedVersion
urn:nbn:de:bsz:14-qucosa2-158342
978-3-8171-1841-0
ger
Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa2-158337
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A15834/zip/
urn:nbn:de:bsz:14-qucosa2-158342
492630453
oai:qucosa:de:qucosa:15858
2021-03-27T15:29:38Z
qucosa:slub
doc-type:book
has-source-swb:true
open_access
ddc:370
ddc:510
ddc:530
status-type:publishedVersion
openaire
Zu den Wechselbeziehungen zwischen Mathematik und Physik an der Universität Leipzig in der Zeit von 1830 bis 1904/05
Karl-Heinz
Schlote
Mathematik
Physik
Wissenschaftsgeschichte
Universitätsgeschichte
Leipzig
510
510
530
530
370
370
SG 575
TB 3821
TB 2380
AL 28500
TB 2300
Universität Leipzig
Physik
Mathematik
Geschichte 1830-1905
Vorwort
1. Einleitung
2. Die Reform der Universität Leipzig
3. Mathematik und Physik an der Leipziger Universität in den ersten Jahrzehnten des 19. Jahrhunderts
4. Die Berufungen der Professoren für Mathematik bzw. Physik bis zur Gründung des Mathematischen Seminars 1881
4.1 Die Repräsentation der Physik in Leipzig durch Fechner, Weber und Hankel
4.2 Die Etablierung der ersten Professur für physikalische Chemie
4.3 Der Bau des Physikalischen Instituts
4.4 Die Besetzung des mathematischen Lehrstuhls
4.4.1 Der Weg zu einem Ordinariat für Astronomie und Mathematik
4.4.2 Die Stärkung der mathematischen Physik
4.4.3 Die Berufung von Felix Klein und die Gründung des Mathematischen Seminars
5. Die Lehrveranstaltungen zur Mathematik und Physik an der Leipziger Universität
5.1 Die Veränderungen in der Lehre von Mathematik und Physik
5.2 Initiativen zu frühen Seminargründungen an der Universität Leipzig
5.2.1 Erdmanns naturwissenschaftliches Seminar
5.2.2 Marbachs mathematisch-naturwissenschaftliches Seminar
5.3 Überblick über die Vorlesungen
5.4 Das mathematisch-physikalische Vorlesungsangebot in Leipzig und an anderen Universitäten
6. Die Forschungsaktivitäten der Leipziger Physik- bzw. Mathematikprofessoren
6.1 Die internationale Forschungssituation
6.2 Wichtige Leipziger Beiträge zur Begründung der Elektrodynamik
6.3 Die Gründung der Königlich Sächsischen Gesellschaft der Wissenschaften
6.4 Hankels Untersuchungen zur Pyroelektrizität und seine Wirbeltheorie der Elektrizität
6.5 Der Nachweis elektrischer Schwingungen durch B. W. Feddersen
6.6 Die Begründung der Psychophysik an der Universität Leipzig
6.7 Neue Impulse in der mathematischen Forschung - A. Mayer und der Ausbau der Variationsrechnung
6.8 Die Förderung der mathematischen Physik durch C. Neumann
6.9 Die Begründung der Astrophysik durch Zöllner
6.10 Wiedemanns 'Enzyklopädie' der Elektrizitätslehre
7. Einschätzung der Wechselbeziehungen zwischen Mathematik und Physik
8. Die Entwicklung des Lehrkörpers am Mathematischen Institut von 1880 bis 1905
8.1 F. Klein und die Anfangsphase des Mathematischen Instituts
8.2 Die Bewältigung der Stagnationsphase am Mathematischen Institut
8.3 Der beginnende Generationswechsel am Mathematischen Institut und die Neuausrichtung des Instituts
8.4 Die Besetzung des astronomischen Ordinariats und die Arbeiten an der Sternwarte
9. Die Entwicklung des Lehrkörpers im Fach Physik bis zur Errichtung des neuen Physikalischen Instituts
9.1 Die Neubesetzung des Ordinariats für Physik und die Schaffung einer Professur für theoretische Physik
9.2 Die Besetzung der beiden Physikordinariate und der Neubau des Instituts
10. Die in den Jahren 1881-1905 gehaltenen Vorlesungen zur mathematischen und theoretischen Physik
11. Theoretische und mathematische Physik in den Forschungen der Leipziger Physiker und Mathematiker in den letzten Jahrzehnten des 19. Jahrhunderts
11.1 Die physikalischen Forschungen bis zur Errichtung des Extraordinariats für theoretische Physik
11.2 Beiträge zur Elektrizitätslehre - von Wiedemann bis Föppl
11.3 Ebert und Drude - die ersten Leipziger Professoren für theoretische Physik
11.4 Thermodynamik und Akustik - die Arbeiten von Wiedeburg und von Oettingen
11.5 Das Intermezzo Boltzmann und der Beginn der Ära Wiener - Des Coudres
11.6 Einige Entwicklungstendenzen der Mathematik
11.7 Die Uniformisierungstheorie und die 'physikalische Mathematik' F. Kleins
11.8 Neumanns Anwendung und Auseinandersetzung mit mechanischen Theorien
11.9 Variationsrechnung und astronomische Störungstheorie - die Arbeitsgebiete von Mayer und Schreibner
11.10 Die neuen Ordinarien S. Lie, O. Hölder und H. Bruns sowie relevante Forschungen der Extraordinarien
11.11 Mathematiker und Physiker in der Königlich Sächsischen Gesellschaft der Wissenschaften
12. Die Veränderungen in den Wechselbeziehungen zwischen Mathematik und Physik
13. Literatur und Quellen
14. Personenverzeichnis
Es gibt wohl kaum Wissenschaftsgebiete, in denen die wechselseitige Beeinflussung stärker ist als zwischen Mathematik und Physik. Eine wichtige Frage ist dabei die nach der konkreten Ausgestaltung dieser Wechselbeziehungen, etwa an einer Universität, oder die nach prägenden Merkmalen in der Entwicklung dieser Beziehungen in einem historischen Zeitabschnitt.
Im Rahmen eines mehrjährigen Akademieprojekts wurden diese Beziehungen an den Universitäten in Leipzig, Halle und Jena für den Zeitraum vom Beginn des 19. bis zur Mitte des 20. Jahrhunderts untersucht und in fünf Bänden dargestellt. Der (vorliegende) erste dieser Bände erschien in den Abhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig (Math.-nat. Klasse, Band 63, Heft 1), die nachfolgenden als eigenständige Reihe unter dem Titel “Studien zur Entwicklung von Mathematik und Physik in ihren Wechselwirkungen“. Ein weiterer und abschließender Band dieser Reihe beinhaltet die Beiträge einer wissenschaftshistorischen Fachtagung im Jahr 2010, die das Thema in einem internationalen Kontext einbettet.
Der vorliegende Band behandelt den Zeitraum von 1830 bis 1905 an der Universität Leipzig. Leipzig gehörte damals zu den bedeutendsten Universitäten Deutschlands. Hervorzuheben ist die überraschende, weil ungeplant erfolgende Stärkung der mathematischen Physik durch die Berufung Karl Neumanns (1868) und die Aktivitäten des PD Karl von der Mühll und des ao. Professors Adolph Mayer. Sie begründeten damit eine die Entwicklung des Mathematischen Instituts prägende Forschungslinie. Ebenso bemerkenswert ist die im Vergleich zu anderen deutschen Universitäten verzögerte Etablierung der theoretischen Physik und der Neubau des Physikalischen Instituts (1904), eine der modernsten Einrichtungen zu jener Zeit, inklusive eines Instituts für theoretische Physik.
S. Hirzel
Stuttgart, Leipzig
Stuttgart, Leipzig
Sächsische Akademie der Wissenschaften zu Leipzig
Leipzig
Leipzig
Sächsische Landesbibliothek – Staats- und Universitätsbibliothek Dresden
Dresden
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2017-07-12
2021-03-27
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Proceedings of the tenth international conference Models in developing mathematics education
September 11 - 17, 2009, Dresden, Saxony, Germany
The Mathematics Education into the 21st Century Project
510
510
SD 2009
Methodik in der Mathematik
Didaktik
Proceedings einer Konferenz mit verschiedenen spezifischen Inhalten
Mathematikausbildung
allgemeine Themen in der Mathematikausbildung
Bildungspolitik und Bildungswesen
Psychologie und Forschung in der Mathematikausbildung
Ausbildung und Unterricht in Mathematik
Methodology of mathematics
didactics
Proceedings of conference of miscellaneous specific interest
mathematics education
General topics in educational mathematics
Educational policy and educational systems
Psychology of and research in mathematics education
Education and instruction in mathematics
This volume contains the papers presented at the International Conference on “Models in Developing Mathematics Education” held from September 11-17, 2009 at The University of Applied Sciences, Dresden, Germany. The Conference was organized jointly by The University of Applied Sciences and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on Our Project Home Page http://math.unipa.it/~grim/21project.htm
It has been our pleasure to edit all of the papers for these Proceedings. Not all papers are about research in mathematics education, a number of them report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators. These Proceedings begin with a Plenary Paper and then the contributions of the Principal Authors in alphabetical name order. We sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
Ludwig
Paditz
Prof. Dr.
Alan
Rogerson
Dr.
2009
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Turning dreams into reality: transformations and paradigm shifts in mathematics education
Proceedings of the eleventh international conference; September 11 - 17, 2011; Rhodes University, Grahamstown
510
510
SD 2011
Methodik in der Mathematik
Didaktik
Proceedings einer Konferenz mit verschiedenen spezifischen Inhalten
Mathematikausbildung
allgemeine Themen in der Mathematikausbildung
Bildungspolitik und Bildungswesen
Psychologie und Forschung in der Mathematikausbildung
Ausbildung und Unterricht in Mathematik
Methodology of mathematics
didactics
Proceedings of conference of miscellaneous specific interest
mathematics education
General topics in educational mathematics
Educational policy and educational systems
Psychology of and research in mathematics education
Education and instruction in mathematics
This volume contains the papers presented at the International Conference on “Turning Dreams into Reality: Transformations and Paradigm Shifts in Mathematics Education” held from September 11-17, 2011 at Rhodes University, Grahamstown, South Africa. The Conference was organized jointly by Rhodes University and The Mathematics Education into the 21st Century Project - an international educational project founded in 1986. Our Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on our Project home page http://math.unipa.it/~grim/21project.htm .
In this year, 2011, we celebrate the 25th anniversary of the founding of our Project, when Manmohan Singh Arora suggested the idea to Fayez Mina and myself around a swimming pool in Bahrain (of all places!) That first meeting was, however, typical of the multi-cultured and global character of our Project and it’s subsequent conferences throughout the world.
These Proceedings begin with the Plenary Papers and then the other contributions in alphabetical name order of the principal authors. We sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
Rhodes University
Grahamstown
Grahamstown
Ludwig
Paditz
Prof. Dr.
Alan
Rogerson
Dr.
2011
2012-02-15
2021-03-27
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Plenary Address: Language and Mathematics, A Model for Mathematics in the 21st Century
David K.
Pugalee
510
510
SD 2009
Kommunikation
mathematische Argumentation
Beurteilung
communication
mathematical reasoning
assessment
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
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Proceedings of the tenth international conference Models in developing mathematics education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 1 - 4
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School-Mathematics all over the world – some differences
Ludwig
Paditz
510
510
SD 2011
Definitionen in der Schulmathematik
verschiedene Definitionen
Deutsches Institut für Normung
DIN
Internationale Organisation für Standardisierung
ISO
Menge der natürlichen Zahlen N
gemischte Zahlen
dritte Wurzel
reelle Potenz mit gebrochenem Exponenten
Haupt-Argument einer komplexen Zahl
alpha-Quantile
rechts- oder linksseitig stetig
ISO 80000-2
Definitions in school mathematics
different definitions
German Institute for Standardization
DIN
International Organization for Standardization
ISO
set of natural numbers
mixed numbers
third root
real power with fractional exponents
main argument of a complex number
alpha-quantiles
right-or left-continuous
ISO 80000-2
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
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HTW Dresden
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2012-02-15
2021-03-27
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Turning dreams into reality: transformations and paradigm shifts in mathematics education. - Grahamstown: Rhodes University, 2011. - S. 1 - 8
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Turning dreams into reality: transformations and paradigm shifts in mathematics education. - Grahamstown: Rhodes University, 2011. - S. 1 - 8
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Proofs and "Puzzles"
Buma
Abramovitz
Miryam
Berezina
Abraham
Berman
Ludmila
Shvartsman
510
510
SD 2009
Mathematisches Denken
Unterricht in Infinitesimalrechnung
Beweise
Sätze
Aufgaben
Mathematical Thinking
Calculus Teaching
Proofs
Theorems
Assignments
It is well known that mathematics students have to be able to understand and prove
theorems. From our experience we know that engineering students should also be able to
do the same, since a good theoretical knowledge of mathematics is essential for solving
practical problems and constructing models.
Proving theorems gives students a much better understanding of the subject, and helps
them to develop mathematical thinking. The proof of a theorem consists of a logical
chain of steps. Students should understand the need and the legitimacy of every step.
Moreover, they have to comprehend the reasoning behind the order of the chain’s steps.
For our research students were provided with proofs whose steps were either written in a
random order or had missing parts. Students were asked to solve the \"puzzle\" – find the
correct logical chain or complete the proof.
These \"puzzles\" were meant to discourage students from simply memorizing the proof of
a theorem. By using our examples students were encouraged to think independently and
came to improve their understanding of the subject.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-10
2021-03-27
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Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 5 - 9
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 5 - 9
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Some Initiatives in Calculus Teaching
Buma
Abramovitz
Miryam
Berezina
Abraham
Berman
Ludmila
Shvartsman
510
510
SD 2009
Mathematisches Denken
SLM Methoden
Annahmen und Folgerungen aus einem Satz
Annahme formulieren
Aufgaben
Mathematical Thinking
SLM Method
Assumptions and Conclusions of a Theorem
Formulation of a Conjecture
Assignments
In our experience of teaching Calculus to engineering undergraduates we have had to grapple
with many different problems. A major hurdle has been students’ inability to appreciate the
importance of the theory. In their view the theoretical part of mathematics is separate from the
computing part. In general, students also believe that they can pass their exams even though they
do not have a real understanding of the theory behind the problems they are required to solve. In
an effort to surmount these difficulties we tried to find ways to make students better understand
the theoretical part of Calculus. This paper describes our experience of teaching Calculus. It
reports on the continuation of our previous research.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-10
2021-03-27
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urn:nbn:de:bsz:14-qucosa-79286
Proceedings of the tenth international conference Models in developing mathematics education
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Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 10 - 14
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 10 - 14
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A Study On Problem Posing-Solving in the Taxicab Geometry and Applying Simcity Computer Game
Tuba
Ada
Aytaç
Kurtulus
510
510
SD 2009
Euklidische Geometrie
Nichteuklidische Geometrie
Taxigeometrie
Problemlösen
Computerspiele
Euclidean geometry
Non-Euclidean geometry
Taxicab geometry
problem posing
problem solving
computer games
Problem-posing is recognized as an important component in the nature of mathematical thinking
(Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with
problem posing in mathematics classroom (English& Grove, 1998). These research has shown that
instructional activities as having students generate problems as a means of improving ability of
problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching
Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by
means of computer game-Simcity- using real life problems posing. This studies’ participants are forty
mathematics teacher candidates taking geometry course. Because of using Simcity computer game,
this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory
for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and
solving from real life problems at Taxicab geometry. In addition to, students applied to problem
solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city,
healty village, university campus, holiday village, etc. interesting of each others.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-10
2021-03-27
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Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 15 - 18
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 15 - 18
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An innovative model for developing critical thinking skills throughmathematical education
Einav
Aizikovitsh
Miriam
Amit
510
510
SD 2009
Wahrscheinlichkeit
Kritisches Denken
Fähigkeiten
Denken auf hohem Niveau
Probability
Critical thinking
abilities
high order thinking
In a challenging and constantly changing world, students are required to develop advanced
thinking skills such as critical systematic thinking, decision making and problem solving. This
challenge requires developing critical thinking abilities which are essential in unfamiliar
situations. A central component in current reforms in mathematics and science studies worldwide
is the transition from the traditional dominant instruction which focuses on algorithmic cognitive
skills towards higher order cognitive skills. The transition includes, a component of scientific
inquiry, learning science from the student''s personal, environmental and social contexts and the
integration of critical thinking. The planning and implementation of learning strategies that
encourage first order thinking among students is not a simple task. In an attempt to put the
importance of this transition in mathematical education to a test, we propose a new method for
mathematical instruction based on the infusion approach put forward by Swartz in 1992. In fact,
the model is derived from two additional theories., that of Ennis (1989) and of Libermann and
Tversky (2001). Union of the two latter is suggested by the infusion theory. The model consists of
a learning unit (30h hours) that focuses primarily on statistics every day life situations, and
implemented in an interactive and supportive environment. It was applied to mathematically
gifted youth of the Kidumatica project at Ben Gurion University. Among the instructed subjects
were bidimensional charts, Bayes law and conditional probability; Critical thinking skills such as
raising questions, seeking for alternatives and doubting were evaluated. We used Cornell tests
(Ennis 1985) to confirm that our students developed critical thinking skills.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
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Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 19 - 22
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 19 - 22
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The “Kidumatica” project - for the promotion of talented students fromunderprivileged backgrounds
Miriam
Amit
510
510
SD 2009
talentierte Studenten
weiterführende wissenschaftliche Studien
Kognition
Mathematikunterricht
talented students
advanced academic studies
cognition
mathematics education
This article describes ‘Kidumatica’ – a highly successful project for the promotion of talented students from underprivileged backgrounds. In its 11 year run, Kidumatica has evolved into a way of life for its many students, allowing them opportunities to realize their potential, enter
advanced academic studies, and successfully enter a society rich in knowledge and achievement. Kidumatica is based on academic research in the fields of excellence, cognition and mathematics
education, and on the social principle of equal opportunity for all and one’s right to self-realization and aspiration, regardless of ethnic background and socio-economic status. Beyond these social/educational purposes, Kidumatica is also a research model and laboratory for testing new programs and teaching methods for gifted students. The following are the basic premises of the Kidumatica model, its goals and how they are achieved, including the recruitment of club members and the mathematical content.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79357
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 23 - 27
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 23 - 27
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2021-03-27T15:32:42Z
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How do rabbits help to integrate teaching of mathematics andinformatics?
Agnis
Andžāns
Laila
Rācene
510
510
SD 2009
Problemlösen
Moderne Elementarmathematik
Satz von Ramsey
Graphentheorie
Diskrete Mathematik
problem solving
modern elementary mathematics
Ramsey theorem
graph theory
discrete mathematics
Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1
rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79360
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 28 - 30
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 28 - 30
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79360
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oai:qucosa:de:qucosa:1670
2021-03-27T15:32:40Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Mathematics brought to life by the Millennium Mathematics Project(Workshop Summary)
Nadia
Baker
510
510
SD 2009
Millennium Mathematikprojekt
Enigma Projekt
Kryptographie
Millennium Mathematics Project
Enigma Project
cryptography
This workshop aims to share the success of the Millennium Mathematics Project (MMP) in bringing mathematics to life for students and teachers. A range of interactive enrichment
programmes and their innovative ideas and resources will be shared. Two MMP outreach projects will be explained in detail as the main focus of the workshop: (1) The Enigma Project, (2) The Risk Roadshow. Both projects travel to primary and secondary schools as well as universities, organisations, science festivals and residential camps, both nationally and internationally.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79382
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 37 - 38
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 37 - 38
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1670/zip/
urn:nbn:de:bsz:14-qucosa-79382
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oai:qucosa:de:qucosa:1671
2021-03-27T15:32:41Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
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ddc:510
openaire
Pre-service teachers’ mathematics profiles and the influence thereof on their instructional behaviour
Hayley
Barnes
510
510
SD 2009
Mathematikunterricht
Vorbereitung
Lehrerausbildung
Mathematik Profile
Fachwissen
fachdidaktische Wissen
Überzeugungen
Mathematik lehren und lernen
Mathematics education
Pre-service
teacher training
mathematics profiles
subject matter knowledge
pedagogical content knowledge
beliefs
teaching and learning of mathematics
In this paper the notion of “mathematics profiles” and “instructional behaviour profiles is introduced. A brief explanation of what these profiles are and how they were constructed and represented for preservice mathematics teachers is provided. An example of one of the participants’ profiles is included as an example. The influence of the pre-service teachers’ mathematics profiles on their instructional
behaviour is then discussed. This is done with regard to using the mathematics profiles as a potential tool to optimise the development of pre-service mathematics teachers’ instructional behaviour towards
a more reform-oriented approach.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79391
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 39 - 42
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 39 - 42
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1671/zip/
urn:nbn:de:bsz:14-qucosa-79391
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oai:qucosa:de:qucosa:1672
2021-03-27T15:34:16Z
qucosa:slub
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ddc:510
openaire
The Relationship between Didactics and Classroom Management:Towards New Tools for the Training of Math Teachers
Michel
Beaudoin
Catherine
Lanaris
510
510
SD 2009
Klassenraum-Management
Didaktik
instrumenteller Konflikt
classroom management
didactics
instrumental conflict
This paper presents the interest of the “instrumental conflict” concept, developed by Marquet (2005), to understand the relationship between didactics and classroom management in the training programs of
math teachers. It also shows some results of a survey, conducted in 2008 among pre-service teachers in the Université du Québec en Outaouais (Canada), revealing a perceived gap between both domains. However, those two domains are closely related during teaching in the classroom. The paper also presents a plan to better understand and improve the situation. Cooperation between classroom
management and didactics specialists is highlighted.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-11
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79400
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 43 - 46
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 43 - 46
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1672/zip/
urn:nbn:de:bsz:14-qucosa-79400
371693136
oai:qucosa:de:qucosa:1673
2021-03-27T15:34:17Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Learning Mathematics through Scientific Contents and Methods
Astrid
Beckmann
510
510
SD 2009
interdisziplinärer Ansatz zwischen Mathematik und Naturwissenschaften
vermeintliche Lücke zwischen formaler Mathematik und authentischer Erfahrung
Erhöhung der Vielseitigkeit der Schüler
physikalische oder biologische Zusammenhänge
Verständnis für das Konzept der Funktionen durch physikalische Experimente
Konstruktion von Kreisdiagrammen
Europäisches ScienceMath Projekt
cross-curricular approach between math and science
perceived gap between formal math and authentic experience
increase of students’ versatility
physical or biological correlations
understanding of the concept of functions through physical experiments
construction of pie charts
European ScienceMath Project
The basic idea of this paper is to outline a cross-curricular approach between mathematics and science. The aim is to close the often perceived gap between formal maths and authentic experience and to
increase the students’ versatility in the use of mathematical terms. Students are to experience maths as logical, interesting and relevant through extra-mathematical references. Concrete physical or biological correlations may initiate mathematical activities, and mathematical terms are to be understood in logical contexts. Examples: physical experiments can lead to a comprehensive understanding of the concept of functions and of the intersection of medians in triangles. Biological topics can lead to the concepts of similarity and proportion as well as to the construction of pie charts. In the European ScienceMath Project a variety of teaching modules was developed and tested in secondary schools.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79411
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 47 - 51
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 47 - 51
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1673/zip/
urn:nbn:de:bsz:14-qucosa-79411
371710421
oai:qucosa:de:qucosa:1674
2021-03-27T15:34:20Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Presentation of the Digital School Journal: Revista Escolar de la Olimpiada Iberoamericana de Matemática, Sponsored by the O.E.I.Organización de Estados Iberoamericanos para la Educación, la Ciencia y la Cultura
Francisco
Bellot Rosado
510
510
SD 2009
kostenlose digitale Schulzeitschrift
REOIM (Revista Escolar de la Olimpíada Iberoamericana de Matemática)
elektronisch verteilt
Zeitschriftenkapitel
Free digital school journal
REOIM
electronically distributed
Journal sections
The purpose of this paper is to present all participants of the Dresden Conference the digital School Journal Revista Escolar de la Olimpiada Iberoamericana de Matemática, online since May-June 2002, with lmost 16,000 subscribers at current issue number 32. Subscribers are based all over the world, but mostly in Spain, Portugal and Latin America.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79432
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 56
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 56
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1674/zip/
urn:nbn:de:bsz:14-qucosa-79432
371710707
oai:qucosa:de:qucosa:1675
2021-03-27T15:34:20Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Rescuing Statistics from the Mathematicians
Mike
Bedwell
510
510
SD 2009
Kontroversen
gewonnenes Wissen
Hypothesen
Wahrheit
Fakten
Controversies
Received wisdom
Hypotheses
Truth
Facts
Drawing on some 30 years’ experience in the UK and Central Europe, the author offers four assertions, three about education generally and the fourth that of the title. There the case is argued that statistics is a branch of logic, and therefore should be taught by experts in such subjects as philosophy and law and not exclusively by athematicians. Education in both Statistics and these other subjects would profit in consequence.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79428
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 52 - 55
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 52 - 55
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1675/zip/
urn:nbn:de:bsz:14-qucosa-79428
371710561
oai:qucosa:de:qucosa:1676
2021-03-27T15:34:14Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
In what case is it possible to speak about Mathematical capability among pre-school children?
Anna V.
Beloshistaya
510
510
SD 2009
mathematische Fähigkeiten
Entwicklung
Schulung
Entwicklung mathematischer Kompetenzen
mathematical abilities
development
training
development of mathematical skills
Most of people have fatal attitude to Mathematics: some of them are capable to learn it form nature, but the others are not. So is their fate – to suffer from it for the whole of life… But it is a rude though natural mistake, as it results from means of mathematical education and its content. Most of parents and teachers are directed on these aspects both in kindergarten and at primary school. Of course, parents
are different. Nevertheless so many parents can’t possibly but speak about achievements of their children. Some start making their own children learn better by the example of success of the others.
They make their children learn long chains of figures with no understanding. It is even more sad to see how a mom asks her 4-year old son: “How much is two plus three?..’ But he replies just because he learned the answer but not calculated. Not only parents but also kindergarten tutors don’t want to understand that drilling for arithmetic has no sense. For a specialist it would take two days only…But teach him how to think logically – is a goal demanding from him, reached by different means.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79444
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 57 - 59
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 57 - 59
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79444
37171222X
oai:qucosa:de:qucosa:1677
2021-03-27T15:34:15Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Possibilities and Challenges of Mathematical Modeling in Teacher’sFormation
Maria
Salett Biembengut
510
510
SD 2009
Geometrie
dekorative Kunst
Kreativität der Kinder
geometry
decorative arts
creativity of children
In this article are the results of research of empirical data from two pedagogical experiences using Mathematical Modeling with two groups: one with 28 students from the last period of a course of
mathematics teachers, and another with 21 teachers of a course of continuing education. The objectives of the course were: teach Mathematical Modeling, and in sequence, modeling as a method
of teaching. The data about the interest for the proposal and the need of the two groups in learning modeling for use in practice was raised from interviews and issues raised and works done by them. Even though the importance of Mathematical Modeling as a method of teaching is not underestimated, some aspects exemplify the difficulties for the participants in changing the concept of teaching and
learning: formation of the participants and the need for formation.
Key-words: Mathematical Modeling, possibilities and challenges.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79455
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 60 - 63
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 60 - 63
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79455
37171396X
oai:qucosa:de:qucosa:1679
2021-03-27T15:34:14Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
How to increase the understanding of differentials by using the Casio-calculator model 9860 G I/II to solve differential equations
Bjørn
Bjørneng
510
510
SD 2009
Casio-Taschenrechner der fx-9860 Serie
Link-Software FA 124
Nutzung eines Grafik-Taschenrechners
Verbesserung des Schüler-Verständnisses
Erstellung von kleinen Programmen
Infinitesimalrechnung
nichtlineare Regression
Casio-calculator fx-9860 series
link-software FA 124
using a graphic calculator
improvement the students understanding
creation of small programs
calculus
nonlinear regression
The major aims of this paper are to present how we can improve the students understanding and involvement in mathematics by using a programming/graphic calculator. I will use differentials as examples such as differentiation ,integrals and differential equations, creating lines of slopes for differential equation of the type y’= f(x,y) . Find the solution of some differential equations by using regression and create the graph connected to the differential equation. As we have different approaches to solving a problem, it is a hope the students interest in mathematics will improve. The tools used will be programming, graphic commands as plot, f-line, etc. One goal is also to show how we can create small programs solving problems in mathematics. For many students this will be a stepping stone for further work with programming. The programs used can be copied using the program FA 124 that can be downloaded from Casios homepages. On request I can send you the programs.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79468
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 64 - 68
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 64 - 68
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1679/zip/
urn:nbn:de:bsz:14-qucosa-79468
371714265
oai:qucosa:de:qucosa:1680
2021-03-27T15:34:25Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Origami-Mathematics Lessons: Researching its Impact and Influence onMathematical Knowledge and Spatial Ability of Students
Norma
Boakes
510
510
SD 2009
Origami
Mathematik
räumliches Vorstellungsvermögen
Leistung
origami
mathematics
spatial ability
achievement
“Origami-mathematics lessons” (Boakes, 2006) blend the ancient art of paper folding with the teaching of mathematics. Though a plethora of publications can be easily found advocating the benefits of Origami in the teaching of mathematics, little research exist to quantify the impact Origami has on the learning and building of mathematical skills. The research presented in this paper targets this common claim focusing on how Origamimathematics lessons taught over an extended period of time impact students’ knowledge of geometry and their spatial visualization abilities. The paper begins with a brief overview of Origami as it relates to teaching mathematics followed by a summary of research done with two age groups: middle school children and college students. Gathered data in these two studies suggest that Origami-mathematics lessons are as beneficial as traditional instructional methods in teaching mathematics.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79472
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 69 - 73
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 69 - 73
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1680/zip/
urn:nbn:de:bsz:14-qucosa-79472
371714893
oai:qucosa:de:qucosa:1681
2021-03-27T15:34:21Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Linking Geometry, Algebra and Calculus with GeoGebra
Josef
Böhm
510
510
SD 2009
Pedal-Kurven
Newton-Raphson-Algorithmus
Räuber-Beute-Modell
Regressionsgerade
pedal curves
Newton-Raphson-algorithm
prey-predator-model
regression line
GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the
features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks
connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the
features of a spreadsheet and the objects of dynamic geometry.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79488
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 74 - 77
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 74 - 77
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1681/zip/
urn:nbn:de:bsz:14-qucosa-79488
371715636
oai:qucosa:de:qucosa:1682
2021-03-27T15:34:22Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Innovations in Educational Research and Teaching of Experimental Calculus
Horacio E.
Bosch
Claudia
Guzner
Mercedes S.
Bergero
Mario A.
Di Blasi
Adriana
Schilardi
Leonor
Carvajal
510
510
SD 2009
Mathematik
Unterricht
computerunterstützt
Technologie
Mathematics
Education
Computer assisted
Technology
For several decades, there have been a varying number of books on Calculus following the classic line of mathematical thought, where Mathematics is taught for everybody by means of rigorous definitions, theorems, and carefully detailed and extensive demonstrations. For mathematical education into the XXI Century the students need to achieve ability in handling of present mathematical tools and concepts from the beginning of their courses. These needs can be achieved today by means of a paradigmatic change in the focus of mathematics teaching: to learn to develop ideas and to experiment and test those ideas in such way that students can verify their own inferences. In this paper we report an educational research in teaching
and learning functions models according to a new paradigm in hands-on experimental mathematics, with applications in the real world, i.e. sciences and engineering by using Computer Algebra Systems. The study of functions is presented, focused into the framing of Exploratory Learning Systems, where students learn
by means of the action and their participation in it. It is designed for teachers working together with students in a computer laboratory like hands-on workshops-type activities on other sciences. In this way students have a more “alive”, “realistic” and “accessible” touch in Calculus.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79493
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 78 - 82
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 78 - 82
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1682/zip/
urn:nbn:de:bsz:14-qucosa-79493
371716055
oai:qucosa:de:qucosa:1683
2021-03-27T15:34:18Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The Best of Both Worlds: Teaching Middle School and College Mathematics
Daniel J.
Brahier
510
510
SD 2009
Schul-Hochschul-Partnerschaften
innovative Ideen in Mathematiklehrer Vorbereitung
Anwendung der Aktionsforschung
Unterricht in K-12 Schulen für die Berufsausbildung
school-university partnerships
innovative ideas in mathematics teacher preparation
applying action research
teaching in K-12 schools for professional development
As a full-time Professor of Mathematics Education, as well as a part-time eighth grade (13 and 14 year olds) mathematics teacher, I have the opportunity to experience the teaching profession from “both sides of the fence.” My university courses are enhanced by my work in the field, while my eighth graders’ learning is strengthened by educational principles studied at the university. In this paper (and
presentation), I will explain this partnership and the benefits to both audiences.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79502
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 83 - 85
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 83 - 85
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1683/zip/
urn:nbn:de:bsz:14-qucosa-79502
371716241
oai:qucosa:de:qucosa:1684
2021-03-27T15:34:19Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Language and Number Values: The Influence of the Explicitness of Number Names on Children’s Understanding of Place Value
Sandra
Browning
510
510
SD 2009
Stellenwert
Sprache
Elementarmathematik
place value
language
elementary mathematics
In recent years, the idea of language influencing the cognitive development of an understanding of place value has received increasing attention. This study explored the influence of using explicit number names on prekindergarten and kindergarten students’ ability to rote count, read two-digit numerals, model two-digit numbers,
and identify the place value of individual digits in two-digit numerals. Through individual student interviews, preand post-assessments were administered to evaluate rote counting, reading five two-digit numerals, modeling five two-digit numbers, and identifying place value in two two-digit numerals. Chi-square tests for independence showed two significant relations: (1) the relationship between the control and treatment group membership on the postassessment
of modeling two-digit numbers and (2) the relationship between place value identifications and group membership. Analysis of the children’s performance and error patterns revealed interesting differences between children taught with explicit number names and children taught with traditional number names. The improvement of the treatment group overall exceeded the improvement of the control group. This study indicates that teaching children to use explicit number names can, indeed, have a positive influence on their understanding of place value.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79517
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 86 - 89
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 86 - 89
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1684/zip/
urn:nbn:de:bsz:14-qucosa-79517
371716462
oai:qucosa:de:qucosa:1685
2021-03-27T15:34:23Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Integrating Technology into the Mathematics Classroom: Instructional Design and Lesson Conversion
Marcia M.
Burrell
Clayton
Cohn
510
510
SD 2009
Lehrerfortbildung
Mathematikausbildung
Lehr-Technologie
Unterrichtsplanung
Einschätzung
Teacher Training
Mathematics Education
Instructional Technology
Lesson Planning
Assessment
The use of technology in Kindergarten to grade 12 classrooms provides opportunities for teachers to employ mathematical rigor, to integrate problem solving strategies and to extend mathematical ways of knowing (Drier, Dawson, & Garofalo, 1999). The presentation consists of two parts. One investigation maps secondary mathematics technology lessons and materials to the elementary school mathematics standards and converts the mathematics concepts to manageable elementary school lessons. The other investigation analyzes pre-service teacher lessons written using ASSURE instructional design format. The major aims of this paper are to present two teacher preparation practices, one for secondary mathematics pre-service teachers (converting secondary materials to elementary materials) and the other for elementary mathematics pre-service teachers (writing lessons using the ASSURE model).
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79535
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 90 - 94
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 90 - 94
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1685/zip/
urn:nbn:de:bsz:14-qucosa-79535
371716683
oai:qucosa:de:qucosa:1686
2021-03-27T15:34:24Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The Role of Dynamic Interactive Technology in Teaching and Learning Statistics
Gail
Burrill
510
510
SD 2009
dynamische interaktive Technologie Normalverteilungskurve
Boxplots
Simulationen
Variation
Dynamic Interactive Technology
Normal curve
Boxplots
Simulations
Variation
Dynamic interactive technology brings new opportunities for helping students learn central statistical concepts. Research and classroom experience can be help identify concepts with which students struggle,
and an \"action-consequence\" pre-made technology document can engage students in exploring these concepts. With the right questions, students can begin to make connections among their background in
mathematics, foundational ideas that undergrid statistics and the relationship these ideas. The ultimate goal is to have students think deeply about simple and basic statistical ideas so they can see how they lead to reasoning and sense making about data and about making decisions about characteristics of a population from a sample.Technology has a critical role in teaching and learning statistics, enabling students to use real data in investigations, to model complex situations based on data, to visualize
relationships using different representations, to move beyond calculations to interpreting statistical processes such as confidence intervals and correlation, and to generate simulations to investigate a variety of problems including laying a foundation for inference. Thus, graphing calculators, spreadsheets, and interactive dynamic software can all be thought of as tools for statistical sense making in the service of developing understanding.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79544
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 95 - 99
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 95 - 99
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1686/zip/
urn:nbn:de:bsz:14-qucosa-79544
371716934
oai:qucosa:de:qucosa:1687
2021-03-27T15:34:29Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Presentations Using Autograph
Douglas
Butler
510
510
SD 2009
Autograph
Software-Präsentation
Sprach-Lokalisierung
Diskussion über Komma-Dezimalpunkt Problem
Web-Ressourcen
Anwendungen in der Analysis
Anwendungen in der Statistik
Grafik-Anwendungen (2D
3D)
Nutzung der Autograph-Werkzeuge
Autograph
software presentation
language localization
discussion on comma-decimal point issue
web resources
applications in calculus
applications in statistics
graphic applications (2D
3D)
using Autograph tools
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79554
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 100
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 100
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1687/zip/
urn:nbn:de:bsz:14-qucosa-79554
371717213
oai:qucosa:de:qucosa:1688
2021-03-27T15:34:30Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Use and misuse of quantitative and graphical Information in StatisticsAn Approach in Teaching
Lucette
Carter
Cécile
Hardouin
510
510
SD 2009
Irreführende statistische Informationen
Simpson Paradoxon
Kausalität und Korrelation
schlechte Grafiken
Misleading Statistical Information
Simpson Paradox
Causality and Correlation
Poor Graphics
Miscellaneous examples of misleading statistical data or interpretation are presented in a form suitable for students in mathematics or Social Sciences during a first course of statistics. The aim is to promote critical thinking when confronted (mainly by the media or scientific papers) by information that is biased, incomplete, poorly defined, or deliberately oriented towards a preconceived target. Starting with the simple manipulation of Simpson paradox, the emphasis is put on the need for counfounding in the analysis of relationship between variables.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79579
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 106 - 110
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 106 - 110
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1688/zip/
urn:nbn:de:bsz:14-qucosa-79579
37171771X
oai:qucosa:de:qucosa:1689
2021-03-27T15:34:28Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
How Involving Secondary Students in the Assessment Process Transforms a Culture of Failure in Mathematics to a Culture of Accountability, Self-Efficacy and Success in Mathematics: Student Action Plans, Assessment, and Cultural Shift
Katharine W.
Clemmer
510
510
SD 2009
sekundäre mathematische Ausbildung
US städtischer Mathematikunterricht
Einschätzung zum Lernen
systemischer Ansatz zum Mathematikunterricht in den Klassen 7-12
innovatives studentisches Lernen
Messung des Schülerengagements in der Mathematik
Secondary Math Education
US Math Urban Education
Assessment for Learning
Systemic approach to 7-12 math education
Innovative student learning
measuring student engagement in mathematics
Learn how to realize a measurable increase in student engagement and achievement in mathematics through a guided, collaborative, and active process grounded in mathematics. Students and teachers collaboratively devise a data-driven plan of action that moves learning
forward for all students and effectively supports at-risk secondary students in urban environments. Learn how teachers in the LMU Math and Science Teaching Program effectively implement assessments as motivations for student achievement and develop opportunities for students to demonstrate comprehension and retention of essential content over time. Students become active participants in the assessment process in an environment where learning is an individual progression and risk-taking is valued and encouraged. Find out how students, guided by teacher-provided descriptive feedback, make decisions in a process of self-reflection in which they critically analyze and compare their learning outcomes to expectations of content mastery. By comparing mastery to current performance,
students utilize failure and engage in error analysis to deconstruct prior shortcomings and devise a plan of action that will move learning forward thereby overcoming failure.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79595
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 116 - 119
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 116 - 119
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1689/zip/
urn:nbn:de:bsz:14-qucosa-79595
371719119
oai:qucosa:de:qucosa:1690
2021-03-27T15:34:26Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
An Alternate Route to Urban Mathematics Teaching: The NYC Teaching Fellows Program
Laurel A.
Cooley
510
510
SD 2009
Mathematikausbildung Lehrerausbildung
Lehrergewinnung
Lehrerfluktuation
Lehrerwechsel
alternative Zertifizierung
Berufseinstieg für Lehrer
Lehrerinduktion
soziale Gerechtigkeit
Mathematics education
teacher education
teacher retention
teacher attrition
teacher turnover
alternative certification
teacher induction
social justice
The NYC Teaching Fellows (NYCTF) program, as the nation’s largest alternative certification program, aims to provide high-needs NYC public schools with highly qualified teachers in such hard-to-staff areas as math, science, and special education. Reports of NYCTF teacher retention are mixed; The New Teacher Project (TNTP) claims high retention rates, but other research indicates that fellow recruits have lower retention rates than other teachers in similar NYC schools – only Teach for America (TFA) exhibits higher attrition (Boyd et al., 2006). After scrutinizing these contrary claims, this paper examines the retention of a recent cohort of approximately 300 Mathematics Teaching Fellows (MTFs) in the NYCTF program, examining MTF’s early attrition, movements from school to school in the NYC system, and professional plans for the future. We also include findings on teacher
induction, school leadership, and school context that affect MTF retention.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79604
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 120 - 123
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 120 - 123
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1690/zip/
urn:nbn:de:bsz:14-qucosa-79604
371719372
oai:qucosa:de:qucosa:1691
2021-03-27T15:34:27Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Analyzing the effects of a linguistic approach to the teaching of algebra: students tell “stories of development” revealing new competencies and conceptions
Annalisa
Cusi
510
510
SD 2009
Algebra als Werkzeug für das Denken
Beweis
studentische Vorstellungen von Algebra
studentische Einstellungen
Entwicklung eines neuen Bewusstseins
algebra as a tool for thinking
proof
students'' visions of algebra
students’ attitudes
development of a new awareness
This work is part of a wide-ranging long-term project aimed at fostering students’ acquisition of symbol sense through teaching experiments on proof in elementary number theory (ENT). In this paper, in particular, we highlight the positive effects of our approach analysing the written reflections that the students involved have produced at the end of the project. These reflections testify an increased level of awareness, developed by students, about the role played by algebraic language as a tool for thinking and a positive evolution in their vision of algebra.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79613
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 124 - 128
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 124 - 128
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1691/zip/
urn:nbn:de:bsz:14-qucosa-79613
371719534
oai:qucosa:de:qucosa:1692
2021-03-27T15:34:26Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Localization of Learning Objects in Mathematics
Valentina
Dagiene
Inga
Zilinskiene
510
510
SD 2009
Mathematikunterricht
Mathematik Lehren
Lernobjekte
Mathematiksoftware
Lokalisierung
mathematische Notation
Informationstechnologie
Mathematics education
teaching mathematics
learning objects
localization
mathematics software
mathematical notation
information technology
Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics.
The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some
problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main
attention is paid to localization of learning objects used for teaching and learning mathematics.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79623
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 129 - 133
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 129 - 133
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1692/zip/
urn:nbn:de:bsz:14-qucosa-79623
371719852
oai:qucosa:de:qucosa:1693
2021-03-27T15:35:51Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Large-Scale Assessment as a Tool for Monitoring Learning and Teaching:The Case of Flanders, Belgium
Erik
De Corte
Rianne
Janssen
Lieven
Verschaffel
510
510
SD 2009
Beurteilung für das Lernen
High-stake-Tests
Item response Theorie
Large-scale Bewertung
Populations-Probe
standardisierte Tests
Assessment for learning
High-stake tests
Item response theory
Large-scale assessment
Population sampling
standardized tests
Traditional tests for large-scale assessment of mathematics learning have been criticized for several reasons, such as their mismatch between the vision of mathematical competence and the content
covered by the test, and their failure to provide relevant information for guiding further learning and instruction. To achieve that large-scale assessments can function as tools for monitoring and
improving learning and teaching, one has to move away from the rationale, the constraints, and the practices of traditional tests. As an illustration this paper presents an alternative approach to largescale
assessment of elementary school mathematics developed in Flanders, Belgium Using models of item response theory, 14 measurement scales were constructed, each representing a cluster of curriculum standards and covering as a whole the mathematics curriculum relating to numbers, measurement and geometry. A representative sample of 5,763 sixth-graders (12-year-olds) belonging to 184 schools participated in the study. Based on expert judgments a cut-off score was set that determines the minimum level that students must achieve on each scale to master the standards. Overall, the more innovative curriculum standards were mastered less well than the more traditional ones. Few gender differences in performance were observed. The advantages of this approach and its further development are discussed.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79638
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 134 - 138
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 134 - 138
info:eu-repo/semantics/openAccess
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urn:nbn:de:bsz:14-qucosa-79638
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2021-03-27T15:35:49Z
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Connections between Mathematics and Arts & Culture: An exploratory Study with Teachers in a South African school
Joseph
Dhlamini
510
510
SD 2009
Mathematik
Kunst und Kultur
Verbindungen
interdisziplinärer Ansatz
Intergration
mathematics
arts and culture
connections
interdisciplinary approach
intergration
This paper presents results of a two year study, at Master’s level, which was undertaken to investigate how two Grade 9 Arts and Culture teachers incorporated mathematics in their Arts and Culture lessons in their classrooms in South Africa. Data from concept mapping activities and subsequent interviews with both teachers were collected and analysed using typological methods of analysis. Data collected from the study revealed that teachers still continue to
grapple with the notion of integration. Lack of proper training and insufficient teacher knowledge seem to be the challenging factors for teachers to navigate successfully through the notion of integrated teaching and learning. Drawing from the theory of situated learning, this paper argues that although integration between mathematics and Arts and Culture is desirable in teaching and learning, it is problematic in practice. The analysis from this study raises
important pedagogical issues about the link between ‘integrated teaching’ and ‘teacher training-and-content knowledge’.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79645
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 139 - 142
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 139 - 142
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79645
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oai:qucosa:de:qucosa:1695
2021-03-27T15:35:50Z
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Mathematical Competitions for University Students
Alexander
Domoshnitsky
Roman
Yavich
510
510
SD 2009
Spiel Methoden in der Erziehung Prozess
Mathematik Wettbewerbe
Blitz-Olympiade
breite Beteiligung
Game methods in education process
mathematics competitions
Blitz olympiad
wide participation
We present several possible forms of mathematical competitions for University students. One of them is Blitz Mathematical Olympiad. It is a team competition, when all teams receive the same problem and are
allotted 10-15 minutes to come up with a solution. This cycle is repeated 6-8 times with different problems. Modern Internet technologies allow us to organize Blitz Mathematical Olympiads for the teams which are in different cities and even countries.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79653
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 143 - 145
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 143 - 145
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79653
371721326
oai:qucosa:de:qucosa:1696
2021-03-27T15:35:52Z
qucosa:slub
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Internet Mathematical Olympiads
Alexander
Domoshnitsky
Roman
Yavich
510
510
SD 2009
Internet-Technologien
mathematische Wettbewerbe
Bewertungssystem
Aufgabensammlung
Internet technologies
mathematical competitions
grading system
list of problems
Modern Internet technologies open new possibilities in a wide spectrum of traditional methods, used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay in their schools or universities in different cities and even different countries and try to solve as many mathematical problems as possible and then submit their solutions to organizers through the Internet. Simple Internet technologies supply audio and video connection between participants and organizers in a time of the
competitions.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79663
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 146 - 148
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 146 - 148
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1696/zip/
urn:nbn:de:bsz:14-qucosa-79663
371721482
oai:qucosa:de:qucosa:1697
2021-03-27T15:35:53Z
qucosa:slub
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Elementary Teacher Candidates’ Understanding of Rational Numbers:An International Perspective
Rose Elaine
Carbone
510
510
SD 2009
Lehramtsstudierende Grundschule
Addition von Brüchen
Problemstellung
elementary teacher candidates
addition of fractions
problem posing
This paper combines data from two different international research studies that used problem posing in analyzing elementary teacher candidates’ understanding of rational numbers. In 2007, a mathematics educator from the United States and a mathematician from Northern Ireland collaborated to investigate their respective elementary teacher candidates’ understanding of addition and division of fractions. A year later, the same US mathematics educator collaborated with a mathematics educator from South Africa on a similar research project that focused solely on the addition of fractions. The results of both studies show that elementary teacher candidates from the three different continents share similar misconceptions regarding the addition of fractions. The misconceptions that emerged were analyzed and used in designing teaching strategies intended to improve elementary teacher candidates’ understanding of rational numbers. The research also suggests that problem posing may improve their understanding of addition of fractions.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79565
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 101 - 105
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 101 - 105
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79565
371717450
oai:qucosa:de:qucosa:1698
2021-03-27T15:35:48Z
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Essential Ingredients that form the basis for Mathematical Learning: What has 20 years of teaching mathematics to teenagers taught me?
Ruth J.
Duffield
510
510
SD 2009
Mathematik-lernende Jugendliche
Hindernisse bei Mathematik-lernenden Jugendlichen
die Rolle von Methoden beim Mathematik-Lernen
Mathematik-Lernen und Jugendliche
aufgetretene Schwierigkeiten bei Mathematik-lernenden Jugendlichen
mathematical learning teenagers
obstacles to maths learning in teenagers
role of methodologies in maths learning
learning maths and teenagers
difficulties encountered in learning maths for teenagers
Educators strive to improve student learning outcomes and there are numerous theories suggesting how this is best achieved. However, application of these theories to the coal face of a classroom is often fraught with obstacles resulting in poor outcomes. Constraints imposed by educational policy, school systems, structures and the individual students themselves, realistically require adaptation of
theoretical techniques if genuine learning is to be imparted to students. This paper discusses some of the issues surrounding the practical implementation of new methodologies into the classroom and
identifies important factors that affect teenagers in their learning of mathematics. Working within the constraints, constantly confronted with obstacles, can be frustrating and demoralising. This paper reflects on twenty years of classroom teaching of mathematics to students with relatively poor socio-economic backgrounds and the lessons learnt from them that may assist teachers to remain enthusiastic and creative with the energy to truly improve mathematics education. Key issues explored in the paper include: ‘Realities of a teacher’s working day’, ‘The learning of mathematics within a government secondary system’, and ‘What can be done to ensure mathematical learning takes place?’
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79675
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 149 - 152
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 149 - 152
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79675
371722160
oai:qucosa:de:qucosa:1700
2021-03-27T15:35:41Z
qucosa:slub
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Exploring mathematical identity as a tool for self-reflection amongst pre-service primary school teachers: “I think you have to be able to explain something in about 100 different ways”
Patricia
Eaton
Maurice
OReilly
510
510
SD 2009
mathematische Identität
Lehramtsstudierende Grundschullehrer
Selbst-Reflexion
Erzählung
Neubewertung
Erfahrungen als Lernende
Schwellen-Praxis
mathematical identity
pre-service primary teachers
self-reflection
narrative
re-evaluation
experiences as learners
emerging practice
A study of students’ mathematical identity was carried out in February 2009 involving participants from two colleges of education, one in Dublin (Republic of Ireland) and one in Belfast (Northern Ireland). All participants were pre-service primary school teachers in the third
year of their B.Ed. programme, having chosen to specialize in mathematics. Data was gathered using a questionnaire (with, mainly, open-ended questions) followed by focus groups, involving the same participants, on each campus. This paper considers how students’ exploration of their mathematical identity led them to deepen their insight into learning and teaching mathematics. Recommendations are made for how the methods used in this research might be beneficial on a larger scale, in different environments.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79689
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 153 - 156
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 153 - 156
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79689
371724546
oai:qucosa:de:qucosa:1701
2021-03-27T15:35:42Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Recognising Torres Strait Islander Women’s Knowledges in their Children’s Mathematics Education
Bronwyn
Ewing
510
510
SD 2009
Einheimisches Mathematikwissen
Torres Strait Inselbewohner
gesellschaft-basierte Forschung
Indigenous mathematics knowledge
Torres Strait Islanders
community-based research
This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-12
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79697
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 157 - 161
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 157 - 161
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1701/zip/
urn:nbn:de:bsz:14-qucosa-79697
371724791
oai:qucosa:de:qucosa:1704
2021-03-27T15:35:43Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
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openaire
Proportional Reasoning Models in Developing Mathematics Education Curricula for Prospective Elementary School Teachers
Beverly J.
Ferrucci
Jack
Carter
Ngan Hoe
Lee
510
510
SD 2009
proportionale Überlegungen
Problemlösung
zukünftige Lehrer
proportional reasoning
problem solving
future teachers
A study of pre-service primary school teachers in Singapore and the United States revealed superior performance by the Singaporeans on proportional reasoning problems. Analysis of solutions showed the Singapore future teachers were more likely to use unitary and
benchmark approaches than were their American counterparts. Conclusions include suggestions for programs intended to improve the performance of prospective elementary school teachers on proportional reasoning problems.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79745
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 162 - 165
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 162 - 165
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-79745
371726344
oai:qucosa:de:qucosa:1705
2021-03-27T15:35:43Z
qucosa:slub
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openaire
Modelling in Mathematics and Informatics: How Should the Elevators Travel so that Chaos Will Stop?
Andreas
Filler
510
510
SD 2009
Mathematische Modellierung
Modellbildung in Mathematik und Informatik
Entwurfsmodelle
Modelltheorie
Mathematical Modelling
Modelling in Mathematics and Informatics
Conceptual Design Models
Modelling Theory
Didactic proposals on modelling in mathematics education mostly give priority to models which describe, explain as well as partially forecast and provide mathematical solutions to real situations. A view of the modelling concept of informatics, which also initiates rapidly generalised deliberations of models, can also make a contribution to the spectrum of models, which are treated in a meaningful sense in mathematics lessons so as to expand some interesting aspects. In this paper, this is illustrated by means of conceptual design models – and, here, especially of process models – using the example of elevator organisation in a multi-storey construction.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79751
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 166 - 171
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 166 - 171
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1705/zip/
urn:nbn:de:bsz:14-qucosa-79751
371726832
oai:qucosa:de:qucosa:1707
2021-03-27T15:35:45Z
qucosa:slub
doc-type:conferenceObject
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openaire
MATRICES AND ROUTING
Ajda
Fošner
510
510
SD 2009
Auswahlpfad
Streckenführung
Routing
Matrizen
selecting paths
routing
matrices
The study of matrices have been of interest to mathematicians for some time. Recently the use of matrices has assumed greater importance also in the fields of management, social science, and natural science because they are very useful in the organization and presentation of data and in the solution of linear equations. The theory of matrices is yet another type of mathematical model which we can use to solve many problems that arise in these fields. The aim of this paper is to show how we can use matrices and their mathematical model to solve some problems in the process of routing. First we will introduce the term of routing and the new approach in the process of selecting paths. We will show some simple examples. We will also pint out how we can learn about matrices in the classroom. At the end we will discuss about advantages and potential disadvantages that may occur in the described technique.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79772
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 172 - 175
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 172 - 175
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1707/zip/
urn:nbn:de:bsz:14-qucosa-79772
371727006
oai:qucosa:de:qucosa:1708
2021-03-27T15:35:37Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Mathematics Professional Learning Communities: Opportunities and Challenges in an Elementary School Context
Douglas
Franks
510
510
SD 2009
Mathematikunterricht
Grundschullehrer
berufliche Weiterbildung
berufliche Lerngemeinschaften
berufliche Zusammenarbeit
Mathematics Teaching
Elementary Teachers
Professional Development
Professional Learning Communities
Professional Collaboration
School-based professional learning communities (PLCs) have become an important means of “building capacity” among teachers in a wide variety of areas, including those with a subject focus. Very often, these PLCs are mandated by administration, and operate under an established structure. This paper describes an attempt by a mathematics coordinator and school level “lead’ teachers to
establish relatively informal PLCs in mathematics in an effort to improve mathematics teaching, and thus student learning, in an environment that focused very much on literacy. The four PLCs created are discussed, as are the opportunities and the challenges that go with the relative freedom offered to the teachers. Sustainability is a central challenge to these groups.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79785
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 176 - 179
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 176 - 179
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1708/zip/
urn:nbn:de:bsz:14-qucosa-79785
37172712X
oai:qucosa:de:qucosa:1710
2021-03-27T15:35:34Z
qucosa:slub
doc-type:conferenceObject
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open_access
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openaire
Impact on Student Achievement of Teacher Participation in K-8 Mathematics Professional Development
Todd
Frauenholtz
Derek F.
Webb
510
510
SD 2009
unmittelbare Lehrerausbildung
berufliche Entwicklung
Mathematikunterricht
Schülerleistungen in Mathematik
Schülerleistungen in der Grundschule
In-service Teacher Training
Professional Development
Mathematics Education
Student Achievement in Mathematics
Elementary School Student Achievement
The purpose of this study is to determine the impact on student achievement of elementary school teachers who participated in professional development in the content area of mathematics. Teachers participated in professional development courses and have accumulated a range from three to eighteen total credits from the summers of 1998 through 2007. The impact is measured by student achievement data collected on standardized tests.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79815
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 180 - 183
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 180 - 183
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1710/zip/
urn:nbn:de:bsz:14-qucosa-79815
371727324
oai:qucosa:de:qucosa:1712
2021-03-27T15:35:31Z
qucosa:slub
doc-type:conferenceObject
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openaire
One mathematical formula in the science textbook: looking into innovative potential of interdisciplinary mathematics teaching
Viktor
Freiman
Danis
Michaud
510
510
SD 2009
Problem-basiertes Lernen
IKT
gemeinsame Forschung
innovative Lehrmethoden
Mathematik in der Mittelschule
Problem-based learning
ICT
collaborative research
innovative teaching practices
middle-school mathematics
Our paper presents some preliminary observation from a collaborative exploratory study linking mathematics, science and reading within a technology enhanced problem-based learning scenario conducted at one French Canadian Elementary and Middle School. Presented in a form of dialogue between teacher and researcher, our findings give some meaningful insight in how an
innovative mathematics teaching can be developed and implemented using a real-world problem solving. Instead of a traditional presentation of material about lighting up homes, participating
mathematics, science and French teachers were working collaboratively with the ICT integration mentor and two university professors helping students investigate a problem from various
perspectives using a variety of cognitive and metacognitive strategies, discussing and sharing the finding with peers and presenting them to a larger audience using media tools. Our preliminary results may prompt further investigation of how innovation in teaching and learning can help students become better critical thinkers and scientifically empowered citizens.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79834
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 184 - 188
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 184 - 188
info:eu-repo/semantics/openAccess
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2021-03-27T15:35:30Z
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A Cross-Cultural Comparison of Algebra 1 Students’ Achievement
Sofokli
Garo
510
510
SD 2009
Leistung
Schüler
Algebra 1
achievement
students
algebra 1
The purpose of this research was to compare American and Albanian students’ achievement in Algebra 1. The study compared algebraic solving abilities of 219 students in a city of Albania and 242 ninth-grade American students, residents of an American region. Albanian sample did not use calculators on the test. Of the American sample, 97 students used calculators on the test, whereas 145 did not use them. The three research questions addressed: (1) students’ mastering of the overall algebraic achievement, (2) students’ mastering of specific domains of algebraic understanding: knowing, applying, and reasoning, and (3) students’ preference of algebraic strategies for solving word-problems. The study found that Albanian
students outperformed American students on the overall achievement. However, American students who used calculators on the test significantly outperformed not only the American group who did not use calculators on the test, but also the entire Albanian sample. In addition, Albanian students scored significantly higher than their American peers both on 2 out of 3 cognitive domains and on using algebraic strategies.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79868
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 195 - 198
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 195 - 198
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1714/zip/
urn:nbn:de:bsz:14-qucosa-79868
371729378
oai:qucosa:de:qucosa:1715
2021-03-27T15:35:32Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
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openaire
THE ROLE OF THE MUSIC TO LEARN GEOMETRICAL TRANSFORMATIONS
Daniela
Galante
510
510
SD 2009
geometrische Transformationen
Kompositionsprozess
Mathematik
Musik
Lehre der didaktischen Situationen
geometrical transformations
compositional process
mathematics
music
theory of didactical situations
This research studies the interaction among the following contexts: natural language, geometrical language and musical language and it can provide new instruments to accord didactical situations and for a deeper understanding of communication processes. It springs from the consideration that the geometrical transformations are usually used in the compositional processes and the “role of the music to learn geometrical transformations” is actually a new study. In the field of the theory of situations by G. Brousseau (1986) we can assume to be in front of a learning teaching-situation including non-teaching situation as the teacher of musical instruments, while transmitting the knowledge of musical language (theoretical-practical) didn’t have the intention to transmit the geometrical transformation.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79850
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 189 - 194
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 189 - 194
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1715/zip/
urn:nbn:de:bsz:14-qucosa-79850
371729157
oai:qucosa:de:qucosa:1716
2021-03-27T15:35:33Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
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ddc:510
openaire
Can Early Algebra lead non-proficient students to a better arithmetical understanding?
Sandra
Gerhard
510
510
SD 2009
Algebra
frühe Algebra
alltägliche Mathematik
Größen
Algebra in der Grundschule
Propädeutische Algebra
Textaufgaben
Alltagsprobleme
Algebra
Early Algebra
Everyday Mathematics
Measurement
Algebra in Primary Schools
word problems
Everyday Life Problems
In mathematics curricula teachers often find the more or less implicit request to link the taught subjects to the previous knowledge of the students, for example using word problems from everyday life. But in today’s multicultural and multisocial society teachers can no longer assume that the children they teach have a more or less equal background and thus everyday live can have a very different meaning for different children. Furthermore there is evidence that good previous knowledge in arithmetic can hinder the approach to other mathematical subjects, like algebra. In this paper I want
to provide a brief overview on how previous knowledge in arithmetic can affect student\''s access to
algebra and therefore present an early algebra teaching project which introduces elementary school children to algebraic notation by measurement in an action-oriented way. Thereby the chosen
approach to algebra explicitly does not come back to the student\''s previous arithmetical knowledge but additionally may support non-proficient students in obtaining more insight in the structure of
calculations and hence may help them to have more success in solving calculations and word problems.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79878
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 199 - 201
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 199 - 201
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1716/zip/
urn:nbn:de:bsz:14-qucosa-79878
37172953X
oai:qucosa:de:qucosa:1717
2021-03-27T15:35:35Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Problems to put students in a role close to a mathematical researcher
Nicolas
Giroud
510
510
SD 2009
Problemlösung
diskrete Mathematik
Forschungssituation für den Unterricht
problem solving
discrete mathematics
research situation for the classroom
In this workshop, we present a model of problem that we call Research Situation for the Classroom (RSC). The aim of a RSC is to put students in a role close to a mathematical researcher in order to
make them work on mathematical thinking/skills. A RSC has some characteristics : the problem is close to a research one, the statement is an easy understandable question, school knowledge are elementary, there is no end, a solved question postponed to new questions... The most important characteristic of a RSC is that students can manage their research by fixing themselves some variable of the problem. So, a RSC is completely different from a problem that students usually do in France. For short : there is no
final answer, students can try to resolve their own questions : a RSC is a large open field where many sub-problems exist; the goal for the students is not to apply a technique: the goal is, as for a researcher,
to search. These type of situations are particularly interesting to develop problem solving skills and mathematical thinking. They can also let students discover that mathematics are “alive” and “realistic”.
This workshop will be split into two parts. First, we propose to put people in the situation of solving a RSC to make them discover practically what is it. After, we present the model of a RSC and some
results of our experimentations.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79881
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 202 - 203
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 202 - 203
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1717/zip/
urn:nbn:de:bsz:14-qucosa-79881
371729629
oai:qucosa:de:qucosa:1718
2021-03-27T15:35:36Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Toward Calculus via Real-time Measurements
Tine
Golež
510
510
SD 2009
Mathematikdidaktik
Infinitesimalrechnung
ICT
Computerunterstützte Messungen
ICT
Informatik
didactics of mathematics
calculus
computer based measurements
ICT
Several years of my experiences in the use of real-time experiments are now upgraded in order to enhance also the teaching of mathematics. The motion sensor device enables us to get real time x(t) and v(t) graphs of a moving object or person. We can productively use these graphs to introduce differentiation on visual level as well as to show the integration procedure. The students are fully involved in the teaching as they are invited to walk in front of the sensor. This approach motivates them by the realistic aspects of mathematical structures. The method could help to fulfill the credo of teaching: comprehension before computation. The steps of such an approach are explained and discussed in further detail below.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79891
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 204 - 208
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 204 - 208
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1718/zip/
urn:nbn:de:bsz:14-qucosa-79891
371729750
oai:qucosa:de:qucosa:1721
2021-03-27T15:38:25Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Problem Fields in Elementary Arithmetic
Günter
Graumann
510
510
SD 2009
Problemfelder
Problemlösen und Probleme finden
elementare Arithmetik
Grundschule
Problem fields
problem solving and finding
elementary arithmetic
primary school
Working with problems and making investigations is an activity one has to learn already very early. Therefore in primary school children should not only learn concepts and solve given tasks. They also should find out knowledge and reasons by themselves. Here you will find some problem fields in elementary arithmetic within children of primary school can make different investigations and find as well as give reasons for special statements. The topics concerned are partitions of numbers, sums of consecutive numbers, figured numbers, sequences and chains, table of hundred and numberwalls.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79913
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 209 - 214
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 209 - 214
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1721/zip/
urn:nbn:de:bsz:14-qucosa-79913
371729912
oai:qucosa:de:qucosa:1722
2021-03-27T15:38:18Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Disrupting linear models of mathematics teaching|learning
Barbara
Graves
Christine
Suurtamm
510
510
SD 2009
Komplexität im Denken
mathematische Untersuchung
Junglehrer
complexity thinking
mathematical inquiry
beginning teachers
In this workshop we present an innovative teaching, learning and research setting that engages beginning teachers in mathematical inquiry as they investigate, represent and connect mathematical ideas through mathematical conversation, reasoning and argument. This workshop connects to the themes of teacher preparation and teaching through problem solving. Drawing on new paradigms to think about teaching and learning, we orient our work within complexity theory
(Davis & Sumara, 2006; Holland, 1998; Johnson, 2001; Maturana & Varela, 1987; Varela, Thompson & Rosch, 1991) to understand teaching|learning as a complex iterative process through which opportunities for learning arise out of dynamic interactions. Varela, Thompson and Rosch, (1991) use the term co-emergence to understand how the individual and the environment inform each other and are “bound together in reciprocal specification and selection” (p.174). In particular we are interested in the conditions that enable the co-emergence of teaching|learning collectives that support the generation of new mathematical and pedagogical ideas and understandings. The setting is a one-week summer math program designed for prospective elementary teachers to deepen particular mathematical concepts taught in elementary school. The program is facilitated by recently graduated secondary mathematics teachers to provide them an opportunity to experience mathematics teaching|learning through rich problems. The data collected include
questionnaires, interviews, and video recordings. Our analyses show that many a-ha moments of mathematical and pedagogical insight are experienced by both groups as they work together throughout the week. In this workshop we will actively engage the audience in an exploration of the mathematics problems that we pose in this unique teaching|learning environment. We will present our data on the participants’ mathematical and pedagogical responses and open a discussion of the implications of our work.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-13
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79920
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 215 - 218
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 215 - 218
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1722/zip/
urn:nbn:de:bsz:14-qucosa-79920
371730007
oai:qucosa:de:qucosa:1724
2021-03-27T15:38:15Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Modelling tasks for learning, teaching, testing and researching
Gilbert
Greefrath
510
510
SD 2009
Modellieren
Problemlösen
offene Aufgaben
Diagnose
modelling
problem solving
open problems
diagnostic tasks
The article deals with a special kind of modelling tass. These problems are used for learning and researching as well. So the results of an empirical study on mathematical modelling of pupils in secondary schools are presented. Pupils of forms 8-10 were observed working on open, realistic problems. These observations were recorded and evaluated. The goal of the presented part of the study is a detailed look at the control processes of modelling problems.
In this context changes between real life control and mathematical control during the control phases are studied and evaluated. We describe in detail the sub phases of controlling and explain their connection with modelling process. The problems used in this project can also be used in math lessons, so this kind of research can put teachers and researchers together. These tasks are suitable to support ongoing in-service development and teacher education.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79945
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 219 - 222
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 219 - 222
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1724/zip/
urn:nbn:de:bsz:14-qucosa-79945
371730112
oai:qucosa:de:qucosa:1725
2021-03-27T15:38:16Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Transcribing an Animation: The case of the Riemann Sums
May
Hamdan
510
510
SD 2009
infinitesimale Zerlegung
Riemann Summen
Infinitesimalrechnung
Forschung zur Mathematikausbildung im Grundstudium
Piaget
Genetic decomposition
Riemann Sums
calculus
Research in Undergraduate Mathematics Education
RUME
Piaget
In this paper I present a theoretical analysis (genetic decomposition) of the cognitive constructions for the concept of infinite Riemann sums following Piaget\''s model of epistemology. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my continual observations of students in the process of learning.
Based on this analysis I plan to suggest instructional procedures that motivate the mental activities described in the proposed genetic decomposition. In a later study, I plan to present empirical data in the form of informal interviews with students at different stages of learning. The analysis of those interviews may suggest a review of my initial genetic decomposition.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-79957
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 223 - 226
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 223 - 226
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1725/zip/
urn:nbn:de:bsz:14-qucosa-79957
371730236
oai:qucosa:de:qucosa:17285
2021-03-29T09:29:29Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Approximation Spaces in the Numerical Analysis of Cauchy Singular Integral Equations
Uwe
Luther
Dr.
510
510
Cauchy-Integral
Lineare singuläre Integralgleichung
Approximation spaces
Cauchy singular integral equation
Collocation method
Quadrature method
Weighted spaces of continuous functions
The paper is devoted to the foundation of
approximation methods for integral equations of
the form (aI+SbI+K)f=g,
where S is the Cauchy singular
integral operator on (-1,1) and K is a weakly
singular integral operator.
Here a,b,g are given functions on (-1,1) and
the unknown function f on (-1,1) is looked for.
It is assumed that a and b are real-valued and
Hölder continuous functions on [-1,1] without
common zeros and that g belongs to some
weighted space of Hölder continuous functions.
In particular, g may have a finite number of
singularities.
Based on known spectral properties of Cauchy
singular integral operators approximation methods
for the numerical solution of the above equation
are constructed, where both aspects the
theoretical convergence and the numerical
practicability are taken into account.
The weighted uniform convergence of these methods
is studied using a general
approach based on the theory of approximation
spaces. With the help of this approach it is
possible to prove simultaneously the stability,
the convergence and results on the order of
convergence of the approximation methods under
consideration.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Peter
Junghanns
Prof. Dr.
Jürgen
Prestin
Prof. Dr.
Maria Rosaria
Capobianco
Prof. Dr.
2004-10-12
2005-06-16
2005-08-01
2021-03-29
doctoralThesis
urn:nbn:de:swb:ch1-200500895
eng
info:eu-repo/semantics/openAccess
thesis.habilitation
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
2
https://monarch.qucosa.de/api/qucosa%3A17285/zip/
urn:nbn:de:swb:ch1-200500895
oai:qucosa:de:qucosa:17329
2021-03-29T09:30:05Z
qucosa:ubc
doc-type:lecture
has-source-swb:false
open_access
ddc:510
openaire
A generalized Neyman-Pearson lemma for hedge problems in incomplete markets
Birgit
Rudloff
510
510
Hedging
Risikomaß
Neyman-Pearson lemma
coherent risk measure
convex duality
hypothesis testing
risk measures
shortfall risk
Some financial problems as minimizing the shortfall risk when hedging in incomplete markets lead to problems belonging to test theory. This paper considers
a generalization of the Neyman-Pearson lemma. With methods of convex duality
we deduce the structure of an optimal randomized test when testing a compound
hypothesis against a simple alternative. We give necessary and sufficient optimality
conditions for the problem.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-10-07
2021-03-29
lecture
urn:nbn:de:swb:ch1-200501316
Tagungsband zum Workshop "Stochastische Analysis", 27.09.2004 - 29.09.2004
http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501214
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A17329/zip/
urn:nbn:de:swb:ch1-200501316
oai:qucosa:de:qucosa:1737
2021-03-27T15:37:38Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Each and Every Student: The Stamford, Connecticut Model for Change in Mathematics
Mona
Hanna
Carrie
Chiappetta
510
510
SD 2009
Mathematikunterricht in der K-12
US städtischer Mathematikunterricht
Systemische Mathematikveränderung
Mathematik Bildungsreform
Lernen im 21. Jahrhundert
K-12 mathematics education
U.S. urban math education
Systemic mathematics change
Mathematics education reform
21st century learning
The major aims of this paper are to: present the background of the mathematics education problem in the Stamford Public School (SPS) district which is common is most U.S cities; explain the need for change in mathematics education; describe the process to systemically transform both the curriculum and instruction of
mathematics thereby ensuring that each and every students is prepared for the 21st century, for higher education, and for success in a global society; and provide ways to measure these changes. The K-12 mathematics education reform model presented can be replicated in other cities and for other academic areas.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80141
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 227 - 230
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 227 - 230
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1737/zip/
urn:nbn:de:bsz:14-qucosa-80141
371730406
oai:qucosa:de:qucosa:1738
2021-03-27T15:37:39Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Folding the circle in half is a text book of information
Bradford
Hansen-Smith
510
510
SD 2009
Kreis
Falten
Einheit
Geometrie
Mathematik
Papier falten
Origami
Kunst des Papierfaltens
hands-on Aktivitäten
Wholemovement
neue Konzepte
circle
folding
unity
geometry
math
folding paper
origami
hands-on activities
wholemovement
new approaches
This paper addresses folding the circle in half and discussing some of over one hundred different mathematical terms and functions generated in that one fold. The simplicity of process in understanding
fundamentals of mathematics by folding circles and observing what is generated is unknown because we only draw pictures of circles. Examples are given about observing and exploring relationships in the circle that are appropriate for first, second, third grade level and beyond. The traditional educational ‘parts-towhole’ approach can only be fully realized through the comprehensive frame of Whole-to-parts by folding the circle. Wholemovement of the circle is not only direct; it is the only context inclusive to progressively understanding parts within unity of the Whole.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80153
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 231 - 234
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 231 - 234
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1738/zip/
urn:nbn:de:bsz:14-qucosa-80153
371730589
oai:qucosa:de:qucosa:1739
2021-03-27T15:37:45Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Using Data Modeling at the Elementary Level to Make Sense of DoingMathematics and Science
Marjorie
Henningsen
Nisreen
Ibrahim
510
510
SD 2009
Datenmodellierung
Elementarmathematik
Lehrerfortbildung
Data Modeling
Elementary Mathematics
Teacher Development
In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80172
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 239 - 241
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 239 - 241
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1739/zip/
urn:nbn:de:bsz:14-qucosa-80172
371730872
oai:qucosa:de:qucosa:1740
2021-03-27T15:37:56Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
CAS and calculation competence of students
Rainer
Heinrich
510
510
SD 2009
CAS
Unterrichtsbeispiele
Rechenfertigkeiten
Experimentierwerkzeug
CAS
Classroom examples
Calculation competence
Experimenting tool
The use of new tools for mathematics at school wins increasingly Importance. It follows from this that they are consquences as well as on aims and contents of mathematics at school us like on methods in
the lessons. It is not unusual, that students and parents and also university professors are to be feared, that the calculation competence is decreasing with the use of CAS. In the lesson should be showed a possible way to developing such competences in the beginning phase of the learning process in Algebra. The examples refer to a level of school mathematics for students in the middle school age. The methods tell apart phases with and without CAS and shows a didactic principles of mathematics lessons in the case of use of CAS handheld technology.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80163
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 235 - 238
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 235 - 238
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1740/zip/
urn:nbn:de:bsz:14-qucosa-80163
371730678
oai:qucosa:de:qucosa:17412
2021-03-29T09:31:16Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Die Anwendung der hyperkomplexen Funktionentheorie auf die Lösung partieller Differentialgleichungen
Uwe
Kähler
510
510
Hyperkomplexe Funktionentheorie
Quaternionenanalysis
Cliffordanalysis
partielle Differentialgleichungen
Stokes-System
Navier-Stokes-System
biharmonische Gleichung
Integraltransformationen
Beltramigleichung
In der vorliegenden Arbeit wird die Methode der Anwendung der hyperkomplexen Funktionentheorie
zur Behandlung partieller Differentialgleichungen über beschränkten Gebieten unter Benutzung
einer orthogonalen Zerlegung des Raumes L_2(U) verallgemeinert. Zum einen kann diese Zerlegung
als direkte Zerlegung über dem Raum L_p(G),p>1, verallgemeinert werden, was die Untersuchung
partieller Differentialgleichungen über allgemeinen Sobolev-Räumen W_p^k(G),p>1,k natürliche Zahl,
ermöglicht. Dies wird am Beispiel des Stokes-Problems demonstriert. Zum anderen wird ein modifizierter
Cauchy-Kern über unbeschränkten Gebieten eingeführt, deren Komplement eine nichtleere offene Menge
enthält. Grundlegende Resultate der Cliffordanalysis über beschränkten Gebieten werden auf diese
Situation verallgemeinert und eine orthogonale Zerlegung des Raumes L_2(G) bewiesen. Diese Resultate
werden im weiteren dazu benutzt, das stationäre Stokes- bzw. Navier-Stokes-Problem in dem allgemeinen
Fall eines unbeschränkten Gebietes zu untersuchen. Im weiteren wird gezeigt, dass sich die entwickelten
Methoden auch auf partielle Differentialgleichungen höherer Ordnung anwenden lassen. Dies wird am
Beispiel der biharmonischen Gleichung mit Randbedingungen, die Komponenten in Normalenrichtung und
tangentieller Richtung besitzen, demonstriert. Am Ende beschäftigen wir uns mit der Verallgemeinerung
der komplexen Methoden von Vekua. Dazu werden hyperkomplexe Verallgemeinerungen des komplexen Pi-Operators
untersucht und auf die Lösung von hyperkomplexen Beltramigleichungen angewandt.
A modified Cauchy kernel is introduced over unbounded domains whose complement contain non-empty open sets.
Basic results on Clifford analysis over bounded domains are now carried over to this more general context.
In the end boundary value problems, e.g. for the Stokes-system or the Navier-Stokes-system, will be studied
in the case of an unbounded domain without using weighted Sobolev spaces. In the latter part of this paper
we deal with hypercomplex generalizations of the complex Pi-operator which turn out to have most of the useful
properties of their complex origin. Afterwards the application of this operator to the solution of hypercomplex
Beltrami equations will be studied.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
1998-09-29
1998-09-01
1998-09-29
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-199800393
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
4
https://monarch.qucosa.de/api/qucosa%3A17412/zip/
urn:nbn:de:bsz:ch1-199800393
oai:qucosa:de:qucosa:17419
2021-03-29T09:31:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Efficient time step parallelization of full multigrid techniques
J.
Weickert
T.
Steidten
510
510
MSC 65N55
This paper deals with parallelization methods for time-dependent
problems where the time steps are shared out among the
processors. A Full Multigrid technique serves as solution
algorithm, hence information of the preceding time step and of
the coarser grid is necessary to compute the solution at each new
grid level. Applying the usual extrapolation formula to process
this information, the parallelization will not be very efficient.
We developed another extrapolation technique which causes a much
higher parallelization effect. Test examples show that no
essential loss of exactness appears, such that the method
presented here shall be well-applicable.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800466
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17419/zip/
urn:nbn:de:bsz:ch1-199800466
oai:qucosa:de:qucosa:1742
2021-03-27T15:38:12Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The use of notebooks in mathematics instruction. What is manageable? What should be avoided? A field report after 10 years of CAS-application
Peter
Hofbauer
510
510
SD 2009
Technologie im Mathematikunterricht
Computeralgebra-Systeme (CAS)
Notebookklassen
Unterrichtskonzepte
Kompetenzorientierung
technology in mathematics instruction
computer algebra systems (CAS)
notebook classes
teaching concepts
competence orientation
Computer Algebra Systems (CAS) have been changing the mathematics instruction requirements for many years. Since the tendency of using CAS in mathematics instruction has been rising for decades and reports have often been positive, the implementation of notebook classes seems to be the consequent next step of mathematics instruction supported by computers. Experiences that have been made with the use of CAS in PC-rooms can be transformed directly into the classroom. Hence the use of CAS is no longer limited to certain rooms. The permanent availability of the notebook with installed CAS offers the chance to realize these concepts that have already been approved with the use of CAS so far. The following speech shall show what these concepts could look like and that the use of notebooks is not only the further development of teaching in PC-classes. Examples from personal experience in teaching will especially show meanders and thought-provoking impulses in order to support teachers finding their way into teaching mathematics instruction in notebook classes successfully.
Please allow me to point out two things in the beginning: (1) Yes, I am a vehement supporter of the use of
notebooks (and the use of CAS in particular) in mathematics instruction. (2) No, I do not believe that teachers
who have chosen another path (or at least partly) are teaching badly.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80182
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 242 - 245
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 242 - 245
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1742/zip/
urn:nbn:de:bsz:14-qucosa-80182
37173102X
oai:qucosa:de:qucosa:17420
2021-03-29T09:31:23Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lokale Realisierung von Vektoroperationen auf Parallelrechnern
U.
Groh
510
510
parallel computers
vector operation
local implementation
distributed memory
MSC 65Y05
For the basic algebraic vector operations several variants of a local
implementation on distributed memory parallel computers are presented and discussed
systematically. In particular necessary and sufficient conditions are shown for the local realizability
of the multiplication matrix by vector.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800478
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17420/zip/
urn:nbn:de:bsz:ch1-199800478
oai:qucosa:de:qucosa:17418
2021-03-29T09:31:21Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A parallel version of the preconditioned conjugate gradient method for boundary element equations
M.
Pester
S.
Rjasanow
510
510
conjugate gradient algorithm
fast Fourier transform
preconditioning
numerical experiments
Galerkin boundary element method
Laplace equation
parallelization
MSC 65N38
MSC 65F10
MSC 65Y05
MSC 65F35
MSC 35J05
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800455
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17418/zip/
urn:nbn:de:bsz:ch1-199800455
oai:qucosa:de:qucosa:17423
2021-03-29T09:31:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Tauextrapolation - theoretische Grundlagen, numerische Experimente und Anwendungen auf die Navier-Stokes-Gleichungen
K.
Bernert
510
510
linear problems
nonlinear problems
improved convergence
one-dimensional test
MSC 76M20
MSC 65N55
MSC 76D05
The paper deals with tau-extrapolation - a modification of the
multigrid method, which leads to solutions with an improved con-
vergence order. The number of numerical operations depends
linearly on the problem size and is not much higher than for a
multigrid method without this modification. The paper starts
with a short mathematical foundation of the tau-extrapolation.
Then follows a careful tuning of some multigrid components
necessary for a successful application of tau-extrapolation. The
next part of the paper presents numerical illustrations to the
theoretical investigations for one- dimensional test problems.
Finally some experience with the use of tau-extrapolation for the
Navier-Stokes equations is given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800506
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17423/zip/
urn:nbn:de:bsz:ch1-199800506
oai:qucosa:de:qucosa:17422
2021-03-29T09:31:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On an automatically parallel generation technique for tetrahedral meshes
G.
Globisch
510
510
Mesh generation
Parallel preprocessing
Finite elements
Domain decomposition
MSC 65Y05
In order to prepare modern finite element analysis a program for
the efficient parallel generation of tetrahedral meshes in a wide
class of three dimensional domains having a generalized cylindric
shape is presented. The applied mesh generation strategy is based
on the decomposition of some 2D-reference domain into single con-
nected subdomains by means of its triangulations the tetrahedral
layers are built up in parallel. Adaptive grid controlling as
well as nodal renumbering algorithms are involved. In the paper
several examples are incorporated to demonstrate both program's
capabilities and the handling with.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800499
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17422/zip/
urn:nbn:de:bsz:ch1-199800499
oai:qucosa:de:qucosa:17424
2021-03-29T09:31:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Implicit extrapolation methods for multilevel finite element computations
M.
Jung
U.
Rüde
510
510
Extrapolation
Finite Elements
Multigrid
Elasticity
MSC 65F10
MSC 65F50
MSC 65N22
MSC 65N50
MSC 65N55
Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800516
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17424/zip/
urn:nbn:de:bsz:ch1-199800516
oai:qucosa:de:qucosa:17428
2021-03-29T09:31:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A parallel preconditioned iterative realization of the panel method in 3D
M.
Pester
S.
Rjasanow
510
510
preconditioning
parallel computation
panel boundary element,method
iterative methods
MIMD computer.
MSC 65N38
MSC 65F10
MSC 35J25
MSC 65F35
MSC 65Y05
The parallel version of precondition iterative techniques is
developed for matrices arising from the panel boundary element
method for three-dimensional simple connected domains with
Dirichlet boundary conditions. Results were obtained on an
nCUBE-2 parallel computer showing that iterative solution methods
are very well suited also in three-dimensional case for
implementation on a MIMD computer and that they are much more
efficient than usual direct solution techniques.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800562
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17428/zip/
urn:nbn:de:bsz:ch1-199800562
oai:qucosa:de:qucosa:17425
2021-03-29T09:31:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Verarbeitung von Sparse-Matrizen in Kompaktspeicherform KLZ/KZU
A.
Meyer
M.
Pester
510
510
sparse matrices
numerical methods
software
MSC 65F50
MSC 65Y05
The paper describes a storage scheme for sparse symmetric or
nonsymmetric matrices which has been developed and used for many
years at the Technical University of Chemnitz. An overview of
existing library subroutines using such matrices is included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800520
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17425/zip/
urn:nbn:de:bsz:ch1-199800520
oai:qucosa:de:qucosa:17429
2021-03-29T09:31:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Preconditioning the Pseudo-Laplacian for finite element simulation of incompressible flow
A.
Meyer
510
510
Finite numerical methods
PDE
BVP
pseudo-laplacian
MSC 65N30
In this paper, we investigate the question of the spectrally equivalence of the so-
called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical
preconditioners for this more complicate matrix. The spectral equivalence is shown to
be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces
considered here.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800574
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17429/zip/
urn:nbn:de:bsz:ch1-199800574
oai:qucosa:de:qucosa:17426
2021-03-29T09:31:28Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Realization and comparison of various mesh refinement strategies near edges
T.
Apel
F.
Milde
510
510
singularities near edges
Fichera corner
finite element methods
convergence
a priori mesh grading algorithms
adaptive mesh,refinement
Poisson's equation
MSC 65N50
MSC 65N30
MSC 35J05
This paper is concerned with mesh refinement techniques for
treating elliptic boundary value problems in domains with re-
entrant edges and corners, and focuses on numerical experiments.
After a section about the model problem and discretization
strategies, their realization in the experimental code FEMPS3D is
described. For two representative examples the numerically
determined error norms are recorded, and various mesh refinement
strategies are compared.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800531
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17426/zip/
urn:nbn:de:bsz:ch1-199800531
oai:qucosa:de:qucosa:1743
2021-03-27T15:38:12Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Community Engagement: Home School Partnership
Marilyn
Holmes
510
510
SD 2009
Einbeziehung der Eltern
verbundene Partnerschaft
kulturelle Integration
gemeinsames Verständnis
Verbundprojekt
wechselseitige Kommunikation
Förderung von Kindern
Parental involvement
Connected Partnership
Cultural inclusion
Shared understandings
Collaborative
Two-way communication
Supporting children
Five year old children starting their formal education in primary schools bring with them a range of informal mathematical understandings. Transitioning from an early childhood setting to the reception class at school can have a profound impact on their developing mathematical concepts. Traditionally
their first teachers (parents, caregivers and whanau) gradually remove the support and encouragement and some of the familiar surroundings of their early childhood centres are no longer there. As children from 5 – 13 years of age spend approximately 85% of their time out of school it is important that their first teachers are encouraged to continue that support. This paper outlines a New Zealand project ‘Home School Partnership: Numeracy’ that gives one approach to enhancing children’s mathematical learning through shared understandings between home and school.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-16
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80198
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 246 - 249
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 246 - 249
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1743/zip/
urn:nbn:de:bsz:14-qucosa-80198
371748704
oai:qucosa:de:qucosa:17427
2021-03-29T09:31:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes
T.
Apel
S.
Nicaise
510
510
anisotropic weighted Sobolev spaces
local interpolation error,estimates
MSC 35A40
MSC 35J05
MSC 65N30
MSC 35B65
This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800553
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17427/zip/
urn:nbn:de:bsz:ch1-199800553
oai:qucosa:de:qucosa:17430
2021-03-29T09:31:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Bibliotheken zur Entwicklung paralleler Algorithmen - Basisroutinen für Kommunikation und Grafik
Matthias
Pester
510
510
Parallelverarbeitung / Programmierung
Visualisierung
Wissenschaftlich-technische Software
message passing
numerical algorithms
The purpose of this paper is to supply a summary of
library subroutines and functions for parallel MIMD
computers. The subroutines have been developed and
continously extended at the University of Chemnitz
since the end of the eighties. In detail, they are
concerned with vector operations, inter-processor
communication and simple graphic output to
workstations. One of the most valuable features is
the machine-independence of the communication
subroutines proposed in this paper for a hypercube
topology of the parallel processors (excepting a
kernel of only two primitive system-dependend
operations). They were implemented and tested for
different hardware and operating systems including
PARIX for transputers and PowerPC, nCube, PVM, MPI.
The vector subroutines are optimized by the use
of C language and unrolled loops (BLAS1-like).
Hardware-optimized BLAS1 routines may be
integrated. The paper includes hints for
programmers how to use the libraries with both
Fortran and C programs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-04
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600429
Preprintreihe des Chemnitzer SFB 393, 02-01; Überarbeitung eines früheren Preprints SPC 95_20
ger
Preprintreihe des Chemnitzer SFB 393, 02-01; Überarbeitung eines früheren Preprints SPC 95_20
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17430/zip/
urn:nbn:de:swb:ch1-200600429
oai:qucosa:de:qucosa:17432
2021-03-29T09:31:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stabilization of large linear systems
C.
He
V.
Mehrmann
510
510
Riccati equation
stabilization
linear
multi-input
control system
MSC 65F05
We discuss numerical methods for the
stabilization of large linear multi-input
control systems of the form x=Ax + Bu via a
feedback of the form u=Fx. The method
discussed in this paper is a stabilization
algorithm that is based on subspace splitting.
This splitting is done via the matrix
sign-function method. Then a projection into
the unstable subspace is performed followed by
a stabilization technique via the solution of
an appropriate algebraic Riccati equation.
There are several possibilities to deal with the
freedom in the choice of the feedback as well
as in the cost functional used in the Riccati
equation. We discuss several optimality criteria
and show that in special cases the feedback
matrix F of minimal spectral norm is obtained
via the Riccati equation with the zero constant term.
A theoretical analysis about the distance to
instability of the closed loop system is given
and furthermore numerical examples are presented
that support the practical experience with
this method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800595
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17432/zip/
urn:nbn:de:bsz:ch1-199800595
oai:qucosa:de:qucosa:17431
2021-03-29T09:31:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A step towards a unified treatment of continuous and discrete time control problems
V.
Mehrmann
510
510
generalized Cayley transformation
generalized algebraic Riccati
equations
discrete algebraic Riccati equations
MSC 93B17
MSC 93C60
MSC 93C55
MSC 49N10
In this paper introduce new approach for
unified theory for continuous and discrete time
(optimal) control problems based on the
generalized Cayley transformation. We also relate
the associated discrete and continuous generalized
algebraic Riccati equations. We demonstrate the
potential of this new approach proving new
result for discrete algebraic Riccati equations.
But we also discuss where this new approach as
well as all other approaches still is
non-satisfactory. We explain a discrepancy
observed between the discrete and continuous
cse and show that this discrepancy is partly due
to the consideration of the wrong analogues. We
also present an idea for a metatheorem that
relates general theorems for discrete and
continuous control problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800581
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17431/zip/
urn:nbn:de:bsz:ch1-199800581
oai:qucosa:de:qucosa:17433
2021-03-29T09:31:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grafik-Ausgabe vom Parallelrechner für 2D-Gebiete
M.
Pester
510
510
MSC 65Y05
MSC 68Q22
The paper mainly describes the user interface of some graphical
visualization tools for parallel finite element applications in
2D (layer problems, deformation problems, fluid dynamics). There
are presented some examples of various methods to display the
numerical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800602
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17433/zip/
urn:nbn:de:bsz:ch1-199800602
oai:qucosa:de:qucosa:17437
2021-03-29T09:31:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh refinement in stabilized Galerkin methods
Thomas
Apel
Gert
Lube
510
510
elliptic boundary value problems
Galerkin finite element methods
anisotropic mesh refinement
MSC 65N30
MSC 65N50
MSC 35J25
The numerical solution of the convection-diffusion-reaction problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least squares type accomodates diffusion-dominated as well as convection- and/or reaction- dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is accomplished using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800640
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17437/zip/
urn:nbn:de:bsz:ch1-199800640
oai:qucosa:de:qucosa:17434
2021-03-29T09:31:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Matrix Sign Function Method and the Computation of Invariant Subspaces
R.
Byers
C.
He
V.
Mehrmann
510
510
matrix sign function
invariant subspaces
stability
Newton
iteration
numerical examples
MSC 65F30
MSC 65F15
A perturbation analysis shows that if a numerically stable
procedure is used to compute the matrix sign function, then it is competitive
with conventional methods for computing invariant subspaces.
Stability analysis of the Newton iteration improves an earlier result of Byers
and confirms that ill-conditioned iterates may cause numerical
instability. Numerical examples demonstrate the theoretical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800619
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17434/zip/
urn:nbn:de:bsz:ch1-199800619
oai:qucosa:de:qucosa:17438
2021-03-29T09:31:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Implementierung eines parallelen vorkonditionierten Schur-Komplement CG-Verfahrens in das Programmpaket FEAP
Mathias
Meisel
Arnd
Meyer
510
510
Schur-Complement
Conjugate Gradient
parallel realisation
domain decomposition
MSC 65Y05
MSC 65N30
A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800651
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17438/zip/
urn:nbn:de:bsz:ch1-199800651
oai:qucosa:de:qucosa:17435
2021-03-29T09:31:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local inequalities for anisotropic finite elements and their application to convection-diffusion problems
Thomas
Apel
Gert
Lube
510
510
MSC 65N30
The paper gives an overview over local inequalities for anisotropic simplicial Lagrangian finite elements. The main original contributions are the estimates for higher derivatives of the interpolation error, the formulation of the assumptions on admissible anisotropic finite elements in terms of geometrical conditions in the three-dimensional case, and an anisotropic variant of the inverse inequality. An application of anisotropic meshes in the context of a stabilized Galerkin method for a convection-diffusion problem is given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800625
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17435/zip/
urn:nbn:de:bsz:ch1-199800625
oai:qucosa:de:qucosa:17439
2021-03-29T09:31:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grafik-Ausgabe vom Parallelrechner für 3D-Gebiete
M.
Meyer
510
510
MSC 65Y05
MSC 68Q22
The paper describes a method for Visualization of computational results in parallel finite element applications for 3D problems. The visualization itself is done on a workstation using a post- processing tool based on GRAPE, which interacts with the parallel program to obtain data.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800669
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17439/zip/
urn:nbn:de:bsz:ch1-199800669
oai:qucosa:de:qucosa:17436
2021-03-29T09:31:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Analysis und Numerik linearer differentiell-algebraischer Gleichungen
Peter
Kunkel
Volker
Mehrmann
510
510
consistent systems
numerical procedures
MSC 65L05
In Analysis and Numerik differential-algebraischer Gleichungen P. Kunkel and V. Mehrmann give a survey of relevant conditions for consistent systems, for existence and uniqueness of solutions, and touch numerical procedures for obtaining the solutions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800633
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17436/zip/
urn:nbn:de:bsz:ch1-199800633
oai:qucosa:de:qucosa:1744
2021-03-27T15:38:06Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Modelling the Transition from Secondary to Tertiary Mathematics Education: Teacher and Lecturer Perspectives
Ye Yoon
Hong
Suzanne
Kerr
Sergiy
Klymchuk
Johanna
McHardy
Priscilla
Murphy
Sue
Spencer
Mike
Thomas
Peter
Watson
510
510
SD 2009
Universität
Übergang
Lehrer
Dozent
Mathematik
Einschätzung
Lehren
University
Transition
Teacher
Lecturer
Mathematics
Assessment
Teaching
The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great
need for improved communication between the two sectors.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80200
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 250 - 254
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 250 - 254
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1744/zip/
urn:nbn:de:bsz:14-qucosa-80200
371749077
oai:qucosa:de:qucosa:17441
2021-03-29T09:31:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ein technologisches Konzept zur Erzeugung adaptiver hierarchischer Netze für FEM-Schemata
U.
Groh
510
510
FEM
adaptive
mesh refinement
irregular
hierarchical
MSC 65Y05
MSC 65N30
Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800686
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17441/zip/
urn:nbn:de:bsz:ch1-199800686
oai:qucosa:de:qucosa:17442
2021-03-29T09:31:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ein Residuenfehlerschätzer für anisotrope Tetraedernetze und Dreiecksnetze in der Finite-Elemente-Methode
G.
Kunert
510
510
finite elements
error estimator
anisotropic solution
stretched elements
tetrahedral mesh
triangular mesh
MSC 65N30
MSC 65N15
Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes such estimators are known but they fail when applied to anisotropic meshes. Rectangular (or cuboidal) anisotropic meshes were already investigated. In this paper an error estimator is presented for tetrahedral or triangular meshes which offer a much greater geometrical flexibility.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800691
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17442/zip/
urn:nbn:de:bsz:ch1-199800691
oai:qucosa:de:qucosa:17440
2021-03-29T09:31:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel solution of finite element equation systems: efficient inter-processor communication
T.
Apel
G.
Haase
A.
Meyer
M.
Pester
510
510
MSC 65Y05
MSC 65N30
This paper deals with the application of domain decomposition methods for the parallel solution of boundary value problems for partial differential equations over a domain $Omegabset R^d$, $d=2,3$. The attention is focused on the conception of efficient communication routines for the data exchange which is necessary for example in the preconditioned cg-algorithm for solving the resulting system of algebraic equations. The paper describes the data structure, different algorithms, and computational tests.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800670
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17440/zip/
urn:nbn:de:bsz:ch1-199800670
oai:qucosa:de:qucosa:17446
2021-03-29T09:31:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Kommunikationstechnologien beim parallelen vorkonditionierten Schur-Komplement CG-Verfahren
M.
Meisel
A.
Meyer
510
510
Conjugate-Gradient
communication
parallelized
MSC 65Y05
Two alternative technologies of communication inside a parallelized Conjugate-Gradient algorithm are presented and compared to the well known hypercubecommunication. The amount of communication is diskussed in detail. A large range of numerical results corroborate the theoretical investigations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800734
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17446/zip/
urn:nbn:de:bsz:ch1-199800734
oai:qucosa:de:qucosa:17443
2021-03-29T09:31:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Canonical forms for linear descriptor systems with variable coefficients
W.
Rath
510
510
descriptor systems
closed loop system
MSC 65Y05
We study linear descriptor systems with rectangular variable coefficient matrices.
Using local and global equivalence transformations we introduce normal and
condensed forms and get sets of characteristic quantities. These quantities allow us to
decide whether a linear descriptor system with variable coefficients is regularizable
by derivative and/or proportional state feedback or not. Regularizable by feedback
means for us that their exist a feedback which makes the closed loop system uniquely
solvable for every consistent initial vector.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800708
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17443/zip/
urn:nbn:de:bsz:ch1-199800708
oai:qucosa:de:qucosa:17444
2021-03-29T09:31:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Placing plenty of poles is pretty preposterous
C.
He
A. J.
Laub
V.
Mehrmann
510
510
control models
pretty preposterous
eigenvalues
ill-conditioned
MSC 65Y05
We discuss the pole placement problem for single-input or multi-input control models of the form _x=Ax+Bu. This is the problem of determining a linear state feedback of the formu=F xsuch that in the closed-loop system _x= (A+BF)x, the matrixA+BFhas a prescribed set of eigenvalues. We analyze the conditioning of this problem and show that it is an intrinsically ill-conditioned problem, and especially so when the system dimension is large. Thus even the best numerical methods for this problem may yield very bad results. On the other hand, we also discuss the question of whether one really needs to solve the pole placement problem. In most circum- stances what is really required is stabilization or that the poles are in a specified region of the complex plane. This related problem may have much better conditioning. We demonstrate this via the example of stabilization.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800712
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17444/zip/
urn:nbn:de:bsz:ch1-199800712
oai:qucosa:de:qucosa:17447
2021-03-29T09:31:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Bibliotheken zur Entwicklung paralleler Algorithmen
G.
Haase
T.
Hommel
A.
Meyer
M.
Pester
510
510
parallel algorithms
message passing
numerical software
computer graphics
MSC 65Y05
MSC 65Y25
The purpose of this paper is to supply a summary of library subroutines and functions for parallel MIMD computers. The subroutines have been developed at the University of Chemnitz during a period of the last five years. In detail, they are concerned with vector operations, inter-processor communication and simple graphic output to workstations. One of the most valuable features is the machine-independence of the communication subroutines proposed in this paper for a hypercube topology of the parallel processors (excepting a kernel of only two primitive system-dependend operations). They were implemented and tested for different hardware and operating systems including transputer, nCube, KSR, PVM. The vector subroutines are optimized by the use of C language and enrolled loops (BLAS1-like). The paper includes hints for using the libraries with both Fortran and C programs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800749
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17447/zip/
urn:nbn:de:bsz:ch1-199800749
oai:qucosa:de:qucosa:17445
2021-03-29T09:31:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Dampening controllers via a Riccati equation approach
J. J.
Hench
C.
He
V.
Kučera
V.
Mehrmann
510
510
linear quadratic controller
dampening feedback
damped dynamics
periodic systems
periodic Riccati equation
MSC 65L05
An algorithm is presented which computes a state feedback for a standard linear system which not only stabilizes, but also dampens the closed-loop system dynamics. In other words, a feedback gain vector is computed such that the eigenvalues of the closed-loop state matrix are within the region of the left half-plane where the magnitude of the real part of each eigenvalue is greater than the imaginary part. This may be accomplished by solving one periodic algebraic Riccati equation and one degenerate Riccati equation. The solution to these equations are computed using numerically robust algorithms. Finally, the periodic Riccati equation is unusual in that it produces one symmetric and one skew symmetric solution, and as a result two different state feedbacks. Both feedbacks dampen the system dynamics, but produce different closed-loop eigenvalues, giving the controller designer greater freedom in choosing a desired feedback.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800720
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17445/zip/
urn:nbn:de:bsz:ch1-199800720
oai:qucosa:de:qucosa:17448
2021-03-29T09:31:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case
P.
Benner
A. J.
Laub
V.
Mehrmann
510
510
benchmark
Riccati equations
MSC 65L05
A collection of benchmark examples is presented for the numerical solution of continuous-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800758
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17448/zip/
urn:nbn:de:bsz:ch1-199800758
oai:qucosa:de:qucosa:17450
2021-03-29T09:31:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Newtons method with exact line search for solving the algebraic Riccati equation
P.
Benner
R.
Byers
510
510
Newton method
algebraic Riccati equation
exact line search step
size control
MSC 65F30
MSC 15A24
This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newton{like method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton's method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800775
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17450/zip/
urn:nbn:de:bsz:ch1-199800775
oai:qucosa:de:qucosa:17449
2021-03-29T09:31:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A collection of benchmark examples for the numerical solution of algebraic Riccati equations II: Discrete-time case
P.
Benner
A. J.
Laub
V.
Mehrmann
510
510
Riccati equations
benchmark
MSC 65L05
This is the second part of a collection of benchmark examples for the numerical solution of algebraic Riccati equations. After presenting examples for the continuous-time case in Part I, our concern in this paper is discrete-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800765
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17449/zip/
urn:nbn:de:bsz:ch1-199800765
oai:qucosa:de:qucosa:17451
2021-03-29T09:31:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallelization of multi-grid methods based on domain decomposition ideas
M.
Jung
510
510
Multi-grid methods
Parallel algorithms
Finite element discretizations
MSC 65N55
MSC 65Y05
MSC 65N30
In the paper, the parallelization of multi-grid methods for solving second-order elliptic boundary value problems in two-dimensional domains is discussed. The parallelization strategy is based on a non-overlapping domain decomposition data structure such that the algorithm is well-suited for an implementation on a parallel machine with MIMD architecture. For getting an algorithm with a good paral- lel performance it is necessary to have as few communication as possible between the processors. In our implementation, communication is only needed within the smoothing procedures and the coarse-grid solver. The interpolation and restriction procedures can be performed without any communication. New variants of smoothers of Gauss-Seidel type having the same communication cost as Jacobi smoothers are presented. For solving the coarse-grid systems iterative methods are proposed that are applied to the corresponding Schur complement system. Three numerical examples, namely a Poisson equation, a magnetic field problem, and a plane linear elasticity problem, demonstrate the efficiency of the parallel multi- grid algorithm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800781
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17451/zip/
urn:nbn:de:bsz:ch1-199800781
oai:qucosa:de:qucosa:1745
2021-03-27T15:38:07Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Linking Teachers and Mathematicians: The AWM Teacher Partnership Program
Pao-sheng
Hsu
Suzanne
Lenhart
Erica
Voolich
510
510
SD 2009
Mathematiker und Lehrer in Partnerschaft
Zusammenarbeit zwischen mathematischen und pädagogischen Gesellschaften
Frauen und Mädchen
Kommunikation zwischen den Gesellschaften
Kultur und Sprachen
mathematician and teacher partnership
collaboration between mathematical and pre-college teaching communities
women and girls
communication between communities
culture and languages
Within a professional organization for women in mathematics in the US, two mathematicians and a middle school teacher organize a program to link teachers of students at the pre-university level
with professionals in the mathematical sciences in and outside of academia to promote collaborations among different communities in the mathematics education of students. This paper describes the program and its operations, some of its experiences, as well as some results from a formative evaluation conducted for the program. Some recommendations are given for potential organizers of similar programs in other countries.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80211
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 255 - 258
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 255 - 258
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1745/zip/
urn:nbn:de:bsz:14-qucosa-80211
371749751
oai:qucosa:de:qucosa:17452
2021-03-29T09:31:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Eigenvibrations of a plate with elastically attached load
Sergey I.
Solov'ëv
510
510
Eigenschwingung
Nichtlineares Eigenwertproblem
Spektraltheorie
natural oscillations
plate
This paper is concerned with the investigation of the nonlinear eigenvalue problem describing the natural oscillations of a plate with a load that elastically attached to it. We study properties of eigenvalues and eigenfunctions of this eigenvalue problem and prove the existence theorem for eigensolutions. Theoretical results are illustrated by numerical experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600638
Preprintreihe des Chemnitzer SFB 393, 03-06
eng
Preprintreihe des Chemnitzer SFB 393, 03-06
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17452/zip/
urn:nbn:de:swb:ch1-200600638
oai:qucosa:de:qucosa:17455
2021-03-29T09:31:50Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Domain Decomposition and Multilevel Techniques for Preconditioning Operators
S. V.
Nepomnyaschikh
510
510
domain decomposition
multilevel
preconditioning
MSC 65N55
Introduction In recent years, domain decomposition methods have been used extensively to efficiently solve boundary value problems for partial differential equations in complex{form domains. On the other hand, multilevel techniques on hierarchical data structures also have developed into an effective tool for the construction and analysis of fast solvers. But direct realization of multilevel techniques on a parallel computer system for the global problem in the original domain involves difficult communication problems. I this paper, we present and analyze a combination of these two approaches: domain decomposition and multilevel decomposition on hierarchical structures to design optimal preconditioning operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800815
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17455/zip/
urn:nbn:de:bsz:ch1-199800815
oai:qucosa:de:qucosa:17453
2021-03-29T09:31:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
P.
Benner
H.
Faßbender
510
510
symplectic Lanczos method
implicit restarting
Hamiltonian matrix
eigenvalues
low rank approximate solution
algebraic Riccati equation
MSC 65F15
MSC 65F50
A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem is presented. The Lanczos vectors are constructed to form a symplectic basis. Breakdowns and near-breakdowns are overcome by inexpensive implicit restarts. The method is used to compute eigenvalues, eigenvectors and invariant subspaces of large and sparse Hamiltonian matrices and low rank approximations to the solution of continuous-time algebraic Riccati equations with large and sparse coefficient matrices.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800797
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17453/zip/
urn:nbn:de:bsz:ch1-199800797
oai:qucosa:de:qucosa:17456
2021-03-29T09:31:51Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel Preconditioners for Plate Problem
H.
Matthes
510
510
Schur-complement
conjugate gradient
plate bending problems
Domain decomposition,preconditioners
parallel
MSC 65Y05
This paper concerns the solution of plate bending problems in domains composed of rectangles. Domain decomposition (DD) is the basic tool used for both the parallelization of the conjugate gradient method and the construction of efficient parallel preconditioners. A so-called Dirich- let DD preconditioner for systems of linear equations arising from the fi- nite element approximation by non-conforming Adini elements is derived. It is based on the non-overlapping DD, a multilevel preconditioner for the Schur-complement and a fast, almost direct solution method for the Dirichlet problem in rectangular domains based on fast Fourier transform. Making use of Xu's theory of the auxiliary space method we construct an optimal preconditioner for plate problems discretized by conforming Bogner-Fox-Schmidt rectangles.
Results of numerical experiments carried out on a multiprocessor sys- tem are given. For the test problems considered the number of iterations is bounded independent of the mesh sizes and independent of the number of subdomains. The resulting parallel preconditioned conjugate gradient method requiresO(h^-2 ln h^-1 ln epsilon^-11) arithmetical operations per processor in order to solve the finite element equations with the relative accuracy epsilon.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800826
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17456/zip/
urn:nbn:de:bsz:ch1-199800826
oai:qucosa:de:qucosa:17454
2021-03-29T09:31:49Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Exact discretizations of two-point boundary value problems
G.
Windisch
510
510
exact discretizations
nonlinear
boundary value problem
tridiagonal
MSC 65L10
In the paper we construct exact three-point discretizations of linear and nonlinear two-point boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal M-matrices in the linear case and M-functions in the nonlinear case.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800804
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17454/zip/
urn:nbn:de:bsz:ch1-199800804
oai:qucosa:de:qucosa:17457
2021-03-29T09:31:52Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
SPC-PM Po 3D --- Users Manual
Th.
Apel
510
510
004
004
MSC 65Y05
The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam\'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800836
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17457/zip/
urn:nbn:de:bsz:ch1-199800836
oai:qucosa:de:qucosa:1746
2021-03-27T15:38:03Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Project work Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization?
Darka
Hvastija
Jasna
Kos
510
510
SD 2009
Mathematikgeschichte
fachübergreifende Projektarbeit
Schule von Athen
History of Mathematics
Cross-curriculum project work
school of Athen
In this paper the project for 15-year-old students with the title Ancient Greece and Rome and the sub-title Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization? is introduced. It shows how to connect mathematics with art, history, physics, geography and philosophy by studying ancient Greek scientists
and their achievements. Collaborative teaching is introduced. The major aim of the project was to show mathematics as a part of human civilization and to follow its development through history. Some topics from theory of numbers and geometry were studied. One part of the project was also a theatre performance, which
should make the students aware of the difficulties of many dedicated mathematicians to find the answers to some problems from the ancient times.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80221
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 259 - 261
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 259 - 261
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1746/zip/
urn:nbn:de:bsz:14-qucosa-80221
371749859
oai:qucosa:de:qucosa:17458
2021-03-29T09:31:52Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
SPC-PM Po 3D --- Programmers Manual
Th.
Apel
F.
Milde
M.
Theß
510
510
004
004
parallel computing
finite element methods
MSC 65Y05
The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800848
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17458/zip/
urn:nbn:de:bsz:ch1-199800848
oai:qucosa:de:qucosa:17459
2021-03-29T09:31:53Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I
S. A.
Ivanov
V. G.
Korneev
510
510
MSC 65N55
MSC 65N30
Abstract P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary re- sults for 1D case, condition number estimates and some inequalities for 2D reference element.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800856
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17459/zip/
urn:nbn:de:bsz:ch1-199800856
oai:qucosa:de:qucosa:17460
2021-03-29T09:31:54Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the preconditioning in the domain decomposition technique for the p-version finite element method. Part II
S. A.
Ivanov
V. G.
Korneev
510
510
Schur complement preconditioner
MSC 65N55
MSC 65N30
P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary results for 1D case, condition number estimates and some inequalities for 2D reference element. Part II is devoted to the derivation of the Schur complement preconditioner and conditionality number estimates for the p-version finite element matrixes. Also DD preconditioning is considered.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800862
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17460/zip/
urn:nbn:de:bsz:ch1-199800862
oai:qucosa:de:qucosa:17464
2021-03-29T09:31:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Zur Berechnung von Spannungs- und Deformationsfeldern an Interface-Ecken im nichtlinearen Deformationsbereich auf Parallelrechnern
M.
Scherzer
A.
Meyer
510
510
parallel
stiffness
deformation field calculation
MSC 65Y05
Using material models on the basis of the flow theory of plasticity the asymptotic behaviour of solid mechanics solutions in crack tips, interface corners etc. strongly depends on the local realized load trajectory. For incrementally proportional load paths the equations determining the asymptotic fields are very simple ones. The paper considers two-dimensional statements in the neighbourhood of an interface corner consisting of two material ranges. At a distance from the corner the finite element nodes of a regular net are established in a polar co-ordinate system together with the displacement degrees of freedom. The main idea of the presented singular and non-singular stress and deformation field calculation at interface corners characterizes an replacement of the corner neighbourhood effect to the surrounding body by introducing stiffness actions which in usual manner can be assembled together with the other element stiffness matrices to the global stiffness matrix of the body. According to this there exists an in teresting invariant stiffness independence in corner and crack neighbourhoods. The applied technique allows extensions to non-proportional local load increments simplifying the mathematical calculations for the presentation of stress and strain fields in this general case. All computations are made on modern parallel computers. Concrete examples show the advantages of the presented approach.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800902
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17464/zip/
urn:nbn:de:bsz:ch1-199800902
oai:qucosa:de:qucosa:17461
2021-03-29T09:31:55Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Thermoelastic Oscillations of Anisotropic Bodies
L.
Jentsch
D.
Natroshvili
510
510
thermoelasticity
oscillations
anisotropic bodies
potential method
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800871
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17461/zip/
urn:nbn:de:bsz:ch1-199800871
oai:qucosa:de:qucosa:17465
2021-03-29T09:31:58Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
P.
Benner
V.
Mehrmann
H.
Xu
510
510
eigenvalue problem
Hamiltonian pencil matrix
symplectic pencil matrix
skew-Hamiltonian matrix
MSC 65F15
A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800915
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17465/zip/
urn:nbn:de:bsz:ch1-199800915
oai:qucosa:de:qucosa:17462
2021-03-29T09:31:56Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Thermoelastic Oscillations of Anisotropic Bodies (Sommerfeld 96 - Workshop)
L.
Jentsch
D.
Natroshvili
510
510
thermoelasticity
oscillations
anisotropic bodies
potential methods
MSC 73D30
MSC 73B40
Three-dimensional basic problems of statics, pseudo-oscillations, general dynamics and steady state oscillations of the thermoelasticity of isotropic bodies have been completely investigated by many authors. In particular, exterior steady state oscillation problems have been studied on the basis of Sommerfeld-Kupradze radiation conditions in the thermoelasticity, and the uniqueness theorems were proved with the help of the well-known Rellich's lemma, since the components of the displacement vector and the temperature in the isotropic case can be represented as a sum of metaharmonic functions . Unfortunately, the methods of investigation of thermoelastic steady state oscillation problems developed for the isotropic case are not applicable in the case of general anisotropy. This is stipulated by a very complicated form of the corresponding characteristic equation which plays a significant role in the study of far field behaviour of solutions to the oscillation equa- tions. We note that the basic and crack type boundary value problems (BVPs) for the pseudo-oscillation equations of the thermoelasticity theory in the anisotropic case are considered in [3,14]. To the best of the authors' knowledge the problems of thermoelastic steady oscillations for anisotropic bodies have not been treated in the scientific literature. In the present paper we will consider a wide class of basic and mixed type BVPs for the equations of thermoelastic steady state oscillations. We will formulate thermoelastic radiation conditions for an anisotropic medium (the generalized Sommerfeld-Kupradze type radiation conditions) and prove the uniqueness theorems in corresponding spaces. To derive these conditions we have essentially applied results of Vainberg. Further, using the potential method and the theory of pseudodifferential equations on manifolds we will prove existence theorems in various functional spaces and establish the smoothness properties of solutions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800886
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17462/zip/
urn:nbn:de:bsz:ch1-199800886
oai:qucosa:de:qucosa:17466
2021-03-29T09:31:59Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
HAMEV and SQRED: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Using Van Loanss Square Reduced Method
P.
Benner
R.
Byers
E.
Barth
510
510
eigenvalues
square-reduced Hamiltonian matrix
skew-Hamiltonian matrix
algebraic Riccati equation
MSC 65F15
MSC 93B40
This paper describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamilto- nian matrix to a square-reduced Hamiltonian uses only orthogonal symplectic similarity transformations. The eigenvalues can then be determined by applying the Hessenberg QR iteration to a matrix of half the order of the Hamiltonian matrix and taking the square roots of the computed values. Using scaling strategies similar to those suggested for algebraic Riccati equations can in some cases improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800926
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17466/zip/
urn:nbn:de:bsz:ch1-199800926
oai:qucosa:de:qucosa:17463
2021-03-29T09:31:56Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Numerical solution of generalized Lyapunov equations
T.
Penzl
510
510
mathematical software
generalized Lyapunov equation
generalized Stein equation
condition estimation
MSC 65F05
MSC 65F15
MSC 93B40
MSC 93B51
Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the Bartels--Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels--Stewart subroutine offers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800893
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17463/zip/
urn:nbn:de:bsz:ch1-199800893
oai:qucosa:de:qucosa:17469
2021-03-29T09:32:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces
B.
Hofmann
O.
Scherzer
510
510
nonlinear operator equations
ill-posedness
Frechet derivative
source conditions
stability estimates
ill-posedness measurres
a posteriori estimates
MSC 65J15
MSC 65J20
MSC 47H15
MSC 47H17
The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800957
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17469/zip/
urn:nbn:de:bsz:ch1-199800957
oai:qucosa:de:qucosa:17468
2021-03-29T09:32:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Navier-Stokes equations as a differential-algebraic system
J.
Weickert
510
510
MSC 76D05
Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800942
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17468/zip/
urn:nbn:de:bsz:ch1-199800942
oai:qucosa:de:qucosa:1747
2021-03-27T15:38:04Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
A Model to Develop Mathematics Education: Modify the Public TraditionalPerceptions of Mathematics-Case of UAE Schools’ Principals
Hanan
Innabi
510
510
SD 2009
Schulleiter Wahrnehmungen
Trainingsprogramm
UAE Mathematik
Principals perceptions
training program
UAE Mathematics
This paper addresses the idea that the successful of mathematics reform demands the support of the full educational community including school principals, parents, and students. One of the most important group that affect mathematics reform is school principals. A project related to modifying UAE principals’ perceptions of mathematics is presented. This project consists three steps. In the first step, principals’ perceptions of the nature of Mathematics and its learning and teaching were examined. Results showed that those principals possess many improper perceptions related to Mathematics. In the second step, a professional training program for promoting school principals\'' understanding of the new vision of teaching and learning mathematics has developed. This training program comprises two integrated phases: Clarification and conviction, and implementations for principal’s role. It includes a
package of paper documents, videotapes, discussion sessions, and group and individual activities. In the third step, the training program is applied on eight principals in UAE. An initial analysis of the qualitative data showed many positive improvements in principals’ perceptions of mathematics education.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80236
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 262 - 266
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 262 - 266
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1747/zip/
urn:nbn:de:bsz:14-qucosa-80236
371749999
oai:qucosa:de:qucosa:17470
2021-03-29T09:32:02Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Three-dimensional mathematical Problems of thermoelasticity of anisotropic Bodies
Lothar
Jentsch
David
Natroshvili
510
510
boundary value problems
thermoelasticity
anisotropic bodies
interface problems
mixed and crack type problems
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 35J55
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
MSC 73C35
MSC 73K20
CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions
1. Basic differential equations of thermoelasticity theory
2. Fundamental matrices
3. Thermo-radiating conditions. Somigliana type integral representations
CHAPTER II. Formulation of Boundary Value and Interface Problems
4. Functional spaces
5. Formulation of basic and mixed BVPs
6. Formulation of crack type problems
7. Formulation of basic and mixed interface problems
CHAPTER III. Uniqueness Theorems
8. Uniqueness theorems in pseudo-oscillation problems
9. Uniqueness theorems in steady state oscillation problems
CHAPTER IV. Potentials and Boundary Integral Operators
10. Thermoelastic steady state oscillation potentials
11. Pseudo-oscillation potentials
CHAPTER V. Regular Boundary Value and Interface Problems
12. Basic BVPs of pseudo-oscillations
13. Basic exterior BVPs of steady state oscillations
14. Basic interface problems of pseudo-oscillations
15. Basic interface problems of steady state oscillations
CHAPTER VI. Mixed and Crack Type Problems
16. Basic mixed BVPs
17. Crack type problems
18. Mixed interface problems of steady state oscillations
19. Mixed interface problems of pseudo-oscillations
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800967
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17470/zip/
urn:nbn:de:bsz:ch1-199800967
oai:qucosa:de:qucosa:17474
2021-03-29T09:32:05Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic Equations
Fredi
Tröltzsch
510
510
optimal control
parabolic equation
semilinear equation
sequential quadratic programming
Lagrange-Newton method
convergence analysis
MSC 49J20
MSC 49M15
MSC 65K10
MSC 49K20
A class of Lagrange-Newton-SQP methods is investigated for optimal control problems
governed by semilinear parabolic initial- boundary value problems. Distributed and boundary
controls are given, restricted by pointwise upper and lower bounds. The convergence of the method
is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition
for the reference solution, local quadratic convergence is proved. The proof is based on the
theory of Newton methods for generalized equations in Banach spaces.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800995
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17474/zip/
urn:nbn:de:bsz:ch1-199800995
oai:qucosa:de:qucosa:17471
2021-03-29T09:32:03Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Interface Crack Problem for Anisotropic Bodies
David
Natroshvili
Shota
Zazashvili
510
510
anisotropic body
interface crack problem
MSC 31A10
MSC 35J55
MSC 73B40
MSC 73C35
MSC 73M25
The two-dimensional interface crack problem is investigated for anisotropic bodies in the Comninou formulation. It is established that, as in the isotropic case, properly incorporating contact zones at the crack tips avoids contradictions connected with the oscillating asymptotic behaviour of physical and mechanical characteristics leading to the overlapping of material. Applying the special integral representation formulae for the displacement field the problem in question is reduced to the scalar singular integral equation with the index equal to -1. The analysis of this equation is given. The comparison with the results of previous authors shows that the integral equations corresponding to the interface crack problems in the anisotropic and isotropic cases are actually the same from the point of view of the theoretical and numerical analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800979
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17471/zip/
urn:nbn:de:bsz:ch1-199800979
oai:qucosa:de:qucosa:17475
2021-03-29T09:32:06Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
Kazimierz
Malanowski
Fredi
Tröltzsch
510
510
optimal control
semilinear parabolic equations
Lipschitz stability
supremum norm
MSC 49K20
MSC 49K40
A class of parametric optimal control problems for semilinear parabolic
equations is considered. Using recent regularity results for solutions of such equations,
sufficient conditions are derived under which the solutions to optimal control problems
are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown
that these conditions are also necessary, provided that the dependence of data on the
parameter is sufficiently strong.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801001
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17475/zip/
urn:nbn:de:bsz:ch1-199801001
oai:qucosa:de:qucosa:17472
2021-03-29T09:32:04Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators
B.
Hofmann
G.
Fleischer
510
510
Linear ill-posed problems
compact and noncompact linear operators in Hilbert spaces
discrete least-squares method
stability rates
singular values
convolution and multiplication operators
Galerkin matrices
condition numbers
increasing rearrangements
MSC 65J20
MSC 47B38
MSC 65R30
In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800987
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17472/zip/
urn:nbn:de:bsz:ch1-199800987
oai:qucosa:de:qucosa:17476
2021-03-29T09:32:07Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Second Order Sufficient Optimality Conditions for Nonlinear Parabolic Control Problems with State Constraints
Jean-Pierre
Raymond
Fredi
Tröltzsch
510
510
Boundary control
distributed control
semilinear parabolic equations
sufficient optimality conditions
pointwise state constraints
MSC 49K20
MSC 35J25
In this paper, optimal control problems for semilinear parabolic equations with
distributed and boundary controls are considered. Pointwise constraints on the control and on
the state are given. Main emphasis is laid on the discussion of second order sufficient optimality
conditions. Sufficiency for local optimality is verified under different assumptions imposed
on the dimension of the domain and on the smoothness of the given data.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801014
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17476/zip/
urn:nbn:de:bsz:ch1-199801014
oai:qucosa:de:qucosa:17478
2021-03-29T09:32:08Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal control
T.
Penzl
510
510
ADI iteration
Smith method
iterative methods
Lyapunov equation
matrix equation
model reduction
balanced truncation
optimal control
Riccati equation
Newton method
MSC 65F30
MSC 65F10
MSC 15A24
MSC 93C05
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801035
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17478/zip/
urn:nbn:de:bsz:ch1-199801035
oai:qucosa:de:qucosa:17482
2021-03-29T09:32:11Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements
Th.
Apel
510
510
MSC 65N30
Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions.
The case of affine elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements.
As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801071
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17482/zip/
urn:nbn:de:bsz:ch1-199801071
oai:qucosa:de:qucosa:1748
2021-03-27T15:38:08Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
A Four Phase Model for Predicting the Probabilistic Situation ofCompound Events
Irma
Jan
Miriam
Amit
510
510
SD 2009
Wahrscheinlichkeit
zusammengesetzte Ereignisse
theoretische und empirische Wahrscheinlichkeit
Stichprobenraum
Zufallsexperiment
Lösungsstrategien
kognitive Hindernisse
begabte Studenten
Probability
compound events
theoretical and empirical probability
sample space
random experiment
solutions strategies
cognitive obstacles
talented students
This paper presents an innovat ive cons t ruct ion of a probabilistic model for predicting chance situations. It describes the construction of a four phase model, derived from an intense qualitative analysis of the written responses of 94 mathematically talented middle school students to the probabilistic compound event problem: “How many doubles are expected when rolling two dice fifty times?” We found
that the students’ comprehension process of compound event situations can be broken down into a four phase model: beliefs, subjective estimations, chance estimations and probabilistic calculations. The paper focuses on the development of the model over the course of the experiment, identifying the process the
students underwent as they attempted to answer the question. We explain each phase as it was reflected in the students\'' rationalizations. All phases, including their definitions and students’ citations, will be presented in the paper. While not every student necessarily goes through all four phases, an awareness and
understanding of them all allows for efficient, effective intervention during the learning process. We found that guidance and learning intervention helped shorten the preliminary phases, leading to more relative time spent on probabilistic calculations.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80241
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 267 - 271
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 267 - 271
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1748/zip/
urn:nbn:de:bsz:14-qucosa-80241
37175013X
oai:qucosa:de:qucosa:17483
2021-03-29T09:32:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh refinement for singularly perturbed reaction diffusion problems
Th.
Apel
G.
Lube
510
510
elliptic boundary value problems
Galerkin finite element methods
anisotropic mesh refinement
MSC 65N30
MSC 65N50
MSC 35J25
The paper is concerned with the finite element resolution of layers appearing
in singularly perturbed problems. A special anisotropic grid of Shishkin type
is constructed for reaction diffusion problems. Estimates of the finite element
error in the energy norm are derived for two methods, namely the standard
Galerkin method and a stabilized Galerkin method. The estimates are uniformly
valid with respect to the (small) diffusion parameter. One ingredient is a
pointwise description of derivatives of the continuous solution. A numerical
example supports the result.
Another key ingredient for the error analysis is a refined estimate for
(higher) derivatives of the interpolation error. The assumptions on admissible
anisotropic finite elements are formulated in terms of geometrical conditions
for triangles and tetrahedra. The application of these estimates is not
restricted to the special problem considered in this paper.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801080
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17483/zip/
urn:nbn:de:bsz:ch1-199801080
oai:qucosa:de:qucosa:17484
2021-03-29T09:32:13Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Scalability, efficiency, and robustness of parallel multilevel solvers for nonlinear equations
B.
Heise
M.
Jung
510
510
004
004
MSC 65Y05
In this paper we compare the performance, scalability, and robustness of different parallel algorithms for the numerical solution of nonlinear boundary value problems arising in the magnetic field computation and in solid mechanics. These problems are discretized by using the finite element method with triangular meshes and piecewise linear functions. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely multigrid methods and conjugate gradient methods with preconditioners based on domain decomposition, multigrid, or BPX techniques, respectively. The basis of the implementation of all solvers is a non-overlapping domain decomposition data structure such that they are well-suited for parallel machines with MIMD architecture.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801090
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17484/zip/
urn:nbn:de:bsz:ch1-199801090
oai:qucosa:de:qucosa:17485
2021-03-29T09:32:14Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Partitionierung von Finite-Elemente-Netzen
U.
Reichel
510
510
MSC 65N30
MSC 65N50
The realization of the finite element method on parallel computers
is usually based on a domain decomposition approach. This paper is
concerned with the problem of finding an optimal decomposition and an
appropriate mapping of the subdomains to the processors. The quality
of this partitioning is measured in several metrics but it is also
expressed in the computing time for solving specific systems of
finite element equations.
The software environment is first described. In particular, the data
structure and the accumulation algorithm are introduced. Then
several partitioning algorithms are compared. Spectral bisection was
used with different modifications including Kernighan-Lin refinement,
post-processing techniques and terminal propagation. The final
recommendations should give good decompositions for all finite
element codes which are based on principles similar to ours.
The paper is a shortened English version of Preprint SFB393/96-18
(Uwe Reichel: Partitionierung von Finite-Elemente-Netzen), SFB 393,
TU Chemnitz-Zwickau, December 1996. To be selfcontained, some material
of Preprint SPC95_5 (see below) is included. The paper appeared as
Preprint SFB393/96-18a, SFB 393, TU Chemnitz-Zwickau, January 1997.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801107
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17485/zip/
urn:nbn:de:bsz:ch1-199801107
oai:qucosa:de:qucosa:17487
2021-03-29T09:32:15Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Two-point boundary value problems with piecewise constant coefficients: weak solution and exact discretization
G.
Windisch
510
510
MSC 65L10
For two-point boundary value problems in weak formulation with piecewise constant coefficients and piecewise continuous right-hand side functions we derive a representation of its weak solution by local Green's functions. Then we use it to generate exact three-point discretizations by Galerkin's method on essentially arbitrary grids. The coarsest possible grid is the set of points at which the piecewise constant coefficients and the right- hand side functions are discontinuous. This grid can be refined to resolve any solution properties like boundary and interior layers much more correctly. The proper basis functions for the Galerkin method are entirely defined by the local Green's functions. The exact discretizations are of completely exponentially fitted type and stable. The system matrices of the resulting tridiagonal systems of linear equations are in any case irreducible M-matrices with a uniformly bounded norm of its inverse.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801123
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17487/zip/
urn:nbn:de:bsz:ch1-199801123
oai:qucosa:de:qucosa:17491
2021-03-29T09:32:18Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Interaction between Thermoelastic and Scalar Oscillation Fields (general anisotropic case)
L.
Jentsch
D
Natroshvili
510
510
Fluid-solid interaction
anisotropic bodies
boundary integral method
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
Three-dimensional mathematical problems of the interaction between thermoelastic
and scalar oscillation fields are considered in a general anisotropic case. An elastic
structure is assumed to be a bounded homogeneous anisortopic body occupying domain
$\Omega^+\sub\R^3$ , where the thermoelastic field is defined, while in the
physically anisotropic unbounded exterior domain $\Omega^-=\R^3\\ \overline{\Omega^+}$
there is defined the scalar field. These two fields
satisfy the differential equations of steady state oscillations in the corresponding
domains along with the transmission conditions of special type on the interface
$\delta\Omega^{+-}$. Uniqueness and existence theorems, for the non-resonance case, are proved
by the reduction of the original interface problems to equivalent systems of boundary
pseudodifferential equations ($\Psi DEs$) . The invertibility of the corresponding
matrix pseudodifferential operators ($\Psi DO$) in appropriate functional spaces is
shown on the basis of generalized Sommerfeld-Kupradze type thermoradiation conditions
for anisotropic bodies. In the resonance case, the co-kernels of the $\Psi DOs$ are
analysed and the efficent conditions of solvability of the transmission problems
are established.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801162
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17491/zip/
urn:nbn:de:bsz:ch1-199801162
oai:qucosa:de:qucosa:17488
2021-03-29T09:32:16Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Variable preconditioning procedures for elliptic problems
M.
Jung
S. V.
Nepomnyaschikh
510
510
MSC 65N30
For solving systems of grid equations approximating elliptic boundary value problems a method of constructing variable preconditioning procedures is presented. The main purpose is to discuss how an efficient preconditioning iterative procedure can be constructed in the case of elliptic problems with disproportional coefficients, e.g. equations with a large coefficient in the reaction term (or a small diffusion coefficient). The optimality of the suggested technique is based on fictitious space and multilevel decom- position methods. Using an additive form of the preconditioners, we intro- duce factors into the preconditioners to optimize the corresponding conver- gence rate. The optimization with respect to these factors is used at each step of the iterative process. The application of this technique to two-level $p$-hierarchical precondi- tioners and domain decomposition methods is considered too.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801137
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17488/zip/
urn:nbn:de:bsz:ch1-199801137
oai:qucosa:de:qucosa:17492
2021-03-29T09:32:19Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Minimum Norm Regularization of Descriptor Systems by Output Feedback
D.
Chu
V.
Mehrmann
510
510
regularization
mixed outputp
differential and algebraic equations
orthogonal matrix transformation
MSC 93B05
MSC 93B40
MSC 93B52
MSC 65F35
We study the regularization problem for linear, constant coefficient descriptor
systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative
mixed output feedback. Necessary and sufficient conditions are given, which guarantee
that there exist output feedbacks such that the closed-loop system is regular, has
index at most one and $E +BG\Gamma$ has
a desired rank, i.e. there is a desired number of differential and algebraic equations.
To resolve the freedom in the choice of the feedback matrices we then discuss how
to obtain the desired regularizing feedback of minimum norm and show that this approach
leads to useful results in the sense of robustness only if the rank of E is
decreased. Numerical procedures are derived to construct the desired feedbacks gains.
These numerical procedures are based on orthogonal matrix transformations which
can be implemented in a numerically stable way.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801177
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17492/zip/
urn:nbn:de:bsz:ch1-199801177
oai:qucosa:de:qucosa:17489
2021-03-29T09:32:17Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On-line visualization in parallel computations
M.
Pester
510
510
parallel algorithms
postprocessing
computer graphics
visualization
MSC 65Y05
MSC 68Q22
MSC 65Y25
The investigation of new parallel algorithms for MIMD computers
requires some postprocessing facilities for quickly evaluating
the behavior of those algorithms We present two kinds of
visualization tool implementations for 2D and 3D finite element
applications to be used on a parallel computer and a host
workstation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801143
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17489/zip/
urn:nbn:de:bsz:ch1-199801143
oai:qucosa:de:qucosa:17493
2021-03-29T09:32:20Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On Ill-Posedness and Local Ill-Posedness of Operator
Equations in Hilbert Spaces
On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces
B.
Hofmann
510
510
Nonlinear inverse problems
oerator equations
ill-posedness
stability estimates
local ill-posedness
Frechet derivative
linearized problem
compact operators
integral equations
parameter identification
MSC 65J20
MSC 47H15
MSC 65J10
MSC 65J15
MSC 65R30
MSC 45G10
In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems
in a Hilbert space setting. We define local ill-posedness of a nonlinear operator
equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear
problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an
appropriate ill-posedness concept for the linarized equation we define intrinsic
ill-posedness for linear operator equations $Ax = y$ and compare this approach with
the ill-posedness definitions due to Hadamard and Nashed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801185
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17493/zip/
urn:nbn:de:bsz:ch1-199801185
oai:qucosa:de:qucosa:1749
2021-03-27T15:38:09Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
From a textbook to an e-learning course (E-learning or e-book?)
Antonín
Jančařík
Jarmila
Novotná
510
510
SD 2009
e-Learning
e-Book
CAS
Flash-Animationen
Java-Scripts
e-Learning
e-Book
CAS
Flash animations
Java Scripts
The main aim of this contribution is to introduce the potential that modern information technologies open to authors converting a teaching material from a printed to an electronic version. The authors
come out of their own experience and propose options that are suitable especially for creation of study materials in mathematics education. Among others the contribution presents the use of flash
animations, java scripts and Computer Algebra Systems.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80251
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 272 - 276
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 272 - 276
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1749/zip/
urn:nbn:de:bsz:14-qucosa-80251
371750288
oai:qucosa:de:qucosa:17494
2021-03-29T09:32:21Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Randkonzentrierte und adaptive hp-FEM
Tino
Eibner
Dipl.-Math. techn.
510
510
Adaptive Steuerung
Finite-Elemente-Methode
Implementation
Präkonditionierung
hp-Version
Die vorliegende Arbeit befasst sich mit verschiedenen Aspekten der hp-FEM.
Insbesondere werden hierbei folgende Punkte genauer untersucht:
1. Das effiziente Aufstellen der Steifigkeitsmatrix auf Referenzelementen, die keine Tensorproduktstruktur besitzen.
2. Eine lokale Konvergenzbetrachtung für die randkonzentrierte hp-FEM.
3. Ein Multilevel-Löser für die randkonzentrierte hp-FEM.
4. Eine Strategie für hp-Adaptivität.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Jens Markus
Melenk
Professor
Jens Markus
Melenk
Professor
Arnd
Meyer
Professor
Boris
Khoromskij
Privatdozent
2006-01-23
2006-06-19
2006-07-12
2021-03-29
doctoralThesis
urn:nbn:de:swb:ch1-200601050
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
2
https://monarch.qucosa.de/api/qucosa%3A17494/zip/
urn:nbn:de:swb:ch1-200601050
oai:qucosa:de:qucosa:17490
2021-03-29T09:32:18Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Mixed Interface Problems of Thermoelastic Pseudo-Oscillations
L.
Jentsch
D.
Natroshvili
I.
Sigua
510
510
mixed interface problems
thermoelastic pseudo-oscillations
pseudodifferential equations
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
Three-dimensional basic and mixed interface problems of the mathematical
theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous
anisotropic bodies. Applying the method of boundary potentials and the theory of
pseudodifferential equations existence and uniqueness theorems of solutions are proved
in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p))
and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results
for solutions to the basic interface problems, it is shown that in the mixed interface
problems the displacement vector and the temperature are Hölder continuous with
exponent 0<alpha<1/2.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801150
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17490/zip/
urn:nbn:de:bsz:ch1-199801150
oai:qucosa:de:qucosa:17495
2021-03-29T09:32:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Autoconvolution Equation and Total Variation Constraints
G.
Fleischer
R.
Gorenflo
B.
Hofmann
510
510
autoconvolution
ill-posed problem
discretization
constrained least squares approach
bounded total variation
MSC 65J20
MSC 45G10
MSC 65R30
This paper is concerned with the numerical analysis of the autoconvolution equation
$x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least
squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where
the regularization is based on a prescribed bound for the total variation of admissible
solutions. This approach includes the case of non-smooth solutions possessing jumps.
Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone
functions are added. The paper is completed by a numerical case study concerning
the determination of non-monotone smooth and non-smooth functions x from the autoconvolution
equation with noisy data y.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801196
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17495/zip/
urn:nbn:de:bsz:ch1-199801196
oai:qucosa:de:qucosa:17496
2021-03-29T09:32:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local theory of a collocation method for Cauchy singular integral equations on an interval
P.
Junghanns
U.
Weber
510
510
Cauchy singular integral equations
collocation methods
stability
MSC 45E05
MSC 45L10
We consider a collocation method for Cauchy singular integral equations on the interval
based on weighted Chebyshev polynomials , where the coefficients of the operator are
piecewise continuous. Stability conditions are derived using Banach algebra methods,
and numerical results are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801203
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17496/zip/
urn:nbn:de:bsz:ch1-199801203
oai:qucosa:de:qucosa:1750
2021-03-27T15:37:49Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Preventing ‘Pushing for Privileged Passage’: A study of a charter school working to step back from tracking
Tina Louise
Johnston
510
510
SD 2009
Einordnung nach Leistungsgruppen
Verfolgen
Mathematik
Grounded Theory
gegenstandsbezogene Theoriebildung
ländlicher Raum
Ability grouping
tracking
mathematics
Grounded Theory
Rural
One charter school’s path to tracking and pushing for privileged passage is examined. The school as it increased in size began to track students first by grade level and then by ability. Realizing that moving mathematics out of the main school program compromised the teaching ideals of the school and potentially student learning. The school has embarked on a program to create a place-based, integrated curriculum developed around mathematics so that mathematics can be reintroduced to multi-age classrooms. Examining the data in terms of trust, size and the behaviors of administrators, teachers and parents at this school in this process are highlighted.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80299
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 282 - 286
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 282 - 286
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1750/zip/
urn:nbn:de:bsz:14-qucosa-80299
371758335
oai:qucosa:de:qucosa:17497
2021-03-29T09:32:23Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On a SQP-multigrid technique for nonlinear parabolic boundary control problems
H.
Goldberg
F.
Tröltzsch
510
510
optimal control
semilinear parabolic equation
multigrig method
SQP method
MSC 49M40
MSC 49M05
An optimal control problem governed by the heat equation with nonlinear boundary
conditions is considered. The objective functional consists of a quadratic terminal
part and a quadratic regularization term. It is known, that an SQP method converges
quadratically to the optimal solution of the problem. To handle the quadratic optimal
control subproblems with high precision, very large scale mathematical programming
problems have to be treated. The constrained problem is reduced to an unconstrained
one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is
applied to solve the unconstrained problems. Some numerical examples illustrate the
behaviour of the method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801210
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17497/zip/
urn:nbn:de:bsz:ch1-199801210
oai:qucosa:de:qucosa:17500
2021-03-29T09:32:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations
G.
Fleischer
B.
Hofmann
510
510
degree of ill-posedness
multiplication op erators
nonlinear inverse problems
parameter identification
MSC 65J20
MSC 47B38
In this paper we deal with aspects of
characterizing the ill-posedn ess of nonlinear
inverse problems based on the discussion of
specific examples. In particular, a parameter
identification problem to a second order
differential equation and its ill-posed
linear components are under consideration.
A new approach to the classification
ofill-posedness degrees for multiplication
operators completes the paper.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801242
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17500/zip/
urn:nbn:de:bsz:ch1-199801242
oai:qucosa:de:qucosa:17498
2021-03-29T09:32:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations
F.
Tröltzsch
510
510
Boundary control
distributed control
linear parabolic equation
control constraints
Lipschitz continuity
supremum norm
MSC 49K20
MSC 49K40
We consider a class of control problems governed by a linear parabolic initial-boundary
value problem with linear-quadratic objective and pointwise constraints on the control.
The control system contains different types of perturbations. They appear in the
linear part of the objective functional, in the right hand side of the equation,
in its boundary condition, and in the initial value. Making use of parabolic regularity
in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm
is improved to the supremum-norm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801229
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17498/zip/
urn:nbn:de:bsz:ch1-199801229
oai:qucosa:de:qucosa:17501
2021-03-29T09:32:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Simulation of Weakly Correlated Functions and its Application to Random Surfaces and Random Polynomials
Benno
Fellenberg
Jürgen vom
Scheidt
Matthias
Richter
510
510
stochastic simulation
random processes
random fields
weakly correlated functions
random polynomials
MSC 65C05
MSC 60G35
The paper is dedicated to the modeling and the
simulation of random processes and fields.
Using the concept and the theory of weakly
correlated functions a consistent representation
of sufficiently smooth random processes
will be derived. Special applications will be
given with respect to the simulation of road
surfaces in vehicle dynamics and to the
confirmation of theoretical results with
respect to the zeros of random polynomials.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801258
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17501/zip/
urn:nbn:de:bsz:ch1-199801258
oai:qucosa:de:qucosa:17499
2021-03-29T09:32:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Estimates for the condition numbers of large semi-definite Toeplitz matrices
A.
Böttcher
S. M.
Grudsky
510
510
Toeplitz operator
Toeplitz matrices
singular values
eigenvalues
Wiener-Hopf
MSC 47B35
This paper is devoted to asymptotic estimates for the condition numbers
$\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$
of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where
$\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes
of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ ,
or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues,
and the finite section method are discussed. We also consider Wiener-Hopf integral
operators and multidimensional Toeplitz operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801238
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17499/zip/
urn:nbn:de:bsz:ch1-199801238
oai:qucosa:de:qucosa:17502
2021-03-29T09:32:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Asymptotic Expansions for Second-Order Moments of Integral Functionals of Weakly Correlated Random Functions
Jrgen vom
Scheidt
Hans-Jrg
Starkloff
Ralf
Wunderlich
510
510
asymptotic expansions
stationary random processes
weakly correlated functions
MSC 60G12
MSC 41A60
In the paper asymptotic expansions for
second-order moments of integral functionals
of a class of random functions are considered.
The random functions are assumed to be
$\epsilon$-correlated, i.e. the values are not
correlated excluding a $\epsilon$-neighbourhood
of each point. The asymptotic expansions are
derived for $\epsilon \to 0$. With the help of
a special weak assumption there are found
easier expansions as in the case of general
weakly correlated functions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801269
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17502/zip/
urn:nbn:de:bsz:ch1-199801269
oai:qucosa:de:qucosa:17503
2021-03-29T09:32:28Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the analytic representation of the correlation function of linear random vibration systems
J.
Gruner
J. vom
Scheidt
R.
Wunderlich
510
510
random vibrations
correlation function
asymptotic expansion
weakly correlated random function
MSC 70L05
MSC 60G10
This paper is devoted to the computation of statistical characteristics of
the response of discrete vibration systems with a random external excitation.
The excitation can act at multiple points and is modeled by a time-shifted
random process and its derivatives up to the second order. Statistical characteristics
of the response are given by expansions as to the correlation length
of a weakly correlated random process which is used in the excitation model.
As the main result analytic expressions of some integrals involved in the expansion terms are derived.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801272
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17503/zip/
urn:nbn:de:bsz:ch1-199801272
oai:qucosa:de:qucosa:17504
2021-03-29T09:32:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local theory of projection methods for Cauchy singular integral equations on an interval
P.
Junghanns
U.Weber
510
510
Cauchy singular integral equation
projection methods
stability
MSC 45E05
MSC 45L10
We consider a finite section (Galerkin) and a collocation method for Cauchy singular
integral equations on the interval based on weighted Chebyshev polymoninals, where
the coefficients of the operator are piecewise continuous.
Stability conditions are derived using Banach algebra techniques, where
also the system case is mentioned. With the help of
appropriate Sobolev spaces a result on convergence rates is proved.
Computational aspects are discussed in order to develop
an effective algorithm. Numerical results, also
for a class of nonlinear singular integral equations,
are presented.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801281
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17504/zip/
urn:nbn:de:bsz:ch1-199801281
oai:qucosa:de:qucosa:17509
2021-03-29T09:32:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
FEM auf irregulären hierarchischen Dreiecksnetzen
U.
Groh
510
510
PDE
FEM
triangular mesh
hierarchical refinement
elliptic model
BPX
Yserentant
precondition
domain decomposition
MSC 65N30
From the viewpoint of the adaptive solution of partial differential equations a finit
e element method on hierarchical triangular meshes is developed permitting hanging nodes
arising from nonuniform hierarchical refinement.
Construction, extension and restriction of the nonuniform hierarchical basis and the
accompanying mesh are described by graphs. The corresponding FE basis is generated by
hierarchical transformation. The characteristic feature of the generalizable concept is the
combination of the conforming hierarchical basis for easily defining and changing the FE
space with an accompanying nonconforming FE basis for the easy assembly of a FE
equations system. For an elliptic model the conforming FEM problem is solved by an iterative
method applied to this nonconforming FEM equations system and modified by
projection into the subspace of conforming basis functions. The iterative method used is the
Yserentant- or BPX-preconditioned conjugate gradient algorithm.
On a MIMD computer system the parallelization by domain decomposition is easy and
efficient to organize both for the generation and solution of the equations system and for
the change of basis and mesh.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801330
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17509/zip/
urn:nbn:de:bsz:ch1-199801330
oai:qucosa:de:qucosa:17505
2021-03-29T09:32:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Multiplication operators and its ill-posedness properties
G.Fleischer
510
510
ill-posed
multiplication operator
MSC 47B38
MSC 65J20
This paper deals with the characterization of multiplication operators,
especially with its behavior in the ill-posed case.
We want to classify the different types and degrees of ill-posedness. We give
some connections between this classification and regularization methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801292
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17505/zip/
urn:nbn:de:bsz:ch1-199801292
oai:qucosa:de:qucosa:1751
2021-03-27T15:37:57Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Understanding Quadratic Functions Using Real World Problems and IT
Nakhshin A.
Karim
510
510
SD 2009
Mathematikausbildung
Informatik
Funktionen mit realen Problemen verstehen
IT
Mathematics Education
Information Technology
Understanding Functions Using Real World Problems
IT
The concept of function is crucial to a great extent in modern mathematics and is considered a major barrier to many mathematics students. Students have difficulty interpreting information related to
functions in general, and quadratic functions in particular. Quadratic Function is one of the topics which are covered in a course which is compulsory for a large number of students in the General Education Program of Zayed University. This program leads to different majors, including Mathematics Education, Business, Information Technology, and other majors. The challenge in teaching Quadratic Function in a course like this is mostly based on the fact that many students think that Quadratic Function is a difficult topic to understand and learn, and some teachers would agree with them that it is difficult to teach.
In this paper, I demonstrate real world problems aimed to improve the students understanding of Quadratic Functions; life problems on this topic support developing student’s knowledge, critical thinking, quantitative reasoning, and analytical skills. This paper also includes examples of the techniques used with graphing of quadratic function, the algebra, and inverses of the same function. International move to improve mathematics curriculum have supported new goals for student’s learning which highlights problem solving skills, reasoning, ability to work in groups and individually, and use of technology. Knowing that information technology plays considerable role in
achieving the above goals, teaching students the concept of Quadratic Functions can be smoothly achieved by using Information Technology in solving real world problems.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80316
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 291 - 295
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 291 - 295
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1751/zip/
urn:nbn:de:bsz:14-qucosa-80316
371751667
oai:qucosa:de:qucosa:17506
2021-03-29T09:32:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A new method for computing the stable invariant subspace of a real Hamiltonian matrix or Breaking Van Loans curse?
P.
Benner
V.
Mehrmann
H.
Xu.
510
510
MSC 65F15
A new backward stable, structure preserving method of complexity
O(n^3) is presented for computing the stable invariant subspace of
a real Hamiltonian matrix and the stabilizing solution of the
continuous-time algebraic Riccati equation. The new method is based
on the relationship between the invariant subspaces of the
Hamiltonian matrix H and the extended matrix /0 H\ and makes use
\H 0/
of the symplectic URV-like decomposition that was recently
introduced by the authors.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801309
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17506/zip/
urn:nbn:de:bsz:ch1-199801309
oai:qucosa:de:qucosa:17510
2021-03-29T09:32:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Interpolation of non-smooth functions on anisotropic finite element meshes
Th.
Apel
510
510
anisotropic weighted Sobolev spaces
local interpolation error,estimates.
MSC 35A40
MSC 35J05
MSC 65N30
MSC 35B65
In this paper, several modifications of the quasi-interpolation operator
of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed.
The modified operators are defined for non-smooth functions and are suited
for the application on anisotropic meshes. The anisotropy of the elements
is reflected in the local stability and approximation error estimates.
As an application, an example is considered where anisotropic finite element
meshes are appropriate, namely the Poisson problem in domains with edges.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801341
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17510/zip/
urn:nbn:de:bsz:ch1-199801341
oai:qucosa:de:qucosa:17507
2021-03-29T09:32:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Rank-revealing top-down ULV factorizations
B.
Benhammouda
510
510
MSC 65F15
Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801313
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17507/zip/
urn:nbn:de:bsz:ch1-199801313
oai:qucosa:de:qucosa:17511
2021-03-29T09:32:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
Th.
Apel
S.
Nicaise
510
510
MSC 65N30
This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801355
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17511/zip/
urn:nbn:de:bsz:ch1-199801355
oai:qucosa:de:qucosa:17508
2021-03-29T09:32:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Convergence of Asynchronous Jacobi-Newton-Iterations
U.
Schrader
510
510
convergence
asynchronous Jacobi-Newton-iterations
nonlinear
equations
MSC 65H10
Asynchronous iterations often converge under different conditions than their syn- chronous counterparts. In this paper we will study the global convergence of Jacobi- Newton-like methods for nonlinear equationsF x = 0. It is a known fact, that the synchronous algorithm converges monotonically, ifF is a convex M-function and the starting valuesx0 andy0 meet the conditionF x04 04F y0 . In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior for an asynchronous computation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801324
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17508/zip/
urn:nbn:de:bsz:ch1-199801324
oai:qucosa:de:qucosa:17518
2021-03-29T09:32:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Parallel Multilevel Preconditioners for Problems of Thin Smooth Shells
M.
Thess
510
510
004
004
thin shell problems
linear partial differential equations
parallel computing
multilevel methods
additive splittings
finite element methods
cooling towers
MSC 65Y05
In the last years multilevel preconditioners like BPX became more and more
popular for solving second-order elliptic finite element discretizations by iterative
methods. P. Oswald has adapted these methods for discretizations of the fourth
order biharmonic problem by rectangular conforming Bogner-Fox-Schmidt elements
and nonconforming Adini elements and has derived optimal estimates for the
condition numbers of the preconditioned linear systems. In this paper we generalize
the results from Oswald to the construction of BPX and Multilevel Diagonal
Scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells of
arbitrary forms where we use Koiter's equations of equilibrium for an homogeneous
and isotropic thin shell, clamped on a part of its boundary and loaded by a
resultant on its middle surface. We use the two discretizations mentioned above and the
preconditioned conjugate gradient method as iterative method. The parallelization
concept is based on a non-overlapping domain decomposition data structure. We
describe the implementations of the multilevel preconditioners. Finally, we show
numerical results for some classes of shells like plates, cylinders, and hyperboloids.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801416
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17518/zip/
urn:nbn:de:bsz:ch1-199801416
oai:qucosa:de:qucosa:17514
2021-03-29T09:32:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Behandlung gekrümmter Oberflächen in einem 3D-FEM-Programm für Parallelrechner
M.
Pester
510
510
004
004
finite element meshes
curved surfaces
mesh refinement
parallel computing
MSC 65Y05
MSC 65N30
The paper presents a method for generating curved
surfaces of 3D finite element meshes by mesh
refinement starting with a very coarse grid.
This is useful for parallel implementations where
the finest meshes should be computed and not read from
large files. The paper deals with simple geometries
as sphere, cylinder, cone. But the method may be
extended to more complicated geometries.
(with 45 figures)
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801386
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17514/zip/
urn:nbn:de:bsz:ch1-199801386
oai:qucosa:de:qucosa:1752
2021-03-27T15:37:54Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Creating and Utilizing Online Assignments in a Calculus Class
Veselin
Jungic
Deborah
Kent
Petra
Menz
510
510
SD 2009
online Hausaufgaben
online Aufgaben
elektronische Hausaufgaben
elektronische Aufgaben
postsekundäre Bildung
universitäre Bildung
Mathematik
Pädagogik
Benotung
Student
Lehrer
Dozent
Software
Technologie
LON-CAPA
Learning Management System
LMS
online assignments
online exercises
online homework
electronic assignments
electronic exercises
electronic homework
post-secondary education
mathematics
pedagogy
grades
student
instructor
software
technology
LON-CAPA
Learning Management System
LMS
The aims of this paper are to present some of the findings about the creation and utilization of online assignments and choice of support software for several calculus classes at Simon Fraser University (SFU) by considering the needs and perspectives of the instructors, students, and administrators. The term online assignment is used for a set of problems that are posted, submitted, graded, and recorded
electronically through a course learning management system (LMS) of choice. The purpose of this note is to contribute to the discussion about a common question detected among research papers on the
theme of online assignments; how can technology be used in teaching so that students benefit the most? Questions are provided to guide an instructor in choosing online assignment problems, and a list of necessary skills is supplied for an instructor to be able to deal effectively with this pedagogical tool.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-04-17
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80301
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 287 - 290
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 287 - 290
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1752/zip/
urn:nbn:de:bsz:14-qucosa-80301
37175092X
oai:qucosa:de:qucosa:17516
2021-03-29T09:32:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The hierarchical preconditioning having unstructured grids
G.
Globisch
S. V.
Nepomnyaschikh
510
510
partial differential equations
parallel computing
multilevel methods
hierarchical preconditioning
finite element methods
automatical grid generation
MSC 65N55
MSC 65N22
MSC 65N22
MSC 78A30
In this paper we present two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801398
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17516/zip/
urn:nbn:de:bsz:ch1-199801398
oai:qucosa:de:qucosa:17520
2021-03-29T09:32:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
ddc:530
openaire
Some Remarks on the Constant in the Strengthened C.B.S. Inequality: Application to $h$- and $p$-Hierarchical Finite Element Discretizations of Elasticity Problems
M.
Jung
J. F.
Maitre
530
530
510
510
finite elements
elasticity problems
hierarchical methods
multilevel methods
MSC 65N30
MSC 65F10
MSC 65N55
MSC 73C02
For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75.
For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements.
Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801431
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17520/zip/
urn:nbn:de:bsz:ch1-199801431
oai:qucosa:de:qucosa:17521
2021-03-29T09:32:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes
G.
Kunert
510
510
finite elements
error estimator
anisotropic solution,
MSC 65N30
MSC 65N15
MSC 35B25
Some boundary value problems yield anisotropic solutions, e.g. solutions
with boundary layers. If such problems are to be solved with the finite
element method (FEM), anisotropically refined meshes can be
advantageous.
In order to construct these meshes or to control the error
one aims at reliable error estimators.
For \emph{isotropic} meshes many estimators are known, but they either fail
when used on \emph{anisotropic} meshes, or they were not applied yet.
For rectangular (or cuboidal) anisotropic meshes a modified
error estimator had already been found.
We are investigating error estimators on anisotropic tetrahedral or
triangular meshes because such grids offer greater geometrical flexibility.
For the Poisson equation a residual error estimator, a local Dirichlet problem
error estimator, and an $L_2$ error estimator are derived, respectively.
Additionally a residual error estimator is presented for a singularly
perturbed reaction diffusion equation.
It is important that the anisotropic mesh corresponds to the anisotropic
solution. Provided that a certain condition is satisfied, we have proven
that all estimators bound the error reliably.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801440
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17521/zip/
urn:nbn:de:bsz:ch1-199801440
oai:qucosa:de:qucosa:1753
2021-03-27T15:37:46Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Individual Approaches in Rich Learning Situations Material-based Learning with Pinboards
Michael
Katzenbach
510
510
SD 2009
Individuelle Zugänge
Lernumgebung
Individualisierung
verständnisorientiert
Steckbrett
Heterogenität
Intelligente Übung
Dynamische Geometrie
Kreativität
Präsentation
Freiarbeit
Koordinatensystem
Symmetrie
Funktion
Bruchrechnung
materialgestützt
individuell
Kommunikation
Entdecken
Vermuten
Operative Serie
Horizontale Vernetzung
Vertikale Vernetzung
Selbstkontrolle
Eigenverantwortung
Grundvorstellung
Transfer
Mentale Operation
Kompetenz
Experimentell
Fehlende Werte
Reichhaltige Lernumgebung
Individual Approach
Learning environment
Individualization
Comprehension-oriented
Pinboard
Heterogeneity
Intelligent exercise
Dynamic geometry
Creativity
Presentation
Coordinate system
Symmetry
Function
Fraction
Material-based
Individual
Communication
Discover
Presume
Structured series
horizontal integration
Vertical integration
Self-control
Self-responsibility
Basic concept
Transfer
Mental operation
Competency
experimental
Missing data
Richlearning situation
Active Approaches provide chances for individual, comprehension-oriented learning and can facilitate the acquirement of general mathematical competencies. Using the example of pinboards, which were developed for different areas of the secondary level, workshop participants experience, discuss and further develop learning tasks, which can be used for free activities, for material based concept
formation, for coping with heterogeneity, for intelligent exercises, as tool for the presentation of students’ work and as basis for games. The material also allows some continuous movements and can thus prepare an insightful usage of dynamic geometry programs. Central Part of the workshop is a work-sharing group work with learning tasks for grades 5 to 8. The workshop will close with a discussion of general aspects of material-based learning.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80328
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 296 - 299
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 296 - 299
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1753/zip/
urn:nbn:de:bsz:14-qucosa-80328
37175173X
oai:qucosa:de:qucosa:17536
2021-03-29T09:32:55Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems
Cornelia
Pester
510
510
Nichtlineares Eigenwertproblem
Operatorbüschel
Spektraltheorie
Hamiltonian eigenvalue symmetry
operator pencil
When the eigenvalues of a given eigenvalue problem are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601470
Preprintreihe des Chemnitzer SFB 393, 04-09
eng
Preprintreihe des Chemnitzer SFB 393, 04-09
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17536/zip/
urn:nbn:de:swb:ch1-200601470
oai:qucosa:de:qucosa:1754
2021-03-27T15:37:47Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Does the parameter represent a fundamental concept of linear algebra?
Stefan-Harald
Kaufmann
510
510
SD 2009
Lineare Algebra
Parameter
Variable
Fundamentales Konzept
Mathematikdidaktik
linear algebra
parameter
variable
fundamental concept
mathematics education
In mathematics the parameter is used as a special kind of a variable. The classification of the terms \"variable\" and \"parameter\" is often done by intuition and changes due to different situations and needs. The history of mathematics shows that these two terms represent the same abstract object in mathematics. In today´s mathematics, compared to variables, the parameter is declared as an unknown
constant measure. This interpretation of parameters can be used in set theory for describing sets with an infinite number of elements. Due to this perspective the structure of vector spaces can be developed as a special structured set theory. Further, the concept of parameters can be seen as a model for developing mathematics education in linear algebra.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80339
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 300 - 301
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 300 - 301
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1754/zip/
urn:nbn:de:bsz:14-qucosa-80339
37175223X
oai:qucosa:de:qucosa:17545
2021-03-29T09:33:02Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Abschätzungen der Hausdorff-Dimension invarianter Mengen dynamischer Systeme auf Mannigfaltigkeiten unter besonderer Berücksichtigung nicht invertierbarer Abbildungen
Astrid
Franz
510
510
Differenzierbares dynamisches System
Abbildungsgrad
Hausdorffsche Dimension
Die exakte Bestimmung der Dimension invarianter Mengen
dynamischer Systeme ist nur in Ausnahmesituationen möglich.
In der vorliegenden Arbeit wird untersucht, wie unter
Ausnutzung von speziellen Eigenschaften des dynamischen
Systems die Hausdorff-Dimension zugehöriger invarianter
Mengen nach oben und unten abgeschätzt werden kann.
Es wird gezeigt, wie der Grad der Nichtinjektivität der
Abbildung, die das dynamische System erzeugt, in die
Beschreibung des Deformationsverhaltens von k-Volumina
einbezogen werden kann, so daß eine Abschwächung der
Kontraktionsbedingung für Hausdorff-Maße erreicht werden
kann. Dazu werden äußere Hausdorff-Integrale über beliebige
nichtnegative Funktionen betrachtet, die im Falle der
Integration über charakteristische Funktionen den
gewichteten Hausdorff-Maßen entsprechen. Schrankensätze, die
sich als verallgemeinerte Transformationssätze für Integrale
ergeben, charakterisieren das Verhalten der äußeren
Integrale bei Transformationen. Diese Schrankensätze eignen
sich, um Kontraktionsbedingungen für die äußeren
Hausdorff-Maße und damit Oberschranken für die
Hausdorff-Dimension zu formulieren.
Ein weiterer Teil der Arbeit ist der Abschwächung des
Konzepts der hyperbolischen Mengen gewidmet. Es werden
Mengen mit einer äquivarianten Zerlegung des
Tangentialbündels betrachtet, d. h. mit einer Zerlegung, die
unter der Tangentialabbildung invariant bleibt. Solch eine
Zerlegung ermöglicht die Betrachtung der auf die jeweiligen
Teilbündel eingeschränkten Tangentialabbildung, entweder in
der ursprünglichen Zeitrichtung oder in umgekehrter
Zeitrichtung. Im Gegensatz zu hyperbolischen Mengen werden
hier aber keine Voraussetzungen bezüglich der Streckungs-
und Stauchungseigenschaften der Tangentialabbildung in den
Teilräumen gestellt. Unter diesen abgeschwächten Bedingungen
können für invariante Mengen von Diffeomorphismen und
Flüssen ähnliche obere Dimensionsschranken wie für
hyperbolische Mengen erreicht werden, die sowohl in der
Sprache der Singulärwerte als auch der globalen
Lyapunov-Exponenten der Tangentialabbildung und der
topologischen Entropie der Abbildung formuliert werden
können. Es wird außerdem gezeigt, daß sich die für Systeme
mit einer äquivarianten Zerlegung des Tangentialbündels
angewandte Beweistechnik auch auf eine spezielle Klasse
nicht injektiver Abbildungen, die sogenannten
k-1-Endomorphismen, anwenden läßt.
Untere Dimensionsschranken für invariante Mengen dynamischer
Systeme lassen sich in der Regel nur durch das Ausnutzen von
Zusatzstrukturen des Systems ableiten. Die Klasse der
k-1-Endomorphismen weist solche speziellen Strukturen auf.
Die Eigenschaften der invarianten Mengen solcher
Endomorphismen ermöglichen die Konstruktion von Minoranten
für die Hausdorff-Maße ohne Verwendung potentialtheoretischer
Hilfsmittel, aus denen sich eine untere Schranke für die
Hausdorff-Dimension ableiten läßt.
Eine breite Palette von Beispielsystemen demonstriert die
Leistungsfähigkeit der hergeleiteten Abschätzungen der
Hausdorff-Dimension. Insbesondere zählen hierzu
Hufeisenabbildungen, iterierte Funktionensysteme und
Julia-Mengen quadratischer Polynome in der komplexen Ebene.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Volker
Reitmann
1999-04-09
1998-12-04
1999-04-09
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-199900135
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Naturwissenschaften
3
https://monarch.qucosa.de/api/qucosa%3A17545/zip/
urn:nbn:de:bsz:ch1-199900135
oai:qucosa:de:qucosa:17544
2021-03-29T09:33:01Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes
Gerd
Kunert
510
510
finite elements;
anisotropic mesh;
tetrahedral mesh;
triangular mesh;
Poisson equation;
singularly perturbed reaction-diffusion equation;
anisotropic a posteriori error estimate;
anisotropic interpolation error estimate;
Many physical problems lead to boundary value problems for partial differential equations, which can be solved with the finite element method. In order to construct adaptive solution algorithms or to measure the error one aims at reliable a posteriori error estimators. Many such estimators are known, as well as their theoretical foundation.
Some boundary value problems yield so-called anisotropic solutions (e.g. with boundary layers). Then anisotropic finite element meshes can be advantageous. However, the common error estimators for isotropic meshes fail when applied to anisotropic meshes, or they were not investigated yet.
For rectangular or cuboidal anisotropic meshes a modified error estimator had already been derived. In this paper error estimators for anisotropic tetrahedral or triangular meshes are considered. Such meshes offer a greater geometrical flexibility.
For the Poisson equation we introduce a residual error estimator, an estimator based on a local problem, several Zienkiewicz-Zhu estimators, and an L_2 error estimator, respectively. A corresponding mathematical theory is given.For a singularly perturbed reaction-diffusion equation a residual error estimator is derived as well. The numerical examples demonstrate that reliable and efficient error estimation is possible on anisotropic meshes.
The analysis basically relies on two important tools, namely anisotropic interpolation error estimates and the so-called bubble functions. Moreover, the correspondence of an anisotropic mesh with an anisotropic solution plays a vital role.
AMS(MOS): 65N30, 65N15, 35B25
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
1999-03-30
1999-01-08
1999-03-30
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-199900124
3-89722-180-2
ISBN 3-89722-180-2, Logos Verlag Berlin
eng
ISBN 3-89722-180-2, Logos Verlag Berlin
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
3
https://monarch.qucosa.de/api/qucosa%3A17544/zip/
urn:nbn:de:bsz:ch1-199900124
oai:qucosa:de:qucosa:1755
2021-03-27T15:37:35Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Using the Media as a Means to Develop Students’ Statistical Concepts
Marian
Kemp
510
510
SD 2009
Fünf-Stufen-Rahmen
Medien
Statistiken
Tabellen
Kompetenz
Rechnen
Meinungsforschung
Schüler der Sekundarstufe
Five Step Framework
Media
Statistics
Tables
Quantitative literacy
Numeracy
Opinion polling
Secondary students
In this era of increasingly fast communication people are being exposed to quantitative information, from national and international sources, through a range of media including newspapers, magazines,
television, radio, pod-casts, YouTube and other areas of the Internet. Contexts include health statistics, environmental issues, traffic statistics, wars, gun laws and so on. It is becoming more and more important that citizens are able to critically read and interpret this information, and to do so requires an understanding of statistical concepts. Research has shown that students are motivated and engaged in learning through the use of authentic, real life tasks. The media provides current information, which can be used to help develop both students’ awareness of how social issues are constructed as well as vital statistical concepts. This paper proposes that secondary school students\'' application of a model for statistical analysis to material taken from media sources, enhances their
understanding of statistical concepts. This model, called the Five Step Framework, is described and exemplified for the particular context of opinion polling.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80341
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 302 - 306
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 302 - 306
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1755/zip/
urn:nbn:de:bsz:14-qucosa-80341
371752531
oai:qucosa:de:qucosa:17549
2021-03-29T09:33:05Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
ddc:530
openaire
Random Walks in Complex Systems - Anomalous Relaxation
Sven
Schubert
530
530
510
510
Fraktal
Hierarchie
Master-Gleichung
Komplexes System
Spinglas
Zustandsraum
Relaxation
Relaxationszeit
Anomale Diffusion
H-Funktion
Random Walk
Ziel dieser Arbeit ist die Untersuchung der Dynamik
in komplexen Systemen. Eine zentrale Rolle spielen
dabei Random Walks, mit deren Hilfe die anomale Relaxation
in solchen Systemen simuliert wird. Die Komplexität der
in dieser Arbeit untersuchten Systeme spiegelt sich
in hohem Maße in deren Zustandsraumstruktur wider.
Nach einer Einführung verschiedener komplexer Systeme wird
kurz auf Algorithmen eingegangen, die bei der Erfassung der
zum Teil sehr großen Zustandsräume eine wichtige Rolle
spielen. Ein sogenannter Branch-and-Bound Algorithmus
wird für die Untersuchung des niedrigenergetischen Anteils
komplexer Zustandsräume eingesetzt.
Die Simulation der Dynamik wird durch Random Walk Prozesse
simuliert und im Wahrscheinlichkeitsbild durch eine Mastergleichung
beschrieben. Auf verschiedene Formen der Mastergleichung und
deren Lösung wird detailliert eingegangen.
Wichtige Anwendungen sind Simulationen von Random Walks auf
Fraktalen bzw. auf hierarchischen Baumstrukturen. Solche
Simulationen lassen den Vergleich mit experimentellen Befunden
zu, wie z.B. der anomalen Diffusion bzw. den Nichtgleichgewichts-
phänomenen in Spingläsern. Anhand einer solchen Modellbildung
können experimentelle Ergebnisse reproduziert und besser verstanden
werden. Ein weiterer wichtiger Beitrag zum Verständnis solcher
Prozesse wird durch einen neu entwickelten Algorithmus zur
Vergröberung des Zustandsraumes geleistet.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
1999-05-01
1999-03-04
1999-05-01
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-199900171
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Naturwissenschaften
3
https://monarch.qucosa.de/api/qucosa%3A17549/zip/
urn:nbn:de:bsz:ch1-199900171
oai:qucosa:de:qucosa:17557
2021-03-29T09:33:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function
Sergio
Barrachina
Peter
Benner
Enrique S.
Quintana-Ortí
510
510
Kontrolltheorie
Matrixproblem
Parallelrechner
Bernoulli equation
control and system theory
matrix sign function
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601684
Preprintreihe des Chemnitzer SFB 393, 05-15
eng
Preprintreihe des Chemnitzer SFB 393, 05-15
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17557/zip/
urn:nbn:de:swb:ch1-200601684
oai:qucosa:de:qucosa:1756
2021-03-27T15:37:40Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
A program for reducing teacher''s resistance to changes in curriculum in centralized education systems. An experience on changes of mathematics text books in Iran based on distinction results
Zohreh
Ketabdar
510
510
SD 2009
Lehrplanänderungen
Wissenschaft
Einstellung
Geschicklichkeit
Problemlösung
Berufsausbildung
changes in curriculum
science
attitude
skill
problem solving
job training during service
Curricula in concentrated educational systems are prepared from an upper-stream reference and hand over teachers’ disposal. Curricula in Iran are compiled in the so-called math curriculum development office and then put at the disposal of teachers. The researches in this regard show that such plans provide some resistance against executing it which are named teacher - proof programs, even it changed to some extent for accept ion, its execution is suspeciable. This research first explains how math books of middle grade were changed as a result of investigations on TIMSS result in year 1995. These investigation show Iranian Books are weakness in problem solving methods as Polya had said. And so curricula developers in Iran tried to integrate Polya\\\''s method in math books and changed curricula based these frame work. Then, it shows how teachers treated these changes. The finding of analyzing the data has been collected in this research through observations and interviews. It is intended that teachers resist against these changes. Finally according to this research, we suggest a model which we refer if it is used through concentrated educational system, we could expect teachers
tolerance against the changes would be decreased and so compiled curricula further matched to executed curricula.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80350
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 307 - 311
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 307 - 311
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1756/zip/
urn:nbn:de:bsz:14-qucosa-80350
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oai:qucosa:de:qucosa:1757
2021-03-27T15:37:31Z
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doc-type:conferenceObject
has-source-swb:true
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openaire
Professional Development for Mathematics Teachers Through Lesson Study
Azimeh Sadat
Khakbaz
510
510
SD 2009
Unterrichtsstudie
Mathematikunterricht
berufliche Weiterbildung
Lesson Study
Mathematics Education
Professional Development
Lesson study is known as an effective Japanese professional development approach for teachers, since 1999.After that, this approach used dramatically as a way for improving teaching and learning in classroom through many countries and by many researchers. Review the literature of lesson study show that
there is one common effort between the researchers to apply this approach. That is to make local model for using this Japanese approach as a localized one to release the unavoidable challenges of applying the method of another educational culture. This paper first reviews the literature on lesson study as a way of teachers\'' professional development, which has been conducted since Meiji Period in Japan and is conducting for today\''s teaching in classroom. Then it clarifies how Iranian mathematics teachers encountered with this method. Finally, the finding of this research addresses a general translated model of lesson study that is preferred to apply lesson study for Iranian culture of education.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80367
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 312 - 316
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 312 - 316
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1757/zip/
urn:nbn:de:bsz:14-qucosa-80367
371753929
oai:qucosa:de:qucosa:1758
2021-03-27T15:37:32Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
An apt perspective of analysis
Nanad
Kishore
Ramesh
Chandra
510
510
SD 2009
Anwendungen
Euklidischer Abstand
Riemann-Abbildung
Poincaré-Vermutung
Elektrodynamik
Maurice Fréchets Abstandsfunktion
applications
Euclidean distance
Riemann mapping
Poincaré conjecture
electrodynamics
Maurice Fréchet distance function
The discourse presented here is aimed at examining the justification of applications of current analysis to real world problems.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80375
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 317 - 318
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 317 - 318
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1758/zip/
urn:nbn:de:bsz:14-qucosa-80375
37175450X
oai:qucosa:de:qucosa:17580
2021-03-29T09:33:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh construction and error estimation in the finite element method
Gerd
Kunert
510
510
adaptive algorithm,
finite element,
anisotropic mesh,
anisotropic function,
error estimation,
Hessian
In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh.
However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators.
Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error.
The focus of this paper is on error estimation on anisotropic meshes.
It is known that such error estimation is reliable and efficient only
if the anisotropic mesh is aligned with the anisotropic solution.
The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution.
The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form.
Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-01-13
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000033
eng
info:eu-repo/semantics/openAccess
18
https://monarch.qucosa.de/api/qucosa%3A17580/zip/
urn:nbn:de:bsz:ch1-200000033
oai:qucosa:de:qucosa:1759
2021-03-27T15:37:41Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Models for harnessing the Internet in mathematics education
Barry
Kissane
510
510
SD 2009
Internet
Lehrer
Schüler
virtuelle Manipulation
Interaktiv
Modell
Internet
Teachers
Students
Virtual manipulative
Interactive
Model
In recent years, the Internet has increasingly been used to provide significant resources for student to learn mathematics and to learn about mathematics, as well as significant resources for teachers to support these. Effective access to and use of these has been hampered in practice by limited facilities in schools and the limited experience of many mathematics teachers with the Internet for mathematical purposes. This paper offers models for understanding the effective use of Internet resources, based on typologies of resources for learning and teaching mathematics. Six categories of Internet resources for mathematics student use are identified: (i) Interactive resources; (ii) Reading interesting materials; (iii) Reference information; (iv) Communication; (v) Problem solving; and (vi) Webquests. Similarly, five categories of Internet resources for mathematics teacher use are identified: (i) Lesson preparation; (ii)
Official advice and support; (iii) Professional engagement; (iv) Commercial activity and support; and (v) Local school web sites. The paper recognises that web resources can be used in a range of ways, including supporting both teaching and learning. The prospects for sound use of the Internet are briefly described in terms of these models of use.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80384
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 319 - 322
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 319 - 322
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1759/zip/
urn:nbn:de:bsz:14-qucosa-80384
371754690
oai:qucosa:de:qucosa:1760
2021-03-27T15:37:50Z
qucosa:slub
doc-type:conferenceObject
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openaire
Cryptography and number theory in the classroom -- Contribution of cryptography to mathematics teaching
Katharina
Klembalski
510
510
SD 2009
Kryptografie
Zahlentheorie
Primzahlen
offene Fragen
Geschichte der Mathematik
RSA
asymmetrische Verschlüsselungsverfahren
cryptography
number theory
prime numbers
open problems
history of mathematics
RSA
public-key cryptosystem
Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to
what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80390
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 323 - 327
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 323 - 327
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1760/zip/
urn:nbn:de:bsz:14-qucosa-80390
371754917
oai:qucosa:de:qucosa:17598
2021-03-29T09:33:46Z
qucosa:ubc
doc-type:masterThesis
has-source-swb:false
open_access
ddc:510
openaire
Comparing Approximations for Risk Measures Related to Sums of Correlated Lognormal Random Variables
Maryna
Karniychuk
M.Sc.
510
510
Risikomaß
Value at Risk
Comonotonicity
Conditional Tail Expectation
Final value
Lognormal approximation
Random variable
Reciprocal Gamma approximation
Risk measure
In this thesis the performances of different approximations are compared for a standard actuarial and
financial problem: the estimation of quantiles and conditional
tail expectations of the final value of a series of discrete cash
flows.
To calculate the risk measures such as quantiles and Conditional
Tail Expectations, one needs the distribution function of the
final wealth. The final value of a series of discrete payments in
the considered model is the sum of dependent lognormal random
variables. Unfortunately, its distribution function cannot be
determined analytically. Thus usually one has to use
time-consuming Monte Carlo simulations. Computational time still
remains a serious drawback of Monte Carlo simulations, thus
several analytical techniques for approximating the distribution
function of final wealth are proposed in the frame of this thesis.
These are the widely used moment-matching approximations and
innovative comonotonic approximations.
Moment-matching methods approximate the unknown distribution
function by a given one in such a way that some characteristics
(in the present case the first two moments) coincide. The ideas of
two well-known approximations are described briefly. Analytical
formulas for valuing quantiles and Conditional Tail Expectations
are derived for both approximations.
Recently, a large group of scientists from Catholic University
Leuven in Belgium has derived comonotonic upper and comonotonic
lower bounds for sums of dependent lognormal random variables.
These bounds are bounds in the terms of "convex order". In order
to provide the theoretical background for comonotonic
approximations several fundamental ordering concepts such as
stochastic dominance, stop-loss and convex order and some
important relations between them are introduced. The last two
concepts are closely related. Both stochastic orders express which
of two random variables is the "less dangerous/more attractive"
one.
The central idea of comonotonic upper bound approximation is to
replace the original sum, presenting final wealth, by a new sum,
for which the components have the same marginal distributions as
the components in the original sum, but with "more dangerous/less
attractive" dependence structure. The upper bound, or saying
mathematically, convex largest sum is obtained when the components
of the sum are the components of comonotonic random vector.
Therefore, fundamental concepts of comonotonicity theory which are
important for the derivation of convex bounds are introduced. The
most wide-spread examples of comonotonicity which emerge in
financial context are described.
In addition to the upper bound a lower bound can be derived as
well. This provides one with a measure of the reliability of the
upper bound. The lower bound approach is based on the technique of
conditioning. It is obtained by applying Jensen's inequality for
conditional expectations to the original sum of dependent random
variables. Two slightly different version of conditioning random
variable are considered in the context of this thesis. They give
rise to two different approaches which are referred to as
comonotonic lower bound and comonotonic "maximal variance" lower
bound approaches.
Special attention is given to the class of distortion risk
measures. It is shown that the quantile risk measure as well as
Conditional Tail Expectation (under some additional conditions)
belong to this class. It is proved that both risk measures being
under consideration are additive for a sum of comonotonic random
variables, i.e. quantile and Conditional Tail Expectation for a
comonotonic upper and lower bounds can easily be obtained by
summing the corresponding risk measures of the marginals involved.
A special subclass of distortion risk measures which is referred
to as class of concave distortion risk measures is also under
consideration. It is shown that quantile risk measure is not a
concave distortion risk measure while Conditional Tail Expectation
(under some additional conditions) is a concave distortion risk
measure. A theoretical justification for the fact that "concave"
Conditional Tail Expectation preserves convex order relation
between random variables is given. It is shown that this property
does not necessarily hold for the quantile risk measure, as it is
not a concave risk measure.
Finally, the accuracy and efficiency of two moment-matching,
comonotonic upper bound, comonotonic lower bound and "maximal
variance" lower bound approximations are examined for a wide range
of parameters by comparing with the results obtained by Monte
Carlo simulation. It is justified by numerical results that,
generally, in the current situation lower bound approach
outperforms other methods. Moreover, the preservation of convex
order relation between the convex bounds for the final wealth by
Conditional Tail Expectation is demonstrated by numerical results.
It is justified numerically that this property does not
necessarily hold true for the quantile.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2006-11-30
2007-01-09
2021-03-29
masterThesis
urn:nbn:de:swb:ch1-200700024
eng
info:eu-repo/semantics/openAccess
master
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
2
https://monarch.qucosa.de/api/qucosa%3A17598/zip/
urn:nbn:de:swb:ch1-200700024
oai:qucosa:de:qucosa:1761
2021-03-27T15:37:51Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Using History to Teach Mathematics
Jacqui
Klowss
510
510
SD 2009
Geschichte der Mathematik
Motivation
Sekundarschule
history of mathematics
motivation
secondary school
Students today need to be taught not only the real life context of their mathematics lessons but also the historical context of the theory behind their mathematics lessons. Using history to teach mathematics, makes your lessons not only interesting but more meaningful to a large percentage of your students as they are interested in knowing the who, how and why about certain rules,
theorems, formulas that they use everyday in class. Students are captivated by learning the history behind mathematicians, rules, etc. and therefore can link the lesson to something in history and a concept. Even learning the mathematics behind historical events motivates and interests them. They cannot get enough!
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80402
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 328 - 330
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 328 - 330
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1761/zip/
urn:nbn:de:bsz:14-qucosa-80402
371755174
oai:qucosa:de:qucosa:1763
2021-03-27T15:38:00Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The use of technology to motivate, to present and to deepen the comprehension of math
Damjan
Kobal
510
510
SD 2009
Motivation
Technologie
Dynamische Geometrie
intuitiv
rational
Fahrradgetriebe
arithmetisches Mittel
Differenzialgetriebe im Auto
Geodäsie
Parabel
Dimmen und Flashen der Scheinwerfer
Funktion
Analog
Digital
Motivation
Technology
Dynamic Geometry
Intuitive
Ratio
Bicycle Gears
Arithmetic Mean
Car Differential
Geodesics
Parabola
Dim and Flash Headlights
Function
Analog
Digital
The aim of the workshop is to present and discuss several ideas which relate to technology as well as to creative teaching. Educational experience, common sense and educational research have all proven how important for comprehensive understanding different cognitive
representations are. We will present and discuss several elementary mathematical ideas of which mechanical realisations mean ingenius technological inventions (for example: ‘car differential’ and ‘digital sound technology’). Technological insights can provide deep intuitive understanding of otherwise abstract mathematical concepts and therefore yield also better comprehension of mathematics. Besides that we will use and present the technology in the form of dynamic geometry programs to show, provoke and motivate rethinking and
deeper understanding of several elementary mathematical concepts.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-02
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80412
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 331 - 332
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 331 - 332
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1763/zip/
urn:nbn:de:bsz:14-qucosa-80412
371755328
oai:qucosa:de:qucosa:1764
2021-03-27T15:38:27Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
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openaire
Experience with solving real-life math problems in DQME II project
L.
Koreňová
M.
Dillingerová
P.
Vankúš
D.
Židová
510
510
SD 2009
IKT
didaktische Software im Mathematikunterricht
Lösung von Alltagsaufgaben
ICT
didactic software in mathematics education
solving real-life tasks
The network "Developing Quality in Mathematics Education II" is a continuation of the associated project "Developing Quality in Mathematics Education" (http://www.dqime.unidortmund. de). In this project participate universities, teacher education institutions and
schools from 11 European countries. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils support developing quality in mathematics education, especially in the area of mathematical modelling. The quality and application of the developed learning materials is also guaranteed by using, comparing and modifying them in eleven different countries. This comparison leads to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus we want to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century. A special feature of this project is the strong connection between theory and practice and between the research and development of mathematics education. In this project our Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava manage testing of translated teaching materials at the high school „Gymnazium Sturovo“. We know that using ICT and didactical software in schools is almost present and wide spread. So we try to focus on several possibilities in solving real-life tasks using this technologies, regard to the fact technologies are hard upon the young generation of students.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80425
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 333 - 335
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 333 - 335
info:eu-repo/semantics/openAccess
1
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oai:qucosa:de:qucosa:17645
2021-03-29T09:34:24Z
qucosa:ubc
doc-type:doctoralThesis
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Anomalous Diffusion and Random Walks on Fractals
Christian Berthold
Schulzky
530
530
510
510
Anomale Diffusion
Fraktal
Entropie
Master-Gleichung
Fokker-Planck-Gleichung
Random Walk
Sierpinski-Dreieck
Sierpinski-Teppich
Widerstandsskalierung
Fraktionale Analysis
H-Funktion
Entropieproduktionsrate
In dieser Arbeit werden verschieden Ansätze diskutiert, die zum Verständnis und zur Beschreibung anomalen Diffusionsverhaltens beitragen, wobei insbesondere zwei unterschiedliche Aspekte hervorgehoben werden. Zum einen wird das Entropieproduktions-Paradoxon beschrieben, welches bei der Analyse der Entropieproduktion bei der anomalen Diffusion, beschrieben durch fraktionale Diffusionsgleichungen auftritt. Andererseits wird ein detaillierter Vergleich zwischen Lösungen verallgemeinerter Diffusionsgleichungen mit numerischen Daten präsentiert, die durch Iteration der Mastergleichung auf verschiedenen Fraktalen produziert worden sind.
Die Entropieproduktionsrate für superdiffusive Prozesse wird berechnet und zeigt einen unerwarteten Anstieg beim Übergang von dissipativer Diffusion zur reversiblen Wellenausbreitung. Dieses Entropieproduktions-Paradoxon ist die direkte Konsequenz einer anwachsenden intrinsischen Rate bei Prozessen mit zunehmendem Wellencharakter. Nach Berücksichtigung dieser Rate zeigt die Entropie den erwarteten monotonen Abfall. Diese Überlegungen werden für generalisierte Entropiedefinitionen, wie die Tsallis- und Renyi-Entropien, fortgeführt.
Der zweite Aspekt bezieht sich auf die anomale Diffusion auf Fraktalen, im Besonderen auf Sierpinski-Dreiecke und -Teppiche. Die entsprechenden Mastergleichungen werden iteriert und die auf diese Weise numerisch gewonnenen Wahrscheinlichkeitsverteilungen werden mit den Lösungen vier verschiedener verallgemeinerter Diffusionsgleichungen verglichen.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2000-08-14
2000-07-14
2000-08-14
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-200000705
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Naturwissenschaften
3
https://monarch.qucosa.de/api/qucosa%3A17645/zip/
urn:nbn:de:bsz:ch1-200000705
oai:qucosa:de:qucosa:17642
2021-03-29T09:34:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh construction and error estimation in the finite element method
Gerd
Kunert
510
510
adaptive algorithm
finite element
anisotropic mesh
anisotropic function
error estimation
Hessian
In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error.
The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution.
The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-07-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000664
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17642/zip/
urn:nbn:de:bsz:ch1-200000664
oai:qucosa:de:qucosa:1765
2021-03-27T15:38:28Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Accompanying “in-service teaching” internships of prospective mathematics teachers – a model for encouraging exchange between theory and practice using the triple coaching approach
Sebastian
Kuntze
Anke
Wagner
Claudia
Wörn
510
510
SD 2009
Lehrer(innen)fortbildung
Lehramtsstudierende
Schulpraktikum
Coaching
professionelles Wissen
teacher development
pre-service teachers
school internship
coaching
professional knowledge
Developing professional expertise of prospective teachers not only in terms of theoretical knowledge but also in terms of competencies of designing challenging and cognitively activating learning opportunities in the mathematics classroom is certainly one of the key aims of internship phases in pre-service mathematics teacher training. As mathematics-related theoretical contents of teacher training and practice-related learning opportunities of school internships are not always linked in an optimal way, this paper aims at discussing a model of an intensive internship phase combined with a triple coaching approach partly integrated in a course accompanying the internship phase.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80432
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 336 - 340
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 336 - 340
info:eu-repo/semantics/openAccess
1
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oai:qucosa:de:qucosa:17664
2021-03-29T09:34:39Z
qucosa:ubc
doc-type:lecture
has-source-swb:false
open_access
ddc:510
openaire
Grundlagen der Differentialgeometrie
Arnd
Meyer
Prof. Dr.
Andreas
Steinbrecher
Dipl. Math.techn.
510
510
Differentialgeometrie
Flächentheorie
Kurventheorie
Vorlesungsscript zur Lehrveranstaltung ¨Differentialgeometrie¨ fuer Mathematiker, Lehramtsstudenten/Gymnasiallehrer Mathematik, Ingenieure und andere Interessenten.
Dieses Vorlesungsscript gibt Einblicke in die Grundlagen der Vektorrechnung, der Kurventheorie und der Flaechentheorie im zwei- bzw. dreidimensionalen Raum. Die entwickelten Theorien werden durch Anwendungsbeispiele untermauert. Weiterhin ist eine Formelsammlung zur Kurven- und Flaechentheorie enthalten.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-11-30
2021-03-29
lecture
urn:nbn:de:bsz:ch1-200000905
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17664/zip/
urn:nbn:de:bsz:ch1-200000905
oai:qucosa:de:qucosa:17660
2021-03-29T09:34:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes
Gerd
Kunert
510
510
004
004
error estimator
anisotropic solution
stretched elements
reaction diffusion equation
singularly perturbed problem
We consider a singularly perturbed reaction-diffusion problem and
derive and rigorously analyse an a posteriori residual error
estimator that can be applied to anisotropic finite element meshes.
The quotient of the upper and lower error bounds is the so-called
matching function which depends on the anisotropy (of the
mesh and the solution) but not on the small perturbation parameter.
This matching function measures how well the anisotropic finite
element mesh corresponds to the anisotropic problem.
Provided this correspondence is sufficiently good, the matching
function is O(1).
Hence one obtains tight error bounds, i.e. the error estimator
is reliable and efficient as well as robust with respect to the
small perturbation parameter.
A numerical example supports the anisotropic error analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-11-09
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000867
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17660/zip/
urn:nbn:de:bsz:ch1-200000867
oai:qucosa:de:qucosa:17668
2021-03-29T09:34:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes
Gerd
Kunert
510
510
error estimator
anisotropic solution
stretched elements
reaction diffusion
singularly perturbed problem equation
Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation.
To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter.
The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well.
A numerical example supports the analysis of our anisotropic error estimator.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-01-03
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100011
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17668/zip/
urn:nbn:de:bsz:ch1-200100011
oai:qucosa:de:qucosa:17672
2021-03-29T09:34:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A note on the energy norm for a singularly perturbed model problem
Gerd
Kunert
510
510
singularly perturbed problem
reaction diffusion equation
adaptive algorithm
error estimator
A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-01-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100062
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17672/zip/
urn:nbn:de:bsz:ch1-200100062
oai:qucosa:de:qucosa:1769
2021-03-27T15:38:18Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects: Two assessment results
Li Tsung Wen
Kuo
Wei-Hao
Cheng
Chih-Chen
Kao
510
510
SD 2009
Indigene Völker
Randgruppen
Mathematik
Taiwan
indigene
mathematics
Taiwan
This research aimed to discuss the indigenous students’ learning effects of mathematics which was based on the self-designed localization and materialization of mathematics activities and had proceeded for one year. The quasi-experimental method was used in
this research. There were 58 indigenous first grade students which were divided into three experimental groups (A, B, C) and one control group (D). Experimental instruments embodied written tests and manipulative tests which were designed by researchers according to the indicators proclaimed by Ministry of Education. The main findings were as followed: (1) The influence of localization and materialization of mathematics activities on the indigenous first grade students’ learning effects was limited. (2) According to the result of Paired T-test of the written and manipulative tests, most of scores of manipulative tests were higher written tests.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80472
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 341 - 346
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 341 - 346
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1769/zip/
urn:nbn:de:bsz:14-qucosa-80472
371756146
oai:qucosa:de:qucosa:17690
2021-03-29T09:35:06Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
ddc:530
openaire
A Comparison of Random Walks with Different Types of Acceptance Probabilities
André
Fachat
530
530
510
510
Monte Carlo
Wahrscheinlichkeit
Physik
Statistische Physik
Theoretische Physik
Gleichgewichtsmodell
Random Walk
Acceptance Probability
Metropolis
Tsallis
Threshold Accepting
Optimaler Schedule
In this thesis random walks similar to the Metropolis algorithm are investigated. Special emphasis is laid on different types of acceptance probabilities, namely Metropolis, Tsallis and Threshold Accepting.
Equilibrium and relaxation properties as well as performance aspects in stochastic optimization are investigated. Analytical investigation of a simple system mimicking an harmonic oscillator yields that a variety of acceptance probabilities, including the abovementioned, result in an equilibrium distribution that is widely dominated by an exponential function.
In the last chapter an optimal optimization schedule for the Tsallis acceptance probability for the idealized barrier is investigated.
In dieser Dissertation werden Random Walks ähnlich dem Metropolis Algorithmus untersucht. Es werden verschiedene Akzeptanzwahrscheinlichkeiten untersucht, dabei werden Metropolis, Tsallis und Threshold Accepting besonders betrachtet.
Gleichgewichts- und Relaxationseigenschaften sowie Performanceaspekte im Bereich der stochastischen Optimierung werden untersucht. Die Analytische Betrachtung eines simplen, dem harmonischen Oszillator ähnlichen Systems zeigt, dass eine Reihe von Akzeptanzwahrscheinlichkeiten, eingeschlossen die oben Erwähnten, eine Gleichgewichtsverteilung ausbilden, die von einer Exponentialfunktion dominiert wird.
Im letzten Kapitel wird der optimale Schedule für die Tsallis Akzeptanzwahrscheinlichkeit für eine idealisierte Barriere untersucht.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2001-03-19
2001-01-12
2001-03-19
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-200100235
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Naturwissenschaften
3
https://monarch.qucosa.de/api/qucosa%3A17690/zip/
urn:nbn:de:bsz:ch1-200100235
oai:qucosa:de:qucosa:1770
2021-03-27T15:39:05Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Helping a Young Child Connect Fact Family Addition and Subtraction using Tools
Terri L.
Kurz
H. Bahadir
Yanik
Jorge
Garcia
510
510
SD 2009
Tatsachen
Addition
Subtraktion
Multiplikation
Division
miteinander verbunden
Werkzeuge
Lernkarten
Zahlenzerlegung
Grundschule
Zahlen und Rechenoperationen
Fact families
addition
subtraction
multiplication
division
interconnected
tools
flashcards
number decomposition
primary school
number and operations
In order to help children become effective at addition and subtraction, it is important to provide them with an opportunity to investigate and discover the interconnectedness of the two operations. Fact families are one method teachers use to try and help children develop and understand how the operations relate to one another. This paper documents a strategy that was used with a seven year old boy to help him connect addition to subtraction. The strategy incorporated flash card tools to help him create logical problems to discover the mathematical relationship of fact families. With just a few trials, the child was able to create and explain problems that demonstrated the interconnectedness of fact families through addition and subtraction. The model was successful in helping the child advance his understanding. Additionally, it can be extended to more complex addition and subtraction problems as well as multiplication and division
fact families.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80491
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 353 - 357
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 353 - 357
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1770/zip/
urn:nbn:de:bsz:14-qucosa-80491
371756804
oai:qucosa:de:qucosa:1771
2021-03-27T15:38:58Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The van Hiele Phases of Learning in studying Cube Dissection
Shi-Pui
Kwan
Ka-Luen
Cheung
510
510
SD 2009
Geometrie
Origami
van-Hiele Phasen des Lernens
geometry
origami
van-Hiele phases of learning
Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major
elements of our design based on the van Hiele learning phases.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80503
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 358 - 363
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 358 - 363
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1771/zip/
urn:nbn:de:bsz:14-qucosa-80503
37175707X
oai:qucosa:de:qucosa:1772
2021-03-27T15:38:57Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Elementary Students’ Construction of Proportional Reasoning Problems: Using Writing to Generalize Conceptual Understanding in Mathematics
Millard
Lamm
David K.
Pugalee
510
510
SD 2009
Problemlösung
Kommunikation
rationale Zahlen
Problem solving
communication
rational number
This study engaged fourth and fifth graders in solving a set of proportional tasks with focused discussion and concept development by the teacher. In order to understand the students’ ability to generalize the concept, they were asked to write problems that reflected the underlying concepts in the tasks and lessons. A qualitative analysis of the student generated problems
show that the majority of the students were able to generalize the concepts. The analysis allowed for a discussion of problems solving approaches and a rich description of how students applied multiplicative reasoning in composing mathematics problems. These results are couched in a discussion of how the students solved the proportional reasoning tasks.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80517
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 364 - 367
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 364 - 367
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1772/zip/
urn:nbn:de:bsz:14-qucosa-80517
37175724X
oai:qucosa:de:qucosa:17723
2021-03-29T09:35:34Z
qucosa:ubc
doc-type:masterThesis
has-source-swb:false
open_access
ddc:510
openaire
Numerical Methods for Structured Matrix Factorizations
Daniel
Kressner
510
510
Software
Periodic Eigenvalue Problems
QZ Algorithm
Toeplitz Matrices
Schur Algorithm
This thesis describes improvements of the periodic QZ algorithm and several variants of the Schur algorithm for block Toeplitz matrices.
Documentation of the available software is included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Daniel
Kressner
2001-06-13
2001-06-13
2021-03-29
masterThesis
urn:nbn:de:bsz:ch1-200100547
eng
info:eu-repo/semantics/openAccess
Diplom
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
3
https://monarch.qucosa.de/api/qucosa%3A17723/zip/
urn:nbn:de:bsz:ch1-200100547
oai:qucosa:de:qucosa:17728
2021-03-29T09:35:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Zienkiewicz-Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
Gerd
Kunert
Serge
Nicaise
510
510
004
004
anisotropic mesh
error estimator
Zienkiewicz-Zhu estimator
recovered gradient
We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large.
Two kinds of Zienkiewicz-Zhu (ZZ) type error estimators are derived which are both based on some recovered gradient. Two different, rigorous analytical approaches yield the equivalence of both ZZ error estimators to a known residual error estimator. Thus reliability and efficiency of the ZZ error estimation is obtained. Particular attention is paid to the requirements on the anisotropic mesh.
The analysis is complemented and confirmed by several numerical examples.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-07-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100599
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17728/zip/
urn:nbn:de:bsz:ch1-200100599
oai:qucosa:de:qucosa:1773
2021-03-27T15:39:04Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
How to teach modeling in mathematics classrooms? The implementationof modeling tasks. Comparing learning arrangements and teachermethods with respect to student’s activities
Céline
Liedmann
510
510
SD 2009
Modellieren
Modellierungsaufgabe
unterichten
Comenius Netzwerk
Modelling
Modelling task
teach
Comenius Network
There is a wide consensus that including mathematical modeling into the curricula is an important aim. A lot of attention has been spent on the realistic problems whereas their embedding in a classroom situation is less investigated so far, although the methodical
arrangements are of major importance for initiating students’ activities. In this paper, the implementation of the modeling task “swimming pool” in mathematics education in two lessons is compared concerning learning arrangement and teaching methods in depth with respect to the students’ activities. Two videos about this implementation will be shown and discussed in this workshop. They are supposed to demonstrate in which different ways teachers engage in modeling. The aim is to show teachers, especially those without
experience in teaching modeling, how modeling tasks can be implemented.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80522
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 368 - 371
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 368 - 371
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1773/zip/
urn:nbn:de:bsz:14-qucosa-80522
371757630
oai:qucosa:de:qucosa:1774
2021-03-27T15:39:08Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
A Collaborative Model for Calculus Reform—A Preliminary Report
Po-Hung
Liu
Ching-Ching
Lin
Tung-Shyan
Chen
Yen-Tung
Chung
Chiu-Hsiung
Liao
Pi-Chuan
Lin
Hwai-En
Tseng
Ruey-Maw
Chen
510
510
SD 2009
Analysis Reform
E-Learning
über die Analysis hinausgehende Mathematik
calculus reform
e-learning
post-calculus mathematics
For the past two decades, both pros and cons of calculus reform have been discussed. A question often asked is, “Has the calculus reform project improved students’ understanding of mathematics?” The advocates of the reform movement claim that reform-based calculus may help students gain an intuitive understanding of mathematical propositions and have a better grasp of the real-world applications. Nonetheless, many still question its effect and argue that calculus reform purges calculus of its mathematical rigor and poorly prepares students for advanced mathematical training. East Asian students often rank in the top 10 of TIMSS and PISA. However, out-performing others in an international comparison may not guarantee their success in the learning of calculus. Taiwanese college students usually have a high failure rate in calculus. The National Science Council of Taiwan therefore initiated several projects in 2008 for improving students’ learning in calculus. This paper provides a preliminary report on one of the projects, PLEASE, and discusses how it was planned to respond to the tenets of calculus reform movement.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-04
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80534
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 372 - 375
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 372 - 375
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1774/zip/
urn:nbn:de:bsz:14-qucosa-80534
371758106
oai:qucosa:de:qucosa:17740
2021-03-29T09:35:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes
Gerd
Kunert
510
510
error estimator
H^1 seminorm
anisotropic mesh
reaction diffusion equation
singularly perturbed problem
The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes.
A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably.
Furthermore three modifications of these estimators are introduced and discussed.
Numerical experiments for all estimators complement and confirm the theoretical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-08-24
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100730
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17740/zip/
urn:nbn:de:bsz:ch1-200100730
oai:qucosa:de:qucosa:1776
2021-03-27T15:38:52Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Changes in the North Carolina Mathematics Curriculum: A Comparative Study, 1920s, 1930’s with 2003
Corey
Lock
David
Pugalee
510
510
SD 2009
Geschichte des Mathematik-Lehrplanes
Vergleich von Mathematik-Lehrplänen aus Vergangenheit und Gegenwart
history of mathematics curriculum
comparison of past and present math curriculum
The purpose of this paper is to compare curriculum documents for K-12 education from the state of North Carolina from two time periods, 1920s and 2003. The historical development of the mathematics curriculum in North Carolina provides a snapshot of the shifts in mathematics teaching and learning. North Carolina, a state in
the southeast of the United States, has had a statewide standard course over a period spanning more than eighty years. A document analysis of printed curriculum standards from allows a description of the mathematics concepts and tasks that were expected of students in those years. The analysis revealed stark contrasts in the focus of mathematics from a very computational emphasis to one of problem solving. The analysis also highlighted the understanding of algebraic concepts and ideas as an essential outcome of current mathematics
programs.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80557
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 376 - 377
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 376 - 377
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-80557
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oai:qucosa:de:qucosa:1777
2021-03-27T15:38:47Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Bridging the gap between technology design and school practice: a specific experiment within the ReMath Project
Laura
Maffei
510
510
SD 2009
Computer-Algebra-Systeme
Lernumgebung Aplusix
Design
Algebra
Darstellungen
semiotische Mediation
computer algebra systems
software Aplusix
design
algebra
representations
semiotic mediation
This contribution describes an experiment carried out by a team within the ReMath (Representing Mathematics with Digital Media) European Project (http://remath.cti.gr). Within this project six digital
dynamic artefacts (DDAs) have been developed, thirteen experiments have been planned (Artigue & al., 2007) and carried out, analysis of the collected data are still in progress. In this contribution, we
focus on the case of the Aplusix DDA (http://aplusix.imag.fr), from the point in which the designers deliver their product to the team in charge of planning the experiment, up to the point in which the
artefact is experimented within the ReMath project.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80562
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 378 - 382
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 378 - 382
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1777/zip/
urn:nbn:de:bsz:14-qucosa-80562
371758904
oai:qucosa:de:qucosa:1778
2021-03-27T15:38:48Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The Effect of Rephrasing Word Problems on the Achievements of Arab Students in Mathematics
Asad
Mahajne
Miriam
Amit
510
510
SD 2009
Mathematik
Umformulierung
Textaufgaben
Erfolge
Araber
Kolloquien
Dialekt
modernes Standard-Arabisch
Muttersprache
Haltung
Gesprochene Sprache
Mathematics
Rephrasing
Word Problems
Achievements
Arabs
colloquia dialect
modern standard Arabic
mother tongue
attitude
Spoken language
Language is the learning device and the device which forms the student''s knowledge in math, his ability to define concepts, express mathematical ideas and solve mathematical problems. Difficulties in the Language are seen more in word problems, clarity and in the way the text is read by the student have a direct effect on the understanding of the problem and therefore, on its solution, could delay the problem solving process. The connection between language and mathematical achievements has a more distinctive significance regarding the Arab student. This is due to the fact that the language which is used in the schools and in textbooks is classical (traditional) Arabic. It is far different than the language used in everyday
conversations with family and friends (the spoken Arabic). Our research examine whether rephrasing word problems can affect the achievements of the Arab students in it. The experimental group received mathematics instruction using learning materials of word problems that were rewritten in a “middle language” closer to the students’ everyday language (spoken Arabic), thus keeping the mathematical level of the problems. The research findings showed that students in the experimental group improved their achievements in word and geometric problems significantly more than students from control group.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80578
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 383 - 385
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 383 - 385
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1778/zip/
urn:nbn:de:bsz:14-qucosa-80578
371759064
oai:qucosa:de:qucosa:17783
2021-03-29T09:36:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grundgleichungen und adaptive Finite-Elemente-Simulation bei "Großen Deformationen"
Basic Equations and adaptive Finite Element Simulation on 'Large Deformations'
Arnd
Meyer
510
510
Deformation <Mathematik>
Fehlerabschätzung
Finite-Elemente-Methode
Simulation
large deformations
Eine einfache Darstellung der Grundgleichungen für
'Große Deformationen' und Herleitung eines geeigneten
Fehlerschätzers für die adaptive FEM.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701960
ger
Chemnitz Scientific Computing Preprints ; 07-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A17783/zip/
urn:nbn:de:bsz:ch1-200701960
oai:qucosa:de:qucosa:1780
2021-03-27T15:39:11Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
OPEN-ENDED APPROACH TO TEACHING AND LEARNING OF HIGHSCHOOL MATHEMATICS
Radley Kebarapetse
Mahlobo
510
510
SD 2009
xSchulmathematik
Mathematikunterricht
Mathematik lernen
offene Herangehensweise
Problemlösung
Lernleistung
Lernerfolg
11. Klasse
School mathematics
mathematics teaching
mathematics learning
open-ended approach
problem solving
learner performance
learner achievement
grade 11
The author shares some of the findings of the research he conducted in 2007 on grade 11 mathematics learners in two schools, one experimental and the other one control. In his study, the author claims that an open-ended approach towards teaching and learning of mathematics enhances understanding of mathematics by the learners. The outcomes of the study can be summarised as follows:
1. In the experimental school, where the author intervened by introducing an open-ended approach to teaching mathematics (by means of giving the learners an open-ended approach compliant worksheet to work on throughout the intervention period), the
performance of the learners in the post-test was better than that of the learners from the control school. Both schools were of similar performance in the pre-test. The two schools wrote the same pre-test and same post-test. Both schools were following common work
schedule.
2. Within the experimental school, post-test performance of the learners in the class where the intervention was monitored throughout the intervention period (thus ensuring compliance of the teacher to the open-ended approach) out-performed those in which monitoring was less frequent.
3. There was no significant difference in performance between learners from the unmonitored experimental class and those from the control class.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80592
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 386 - 389
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 386 - 389
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1780/zip/
urn:nbn:de:bsz:14-qucosa-80592
371759315
oai:qucosa:de:qucosa:17803
2021-03-29T09:36:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for convection dominated problems on anisotropic meshes
Gerd
Kunert
510
510
error estimator
anisotropic solution
stretched elements
convection diffusion equation
singularly perturbed problem
A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously.
The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated.
The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers.
Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-03-22
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200200255
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17803/zip/
urn:nbn:de:bsz:ch1-200200255
oai:qucosa:de:qucosa:1781
2021-03-27T15:39:12Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Mathematics and Mathematics Education Development in Finland: the impact of curriculum changes on IEA, IMO and PISA results
George
Malaty
510
510
SD 2009
Mittag-Leffler
Hjalmar Mellin
Ernst Leonard Lindelöf
Rolf Herman Nevanlinna
Lars Valerian Ahlfors
Ernst Bonsdorff
Kalle Väisälä
Elite
Lehrplanänderungen
Unterrichtsstunden
Bildungsreformen
Mathematikolympiaden
Vergleichsstudien
IEA
TIMSS
PISA
PISA
Formeln
Algorithmen
Unlogisches
Problemlösen
Alltagsmathematik
Mittag-Leffler
Hjalmar Mellin
Ernst Leonard Lindelöf
Rolf Herman Nevanlinna
Lars Valerian Ahlfors
Ernst Bonsdorff
Kalle Väisälä
elite
curriculum changes
teaching hours
reforms
Olympiads
comparative studies
IEA
TIMSS
PISA
PISA
formulas
algorithms
illogic
problem-solving
everyday life mathematics
Mathematics has got roots in Finland in the last quarter of the 19th century and came to flourish in the first quarter of the next century. In the first quarter of the 20th century, mathematicians were involved in teaching mathematics at schools and writing school textbooks. This involvement decreased and came to an end by the launching of the ‘New Math’ project. Mathematics education for elite was of positive affect to higher education, and this has changed by the spread of education, the decrease of mathematics teaching hours at schools and the changes in school mathematical curricula. The impact of curriculum changes is evident in Finnish students’ performance in the IEA comparative studies, PISA and IMO.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80604
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 390 - 394
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 390 - 394
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1781/zip/
urn:nbn:de:bsz:14-qucosa-80604
371759439
oai:qucosa:de:qucosa:1782
2021-03-27T15:38:59Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
A class practice to improve student’s attitude towards mathematics
Maria Flavia
Mammana
Mario
Pennisi
510
510
SD 2009
Mathematiklabor
Lehren/Lernen mit Technologieunterstützung
Dynamische Geometrie
Selbstwirksamkeit
Math laboratory
teaching/learning with technology
Dynamic Geometry systems
self-efficay
For many students, mathematics, traditionally thought to be difficult and dull, is often considered inaccessible, generating a negative attitude towards it. In order to encourage a positive attitude towards mathematics, we propose class practices that, through research activities, will lead the students to experiment a similar path to the one that has given, as a final product, a structured theory, so as to enhance their self-efficacy, give a correct vision of the discipline and stimulate positive emotions. This can be realized, for example, as a “laboratory activity” in which the students compare ideas, intuitions, arguments, and work together to obtain results, using their critical
capabilities in a collaborative learning activity. A team of university professors and high school teachers has developed a laboratory activity that focuses on some properties of quadrilaterals. The activity has at any rate been experimented in different first biennium
classes of some high schools and has obtained very good results.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80613
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 395 - 398
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 395 - 398
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1782/zip/
urn:nbn:de:bsz:14-qucosa-80613
371759781
oai:qucosa:de:qucosa:1784
2021-03-27T15:39:13Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Identifying Modelling Tasks
Stefanie
Meier
510
510
SD 2009
Modellieren
Modellierungskreislauf
Modellierungsaufgabe
Comenius Netzwerk
Deskriptoren für Modellierungsaufgaben
Modelling
Modelling circle
Modelling task
Comenius Network
Descriptors for modelling tasks
The Comenius Network Project “Developing Quality in Mathematics Education II” funded by the European Commission consists of partners from schools, universities and teacher training centres from eleven European countries. One advantage of the project is the mutual exchange between teachers, teacher trainers and researchers in developing learning material. To support the teachers most effectively the researchers asked the teachers what they wanted the researchers to do. The answer was also a question: How can we
identify (good) modelling tasks? A discussion ensued in the research group of this project which resulted in a list of descriptors characterising modelling tasks. This paper focuses on the theoretical background of mathematical modelling and will thereby substantiate the list of descriptors for modelling tasks.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80629
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 399 - 403
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 399 - 403
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1784/zip/
urn:nbn:de:bsz:14-qucosa-80629
371760038
oai:qucosa:de:qucosa:17847
2021-03-29T09:37:12Z
qucosa:ubc
doc-type:conferenceObject
has-source-swb:false
open_access
ddc:510
openaire
Finite dimensional stochastic differential inclusions
Anne
Bauwe
Wilfried
Grecksch
510
510
Ito-Formel
Stochastische Analysis
Itô formula of the square
Lipschitz continuous set-valued mapping
Yosida approximation
maximal monotone operator
stochastic differential inclusion
This paper offers an existence result for finite dimensional stochastic differential
inclusions with maximal monotone drift and diffusion terms. Kravets studied only
set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions
in an infinite dimensional context.
In the proof we make use of the Yosida approximation of maximal monotone operators
to achieve stochastic differential equations which are solvable by a theorem
of Krylov and Rozovskij [7]. The selection property is verified with certain properties
of the considered set-valued maps. Concerning Lipschitz continuous set-valued
diffusion terms, uniqueness holds. At last two examples for application are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-05-16
2021-03-29
conferenceObject
urn:nbn:de:bsz:ch1-200800515
Tagungsband zum Workshop "Stochastische Analysis", 20.09.2006 - 22.09.2006
http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800505
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A17847/zip/
urn:nbn:de:bsz:ch1-200800515
oai:qucosa:de:qucosa:1785
2021-03-27T15:39:14Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Paper&Pencil Skills in the 21st Century, a Dichotomy?
Hartwig
Meissner
Annabella
Diephaus
510
510
SD 2009
Dichotomie
Zahlengefühl
Taschenrechner
Kopfrechnen
Schriftliches Rechnen
Schätzen
Überschlagen Versuchen und Probieren
dichotomy
number sense
calculators
mental arithmetic
paper-and-pencil skills
estimation
approximation
One-Way-Principle
There is a worldwide development, better to say a non-development: We teach paper & pencil skills in primary schools almost like we did 30 or 50 or 100 years ago. Till today the primary school teachers spend up to more than 100 hours in the class room to teach and to train old fashioned algorithms though in daily life situations and for business purposes everybody uses a calculator. Why do we waste so much time of our children to teach them things which later on they will not need? We see an emotional dichotomy. Despite the research results from many research projects in many countries there still is the fear that the use of calculators in primary grades will harm mental arithmetic and estimation skills. To explain and to overcome that fear we will reflect the nature of number sense and of paper&pencil skills more carefully. We realize that the development of number sense is an intuitive and unconscious mental process while the ability to get an exact calculation result is trained logically and consciously. To overcome the above dichotomy we must solve the hidden dichotomy number sense versus precise calculation result. We need a new balance. Different types of examples will be given how we can further the development of number sense in a technology dominated curriculum.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80642
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 404 - 408
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 404 - 408
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1785/zip/
urn:nbn:de:bsz:14-qucosa-80642
371760380
oai:qucosa:de:qucosa:1786
2021-03-27T15:39:19Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
HOW TO SOLVE IT
Luigi
Menna
510
510
SD 2009
Problemlösung
heuristische Strategien
Argumentationen im Vergleich zum Beweis
technologische Hilfsmittel
Lehre der didaktischen Situationen
problem solving
heuristic strategies
argumentations vs proof
technological tools
theory of didactical situations
This work is a reflection on the results of an experimentation carried out on secondary school students of between 16 and 18 from various classes. The experimentation aims at identifying the implicit ideas they use when asked to solve a certain mathematical problem. In particular, in giving them these problems an heuristic approach was suggested, and the differences between this and a purely deductive approach were measured. Analyzing the different approaches used by the students and the difficulties they had in distinguishing between argumentative and demonstrative operations has given rise to a reflection on the use of software such as Geogebra and Excel.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80655
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 409 - 412
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 409 - 412
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1786/zip/
urn:nbn:de:bsz:14-qucosa-80655
371760623
oai:qucosa:de:qucosa:1787
2021-03-27T15:39:20Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Tasks for tests and A-levels using CAS
Heidi
Metzger-Schuhäker
510
510
SD 2009
Schularbeitsaufgaben
Abituraufgaben
Maturaaufgaben
computerunterstützter Mathematikunterricht
Technologieeinsatz
Computeralgebrasystem (CAS)
Sekundarstufe 2
Notebookklassen
anwendungsorientierte Aufgaben
Computerunterstützung
Finanzmathematik
Wahrscheinlichkeitsrechnung
Lorenzfläche
Ginikoeffizient
task for tests
A-levels
secondary level 2
technology in mathematics
computer algebra systems (CAS)
notebook classes
application-oriented test tasks
final examinations
Financial mathematics
probability theory
Lorenz surface
Gini coefficient
Tasks for different years of the secondary level II are presented on the basis of long lasting experience with computer-assisted mathematics instruction. They include applications of mathematical skills as well as the testing of theoretical knowledge. Finally relevant A-levels tasks are presented that integrate different mathematical contents into every day connections from economy, medical science, sports asf.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80669
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 413 - 416
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 413 - 416
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1787/zip/
urn:nbn:de:bsz:14-qucosa-80669
371760984
oai:qucosa:de:qucosa:1788
2021-03-27T15:39:17Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Models of Mathematics Curriculum Development in Egypt
Fayez M.
Mina
510
510
SD 2009
Modellierung
Mathematiklehrpläne
Lehrplanentwicklung
Models
mathematics curricula
curriculum development
The need for developing mathematics curricula was clarified. Models of
mathematics curriculum development in Egypt were identified as: \"Temporary Committees\" (TC), center of developing curriculum and educational materials (CDCEM), \"National conferences\" (NC) and \"Educational standards\" (ES). The advantages and disadvantages of
each one of these models were evaluated. Then a new model was suggested covering the whole advantages of these models and avoiding their disadvantages.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80674
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 417 - 419
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 417 - 419
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1788/zip/
urn:nbn:de:bsz:14-qucosa-80674
371761174
oai:qucosa:de:qucosa:17888
2021-03-29T09:37:45Z
qucosa:ubc
doc-type:doctoralThesis
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open_access
ddc:004
ddc:510
ddc:620
ddc:621.3
openaire
Optimierung hochpoliger Dauermagnetmotoren unter Verwendung der Finiten Elemente Methode und der Evolutionsstrategie
Design Optimization of Permanent Magnet Motors by Evolution Strategies and Finite Element Analysis
Dirk
Bochnia
620
620
510
510
004
004
Modellierung
Dauermagneterregter Synchronmotor
Magnetisches Wechselfeld
Wirbelstromverlust
Elektrische Maschine
Optimierung
Optimierung / Nebenbedingung
Optimierungsproblem
Evolutionsstrategie
Finite-Elemente-Methode
The power and force density of electric motors becomes higher and higher and it is very important to design most optimal machines. Conventional methods dont reach this aim in any case. A new approach is presented combining Evolutionary Strategies and Finite Element Analysis to obtain reliable results.
Die Anforderungen an elektrische Antriebe sind sehr hoch. Nur optimal konstruierte Maschinen können ihnen genügen. Es wird ein Instrumentarium vorgestellt, welches eine rechnergestützte automatische Optimierung des magnetischen Kreises der elektrischen Maschine gestattet. Als Modellierungsgrundlage wird die Finite-Elemente-Methode verwendet. Die Optimierung erfolgt mit der Evolutionsstrategie.
Aufgrund des hohen Rechenaufwandes der FEM wird insbesondere darauf eingegangen, ein Modell zu schaffen, dass möglichst viel Information bei hoher Genauigkeit und geringstem numerischen Aufwand liefert. Entsprechende Möglichkeiten der Simulation magnetischer und thermischer Felder mit der FEM werden besprochen. Außerdem wird ein Verfahren vorgestellt, welches die Ermittlung der magnetischen Verluste ohne transienter Feldberechnungen erlaubt.
Die Modellierung wird speziell am Beispiel eines hochpoligen permanenterregten Synchronmotors in Außenläuferbauweise erläutert. Die Ergebnisse der Simulation werden mit Messungen verglichen. Weiterhin werden die Ergebnisse verschiedener konkreter Optimierungsläufe vorgestellt.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Prof. Dr.-Ing. Wilfried
Hofmann
Prof. Dr.-Ing. Wolfram
Dötzel
Prof. Dr.-Ing. Hellmut
Hupe
2002-09-11
2002-05-23
2002-09-19
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-200201086
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Elektrotechnik und Informationstechnik
2
https://monarch.qucosa.de/api/qucosa%3A17888/zip/
urn:nbn:de:bsz:ch1-200201086
oai:qucosa:de:qucosa:1789
2021-03-27T15:39:18Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
TO TEACH COMBINATORICS, USING SELECTED PROBLEMS
Laurentiu
Modan
510
510
SD 2009
Arrangement
Mächtigkeit
Kombinatorik
Zählprinzip
Ziffer
Anzahl der Funktionen
Permutationen
arrangement
cardinal
combinatorics
combination
counting principle
digit
number of the functions
permutation
In 1972, professor Grigore Moisil, the most famous Romanian academician for Mathematics, said about Combinatorics, that it is “an opportunity of a renewed gladness”, because “each problem in the domain asks for its solving, an expenditure without any economy of the human intelligence”. More, the research methods, used in Combinatorics, are different from a problem to the other! This is the explanation for the existence of my actual paper, in which I propose to teach Combinatorics, using selected problems. MS classification: 05A05, 97D50.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80681
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 420 - 422
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 420 - 422
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1789/zip/
urn:nbn:de:bsz:14-qucosa-80681
371761387
oai:qucosa:de:qucosa:1790
2021-03-27T15:39:16Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Exploring the mathematics that children read in the world: A case study of Grade 8 learners in a South African School
Lesego Brenda
Mokotedi
510
510
SD 2009
Kontext
Verbindungen
sehen
Zahlen und Zahlenkenntnis
Contexts
connections
seeing
number and number knowledge
This paper presents a qualitative study in which an attempt was made to extend the debate surrounding the use of real life contexts to make mathematics more meaningful and real. The study investigated Grade 8 learners’ knowledge of number, understanding of number concepts and the kinds of connections they make between number and the context in which number is used. An important aspect of the study’s methodological approach involved an examination of the comments that learners made about what they said they know about number. A response to the question: “Why is the number in the picture?” provided a framework for establishing how learners saw relationships between number and the context in which numbers are used. A face scenario with four questions was given to learners to elicit these relationships. Results pointed to the usefulness of real life contexts as tools that have a central role in uncovering what learners know about number and how they use that knowledge to understand situations that call for proficiency in mathematics.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80705
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 427 - 430
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 427 - 430
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1790/zip/
urn:nbn:de:bsz:14-qucosa-80705
371763304
oai:qucosa:de:qucosa:1791
2021-03-27T15:39:15Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
On Teaching Quality Improvement of a Mathematical Topic Using Artificial Neural Networks Modeling (With a Case Study)
Hassan M.
Mustafa
Ayoub
Al-Hamadi
510
510
SD 2009
Künstliche neuronale Netze
Learning-Performance Evaluation
Assoziativspeicher
Artificial Neural Networks
Learning Performance Evaluation
Associative Memory
This paper inspired by simulation by Artificial Neural Networks (ANNs) applied recently for evaluation of phonics methodology to teach children "how to read". A novel approach for teaching a mathematical topic using a computer aided learning (CAL) package applied at educational field (a children classroom). Interesting practical results obtained after field application of suggested CAL package with and without associated teacher''s voice. Presented study highly recommends application of a novel teaching trend based on behaviorism and individuals'' learning styles. That is to improve
quality of children mathematical learning performance.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80718
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 431 - 435
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 431 - 435
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1791/zip/
urn:nbn:de:bsz:14-qucosa-80718
371763673
oai:qucosa:de:qucosa:17916
2021-03-29T09:38:08Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:004
ddc:020
ddc:510
openaire
Generische Bücher - ein graphentheoretisches Modell zur logischen Strukturierung von Büchern in on-Demand-Publikationsprozessen
Klaus
Kreulich
510
510
020
020
004
004
Elektronisches Publizieren
Buch
XML
SGML
Hypertext
Kohärenz
Book-on-Demand
Print-on-Demand
Cross-Media Publishing
Logische Struktur
A detailed english description (three pages) is enclosed in the publication.
Die heutige Menge an textuellen Informationen erfordert vom Interessenten eine adäquate Selektion und Rezeption. Als printmedientechnischer Beitrag zur Lösung dieser Problematik wird das Book-on-Demand- (BoD) Verfahren in Verbindung mit einer individuellen Auswahl von Buchinhalten genutzt. Dazu wird in der vorliegenden Arbeit ein Formalismus entwickelt, der im Rahmen eines BoD-Workflows die kontextspezifische logische Neustrukturierung von Einheiten eines bestehenden elektronischen Buches automatisiert. Als Grundlage dient das aus der Graphentheorie bekannte Modell des minimalen Spannbaums (MSB). Bei der Bildung des MSB werden vor allem die primäre, vom Autor des bestehenden Buches vorgegebene, logische Struktur und eine dem Buch zu Grunde liegende Taxonomie ausgewertet. Für eine prototypische Implementierung des formalen Modells wird eine geeignete Softwarearchitektur für XML-kodierte Bücher entwickelt. Die Bewertung der resultierenden Buchgliederungen wird durch neuartige Metriken für logische Strukturen unterstützt.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Arved Carl
Hübler
Prof. Dr.
Arved Carl
Hübler
Prof. Dr.
Birgit
Awiszus
Prof. Dr.
Christian
Wolff
Priv.-Doz. Dr. habil.
2002-04-22
2002-09-24
2002-11-26
2021-03-29
doctoralThesis
urn:nbn:de:bsz:ch1-200201359
ger
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Maschinenbau und Verfahrenstechnik
2
https://monarch.qucosa.de/api/qucosa%3A17916/zip/
urn:nbn:de:bsz:ch1-200201359
oai:qucosa:de:qucosa:1792
2021-03-27T15:39:09Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
New Forms of Assessment in the South African Curriculum Assessment Guidelines: What Powers do Teachers Hold?
Willy
Mwakapenda
510
510
SD 2009
Mathematikunterricht
Einschätzung
Lehrerwirksamkeit
Lehrplan-Politik
mathematics education
assessment
teacher power
curriculum policy
This article opens up a discussion on the power that teachers have in mathematics curriculum at the Further Education and Training level. It is related to the general question: who holds the power in school mathematics education in South Africa? To what extent is the teacher given an opportunity to exercise their power in mathematics assessment? If the teacher is given power, what does that power allow teachers to do, and under what conditions does this happen? The case of mathematics is presented here to illustrate the above complex questions of teacher power in new forms of assessment in the curriculum.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80726
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 436 - 439
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 436 - 439
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1792/zip/
urn:nbn:de:bsz:14-qucosa-80726
371763770
oai:qucosa:de:qucosa:1793
2021-03-27T15:39:01Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Investigating Elementary Teachers’ Mathematical Knowledge for TeachingGeometry: The Case of Classification of Quadrilaterals
Dicky
Ng
510
510
SD 2009
mathematisches Wissen für die Lehre
Geometrie
Klassifizierung von Vierecken
Grundschullehrer
mathematical knowledge for teaching
geometry
classification of quadrilaterals
elementary teachers
This paper examines the mathematical knowledge for teaching (MKT) in Indonesia, specifically in school geometry content. A translated and adapted version of the MKT measures developed by the Learning Mathematics for Teaching (LMT) project was administered to 210 Indonesian primary and junior high teachers. Psychometric analyses revealed that items related to classification of quadrilaterals were difficult for these teachers. Further interactions with teachers in a professional development setting confirmed that teachers held a set of exclusive definitions of quadrilaterals.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80730
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 440 - 444
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 440 - 444
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1793/zip/
urn:nbn:de:bsz:14-qucosa-80730
371763959
oai:qucosa:de:qucosa:17935
2021-03-29T09:38:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
An Asymptotic Approach to Progressive Censoring
Asymptotics for Progressive Censoring
Glenn
Hofmann
Erhard
Cramer
N.
Balakrishnan
Gerd
Kunert
510
510
Order statistics
best linear estimation
extreme value distribution
generalized
variance
optimal censoring scheme
progressive censoring
Weibull distribution
normal distribution
Progressive Type-II censoring was introduced by Cohen (1963) and has since been
the topic of much research. The question stands whether it is sensible to use this
sampling plan by design, instead of regular Type-II right censoring. We introduce
an asymptotic progressive censoring model, and find optimal censoring schemes for
location-scale families. Our optimality criterion is the determinant of the 2x2 covariance
matrix of the asymptotic best linear unbiased estimators. We present an explicit
expression for this criterion, and conditions for its boundedness. By means of numerical
optimization, we determine optimal censoring schemes for the extreme value,
the Weibull and the normal distributions. In many situations, it is shown that these
progressive schemes significantly improve upon regular Type-II right censoring.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-12-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200201539
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17935/zip/
urn:nbn:de:bsz:ch1-200201539
oai:qucosa:de:qucosa:1794
2021-03-27T15:39:02Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Mathematics Teacher TPACK Standards and Revising Teacher Preparation
Margaret
Niess
510
510
SD 2009
Lehrerwissen
Technologie
Lehrerausbildung
Lehrerfortbildung
teacher knowledge
technology
preservice mathematics teacher preparation
inservice mathematics teacher preparation
What knowledge do teachers need for integrating appropriate digital technologies in teaching mathematics? An overarching construct called TPACK is proposed as the interconnection and intersection of knowledge among technology, pedagogy, and content and is referred to as the total knowledge package for teaching mathematics with technology. Five stages in the process of developing TPACK - recognizing, accepting, adapting, exploring, and adapting – describe the process of teachers’ learning to integrate technology. Teachers learn to teach mathematics from their own learning – K-12 mathematics - collegiate mathematics coursework, teacher preparation program, field experiences and professional development as they teach mathematics. The challenge is to identify appropriate experiences to guide this integration of technology in teaching
mathematics in ways that develop TPACK. A framework for these experiences directs attention to emergent social and psychological perspectives.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80742
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 445 - 449
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 445 - 449
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1794/zip/
urn:nbn:de:bsz:14-qucosa-80742
371764114
oai:qucosa:de:qucosa:17950
2021-03-29T09:38:38Z
qucosa:ubc
doc-type:PeriodicalPart
has-source-swb:false
open_access
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ddc:300
ddc:340
ddc:510
status-type:publishedVersion
openaire
TU-Spektrum 3/1999, Magazin der Technischen Universität Chemnitz
Mario
Steinebach
Hubert J.
Gieß
Christine
Häckel-Riffler
Daniela
Lopez
Peggy
Schellenberger
Skulptur
ZSB
000
000
300
300
510
510
340
340
Campus
Informatik
Der Hammer fällt noch lange nicht
Uni stellt sich den Herausforderungen des 21. Jahrhunderts
Neuer Mathe-Dekan
Gedankenaustausch in einer Welt der Netze
Ein Symbol für Uni und Stadt: Der Halbleiter von Chemnitz
Große Aussichten für einen kleinen Baum
Immer den richtigen Nerv treffen
Abschied von den Zettel-Katalogen
Internationalität als Markenzeichen
Rekordverdächtiger Start ins neue Semester
Lehramtsausbildung läuft in Chemnitz aus
Soziologen fühlen Chemnitzer Lehre auf den Zahn
Knete, Heu, Kies, Mücken, Zaster, Moos, Kohle, Zunder
30 Drahtesel in vier Monaten spurlos verschwunden
13 neue Auszubildende an der Uni
Der Karriere-Kick für Frauen: Informatik in Chemnitz
Drum prüfe, wer sich ewig bindet...
Zum Testen freigegeben: Das Fernlern-Programm ReLaTeD
Was man mit Linearer Algebra alles anfangen kann
Lässt sich Innovation lehren? Oder sogar lernen?
Rote Karte für den gelben Riesen
BECKMANN-INSTITUT für Technologieentwicklung e. V.
Zwei starke Partner wollen sich zusammentun
Die Wiedervereinigung muss in den Köpfen stattfinden
Hochschulen gründen Arbeitsgruppe für internationales Marketing
Ein schönes Geschenk für Goethe zum 250. Geburtstag
Grenzüberschreitender Forscherdrang
Bulgarische Wissenschaftler zu Gast
klein - kleiner - mikro
Pfiffige Dolmetscher retten Tausende von Programmierstunden
Preiswertes aus der Bronzezeit
Verdiente Ehrung für einen gestandenen
Konstrukteur
Preise für die Besten
Großer Bahnhof zum 90. Geburtstag
Der steinige Weg in die Marktwirtschaft
4. Dagstuhl-Seminar zum Geometrischen Modellieren
Geisteswissenschaften - wozu?
Vom Untergang einer Diktatur
In Chemnitz wird tüchtig geschafft!
Erfolgreich mit Fasern der ganz besonderen Art
Zukunftschancen der Unis in internationaler Perspektive
200 rohe Eier geworfen und wieder aufgefangen
Pech und Glück liegen auf der Matte eng beieinander
Inmotion- immer in Bewegung
Rauschende Uni-Ballnacht im Renaissance Chemnitz Hotel
4 mal im Jahr erscheinende Zeitschrift über aktuelle Themen der TU Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2002-12-19
2021-03-29
PeriodicalPart
publishedVersion
urn:nbn:de:bsz:ch1-200201697
TU-Spektrum
http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-63097
ger
3/1999
urn:nbn:de:bsz:ch1-qucosa-63097
info:eu-repo/semantics/openAccess
1
https://monarch.qucosa.de/api/qucosa%3A17950/zip/
urn:nbn:de:bsz:ch1-200201697
oai:qucosa:de:qucosa:1795
2021-03-27T15:39:10Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Balancing the Use of Technology and Traditional Approaches in TeachingMathematics within Business Courses
Mehryar
Nooriafshar
510
510
SD 2009
Technologie
quantitativ
Unterricht
traditionell
Technology
Quantitative
Teaching
Traditional
Technologies associated with modern computing are being commonly used in education. Over the past few years, the usage has increased considerably. This increase is also attributed to the availability of more improved technology products and services at much lower costs.
As a result, many successful educational multimedia products have been developed which have made significant contributions to learning and teaching mathematics at various levels. However, it is not always clear what exactly the position of technology in education is. In
other words, to what extent does the technology-aided means of learning enhance learning and add value to the conventional materials? How are they supposed to supersede or excel
the learning effectiveness of traditional methods of teaching? This paper explores the possibilities of utilizing the latest technologies such as Virtual Reality (VR) environments and Tablet PCs in conjunction with the traditional approaches and concepts in creating a balanced and more effective learning and teaching conditions. It also
demonstrates how the creation of a situation where ‘one cannot see the wood for the trees’ can be avoided by striking the right balance.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80771
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 450 - 453
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 450 - 453
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1795/zip/
urn:nbn:de:bsz:14-qucosa-80771
371764270
oai:qucosa:de:qucosa:1796
2021-03-27T15:39:10Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Chapter-spanning Review: Teaching Method for Networking in Math Lessons
Swetlana
Nordheimer
510
510
SD 2009
Vernetzungen
Verbindungen
Sekundarstufe
Lehrexperiment
Problemlösen
Problemstellung
networking
connections
secondary
teaching experiment
problem-solving
problem-posing
Central to this article is networking in math lessons, whereby concentration is placed on the construction of a student-focused teaching method for the networking of mathematical knowledge in the lower secondary. Firstly, normative standards and descriptive results will be compared. Secondly, several already existing teaching methods for networking in math lessons will be added to the method of „chapter-spanning task variation“. Using this method, attention is be placed on the integration of mathematical content and specific
social netowrk-form (e.g. teacher led classes, group-work etc.). This paper will be concluded with the presentation of the testing of the method in the school context).
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80786
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 454 - 458
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 454 - 458
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1796/zip/
urn:nbn:de:bsz:14-qucosa-80786
371764440
oai:qucosa:de:qucosa:17956
2021-03-29T09:38:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for the Stokes problem: Anisotropic and isotropic discretizations
A posteriori Fehlerschätzer für das Stokes Problem: Anisotrope und isotrope Diskretisierungen
Emmanuel
Creusé
Dr.
Gerd
Kunert
Dr.
Serge
Nicaise
Prof.
510
510
Stokes problem
anisotropic solution
error estimator
stretched elements
The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail.
Our analysis covers two- and three-dimensional domains, conforming and nonconforming discretizations as well as different elements.
This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented.
Lower and upper error bounds form the main result with minimal assumptions on the elements. The lower error bound is uniform with respect to the mesh anisotropy with the exception of nonconforming 3D discretizations made of pentahedra or hexahedra. The upper error bound depends on a proper alignment of the anisotropy of the mesh which is a common feature of anisotropic error estimation.
In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally. Some of the corresponding results seem to be novel (in particular for 3D domains), and cover element pairs of practical importance.
The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2003-01-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200300057
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17956/zip/
urn:nbn:de:bsz:ch1-200300057
oai:qucosa:de:qucosa:17960
2021-03-29T09:38:47Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:510
openaire
Approximation Methods for Two Classes of Singular Integral Equations
Alexander
Rogozhin
Dipl.-Math.
510
510
Banach algebra methods
Cauchy singular integral equation
Collocation method
Discrete convergence theory
Multigrid iteration methods
Radiation transfer problem
Splitting property
Stability
The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too.
In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation
we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigated.
Die Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert.
Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Peter
Junghanns
Prof. Dr.
Gennadi
Vainikko
Prof. Dr.
Steffen
Roch
PD Dr.
2002-06-10
2002-12-13
2003-01-29
2021-03-29
doctoralThesis
urn:nbn:de:swb:ch1-200300091
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
4
https://monarch.qucosa.de/api/qucosa%3A17960/zip/
urn:nbn:de:swb:ch1-200300091
oai:qucosa:de:qucosa:17958
2021-03-29T09:38:45Z
qucosa:ubc
doc-type:lecture
has-source-swb:false
open_access
ddc:510
openaire
Illustration of stochastic processes and the finite difference method in finance
Tino
Kluge
510
510
Animation
Black-Scholes-Modell
Finite-Differenzen-Methode
Pfad <Mathematik>
Stochastik
Stochastische partielle Differentialgleichung
Stochastischer Prozess
The presentation shows sample paths of stochastic processes in form of animations. Those stochastic procsses are usually used to model financial quantities like exchange rates, interest rates and stock prices.
In the second part the solution of the Black-Scholes PDE using the finite difference method is illustrated.
Der Vortrag zeigt Animationen von Realisierungen stochstischer Prozesse, die zur Modellierung von Groessen im Finanzbereich haeufig verwendet werden
(z.B. Wechselkurse, Zinskurse, Aktienkurse).
Im zweiten Teil wird die Loesung der Black-Scholes
Partiellen Differentialgleichung mittels Finitem Differenzenverfahren graphisch veranschaulicht.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2003-01-22
2021-03-29
lecture
urn:nbn:de:bsz:ch1-200300079
eng
info:eu-repo/semantics/openAccess
49
https://monarch.qucosa.de/api/qucosa%3A17958/zip/
urn:nbn:de:bsz:ch1-200300079
oai:qucosa:de:qucosa:17959
2021-03-29T09:38:46Z
qucosa:ubc
doc-type:masterThesis
has-source-swb:false
open_access
ddc:510
status-type:acceptedVersion
openaire
Pricing derivatives in stochastic volatility models using the finite difference method
Tino
Kluge
Heston modell
lokaler Fehler
nicht-uniformes Gitternetz
stochastic volatility
510
510
Finanzmathematik
Finite-Differenzen-Methode
The Heston stochastic volatility model is one extension of the Black-Scholes model which describes the money markets more accurately so that more realistic prices for derivative products are obtained. From the stochastic differential equation of the underlying financial product a partial differential equation (p.d.e.) for the value function of an option can be derived. This p.d.e. can be solved with the finite difference method (f.d.m.). The stability and consistency of the method is examined. Furthermore a boundary condition is proposed to reduce the numerical error. Finally a non uniform structured grid is derived which is fairly optimal for the numerical result in the most interesting point.
Das stochastische Volatilitaetsmodell von Heston ist eines der Erweiterungen des Black-Scholes-Modells.
Von der stochastischen Differentialgleichung fuer den unterliegenden Prozess kann eine partielle Differentialgleichung fuer die Wertfunktion einer Option abgeleitet werden. Es wird die Loesung mittels Finiter Differenzenmethode untersucht
(Konsistenz, Stabilitaet). Weiterhin wird eine Randbedingung und ein spezielles nicht-uniformes Netz vorgeschlagen, was zu einer starken Reduzierung des numerischen Fehlers der Wertfunktion in einem ganz bestimmten Punkt fuehrt.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2002-08-21
2003-01-23
2021-03-29
masterThesis
acceptedVersion
urn:nbn:de:bsz:ch1-200300086
eng
info:eu-repo/semantics/openAccess
Diplom
Technische Universität Chemnitz
Chemnitz
Fakultät für Mathematik
0
https://monarch.qucosa.de/api/qucosa%3A17959/zip/
urn:nbn:de:bsz:ch1-200300086
oai:qucosa:de:qucosa:1797
2021-03-27T15:38:53Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Students’ knowledge of Application of Mathematics – From Diagnostics toInnovations
Reinhard
Oldenburg
510
510
SD 2009
Rechnergestützte Mathematik
Fundamentale Ideen
Schülervorstellungen
computer based mathematics
fundamental ideas
student conceptions
The results of a questionnaire that should reveal students’ knowledge about the use of computers in mathematics and the relevance of applications of mathematics in our society clearly show that current
math teaching does not provide adequate ideas about the importance of computers. We describe the results and give examples of mathematical activities that are suitable to both foster mathematical
concepts and widen the mathematical view. Possible changes in the curriculum are discussed.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80794
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 459 - 463
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 459 - 463
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1797/zip/
urn:nbn:de:bsz:14-qucosa-80794
371764580
oai:qucosa:de:qucosa:1798
2021-03-27T15:38:54Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
From Physical Model To Proof For Understanding Via DGS:Interplay Among Environments
Iman M.
Osta
510
510
SD 2009
Geometrie
Dynamische Geometrie Software
Beweis
Kegelschnitte
Mathematik in der Sekundarstufe
Lehramts-studierende
geometrisches Denken
Geometry
Dynamic Geometry Software
Proof
Conics
Secondary Mathematics
Pre-Service Teachers
Geometric Thinking
The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the
physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-07
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80806
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 464 - 468
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 464 - 468
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1798/zip/
urn:nbn:de:bsz:14-qucosa-80806
371764696
oai:qucosa:de:qucosa:1799
2021-03-27T15:38:49Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Using ClassPad-technology in the education of students of electricalengineering (Fourier- and Laplace-Transformation)
Ludwig
Paditz
510
510
SD 2009
ClassPad
CAS Software
Fourier-Transformation
Laplace-Transformation
lineare Differentialgleichung
gewöhnliche Dgl
schnelle Fourier Transformation
FFT
Fourier Polynom
Tabellenkalkulation
grafische Darstellung
Studierende der Elektrotechnik
ClassPad
CAS software
Fourier transform
Laplace transform
linear differential equation
ODE
fast Fourier transform
FFT
Fourier polynomial
spreadsheet application
graphical representation
students of electrical engineering
By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields
of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the
Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-09
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80814
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 469 - 474
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 469 - 474
info:eu-repo/semantics/openAccess
1
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urn:nbn:de:bsz:14-qucosa-80814
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oai:qucosa:de:qucosa:17990
2021-03-29T09:39:12Z
qucosa:ubc
doc-type:doctoralThesis
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
A Direct Approach for the Segmentation of Unorganized Points and Recognition of Simple Algebraic Surfaces
Ein direktes Verfahren zur Segmentierung unstrukturierter Punktdaten und Bestimmung algebraischer Oberflächenelemente
Marek
Vanco
Dipl.-Inf. (SK)
510
510
004
004
algebraic surfaces
reconstruction
segmentation
surface fitting
In Reverse Engineering a physical object is digitally
reconstructed from a set of boundary points. In the segmentation phase
these points are grouped into subsets to facilitate consecutive steps
as surface fitting. In this thesis we present a segmentation
method with subsequent classification of simple algebraic surfaces.
Our method is direct in the sense that it operates directly on the
point set in contrast to other approaches that are based on a
triangulation of the data set.
The reconstruction process involves a fast algorithm for $k$-nearest
neighbors search and an estimation of first and second order surface
properties. The first order segmentation, that is based on normal
vectors, provides an initial subdivision of the surface and detects
sharp edges as well as flat or highly curved areas. One of the main
features of our method is to proceed by alternating the steps of
segmentation and normal vector estimation. The second order
segmentation subdivides the surface according to principal curvatures
and provides a sufficient foundation for the classification of simple
algebraic surfaces. If the boundary of the original object contains
such surfaces the segmentation is optimized based on the result of a
surface fitting procedure.
Im Reverse Engineering wird ein existierendes Objekt aus einer Menge
von Oberflächenpunkten digital rekonstruiert. Während der
Segmentierungsphase werden diese Punkte in Teilmengen zusammengefügt,
um die nachfolgenden Schritte wie Flächenerkennung (surface fitting)
zu vereinfachen. Wir präsentieren in dieser Arbeit eine Methode zur
Segmentierung der Punkte und die anschließende Klassifikation
einfacher algebraischen Flächen. Unser Verfahren ist direkt in dem
Sinne, dass es direkt an den Punkten arbeitet, im Gegensatz zu
anderen Verfahren, die auf einer Triangulierung der Punktmenge
basieren.
Der Rekonstruktionsprozess schließt einen neuen Algorithmus zur
Berechnung der k-nächsten Nachbarn eines Oberflächenpunktes und
Verfahren zur Schätzung der Flächeneigenschaften ersten und zweiten
Grades ein. Die normalenbasierte Segmentierung (Segmentierung ersten
Grades) liefert eine Aufteilung des Objektes und detekiert scharfe
Kanten, sowie flache oder stark gekrümmte Gebiete des Objektes. Ein
zentrales Element unserer Methode ist die Wiederholung der Schritte
der Segmentierung und der Schätzung der Normalen. Erst die Iteration
ermöglicht die Schätzung der Normalen in der benötigten Genauigkeit
und die Generierung einer zufriedenstellender Segmentierung. Die
Segmentierung zweiten Grades teilt die Oberfläche nach den
Hauptkrümmungen auf und bietet eine zuverlässige Grundlage für die
Klassifizierung einfacher algebraischen Flächen. Falls der Rand des
Ausgangsobjektes solche Flächen enthält, wird der
Segmentierungsprozess auf der Grundlage des Ergebnisses der
Flächenerkennungsprozedur optimiert.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Guido
Brunnett
Prof. Dr.
Guido
Brunnett
Prof. Dr.
Beat
Brüderlin
Prof. Dr.
Hans
Hagen
Prof. Dr.
2002-10-10
2003-04-04
2003-06-02
2021-03-29
doctoralThesis
urn:nbn:de:swb:ch1-200300486
eng
info:eu-repo/semantics/openAccess
thesis.doctoral
Technische Universität Chemnitz
Chemnitz
Fakultät für Informatik
2
https://monarch.qucosa.de/api/qucosa%3A17990/zip/
urn:nbn:de:swb:ch1-200300486
oai:qucosa:de:qucosa:1800
2021-03-27T15:36:48Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
The Learning of Mathematics for Limited English Proficient Learners:Preparation of Doctoral Level Candidates
Theresa
Perez
David K.
Pugalee
510
510
SD 2009
Sprache
Kommunikation
Lehrplan
language
communication
curriculum
Across the United States, there is a growing number of students for whom English is not their first language. These students experience many challenges adjusting to new educational environments. These students are often denied access to the full curriculum in mathematics
(Reyes & Fletcher, 2003) and the resulting opportunities for higher level educational experiences in mathematics and the resulting higher economic employment options. Educators need support in understanding and responding to the linguistic and cultural challenges that these students face in learning mathematics. A course entitled Language, Culture, Mathematics and the LEP Learner is part of the doctoral courses available to Curriculum and Instruction students at UNC Charlotte. The course focuses on theoretical and applied models of teaching and learning mathematics for English as Second Language Learners. Research and current practice are reviewed with an emphasis on the design, implementation, and assessment of instruction for this population of learners. A qualitative analysis of students’ final research projects using narrative analysis methodologies showed that students (1) position issues within a larger sociocultural framework (2) advocate for the negotiation of pedagogical principles that blend language learning strategies with effective mathematics pedagogy and (3) identify assessment policies and processes that are supportive and limiting for these learners.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-09
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80823
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 481 - 485
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 481 - 485
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1800/zip/
urn:nbn:de:bsz:14-qucosa-80823
371765242
oai:qucosa:de:qucosa:1801
2021-03-27T15:36:42Z
qucosa:slub
doc-type:conferenceObject
has-source-swb:true
open_access
ddc:510
openaire
Cooperative Learning and Peer Tutoring to Promote Students’ Mathematics Education
Angela
Pesci
510
510
SD 2009
Gemeinschaftliches Lernen
kooperative Lernformen
Nachhilfe
Mathematikunterricht
Mathematische Hochschullehre
Cooperative Learning
Peer Tutoring
Students'' Mathematics Education
On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve.
Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-09
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80833
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 486 - 490
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 486 - 490
info:eu-repo/semantics/openAccess
1
https://slub.qucosa.de/api/qucosa%3A1801/zip/
urn:nbn:de:bsz:14-qucosa-80833
371765358
oai:qucosa:de:qucosa:1802
2021-03-27T15:36:43Z
qucosa:slub
doc-type:conferenceObject
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Building leadership capacity in the development and sharing of mathematics learning resources, across disciplines, across universities
Anne L.
Porter
510
510
SD 2009
Führungskapazität
gemeinsame Nutzung der Mathematik-Unterrichtsressourcen
Lernunterstützung
Führung
Leadership capacity
sharing mathematics teaching resources
learning support
leadership
In this paper we examine an Australian project in which we seek to develop leadership capacity in staff and students throughout the country, such that they may contribute to and lead others to contribute to the development and sharing of learning support resources for mathematics and statistics across disciplines and universities. One of the tangible outputs is a set of video based learning support resources that can be embedded in subjects across
disciplines and shared across institutions. However the guiding aim is to develop leadership capacity, in its simplest form leading others to lead others to contribute to the project. Leadership may also be developed and exercised across different aspects of the project
whether it be mapping needs, drawing together disciplines groups, finding ways to recognise and reward those engaged in the process, developing resources and the associated skills, ensuring copyright adherence, creating learning designs for optimal use of resources,
evaluating the impact on student outcomes, peer review and the dissemination of findings.
Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
Dresden
Zellescher Weg 18, 01069 Dresden, Germany
HTW Dresden
Dresden
Dresden
2012-05-09
2021-03-27
conferenceObject
urn:nbn:de:bsz:14-qucosa-80842
Proceedings of the tenth international conference Models in developing mathematics education
http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79236
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 491 - 495
eng
Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 491 - 495
info:eu-repo/semantics/openAccess
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urn:nbn:de:bsz:14-qucosa-80842
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