TY - JOUR
AU - Winkler, Michael
ID - 35617
JF - Applied Mathematics Letters
TI - Boundedness in a three-dimensional Keller-Segel-Stokes system with subcritical sensitivity.
VL - 112
ER -
TY - JOUR
AU - Winkler, Michael
ID - 35613
JF - Transactions of the American Mathematical Society
TI - Does spatial homogeneity ultimately prevail in nutrient taxis systems? A paradigm for structure support by rapid diffusion decay in an autonomous parabolic flow.
VL - 374
ER -
TY - JOUR
AU - Rösler, Margit
AU - Voit, Michael
ID - 37659
IS - 3
JF - Proceedings of the American Mathematical Society
KW - Applied Mathematics
KW - General Mathematics
SN - 0002-9939
TI - Positive intertwiners for Bessel functions of type B
VL - 149
ER -
TY - JOUR
AU - Tao, Youshan
AU - Winkler, Michael
ID - 35603
JF - Journal of Functional Analysis
TI - A fully cross-diffusive two-component evolution system: Existence and qualitative analysis via entropy-consistent thin-film-type approximation.
VL - 281
ER -
TY - JOUR
AU - Tao, Youshan
AU - Winkler, Michael
ID - 35606
JF - Nonlinear Analysis, Theory, Methods and Applications
TI - The dampening role of large repulsive convection in a chemotaxis system modeling tumor angiogenesis.
VL - 208
ER -
TY - JOUR
AU - Wang, Yulan
AU - Winkler, Michael
AU - Xiang, Zhaoyin
ID - 35612
JF - Science China Mathematics
TI - Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption.
VL - 64
ER -
TY - JOUR
AU - Ding, Mengyao
AU - Winkler, Michael
ID - 35601
JF - Nonlinear Differential Equatiions and Applicatiions
TI - Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities.
VL - 28
ER -
TY - JOUR
AU - Tao, Youshan
AU - Winkler, Michael
ID - 35605
JF - Communications in Mathematical Sciences
TI - Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.
VL - 19
ER -
TY - JOUR
AU - Tao, Youshan
AU - Winkler, Michael
ID - 35604
JF - SIAM Journal on Mathematical Analysis
TI - Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection.
VL - 53
ER -
TY - JOUR
AU - Wang, Yulan
AU - Winkler, Michael
AU - Xiang, Zhaoyin
ID - 35610
JF - Communications in Partial Differential Equations
TI - Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.
VL - 46
ER -
TY - JOUR
AU - Wang, Yulan
AU - Winkler, Michael
AU - Xiang, Zhaoyin
ID - 35611
JF - Advances in Nonlinear Analysis
TI - Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation
VL - 10
ER -
TY - JOUR
AU - Tao, Youshan
AU - Winkler, Michael
ID - 35608
IS - --A
JF - Discrete and Continuous Dynamical Systems
TI - Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction
VL - 41
ER -
TY - JOUR
AB - In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields.
AU - Klüners, Jürgen
AU - Komatsu, Toru
ID - 34840
IS - 329
JF - Mathematics of Computation
KW - Applied Mathematics
KW - Computational Mathematics
KW - Algebra and Number Theory
SN - 0025-5718
TI - Imaginary multiquadratic number fields with class group of exponent $3$ and $5$
VL - 90
ER -
TY - JOUR
AB - Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields.
AU - Kirschmer, Markus
AU - Narbonne, Fabien
AU - Ritzenthaler, Christophe
AU - Robert, Damien
ID - 34912
IS - 333
JF - Mathematics of Computation
KW - Applied Mathematics
KW - Computational Mathematics
KW - Algebra and Number Theory
SN - 0025-5718
TI - Spanning the isogeny class of a power of an elliptic curve
VL - 91
ER -
TY - JOUR
AB - This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples.
AU - Burban, Igor
AU - Abedin, R.
ID - 44329
IS - 2
JF - Communications in Mathematical Physics
TI - Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
VL - 387
ER -
TY - JOUR
AB - The role of domain-specific content knowledge is discussed controversially for the early childhood context. Therefore, this review aims at untangling the research on domain-specific content knowledge for early childhood educators by systematically reviewing the conceptual and operational definition of and results on early childhood educators' content knowledge in different domains. Using the scientific databases ERIC, PsycInfo and Web of Sciences, we identified 36 studies on early childhood educators' domain-specific content knowledge. By comparing these studies, we found that conceptualizations of early childhood educators' content knowledge move on a continuum between a scientific related perspective and a practice related perspective. The scientific related perspective defines content knowledge as the knowledge of key concepts, facts and rules of the domain integrating knowledge taught in primary, secondary or upper secondary school. The practice related perspective includes knowledge of key concepts, facts and rules of the domain limited to the knowledge explicitly relevant for teaching in early childhood education as well as selected domain-specific knowledge of children and teaching. Our review shows that the results and implications drawn by the study authors depend on how these authors conceptualize early childhood educators' content knowledge on this continuum. Further research, therefore, needs to consider carefully how early childhood educators' content knowledge is conceptualized. The paper further discusses gaps in this research field, such as validating methods for measuring early childhood educators' content knowledge or implementing more rigorous experimental designs to examine effects of early childhood educators' content knowledge.
AU - Bruns, Julia
AU - Gasteiger, Hedwig
AU - Strahl, Carolin
ID - 34822
IS - 2
JF - Review of Education
KW - content knowledge
KW - domain-specific learning
KW - early childhood education
KW - teacher knowledge
SN - 2049-6613
TI - Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review
VL - 9
ER -
TY - JOUR
AU - Bruns, Julia
AU - Schopferer, T.
ID - 45687
JF - . TPS – Theorie und Praxis der Sozialpädagogik
TI - Eine mustergültige Wissenschaft
VL - 11
ER -
TY - CONF
AU - Jensen, Solveig
AU - Gasteiger, Hedwig
AU - Bruns, Julia
ED - Inprasitha, Maitree
ED - Changsri, Narumon
ED - Boonsena, Nisakorn
ID - 36527
T2 - Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education
TI - Place value and regrouping as seperate constructs of place value understanding
VL - 3
ER -
TY - JOUR
AU - Bruns, Julia
AU - Gasteiger, Hedwig
AU - Strahl, Carolin
ID - 34823
IS - 2
JF - Review of Education
SN - 2049-6613
TI - Context and Implications Document for: Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review
VL - 9
ER -
TY - CONF
AU - Jensen, Solveig
AU - Gasteiger, Hedwig
AU - Bruns, Julia
ID - 36536
T2 - Beiträge zum Mathematikunterricht 2021
TI - Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte
ER -
TY - JOUR
AU - Schönherr, Johanna
AU - Blomberg, J.
AU - Schukajlow, S.
AU - Leopold, C.
ID - 45342
JF - Contemporary Educational Psychology
TI - Do emotions and prior performance facilitate the use of the learner-generated drawing strategy? Effects of enjoyment, anxiety, and intramathematical performance on the use of the drawing strategy and modelling performance
VL - 65
ER -
TY - JOUR
AU - Schönherr, Johanna
AU - Schukajlow, S.
AU - Blomberg, J.
AU - Leopold, C.
ID - 45333
JF - Mathematical Thinking and Learning
TI - Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry
ER -
TY - JOUR
AU - Schönherr, Johanna
AU - Schukajlow, S.
AU - Blomberg, J.
AU - Leopold, C.
ID - 45343
JF - Learning and Instruction
TI - The role of strategy-based motivation in mathematical problem solving: The case of learner-generated drawings
VL - 80
ER -
TY - JOUR
AU - Schönherr, Johanna
AU - Schukajlow, S.
AU - Blomberg, J.
ID - 45335
JF - mathematik lehren
TI - Was ist eine gute Skizze? Strategiewissen beim mathematischen Modellieren im Bereich der Geometrie fördern
VL - 224
ER -
TY - JOUR
AU - Black, Tobias
AU - Fuest, Mario
AU - Lankeit, Johannes
ID - 34673
IS - 3
JF - Zeitschrift für angewandte Mathematik und Physik
KW - Applied Mathematics
KW - General Physics and Astronomy
KW - General Mathematics
SN - 0044-2275
TI - Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems
VL - 72
ER -
TY - JOUR
AU - Black, Tobias
AU - Wu, Chunyan
ID - 34675
IS - 4
JF - Zeitschrift für angewandte Mathematik und Physik
KW - Applied Mathematics
KW - General Physics and Astronomy
KW - General Mathematics
SN - 0044-2275
TI - Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation
VL - 72
ER -
TY - JOUR
AU - Dröse, Jennifer
AU - Prediger, S.
AU - Neugebauer, P.
AU - Danhier, R. D.
AU - Mertins, B.
ID - 45381
JF - International Electronic Journal of Mathematics Education, 16(1), em0625
TI - Investigating students' processes of noticing and interpreting syntactic language features in word problem solving through eye-tracking
ER -
TY - JOUR
AU - Dröse, Jennifer
AU - Prediger, S.
ID - 45380
JF - Studies in Educational Evaluation, 68 (100953)
TI - Identifying obstacles is not enough for everybody – Differential efficacy of an intervention fostering fifth graders’ comprehension for word problems
ER -
TY - JOUR
AU - Häsel-Weide, Uta
AU - Seitz, Simone
AU - Wallner, Melina
AU - Wilke, Yannik
AU - Heckmann, Lara
ID - 31578
IS - 1
JF - QfI - Qualifizierung für Inklusion. Online-Zeitschrift zur Forschung über Aus-, Fort- und Weiterbildung pädagogischer Fachkräfte
TI - Mit Aufgaben im inklusiven Mathematikunterricht professionell umgehen - Erkenntnisse einer Interviewstudie mit Lehrpersonen der Sekundarstufe
VL - 3
ER -
TY - CONF
AU - Hattermann, Mathias
AU - Häsel-Weide, Uta
AU - Wallner, Melina
ED - Inprasitha, M.
ED - Changsri, N.
ED - Boonsena, N.
ID - 31583
T2 - Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education
TI - Conceptualiziation processes of 6th graders for rotational symmetry
VL - 3
ER -
TY - CONF
AB - The first order optimality conditions of optimal control problems (OCPs) can
be regarded as boundary value problems for Hamiltonian systems. Variational or
symplectic discretisation methods are classically known for their excellent
long term behaviour. As boundary value problems are posed on intervals of
fixed, moderate length, it is not immediately clear whether methods can profit
from structure preservation in this context. When parameters are present,
solutions can undergo bifurcations, for instance, two solutions can merge and
annihilate one another as parameters are varied. We will show that generic
bifurcations of an OCP are preserved under discretisation when the OCP is
either directly discretised to a discrete OCP (direct method) or translated
into a Hamiltonian boundary value problem using first order necessary
conditions of optimality which is then solved using a symplectic integrator
(indirect method). Moreover, certain bifurcations break when a non-symplectic
scheme is used. The general phenomenon is illustrated on the example of a cut
locus of an ellipsoid.
AU - Offen, Christian
AU - Ober-Blöbaum, Sina
ID - 22894
KW - optimal control
KW - catastrophe theory
KW - bifurcations
KW - variational methods
KW - symplectic integrators
SN - 2405-8963
TI - Bifurcation preserving discretisations of optimal control problems
VL - 54(19)
ER -
TY - CONF
AU - Ridderbusch, Steffen
AU - Offen, Christian
AU - Ober-Blöbaum, Sina
AU - Goulart, Paul
ID - 21572
T2 - 2021 60th IEEE Conference on Decision and Control (CDC)
TI - Learning ODE Models with Qualitative Structure Using Gaussian Processes
ER -
TY - CONF
AB - We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.
AU - Vertovec, Nikolaus
AU - Ober-Blöbaum, Sina
AU - Margellos, Kostas
ID - 21592
TI - Multi-objective minimum time optimal control for low-thrust trajectory design
ER -
TY - CONF
AU - Jiménez, F.
AU - Ober-Blöbaum, Sina
ID - 29868
T2 - Nichtlineare Sci 31
TI - Fractional Damping Through Restricted Calculus of Variations
VL - 46
ER -
TY - JOUR
AB - ZusammenfassungZu den ersten geometrischen Begriffen, die Kinder bereits im Elementar- und Primarbereich lernen, zählen u. a. Viereck, Rechteck und Quadrat. Studien zeigen, dass Lernende bereits früh individuelle Vorstellungen, sog. individuelle Begriffskonzepte, zu diesen Begriffen aufbauen. Zwar wird die Entwicklung von Begriffsverständnis in verschiedenen mathematikdidaktischen Stufenmodellen dargestellt, diese sind jedoch generisch und beschreiben nicht explizit die Entwicklung der ersten individuellen Begriffskonzepte von Lernenden zu Viereck, Rechteck und Quadrat. Aus empirischer Sicht liegen verschiedene Studien vor, die einzelne Aspekte der individuellen Begriffskonzepte von Lernenden unterschiedlicher Altersgruppen zu diesen Begriffen ausleuchten. Um Begriffsbildungsprozesse aus empirischer Sicht detaillierter entlang der jeweils vorherrschenden individuellen Begriffskonzepte zu beschreiben, fehlen insbesondere Studien in der Grundschule, die alle vier Klassenstufen betrachten und dabei differenzierte Erkenntnisse zu verschiedenen theoretischen Indikatoren des Begriffsverständnisses liefern. Daher geht die vorliegende Studie der Frage nach, welches Verständnis der Begriffe Viereck, Rechteck und Quadrat Schülerinnen und Schüler der Jahrgangsstufen 1, 2, 3 und 4 zeigen. Dazu wurde eine Quasi-Längsschnittstudie mit N = 456 Grundschulkindern (ca. 100 pro Jahrgangsstufe) durchgeführt. Die Ergebnisse geben detaillierte Einblicke in die individuellen Begriffskonzepte der Lernenden und zeigen, dass Lernende zunehmend Eigenschaften der Figuren berücksichtigen, jedoch individuelle Begriffskonzepte über lange Zeit auch prototypisch geprägt sind. Implikationen dieser Ergebnisse für Forschung und Praxis werden diskutiert.
AU - Bruns, Julia
AU - Unterhauser, Elisabeth
AU - Gasteiger, Hedwig
ID - 34827
IS - 2
JF - Journal für Mathematik-Didaktik
KW - Education
KW - General Mathematics
SN - 0173-5322
TI - Geometrisches Begriffsverständnis in der Grundschule am Beispiel der Begriffe Viereck, Rechteck und Quadrat
VL - 42
ER -
TY - JOUR
AU - Prediger, Susanne
AU - Dröse, Jennifer
ID - 45382
JF - Lernen und Lernstörungen, 10(2)
TI - Fehlerbearbeitung bei mathematischen Textaufgaben – Sprachliche und strategische Fehlerursachen und ihre Bearbeitung
ER -
TY - JOUR
AB - AbstractMathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded support sessions (N = 36), we constructed a process model that divides consultations into four ideal–typical phases. In the individual consultations, forward or backward leaps occur, but overall the model seems to describe the data well. A high intercoder reliability shows that it can be applied consistently on real data by different researchers. An analysis of the consultations between students and tutors shows that both mainly work on past attempts or thoughts of the students to solve the exercise or problems and on concrete strategies to solve a problem within the session. In contrast, very little time is dedicated to summarizing and reflecting the solution. The data allows for a more in-depth discussion of what constitutes quality in advising processes and how it might be further explored. Practically, the model may structure support sessions and help in focussing on different goals in different phases.
AU - Schürmann, Mirko
AU - Panse, Anja
AU - Shaikh, Zain
AU - Biehler, Rolf
AU - Schaper, Niclas
AU - Liebendörfer, Michael
AU - Hilgert, Joachim
ID - 35702
IS - 1
JF - International Journal of Research in Undergraduate Mathematics Education
KW - Education
KW - Mathematics (miscellaneous)
SN - 2198-9745
TI - Consultation Phases in Mathematics Learning and Support Centres
VL - 8
ER -
TY - JOUR
AU - Guillarmou, Colin
AU - Hilgert, Joachim
AU - Weich, Tobias
ID - 31263
JF - Annales Henri Lebesgue
SN - 2644-9463
TI - High frequency limits for invariant Ruelle densities
VL - 4
ER -
TY - JOUR
AU - Brennecken, Dominik
AU - Hilgert, Joachim
AU - Ciardo, Lorenzo
ID - 36271
IS - 2
JF - Journal of Lie Theory
TI - Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)
VL - 31
ER -
TY - BOOK
ED - Hilgert, Joachim
ED - Hilgert, I.
ID - 51493
TI - Mathematik - Ein Reiseführer 2. Auflage
ER -
TY - GEN
AU - Hilgert, Joachim
AU - Weich, Tobias
AU - Wolf, L.
ID - 51503
TI - Higher-rank quantum-classical correspondence
ER -
TY - GEN
AU - Hilgert, Joachim
ID - 51556
T2 - Mathematische Semesterberichte
TI - Philip Ording: 99 Variations on a Proof. Princeton University Press 2019
VL - 68
ER -
TY - GEN
AU - Hilgert, Joachim
ID - 51555
T2 - Mathematische Semesterberichte
TI - Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020
VL - 68
ER -
TY - CHAP
AU - Rezat, Sebastian
AU - Schacht, Florian
AU - Häsel-Weide, Uta
ED - Clark-Wilson, A.
ED - Donevska-Todorova, A.
ED - Faggiano, E.
ED - Trgalová , J.
ED - Weigang, H.-G.
ID - 34161
T2 - Mathematics Education in the Digital Age. Learning, Practice and Theory
TI - Challenges of making sense of tasks and automated feedback in digital mathematics textbooks
ER -
TY - JOUR
AB - We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of the breaking of umbilic bifurcations by nonysmplectic integrators. We discover extra structure induced from certain types of boundary value problems, including classical Dirichlet problems, that is useful to locate bifurcations. Geodesics connecting two points are an example of a Hamiltonian boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator that easily computes geodesics and their bifurcations. Finally, we study the periodic pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian systems. It is not preserved by either symplectic on nonsymplectic integrators, but in some circumstances symplecticity greatly reduces the error.
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19938
IS - 6
JF - Foundations of Computational Mathematics
TI - Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
VL - 20
ER -
TY - JOUR
AU - Kreusser, Lisa Maria
AU - McLachlan, Robert I
AU - Offen, Christian
ID - 19939
IS - 5
JF - Nonlinearity
SN - 0951-7715
TI - Detection of high codimensional bifurcations in variational PDEs
VL - 33
ER -
TY - CHAP
AB - Many dynamical systems possess symmetries, e.g. rotational and translational invariances of mechanical systems. These can be beneficially exploited in the design of numerical optimal control methods. We present a model predictive control scheme which is based on a library of precomputed motion primitives. The primitives are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim primitives as relative equilibria w.r.t. this symmetry, play a crucial role in the algorithm. The approach is illustrated using an academic mobile robot example.
AU - Flaßkamp, Kathrin
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
ED - Junge, Oliver
ED - Schütze, Oliver
ED - Froyland, Gary
ED - Ober-Blöbaum, Sina
ED - Padberg-Gehle, Kathrin
ID - 17411
SN - 2198-4182
T2 - Advances in Dynamics, Optimization and Computation
TI - Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach
ER -
TY - JOUR
AB - Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.
AU - Klus, Stefan
AU - Nüske, Feliks
AU - Hamzi, Boumediene
ID - 21819
JF - Entropy
SN - 1099-4300
TI - Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
ER -
TY - JOUR
AU - Hochmuth, Reinhard
AU - Liebendörfer, Michael
AU - Biehler, Rolf
AU - Eichler, Andreas
ID - 16964
JF - Neues Handbuch Hochschullehre
TI - Das Kompetenzzentrum Hochschuldidaktik Mathematik (khdm)
VL - 95
ER -
TY - JOUR
AB - Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objectives into such problems. The challenge with such problems, however, is that the dimensions of the solution sets—the so-called Pareto sets and fronts—grow with the number of objectives. It is thus no longer possible to compute or to approximate the entire solution set of a given problem that contains many (e.g. more than three) objectives. On the other hand, the computation of single solutions (e.g. via scalarization methods) leads to unsatisfying results in many cases, even if user preferences are incorporated. In this article, the Pareto Explorer tool is presented—a global/local exploration tool for the treatment of many-objective optimization problems (MaOPs). In the first step, a solution of the problem is computed via a global search algorithm that ideally already includes user preferences. In the second step, a local search along the Pareto set/front of the given MaOP is performed in user specified directions. For this, several continuation-like procedures are proposed that can incorporate preferences defined in decision, objective, or in weight space. The applicability and usefulness of Pareto Explorer is demonstrated on benchmark problems as well as on an application from industrial laundry design.
AU - Schütze, Oliver
AU - Cuate, Oliver
AU - Martín, Adanay
AU - Peitz, Sebastian
AU - Dellnitz, Michael
ID - 10596
IS - 5
JF - Engineering Optimization
SN - 0305-215X
TI - Pareto Explorer: a global/local exploration tool for many-objective optimization problems
VL - 52
ER -
TY - JOUR
AB - We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.
AU - Klus, Stefan
AU - Nüske, Feliks
AU - Peitz, Sebastian
AU - Niemann, Jan-Hendrik
AU - Clementi, Cecilia
AU - Schütte, Christof
ID - 16288
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
TI - Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
VL - 406
ER -
TY - CHAP
AB - In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, proper orthogonal decomposition (POD) has been most widely used in the past in order to derive such models. Due to the huge advances concerning both theory as well as the numerical approximation, a very promising alternative based on the Koopman operator has recently emerged. In this chapter, we present two control strategies for model predictive control of nonlinear PDEs using data-efficient approximations of the Koopman operator. In the first one, the dynamic control system is replaced by a small number of autonomous systems with different yet constant inputs. The control problem is consequently transformed into a switching problem. In the second approach, a bilinear surrogate model is obtained via a convex combination of these autonomous systems. Using a recent convergence result for extended dynamic mode decomposition (EDMD), convergence of the reduced objective function can be shown. We study the properties of these two strategies with respect to solution quality, data requirements, and complexity of the resulting optimization problem using the 1-dimensional Burgers equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an extension for online adaptivity is presented.
AU - Peitz, Sebastian
AU - Klus, Stefan
ID - 16289
SN - 0170-8643
T2 - Lecture Notes in Control and Information Sciences
TI - Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models Based on the Koopman Operator
VL - 484
ER -
TY - JOUR
AB - The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles), security (e.g., tracking airborne contamination), and health (e.g., artificial hearts and artificial respiration). However, the high-dimensional, nonlinear, and multi-scale dynamics make real-time feedback control infeasible. Fortunately, these high- dimensional systems exhibit dominant, low-dimensional patterns of activity that can be exploited for effective control in the sense that knowledge of the entire state of a system is not required. Advances in machine learning have the potential to revolutionize flow control given its ability to extract principled, low-rank feature spaces characterizing such complex systems.We present a novel deep learning modelpredictive control framework that exploits low-rank features of the flow in order to achieve considerable improvements to control performance. Instead of predicting the entire fluid state, we use a recurrent neural network (RNN) to accurately predict the control relevant quantities of the system, which are then embedded into an MPC framework to construct a feedback loop. In order to lower the data requirements and to improve the prediction accuracy and thus the control performance, incoming sensor data are used to update the RNN online. The results are validated using varying fluid flow examples of increasing complexity.
AU - Bieker, Katharina
AU - Peitz, Sebastian
AU - Brunton, Steven L.
AU - Kutz, J. Nathan
AU - Dellnitz, Michael
ID - 16290
JF - Theoretical and Computational Fluid Dynamics
SN - 0935-4964
TI - Deep model predictive flow control with limited sensor data and online learning
VL - 34
ER -
TY - JOUR
AB - In recent years, the success of the Koopman operator in dynamical systems
analysis has also fueled the development of Koopman operator-based control
frameworks. In order to preserve the relatively low data requirements for an
approximation via Dynamic Mode Decomposition, a quantization approach was
recently proposed in [Peitz & Klus, Automatica 106, 2019]. This way, control
of nonlinear dynamical systems can be realized by means of switched systems
techniques, using only a finite set of autonomous Koopman operator-based
reduced models. These individual systems can be approximated very efficiently
from data. The main idea is to transform a control system into a set of
autonomous systems for which the optimal switching sequence has to be computed.
In this article, we extend these results to continuous control inputs using
relaxation. This way, we combine the advantages of the data efficiency of
approximating a finite set of autonomous systems with continuous controls. We
show that when using the Koopman generator, this relaxation --- realized by
linear interpolation between two operators --- does not introduce any error for
control affine systems. This allows us to control high-dimensional nonlinear
systems using bilinear, low-dimensional surrogate models. The efficiency of the
proposed approach is demonstrated using several examples with increasing
complexity, from the Duffing oscillator to the chaotic fluidic pinball.
AU - Peitz, Sebastian
AU - Otto, Samuel E.
AU - Rowley, Clarence W.
ID - 16309
IS - 3
JF - SIAM Journal on Applied Dynamical Systems
TI - Data-Driven Model Predictive Control using Interpolated Koopman Generators
VL - 19
ER -
TY - CHAP
AB - Diagrammatisches Schlie{\ss}en wird im Zusammenhang mit dem Lernen von Mathmematik und ihrer Symbolsprache als wesentliche Theorie der Wissenskonstruktion diskutiert. Dabei wird h{\"{a}}ufig davon ausgegangen, dass die Wissenskonstruktion im Sinne diagrammatischen Schlie{\ss}ens erfolgt. Deskriptive Rekonstruktionen diagrammatischen Schlie{\ss}ens bei Lernenden stellen jedoch ein Desiderat der mathematikdidaktischen Forschung dar. Der vorliegende Beitrag befasst sich mit der Fragestellung, wie sich diagrammatisches Schlie{\ss}en bei Lernenden rekonstruieren l{\"{a}}sst. Als m{\"{o}}gliche Werkzeuge f{\"{u}}r eine solche Rekonstruktion werden Toulmins Argumentationsschema und Vergnauds Schema-Begriff exemplarisch angewandt, um das diagrammatische Schlie{\ss}en eines Sch{\"{u}}lerpaars beim Einstieg in die Subtraktion negativer Zahlen zu rekonstruieren. Abschlie{\ss}end wird die tats{\"{a}}chliche Eignung der beiden Ans{\"{a}}tze zur Rekonstruktion diagrammatischen Schlie{\ss}ens diskutiert.
AU - Schumacher, Jan
AU - Rezat, Sebastian
ED - Kadunz, Gert
ID - 13108
T2 - Zeichen und Sprache im Mathematikunterricht
TI - Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge
ER -
TY - CONF
AU - Schumacher, Jan
ID - 31873
TI - Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik
ER -
TY - JOUR
AB - In this work we present a set-oriented path following method for the computation of relative global
attractors of parameter-dependent dynamical systems. We start with an initial approximation of the
relative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.
By using previously obtained approximations of the parameter-dependent relative global attractor
we can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole
subdivision procedure. We illustrate the feasibility of the set-oriented path following method by
exploring the dynamics in low-dimensional models for shear flows during the transition to turbulence
and of large-scale atmospheric regime changes .
AU - Gerlach, Raphael
AU - Ziessler, Adrian
AU - Eckhardt, Bruno
AU - Dellnitz, Michael
ID - 16710
JF - SIAM Journal on Applied Dynamical Systems
SN - 1536-0040
TI - A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors
ER -
TY - JOUR
AU - Amiri, Habib
AU - Glöckner, Helge
AU - Schmeding, Alexander
ID - 34789
IS - 5
JF - Archivum Mathematicum
KW - 22A22
KW - 22E65
KW - 22E67
KW - 46T10
KW - 47H30
KW - 58D15
KW - 58H05
SN - 0044-8753
TI - Lie groupoids of mappings taking values in a Lie groupoid
VL - 56
ER -
TY - JOUR
AU - Glöckner, Helge
AU - Masbough, Niku
ID - 34787
JF - Topology Proceedings
KW - 54B10
KW - 54D45
KW - 54D50
SN - 0146-4124
TI - Products of regular locally compact spaces are k_R-spaces
VL - 55
ER -
TY - GEN
AB - For suitable finite-dimensional smooth manifolds M (possibly with various
kinds of boundary or corners), locally convex topological vector spaces F and
non-negative integers k, we construct continuous linear operators S_n from the
space of F-valued k times continuously differentiable functions on M to the
corresponding space of smooth functions such that S_n(f) converges to f in
C^k(M,F) as n tends to infinity, uniformly for f in compact subsets of
C^k(M,F). We also study the existence of continuous linear right inverses for
restriction maps from C^k(M,F) to C^k(L,F) if L is a closed subset of M,
endowed with a C^k-manifold structure turning the inclusion map from L to M
into a C^k-map. Moreover, we construct continuous linear right inverses for
restriction operators between spaces of sections in vector bundles in many
situations, and smooth local right inverses for restriction operators between
manifolds of mappings. We also obtain smoothing results for sections in fibre
bundles.
AU - Glöckner, Helge
ID - 34808
T2 - arXiv:2006.00254
TI - Smoothing operators for vector-valued functions and extension operators
ER -
TY - GEN
AB - Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all
real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space
${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of
time-dependent real-analytic vector fields on $M$ which are integrable
functions in time, and their dependence on the time-dependent vector field.
Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each
$[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an
absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$.
As tools for the proof, we develop several new results concerning
$L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$,
which will be useful also for the discussion of other classes of groups.
Moreover, we obtain new results concerning the continuity and complex
analyticity of non-linear mappings on open subsets of locally convex direct
limits.
AU - Glöckner, Helge
ID - 34807
T2 - arXiv:2007.15611
TI - Lie groups of real analytic diffeomorphisms are L^1-regular
ER -
TY - JOUR
AU - Limebeer, D. J. N.
AU - Ober-Blöbaum, Sina
AU - Farshi, F. H.
ID - 29399
JF - IEEE Transactions on Automatic Control
TI - Variational integrators for dissipative systems
VL - 65(4)
ER -
TY - JOUR
AB - In real-world problems, uncertainties (e.g., errors in the measurement,
precision errors) often lead to poor performance of numerical algorithms when
not explicitly taken into account. This is also the case for control problems,
where optimal solutions can degrade in quality or even become infeasible. Thus,
there is the need to design methods that can handle uncertainty. In this work,
we consider nonlinear multi-objective optimal control problems with uncertainty
on the initial conditions, and in particular their incorporation into a
feedback loop via model predictive control (MPC). In multi-objective optimal
control, an optimal compromise between multiple conflicting criteria has to be
found. For such problems, not much has been reported in terms of uncertainties.
To address this problem class, we design an offline/online framework to compute
an approximation of efficient control strategies. This approach is closely
related to explicit MPC for nonlinear systems, where the potentially expensive
optimization problem is solved in an offline phase in order to enable fast
solutions in the online phase. In order to reduce the numerical cost of the
offline phase, we exploit symmetries in the control problems. Furthermore, in
order to ensure optimality of the solutions, we include an additional online
optimization step, which is considerably cheaper than the original
multi-objective optimization problem. We test our framework on a car
maneuvering problem where safety and speed are the objectives. The
multi-objective framework allows for online adaptations of the desired
objective. Alternatively, an automatic scalarizing procedure yields very
efficient feedback controls. Our results show that the method is capable of
designing driving strategies that deal better with uncertainties in the initial
conditions, which translates into potentially safer and faster driving
strategies.
AU - Hernández Castellanos, Carlos Ignacio
AU - Ober-Blöbaum, Sina
AU - Peitz, Sebastian
ID - 16297
JF - International Journal of Robust and Nonlinear Control
TI - Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty
VL - 30(17)
ER -
TY - JOUR
AU - Hernández Castellanos, C. I. O.
AU - Schütze, G.
AU - Sun, J.-Q.
AU - Ober-Blöbaum, Sina
AU - Morales-Luna, G.
ID - 29398
JF - Mathematics
TI - Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping
VL - 8(11):1959
ER -
TY - CONF
AU - Lishkova, Y.
AU - Ober-Blöbaum, Sina
AU - Cannon, M.
AU - Leyendecker, S.
ID - 29422
T2 - Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe
TI - A multirate variational approach to simulation and optimal control for flexible spacecraft
ER -
TY - CONF
AU - Faulwasser, T.
AU - Flaßkamp, K.
AU - Ober-Blöbaum, Sina
AU - Worthmann, K.
ID - 29423
T2 - 24th International Symposium on Mathematical Theory of Networks and Systems
TI - A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems
ER -
TY - CONF
AU - Cresson, J.
AU - Jiménez, F.
AU - Ober-Blöbaum, Sina
ID - 29424
T2 - 24th International Symposium on Mathematical Theory of Networks and Systems
TI - Modelling of the convection-diffusion equation through fractional restricted calculus of variations
ER -
TY - JOUR
AU - Jean, Frédéric
AU - Maslovskaya, Sofya
AU - Zelenko, Igor
ID - 29545
IS - 1
JF - Geometriae Dedicata
KW - Geometry and Topology
SN - 0046-5755
TI - On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry
VL - 213
ER -
TY - GEN
AU - Maslovskaya, Sofya
AU - Caillau, Jean-Baptiste
AU - Djema, Walid
AU - Giraldi, Laetitia
AU - Jean-Luc, Jean-Luc
AU - Pomet, Jean-Baptiste
ID - 29546
TI - The turnpike property in maximization of microbial metabolite production
ER -
TY - JOUR
AB - AbstractGiven a closed orientable hyperbolic manifold of dimension $$\ne 3$$
≠
3
we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.
AU - Küster, Benjamin
AU - Weich, Tobias
ID - 31264
IS - 2
JF - Communications in Mathematical Physics
KW - Mathematical Physics
KW - Statistical and Nonlinear Physics
SN - 0010-3616
TI - Pollicott-Ruelle Resonant States and Betti Numbers
VL - 378
ER -
TY - CONF
AU - Hoffmann, Max
ED - Siller, Hans-Stefan
ED - Weigel, Wolfgang
ED - Wörler, Jan Franz
ID - 31372
T2 - Beiträge zum Mathematikunterricht 2020
TI - Schnittstellenaktivitäten zum Kongruenzsatz WSW
ER -
TY - GEN
AU - Hoffmann, Max
ID - 31386
T2 - Mathematische Semesterberichte
TI - Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations
VL - 67
ER -
TY - GEN
AU - Hoffmann, Max
ID - 31384
T2 - Mathematische Semesterberichte
TI - Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose
VL - 67
ER -
TY - BOOK
ED - Hoffmann, Max
ID - 31381
TI - Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft
ER -
TY - CHAP
AU - Häsel-Weide, Uta
AU - Nührenbörger, Marcus
ED - Hecker, Ulrich
ED - Lassek, Maresi
ED - Ramseger, Jörg
ID - 31551
T2 - Kinder lernen Zukunft – Anforderungen und tragfähige Grundlagen
TI - Tragfähige Grundlagen
VL - Band 150
ER -
TY - CHAP
AU - Heckmann, Lara
AU - Häsel-Weide, Uta
ED - Siller, Hans-Stefan
ED - Weigel, Wolfgang
ED - Wörler, Jan Franz
ID - 31552
SN - 978-3-95987-139-6
T2 - Beiträge zum Mathematikunterricht 2020
TI - Aufgaben für den inklusiven Mathematikunterricht - aus der Sicht von Lehrkräften.
ER -
TY - CHAP
AU - Häsel-Weide, Uta
ED - Heimlich, Ulrich
ED - Wember, Franz B.
ID - 31549
SN - 978-3170355699
T2 - Didaktik des Unterrichts bei Lernschwierigkeiten: Ein Handbuch für Studium und Praxis
TI - Sachrechnen
ER -
TY - CHAP
AU - Häsel-Weide, Uta
ED - Cramer, Colin
ED - König, Johannes
ED - Rothland, Martin
ED - Blömeke, Sigrid
ID - 31550
SN - 978-3-8252-5473-5
T2 - Handbuch Lehrerinnen- und Lehrerbildung
TI - Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.
ER -
TY - GEN
AB - Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik, der neben der Optimierung und der Stochastik die Grundlage für praktisch alle Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt werden können.
Behandelte Themen sind:
Der Vektorraum der reellen Zahlentupel, reelle Vektorräume allgemein
Lineare Abbildungen
Matrizen
Koordinaten und darstellende Matrizen
Lineare Gleichungssysteme, Gaußalgorithmus
Determinante
Ein Ausblick auf nichtlineare Techniken, die für neuronale Netzwerke relevant sind.
AU - Schramm, Thomas
AU - Gasser, Ingenuin
AU - Schwenker, Sören
AU - Seiler, Ruedi
AU - Lohse, Alexander
AU - Zobel, Kay
ID - 33273
TI - Linear Algebra driven by Data Science
ER -
TY - JOUR
AB - We derive a criterium for the almost sure finiteness of perpetual integrals of L ́evy
processes for a class of real functions including all continuous functions and for general one-
dimensional L ́evy processes that drifts to plus infinity. This generalizes previous work of D ̈oring
and Kyprianou, who considered L ́evy processes having a local time, leaving the general case as an
open problem. It turns out, that the criterium in the general situation simplifies significantly in
the situation, where the process has a local time, but we also demonstrate that in general our cri-
terium can not be reduced. This answers an open problem posed in D ̈oring, L. and Kyprianou, A.
(2015).
AU - Kolb, Martin
AU - Savov, Mladen
ID - 33282
IS - 2
JF - Bernoulli
KW - L ́evy processes
KW - Perpetual integrals
KW - Potential measures
TI - A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
VL - 26
ER -
TY - JOUR
AB - Reciprocal relations are binary relations Q with entries Q(i,j)∈[0,1], and such that Q(i,j)+Q(j,i)=1. Relations of this kind occur quite naturally in various domains, such as preference modeling and preference learning. For example, Q(i,j) could be the fraction of voters in a population who prefer candidate i to candidate j. In the literature, various attempts have been made at generalizing the notion of transitivity to reciprocal relations. In this paper, we compare three important frameworks of generalized transitivity: g-stochastic transitivity, T-transitivity, and cycle-transitivity. To this end, we introduce E-transitivity as an even more general notion. We also use this framework to extend an existing hierarchy of different types of transitivity. As an illustration, we study transitivity properties of probabilities of pairwise preferences, which are induced as marginals of an underlying probability distribution on rankings (strict total orders) of a set of alternatives. In particular, we analyze the interesting case of the so-called Babington Smith model, a parametric family of distributions of that kind.
AU - Haddenhorst, Björn
AU - Hüllermeier, Eyke
AU - Kolb, Martin
ID - 33330
IS - 2
JF - International Journal of Approximate Reasoning
TI - Generalized transitivity: A systematic comparison of concepts with an application to preferences in the Babington Smith model
VL - 119
ER -
TY - JOUR
AU - Hesse, Kerstin
AU - Sloan, Ian H.
AU - Womersley, Robert S.
ID - 34629
JF - Journal of Computational and Applied Mathematics
KW - Applied Mathematics
KW - Computational Mathematics
SN - 0377-0427
TI - Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data
VL - 382
ER -
TY - CHAP
AU - Hesse, Kerstin
ED - Hickernell, Fred J.
ED - Kritzer, Peter
ID - 34632
SN - 9783110633115
T2 - Multivariate Algorithms and Information-Based Complexity
TI - RBF-based penalized least-squares approximation of noisy scattered data on the sphere
ER -
TY - JOUR
AU - Hanusch, Maximilian
ID - 34828
IS - 1
JF - Indagationes Mathematicae
KW - regularity of Lie groups
SN - 0019-3577
TI - The regularity problem for Lie groups with asymptotic estimate Lie algebras
VL - 31
ER -
TY - JOUR
AU - Hanusch, Maximilian
ID - 34830
IS - 1
JF - Journal of Lie Theory
KW - Lie theory
KW - strong Trotter property
TI - The Strong Trotter Property for Locally μ-convex Lie Groups
VL - 30
ER -
TY - CONF
AU - Biehler, Rolf
AU - Fleischer, Yannik
AU - Budde, Lea
AU - Frischemeier, Daniel
AU - Gerstenberger, Dietrich
AU - Podworny, Susanne
AU - Schulte, Carsten
ED - Arnold, P.
ID - 35814
T2 - New Skills in the Changing World of Statistics Education Proceedings of the Roundtable conference of the International Association for Statistical Education (IASE)
TI - Data science education in secondary schools: Teaching and learning decision trees with CODAP and Jupyter Notebooks as an example of integrating machine learning into statistics education
ER -
TY - CHAP
AU - Lankeit, Elisa
AU - Biehler, Rolf
ED - Hausberger, T.
ED - Bosch, M.
ED - Chelloughi, F.
ID - 35912
T2 - Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
TI - “I only know the absolute value function”–About students’ concept images and example spaces concerning continuity and differentiability
ER -
TY - CHAP
AU - Lankeit, Elisa
AU - Bauer, T.
AU - Biehler, Rolf
ED - Siller, H.-S.
ED - Weigel, W.
ED - Wörler, J. F.
ID - 35911
T2 - Beiträge zum Mathematikunterricht 2020
TI - Votingfragen in den Übungen zur Analysis – Wirkung verschiedener Einsatzszenarien
ER -
TY - JOUR
AU - Lünne, Steffen
AU - Schnell, Susanne
AU - Biehler, Rolf
ID - 35701
IS - 5
JF - European Journal of Teacher Education
KW - Education
SN - 0261-9768
TI - Motivation of out-of-field teachers for participating in professional development courses in mathematics
VL - 44
ER -
TY - CHAP
AU - Barzel, Bärbel
AU - Biehler, Rolf
ED - Zehetmeier, Stefan
ED - Potari, Despina
ED - Ribeiro, Miguel
ID - 35808
T2 - Professional development and knowledge of mathematics teachers
TI - Theory-Based Design of Professional Development for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools
ER -
TY - CHAP
AU - Biehler, Rolf
AU - Durand-Guerrier, Viviane
ED - Hausberger, T.
ED - Bosch, M.
ED - Chelloughi, F.
ID - 35811
KW - Number Theory
KW - Algebra
KW - Discrete Mathematics
KW - Logic
KW - Research in University Mathematics Edcuation
T2 - Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
TI - University Mathematics Didactic Research on Number Theory, Algebra, Discrete Mathematics, Logic
ER -
TY - CHAP
AU - Budde, Lea
AU - Frischemeier, Daniel
AU - Biehler, Rolf
AU - Fleischer, Yannik
AU - Gerstenberger, Dietrich
AU - Podworny, Susanne
AU - Schulte, Carsten
ED - Arnold, P.
ID - 35821
T2 - New Skills in the Changing World of Statistics Education: Proceedings of the Roundtable conference of the International Association for Statistical Education (IASE), July 2020
TI - Data Science Education in Secondary School: How to Develop Statistical Reasoning When Exploring Data Using CODAP
ER -
TY - CHAP
AU - Biehler, Rolf
AU - Kempen, Leander
AU - Paravicini, Walther
ED - Siller, H.-S.
ED - Weigel, W.
ED - Wörler, J. F.
ID - 35819
T2 - Beiträge zum Mathematikunterricht 2020
TI - Hochschuldidaktik Mathematik: Fachbezogenes Design und empirische Studien
ER -
TY - JOUR
AB - AbstractThe derivative concept plays a major role in economics. However, its use in economics is very heterogeneous, sometimes inconsistent, and contradicts students’ prior knowledge from school. This applies in particular to the common economic interpretation of the derivative as the amount of change while increasing the production by one unit. Hence, in calculus courses for economics students, learners should acquire an understanding of the derivative that is mathematically acceptable and connected to their prior knowledge, but which also takes into account its practical use in economics. In this paper we first develop a theoretical model describing such an understanding of the derivative for economics students. We then present an exploratory study investigating the extent to which economics students have such an understanding after their calculus course. The results indicate that many of them might not have acquired this kind of understanding, in particular concerning the common economic interpretation of the derivative. The study furthermore yields possible gaps in students’ understanding and possible misconceptions.
AU - Feudel, Frank
AU - Biehler, Rolf
ID - 35822
IS - 1
JF - Journal für Mathematik-Didaktik
KW - Education
KW - General Mathematics
SN - 0173-5322
TI - Students’ Understanding of the Derivative Concept in the Context of Mathematics for Economics
VL - 42
ER -
TY - CHAP
AU - Fleischer, Yannik
AU - Biehler, Rolf
ED - Siller, H.-S.
ED - Weigel, W.
ED - Wörler, J. F.
ID - 35823
T2 - Beiträge zum Mathematikunterricht 2020
TI - Automatisierte Entscheidungsverfahren als Thema im allgemeinbildenden Mathematikunterricht
ER -
TY - JOUR
AU - Griese, Birgit
AU - Nieszporek, Ralf
AU - Biehler, Rolf
ID - 35826
IS - 1
JF - Stochastik in der Schule
TI - Frei verfügbare Materialien für Unterricht und Fortbildung: Stochastik verständnisorientiert unterrichten
VL - 40
ER -
TY - JOUR
AU - Kempen, Leander
AU - Biehler, Rolf
ID - 35709
JF - Frontiers in Psychology
KW - General Psychology
SN - 1664-1078
TI - Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology
VL - 11
ER -
TY - CHAP
AU - Kempen, Leander
AU - Krämer, Sandra
AU - Biehler, Rolf
ED - Hausberger, T.
ED - Bosch, M.
ED - Chelloughi, F.
ID - 35829
T2 - Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2020, 12-19 September 2020)
TI - Investigating high school graduates’ personal meaning of the notion of “mathematical proof”
ER -
TY - CHAP
AU - Kempen, Leander
AU - Krämer, Sandra
AU - Biehler, Rolf
ED - Siller, H.-S.
ED - Weigel, W.
ED - Wörler, J. F.
ID - 35827
T2 - Beiträge zum Mathematikunterricht 2020
TI - Was verstehen Schülerinnen und Schüler unter „Beweis“? – ausgewählte Ergebnisse einer Pilotstudie
ER -
TY - CHAP
AU - Lünne, Steffen
AU - Schnell, Susanne
AU - Biehler, Rolf
ED - Porsch, R.
ED - Rösken-Winter, B.
ID - 35914
SN - 9783658272920
T2 - Professionelles Handeln im fachfremd erteilten Mathematikunterricht
TI - Ffunt@OWL – Konzept und Gestaltungsprinzipien zur Qualifizierung fachfremd Mathematik unterrichtender Lehrkräfte der Sekundarstufe I
ER -