@inbook{56257, author = {{Mai, Tobias and Biehler, Rolf}}, booktitle = {{Proceedings of the Third International Conference on Mathametics Textbook research and Development}}, editor = {{Rezat, S. and Lianghuo, F. and Hattermann, M. and Schumacher, J. and Wuschke, H.}}, pages = {{233--238}}, publisher = {{Universitätsbibliothek Paderborn}}, title = {{{On the Introduction of Vectors in German Textbooks for Upper Secondary School}}}, volume = {{16}}, year = {{2019}}, } @article{56255, author = {{Kempen, Leander and Biehler, Rolf}}, issn = {{1863-9690}}, journal = {{ZDM}}, number = {{5}}, pages = {{731--746}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Fostering first-year pre-service teachers’ proof competencies}}}, doi = {{10.1007/s11858-019-01035-x}}, volume = {{51}}, year = {{2019}}, } @inbook{56256, author = {{Lankeit, Elisa and Biehler, Rolf}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2018}}, editor = {{Klinger, M. and Schüler-Meyer, A. and Wessel, L.}}, pages = {{117--131}}, publisher = {{WTM-Verlag}}, title = {{{Vorstellung einer Aufgabe zu den Zusammenhängen verschiedener Differenzierbarkeitsbegriffe im Mehrdimensionalen}}}, year = {{2019}}, } @inbook{56789, author = {{Nieszporek, Ralf and Biehler, Rolf and Griese, Birgit}}, booktitle = {{Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Sta-tistics (ICOTS10, July, 2018), Kyoto, Japan}}, editor = {{Sorto, M.A. and White, A. and Guyot, L.}}, publisher = {{International Statistical Institute}}, title = {{{Developments of teachers’ knowledge facets in teaching statistics with digital tools measured with retrospective self-assessment}}}, year = {{2019}}, } @inproceedings{56246, author = {{Biehler, Rolf}}, booktitle = {{Calculus in upper secondary and beginning university mathematics—Conference proceedings}}, editor = {{Monaghan, J. and Nardi, E. and Dreyfus, T.}}, pages = {{4–17}}, publisher = {{MatRIC}}, title = {{{The transition from calculus and to analysis—Conceptual analyses and supporting steps for students}}}, year = {{2019}}, } @inproceedings{14848, abstract = {{Data Science und Big Data durchdringt in ihren diversen Facetten unser tägliches Leben– kaum ein Tag, an dem nicht verschiedene Meldungen über technische Innovationen, Einsatzmöglichkeiten von Künstlicher Intelligenz (KI) und Maschinelles Lernen (ML) und ihre ethischen sowie gesellschaftlichen Implikationen in den unterschiedlichen Medien diskutiert werden. Aus diesem Grund erscheint es uns immens wichtig, diese Fragestellungen und Technologien auch in den Unterricht der Sekundarstufe II zu integrieren. Um diesem Anspruch gerecht zu werden, entwickelten wir im Rahmen eines Forschungsprojekts ein Curriculum, welches wir als konkretes Unterrichtskonzept innerhalb eines Projektkurses erprobt, evaluiert weiterentwickelt wird. Bei der Implementierung entschieden wir uns, zur aktiven Umsetzung von Konzepten von ML als Plattform Jupyter Notebook mit Python zu verwenden, da diese Umgebung durch die Verbindung von Code und Hypertext zur Dokumentation und Erklärung Medienbrüche im Lernprozess verringern kann. Zudem ist Python zur Implementierung der Methoden von ML sehr gut geeignet. Im Themenfeld des ML als Teilgebiet der KI legen wir den Fokus auf zwei unterschiedliche Lernverfahren um verschieden Aspekte von ML, u.A. wie Nachvollziehbarkeit unter gesellschaftlichen Gesichtspunkten zu vermitteln. Diese sind Künstliche Neuronale Netze (bei denen die Berechnung und Bedeutung der Kantengewichte zwischen den Neuronen für den Menschen insbesondere bei komplexeren Netzen kaum nachvollziehbar erschienen) und Entscheidungsbäume (strukturierte und gerichtete Bäume zur Darstellung von Entscheidungsregeln, welche auch für Schülerinnen und Schüler meist gut nachvollziehbares und verständliches KI-Modell darstellen). In diesem Workshop stellen wir konkrete Umsetzungsbeispiele inklusive der Programmierung für beide Verfahren mit Jupyter Notebook und Python als Teil einer Unterrichtssequenz vor und diskutieren diese.}}, author = {{Schlichtig, Michael and Opel, Simone and Schulte, Carsten and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Wassong, Thomas}}, booktitle = {{Informatik für alle}}, editor = {{Pasternak, Arno}}, isbn = {{978-3-88579-682-4}}, location = {{Dortmund, Germany}}, pages = {{ 385 }}, publisher = {{Gesellschaft für Informatik}}, title = {{{Maschinelles Lernen im Unterricht mit Jupyter Notebook}}}, year = {{2019}}, } @inproceedings{14847, abstract = {{Die Bereiche „Data Science“ und „Big Data“ sowie ihre technischen, ethischen und gesellschaftlichen Auswirkungen werden zunehmend nicht nur in der Wissenschaft, sondern auch in diversen Medien diskutiert und somit verstärkt auch zu einem wichtigen Thema für alle. Um den Schülerinnen und Schülern der Sekundarstufe II einen theoretisch und fachwissenschaftlich fundierten Einstieg in diesen Themenbereich zu ermöglichen, wurde ein erster Entwurf eines interdisziplinären Curriculums entwickelt, das neben fachlichen Aspekten von Data Science einen Fokus auf sich hieraus ergebende gesellschaftliche Fragestellungen legt. Es werden neben der Konzeption des Kurses die bisherigen Erfahrungen aus der Durchführung – insbesondere in Hinsicht der darin enthaltenen Unterrichtseinheit zum Maschinellen Lernen - berichtet, sowie die sich hieraus ergebenden Implikationen für die Weiterentwicklung dargestellt und diskutiert.}}, author = {{Opel, Simone and Schlichtig, Michael and Schulte, Carsten and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Wassong, Thomas}}, booktitle = {{Informatik für alle}}, editor = {{Pasternak, Arno}}, isbn = {{978-3-88579-682-4}}, location = {{Dortmund, Germany}}, pages = {{ 285--294 }}, publisher = {{Gesellschaft für Informatik}}, title = {{{Entwicklung und Reflexion einer Unterrichtssequenz zum Maschinellen Lernen als Aspekt von Data Science in der Sekundarstufe II}}}, year = {{2019}}, } @unpublished{64769, author = {{Nikitin, Natalie}}, title = {{{Measurable regularity of infinite-dimensional Lie groups based on Lusin measurability}}}, year = {{2019}}, } @article{64756, author = {{Walter, Boris}}, issn = {{0019-3577}}, journal = {{Indagationes Mathematicae}}, keywords = {{58D05, 57S05, 22E65, 58D15, 58B10}}, number = {{4}}, pages = {{669–705}}, title = {{{Weighted diffeomorphism groups of Riemannian manifolds}}}, doi = {{10.1016/j.indag.2019.03.003}}, volume = {{30}}, year = {{2019}}, } @article{64630, author = {{Glöckner, Helge}}, issn = {{0008-414X}}, journal = {{Canadian Journal of Mathematics}}, keywords = {{22E65, 22A05, 22E67, 46A13, 46M40, 58D05}}, number = {{1}}, pages = {{131–152}}, title = {{{Completeness of infinite-dimensional Lie groups in their left uniformity}}}, doi = {{10.4153/CJM-2017-048-5}}, volume = {{71}}, year = {{2019}}, } @inbook{62712, author = {{Opel, Simone and Schlichtig, Michael and Schulte, Carsten and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Wassong, Thomas}}, booktitle = {{Informatik für alle - 18. GI-Fachtagung Informatik und Schule, 16.-18. September 2019, Dortmund}}, editor = {{Pasternak, A.}}, isbn = {{978-3-88579-682-4}}, pages = {{285–294}}, publisher = {{Gesellschaft für Informatik}}, title = {{{Entwicklung und Reflexion einer Unterrichtssequenz zum Maschinellen Lernen als Aspekt von Data Science in der Sekundarstufe II}}}, doi = {{10.18420/infos2019-c14}}, year = {{2019}}, } @misc{8482, author = {{Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes, Leander}}, title = {{{Arbitrary sensitivity for inverse problems in piezoelectricity}}}, year = {{2019}}, } @article{19935, abstract = {{A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples. }}, author = {{McLachlan, Robert I and Offen, Christian}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, pages = {{2895--2927}}, title = {{{Bifurcation of solutions to Hamiltonian boundary value problems}}}, doi = {{10.1088/1361-6544/aab630}}, year = {{2018}}, } @article{19937, abstract = {{Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, nonexistence of attractors, and good behaviour of statistical properties. These all refer to {\em long-time} behaviour. They are directly connected to the dynamical behaviour of symplectic maps φ:M→M' on the phase space under iteration. Boundary value problems, in contrast, are posed for fixed (and often quite short) times. Symplecticity manifests as a symplectic map φ:M→M' which is not iterated. Is there any point, therefore, for a symplectic integrator to be used on a Hamiltonian boundary value problem? In this paper we announce results that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not.}}, author = {{McLachlan, Robert I and Offen, Christian}}, issn = {{1017-1398}}, journal = {{Numerical Algorithms}}, pages = {{1219--1233}}, title = {{{Symplectic integration of boundary value problems}}}, doi = {{10.1007/s11075-018-0599-7}}, year = {{2018}}, } @unpublished{21634, abstract = {{Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This is a challenging task with a lot of constraints, since the model order is directly linked to the number of system states. Even though white-box models show suitable performance in most cases, parasitic real-world effects often cannot be modeled satisfactorily with an expedient computational load. Hence, a Koopman operator-based model reduction technique is presented which directly links the control action to the system's outputs in a black-box fashion. The Koopman operator is a linear but infinite-dimensional operator describing the dynamics of observables of nonlinear autonomous dynamical systems which can be nicely applied to the switching principle of power electronic devices. Following this data-driven approach, the model order and the number of system states are decoupled which allows us to consider more complex systems. Extensive experimental tests with an automotive-type permanent magnet synchronous motor fed by an IGBT 2-level inverter prove the feasibility of the proposed modeling technique in a finite-set model predictive control application.}}, author = {{Hanke, Sören and Peitz, Sebastian and Wallscheid, Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}}, booktitle = {{arXiv:1804.00854}}, title = {{{Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives}}}, year = {{2018}}, } @article{21940, author = {{Litzinger, Florian and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk, Richard and Noé, Frank and Clementi, Cecilia}}, issn = {{1549-9618}}, journal = {{Journal of Chemical Theory and Computation}}, pages = {{2771--2783}}, title = {{{Rapid Calculation of Molecular Kinetics Using Compressed Sensing}}}, doi = {{10.1021/acs.jctc.8b00089}}, year = {{2018}}, } @article{21941, author = {{Klus, Stefan and Nüske, Feliks and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and Noé, Frank}}, issn = {{0938-8974}}, journal = {{Journal of Nonlinear Science}}, pages = {{985--1010}}, title = {{{Data-Driven Model Reduction and Transfer Operator Approximation}}}, doi = {{10.1007/s00332-017-9437-7}}, year = {{2018}}, } @article{21942, author = {{Boninsegna, Lorenzo and Nüske, Feliks and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Sparse learning of stochastic dynamical equations}}}, doi = {{10.1063/1.5018409}}, year = {{2018}}, } @article{21943, author = {{Hruska, Eugen and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Quantitative comparison of adaptive sampling methods for protein dynamics}}}, doi = {{10.1063/1.5053582}}, year = {{2018}}, } @inproceedings{7766, author = {{Schumacher, Jan}}, booktitle = {{Beiträge zum Mathematikunterricht 2018}}, publisher = {{WTM-Verlag}}, title = {{{Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen}}}, year = {{2018}}, }