@book{45331, author = {{Schönherr, Johanna}}, publisher = {{Springer Spektrum}}, title = {{{Selbst erstellte Skizzen beim mathematischen Modellieren: Ergebnisse einer empirischen Untersuchung [Self-generated drawings for modelling problems: Findings of an empirical study]}}}, year = {{2019}}, } @article{21, abstract = {{We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter q always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.}}, author = {{Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}}, journal = {{Communications in Computational Physics}}, number = {{2}}, pages = {{564--585}}, publisher = {{Global Science Press}}, title = {{{A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}}}, doi = {{10.4208/cicp.OA-2018-0053}}, volume = {{25}}, year = {{2019}}, } @unpublished{16711, abstract = {{Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the original set. In order to additionally reveal their geometry we use diffusion mapst o find intrinsic coordinates. We illustrate our results on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky equation, as well as for the attractor of the Mackey-Glass delay differential equation.}}, author = {{Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}}, booktitle = {{arXiv:1902.08824}}, title = {{{Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems}}}, year = {{2019}}, } @article{56248, author = {{Engel, Joachim and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Schiller, Achim and Martignon, Laura}}, issn = {{1863-8155}}, journal = {{AStA Wirtschafts- und Sozialstatistisches Archiv}}, number = {{1}}, pages = {{113--114}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Erratum to: Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy}}}, doi = {{10.1007/s11943-019-00266-4}}, volume = {{14}}, year = {{2019}}, } @inbook{56245, author = {{Biehler, Rolf}}, booktitle = {{ICME-13 Monographs}}, editor = {{Jahnke, H. N. and Hefendehl-Hebeker, L.}}, isbn = {{9783030110680}}, issn = {{2520-8322}}, publisher = {{Springer International Publishing}}, title = {{{Allgemeinbildung, Mathematical Literacy, and Competence Orientation}}}, doi = {{10.1007/978-3-030-11069-7_6}}, year = {{2019}}, } @inbook{56247, author = {{Biehler, Rolf}}, booktitle = {{Proceedings of the Third International Virtual Congress of Statistical Education}}, editor = {{Contreras, J. M. and Gea, M. M. and Lopez-Martin, M. M. and Molina-Portillo, E.}}, publisher = {{Universidad de Granada}}, title = {{{Software for learning and for doing statistics and probability–Looking back and looking forward from a personal perspective}}}, year = {{2019}}, } @article{56252, author = {{Frischemeier, Daniel and Podworny, Susanne and Biehler, Rolf}}, journal = {{Stochastik in der Schule}}, number = {{1}}, pages = {{26--33}}, title = {{{Chancen und Herausforderungen für die Implementation von Zivilstatistiken in der Lehramtsausbildung}}}, volume = {{39}}, year = {{2019}}, } @inbook{56259, author = {{Nieszporek, Ralf and Biehler, Rolf}}, booktitle = {{Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education}}, editor = {{Jankvist, U. T. and van den Heuvel-Panhuizen, M. and Veldhuis, M.}}, publisher = {{Freudenthal Group & Freudenthal Institute, Utrecht University and ERME}}, title = {{{Retrospective competence assessment in a PD course on teaching statistics with digital tools in upper secondary schools}}}, year = {{2019}}, } @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}}, } @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}}, }