TY - GEN AB - We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane. AU - Schütte, Philipp AU - Weich, Tobias AU - Delarue, Benjamin ID - 31058 TI - Resonances and weighted zeta functions for obstacle scattering via smooth models ER - TY - GEN AU - Hoffmann, Max ID - 31385 T2 - Mathematische Semesterberichte TI - Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie VL - 68 ER - TY - CHAP AU - Hoffmann, Max ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 31364 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert TI - Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn ER - TY - JOUR AB - Abstract For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory. AU - Küster, Benjamin AU - Weich, Tobias ID - 31261 IS - 11 JF - International Mathematics Research Notices KW - General Mathematics SN - 1073-7928 TI - Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces VL - 2021 ER - TY - JOUR AU - Häsel-Weide, Uta AU - Nührenbürger, Marcus ID - 31576 IS - 14 JF - Zeitschrift für Grundschulforschung (ZfG) TI - Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. ER - TY - JOUR AU - Häsel-Weide, Uta AU - Schöttler, Christian ID - 31577 IS - 2 JF - Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP) SN - 2701-9012 TI - Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen ER - TY - JOUR AU - Li, Jiaao AU - Ma, Yulai AU - Shi, Yongtang AU - Wang, Weifan AU - Wu, Yezhou ID - 32810 JF - European Journal of Combinatorics KW - Discrete Mathematics and Combinatorics SN - 0195-6698 TI - On 3-flow-critical graphs VL - 100 ER - TY - JOUR AB - The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold. AU - Kolb, Martin AU - Weich, Tobias AU - Wolf, Lasse ID - 33278 IS - 4 JF - Annales Henri Poincaré TI - Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature VL - 23 ER - TY - GEN AU - Weich, Tobias AU - Budde, Julia ID - 32099 T2 - arXiv:2103.02968v1 TI - Wave Front Sets of Nilpotent Lie Group Representations ER - TY - JOUR AB - While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction. AU - Richthammer, Thomas AU - Fiedler, Michael ID - 33481 JF - Stochastic Processes and their Applications TI - A lower bound on the displacement of particles in 2D Gibbsian particle systems VL - 132 ER - TY - JOUR AU - Hanusch, Maximilian ID - 34818 JF - Differential Geometry and its Applications KW - Geometry and Topology KW - Analysis SN - 0926-2245 TI - Symmetries of analytic curves VL - 74 ER - TY - CHAP AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35720 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Mathematikvorkurse als Brücke in das Studium–Einführung ER - TY - CHAP AU - Biehler, Rolf AU - Eichler, Andreas AU - Hochmuth, Reinhard AU - Rach, Stefanie AU - Schaper, Niclas ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35730 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert ER - TY - JOUR AU - Biehler, Rolf AU - Fleischer, Yannik ID - 35737 JF - Teaching Statistics KW - Education KW - Statistics and Probability SN - 0141-982X TI - Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks VL - 43 ER - TY - BOOK ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35734 SN - 2197-8751 TI - Lehrinnovationen in der Hochschulmathematik ER - TY - CHAP AU - Frischemeier, Daniel AU - Podworny, Susanne AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35752 SN - 2197-8751 T2 - Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik TI - Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“ ER - TY - CHAP AU - Fleischmann, Yael AU - Biehler, Rolf AU - Gold, Alexander AU - Mai, Tobias ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35746 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Integration digitaler Lernmaterialien in die Präsenzlehre am Beispiel des Mathematikvorkurses für Ingenieure an der Universität Paderborn ER - TY - JOUR AU - Frischemeier, Daniel AU - Biehler, Rolf AU - Podworny, Susanne AU - Budde, Lea ID - 35751 IS - S1 JF - Teaching Statistics KW - Education KW - Statistics and Probability SN - 0141-982X TI - A first introduction to data science education in secondary schools: Teaching and learning about data exploration withCODAPusing survey data VL - 43 ER - TY - JOUR AU - Biehler, Rolf AU - Weigand, Hans-Georg ID - 35744 IS - 228 JF - mathematik lehren TI - 3D-Geometrie–virtuell und real VL - 2021 ER - TY - CHAP AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Blum, Werner AU - Achmetli, Kay AU - Rode, Jana AU - Krawitz, Janina AU - Schukajlow, Stanislaw AU - Bender, Peter AU - Haase, Jürgen ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35757 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation ER - TY - CHAP AU - Gold, Alexander AU - Fleischmann, Yael AU - Mai, Tobias AU - Biehler, Rolf AU - Kempen, Leander ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35755 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Die Online-Lernmaterialien im Online-Mathematikvorkurs studiVEMINT: Konzeption und Ergebnisse von Nutzer- und Evaluationsstudien ER - TY - CHAP AU - Kempen, Leander AU - Biehler, Rolf ED - Biehler, Rolf ED - Eichler, Andreas ED - Hochmuth, Reinhard ED - Rach, Stefanie ED - Schaper, Niclas ID - 35776 SN - 2197-8751 T2 - Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik TI - Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“ ER - TY - JOUR AU - Höper, Lukas AU - Malin, Leah AU - Biehler, Rolf ID - 35761 IS - 228 JF - mathematik lehren TI - Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik VL - 2021 ER - TY - JOUR AU - Hüsing, Sven AU - Weiser, Niklas AU - Biehler, Rolf ID - 35763 IS - 228 JF - mathematik lehren TI - Faszination 3D-Film: Entwicklung einer 3D-Konstruktion VL - 2021 ER - TY - JOUR AB - AbstractThe aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research. AU - Pepin, Birgit AU - Biehler, Rolf AU - Gueudet, Ghislaine ID - 35778 IS - 2 JF - International Journal of Research in Undergraduate Mathematics Education KW - Education KW - Mathematics (miscellaneous) SN - 2198-9745 TI - Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices VL - 7 ER - TY - JOUR AU - Podworny, Susanne AU - Biehler, Rolf ID - 35781 IS - 4 JF - Mathematical Thinking and Learning KW - Developmental and Educational Psychology KW - Education KW - General Mathematics SN - 1098-6065 TI - The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study VL - 24 ER - TY - CHAP AU - Winsløw, Carl AU - Biehler, Rolf AU - Jaworski, Barbara AU - Rønning, Frode AU - Wawro, Megan ED - Durand-Guerrier, V. ED - Hochmuth, R. ED - Nardi, E. ED - Winsløw, C. ID - 35704 SN - 9780429346859 T2 - Research and Development in University Mathematics Education TI - Education and professional development of university mathematics teachers ER - TY - JOUR AU - Schürmann, Mirko AU - Liebendörfer, Michael AU - Gildehaus, Lara AU - Schaper, Niclas AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Lankeit, Elisa AU - Kuklinski, Christiane AU - Ruge, Johanna ID - 24786 JF - Sigma newsletter TI - Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany VL - 22 ER - TY - CHAP AU - Rach, Stefanie AU - Liebendörfer, Michael ED - Hein, Kerstin ED - Heil, Cathleen ED - Ruwisch, Silke ED - Prediger, Susanne ID - 37485 SN - 978-3-95987-184-6 T2 - Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021) TI - Die Bedeutung affektiver Merkmale beim Mathematiklernen ER - TY - JOUR AB - Abstract Due to the COVID-19 crisis, many courses have been offered digitally. Using data from n = 1,173 business students participating in a preparatory mathematics course at a German university that covered the same content as in 2018, 2019 and 2020, we examine how students’ participation and the effect of the preparatory course changed. The data show that the participation rate has fallen slightly, but students’ participation is rather similar to preceding years. Interestingly, students have participated more intensively. There are clear signs of dishonesty in the self-test (use of a calculator) and significant changes in predictors of performance. In particular, the effect of students’ engagement in the course on their performance substantially increased. Further, we found a gender gap in performance affecting women. Finally, the data show that digital courses can be as effective as on-campus courses. AU - Büchele, Stefan AU - Liebendörfer, Michael AU - Lankeit, Elisa ID - 37474 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university VL - 40 ER - TY - JOUR AB - Das gymnasiale Lehramtsstudium der Mathematik ist an deutschen Universitäten unterschiedlich organisiert. Traditionell wurden am Studienbeginn die Fachvorlesungen zur Analysis und Linearen Algebra gemeinsam mit Fachstudierenden gehört. In jüngerer Zeit verbreiten sich alternative Modelle z. B. mit Brückenvorlesungen, die oft spezifisch für das Gymnasiallehramt angeboten werden. Sie können gemeinsame Veranstaltungen mit Fachstudierenden ergänzen oder ersetzen. Dieser Beitrag zeigt auf, welche Modelle wie häufig verbreitet sind, und spricht an, welche hochschuldidaktischen Fragen an der Studiengestaltung hängen. AU - Gildehaus, Lara AU - Göller, Robin AU - Liebendörfer, Michael ID - 37483 IS - 111 JF - Mitteilungen der Gesellschaft für Didaktik der Mathematik SN - 2512-9155 TI - Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland VL - 47 ER - TY - CONF AU - Vajen, Bastian AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Wolf, Christoph ED - Kenner, Steve ED - Oeftering, T. ID - 37481 T2 - Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot TI - Mathematisierung als Herausforderung für die politische Bildung ER - TY - CHAP AU - Göller, Robin AU - Gildehaus, Lara AU - Liebendörfer, Michael AU - Steuding, Jörn ED - Blunck, Andrea ED - Motzer, Renate ID - 37480 T2 - Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik TI - Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik VL - 5 ER - TY - CONF AU - Haak, Inka AU - Gildehaus, Lara AU - Liebendörfer, Michael ID - 37478 T2 - Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch? TI - Genese und Funktionen von Lerngruppen in der Studieneingangsphase ER - TY - JOUR AB - Abstract We investigated university students’ study of mathematics in the digital setting context of the COVID-19 pandemic. We gathered data from a survey of 89 students enrolled in a ‘Linear Algebra 1’ course including affective variables, learning strategies, social relatedness and resources considered useful. The results indicate students’ high effort and self-regulation and a high variation in affective characteristics and social relatedness. All the traditional aspects of mathematics teaching (lecture, tutorials and lecture notes) were rated as particularly useful. In addition, the videos from external resources were rated as equally useful as the teaching team’s videos. In contrast, traditional literature such as textbooks was rarely considered useful. The most useful resource rated was communication with peers, underlining the important role of social learning despite fully digital learning environments. Finally, a cluster analysis based on students’ rated usefulness of the resources led to three different user-types. Whereas the ‘digitals’ find the external digital resources very useful (videos, webpages, etc.), the ‘traditionalists’ rate the digitalized traditional resources best (lecture, tutorials, etc.). All resources receive uniformly good ratings from a third group (‘all resource users’). We reflect on our findings in light of the pandemic and describe directions for future research. AU - Kempen, Leander AU - Liebendörfer, Michael ID - 37473 IS - 4 JF - Teaching Mathematics and its Applications: An International Journal of the IMA KW - Education KW - General Mathematics SN - 0268-3679 TI - University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics VL - 40 ER - TY - CONF AU - Liebendörfer, Michael AU - Hochmuth, Reinhard AU - Rode, Jana AU - Schukajlow, Stanislaw ED - Inprasitha, M. ED - Changsri, N. ED - Boonsena, N. ID - 37487 T2 - Interim Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education TI - The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers VL - 3 ER - TY - JOUR AU - Krapf, Regula AU - Liebendörfer, Michael ID - 37494 IS - 44 JF - mathematica didactica KW - Extrinsische Motivation TI - Was bewirkt die Pflichtabgabe von Übungsaufgaben in der Hochschulmathematik? – Ein empirischer Vergleich VL - 2 ER - TY - JOUR AU - Winkler, Michael ID - 35616 JF - Nonlinear Analysis: Real World Applications TI - Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with gradient-dependent flux limitation. VL - 59 ER - TY - JOUR AU - Winkler, Michael ID - 35615 JF - Zeitschrift für Angewandte Mathematik und Physik TI - Suppressing blow-up by gradient-dependent flux limitation in a planar Keller-Segel-Navier-Stokes system. VL - 72 ER - TY - JOUR AU - Winkler, Michael ID - 35614 JF - International Mathematics Research Notices TI - Can rotational fluxes impede the tendency toward spatial homogeneity in nutrient taxis (-Stokes) systems? VL - 2021 ER - 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 -