@article{51841,
  abstract     = {{athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.}},
  author       = {{Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and Hoffmann, Max}},
  journal      = {{mathematik lehren}},
  pages        = {{42 -- 47}},
  title        = {{{Digitalisierung als Chance für alle Prinzipien guten Unterrichts}}},
  volume       = {{242}},
  year         = {{2024}},
}

@inbook{50554,
  author       = {{Prediger, Susanne and Wessel, Lena}},
  booktitle    = {{Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}},
  editor       = {{Efing, Christian and Kalkavan-Aydin, Zeynep}},
  isbn         = {{978-3-11-074544-3}},
  pages        = {{363--372}},
  publisher    = {{DE GRUYTER}},
  title        = {{{31 Sprachbildung im berufsbezogenen Mathematikunterricht.}}},
  volume       = {{Band 3}},
  year         = {{2024}},
}

@article{51207,
  abstract     = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of
non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times
G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the
asymptotic growth of $\Gamma$ in the two direction defined by the two factors.
We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of
$\Gamma$.}},
  author       = {{Weich, Tobias and Wolf, Lasse Lennart}},
  journal      = {{Geom Dedicata}},
  title        = {{{Temperedness of locally symmetric spaces: The product case}}},
  doi          = {{https://doi.org/10.1007/s10711-024-00904-4}},
  volume       = {{218}},
  year         = {{2024}},
}

@article{54078,
  author       = {{Häsel-Weide, Uta and Graf, Lara Marie and Höveler, K. and Nührenbörger, M.}},
  journal      = {{HLZ – Herausforderung Lehrer*innenbildung}},
  number       = {{1}},
  title        = {{{Fachbezogene Professionalisierung von fachfremd Mathematik unterrichtenden Lehrkräften: Retrospektive Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten beim Mathematiklernen im Anfangsunterricht der Grundschule}}},
  doi          = {{10.11576/hlz-6727}},
  volume       = {{7}},
  year         = {{2024}},
}

@article{54144,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>In this paper, we propose a novel conceptual framework tailored for modeling the meaning of mathematical concepts in university-level mathematics, addressing their rigorous nature and their relationships with related concepts as well as interpretations in various contexts. Within this framework, we present a model of meaning for the concepts of total differentiability and total derivative that provides a variety of possible interpretations and aspects. We then use the proposed model of meaning as a tool for analyzing three different textbooks for mathematics majors on the topic of multidimensional differentiability. Our paper is an example of a subject matter analysis of a topic in university mathematics carried out in a structured way. The model of meaning for total differentiability presented in this paper could inspire course design and analysis including the design of assignments and assessments for students. Moreover, it could serve as a valuable research tool for further analyses. For example, it could be used as a framework for analyzing courses taught or as a basis for developing a test instrument to assess students’ understanding. With our textbook analysis, we begin to examine the landscape of textbooks regarding differentiability concepts in the multidimensional case, shedding light on the diversity of meaning facets that are covered in the textbooks. These results could be useful for guiding instructors and learners in selecting and using textbooks for teaching and learning based on their respective needs.</jats:p>}},
  author       = {{Lankeit, Elisa and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{The meaning landscape of the concept of the total derivative in multivariable real analysis textbooks: an analysis based on a new model of meaning}}},
  doi          = {{10.1007/s11858-024-01584-w}},
  year         = {{2024}},
}

@article{53534,
  abstract     = {{It is known that the notion of a transitive subgroup of a permutation group
$G$ extends naturally to subsets of $G$. We consider subsets of the general
linear group $\operatorname{GL}(n,q)$ acting transitively on flag-like
structures, which are common generalisations of $t$-dimensional subspaces of
$\mathbb{F}_q^n$ and bases of $t$-dimensional subspaces of $\mathbb{F}_q^n$. We
give structural characterisations of transitive subsets of
$\operatorname{GL}(n,q)$ using the character theory of $\operatorname{GL}(n,q)$
and interpret such subsets as designs in the conjugacy class association
scheme of $\operatorname{GL}(n,q)$. In particular we generalise a theorem of
Perin on subgroups of $\operatorname{GL}(n,q)$ acting transitively on
$t$-dimensional subspaces. We survey transitive subgroups of
$\operatorname{GL}(n,q)$, showing that there is no subgroup of
$\operatorname{GL}(n,q)$ with $1<t<n$ acting transitively on $t$-dimensional
subspaces unless it contains $\operatorname{SL}(n,q)$ or is one of two
exceptional groups. On the other hand, for all fixed $t$, we show that there
exist nontrivial subsets of $\operatorname{GL}(n,q)$ that are transitive on
linearly independent $t$-tuples of $\mathbb{F}_q^n$, which also shows the
existence of nontrivial subsets of $\operatorname{GL}(n,q)$ that are transitive
on more general flag-like structures. We establish connections with orthogonal
polynomials, namely the Al-Salam-Carlitz polynomials, and generalise a result
by Rudvalis and Shinoda on the distribution of the number of fixed points of
the elements in $\operatorname{GL}(n,q)$. Many of our results can be
interpreted as $q$-analogs of corresponding results for the symmetric group.}},
  author       = {{Ernst, Alena and Schmidt, Kai-Uwe}},
  journal      = {{Mathematische Zeitschrift}},
  number       = {{45}},
  title        = {{{Transitivity in finite general linear groups}}},
  doi          = {{10.1007/s00209-024-03511-x}},
  volume       = {{307}},
  year         = {{2024}},
}

@article{32447,
  abstract     = {{We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.}},
  author       = {{Sonntag, Konstantin and Peitz, Sebastian}},
  issn         = {{1095-7189}},
  journal      = {{SIAM Journal on Optimization}},
  keywords     = {{multiobjective optimization, Pareto optimization, Lyapunov analysis, gradient-likedynamical systems, inertial dynamics, asymptotic vanishing damping, fast convergence}},
  number       = {{3}},
  pages        = {{2259 -- 2286}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  title        = {{{Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping}}},
  doi          = {{10.1137/23M1588512}},
  volume       = {{34}},
  year         = {{2024}},
}

@inproceedings{55191,
  author       = {{Rezat, Sebastian and Visnovska, Jana and Yan, Guorui and Leshota, Moneoang and Sabra, Hussein}},
  booktitle    = {{Proceedings of the 14th International Congress on Mathematical Education}},
  keywords     = {{Mathematics, Mathematik, Textbook, Curriculum Resources, Schulbuch}},
  pages        = {{537–545}},
  publisher    = {{World Scientific}},
  title        = {{{Topic Study Group 41: Research and development on textbooks and resources for learning and teaching mathematics}}},
  doi          = {{10.1142/9789811287152_0065}},
  volume       = {{1}},
  year         = {{2024}},
}

@article{55276,
  author       = {{Minelli, P. and Sourmelidis, A. and Technau, Marc}},
  journal      = {{Int. Math. Res. Not. IMRN}},
  number       = {{10}},
  pages        = {{8485–8502}},
  title        = {{{On restricted averages of Dedekind sums}}},
  doi          = {{10.1093/imrn/rnad283}},
  volume       = {{2024}},
  year         = {{2024}},
}

@article{55278,
  author       = {{Technau, Marc}},
  journal      = {{Proc. Amer. Math. Soc.}},
  number       = {{1}},
  pages        = {{63–69}},
  title        = {{{Remark on the Farey fraction spin chain}}},
  doi          = {{10.1090/proc/16520}},
  volume       = {{152}},
  year         = {{2024}},
}

@book{55193,
  author       = {{Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}},
  isbn         = {{9783662673560}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}}},
  doi          = {{10.1007/978-3-662-67357-7}},
  year         = {{2024}},
}

@article{46469,
  abstract     = {{We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation. }},
  author       = {{Offen, Christian and Ober-Blöbaum, Sina}},
  issn         = {{1054-1500}},
  journal      = {{Chaos}},
  number       = {{1}},
  publisher    = {{AIP Publishing}},
  title        = {{{Learning of discrete models of variational PDEs from data}}},
  doi          = {{10.1063/5.0172287}},
  volume       = {{34}},
  year         = {{2024}},
}

@unpublished{55159,
  abstract     = {{We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.
The article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.}},
  author       = {{Offen, Christian}},
  keywords     = {{System identification, inverse problem of variational calculus, Gaussian process, Lagrangian learning, physics informed machine learning, geometry aware learning}},
  pages        = {{28}},
  title        = {{{Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}}},
  year         = {{2024}},
}

@article{55667,
  abstract     = {{<jats:p>This study investigates how 11- to 12-year-old students construct data-based decision trees using data cards for classification purposes. We examine the students' heuristics and reasoning during this process. The research is based on an eight-week teaching unit during which students labeled data, built decision trees, and assessed them using test data. They learned to manually construct decision trees to classify food items as recommendable or not. They utilized data cards with a heuristic that is a simplified form of a machine learning algorithm. We report on evidence that this topic is teachable to middle school students, along with insights for refining our teaching approach and broader implications for teaching machine learning at the school level.</jats:p>}},
  author       = {{Fleischer, Franz Yannik and Podworny, Susanne and Biehler, Rolf}},
  issn         = {{1570-1824}},
  journal      = {{Statistics Education Research Journal}},
  number       = {{1}},
  publisher    = {{International Association for Statistical Education}},
  title        = {{{Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School}}},
  doi          = {{10.52041/serj.v23i1.450}},
  volume       = {{23}},
  year         = {{2024}},
}

@inbook{55756,
  author       = {{Biehler, Rolf and Frischemeier, Daniel}},
  booktitle    = {{Inklusives Lehren und Lernen von Mathematik}},
  isbn         = {{9783658439637}},
  publisher    = {{Springer Fachmedien Wiesbaden}},
  title        = {{{Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe}}},
  doi          = {{10.1007/978-3-658-43964-4_13}},
  year         = {{2024}},
}

@book{55758,
  author       = {{Biehler, Rolf and Frischemeier, Daniel}},
  publisher    = {{Klett Kallmeyer}},
  title        = {{{Daten-Spürnasen auf Spurensuche: Datenanalyse in der Grundschule mit digitalen Werkzeugen}}},
  year         = {{2024}},
}

@article{45972,
  author       = {{Kovács, Balázs}},
  journal      = {{SIAM Journal on Scientific Computing}},
  number       = {{2}},
  pages        = {{A645----A669}},
  title        = {{{Numerical surgery for mean curvature flow of surfaces}}},
  doi          = {{10.1137/22M1531919}},
  volume       = {{46}},
  year         = {{2024}},
}

@article{53300,
  author       = {{Brennecken, Dominik}},
  issn         = {{0022-247X}},
  journal      = {{Journal of Mathematical Analysis and Applications}},
  keywords     = {{Applied Mathematics, Analysis}},
  number       = {{2}},
  publisher    = {{Elsevier BV}},
  title        = {{{Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}}},
  doi          = {{10.1016/j.jmaa.2024.128125}},
  volume       = {{535}},
  year         = {{2024}},
}

@article{56016,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Special tasks for pre-service teachers (PSTs) in university mathematics courses (“interface tasks”) are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.</jats:p>}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures}}},
  doi          = {{10.1007/s11858-024-01633-4}},
  year         = {{2024}},
}

@inbook{56001,
  author       = {{Brennecken, Dominik and Rösler, Margit}},
  booktitle    = {{Women in Analysis and PDE}},
  editor       = {{Chatzakou, Marianna and Ruzhansky, Michael and Stoeva, Diana}},
  isbn         = {{978-3-031-57004-9}},
  pages        = {{425}},
  publisher    = {{Birkhäuser Cham}},
  title        = {{{The Laplace transform in Dunkl theory}}},
  volume       = {{5}},
  year         = {{2024}},
}