@article{59053, author = {{Frischemeier, Daniel and Biehler, Rolf}}, journal = {{Stochastik in der Schule}}, number = {{1}}, pages = {{22--33}}, title = {{{Förderung von statistischem Denken im Mathematikunterricht der Primarstufe: Bedeutsame Ideen und Förderungsmöglichkeiten}}}, volume = {{45}}, year = {{2025}}, } @article{59169, abstract = {{An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. Let G and H be r-graphs. An H-coloring of G is a mapping such that each r adjacent edges of G are mapped to r adjacent edges of H. For every , let be an inclusion-wise minimal set of connected r-graphs, such that for every connected r-graph G there is an which colors G. The Petersen Coloring Conjecture states that consists of the Petersen graph P. We show that if true, then this is a very exclusive situation. Our main result is that either or is an infinite set and if , then is an infinite set. In particular, for all , is unique. We first characterize and then prove that if contains more than one element, then it is an infinite set. To obtain our main result we show that contains the smallest r-graphs of class 2 and the smallest poorly matchable r-graphs, and we determine the smallest r-graphs of class 2.}}, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak H.}}, issn = {{0209-9683}}, journal = {{Combinatorica}}, number = {{2}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Sets of r-Graphs that Color All r-Graphs}}}, doi = {{10.1007/s00493-025-00144-4}}, volume = {{45}}, year = {{2025}}, } @article{60205, author = {{Black, Tobias}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, publisher = {{Elsevier BV}}, title = {{{Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier–Stokes system}}}, doi = {{10.1016/j.jde.2025.113555}}, volume = {{443}}, year = {{2025}}, } @unpublished{60293, abstract = {{In this work, we present a complete characterization of the covariance structure of number statistics in boxes for hyperuniform point processes. Under a standard integrability assumption, the covariance depends solely on the overlap of the faces of the box. Beyond this assumption, a novel interpolating covariance structure emerges. This enables us to identify a limiting Gaussian 'coarse-grained' process, counting the number of points in large boxes as a function of the box position. Depending on the integrability assumption, this process may be continuous or discontinuous, e.g. in d=1 it is given by an increment process of a fractional Brownian motion.}}, author = {{Jalowy, Jonas and Stange, Hanna}}, booktitle = {{arXiv:2506.13661}}, title = {{{Box-Covariances of Hyperuniform Point Processes}}}, year = {{2025}}, } @article{60351, abstract = {{This article is a short summary of the report of survey team 3, presented to the 15th International Congress on Mathematical Education (ICME-15) in Sydney in July 2024.}}, author = {{Biehler, Rolf and Kawakami, Takashi and Lampen, Erna and Weiland, Travis and Zapata-Cardona, Lucía}}, issn = {{2747-7894}}, journal = {{European Mathematical Society Magazine}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Statistics and data science education as a vehicle for empowering citizens – short summary of a survey}}}, doi = {{10.4171/mag/257}}, year = {{2025}}, } @article{53805, abstract = {{The article introduces a method to learn dynamical systems that are governed by Euler–Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian, including of Hamiltonian functions (energy) and symplectic structures, which is of interest in the context of system identification. The article overcomes major practical and theoretical difficulties related to the ill-posedness of the identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex minimisation problems in reproducing kernel Hilbert spaces.}}, author = {{Offen, Christian}}, journal = {{Mathematics of Computation}}, publisher = {{American Mathematical Society}}, title = {{{Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}}}, doi = {{10.1090/mcom/4120}}, year = {{2025}}, } @article{60495, author = {{Podworny, Susanne and Fleischer, Yannik and Biehler, Rolf}}, journal = {{Stochastik in der Schule}}, number = {{2}}, pages = {{9--16}}, title = {{{Explorative Datenanalyse in der Schule – Analyse der Mediennutzung von Jugendlichen mit den YOU‑PB Daten}}}, volume = {{45}}, year = {{2025}}, } @inbook{60532, author = {{Biehler, Rolf and Schulte, Carsten}}, booktitle = {{Proceedings of the 1st Symposium on Integrating AI and Data Science into School Education Across Disciplines (AIDEA 1 2025), Salzburg, Austria}}, title = {{{Lessons Learned from the ProDaBi Project: Shaping Perspectives at the Intersection of Data, AI, and Education Towards Fostering AI and Data Science Literacy in Schools Across Disciplines.}}}, year = {{2025}}, } @inbook{60816, author = {{Häsel-Weide, Uta and Hußmann, S. and Nührenbörger, M.}}, booktitle = {{Rechnen richtig lernen - flexibel, für alle und von Anfang an. Fachdidaktische Hintergründe und Lernangebote für die Grundschule}}, editor = {{Rechtsteiner, C.}}, pages = {{71--80}}, publisher = {{Klett Kallmeyer}}, title = {{{ Flexibles Addieren und Subtrahieren im Zahlenraum bis 100}}}, year = {{2025}}, } @inproceedings{60860, author = {{Fleischer, Franz Yannik and Biehler, Rolf}}, booktitle = {{Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, Vol. 1 }}, editor = {{Cornejo, C. and Felmer, P. and Gomez, D.M. and Dartnell, P. and Araya, P. and Peri, A. and Randolph, V.}}, pages = {{267--274}}, title = {{{ANALYZING STUDENTS’INFORMAL APPROACHES TO CREATING DECISION TREES IN THE CLASSROOM}}}, year = {{2025}}, } @article{61042, abstract = {{We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs.}}, author = {{Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}}, issn = {{0925-9899}}, journal = {{Journal of Algebraic Combinatorics}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On token signed graphs}}}, doi = {{10.1007/s10801-025-01416-4}}, volume = {{62}}, year = {{2025}}, } @article{61125, author = {{Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Reich, Birte}}, journal = {{Mitteilungen der Deutschen Mathematiker-Vereinigung}}, number = {{3}}, pages = {{170–171}}, publisher = {{De Gruyter}}, title = {{{studiVEMINT Mathematik-Online-Vorkurs jetzt mit 300 integrierten Lernvideos frei verfügbar}}}, volume = {{33}}, year = {{2025}}, } @article{54970, author = {{Quack, Carolin and Bruns, Julia}}, journal = {{Frühe Bildung}}, number = {{2}}, pages = {{72--78}}, title = {{{Mathematikbezogenes Wissen, Einstellungen und Lerngelegenheiten als Einflussfaktoren der situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachkräfte}}}, doi = {{https://doi.org/10.1026/2191-9186/a000712}}, volume = {{14}}, year = {{2025}}, } @article{62291, abstract = {{In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $\infty$. In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions. We cover Touchard, Fubini, Eulerian, Narayana and little $q$-Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices.}}, title = {{{Zeros and exponential profiles of polynomials II: Examples}}}, doi = {{10.48550/ARXIV.2509.11248}}, year = {{2025}}, } @article{56131, abstract = {{This article provides a comprehensive mathematical-didactic analysis of how the highly relevant topic symmetry can be prepared for the university education of PSTs. Methodologically, the analysis is embedded in a design research cycle and serves as preparation for the actual design of learning activities. The procedure of "specifying and structuring" learning objects is used and adapted in such a way that, in addition to mathematical aspects, profession-oriented references to school mathematics are also considered. An essential result of the analysis is the formulation of so-called interface aspects to symmetry, which prove to be helpful in establishing such references. }}, author = {{Hoffmann, Max}}, journal = {{Recherches en Didactique des Mathématiques}}, number = {{2}}, pages = {{85--120}}, title = {{{Symmetry as a Topic for the University Education of Pre-Service Teachers}}}, doi = {{10.46298/rdm.14256}}, volume = {{45}}, year = {{2025}}, } @inproceedings{65246, author = {{Hoffmann, Max}}, booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}}, editor = {{Bosch, Marianna and Bolondi, Giorgio and Carreira, Susana and Gaidoschik, Michael and Spagnolo, Camilla}}, pages = {{2245--2252}}, publisher = {{Free University of Bozen-Bolzano and ERME}}, title = {{{Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry}}}, year = {{2025}}, } @article{53413, abstract = {{For negatively curved symmetric spaces it is known that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms.}}, author = {{Delarue, Benjamin and Hilgert, Joachim}}, issn = {{0949-5932}}, journal = {{Journal of Lie Theory}}, number = {{(4)}}, pages = {{787----804}}, title = {{{Quantum resonances and scattering poles of classical rank one locally symmetric spaces}}}, volume = {{35}}, year = {{2025}}, } @article{65657, author = {{Hoffmann, Jan Sören and Stoppel, Hans-Jürgen}}, journal = {{mathematik lehren}}, number = {{253}}, pages = {{8--12}}, title = {{{Das Sieb des Eratosthenes}}}, year = {{2025}}, } @article{65713, author = {{Stoppel, Hans-Jürgen and Plangg, Simon and Büscher, Carina}}, journal = {{mathemathik lehren}}, number = {{253}}, pages = {{2--7}}, publisher = {{Friedrich Verlag}}, title = {{{Mathematik weiterdenken - Wie informatisches Denken die Mathematik stärkt}}}, year = {{2025}}, } @inbook{64806, author = {{Biehler, Rolf and Kawakami, T. and Lampen, E. and Weiland, T. and Zapata-Cardona, L.}}, booktitle = {{Proceedings of the 15th International Congress on Mathematical Education}}, editor = {{Beswick, K. and Kaur, B. and Makar, K. and Ochoviet, C. and Venkat, H.}}, pages = {{198--203}}, publisher = {{MERGA}}, title = {{{Statistics and data science education as a vehicle for empowering citizens – short summary of a survey}}}, volume = {{1}}, year = {{2025}}, }