@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@unpublished{55159,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}},
}

@inbook{56021,
  author       = {{Häsel-Weide, Uta and Nührenbörger, M.}},
  booktitle    = {{Inklusives Lehren und Lernen von Mathematik: Konzepte und Beispiele mit Fokus auf Grund- und Förderschule}},
  editor       = {{Barzel, B. and Büchter, A. and Rütten, C. and Schacht, F. and Weskamp-Kleine, S.}},
  pages        = {{97--113}},
  publisher    = {{Springer Fachmedien Wiesbaden}},
  title        = {{{Produktives Fördern im inklusiven Mathematikunterricht}}},
  doi          = {{https://doi.org/10.1007/978-3-658-43964-4_7 }},
  year         = {{2024}},
}

@article{56022,
  author       = {{Häsel-Weide, Uta and Wallner, Melina}},
  journal      = {{Journal für Mathematik-Didaktik}},
  number       = {{2}},
  title        = {{{Achsensymmetrisch?! Praktiken, soziale und sozio-mathematische Normen der Begründung der Achsensymmetrie ebener Figuren in der Grundschule}}},
  doi          = {{https://doi.org/10.1007/s13138-024-00241-9}},
  volume       = {{45}},
  year         = {{2024}},
}

@article{56197,
  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}},
}

@unpublished{56114,
  author       = {{Pinaud, Matthieu}},
  title        = {{{Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups}}},
  year         = {{2024}},
}

@book{56199,
  editor       = {{Liebendörfer, Michael and Schmitz, Angelika and Biehler, Rolf}},
  title        = {{{Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln}}},
  year         = {{2024}},
}

@article{56366,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl convolution  of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system  we consider the Riesz distributions  and prove that their Dunkl convolution exists and that  holds.</jats:p>}},
  author       = {{Brennecken, Dominik}},
  issn         = {{0025-584X}},
  journal      = {{Mathematische Nachrichten}},
  publisher    = {{Wiley}},
  title        = {{{Dunkl convolution and elliptic regularity for Dunkl operators}}},
  doi          = {{10.1002/mana.202300370}},
  year         = {{2024}},
}

@article{56497,
  author       = {{Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}},
  issn         = {{0012-365X}},
  journal      = {{Discrete Mathematics}},
  number       = {{1}},
  publisher    = {{Elsevier BV}},
  title        = {{{Critically 3-frustrated signed graphs}}},
  doi          = {{10.1016/j.disc.2024.114258}},
  volume       = {{348}},
  year         = {{2024}},
}

@article{56584,
  author       = {{Suri, Ali}},
  journal      = {{Journal of Geometry and Physics}},
  pages        = {{105109}},
  title        = {{{Curvature and stability of quasi-geostrophic motion}}},
  volume       = {{198}},
  year         = {{2024}},
}

@article{56585,
  author       = {{Suri, Ali}},
  journal      = {{Journal of Geometry and Physics}},
  pages        = {{105333}},
  title        = {{{Conjugate points along spherical harmonics}}},
  volume       = {{206}},
  year         = {{2024}},
}

@unpublished{56583,
  author       = {{Glöckner, Helge and Suri, Ali}},
  title        = {{{L^1-regularity of strong ILB-Lie groups}}},
  year         = {{2024}},
}