@article{46100, author = {{Hinrichs, Benjamin and Janssen, Daan W. and Ziebell, Jobst}}, issn = {{0022-247X}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Applied Mathematics, Analysis}}, number = {{1}}, publisher = {{Elsevier BV}}, title = {{{Super-Gaussian decay of exponentials: A sufficient condition}}}, doi = {{10.1016/j.jmaa.2023.127558}}, volume = {{528}}, year = {{2023}}, } @unpublished{46117, abstract = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in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 L.}}, booktitle = {{arXiv:2304.09573}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, year = {{2023}}, } @article{46155, author = {{Bruns, Julia and Hagena, Maike and Gasteiger, Hedwig}}, issn = {{0742-051X}}, journal = {{Teaching and Teacher Education}}, keywords = {{Education}}, publisher = {{Elsevier BV}}, title = {{{Professional Development Enacted by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?}}}, doi = {{10.1016/j.tate.2023.104270}}, volume = {{132}}, year = {{2023}}, } @book{46157, editor = {{Biehler, Rolf and Liebendörfer, Michael and Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}}, isbn = {{9783031141744}}, issn = {{1869-4918}}, publisher = {{Springer International Publishing}}, title = {{{Practice-Oriented Research in Tertiary Mathematics Education}}}, doi = {{10.1007/978-3-031-14175-1}}, year = {{2023}}, } @article{46256, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0895-4801}}, journal = {{SIAM Journal on Discrete Mathematics}}, keywords = {{General Mathematics}}, number = {{3}}, pages = {{1548--1565}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}}}, doi = {{10.1137/22m1500654}}, volume = {{37}}, year = {{2023}}, } @inproceedings{42163, abstract = {{The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.}}, author = {{Offen, Christian and Ober-Blöbaum, Sina}}, booktitle = {{Geometric Science of Information}}, editor = {{Nielsen, F and Barbaresco, F}}, keywords = {{System identification, discrete Lagrangians, travelling waves}}, location = {{Saint-Malo, Palais du Grand Large, France}}, pages = {{569--579}}, publisher = {{Springer, Cham.}}, title = {{{Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}}}, doi = {{10.1007/978-3-031-38271-0_57}}, volume = {{14071}}, year = {{2023}}, } @article{29240, abstract = {{The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this, we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.}}, author = {{Ober-Blöbaum, Sina and Offen, Christian}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Lagrangian learning, variational backward error analysis, modified Lagrangian, variational integrators, physics informed learning}}, pages = {{114780}}, publisher = {{Elsevier}}, title = {{{Variational Learning of Euler–Lagrange Dynamics from Data}}}, doi = {{10.1016/j.cam.2022.114780}}, volume = {{421}}, year = {{2023}}, } @article{29236, abstract = {{The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.}}, author = {{McLachlan, Robert and Offen, Christian}}, journal = {{Journal of Geometric Mechanics}}, keywords = {{variational integrators, backward error analysis, Euler--Lagrange equations, multistep methods, conjugate symplectic methods}}, number = {{1}}, pages = {{98--115}}, publisher = {{AIMS Press}}, title = {{{Backward error analysis for conjugate symplectic methods}}}, doi = {{10.3934/jgm.2023005}}, volume = {{15}}, year = {{2023}}, } @article{37654, abstract = {{Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.}}, author = {{Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}}, issn = {{1054-1500}}, journal = {{Chaos}}, number = {{6}}, publisher = {{AIP Publishing}}, title = {{{Hamiltonian Neural Networks with Automatic Symmetry Detection}}}, doi = {{10.1063/5.0142969}}, volume = {{33}}, year = {{2023}}, } @article{23428, abstract = {{The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d. samples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the best of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.}}, author = {{Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}}, journal = {{Journal of Nonlinear Science}}, title = {{{Finite-data error bounds for Koopman-based prediction and control}}}, doi = {{10.1007/s00332-022-09862-1}}, volume = {{33}}, year = {{2023}}, } @article{21600, abstract = {{Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML.}}, author = {{Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}}, journal = {{SIAM Journal on Scientific Computing}}, number = {{2}}, pages = {{A579--A595}}, title = {{{Efficient time stepping for numerical integration using reinforcement learning}}}, doi = {{10.1137/21M1412682}}, volume = {{45}}, year = {{2023}}, } @inproceedings{46757, author = {{Schwerin, Imke and Häsel-Weide, Uta}}, booktitle = {{International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}}, editor = {{Novotna, J. and Moraova, H.}}, location = {{Prag}}, pages = {{297--305}}, publisher = {{Charles University}}, title = {{{Second grader´s understanding of doubling and halfing in various representations}}}, year = {{2023}}, } @inbook{46758, author = {{Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}}, booktitle = {{Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre}}, editor = {{Vöing, N. and Schmidt, R. and Neiske, I.}}, pages = {{297--318}}, publisher = {{Visual Ink Publishing}}, title = {{{Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern}}}, year = {{2023}}, } @inbook{47416, author = {{Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel}}, booktitle = {{Handbuch der Mathematikdidaktik}}, editor = {{Bruder, Regina and Büchter, A. and Gasteiger, H. and Schmidt-Thieme, B. and Weigand, HG.}}, isbn = {{9783662666036}}, publisher = {{Springer}}, title = {{{Stochastik: Leitidee Daten und Zufall}}}, doi = {{10.1007/978-3-662-66604-3_8}}, year = {{2023}}, } @unpublished{47534, abstract = {{In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is well-known, the corresponding Hamiltonian can be defined with the help of an energy renormalization. First, we review a Feynman-Kac formula for the semigroup generated by this Hamiltonian proven by the authors in a recent preprint (where several matter particles and exterior potentials are treated as well). After that, we employ a few technical key relations and estimates obtained in our preprint to present an otherwise self-contained derivation of new Feynman-Kac formulas for the fiber Hamiltonians attached to fixed total momenta of the translation invariant system. We conclude by inferring an alternative derivation of the Feynman-Kac formula for the full translation invariant Hamiltonian.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{arXiv:2309.09005}}, title = {{{Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}}}, year = {{2023}}, } @inbook{48042, author = {{Biehler, Rolf and Frischemeier, Daniel and Gould, Ronald and Pfannkuch, Maxine}}, booktitle = {{Handbook of Digital Resources in Mathematics Education}}, editor = {{Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}}, publisher = {{Springer International Publishing}}, title = {{{Impacts of Digitalization on Content and Goals of Statistics Education}}}, year = {{2023}}, } @inbook{48319, author = {{Leiss, Dominik and Gerlach, Kerstin and Wessel, Lena and Schmidt-Thieme, Barbara}}, booktitle = {{Handbuch der Mathematikdidaktik}}, isbn = {{9783662666036}}, pages = {{561--595}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Sprache und Mathematiklernen}}}, doi = {{10.1007/978-3-662-66604-3_18}}, year = {{2023}}, } @inbook{48480, author = {{Kortmeyer, Jörg and Biehler, Rolf}}, booktitle = {{The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference}}, editor = {{Dreyfus, T. and Gonzalez-Martin, A. S. and Nardi, E. and Monaghan, J. and Thompson, P. W.}}, pages = {{121--124}}, publisher = {{MatRIC}}, title = {{{The use of integrals for accumulation and mean values in basic electrical engineering courses}}}, year = {{2023}}, } @article{49049, author = {{Biehler, Rolf and Krüger, Katja}}, journal = {{GDM-Mitteilungen}}, number = {{115}}, pages = {{57--65}}, title = {{{Von Glückstal (Ukraine) nach Frankfurt: Problemlösen, Algorithmen, Stochastik – Nachruf auf Arthur Engel}}}, year = {{2023}}, } @inproceedings{46756, author = {{Wallner, Melina and Häsel-Weide, Uta}}, booktitle = {{International Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education}}, editor = {{Novotna, J. and Moraova, H.}}, location = {{Prag}}, pages = {{346--354}}, publisher = {{Charles University}}, title = {{{Conceptual understanding of third grades for axial symmetry}}}, year = {{2023}}, } @article{49326, abstract = {{Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0036-1399}}, journal = {{SIAM Journal on Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{6}}, pages = {{2329--2353}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}}}, doi = {{10.1137/23m1561075}}, volume = {{83}}, year = {{2023}}, } @unpublished{49371, abstract = {{To model dynamical systems on networks with higher order (non-pairwise) interactions, we recently introduced a new class of ODEs on hypernetworks. Here we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady state branch "reluctant" if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady state branch.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, booktitle = {{arXiv:2311.17186}}, title = {{{Higher order interactions lead to "reluctant" synchrony breaking}}}, year = {{2023}}, } @article{49372, author = {{Klüners, Jürgen and Wang, Jiuya}}, issn = {{2730-9657}}, journal = {{La Matematica}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Idélic Approach in Enumerating Heisenberg Extensions}}}, doi = {{10.1007/s44007-023-00067-w}}, year = {{2023}}, } @article{49425, author = {{Seitz, Simone and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}}, journal = {{Teachers and Teaching}}, pages = {{1--16}}, title = {{{Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research}}}, doi = {{https://doi.org/10.1080/13540602.2023.2284876 }}, year = {{2023}}, } @inproceedings{34135, abstract = {{By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.}}, author = {{Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}}, booktitle = {{IFAC-PapersOnLine}}, location = {{ Yokohama, Japan}}, number = {{2}}, pages = {{3203--3210}}, publisher = {{Elsevier}}, title = {{{Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}}}, doi = {{10.1016/j.ifacol.2023.10.1457}}, volume = {{56}}, year = {{2023}}, } @unpublished{44840, abstract = {{In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a gathering protocol as a system of ordinary differential equations whose equilibria are exactly all possible gathering points. Then, we find necessary and sufficient conditions for the structure of the underlying interaction graph such that the protocol is stable and converging, i.e., gathering, in the distributive computing sense by using tools from dynamical systems. Moreover, these tools allow for a more fine grained analysis in terms of speed of convergence in the dynamical systems sense. In fact, we derive a decomposition of the state space into stable invariant subspaces with different convergence rates. In particular, this decomposition is identical for every (linear) circulant gathering protocol, whereas only the convergence rates depend on the weights in interaction graph itself.}}, author = {{Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}}, booktitle = {{arXiv:2305.06632}}, keywords = {{Dynamical Systems, Coupled Systems, Distributed Computing, Robot Swarms, Autonomous Mobile Robots, Gathering}}, pages = {{38}}, title = {{{On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}}}, year = {{2023}}, } @article{50298, abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.}}, author = {{Schmidt, Kai-Uwe and Weiß, Charlene}}, journal = {{Combinatorial Theory}}, number = {{1}}, title = {{{Packings and Steiner systems in polar spaces}}}, doi = {{10.5070/c63160424}}, volume = {{3}}, year = {{2023}}, } @article{50297, abstract = {{We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled.}}, author = {{Schmidt, Kai‐Uwe and Weiß, Charlene}}, journal = {{Journal of Combinatorial Designs}}, number = {{9}}, pages = {{422--431}}, publisher = {{Wiley}}, title = {{{Existence of small ordered orthogonal arrays}}}, doi = {{10.1002/jcd.21903}}, volume = {{31}}, year = {{2023}}, } @phdthesis{50300, abstract = {{Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases.}}, author = {{Weiß, Charlene}}, title = {{{Linear programming bounds in classical association schemes}}}, doi = {{10.17619/UNIPB/1-1672}}, year = {{2023}}, } @unpublished{50299, abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space over $\mathbb{F}_p$ equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic $t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$ designs in polar spaces exist for all $t$ and $p$ provided that $k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a probabilistic method by Kuperberg, Lovett, and Peled, and it is thus nonconstructive.}}, author = {{Weiß, Charlene}}, booktitle = {{arXiv:2311.08288}}, title = {{{Nontrivial $t$-designs in polar spaces exist for all $t$}}}, year = {{2023}}, } @article{48596, author = {{Häsel-Weide, Uta and Schmidt, R. and Büker, Petra}}, journal = {{Zeitschrift für Schul- Und Professionsentwicklung. (PFLB)}}, number = {{1}}, pages = {{215--229}}, title = {{{„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung}}}, volume = {{5}}, year = {{2023}}, } @inproceedings{51131, author = {{Graf, Lara Marie and Häsel-Weide, Uta and Höveler, K. and Nührenbörger, M.}}, booktitle = {{Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)}}, editor = {{Drijvers, P. and Csapodi, C. and Palmér, H. and Gosztonyi, K. and Kónya, E.}}, pages = {{3203--3210}}, title = {{{Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics}}}, year = {{2023}}, } @article{31189, abstract = {{Given a geometrically finite hyperbolic surface of infinite volume it is a classical result of Patterson that the positive Laplace-Beltrami operator has no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of this result for the joint $L^2$-eigenvalues of the algebra of commuting differential operators on Riemannian locally symmetric spaces $\Gamma\backslash G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on the geodesic and the Satake compactifications which imply the absence of the corresponding principal eigenvalues. A large class of examples fulfilling these assumptions are the non-compact quotients by Anosov subgroups.}}, author = {{Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Communications in Mathematical Physics}}, title = {{{Absence of principal eigenvalues for higher rank locally symmetric spaces}}}, doi = {{https://doi.org/10.1007/s00220-023-04819-1}}, volume = {{403}}, year = {{2023}}, } @article{31059, abstract = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}}, author = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}}, journal = {{Communications in Mathematical Physics}}, pages = {{655--678}}, title = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}}, doi = {{ttps://doi.org/10.1007/s00220-022-04538-z}}, volume = {{398}}, year = {{2023}}, } @unpublished{51206, abstract = {{We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of meromorphically continued weighted zeta functions established by the authors together with Barkhofen (2021). To make this applicable for numerics we express the weighted zeta as the logarithmic derivative of a suitable parameter dependent Fredholm determinant similar to Borthwick (2014). As an additional difficulty our transfer operator has to include a contracting direction which we account for with techniques developed by Rugh (1992). We achieve a further improvement in convergence speed for our algorithm in the case of surfaces with additional symmetries by proving and applying a symmetry reduction of weighted zeta functions.}}, author = {{Schütte, Philipp and Weich, Tobias}}, booktitle = {{arXiv:2308.13463}}, title = {{{Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions}}}, year = {{2023}}, } @unpublished{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}}, booktitle = {{arXiv:2304.09573}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, year = {{2023}}, } @article{51351, author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0166-218X}}, journal = {{Discrete Applied Mathematics}}, keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics}}, pages = {{185--189}}, publisher = {{Elsevier BV}}, title = {{{Bounds for the chromatic index of signed multigraphs}}}, doi = {{10.1016/j.dam.2023.05.008}}, volume = {{337}}, year = {{2023}}, } @inbook{45190, author = {{Cappello, Chiara and Steffen, Eckhard}}, booktitle = {{The Digital Twin of Humans}}, isbn = {{9783031261039}}, pages = {{93----110}}, publisher = {{Springer International Publishing}}, title = {{{Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}}}, doi = {{10.1007/978-3-031-26104-6_5}}, year = {{2023}}, } @article{51357, author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0012-365X}}, journal = {{Discrete Mathematics}}, keywords = {{Discrete Mathematics and Combinatorics, Theoretical Computer Science}}, publisher = {{Elsevier BV}}, title = {{{Rotation r-graphs}}}, doi = {{10.1016/j.disc.2023.113457}}, year = {{2023}}, } @unpublished{51375, abstract = {{We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11 (2020)]. We provide a Lieb-Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb-Robinson bounds.}}, author = {{Hinrichs, Benjamin and Lemm, Marius and Siebert, Oliver}}, booktitle = {{arXiv:2310.17736}}, title = {{{On Lieb-Robinson bounds for a class of continuum fermions}}}, year = {{2023}}, } @unpublished{51376, abstract = {{In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.}}, author = {{Hinrichs, Benjamin and Lampart, Jonas}}, booktitle = {{arXiv:2311.05361}}, title = {{{A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate}}}, year = {{2023}}, } @article{31190, abstract = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$.}}, author = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Analysis & PDE}}, number = {{10}}, pages = {{2241–2265}}, publisher = {{MSP}}, title = {{{Higher rank quantum-classical correspondence}}}, volume = {{16}}, year = {{2023}}, } @unpublished{51205, abstract = {{We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators.}}, author = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}}, booktitle = {{arXiv:2307.10876}}, title = {{{Spectral correspondences for finite graphs without dead ends}}}, year = {{2023}}, } @article{31210, abstract = {{In this paper we complete the program of relating the Laplace spectrum for rank one compact locally symmetric spaces with the first band Ruelle-Pollicott resonances of the geodesic flow on its sphere bundle. This program was started by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for general rank one spaces. Except for the case of hyperbolic surfaces a countable set of exceptional spectral parameters always left untreated since the corresponding Poisson transforms are neither injective nor surjective. We use vector valued Poisson transforms to treat also the exceptional spectral parameters. For surfaces the exceptional spectral parameters lead to discrete series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the situation is more complicated, but can be described completely.}}, author = {{Arends, Christian and Hilgert, Joachim}}, issn = {{2270-518X}}, journal = {{Journal de l’École polytechnique — Mathématiques}}, keywords = {{Ruelle resonances, Poisson transforms, locally symmetric spaces, principal series representations}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}}}, doi = {{10.5802/jep.220}}, volume = {{10}}, year = {{2023}}, } @article{51383, author = {{Hilgert, Joachim and Arends, C.}}, journal = {{J. de l'École polytechnique — Mathématiques}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}}}, volume = {{10}}, year = {{2023}}, } @article{51384, author = {{Hilgert, Joachim and Glöckner, H.}}, journal = {{J. Diff. Equations}}, pages = {{186--232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, volume = {{343}}, year = {{2023}}, } @unpublished{51499, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{A pairing formula for resonant states on finite regular graphs}}}, year = {{2023}}, } @unpublished{51500, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{Edge Laplacians and vector valued Poisson transforms for graphs}}}, year = {{2023}}, } @unpublished{51502, author = {{Hilgert, Joachim and Baier, T. and Kaya, O. and Mourao, J. and Nunes, J.}}, title = {{{Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem}}}, year = {{2023}}, } @unpublished{51521, author = {{Hilgert, Joachim and Guedes Bonthonneau, Y. and Guillarmou, C. and Weich, Tobias}}, title = {{{Ruelle-Taylor resonances of Anosov actions}}}, year = {{2023}}, } @unpublished{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 laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. 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 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}}, booktitle = {{arXiv:2307.00975}}, title = {{{Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping}}}, year = {{2023}}, } @unpublished{46578, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".}}, author = {{Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}}, booktitle = {{arXiv:2308.01113}}, title = {{{Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}}}, year = {{2023}}, } @article{34803, author = {{Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}}, journal = {{BIT Numerical Mathematics}}, publisher = {{Springer}}, title = {{{Deep neural networks on diffeomorphism groups for optimal shape reparametrization}}}, doi = {{10.1007/s10543-023-00989-05}}, volume = {{63}}, year = {{2023}}, } @article{34793, author = {{Glöckner, Helge and Hilgert, Joachim}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{22E65, 28B05, 34A12, 34H05, 46E30, 46E40}}, pages = {{186–232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, doi = {{10.1016/j.jde.2022.10.001}}, volume = {{343}}, year = {{2023}}, } @article{34805, abstract = {{Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.}}, author = {{Glöckner, Helge}}, journal = {{Journal of Convex Analysis}}, number = {{1}}, pages = {{343--358}}, publisher = {{Heldermann}}, title = {{{Diffeomorphism groups of convex polytopes}}}, volume = {{30}}, year = {{2023}}, } @article{34801, author = {{Glöckner, Helge and Tárrega, Luis}}, journal = {{Journal of Lie Theory}}, number = {{1}}, pages = {{271--296}}, publisher = {{Heldermann}}, title = {{{Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }}}, volume = {{33}}, year = {{2023}}, } @book{45191, editor = {{Gräßler, Iris and Maier, Günter W. and Steffen, Eckhard and Roesmann, Daniel}}, isbn = {{9783031261039}}, publisher = {{Springer International Publishing}}, title = {{{The Digital Twin of Humans}}}, doi = {{10.1007/978-3-031-26104-6}}, year = {{2023}}, } @article{52806, author = {{Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, pages = {{1--26}}, publisher = {{Informa UK Limited}}, title = {{{Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}}}, doi = {{10.1080/0020739x.2023.2184282}}, year = {{2023}}, } @inbook{52811, author = {{Biehler, Rolf and Guntermann, Dominik and Liebendörfer, Michael and Krämer, Sandra and Schlüter, Sarah}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{407–410}}, publisher = {{WTM}}, title = {{{Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{1}}, year = {{2023}}, } @inbook{52810, author = {{Göller, Robin and Gildehaus, Lara and Liebendörfer, Michael and Besser, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{66–80}}, publisher = {{WTM}}, title = {{{Erfassung und Vergleich (mathematischer) Eingangsvoraussetzungen angehender Studierender verschiedener mathematikhaltiger Studiengänge}}}, year = {{2023}}, } @inbook{52809, author = {{Kempen, Leander and Liebendörfer, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{91–106}}, publisher = {{WTM}}, title = {{{Zu digital - zu viel - zu schwer? Qualitative Einsichten in das Erleben und Handeln von Erstsemester-Studierenden der Mathematik während der Corona-Pandemie}}}, year = {{2023}}, } @inbook{52813, author = {{Schlüter, Sarah and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{1177–1180}}, publisher = {{WTM}}, title = {{{Bearbeitungsmuster von Studierenden im Umgang mit formalen Definitionen im Kontext konstanter Folgen}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @inbook{52812, author = {{Krämer, Sandra and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{949–952}}, publisher = {{WTM}}, title = {{{Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @article{52807, abstract = {{Many preservice mathematics teachers lose their motivation during their first year at university. This phenomenon has been repeatedly described in recent years but is not yet fully under­stood. Since motivation may relate to different objects such as mathematics or teaching, we aim to qualitatively reconstruct different facets of the central motivational constructs of Situated-Expectancy-Value theory (intrinsic value, attainment value, utility value, cost, and expectancy of success) for preservice mathematics teachers. The analysis of longitudinal group interviews of 14 pre­service higher-secondary mathematic teachers from a German university revealed different objects of motivation (e.g., teaching mathematics, scientific mathematics, procedural mathematics, or proof-based mathematics) in preservice teachers' values and expectancy of success. Furthermore, relations between those values and expectancy of success were identified that played a significant role in preservice teachers’ motivational development over their first semester (e.g., relations of attain­ment value for scientific mathematics and psychological cost). Theoretical and practical implications towards a teaching-specific conceptualization of expectancy of success and values and value interventions are being discussed.}}, title = {{{Preservice teachers’ mathematics-related values and expectancy in the transition from school to university}}}, doi = {{10.48489/QUADRANTE.31191}}, year = {{2023}}, } @inbook{16296, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate as is the case for models governed by partial differential equations (PDEs). To decrease the numerical effort to an affordable amount, surrogate models can be used to replace the expensive PDE evaluations. Existing multiobjective optimization methods using model reduction are limited either to low parameter dimensions or to few (ideally two) objectives. In this article, we present a combination of the reduced basis model reduction method with a continuation approach using inexact gradients. The resulting approach can handle an arbitrary number of objectives while yielding a significant reduction in computing time.}}, author = {{Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{Non-Smooth and Complementarity-Based Distributed Parameter Systems}}, editor = {{Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}}, isbn = {{978-3-030-79392-0}}, pages = {{43--76}}, publisher = {{Springer}}, title = {{{ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}}}, doi = {{10.1007/978-3-030-79393-7_3}}, year = {{2022}}, } @inbook{30294, abstract = {{With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios.}}, author = {{Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}}, booktitle = {{German Success Stories in Industrial Mathematics}}, editor = {{Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}}, isbn = {{9783030814540}}, issn = {{1612-3956}}, publisher = {{Springer International Publishing}}, title = {{{Efficient Virtual Design and Testing of Autonomous Vehicles}}}, doi = {{10.1007/978-3-030-81455-7_23}}, volume = {{35}}, year = {{2022}}, } @article{30490, author = {{Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}}, journal = {{AIMS}}, pages = {{57--89}}, title = {{{Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations}}}, volume = {{14(1)}}, year = {{2022}}, } @article{30861, abstract = {{AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.}}, author = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}}, issn = {{0022-3239}}, journal = {{Journal of Optimization Theory and Applications}}, keywords = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Turnpike Property in Optimal Microbial Metabolite Production}}}, doi = {{10.1007/s10957-022-02023-0}}, year = {{2022}}, } @article{31982, abstract = {{AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\Sigma $$ Σ with Betti number $$b_1$$ b 1 , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$ 4 - b 1 , while in the hyperbolic case it is equal to $$4-2b_1$$ 4 - 2 b 1 . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $$S\Sigma $$ S Σ with harmonic 1-forms on $$\Sigma $$ Σ .}}, author = {{Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}}, issn = {{0020-9910}}, journal = {{Inventiones mathematicae}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{303--394}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}}}, doi = {{10.1007/s00222-022-01108-x}}, volume = {{229}}, year = {{2022}}, } @inbook{32233, author = {{Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}}, booktitle = {{Anfangsunterricht für alle Kinder - Willkommen in der Schule!}}, editor = {{Gutzmann, M. and Carle, U.}}, pages = {{200--215}}, title = {{{Symmetrieverständnis von Anfang an}}}, year = {{2022}}, } @inbook{32339, author = {{Häsel-Weide, Uta and Seitz, S. and Wallner, Melina and Wilke, Y.}}, booktitle = {{Qualifizierung für Inklusion. Sekundarstufe}}, editor = {{Lutz, D. and Becker, J. and Buchhaupt, F. and Katzenbach, D. and Strecker, A. and Urban, M.}}, pages = {{83--100}}, publisher = {{Waxmann}}, title = {{{Professionalisierung für inklusiven Mathematikunterricht. Interdisziplinäre Seminarkonzeption zur reflexiven Professionalisierung angehender Mathematiklehrkräfte in der Sekundarstufe}}}, year = {{2022}}, } @article{32338, author = {{Hähn, K. and Häsel-Weide, Uta and Scherer, P.}}, journal = {{QfI - Qualifizierung für Inklusion}}, number = {{2}}, title = {{{Diagnosegeleitete Förderung im inklusiven Mathematikunterricht der Grundschule – Professionalisierung durch reflektierte Handlungspraxis in der Lehrer*innenbildung.}}}, volume = {{3}}, year = {{2022}}, } @article{29673, abstract = {{Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.}}, author = {{Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}}, journal = {{Journal of Physics A: Mathematical and Theoretical}}, number = {{31}}, pages = {{314002}}, publisher = {{IOP Publishing Ltd.}}, title = {{{Koopman analysis of quantum systems}}}, doi = {{10.1088/1751-8121/ac7d22}}, volume = {{55}}, year = {{2022}}, } @unpublished{34618, abstract = {{In this article, we show how second-order derivative information can be incorporated into gradient sampling methods for nonsmooth optimization. The second-order information we consider is essentially the set of coefficients of all second-order Taylor expansions of the objective in a closed ball around a given point. Based on this concept, we define a model of the objective as the maximum of these Taylor expansions. Iteratively minimizing this model (constrained to the closed ball) results in a simple descent method, for which we prove convergence to minimal points in case the objective is convex. To obtain an implementable method, we construct an approximation scheme for the second-order information based on sampling objective values, gradients and Hessian matrices at finitely many points. Using a set of test problems, we compare the resulting method to five other available solvers. Considering the number of function evaluations, the results suggest that the method we propose is superior to the standard gradient sampling method, and competitive compared to other methods.}}, author = {{Gebken, Bennet}}, booktitle = {{arXiv:2210.04579}}, title = {{{Using second-order information in gradient sampling methods for nonsmooth optimization}}}, year = {{2022}}, } @article{34792, author = {{Glöckner, Helge}}, issn = {{2070-0466}}, journal = {{p-Adic Numbers, Ultrametric Analysis, and Applications}}, keywords = {{20Exx, 22Exx, 32Cxx}}, number = {{2}}, pages = {{138–144}}, title = {{{Non-Lie subgroups in Lie groups over local fields of positive characteristic}}}, doi = {{10.1134/S2070046622020042}}, volume = {{14}}, year = {{2022}}, } @article{34791, author = {{Glöckner, Helge and Schmeding, Alexander}}, issn = {{0232-704X}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{58D15, 22E65, 26E15, 26E20, 46E40, 46T20, 58A05}}, number = {{2}}, pages = {{359–398}}, title = {{{Manifolds of mappings on Cartesian products}}}, doi = {{10.1007/s10455-021-09816-y}}, volume = {{61}}, year = {{2022}}, } @article{34796, abstract = {{We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.}}, author = {{Glöckner, Helge}}, issn = {{2075-1680}}, journal = {{Axioms}}, number = {{5}}, title = {{{Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces}}}, doi = {{10.3390/axioms11050221}}, volume = {{11}}, year = {{2022}}, } @unpublished{34804, abstract = {{Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with valued in complex Banach-Lie groups.}}, author = {{Glöckner, Helge}}, booktitle = {{arXiv:2206.11711}}, title = {{{Birkhoff decompositions for loop groups with coefficient algebras}}}, year = {{2022}}, } @phdthesis{31556, abstract = {{Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten. Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor gefunden werden soll, für den die Datenpunkte kritisch sind.}}, author = {{Gebken, Bennet}}, title = {{{Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective optimization}}}, doi = {{10.17619/UNIPB/1-1327}}, year = {{2022}}, } @unpublished{33150, abstract = {{In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem.}}, author = {{Berkemeier, Manuel Bastian and Peitz, Sebastian}}, booktitle = {{arXiv:2208.12094}}, title = {{{Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}}}, year = {{2022}}, } @article{20731, abstract = {{We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e.g., for the training of neural networks). Sparsity is an important feature to ensure robustness against noisy data, but also to find models that are interpretable and easy to analyze due to the small number of relevant terms. It is common practice to enforce sparsity by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when we minimize the main objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the weighting method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method which is specifically tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our method can be seen as a generalization of well-known homotopy methods for linear regression problems to the nonlinear case. Several numerical examples - including neural network training - demonstrate our theoretical findings and the additional insight that can be gained by this multiobjective approach.}}, author = {{Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian}}, journal = {{IEEE Transactions on Pattern Analysis and Machine Intelligence}}, number = {{11}}, pages = {{7797--7808}}, publisher = {{IEEE}}, title = {{{On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation}}}, doi = {{10.1109/TPAMI.2021.3114962}}, volume = {{44}}, year = {{2022}}, } @article{31193, abstract = {{AbstractThe kinetic Brownian motion on the sphere bundle of a Riemannian manifold $$\mathbb {M}$$ M is a stochastic process that models a random perturbation of the geodesic flow. If $$\mathbb {M}$$ M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the $$L^2$$ L 2 -spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.}}, author = {{Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{4}}, pages = {{1283--1296}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}}}, doi = {{10.1007/s00023-021-01121-5}}, volume = {{23}}, year = {{2022}}, } @article{35306, author = {{Guedes Bonthonneau, Yannick and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{3}}, pages = {{851--923}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}}}, doi = {{10.4171/jems/1103}}, volume = {{24}}, year = {{2022}}, } @article{34633, author = {{Hesse, Kerstin and Le Gia, Quoc Thong}}, issn = {{0377-0427}}, journal = {{Journal of Computational and Applied Mathematics}}, keywords = {{Applied Mathematics, Computational Mathematics}}, publisher = {{Elsevier BV}}, title = {{{L_2 error estimates for polynomial discrete penalized least-squares approximation on the sphere from noisy data}}}, doi = {{10.1016/j.cam.2022.114118}}, volume = {{408}}, year = {{2022}}, } @article{34817, author = {{Hanusch, Maximilian}}, issn = {{1019-8385}}, journal = {{Communications in Analysis and Geometry}}, keywords = {{regularity of Lie groups}}, number = {{1}}, pages = {{53--152}}, publisher = {{International Press of Boston}}, title = {{{Regularity of Lie groups}}}, doi = {{10.4310/cag.2022.v30.n1.a2}}, volume = {{30}}, year = {{2022}}, } @techreport{34856, author = {{Hanusch, Maximilian}}, pages = {{385}}, publisher = {{https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}}, title = {{{Analysis 1 und 2 Skript/Buch}}}, year = {{2022}}, } @article{35644, author = {{Kolb, Martin and Klump, Alexander}}, journal = {{Theory of Probability and its Applications}}, number = {{4}}, pages = {{717--744}}, publisher = {{Society for Industrial and Applied Mathematics}}, title = {{{Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}}}, volume = {{67}}, year = {{2022}}, } @article{35649, abstract = {{Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik Pal we study a Fleming-Viot-type particle system consisting of independently moving particles each driven by generalized Bessel processes on the positive real line. Upon hitting the boundary {0} this particle is killed and an uniformly chosen different one branches into two particles. Using the symmetry of the model and the self similarity property of Bessel processes, we obtain a criterion to decide whether the particles converge to the origin at a finite time. This addresses open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate the case of three moving particles and refine the general result of [6, Theorem 1.1(ii)] extending the regime of drift parameters, where convergence does not occur – even to values, where it does occur when considering the case of only two particles.}}, author = {{Kolb, Martin and Liesenfeld, Matthias}}, journal = {{Electronic Journal of Probability}}, number = {{27}}, pages = {{1--28}}, publisher = {{Institute of Mathematical Statistics}}, title = {{{On non-extinction in a Fleming-Viot-type particle model with Bessel drift}}}, doi = {{https://doi.org/10.1214/22-EJP866}}, year = {{2022}}, } @article{35650, abstract = {{We consider autoregressive sequences Xn = aXn−1 + ξn and Mn = max{aMn−1 , ξn} with a constant a ∈ (0, 1) and with positive, in- dependent and identically distributed innovations {ξk }. It is known that if P(ξ1 > x) ∼ d log x with some d ∈ (0, − log a) then the chains {Xn} and {Mn} are null recurrent. We investigate the tail behaviour of recurrence times in this case of logarithmically decaying tails. More precisely, we show that the tails of recurrence times are regularly varying of index −1 − d/ log a. We also prove limit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0. Furthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn} in the case when these chains are positive recurrent and the tail of log ξ1 is subexponential.}}, author = {{Denisov, Denis and Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}}, journal = {{Electronic Journal of Probability}}, pages = {{1--43}}, publisher = {{Institute of Mathematical Statistics}}, title = {{{Persistence of autoregressive sequences with logarithmic tails}}}, doi = {{https://doi.org/10.48550/arXiv.2203.14772}}, volume = {{27}}, year = {{2022}}, } @article{35685, author = {{Liebendörfer, Michael and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, number = {{5}}, pages = {{1133--1152}}, publisher = {{Informa UK Limited}}, title = {{{The role of learning strategies for performance in mathematics courses for engineers}}}, doi = {{10.1080/0020739x.2021.2023772}}, volume = {{53}}, year = {{2022}}, } @article{35718, author = {{Biehler, Rolf and Langlotz, Hubert and Zappe, Wilfried}}, journal = {{mathematik lehren}}, number = {{232}}, pages = {{41–45}}, publisher = {{Friedrich Verlag}}, title = {{{Alles normal?! Daten auf Normalverteilung prüfen–mit schulischen Mitteln}}}, volume = {{2022}}, year = {{2022}}, } @inbook{35696, abstract = {{The data age has led to curriculum developments promoting the relevance of stochastics in mathematics education. This has resulted in an increased demand for teacher professional development (PD) courses, and thus in a rising number of facilitators for this purpose. Their expertise, however, remains under-researched, even though facilitators are the crucial factor in PD success. Our study aims at revealing how one aspect of facilitator expertise, orientation, is connected to other aspects: views on content goals, perception of possible challenges, and attitude towards teaching resources. The explorations reveal differing orientations and learning goals with identical teaching resources for two facilitators who had also been working as a team for the re-design of the PD course for years.}}, author = {{Nieszporek, Ralf and Griese, Birgit and Biehler, Rolf}}, booktitle = {{Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics}}, editor = {{Peters, S. A. and Zapata-Cardona, L. and Bonafini, F. and Fan, A.}}, publisher = {{International Association for Statistical Education}}, title = {{{Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability}}}, doi = {{10.52041/iase.icots11.t4b2}}, year = {{2022}}, } @inproceedings{34919, abstract = {{Fundamental ideas (Burrill & Biehler, 2011) have been specified to structure the curriculum across different age levels and to focus on and revisit the most important ideas. Such ideas must be based on an epistemological analysis of the scientific domain of statistics and its applications. Because these domains are changing, fundamental ideas have to be revisited from time to time. In particular, data science and machine learning have led to new methods and applications in society that must be considered for updating fundamental ideas.}}, author = {{Biehler, Rolf}}, booktitle = {{Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics}}, editor = {{Peters, S. A. and Zapata-Cardona, L. and Bonafini, F. and Fan, A.}}, publisher = {{International Association for Statistical Education}}, title = {{{Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications}}}, doi = {{10.52041/iase.icots11.t1a2}}, year = {{2022}}, } @article{34920, abstract = {{A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from a statistics education research perspective. Data science education is rapidly developing but research into data science education is still in its infancy. The current issue presents a snapshot of this developing field.}}, author = {{Biehler, Rolf and De Veaux, Richard and Engel, Joachim and Kazak, Sibel and Frischemeier, Daniel}}, issn = {{1570-1824}}, journal = {{Statistics Education Research Journal}}, keywords = {{Education, Statistics and Probability}}, number = {{2}}, publisher = {{International Association for Statistical Education}}, title = {{{Editorial: Research on Data Science Education}}}, doi = {{10.52041/serj.v21i2.606}}, volume = {{21}}, year = {{2022}}, } @article{35926, author = {{Biehler, Rolf and Griese, Birgit}}, journal = {{mathematik lehren}}, number = {{232}}, pages = {{2–6}}, publisher = {{Friedrich Verlag}}, title = {{{Modellieren im Stochastikunterricht: Annahmen hinterfragen, Ergebnisse validieren}}}, volume = {{2022}}, year = {{2022}}, } @inproceedings{31367, author = {{Hoffmann, Max and Biehler, Rolf}}, booktitle = {{ Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen }}, editor = {{Halverscheid, Stefan and Kersten, Ina and Schmidt-Thieme, Barbara}}, pages = {{351--368}}, publisher = {{Springer Spektrum}}, title = {{{Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.}}}, year = {{2022}}, } @inproceedings{31365, author = {{Biehler, Rolf and Hoffmann, Max}}, booktitle = {{ Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik}}, editor = {{Isaev, Viktor and Eichler, Andreas and Loose, Frank}}, isbn = {{9783662639474}}, issn = {{2197-8751}}, pages = {{ 49–72}}, publisher = {{Springer}}, title = {{{Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium}}}, doi = {{10.1007/978-3-662-63948-1_4}}, year = {{2022}}, } @misc{35698, author = {{Schürmann, Mirko and Büdenbender-Kuklinski, C. and Lankeit, Elisa and Liebendörfer, Michael and Hochmuth, R. and Biehler, Rolf and Schaper, N.}}, publisher = {{LibreCat University}}, title = {{{Dokumentation der Erhebungsinstrumente des Projekts WiGeMath}}}, doi = {{10.17170/KOBRA-202205176188}}, year = {{2022}}, } @article{37470, abstract = {{AbstractWhen the COVID-19 pandemic began, many universities switched to fully online teaching. This unexpected switching to online teaching was challenging for both teachers and students, and restrictions that were put in place because of pandemic made this challenge even greater. However, new ways of teaching might also open new opportunities for students’ learning. The research question driving our study was as follows: how do students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online as offered during the COVID-19 pandemic? We report on a longitudinal, qualitative study in which students recorded a brief audio diary twice a week over one whole semester (14 weeks). We focused on three students who completed 70 interviews in total and finished the semester with varying degrees of success. The results show how the students structured their studying (e.g., the roles that deadlines or synchronous teaching events played). They illustrate the strengths and limitations of digital materials provided by the lecturer and the use of complementary media. Further, the pandemic uncovered the double-edged role of simple, often anonymous exchanges (e.g., via Discord servers), with few binding forces for either side, and the significance of stable learning partnerships for students’ success. Our research highlights aspects that should be focal points when comparing traditional instruction and online instruction during the pandemic from a self-regulatory perspective. Practical implications refer to how these aspects can be combined sensibly in fully online courses, but also in blended learning contexts.}}, author = {{Liebendörfer, Michael and Kempen, Leander and Schukajlow, Stanislaw}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, keywords = {{General Mathematics, Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{First-year university students' self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study}}}, doi = {{10.1007/s11858-022-01444-5}}, year = {{2022}}, } @article{37472, abstract = {{AbstractAs earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher education is proposed, consisting of relevance content and relevance reasons. We investigate students' relevance perceptions of mathematical topics and of topics’ complexities, as well as their rating of individual and societal/ vocational relevance reasons, all in relation to their perception of the relevance of their overall program of study. Contrary to earlier research findings, our results suggest that mathematics teaching students already do attribute relevance to many content areas and that a preparation for the teaching profession is not the only reason for them to assign relevance. There also seem to be many students who would attribute relevance if they could develop as individuals and pursue their interests. We suggest that giving students opportunities to set individual priorities in their studies could hence support their relevance assessments. As low relevance assessments seem to be connected to students’ motivational problems, students might profit from motivational support, as well.}}, author = {{Büdenbender-Kuklinski, Christiane and Hochmuth, Reinhard and Liebendörfer, Michael}}, issn = {{2198-9745}}, journal = {{International Journal of Research in Undergraduate Mathematics Education}}, keywords = {{Education, Mathematics (miscellaneous)}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students}}}, doi = {{10.1007/s40753-022-00188-7}}, year = {{2022}}, }