@article{31263,
  author       = {{Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{2644-9463}},
  journal      = {{Annales Henri Lebesgue}},
  pages        = {{81--119}},
  publisher    = {{Cellule MathDoc/CEDRAM}},
  title        = {{{High frequency limits for invariant Ruelle densities}}},
  doi          = {{10.5802/ahl.67}},
  volume       = {{4}},
  year         = {{2021}},
}

@article{36271,
  author       = {{Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}},
  journal      = {{Journal of Lie Theory}},
  number       = {{2}},
  pages        = {{459----468}},
  publisher    = {{Heldermann Verlag}},
  title        = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}}},
  doi          = {{10.48550/arXiv.2008.07479}},
  volume       = {{31}},
  year         = {{2021}},
}

@misc{51556,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{171–173}},
  title        = {{{Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-021-00295-7}},
  volume       = {{68}},
  year         = {{2021}},
}

@misc{51555,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{175–177}},
  title        = {{{Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}}},
  doi          = {{10.1007/s00591-021-00296-6}},
  volume       = {{68}},
  year         = {{2021}},
}

@article{45967,
  author       = {{Binz, Tim and Kovács, Balázs}},
  journal      = {{arXiv}},
  title        = {{{A convergent finite element algorithm for mean curvature flow in higher codimension}}},
  year         = {{2021}},
}

@article{45962,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>}},
  author       = {{Binz, Tim and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2545--2588}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}}},
  doi          = {{10.1093/imanum/drab043}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45957,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>}},
  author       = {{Harder, Paula and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2589--2620}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}}},
  doi          = {{10.1093/imanum/drab045}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45961,
  author       = {{Nick, Jörg and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{997--1000}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-021-01196-6}},
  volume       = {{147}},
  year         = {{2021}},
}

@article{45959,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{595--643}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for Willmore flow of closed surfaces}}},
  doi          = {{10.1007/s00211-021-01238-z}},
  volume       = {{149}},
  year         = {{2021}},
}

@article{34629,
  author       = {{Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data}}},
  doi          = {{10.1016/j.cam.2020.113061}},
  volume       = {{382}},
  year         = {{2021}},
}

@article{32006,
  author       = {{Guillarmou, Colin and Küster, Benjamin}},
  issn         = {{1424-0637}},
  journal      = {{Annales Henri Poincaré}},
  keywords     = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
  number       = {{11}},
  pages        = {{3565--3617}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}}},
  doi          = {{10.1007/s00023-021-01068-7}},
  volume       = {{22}},
  year         = {{2021}},
}

@article{53363,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.</jats:p>}},
  author       = {{Rezat, Sebastian and Fan, Lianghuo and Pepin, Birgit}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  number       = {{6}},
  pages        = {{1189--1206}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Mathematics textbooks and curriculum resources as instruments for change}}},
  doi          = {{10.1007/s11858-021-01309-3}},
  volume       = {{53}},
  year         = {{2021}},
}

@inbook{34161,
  author       = {{Rezat, Sebastian and Schacht, Florian and Häsel-Weide, Uta}},
  booktitle    = {{Mathematics Education in the Digital Age. Learning, Practice and Theory}},
  editor       = {{Clark-Wilson, A. and Donevska-Todorova, A. and Faggiano, E. and Trgalová , J. and Weigang, H.-G.}},
  pages        = {{168--184}},
  publisher    = {{Routledge}},
  title        = {{{Challenges of making sense of tasks and automated feedback in digital mathematics textbooks}}},
  doi          = {{10.4324/9781003137580}},
  year         = {{2021}},
}

@article{44683,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students’ solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly quantitative research on the effectiveness of feedback in general, very little is known about how feedback actually affects students’ individual content specific learning processes and conceptual development. A theoretical framework based on Rabardel’s theory of the instrument and Vergnaud’s theory of conceptual fields is developed to study qualitatively how feedback actually functions in the learning process. This framework was applied in a case study of two elementary school students’ learning processes when working on a probability task from a German 3rd grade digital textbook. The analysis allowed detailed reconstruction of how students made sense of the information provided by the feedback and adjusted their behavior accordingly. This in-depth analysis unveiled that feedback does not necessarily foster conceptual development in the desired way, and a correct solution does not always coincide with conceptual understanding. The results point to some obstacles that students face when working individually on tasks from digital mathematics textbooks with automated feedback, and indicate that feedback needs to be developed in design-based research cycles in order to yield the desired effects.</jats:p>}},
  author       = {{Rezat, Sebastian}},
  issn         = {{1863-9690}},
  journal      = {{ZDM Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  number       = {{6}},
  pages        = {{1433--1445}},
  publisher    = {{Springer}},
  title        = {{{How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies}}},
  doi          = {{10.1007/s11858-021-01263-0}},
  volume       = {{53}},
  year         = {{2021}},
}

@inbook{35757,
  author       = {{Hochmuth, Reinhard and Biehler, Rolf and Blum, Werner and Achmetli, Kay and Rode, Jana and Krawitz, Janina and Schukajlow, Stanislaw and Bender, Peter and Haase, Jürgen}},
  booktitle    = {{Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{611--644}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation}}},
  doi          = {{10.1007/978-3-662-62854-6_24}},
  year         = {{2021}},
}

@inbook{35746,
  author       = {{Fleischmann, Yael and Biehler, Rolf and Gold, Alexander and Mai, Tobias}},
  booktitle    = {{Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{321--363}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Integration digitaler Lernmaterialien in die Präsenzlehre am Beispiel des Mathematikvorkurses für Ingenieure an der Universität Paderborn}}},
  doi          = {{10.1007/978-3-662-62854-6_15}},
  year         = {{2021}},
}

@inbook{35755,
  author       = {{Gold, Alexander and Fleischmann, Yael and Mai, Tobias and Biehler, Rolf and Kempen, Leander}},
  booktitle    = {{Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{365--397}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Die Online-Lernmaterialien im Online-Mathematikvorkurs studiVEMINT: Konzeption und Ergebnisse von Nutzer- und Evaluationsstudien}}},
  doi          = {{10.1007/978-3-662-62854-6_16}},
  year         = {{2021}},
}

@inbook{35730,
  author       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  booktitle    = {{Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{1--6}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert}}},
  doi          = {{10.1007/978-3-662-62854-6_1}},
  year         = {{2021}},
}

@inbook{35720,
  author       = {{Biehler, Rolf}},
  booktitle    = {{Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  pages        = {{285–290}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Mathematikvorkurse als Brücke in das Studium–Einführung}}},
  doi          = {{10.1007/978-3-662-62854-6_13}},
  year         = {{2021}},
}

@book{35734,
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Lehrinnovationen in der Hochschulmathematik}}},
  doi          = {{10.1007/978-3-662-62854-6}},
  year         = {{2021}},
}