@misc{51560,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{297–299}},
  title        = {{{David M. Bressoud: Calculus Reordered -- A History of the Big Ideas. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-020-00280-6}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51564,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{97–98}},
  title        = {{{Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage (Springer 2017)}}},
  doi          = {{10.1007/s00591-019-00254-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51563,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{109–111}},
  title        = {{{Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019)}}},
  doi          = {{10.1007/s00591-019-00254-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@article{45954,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45953,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45955,
  author       = {{Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{995--1038}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}}},
  doi          = {{10.1090/mcom/3597}},
  volume       = {{90}},
  year         = {{2020}},
}

@article{45952,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{1463-9963}},
  journal      = {{Interfaces and Free Boundaries}},
  keywords     = {{Applied Mathematics}},
  number       = {{4}},
  pages        = {{443--464}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}}},
  doi          = {{10.4171/ifb/446}},
  volume       = {{22}},
  year         = {{2020}},
}

@inbook{34632,
  author       = {{Hesse, Kerstin}},
  booktitle    = {{Multivariate Algorithms and Information-Based Complexity}},
  editor       = {{Hickernell, Fred J. and Kritzer, Peter}},
  isbn         = {{9783110633115}},
  pages        = {{33--42 }},
  publisher    = {{De Gruyter}},
  title        = {{{RBF-based penalized least-squares approximation of noisy scattered data on the sphere}}},
  year         = {{2020}},
}

@article{53415,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\ne 3$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mo>≠</mml:mo>
                    <mml:mn>3</mml:mn>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.
</jats:p>}},
  author       = {{Küster, Benjamin and Weich, Tobias}},
  issn         = {{0010-3616}},
  journal      = {{Communications in Mathematical Physics}},
  keywords     = {{Mathematical Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{917--941}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Pollicott-Ruelle Resonant States and Betti Numbers}}},
  doi          = {{10.1007/s00220-020-03793-2}},
  volume       = {{378}},
  year         = {{2020}},
}

@inbook{44685,
  author       = {{Schumacher, Jan and Rezat, Sebastian}},
  booktitle    = {{Zeichen und Sprache im Mathematikunterricht: Semiotik in Theorie und Praxis}},
  editor       = {{Kadunz, Gert}},
  isbn         = {{9783662611937}},
  pages        = {{85–112}},
  publisher    = {{Springer}},
  title        = {{{Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen}}},
  doi          = {{10.1007/978-3-662-61194-4_5}},
  year         = {{2020}},
}

@inbook{44688,
  author       = {{Rezat, Sebastian}},
  booktitle    = {{Mobile Medien im Schulkontext}},
  editor       = {{Meister, Dorothee and Ilka, Mindt}},
  isbn         = {{9783658290382}},
  issn         = {{2512-112X}},
  publisher    = {{Springer}},
  title        = {{{Mathematiklernen mit digitalen Schulbüchern im Spannungsfeld zwischen Individualisierung und Kooperation}}},
  doi          = {{10.1007/978-3-658-29039-9_10}},
  year         = {{2020}},
}

@article{46159,
  author       = {{Leuders, Timo and Wessel, Lena}},
  issn         = {{0933-422X}},
  journal      = {{Pädagogik 2/2020}},
  number       = {{2}},
  pages        = {{26--30}},
  publisher    = {{Beltz Verlagsgruppe}},
  title        = {{{Differenziertes Üben gestalten. Zwischen Umsetzung in der Praxis und Fundierung in der Forschung.}}},
  year         = {{2020}},
}

@article{46158,
  author       = {{Wessel, Lena and Kuzu, T. and Prediger, Susanne}},
  journal      = {{Sprachbildender Mathematikunterricht in der Sekundarstufe - ein forschungsbasiertes Praxisbuch}},
  pages        = {{148–151}},
  title        = {{{Sprachbildender Vorstellungsaufbau für verschiedene mathematische Konzepte: Brüche in Klasse 6}}},
  year         = {{2020}},
}

@inbook{48405,
  author       = {{Sprütten, F. and Wessel, Lena and Zentgraf, K. and Prediger, S.}},
  booktitle    = {{Sprachbildender Mathematikunterricht in der Sekundarstufe. Ein forschungsbasiertes Praxisbuch}},
  editor       = {{Prediger, S.}},
  pages        = {{115--130}},
  publisher    = {{Cornelsen Skriptor}},
  title        = {{{Fach- und sprachintegrierte Ansätze für Neuzugewanderte}}},
  year         = {{2020}},
}

@book{48406,
  author       = {{Wessel, Lena and Prediger, S. and Stein, A. and Wijers, M. and Jonker, V.}},
  publisher    = {{DZLM}},
  title        = {{{Language for Mathematics in Vocational Contexts. Handbook for teachers and facilitators}}},
  year         = {{2020}},
}

@article{35701,
  author       = {{Lünne, Steffen and Schnell, Susanne and Biehler, Rolf}},
  issn         = {{0261-9768}},
  journal      = {{European Journal of Teacher Education}},
  keywords     = {{Education}},
  number       = {{5}},
  pages        = {{688--705}},
  publisher    = {{Informa UK Limited}},
  title        = {{{Motivation of out-of-field teachers for participating in professional development courses in mathematics}}},
  doi          = {{10.1080/02619768.2020.1793950}},
  volume       = {{44}},
  year         = {{2020}},
}

@inbook{35808,
  author       = {{Barzel, Bärbel and Biehler, Rolf}},
  booktitle    = {{Professional development and knowledge of mathematics teachers}},
  editor       = {{Zehetmeier, Stefan and Potari, Despina and Ribeiro, Miguel}},
  pages        = {{163–192}},
  publisher    = {{Routledge}},
  title        = {{{Theory-Based Design of Professional Development for Upper Secondary Teachers–Focusing on the Content-Specific Use of Digital Tools}}},
  year         = {{2020}},
}

@article{35822,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The derivative concept plays a major role in economics. However, its use in economics is very heterogeneous, sometimes inconsistent, and contradicts students’ prior knowledge from school. This applies in particular to the common economic interpretation of the derivative as the amount of change while increasing the production by one unit. Hence, in calculus courses for economics students, learners should acquire an understanding of the derivative that is mathematically acceptable and connected to their prior knowledge, but which also takes into account its practical use in economics. In this paper we first develop a theoretical model describing such an understanding of the derivative for economics students. We then present an exploratory study investigating the extent to which economics students have such an understanding after their calculus course. The results indicate that many of them might not have acquired this kind of understanding, in particular concerning the common economic interpretation of the derivative. The study furthermore yields possible gaps in students’ understanding and possible misconceptions.</jats:p>}},
  author       = {{Feudel, Frank and Biehler, Rolf}},
  issn         = {{0173-5322}},
  journal      = {{Journal für Mathematik-Didaktik}},
  keywords     = {{Education, General Mathematics}},
  number       = {{1}},
  pages        = {{273--305}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Students’ Understanding of the Derivative Concept in the Context of Mathematics for Economics}}},
  doi          = {{10.1007/s13138-020-00174-z}},
  volume       = {{42}},
  year         = {{2020}},
}

@article{35709,
  author       = {{Kempen, Leander and Biehler, Rolf}},
  issn         = {{1664-1078}},
  journal      = {{Frontiers in Psychology}},
  keywords     = {{General Psychology}},
  pages        = {{1180}},
  publisher    = {{Frontiers Media SA}},
  title        = {{{Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology}}},
  doi          = {{10.3389/fpsyg.2020.01180}},
  volume       = {{11}},
  year         = {{2020}},
}

@inbook{35827,
  author       = {{Kempen, Leander and Krämer, Sandra and Biehler, Rolf}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2020}},
  editor       = {{Siller, H.-S. and Weigel, W. and Wörler, J. F.}},
  pages        = {{489--492}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Was verstehen Schülerinnen und Schüler unter „Beweis“? – ausgewählte Ergebnisse einer Pilotstudie}}},
  doi          = {{10.17877/DE290R-21418}},
  year         = {{2020}},
}