@inproceedings{45391,
  author       = {{Delucchi, R. and Neugebauer, P. and Dröse, Jennifer and Prediger, Susanne and Mertins, B.}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2019 }},
  editor       = {{Frank, A. and Krauss, S. and Binder, K.}},
  pages        = {{1239--1242}},
  publisher    = {{WTM}},
  title        = {{{Eye-Tracking-Studie zum Erfassen von Referenzstrukturen in Textaufgaben der Klasse 5}}},
  year         = {{2019}},
}

@article{16708,
  abstract     = {{ In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to
the computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems.
To this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for
the computation of such objects of finite dimensional systems with the results obtained in the work
of Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis
of partial differential equations and illustrate its feasibility by computing unstable manifolds of the
one-dimensional Kuramoto--Sivashinsky equation as well as for the Mackey--Glass delay differential
equation.
}},
  author       = {{Ziessler, Adrian and Dellnitz, Michael and Gerlach, Raphael}},
  issn         = {{1536-0040}},
  journal      = {{SIAM Journal on Applied Dynamical Systems}},
  number       = {{3}},
  pages        = {{1265--1292}},
  title        = {{{The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques}}},
  doi          = {{10.1137/18m1204395}},
  volume       = {{18}},
  year         = {{2019}},
}

@article{34917,
  abstract     = {{We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).}},
  author       = {{Kirschmer, Markus and Nebe, Gabriele}},
  issn         = {{1793-0421}},
  journal      = {{International Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{02}},
  pages        = {{309--325}},
  publisher    = {{World Scientific Pub Co Pte Lt}},
  title        = {{{Quaternary quadratic lattices over number fields}}},
  doi          = {{10.1142/s1793042119500131}},
  volume       = {{15}},
  year         = {{2019}},
}

@article{34916,
  abstract     = {{We describe the powers of irreducible polynomials occurring as characteristic polynomials of automorphisms of even unimodular lattices over number fields. This generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.}},
  author       = {{Kirschmer, Markus}},
  issn         = {{0022-314X}},
  journal      = {{Journal of Number Theory}},
  keywords     = {{Algebra and Number Theory}},
  pages        = {{121--134}},
  publisher    = {{Elsevier BV}},
  title        = {{{Automorphisms of even unimodular lattices over number fields}}},
  doi          = {{10.1016/j.jnt.2018.08.004}},
  volume       = {{197}},
  year         = {{2019}},
}

@misc{31302,
  author       = {{Schütte, Philipp}},
  title        = {{{Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces}}},
  year         = {{2019}},
}

@article{51387,
  author       = {{Hilgert, Joachim and Parthasarathy, A. and Hansen, S.}},
  journal      = {{Inter. Math. Research Notices}},
  pages        = {{6362--6389}},
  title        = {{{Resonances and Scattering Poles in Symmetric Spaces of Rank One}}},
  volume       = {{20}},
  year         = {{2019}},
}

@misc{51568,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{247–249}},
  title        = {{{Lizhen Ji und Athanase Papadopoulos (Hrsg.): Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics. European Mathematical Society 2015}}},
  doi          = {{10.1007/s00591-018-0233-8}},
  volume       = {{66}},
  year         = {{2019}},
}

@misc{51566,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{261–262}},
  title        = {{{Brian W. Kernighan: Millions billions zillions – defending yourself in a world of too many numbers. Princeton University Press 2018}}},
  doi          = {{10.1007/s00591-019-00251-6}},
  volume       = {{66}},
  year         = {{2019}},
}

@misc{51567,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte }},
  pages        = {{257–258}},
  title        = {{{Joseph Honerkamp: Denken in Strukturen und seine Geschichte – Von der Kraft des mathematischen Beweises (Springer 2018)}}},
  doi          = {{10.1007/s00591-018-0234-7}},
  volume       = {{66}},
  year         = {{2019}},
}

@misc{51569,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{127--129}},
  title        = {{{Øystein Linnebo: Philosophy of Mathematics (Princeton University Press 2017)}}},
  doi          = {{10.1007/s00591-018-0226-7}},
  volume       = {{66}},
  year         = {{2019}},
}

@misc{51565,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{263–264}},
  title        = {{{Jost-Hinrich Eschenburg: Sternstunden der Mathematik. Springer 2017}}},
  doi          = {{10.1007/s00591-019-00247-2}},
  volume       = {{66}},
  year         = {{2019}},
}

@article{45948,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{797--853}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for mean curvature flow of closed surfaces}}},
  doi          = {{10.1007/s00211-019-01074-2}},
  volume       = {{143}},
  year         = {{2019}},
}

@inproceedings{52510,
  author       = {{Werth, Gerda}},
  booktitle    = {{Beiträge zum Mathematikunterricht}},
  editor       = {{Frank, Andreas and Krauss, Stefan  and Binder, Karin}},
  location     = {{Regensburg}},
  publisher    = {{WTM}},
  title        = {{{Mathilde Vaerting. Deutschlands erste Mathematikdidaktikderin}}},
  year         = {{2019}},
}

@article{53416,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>}},
  author       = {{Küster, Benjamin and Weich, Tobias}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  keywords     = {{General Mathematics}},
  number       = {{11}},
  pages        = {{8225--8296}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}}},
  doi          = {{10.1093/imrn/rnz068}},
  volume       = {{2021}},
  year         = {{2019}},
}

@article{33598,
  author       = {{Rezat, Sara and Rezat, Sebastian}},
  journal      = {{In: Mathematik differenziert 3/2019}},
  pages        = {{30--37}},
  title        = {{{„...weil man Fermi-Aufgaben so rechnet“. Modelltexte als sprachliche Ressource für das Erklären von Lösungswegen bei Fermi-Aufgaben}}},
  year         = {{2019}},
}

@inbook{44684,
  author       = {{Vollstedt, Maike and Rezat, Sebastian}},
  booktitle    = {{Compendium for Early Career Researchers in Mathematics Education}},
  editor       = {{Kaiser, Gabriele and Presmeg, Norma}},
  isbn         = {{9783030156350}},
  issn         = {{2520-8322}},
  publisher    = {{Springer International Publishing}},
  title        = {{{An Introduction to Grounded Theory with a Special Focus on Axial Coding and the Coding Paradigm}}},
  doi          = {{10.1007/978-3-030-15636-7_4}},
  year         = {{2019}},
}

@article{46156,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Although the teaching of vocabulary in mathematics lessons is requested in content- and language-integrated lesson designs, the clarification of the specific lexical language demands is still an open question for many mathematical topics. In a content- and language-integrated lesson design towards understanding the concept of equivalent fractions, the vocabulary (words and phrases) used by 17 students has been analyzed with qualitative means of data analysis. The qualitative in-depth analyses underline the importance of meaning-related vocabulary for making structural relations between the fractions in view explicit. Quantitative analyses of inventoried vocabulary for the four categories “self-initiated by students,” “triggered by teaching material,” “triggered by teacher,” or “triggered by peers” show the relations of collective and autonomous vocabularies from which the students retrieve their lexical means in oral and written language production.</jats:p>}},
  author       = {{Wessel, Lena}},
  issn         = {{1033-2170}},
  journal      = {{Mathematics Education Research Journal}},
  keywords     = {{Education, General Mathematics}},
  number       = {{4}},
  pages        = {{653--681}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Vocabulary in learning processes towards conceptual understanding of equivalent fractions—specifying students’ language demands on the basis of lexical trace analyses}}},
  doi          = {{10.1007/s13394-019-00284-z}},
  volume       = {{32}},
  year         = {{2019}},
}

@inbook{48320,
  author       = {{Leuders, Timo and Wessel, Lena}},
  booktitle    = {{Professionsorientierung in der Lehrerbildung: Kompetenzorientiertes Lehren nach dem 4-Component-Instructional-Design-Modell}},
  editor       = {{Kreutz, J. and Leuders, Timo and Hellmann, T.}},
  pages        = {{117--134}},
  publisher    = {{Springer}},
  title        = {{{3.5 Kompetenzorientierte Didaktik der Analysis durch Orientierung an real-life tasks–Ein Beispiel für ein Lehrdesign nach dem 4C/ID-Modell}}},
  year         = {{2019}},
}

@book{48376,
  abstract     = {{<jats:p>„Vielfalt, die verbindet“ ist ein Leitmotiv, welches das Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2018 in Essen gut beschreibt. Zu diesem kamen Akteure von Fachhochschulen und Universitäten mit fachmathematischer wie fachdidaktischer Perspektive vom 9. bis 10. November zusammen, um die Problematik des Übergangs von Schule zu Hochschule im Kontext mathematischer Studiengänge zu diskutieren. Der vorliegende Band bündelt die vielfältigen Projekte und Forschungsaktivitäten rund um den Übergang Schule–Hochschule und zeigt Innovationen innerhalb der mathematischen Hochschullehre gleichermaßen praxisorientiert wie theoretisch fundiert auf. Neben drei Hauptbeiträgen von Bärbel Barzel, Frode Rønning sowie Nimet Sarikaya und Peter Furlan umfasst der Band weitere 13 Sektionsbeiträge, welche u. a. die nebenstehenden Schwerpunkte fokussieren. • Heranführen von Studierenden an hochschulmathematische Denk- und Arbeitsweisen • Anpassung von Strukturen und Aufgaben für einen konstruktiven Übergang von Schule zu Hochschule • Bewährte Unterstützungsmaßnahmen für ein erfolgreiches Selbstlernen, z. B. in Form von Peer Instruction. • Etablierte Flipped-Classroom- und Blended-Learning-Formate  • Messung vielfältiger Fähigkeitsprofile von Studierenden beim Eintritt in die Hochschule • Chancen der Digitalisierung nutzen: Lehren und Lernen mit digitalen Medien, z. B. mithilfe von Lernvideo oder durch dynamische Visualisierungen • Umgang mit zunehmender Heterogenität und unterschiedlichem Vorwissen auf Seite der Studierenden • Konzepte problembasierten Lernens in die Hochschullehre integrieren • Steigerung der Motivation von Studierenden • Umgang mit der doppelten Diskontinuität mathematischer Lehramtsstudiengänge</jats:p>}},
  editor       = {{Klinger, Marcel and Schüler-Meyer, Alexander and Wessel, Lena}},
  isbn         = {{9783959870986}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2018}}},
  doi          = {{10.37626/ga9783959870986.0}},
  volume       = {{6}},
  year         = {{2019}},
}

@inproceedings{48409,
  author       = {{Wessel, Lena}},
  booktitle    = {{Eleventh Congress of the European Society for Research in Mathematics Education (CERME11)}},
  editor       = {{Jankvist, Uffe Thomas and van den Heuvel-Panhuizen, Marja and Veldhuis, Michiel}},
  keywords     = {{Vocational education, language, percentages, scaffolding, design research}},
  number       = {{12}},
  publisher    = {{Freudenthal Group}},
  title        = {{{How theories of language-responsive mathematics can inform teaching designs for vocational mathematics}}},
  volume       = {{TWG07}},
  year         = {{2019}},
}