The institute participates in beginners' and export lectures, teaches basic and advanced B.Sc. and B.A. courses in algebra and geometry and offers M.Sc. courses in group and character theory, Lie theory and (algebraic) geometry. In addition to learning abstract theories special emphasis is placed on an algorithmically oriented education in the field of theoretical mathematics. This also includes the use and development of appropriate software packages and of programming languages.
Algorithmically oriented teaching in the field of algebra and geometry
The IDSC designed the lecture track "Groups, Algorithms, Geometries and Applications" for undergraduate students of mathematics. This track conveys computational methods in algebra and geometry and also forms the basis for subsequent theoretical specialisations in the fields of algebraic geometry and group theory at graduate level.
| Year | Title | Supervisor |
|---|---|---|
| 2023 | The Theorem of Riemann-Roch | Prof. Frederik Witt |
| 2022 | Sphere packings constructed by binary block cedy via of the construction A | Prof. Frederik Witt Priv. Doz. Dr. Anda Degeratu |
| 2022 | Topological data analysis with the Vietoris-Rips complex, two examples in polymake | Prof. Frederik Witt |
| 2021 | Desargues and Pappus Theorem in Projective Geometry | Prof. Frederik Witt |
| 2021 | Mathieu groups | Prof. Frederik Witt |
| 2020 | Gravitationswellen | Priv. Doz. Dr. Anda Degeratu |
| 2020 | Passierbare Schwarzschild-Wurmlöcher | Priv. Doz. Dr. Anda Degeratu |
| 2020 | Zusammenbruch eines Sterns und Entstehung von schwarzen Löchern | Priv. Doz. Dr. Anda Degeratu |
| 2020 | The tropical Grassmannian variety | Prof. Frederik Witt |
|
2019 |
Die Schwarzschild-Metrik | Priv. Doz. Dr. Anda Degeratu |
| 2019 | On the classification of complex surfaces | Prof. Frederik Witt |
| 2016 | Toric Ideals, Gröbner Bases and the Knapsack Problem | Prof. Frederik Witt |
| 2016 | Sylowzahlen | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Zum Satz von Schur - Zassenhaus | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Quadratsummen | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Irreduzible Polynome | Apl. Prof. Wolfgang Kimmerle |
| Year | Title | Supervisor |
|---|---|---|
| 2022 | Elliptic curves and Galois expansions of Q | Prof. Frederik Witt |
| 2022 | Protein Sequences and Tropical Geometry | Prof. Frederik Witt |
| 2021 | Toric Co-Higgs bundles and prevalued vector spaces | Prof. Frederik Witt |
| 2019 | Neural networks and Gröbner bases | Prof. Frederik Witt |
| 2019 | Gravitational Waves in the Presence of Cosmological Constant | Priv. Doz. Dr. Anda Degeratu |
| 2019 | Zum Beweis des F*-Theorems für ganzzahlige Gruppenringe | Apl. Prof. Wolfgang Kimmerle |
| 2018 | Gravitational Waves in the Presence of Cosmological Constant | Priv. Doz. Dr. Anda Degeratu |
| 2017 | Quotients of algebraic varieties | Prof. Frederik Witt |
| 2016 | Limiting configurations from a Hermitian point of view | Prof. Frederik Witt |
| 2016 | Hodge Theory on Noncompact Manifolds | Prof. Frederik Witt |
| 2014 | Multiplikative Jordanzerlegung in ganzzahligen Gruppenringen | Apl. Prof. Wolfgang Kimmerle |
Algebra and geometry also form the theoretical core of teachers' training in mathematics where the IDSC makes a substantial contribution with regard to contents. It also offers advanced lectures and seminars.
| Year | Title | Supervisor |
|---|---|---|
| 2021 | Die Sätze von Desargues und Pappus in der projektiven Geometrie | Prof. Frederik Witt |
| 2019 | Die Picard- und Jacobi-Varietät einer Riemannschen Fläche | Prof. Frederik Witt |
| 2020 | Platonische Körper in der Theorie und Praxis | Prof. Frederik Witt |
| 2017 | Verschiedene Beweise des Fundamentalsatzes der Algebra | Apl. Prof. Wolfgang Kimmerle |
| 2017 | Berechnung von Galoisgruppen bei Polynomen kleineren Grades | Apl. Prof. Wolfgang Kimmerle |
| 2017 | Zur Transzendenz von \pi | Apl. Prof. Wolfgang Kimmerle |
| 2017 | Restklassen und Kryptographie | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Über das Waringsche Problem | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Algebraische Behandlung klassischer Konstruktionsprobleme | Apl. Prof. Wolfgang Kimmerle |
| 2014 | RSA-Verfahren und Primzahltests | Apl. Prof. Wolfgang Kimmerle |
| Year | Title | Supervisor |
|---|---|---|
| 2019 | Neuronale Netze und Gröbnerbasen | Prof. Frederik Witt |
| 2017 | Charakterisierung transitiver Permutationsgruppen | Apl. Prof. Wolfgang Kimmerle |
| 2016 | Endliche projektive Inzidenzebenen | Apl. Prof. Wolfgang Kimmerle |
| 2015 | Kreisteilungskörper | Apl. Prof. Wolfgang Kimmerle |
The institute also participates in the export lectures "Mathematics for Computer Scientists and Software Engineers" and "HM3 (advanced)" of LExMath.
Further information can be found on the personal pages of the lecturers and in the institute's teaching schedule.
Further teaching activities of the IDSC
- Lecture series "Mathe Macht!" (in german): Maths in industrial applications
- Collection of mathematical models for educational and popularisation purposes