ADAM project: Anticipating the Digital Age of Mathematics

From 2022 to 2024 Prof. Immi Halupczok and I were principal investigators on the experimental teaching project ADAM. The outputs of this project include the Lean Game Server and the interactive educational game

Robo
which illustrates the use of the interactive proof assistant Lean with problems typical for university entry-level mathematics. Further details are documented on the project pages.

Anki decks

Anki is a flash card program that can help learn definitions quickly and efficiently. The following Anki decks contain the essential definitions from my respective undergraduate courses (in German):
Lineare Algebra I
Einführung in die Topologie
For other decks covering university level mathematics, see for example the websites of St. Catharine's College Maths Society (Cambridge) or of Patrick Steven. (I cannot guarantee for the quality of all decks available on these sites.)

For the add-on that I have developed for creating and main­taining such LaTeX-based Anki decks, see Anki's official listing or GitHub.

Lecture courses

Algebraic Topology I (Winter 2024/25, Winter 2019/20, Winter 2017/18, …)
Algebraic Topology II Sommer 2025 (previously Summer 2018, Winter 2015/16)
Algebraic Topology III (planned for Winter 2025/26, previously Winter 2018/19)
Homological Algebra (Summer 2024, Summer 2016)
Linear Algebra II (Summer 2022)
Linear Algebra I (Winter 2021/22, Summer 2021, Summer 2017)
First course in Topology (Summer 2019, Winter 2016/17)
Algebraic Geometry (Winter 2014/15, LMU)

Seminars

Game Over or QED? Sommer 2025  (previously Summer 2024)

Introduction to the interactive theorem prover Lean.

Stone spaces Winter 2024/25
Quadratic Forms (Winter 2021/22)
Topological K-theory (Winter 2018/19, Summer 2016)
Topological Data Analysis (Summer 2018)
co-organized with Dr. Oihana Garaialde Ocaña
Algebraic K-theory (Winter 2017/18)
Oberseminar, co-organized with Prof. I. Halupczok, Prof. B. Klopsch, Prof. S. Schröer
Knot theory (Summer 2017)
co-organized with Dr. Peter Arndt
The Milnor Conjectures (Winter 2015/16)
Oberseminar, co-organized with Prof. B. Klopsch, Prof. S. Schröer
Number theory (Winter 2014/15, LMU)

Examples classes/Tutorials

(Bergische Universität Wuppertal)

Linear Algebra I (Winter 2011/12, Winter 2012/13)
Linear Algebra II (Summer 2013)
A first course in Algebra (Summer 2014)

Analysis I (Summer 2012)
Analysis on Manifolds(Summer 2012)

A first course in Topology (Winter 2013/14)
Topology (Summer 2013)

Supervisions

(University of Cambridge)

Part II Algebraic Geometry (Michaelmas 2009)
Part II Differential Geometry (Lent 2008, Lent 2009)
Part II Algebraic Topology (Michaelmas 2008)