Lecture Notes

These are a selection of my notes of courses taught at Uni Bonn or HHU. If you're interested in the code, have a look on Github.

Galois Cohomology of Algebraic Groups

Ring lecture

The cohomological approach to arithmetic problems like rational points and classification of algebraic groups, progressing from algebraic number theory foundations through Poitou-Tate duality to applications for simple groups over number fields.

Bridging Model Theory and Machine Learning

Bachelor's thesis

Proof of the equivalence between NIP and stable theories in model theory and PAC and online learnable concept classes in computational learning theory

Introduction to Statistics

Lecture notes

Fundamental statistical concepts including probability distributions, hypothesis testing, confidence intervals, likelihood methods, information theory, empirical distributions, and regression analysis.

Topology I

Lecture notes

Homology theory from Eilenberg-Steenrod axioms to computational tools like simplicial, singular, and cellular homology, along with cohomology, homological algebra, and applications to geometric problems.

Introduction to Discrete Mathematics

Lecture notes

Fundamental graph algorithms (including Euler paths, shortest paths, spanning trees, maximum flows), computational complexity theory (P, NP, NP-completeness), and key theorems like Cook's theorem and Menger's theorems.

Algebra I

Lecture notes

Commutative algebra, homological algebra, algebraic geometry through Nullstellensatz and Krull dimension, plus algebraic number theory up to Hilbert class fields and a theorem of Gauss.