Course Title: Discrete Mathematics

The course will offer a panorama view of Discrete Mathematics,
which is a core subject of mathematics with impact on algebra, topology and geometry.
The didactic emphasis will be put on rigorous proofs coupled with the structural
understanding of the concepts and their interactions.

Discrete structures are the main building blocks in algorithm design, and
the class will also cover some algorithmic aspects, making it of interest to CS majors.
Furthermore, counting techniques and asymptotic estimates are of use in
discrete probability, so the class is also suitable for math majors interested
in statistics.

The course can be taken by both Mathematics and CS majors,
both as a Bachelor as well as a Master class.

Target audience: 
- B.Sc.& M.Sc. Mathematik/Mathematics 
- B.Sc.& M.Sc. Industrial mathematics & Data Science 
- B.Sc.& M.Sc. Informatik

Course language: Englisch/Deutsch

Winter Term 25/26: 14 weeks (9 CP) for Math students, 10 weeks (6 CP) for CS students

Main Topics:

- Enumerative Combinatorics
  - Counting techniques
  - Principle of Inclusion-Exclusion (PIE)
  - Stirling and other combinatorially defined numbers
  - The method of generating functions
  - Asymptotic estimates

- Extremal Combinatorics
  - Sperner theory
  - Lubell Yamamoto Meshalkin inequalities
  - Turan theorem
  - Erdos-Ko-Rado theorem
  - Kruskal-Katona theorem

- Discrete structures
  - Graphs and their structural theory
  - Posets, lattices, generalization of PIE
  - Matroids

- (non CS part) Algebraic Enumeration
   - Polya's enumeration theory
   - Introduction to Algebraic Graph Theory 
   - Further Applications of Linear Algebra

Sample Literature:

- Peter Cameron, "Combinatorics: Topics, Techniques, Algorithms"
- J.H. van Lint, R.M. Wilson, "A course in Combinatorics"
- Norman Biggs, "Discrete Mathematics"