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Discrete Mathematics
Diskrete Mathematik
Last Updated: 2026-02-05 15:00:01
Abstract
Part 1: Introduction to discrete optimization (shortest path, spanning trees, max flow, bipartite matching, linear assignment, LP as tool for proving optimality).Part 2: introduction to the algebra of finite fields, construction and application to 2-errors- correcting codes.
Objective
Introduction to discrete mathematics.
Content
Basic material: mathematical logic (propositional calculus, predicate calculus), set theory, relations and structures. Algebra: groups, rings, finite fields. Combinatorics: recursions, the principle of induction, techniques of counting (the pigeonhole principle, the principle of inclusion and exclusion), permutations, generating functions, solving recursions with generating functions. Graph theory: definition, isomorphism, connectivity, trees, graph coloring, planar graphs (Theorems of Euler and Kuratowski), incidence and adjacency matrix, digraphs, weighted graphs and networks, shortest paths in graphs and networks, the Minimum Spanning Tree Problem, complexity classes P and NP, the Travelling Salesman Problem.
Resources
Literature
Martin Aigner: Diskrete Mathematik, vieweg studium, 1993
General Information
- Language
- German
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- Alle in der Vorlesung verteilte Fotokopien + 5 beidseitig von Hand beschriebene A4-Blätter, keine Taschenrechner.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Diskrete Mathematik |
|
2 h weekly |
| exercise | Diskrete Mathematik |
|
1 h weekly |