After successful completion of the course, students are able to carry out graph theoretical proofs, to describe important graph theoretical concepts and algorithms, to understand advanced methods in combinatorics, number theory and algebra as well as to explain application of the theory of finite fields.

Advanced Combinatorics, Graph Theory, Number Theory, Polynomials over Finite Fields

The discussion of the modalities of the lecture as well as the accompanying exercises is done in course of the first lecture.

More concrete information will be made available as soon as the situation allows it.

D. Jungnickel: Graphs, Networks and Algorithms

M. Aigner: Combinatorial Theory

R. Diestel: Graph Theory

W. Tutte: Introduction to the Theory of Matroids

Algorithms 1 Hamiltonian cycles(http://research.cyber.ee/~peeter/teaching/graafid08s/previous/loeng3eng.pdf)

L. Comtet: Advanced Combinatorics

M. Bona: Introduction to Enumerative Combinatorics

M. Aigner: A Course in Enumeration

P. Flajolet and R. Sedgewick: Analytic Combinatorics

B. van der Waerden: Algebra (Vol.1)

T. Hungerford: Algebra

R. Lidl and H. Niederreiter: Finite Fields

F. McWilliams and N. Sloane: The Theory of Error-Correcting Codes

The subjects of the mathematics courses of the first year in the curriculum of the bachelor studies is a prerequisite. This includes in particular some basic mathematical methods like induction, functions, relations, congruences as well as basic graph theory, algebra and linear algebra.