Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage, graphentheoretische Beweise zu führen, grundlegende Konzepte und Algorithmen der Graphentheorie zu beschreiben, höhere Methoden aus Kombinatorik, Algebra und Zahlentheorie zu verstehen, Anwendungen der Theorie der endlichen Körper zu erklären.
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.
