Discrete mathematics 1000-134MAD
Combinatorics
Basic counting principles.
Binomial coefficients and combinatorial proofs.
The principle of inclusion and exclusion.
Recurrence relations and generating functions.
Counting of orbits and Burnside's lemma.
Graph theory
Introductory concepts.
Eulerian circuits and Hamiltonian cycles.
Trees.
Planarity.
Colorings.
Matchings.
Type of course
Course coordinators
Learning outcomes
Students:
- know basic counting principles;
- use binomial coefficients and combinatorial proofs;
- are familiar with Stirling, Bell and Catalan numbers;
- use the principle of inclusion and exclusion;
- understand recurrence relations and use generating functions;
- know how to count orbits and use Burnside's lemma;
- are familiar with basic concepts of graph theory;
- identify and use Eulerian circuits and Hamiltonian cycles in graphs;
- know the basic properties of and theorems about trees;
- are familiar with planar graphs and Euler's formula;
- know basic theorems about colorings of graphs;
- know and use Hall's Marriage Theorem.
Bibliography
Victor Bryant, Aspects of combinatorics, Cambridge University Press 1993.
Robin J. Wilson, Introduction to graph theory, Addison Wesley Lingman Ltd., London.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: