Discrete mathematics 1000-134MAD

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.

Victor Bryant, Aspects of combinatorics, Cambridge University Press 1993.
Robin J. Wilson, Introduction to graph theory, Addison Wesley Lingman Ltd., London.