The aim of the course is to provide the student with a basic introduction to the techniques of combinatorial mathematics and of graph theory. During lab hours students solve problems, either at the board or individually, under the supervision of a teacher.

Sets and functions, basic calculus, elementary combinatorics.

Integers: the well-ordering axiom, strong and weak form of the induction principle. Recursive definitions. Functions and counting, the pigeonhole principle, the multiplicative principle. Ordered and unordered selections with and without repetition. Permutations, binomial and multinomial coefficients, the binomial formula. The sieve principle. Generating functions and recursive linear relations. Ordered and unordered graphs, walks, paths, cycles. Eulerian walks and Hamiltonian cycles. Trees. Combinatorics of graphs. Planar graphs, Euler formula and its corollaries. Colourings and the chromatic number. Applications and examples.

Norman L. Biggs, Discrete Mathematics, Clarendon Press, Oxford, 1985.