To provide an introduction to the problems and methods of Combinatorics, particularly to those areas of the subject with the widest applications such as pairings problems, the inclusion-exclusion principle, recurrence relations, partitions and the elementary theory of symmetric functions.

(LO1) Recognise the types of problem to which the methods of combinatorics apply and model these problems.

(LO2) Solve counting and arrangement problems.

(LO3) Solve general recurrence relations using the generating function method.

(LO4) Apply the elementary theory of partitions to the study of symmetric functions.

Principles of counting.
Selections, permutations and multinomial coefficients.
The inclusion-exclusion principle.
Pairings and Hall's theorem.
Recurrences, power series and generating functions.
Generating functions and Stirling numbers.
Graphs and Euler's theorem.
Species, a modern view of generating functions.
Symmetric groups and symmetric polynomials.
Signature and alternating groups.
Cycle types and conjugacy classes in symmetric groups.
Young diagrams and irreducible representations of S_n.