MTH3167

Combinatorics

(SCI)

6 points + Second semester + Gippsland/Distance (both in odd numbered years only) + Prerequisites: MAT1085, MTH2111 + Prohibitions: MAP2032, MAT3057, GAS3614

Synopsis: This subject aims to introduce and develop the theory and applications of combinatorial (counting) methods. Principles of enumeration: elementary counting principles, permutations and combinations, generating functions, recurrence relations, the principle of inclusion-exclusion. Combinatorial structures: block designs, Latin squares, difference sets, directed and undirected graphs, combinatorial matrices, systems of distinct representatives. Applications: design of experiments, error correcting codes, assignment problems, network flows, applications of graph theory. Emphasis is placed on algorithms.

Assessment: Two assignments: 30% + Examination (3 hours): 70%