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MTH3167 - Combinatorics

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate Faculty of Science

Leader: Dr John Arkinstall


Gippsland Second semester 2007 (Off-campus)


This unit 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.


On completion of this unit students will have: developed dexterity and skill in the use and choice of counting techniques; achieved a basic understanding of graph theory and in the use of algorithms, both in the proof of graph theory results and in computation; and be able to understand the application of combinatorial methods in the theory of designs and in combinatorial optimisation.


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


MAT1085, MTH2111