units

MTH3167

Faculty of Science

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Monash University Handbook 2010 Undergraduate - Unit

6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

LevelUndergraduate
FacultyFaculty of Science
OfferedNot offered in 2010
Coordinator(s)Dr John Arkinstall

Synopsis

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.

Objectives

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.

Assessment

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

Prerequisites

MAT1085, MTH2111