Handbook 1996 : Faculty of Science (Volume 4 page 207)
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618-131 Discrete Mathematics (Advanced)

Note: Students may not gain credit for both 618-131 and any of 618-141 (1995 Handbook), 618-251, or the Mathematical Sciences subject 617-170 Discrete Mathematics and Statistics (1994 Handbook).

Credit points: 12.5

Coordinator: Professor C F Miller.

Prerequisite: Invitation by the Head of Department.

Contact: 39 lectures (three a week) 13 x 1-hour tutorials and 39 hours problem solving.

Timetable: First semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the notion of validity of a mathematical formula
• the concept of a mathematical proof
• the principle of mathematical induction
• the use of logical notation
• countability and uncountability

Have developed:

• skills and experience in using the language of sets, functions and relations
• skills in counting and combinatorics
• elementary skills in analysing graphs
• the ability to prove simple theorems properly
• skills in proving results by mathematical induction.

Appreciate:

• the need for mathematical rigour
• the variety of applications of discrete mathematical techniques

Content:

The natural numbers: well-ordering, forms of mathematical induction, division algorithm, greatest common divisor, prime factorization, recursion. Combinatorics: graphs and trees, paths, cycles, counting principles. Logic: logical notation, propositional connectives, quantifiers, truth tables, logical validity, counter-examples, methods of proof. Set theory: sets and set operations, functions, relations, orderings, equivalence relations and partitions, cardinality, countable and uncountable sets. Additional topics selected from: difference equations, generating functions, graph theory.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

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Handbook 1996 : Faculty of Science (Volume 4 page 207)

Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.