MA33210 - DISCRETE MATHEMATICS

Module Identifier	MA33210
Module Title	DISCRETE MATHEMATICS
Academic Year	2001/2002
Co-ordinator	Dr V Mavron
Semester	Semester 2
Pre-Requisite	MA12510 or MA12610 or equivalent
Mutually Exclusive	MA22210 Not available to students who have taken MA22210
Course delivery	Lecture	19 x 1 hour lectures
	Seminars / Tutorials	3 x 1 hour example classes
Assessment	Exam	2 Hours (written examination)	100%
	Resit assessment	2 Hours (written examination)	100%

General description

This module will aim to cover the basics of classical combinatorics, the emphasis being on techniques rather than theory. The key ideas are those of selections, permutations and partitions.

Aims

To understand the concepts of selection and permutation and to recognise when and how to use some basic counting techniques.

Learning outcomes

On completion of this module, a student should be able to:

interpret problems in appropriate contexts and apply general counting principles to particular situations.
illustrate the principle of inclusion-exclusion and the pigeonhole principle by simple applications.
solve second order linear difference equations
model problems with difference equations;
describe concepts of certain combinatorial structures, e.g. codes, latin squares and balanced designs, and apply counting techniques to the investigation of their parameters.

Syllabus

1. Permutations and selections. Binomial coefficient. Identities involving binomial coefficients. Selections with repetition allowed. Multinomial coefficients. The Pigeonhole Principle.
2. Partitions of integers. Ferrer's Diagrams.
3. Principle of Inclusion and Exclusion. Derangements. Partitions of sets. Stirling numbers of the second kind.
4. Homogeneous second order linear difference equations. Simple inhomogeneous cases.
5. Latin squares. Orthogonality. Balanced designs.
6. Codes. Hamming distance. Error detection and correction.

Reading Lists

Books
** Recommended Text
R P Grimaldi. (1999) Discrete Combinatorial Mathematics. 4th. Addison-Wesley 0201304244
I Anderson. (1974) A First Course in Combinatorial Mathematics. OUP 0198596170
** Supplementary Text
C L Liu. (1985) Elements of Discrete Mathematics. 2nd. McGraw-Hill 007038133X
N Biggs. (1989) Discrete Mathematics. OUP 0198534272