Module Information

Module Identifier
MA33210
Module Title
DISCRETE MATHEMATICS
Academic Year
2010/2011
Co-ordinator
Professor V Mavron
Semester
Intended for use in future years
Pre-Requisite
MA21410

Course Delivery

Delivery Type Delivery length / details
Lecture 19 Hours. (19 x 1 hour lectures)
Seminars / Tutorials 3 Hours. (3 x 1 hour example classes)
 

Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 Hours   (written examination)  100%

Learning Outcomes

On completion of this module, a student should be able to:
1. interpret problems in appropriate contexts and apply general counting principles to particular situations.
2. illustrate the principle of inclusion-exclusion and the pigeonhole principle by simple applications.
3. solve second order linear difference equations
4. model problems with difference equations;
5. describe concepts of certain combinatorial structures, e.g. codes, latin squares and balanced designs, and apply counting techniques to the investigation of their parameters.

Brief 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.

Content

1. Permutations and selections. Binomial coefficient. Identities involving binomial coefficients. Selections with repetition allowed. Multinomial coefficients. The Pigeonhole Principle.
2. Partitions of integers. Ferrers' 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 List

Recommended Text
R P Grimaldi (1999) Discrete Combinatorial Mathematics 4th Addison-Wesley Primo search Supplementary Text
C L Liu (1985) Elements of Discrete Mathematics 2nd McGraw-Hill Primo search I Anderson (1974) A First Course in Combinatorial Mathematics OUP Primo search Recommended Background
N Biggs (1992) Discrete Mathematics Rev. Ed. OUP Primo search

Notes

This module is at CQFW Level 6