|Module Title||DISCRETE MATHEMATICS|
|Co-ordinator||Dr V C Mavron|
|Pre-Requisite||MA12510 or MA12610 or equivalent|
|Mutually Exclusive||MA22210 Not available to students who have taken MA22210|
|Course delivery||Lecture||19 x 1hour lectures|
|Seminars / Tutorials||3 x 1hour example classes|
|Assessment||Exam||2 Hours (written examination)||100%|
|Resit assessment||2 Hours (written examination)||100%|
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.
To understand the concepts of selection and permutation and to recognise when and how to use some basic counting techniques.
On completion of this module, a student should be able to:
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.
** Recommended Text
R P Grimaldi. Discrete Combinatorial Mathematics. Addison-Wesley
I Anderson. A First Course in Combinatorial Analysis. OUP
** Supplementary Text
C L Liu. Elements of Discrete Mathematics. McGraw-Hill
N Biggs. Discrete Mathematics. OUP