Module Identifier | MA33210 | ||

Module Title | DISCRETE MATHEMATICS | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr V C 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 1hour lectures | |

Seminars / Tutorials | 3 x 1hour 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. 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.

**Reading Lists**

**Books**
**** 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