Module Identifier MA33210  
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.

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:

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
** 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