# Undergraduate Catalogue of Courses 2012/2013

## MATHEMATICS

MA 2004

SETS AND ALGEBRAIC STRUCTURES

CREDIT POINTS 15

*Course Co-ordinator:* Dr R Hepworth

*Pre-requisite(s):*
MA 1006 or, with the permission of the Head of Mathematical Sciences, MA 1507.

This course provides an introduction to algebraic structures and elementary number theory.

The course includes a discussion of:

- Sets (notation, functions, injections, surjections, bijections)
- Countability of the rational numbers and uncountability of the real numbers
- The integers and factorisation
- Prime numbers, Euclidean algorithm, uniqueness of factorisation
- The integers modulo n
- Equivalence relations
- Permutations
- Group axioms
- The symmetric group
- Lagrange's Theorem
- Fermat's Little Theorem
- Definition of commutative ring and of a field with examples, especially polynomial rings
- Vector spaces and linear transformations.

3 one-hour lectures and 1 tutorial per week (to be arranged).

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper, maximum resit (100%) and resit (80%) with in-course assessment (20%).