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%).