MA211      Half Unit
Algebra and Number Theory

This information is for the 2025/26 session.

Course Convenor

Availability

Requisites

Pre-requisites:

Students must have completed MA100 and MA103 before taking this course.

The aim of this course is to continue (from MA103) the study of abstract algebraic structures. There are two main strands in the course. First, we develop further the theory of groups, using permutation groups as a key example. We investigate the important concepts of normal subgroups and quotient groups. Secondly, we introduce rings, and study factorisation in rings, where we also look at some connections with number theory. Groups: Review of basic group theory; permutations and permutation groups; homomorphisms; conjugation, normal subgroups and quotient groups; the first isomorphism theorem for groups. Rings: basic properties of rings and examples (including polynomial rings, matrix rings, and number rings); subrings, ideals and ring homomorphisms; divisibility in integral domains; greatest common divisors; Euclidean rings and unique factorisation; applications to number theory; principal ideal domains.

20 hours of lectures and 10 hours of classes in the Autumn Term.

Written answers to set problems will be expected on a weekly basis.

A Book of Abstract Algebra, Charles C Pinter, (Dover, 2nd edition, 2010);

Introduction to Algebra, Peter J Cameron (OUP 1988);

Rings, Fields and Groups: Introduction to Abstract Algebra, Reg Allenby (Butterworth-Heinemann, 2nd edition 1991).

Exam (90%), duration: 120 Minutes in the Spring exam period

Continuous assessment (10%)