## Availabilities:

Not currently available in 2020

## Unit Summary

### Unit type

UG Coursework Unit

12

7

### Former School/College

Former School of Education

### Pre-requisites

MAT10722 - Complex Analysis

## Unit aim

Extends the concepts introduced in Mathematical Ideas, Calculus and Linear Algebra analysis to Group Theory. Group Theory also develops ring theory and vector spaces. Topics from Group Theory include Cyclic, Abelian and permutation groups, Finite and Infinite groups, Lagrange's theorem as well as ring theory, Euclidean domains and polynomial rings and modules and vector spaces.

## Unit content

Group Theory (Topics 1 to 10)

1. Definitions and examples of groups
2. Cyclic, Abelian and permutation groups
3. Finite and Infinite groups
4. Lagrange's theorem, Abstract group theorems
5. Cosets and sub-groups
6. Introduction to rings
7. Euclidean, principal ideal and unique factorisation domains
8. Polynomial rings
9. Introduction to module theory, vector spaces and modules over principal ideal domains
10. Field theory and Galois theory

## Learning outcomes

Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.

On completion of this unit, students should be able to:

1. correctly use concepts and techniques of group theory in known contexts
• GA1:
• GA4:
2. correctly apply concepts and techniques of group theory to new contexts
• GA1:
• GA2:
• GA4:
3. use appropriate techniques from group theory to solve 'real world' problems
• GA4:
4. effectively communicate mathematical ideas, processes and results at different levels of formality
• GA6: