## Availabilities:

Not currently available in 2015

## Unit Summary

### Unit type

UG Coursework Unit

12

7

### Former School/College

Former School of Education

### Pre-requisites

MAT10722 - Complex Analysis and Group Theory

## Unit aim

Extends the concepts developed in introductory complex analysis to applications of complex analysis. Introductory Group Theory is also developed to ring theory and vector spaces. Topics from complex analysis include applications of residues, mappings by elementary functions and conformal mappings and their applications. Topics from Group Theory include ring theory, Euclidean domains and polynomial rings as well as modules and vector spaces.

## Unit content

Complex Analysis (Topics 1 to 5)
1.    Applications of residues
2.    Mapping by elementary functions
3.    Conformal mapping
4.    Applications of conformal mapping
5.    The Schwarz-Christoffel transformation & integral formulas of the Poisson Type
Group Theory (Topics 6 to 10)
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 complex analysis and group theory in known contexts
• GA1:
• GA4:
2. correctly apply concepts and techniques of complex analysis and group theory to new contexts
• GA1:
• GA2:
• GA4:
3. effectively communicate mathematical ideas, processes and results at different levels of formality
• GA1:
• GA4:
• GA6: