## Availabilities:

Location Domestic International
Online Session 1 Session 1

## Unit Summary

### Unit type

UG Coursework Unit

12

7

### Former School/College

Former School of Education

## Unit aim

Extends the concepts developed in Calculus to functions of a complex variable. Group theory is also introduced. Topics from complex analysis include derivatives, Cauchy-Riemann equations, integration, power series methods, residues and poles. Topics from group theory include definition of a group and examples of groups, Lagrange's theorem.

## Unit content

Complex Analysis (Topics 1 to 5) - Functions of a complex variable - Limits and continuity - Derivatives - Cauchy-Riemann equations - Analytic functions - Integration - Cauchy's theorem - Power series methods - Zeros and singularities - Residues and poles.

Group Theory (Topics 6 to 10) - Definitions and examples of groups - Cyclic, Abelian and permutation groups - Finite and infinite groups - Lagrange's theorem - Abstract group theorems - Cosets. Subgroups.

## 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. demonstrate a sound knowledge and understanding of complex analysis and group theory
• GA1:
• GA4:
2. demonstrate a proficiency in applying techniques from complex analysis and group theory
• GA1:
• GA4:
3. use appropriate techniques from complex analysis or group theory to solve 'real world' problems
• GA4:
• GA6:
4. communicate mathematical ideas, processes and results effectively at different levels of formality.
• GA4:
• GA6:

## Prescribed texts

• Prescribed text information is not currently available.
Prescribed texts may change in future teaching periods.