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Online Session 1 Session 1

Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Advanced

Former School/College

Former School of Education

Pre-requisites

MAT10719 - Calculus AND MAT10720 - Linear Algebra

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.

GA1: , GA2: , GA3: , GA4: , GA5: , GA6: , GA7:
On completion of this unit, students should be able to: GA1 GA2 GA3 GA4 GA5 GA6 GA7
1 demonstrate a sound knowledge and understanding of complex analysis and group theory
2 demonstrate a proficiency in applying techniques from complex analysis and group theory
3 use appropriate techniques from complex analysis or group theory to solve 'real world' problems
4 communicate mathematical ideas, processes and results effectively at different levels of formality.

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.