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Unit of Study MAT10722 - Complex Analysis and Group Theory (2014)

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Unit Snapshot

  • Unit type

    UG Coursework Unit

  • Credit points

    12

  • AQF level

    7

  • Level of learning

    Advanced

  • Former School/College

    Former School of Education

  • Enrolment information

    N/A

Unit description

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.

Availabilities

Location Domestic International
Online Session 1 Session 1

Learning outcomes and graduate attributes

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:

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
Learning outcome count Learning outcome description 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 learning resources

Prescribed Texts
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Prescribed Learning Resources may change in future Teaching Periods.