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 contentComplex 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.
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.
Learning outcomes and graduate attributes
|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||Intellectual rigour||Knowledge of a discipline|
|2||demonstrate a proficiency in applying techniques from complex analysis and group theory||Intellectual rigour||Knowledge of a discipline|
|3||use appropriate techniques from complex analysis or group theory to solve 'real world' problems||Knowledge of a discipline||Communication and social skills|
|4||communicate mathematical ideas, processes and results effectively at different levels of formality.||Knowledge of a discipline||Communication and social skills|
- This text is for Complex Analsyis: Wunsch, D, 2005, Complex Variables with Applications, 3rd edn, Pearson, Boston, MA.
- This text is for Group Theory: Gallian, JA, 2013, Contemporary Abstract Algebra, 8th edn, Cengage.
Teaching and assessment
Commonwealth Supported courses
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Commencing 2015 Commonwealth Supported only. Student contribution band: 2
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