Extends the concepts introduced in Mathematical Ideas, Calculus and Linear Algebra analysis to Group Theory. Group Theory also develops ring theory and vector spaces. Topics from Group Theory include Cyclic, Abelian and permutation groups, Finite and Infinite groups, Lagrange's theorem as well as ring theory, Euclidean domains and polynomial rings and modules and vector spaces.
Group Theory (Topics 1 to 10)
- Definitions and examples of groups
- Cyclic, Abelian and permutation groups
- Finite and Infinite groups
- Lagrange's theorem, Abstract group theorems
- Cosets and sub-groups
- Introduction to rings
- Euclidean, principal ideal and unique factorisation domains
- Polynomial rings
- Introduction to module theory, vector spaces and modules over principal ideal domains
- Field theory and Galois theory
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||correctly use concepts and techniques of group theory in known contexts||Intellectual rigour||Knowledge of a discipline|
|2||correctly apply concepts and techniques of group theory to new contexts||Intellectual rigour||Creativity||Knowledge of a discipline|
|3||use appropriate techniques from group theory to solve 'real world' problems||Knowledge of a discipline|
|4||effectively communicate mathematical ideas, processes and results at different levels of formality||Communication and social skills|
Teaching and assessment
Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.
Commencing 2016 Commonwealth Supported only. Student contribution band: 2
Please check the international course and fee list to determine the relevant fees.