MAT30001 - Group Theory (2017)

Not currently available in 2017

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)

1. Definitions and examples of groups
2. Cyclic, Abelian and permutation groups
3. Finite and Infinite groups
4. Lagrange's theorem, Abstract group theorems
5. Cosets and sub-groups
6. Introduction to rings
7. Euclidean, principal ideal and unique factorisation domains
8. Polynomial rings
9. Introduction to module theory, vector spaces and modules over principal ideal domains
10. Field theory and Galois theory

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.