Extends the application of the familiar algebraic laws for adding and multiplying numbers, matrices and vectors to other contexts. Depending on just which laws are satisfied, the algebraic structures studied are called groups, rings and fields. These concepts underlie much of modern mathematics, and are essential background for research in any area of pure mathematics.
Not currently offered.
This Course was last offered in Semester 2 - 2019.
On successful completion of the course students will be able to:
1. Demonstrate an understanding of algebra consistent with current research in the discipline;
2. Demonstrate the ability to work within abstract algebraic frameworks;
3. Demonstrate cumulative knowledge of algebra consistent with being at a senior tertiary level.
- Groups and subgroups
- Homomorphisms and factor groups
- Permutation groups
- Groups acting on sets
- Abelian groups
- Rings and modules
- Integral domains
- Homomorphisms and factor rings
- Prime ideals and maximal ideals
- Unique factorisation domains
Formal Examination: Examination
Presentation: Oral Presentations
Written Assignment: Short Answer Questions
In Term Test: Mid-Semester Take Home Test