Algebra

Description

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.

Availability

Callaghan

  • Semester 2 - 2016
  • Semester 2 - 2017

Learning Outcomes

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.

Content

  • Groups and subgroups
  • Homomorphisms and factor groups
  • Permutation groups
  • Groups acting on sets
  • Abelian groups
  • Rings and modules
  • Integral domains
  • Fields
  • Homomorphisms and factor rings
  • Prime ideals and maximal ideals
  • Unique factorisation domains

Assumed Knowledge

MATH2320

Assessment Items

Formal Examination: Examination

Presentation: Oral Presentations

Written Assignment: Short Answer Questions

In Term Test: Mid-Semester Take Home Test

Contact Hours

Callaghan

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term