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 Campus

  • Semester 1 - 2015

Learning Outcomes

1. Hold an algebraic background consistent with current research in the discipline

2. Be able to work within abstract algebraic frameworks

3. Had been provided with an overview of algebra covered in previous years of study.

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: Presentation

Essay: Essay / Written Assignment

Contact Hours

Lecture

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