The University of Newcastle, Australia
Available in 2019

Course handbook

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.


Availability2019 Course Timetables

Callaghan

  • Semester 2 - 2019

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

MATH3120AlgebraExtends 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.FSCITFaculty of Science724School of Mathematical and Physical Sciences1030005980Semester 2 - 2019CALLAGHANCallaghan2019MATH2320 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 YOn successful completion of this course, students will be able to:1Demonstrate an understanding of algebra consistent with current research in the discipline;2Demonstrate the ability to work within abstract algebraic frameworks;3Demonstrate cumulative knowledge of algebra consistent with being at a senior tertiary level. Formal Examination: ExaminationPresentation: Oral PresentationsWritten Assignment: Short Answer QuestionsIn Term Test: Mid-Semester Take Home Test CallaghanLectureFace to Face On Campus3hour(s)per Week for0Full Term0


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