Details for Abstract Algebra and Number Theory

This subject is required in the major and minor mathematics structure of the B.Ed. (Secondary)


Quick Info

  • Currently offered by Alphacrucis: Yes
  • Course code: MAT301
  • Credit points: 10
  • Subject coordinator: Stephen Brinton

Prerequisites

The following courses are prerequisites:

Awards offering Abstract Algebra and Number Theory

This unit is offered as a part of the following awards:

Unit Content

Outcomes

  1. Explain the concepts of an algebraic system, derive and comprehend its properties and construct simple proofs relating to groups, rings and fields;
  2. Employ number systems as examples of algebraic structures and execute classical number theory algorithms including linear Diophantine equations and asymptotic properties of prime numbers through Fermat’s and Wilson’s theorems;
  3. Demonstrate problem solving skills using the concepts presented;
  4. Demonstrate knowledge of the concepts presented through the entire semester in context and the ability to use these concepts to make reasoned, logical answers with sound mathematical reasoning.

Subject Content

  • Introduction to groups
  • Homomorphisms and factor groups
  • Introduction to rings and fields
  • Unique factorisation
  • Linear diophantine equations
  • Congruences
  • Fermat’s and Wilson’s theorems

This course may be offered in the following formats

  • Onsite (on campus)
  • Online (e-Learning)
  • Intensive

Please consult your course prospectus or enquire about how and when this course will be offered next at Alphacrucis College.

Assessment Methods

  • Worksheets (30%)
  • Online Exam/Activities (30%)
  • Final Examination (40%) 

Prescribed Text

  • Primary readings provided