Abstract Algebra and Number Theory

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

Awards offering Abstract Algebra and Number Theory

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

• Bachelor of Arts
• Bachelor of Arts and Bachelor of Applied Social Science
• Bachelor of Arts and Bachelor of Business
• Bachelor of Arts and Bachelor of Education (Secondary)
• Bachelor of Arts (Education Studies)
• Bachelor of Education (Secondary)
• Diploma of Arts
• Undergraduate Certificate in Arts

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 University College.

Assessment Methods

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

Prescribed Text

• Primary readings provided