Availabilities:

Not currently available in 2020

Unit description

Extends the concepts introduced in Mathematical Ideas, Calculus and Linear Algebra analysis to Group Theory. Group Theory also develops ring theory and vector spaces. Topics from Group Theory include Cyclic, Abelian and permutation groups, Finite and Infinite groups, Lagrange's theorem as well as ring theory, Euclidean domains and polynomial rings and modules and vector spaces.

Unit content

Group Theory (Topics 1 to 10)

  1. Definitions and examples of groups
  2. Cyclic, Abelian and permutation groups
  3. Finite and Infinite groups
  4. Lagrange's theorem, Abstract group theorems
  5. Cosets and sub-groups
  6. Introduction to rings
  7. Euclidean, principal ideal and unique factorisation domains
  8. Polynomial rings
  9. Introduction to module theory, vector spaces and modules over principal ideal domains
  10. Field theory and Galois theory

Learning outcomes

Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
On completion of this unit, students should be able to:GA1GA2GA3GA4GA5GA6GA7
1correctly use concepts and techniques of group theory in known contextsIntellectual rigourKnowledge of a discipline
2correctly apply concepts and techniques of group theory to new contextsIntellectual rigourCreativityKnowledge of a discipline
3use appropriate techniques from group theory to solve 'real world' problemsKnowledge of a discipline
4effectively communicate mathematical ideas, processes and results at different levels of formalityCommunication and social skills

On completion of this unit, students should be able to:

  1. correctly use concepts and techniques of group theory in known contexts
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
  2. correctly apply concepts and techniques of group theory to new contexts
    • GA1: Intellectual rigour
    • GA2: Creativity
    • GA4: Knowledge of a discipline
  3. use appropriate techniques from group theory to solve 'real world' problems
    • GA4: Knowledge of a discipline
  4. effectively communicate mathematical ideas, processes and results at different levels of formality
    • GA6: Communication and social skills

Teaching and assessment

Notice

Intensive offerings may or may not be scheduled in every session. Please refer to the timetable for further details.

Southern Cross University employs different teaching methods within units to provide students with the flexibility to choose the mode of learning that best suits them. SCU academics strive to use the latest approaches and, as a result, the learning modes and materials may change. The most current information regarding a unit will be provided to enrolled students at the beginning of the study session.

Fee information

Domestic

Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.
Commencing 2020 Commonwealth Supported only. Student contribution band: 2

Fee paying courses
For POSTGRADUATE or UNDERGRADUATE full fee paying courses please check Domestic Postgraduate Fees OR Domestic Undergraduate Fees

International

Please check the international course and fee list to determine the relevant fees.

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