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Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Advanced

Former School/College

Former School of Education

Unit aim

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: GA1 GA2 GA3 GA4 GA5 GA6 GA7
1 correctly use concepts and techniques of complex analysis and group theory in known contexts Intellectual rigour Knowledge of a discipline
2 correctly apply concepts and techniques of complex analysis and group theory to new contexts Intellectual rigour Creativity Knowledge of a discipline
3 effectively communicate mathematical ideas, processes and results at different levels of formality Intellectual rigour Knowledge of a discipline Communication and social skills

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

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