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Course Module Information
Course Modules
MA532: Groups I
Semester 1 | Credits: 5
Introduction to Group Theory. Topics covered include the group axioms, symmetries, permutations, cyclic groups, dihedral groups, small groups of matrices, homomorphisms, normal subgroups, Isomorphism Theorems, automorphism groups, free groups, relators and presentations.
(Language of instruction: English)
Learning Outcomes
- Explain what a group is and use the definition of a group to identify examples and non-examples.
- Use the language and terminology of group theory in an accurate and knowledgeable way.
- Give examples of groups with certain specified properties, and determine whether a given group has a specified property.
- Describe symmetries of geometric objects in terms of permutations or matrices;
- State and prove some significant theorems of group theory.
- Critically assess proposed proofs of statements in group theory, and compose some independent proofs.
Assessments
- Written Assessment (70%)
- Continuous Assessment (30%)
Teachers
- NOELLE GANNON:
Research Profile |
Email
- RACHEL QUINLAN:
Research Profile |
Email
Reading List
- "An Introduction to the Theory of Groups" by J. J. Rotman
Publisher: Springer - "A Course in the Theory of Groups," by D. J. S. Robinson
Publisher: Springer - "Stoy, Groups and Geometry" by P. M. Neumann & G. A
Publisher: P. M. Neumann & G. A - "Topics in Group Theory," by G. Smith & O. Tabachnikova
Publisher: Springer - "The Theory of Groups" by I. D. Macdonald
Publisher: Clarendon Press, - "Combinatorial Group Theory" by R. C. Lyndon & P. E. Schupp
Publisher: Springer - "Theory of Groups of Finite Order" by W. Burnside
Publisher: CUP - "Finite Group" by B. Huppert & N. Blackburn
Publisher: Springer
Note: Module offerings and details may be subject to change.