MAT3191

Group theory

Coordinator: Dr Paul Cally

4 points - Two 1-hour lectures per week - First semester - Clayton - Prerequisites: MAT2020 - Prohibitions: MAP2021

Objectives On the completion of this subject, students will be familiar with some foundations for the study of abstract algebra; understand that different objects can have the same abstract structure; understand how the concept of symmetry is captured by a group concept; recognise symmetry in different branches of mathematics; learn the basic concepts of group theory and the basic theorems relating to these concepts; apply knowledge of group structure to the solution of mathematical problems.

Synopsis Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the fundamental homomorphism theorem.

Assessment Examination (2 hours): 80% - Assignments: 20%

Recommended texts

Fraleigh J B A first course in abstract algebra 5th edn, Addison-Wesley, 1994

Back to the 1999 Science Handbook