Authorised by Academic Registrar, April 1996
Objectives On the completion of this subject students will be familiar with some foundations for the study of abstract algebra; understand the idea that different objects can have the same abstract structure; understand how the concept of symmetry is captured by the group concept; recognise symmetry in different branches of mathematics, such as number theory, geometry and linear algebra; learn the basic concepts of group theory: isomorphism, homomorphism, kernel, normal subgroup; learn the basic theorems relating to these concepts; apply knowledge of group structure to the solution of mathematical problems.
Synopsis Group theory as the theory of symmetry. Groups in geometry, number theory and linear algebra. Subgroups, normal subgroups and homomorphisms - the fundamental concepts and theorems. Representation of groups by permutations and matrices.
Assessment Examinations (1.5 hours): 80% + Assignments: 20%