Groups and symmetry
4 points * First semester * Clayton * Prerequisites: A 12-point sequence in first-year mathematics including MAT1010 or MAT1020 (a credit grade or higher in MAT1050 is an acceptable alternative to a pass in MAT1010) * Prohibitions: GAS2614
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%
Prescribed texts
Fraleigh J B A first course in abstract algebra Addison-Wesley
Recommended texts
Armstrong M A Groups and symmetry Springer-Verlag, 1988
Clark A Elements of abstract algebra Dover, 1984
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