Applied Group Theory

Group theory is widely used in many fields outside mathematics. The reason this occurs is that the algebraic structure which defines a group is naturally the property of the set of symmetries of a physical system. Paying attention to this fact, and using results from group representation theory (some of which we will study in this course), it is often possible to radically simplify practical calculations in these fields.

The course will provide an introduction to group theory, both for finite groups and continuous groups, as well as an introduction to group representation theory. No previous knowledge of group theory will be assumed, but a background in linear algebra is essential. The course will begin with a review of the formal aspects of linear algebra (vector spaces, linear transformations, dimensions, bases, inner products for complex vector spaces, etc.) necessary for the remainder of the course.

There is no official text. A copy of the class notes will be available at the library, and a series of reference texts will be on reserve at the library.