to group theory and its applications in the physical sciences.
Finite groups. Compact Lie groups. Representation theory, tensor
representations of classical Lie groups, classification of semi-simple Lie
Group theory is widely used in many fields outside mathematics. This is a
consequence of the fact 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. In addition to the official prerequisites, it is highly
recommended that students also have passed MATH 2015 and MATH 2270.
Note also the timetable change for MATH 4241 --
MWF 11:30 in Founders College 108.
Prerequisite:AS/SC/AK/MATH 2222 3.0 -- or equivalent.
Coordinator: Kim Maltman