This course will introduce you to many of the classical techniques in this area. This will be a hands-on and computational course stressing problem solving. The methods and ideas discussed have proved to be useful in every area of mathematics. If G is a finite group, then a complex matrix representation of degree of G is simply a group homomorphism from G into the group of invertible n by n matrices with entries in the complex numbers. It turns out that knowledge of these functions can give extension information about G, including its entire normal subgroup structure.
Character theory is an extremely powerful tool for studying finite groups.
The object of the course will be an introduction to the complex character theory of finite groups. Topics in Applied Mathematics. This course will be a combination of traditional lecture style and research seminar with most presented by the instructor.