MATH 405
Representation Theory and Special Functions
Last Offered Spring 2022
Division III Quantitative/Formal Reasoning
This course is not offered in the current catalog

Representation theory is at the heart of much of modern mathematics. It provides a link between ideas of symmetries, groups and matrices. It has applications from number theory to Fourier Analysis to elementary particle theory. In part, representation theory is a method for producing interesting functions. While not having a single definition, special functions are “functions that have names.” Over the last few hundred years, scientists have needed to define and develop certain families of functions, in order to describe different physical phenomena. These families started to be named, and include Bessel functions, Hermite functions, Laguerre functions and more generally hypergeometric functions. In recent years it has been seen that these different types of functions are best understood through the lens of symmetry and in particular via representation theory. This course will be an introduction to representation theory, starting with finite groups, while at the same time being an introduction to special functions. Thus the course will be a mix of abstract algebra, matrices, calculus and analysis.