MAT 317-01 - Advanced Topics in Analysis

4 credits (Fall)

Fourier Analysis. Over two hundred years ago, Joseph Fourier solved the heat equation by discovering that solutions can be expressed as infinite series of sinusoidal waves. This discovery marked the beginning of the field and methodology we now call Fourier Analysis, which has since become deeply woven into mathematics, physics, engineering, and computer science. It plays fundamental roles in signal processing, differential equations, quantum mechanics, and perhaps more surprisingly, number theory, combinatorics, representation theory, and algorithm efficiency. This course will begin with the necessary dose of complex numbers, inner products, and function spaces involved in the study of Fourier series. We will then make our way into other types and applications of Fourier transforms, investigating the beautiful Inversion Theorem, Plancherel Theorem, and Poisson summation formula along the way. In the later part of the course each student will find a Fourier-related topic to their liking and present it to the class.

Prerequisite: MAT 316 with grade S, C, or better.
Instructor: Webster