MAT 317-01 - Advanced Topics in Analysis

4 credits (Fall)

Complex Analysis: Complex analysis is a fundamental area of mathematics with applications in disperate areas ranging from geometry and number theory to engineering and physics and everything in between. This course serves as an introduction to the basic theory of functions of one complex variable with an eye towards applications. The starting point will be the algebra, geometry, and topology of the complex plane. From there, topics covered will include analytic functions and the Cauchy-Riemann equations, harmonic functions, the logarithm and other elementary functions of a complex variable, series, integration of complex functions, the Cauchy integral theorem, and the residue theorem. Along the way, we will emphasize applications to various other areas of mathematics and science.

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