Math 534, Complex Analysis

Autumn 2019

Instructor: Steffen Rohde (Autumn and Winter), Jayadev Athreya in Spring 2020

Office Hours: M 12:30-1:20 and by appointment, in PDL-C337

Course Description:

Complex analysis is a classical, well developed and elegant theory that provides indispensable tools for many areas of mathematics. At the same time, it is an active field of modern mathematical research that periodically re-appears at the core of major developments (for instance complex dynamics in the 80’ and 90’, and SLE since 2000). This entry level graduate course covers the basic theory of functions of one complex variable.

Prerequisite is a solid knowledge of advanced undergraduate real analysis such as taught in Math 424-426.

The first two quarters will be based on Don Marshall’s book “Complex Analysis”. We will roughly cover Chapters 1-8 in Fall. There are several other excellent textbooks available. I have put the classic “Complex Analysis” by Lars Ahlfors (McGraw-Hill), as well as “Functions of one complex variable” by John Conway (Springer), “Complex Analysis” by Ted Gamelin (Springer), and “A course in complex analysis and Riemann surfaces” by Wilhelm Schlag (AMS) on the course reserve in the math library.

Grades will be determined from homework (40%), participation in class (5%), the midterm exam on November 4 (20%) and the final exam on December 11, 2:30-4:20pm (35%).

Homework 1, due October 2: Problems 1.8, 1.9 and 1.10 in Marshall’s book