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. The first quarter is part of the first year graduate core “Analysis” sequence (the Analysis sequence continues as “Real Analysis” in Winter and Spring).

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

The first two quarters will be based on Don Marshall’s book “Complex Analysis”. We will roughly cover Chapters 1-7 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

Homework 2, due October 11: Problems 2.9-2.13

Homework 3, due October 16: Problems 2.14, 2.15, 3.7, 3.13

Homework 4, due October 23: Problems 3.8-3.12

Homework 5, due November 1: Problems 4.6-4.10

Homework 6, due November 18: Problems 4.5, 4.11, 4.12, 5.7, 5.8

Homework 7, due November 27: Problems 5.9-5.12

Homework 8, due December 6: Problems 6.7, 6.8, 6.10, 6.11. Extra credit: Where does Newton’s method for a quadratic polynomial converge?

Our grader Joonyong Choi holds his office hour Fridays 9:00 - 11:00am in PDL C-111.