**Math 535, Complex Analysis**

**Winter 2018**

Instructor: Steffen Rohde (Autumn and Winter), Jayadev
Athreya in Spring 2018

Office Hours: M 1:30-2:20 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 topics covered include complex numbers, analytic functions and power
series, integral representation and Cauchy’s theorem, sequences of analytic
functions, simply connected domains and the Riemann mapping theorem,
approximation theory, analytic continuation, entire and meromorphic
functions, special functions, harmonic functions, Riemann surfaces and the uniformization theorem.

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

The course will be based on Chapters 1-5 and parts of Chapter 8 of
Wilhelm Schlag’s book

“A course in
complex analysis and Riemann surfaces”, which is electronically
accessible at our library, and is also on the course reserve in the math library. 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) and “Complex Analysis” by Ted Gamelin (Springer)
on the course reserve in the math library.

Grades will be determined from homework (40%), participation in class
(10%), the midterm exam (20%) and the
final exam (30%).