Math 535, Complex Analysis
Instructor: Steffen Rohde (Autumn and Winter), Jayadev Athreya in Spring 2018
Office Hours: M 1:30-2:20 and by appointment, in PDL-C337
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%).