The topics covered in the first two quarters include complex numbers, analytic functions and power series, integral representation (Cauchy's theorem), sequences of analytic functions, simply connected domains and the Riemann mapping theorem, approximation theory, analytic continuation, entire and meromorphic functions.  During the third quarter, a selection of the following topics will be discussed: Special functions and the prime number theorem, Riemann surfaces and the uniformization theorem, spaces of analytic functions, conformal mappings, complex dynamics.

Prerequisite: Real Analysis as covered in 424-426.

Textbook: for the first two quarters, John B. Conway, Functions of one complex variable, Springer. Another source I'll occasionally be drawing from is Lars Ahlfors, Complex Analysis.

Grades: will be determined from homework (30%), one midterm exam (30%), and the final exam (40%).