This will be a continuation of Math 503. It is a fundamental course for anyone who wants to pursue their further studies in pure mathematics. The following two parts will be covered:
(1) Classical Complex Analysis and (2) Riemann surfaces.
Part 1. Classical Complex Analysis. We will discuss topics not covered in Math 503, such as the invariant metrics, Picard theorems, elliptic functions.
Part 2. Introduction to Riemann surfaces. Hyperbolic geometry, uniformization theorem, Riemann-Roch theorem, Abel theorem.
Notes written by the Instructor to be distributed during the lectures