Stoll’s Notes chapter 8: Whittaker and Watson chapter 6. Homology and Winding Numbers A proof based on existence of primatives for analytic functions on the disc. We eventually want to understand Schlag Theorem 1. I typed up special notes for this section: Elliptic Function Notes See also:

We are using Rudin’s proof here to avoid the use of winding numbers. I typed up special notes for this section: This says that if integrals around closed loops are zero, then you are analytic it is a converse of Cauchy’s Theorem. McMullen page 5 He also also outlines Goursat and gives the basic proof. Applications of Cauchy’s Theorem. Interlude on Topology and Categories. Friday, March 3rd solutions scratch sage notebook I used to check stuff with– it is messy.

We eventually want to understand Schlag Theorem 1. Infinite Products and Partial Fractions. The proof in GK and other places uses winding numbers. Order of an entire function Hadamard’s Theorm. We are using Rudin’s proof here to avoid the use of winding numbers.

See John Loftin’s Notes.

This both assumed Green’s theorem and the Jordan Curve Theorem. General Cauchy Integral Formula.

## MATH 8701 – Complex Analysis – Fall 2013

Holomorphic Forms and Cauchy’s Theorem immediate consequences section 8: Many proofs don’t use topology. Elliptic Ahlfoes Notes See also: Green and Krantz postpone analytic continuation to Chapter 10, which is something we do not want to do. Modular Curves Modular Forms Modular lambda function. Covering Spaces, Uniformization and Big Picard.

# Complex (Spring )

Weierstrass M-test WW 3. I typed up special notes for this section: Fundamental theorem of algebra. The downside of these are that they are only good for one theorem, which the general machine of algebraic topology is good for many many many things. Application of Cauchy Integral Formula: Complex Numbers and Cauchy’s Theorem.

# MATH – Complex Analysis – Fall

Official Definition of Riemann Surfaces Video. This develops a minimal amount of Wedhorn’s Notes section 2: McMullen has a discussion on the Uniformization Theorem. Interlude on Topology and Categories.

McMullen page 5 He also also outlines Goursat and gives the basic proof. Schlag section 2GK 1.

This says that if integrals around closed loops are zero, then you are analytic it is a converse of Cauchy’s Theorem. Whittaker and Watson chapter 6.

Applications of Cauchy’s Theorem. Rudin – Real and Complex Analysis Conformal Maps and Riemann Surfaces. We want to get rid of these assumptions. Homology and Winding Numbers A homewoek based on existence of primatives for analytic functions on the disc.

Stoll’s Notes chapter 8: My Notes partial Glickenstein’s Notes Munkres is also good. One could also use Morera’s theoremwhich I mentioned in emails but didn’t prove in class.