Course outline: This course will be an introduction to analytic functions of one complex variable. Topics include: Complex numbers and their topology, analytic functions, conformal mappings, Möbius transformations, complex integration, Cauchy's Theorem and Integral Formula, the Open Mapping Theorem, isolated singularities and their classification, calculus of residues, the Argument Principle, and Schwarz's Lemma.

Textbook: Functions of One Complex Variable I by John Conway.

We will cover most of Chapters I-VI.

Prerequisites: An undergraduate course in complex analysis is helpful but not really necessary.

Homework policy: Homework assignments will be posted on the course webpage, and will typically be due on Wednessdays. No late homework will be accepted, but I will drop your lowest homework score. I encourage you to start early and to discuss the problems with other students. By all means come by my office hours if you have trouble with a problem. The only real caveat to group work is that you must write up your own solutions, in your own words.