Math 220A - Complex Analysis

Welcome to Math 220a!

Course description:

This course provides an introduction to complex analysis. We will cover holomorphic and meromorphic functions, Taylor and Laurent expansions, Cauchy's theorem and its applications, calculus of residues, the argument principle, harmonic functions, sequences of holomorphic functions, infinite products, Weierstrass factorization theorem, Mittag-Leffler theorem.

Math 220 is a three quarter sequence. Jim Agler and Kiran Kedlaya will teach Math 220b and Math 220c in Winter and Spring.

Instructor: Dragos Oprea, doprea "at", AP&M 6-101.

Lectures: WF, 12:30-1:50, AP&M B-412.

Office hours:

Wednesday 2-4 in AP&M 6-101.

I am available for questions after lecture or by appointment. Also, feel free to drop in if you see me in my office.

Textbook: Complex Analysis by Lars Ahlfors.


The minimal prerequesites are Math 140 A-B. However, this is a graduate level course, so at times, we may use notions from related fields, including topology and real analysis. I am happy to discuss prerequisites on an individual basis. If you are unsure, please don't hesitate to contact me.

There will be a Midterm on November 2, in class, as well as a Final Exam on December 8, 11:30-2:30. The final grade will be based the following scheme:

20% homeworks and regular attendance of lectures, 30% Midterm, 50 % Final Exam.

The problem sets are mandatory and are a very important part of the course. The problem sets are due in class.

Important dates:


Lecture Summaries


Homework 1 due Wednesday, October 5 - PDF

Homework 2 due Friday, October 14 - PDF

Homework 3 due Friday, October 21 - PDF

Homework 4 due Friday, October 28 - PDF

Practice problems for the midterm - PDF

Midterm from Fall 2015 - PDF

Midterm - PDF

Homework 5 due Friday, November 18 - PDF

Homework 6 due Friday, December 3 - PDF

Final from Fall 2015 - PDF. We did not discuss the material needed for 3 and 8(ii) this quarter.

Topics for Final and Practice Sheet - PDF

Final Exam - PDF