Math 660 -- Complex Analysis I

Instructor: Harry Tamvakis

Lectures: TuTh 2:00-3:15, MTH 0305

Office: 4419 Mathematics Building
Office hours: By appointment
Telephone: (301)-405-5120
E-mail: harryt@umd.edu

Course guide:

Text: Raghavan Narasimhan and Yves Nievergelt, Complex Analysis in One Variable, Birkhauser 2001.

Content:
This is a graduate course in complex analysis. I will assume that people taking this course have seen some complex analysis before, at the undergraduate level. The goal of the course is to show how complex analysis interacts naturally with other branches of mathematics, such as topology and functional analysis. We will cover the following topics: (i) the classical theory of complex functions of a single variable, (ii) covering spaces, the monodromy theorem and applications, (iii) Runge's theorem and the Mittag-Leffler and Weierstrass theorems, (iv) the Riemann mapping theorem. If time permits, we will discuss additional topics: harmonic functions and the Dirichlet problem, Riemann surfaces and the uniformization theorem.

Homework:
The best and only way to learn mathematics is to do mathematics! Your weekly homework assignments are therefore the most important part of this course. Homework will be assigned on Thursday and is due after class on the Thursday of the following week. I urge you to submit all of your assignments on time - however my policy is to allow up to TWO late homework assignments per student, which should be turned in at most two weeks after their due date. Any further late assignments will not be graded. You may discuss the problems with others and work in groups if you wish, but whatever you turn in should be written up on your own. The extra credit problems are optional - they can improve your grade, but you do not need to solve them to do well in the course. People looking for a challenge are encouraged to attempt them! Our homework grader is Jing Zhou, and her email is jingzhou@umd.edu. She has office hours on Wednesdays, 10:00 - 11:00 am, in 4310 Kirwan Hall. Please contact her with any questions you may have about the homework grading and solutions to the problems.

Exams:
We will have one midterm exam during the course. The midterm will be a take home exam, beginning on Tuesday, March 31 at 2:00 pm , and due by 12:00 noon on the following day. Make-up exams will only be given for compelling and documented reasons.

Grading Policy:
The course grade will be determined by adding your midterm score (50%) to your homework total (50%). Participating in class and working on extra credit problems is encouraged and will help to improve your grade.

READ THIS:
University of Maryland course related policies. Includes a discussion of academic integrity, the honor pledge, and accomodations for students with disabilities.

Office Hours:
Feel free to come by my office and talk at any time, either by chance or by appointment.

Remote Teaching:
Starting with week 8 of the class I will be posting my Lecture Notes online.


HOMEWORK

Assignment 1 (Due 2/6/20): ps, pdf, tex

Assignment 2 (Due 2/13/20): ps, pdf, tex

Assignment 3 (Due 2/20/20): ps, pdf, tex

Assignment 4 (Due 2/27/20): ps, pdf, tex

Assignment 5 (Due 3/5/20): ps, pdf, tex

Assignment 6 (Due 3/12/20): ps, pdf, tex

Midterm exam (3/31/20): ps, pdf
Solutions to the midterm: ps, pdf

Assignment 7 (Due 4/9/20): ps, pdf, tex

Assignment 8 (Due 4/16/20): ps, pdf, tex

Assignment 9 (Due 4/23/20): ps, pdf, tex

Assignment 10 (Due 4/30/20): ps, pdf, tex

Assignment 11 (Due 5/7/20): ps, pdf, tex