Math 535: Complex Analysis

David Dumas

University of Illinois at Chicago
Spring 2010

NOTE: This is the home page of a complex analysis course from 2010.
You might be looking for Math 535, Spring 2016.
The image of the streets of Chicago under a Riemann mapping from the complement of Lake Michigan to the unit disk. The unit circle represents the lake shore, with Navy Pier at z = 1.

General information

CRN 19436
Lectures MWF 12:00 - 12:50pm in SEO 636
Main Text Complex Analysis by Lars Ahlfors, 3ed.
ISBN-13: 978-0070006577
Supplementary Texts Gamelin
Bak & Newman
Instructor David Dumas (
Office hours Mondays and Wednesdays 2-3pm in SEO 503
Extra office hours: 1-3pm on May 2 and May 3
Homework Policies Homework problems will be assigned on Mondays and Wednesdays (see assignments).
Homework is due by 4pm on the first lecture day of each week (usually Monday) and can be turned in during lecture or directly to the grader's mailbox (Paul Reschke) in the mailroom on the 3rd floor of SEO.
The list of challenge problems (see course materials) will be updated on a regular basis; you must complete four of these problems during the semester, with at least two of them submitted before the midterm exam.
Late homework will not be accepted.
You can discuss the homework with other students, but you must write (and understand!) your own solutions.
The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!

Course materials

These documents are available for download in PDF format.

Important Dates

There will be one midterm exam and a cumulative final exam.
Midterm Exam Wed, Mar 3 In class
Final Exam Tues, May 4 8:00-10:00am in SEO 427


Your course grade will be determined on the following basis:
Homework 30%
Midterm Exam 30%
Final Exam 40%

When computing your homework grade, the lowest weekly homework score will be dropped, and the remaining scores will be averaged with your challenge problem scores. (That is, each challenge problem is worth as much as a weekly homework assignment!)


Date Reading
Apr 14 Sections 6.1, 6.2
Mar 29 Sections 5.1, 5.2 and 5.5
Feb 10 Chapter 4
Jan 20 Chapter 3
Jan 13 Chapter 2
Jan 11 Chapter 1


The list of homework problems was last updated on Monday, April 19. The most recently assigned problems are shown in green.

Hwk # Due Problems
14 Mon, Apr 26 Section 5.5.5(p227): 3
Problems from Lecture 39
Problems from Lecture 40
13 Mon, Apr 19 Section 5.2.2(p193): 1,2
Section 5.2.3(p198): 5
Section 5.5.5(p227): 1,2
12 Mon, Apr 12 Section 5.1.1(p178): 2*
Section 5.1.2(p184): 1,5
Section 5.1.3(p186): 1,4
Section 5.2.1(p190): 1
* Typographical error in the text: The series should be ζ(z) = Σ n-z.
11 Mon, Apr 5 Section 4.6.2(p166): 1,2
Section 4.6.4(p171): 4
Problems from Lecture 31
10 Mon, Mar 29 Section 4.5.3(p161): 1,3a,3b,3c
Problems from Lecture 27
Problems from Lecture 28
9 Mon, Mar 15 Section 4.3.3(p133): 1,3,4
Section 4.3.4(p136): 1,2
8 Mon, Mar 8 Section 4.3.2(p129): 4,5,6
7 Mon, Mar 1 Section 4.2.2(p120): 1,2,3
Section 4.2.3(p123): 1,3,5
6 Mon, Feb 22 Section 3.4.2(p96): 2*
Section 4.1.3(p108): 1,2,3,4,5,6
* Use a Möbius transformation to simplify the problem.
5 Mon, Feb 15 Section 3.3.1(p78): 2,4
Section 3.3.2(p80): 1,4, 2,3
Section 3.3.5(p88): 6
Problems from Lecture 13
4 Mon, Feb 8 Section 2.3.4(p47): 5,6,7
Section 3.2.2(p72): 1,2
Problems from Lecture 9
3 Mon, Feb 1 Section 2.2.3(p37): 2,3
Section 2.2.4(p41): 3,8,9
Section 3.1.2(p53): 1
Section 3.1.4(p63): 5*
* Note: See the definition of totally bounded on p60.
2 Mon, Jan 25 Section 2.1.2(p28): 3
Section 2.1.4(p32): 4,6
Problems from Lecture 5
1 Wed, Jan 20 Section 1.1.4(p9): 3
Section 1.1.5(p11): 1
Section 1.2.1(p15): 2
Section 1.2.3(p17): 5
Section 2.1.2(p28): 2,4
Section 2.1.4(p32): 2,3

Other Resources

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