Math 6220 - Complex Analysis
Spring 2007

Ken Bromberg
Office: JWB 303
Phone: 581-7916

Meeting place and time: MWF 12:55 - 1:45 in JWB 308 and T 3:30 in LCB 323
There will be no class on Tuesday, January 16 and Tuesday, February 20 (the days after the MLK and President's day breaks).

Text: Lars V. Ahlfors, Complex Analysis, 3rd Ed. Although the book is quite expensive you can almost surely find a much cheaper used copy on Amazon or

Course description: This will be a standard first year graduate class in complex analysis and it will prepare students for the complex analysis half of the analysis prelim. For most of the course we will probably follow the text but in some places I will take a different approach. The main novel feature of the course will be that we will use 2-dimensional hyperbolic geometry to prove some of the standard compactness results for holomorphic maps.

Homework: There will be weekly homework assignments. Some subset of each assignment will be graded. Late homework will not be accepted.
Due Date
Wednesday, January 17
Chapter 1
1.1: 1,2,3; 1.2: 1,2,3,4 (don't hand in)
1.4: 3; 1.5: 1; 2.1: 2; 2.2: 4
Homework 1
Wednesday, January 24
Chapter 1
2.4: 2
Chapter 2
1.2: 1, 3, 4, 7; 1.4:  2, 3
Homework 2
Wednesday, January 31
Chapter 2
2.4: 6, 7, 8
Chapter 3
2.2: 1

Wednesday, Febuary 14
Notes and problems on conformal metrics

Wednesday, Febuary 28
Chapter 4
1.3: 6
2.3: 2, 4
3.2: 2, 4
3.3: 4

Friday, March 16
Chapter 4
4.7: 4
5.2: 1
5.3: 1, 3 (Do as many of these as you can bear.)
6.2: 2

Problem sets and problem sessions: Each problem will be assigned to a student to write up in LaTeX with each week one student responsible for compiling all the solutions it a single solution set which I will post. Tuesday's class will be a problem session. The student who prepared a particular problem will have the opportunity to present their problem at the board. This is strongly encouraged but not mandatory nor is attendence to the problem session mandatory. If there is not a student volunteer  I will do the problem. The LaTeXing assignments can be found here.

Final: The final is 1-2:30 PM on Friday, April 27. It will be replica of the complex analysis half of the analysis prelim.

Grades: Your grade will be determined by your homework scores and the final. Roughly speaking if I think you have a good chance of passing the prelim you will get an A.