Math 6220 - Complex Analysis
Spring 2011

Instructor:
Ken Bromberg
Office: JWB 303
Phone: 581-7916
Email: bromberg@math.utah.edu

Meeting place and time: MWF 2:00 - 1:50 in AEB 306

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 abe.com.

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.

We will start in Chapter 2 of the book. Chapter 1 covers the basic arithmetic, algebra and geometry of complex numbers which I'm assuming most of you are familiar with. The first homework assignment (which won't be turned in) covers this material. If there is interest I can go over some of these problems in class.

Homework:

 Due Date Assignment Not to be handed in Chapter 1 1.1: 1,2,3; 1.2: 1,2,3,4; 1.4: 1,2,3,4,5; 1.5: 1,2,3,4; 2.1: 2,4; 2.2: 1,2,4,5; 2.3: 1,2,5; 2.4: 1,4 Friday, January 28 Chapter 2 1.2: 1,2,4,5; 1.4: 2,3,4 Extra problems Solution to extra problems Monday, Febuary 14 Chapter 2 2.4: 7,8 Chapter 3 1.3: 3,4; 3.1: 1,3,4; 3.2: 4; 3.3: 6; 3.5: 4 Friday, March 4 Chapter 4 1.3: 4,5,6; 2.1: 1; 2.2: 2 3.2: 2,3,4; 3.3: 4 Extra problem Friday, March 18 Chapter 4 3.4: 1,2; 4.7: 1,4,5 Friday, April 8 Chapter 4 5.2: 2; 5.3: 1 (don't hand in), 3a,3c,3f 6.2: 1,2; 6.4: 1,2; 6.5: 3,5 Wednesday, April 27 Chapter 5 1.1: 1,2,3; 1.2: 3,5; 1.3: 1 2.2: 2,3; 5.4: 1,4