Math 6220 - Complex Analysis

Spring 2011

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 |

Grades:

For math graduate students if you do well enough on the final that I think you would most likely pass the real analysis half of the prelim you will receive an A. If you make a serious effort to do all of the homework you will get no less than a B. If you do neither of these things your grade may be a C or worse.

If you are an undergrad or a grad student in a different department I recommend taking the class pass-fail. If you are in one of these two groups you should come talk to me individually so we can come to an agreement about the basis of your grade.

Most importantly if at anytime you are concerned about how you are doing in the class you should come talk with me.