# Home page of Math 520AB

Complex Analysis

Fall 2005 - Spring 2006

## Course Overview:

The goal of the first semester of this course is to give students a solid grounding in the fundamentals of analytic functions of one complex variable, complemented by the study of particular functions (such as Euler's Gamma function, Riemann's theta and zeta functions, and elliptic functions) and their applications to other fields. If time permits we will also discuss the most basic facts about functions of several complex variables. The second semester will be devoted entirely to Riemann surfaces. Although no prior exposure to complex analysis will be assumed, students without any such exposure may find the pace gruelling

## Policies:

**Class meetings:** MWF 2:00 - 2:50 in Math 320. The course will mostly be in the traditional lecture format, occasionally supplemented by student presentations of homework solutions. If there is demand, a discussion hour may be added.
**Texts:**
- Fall: "Complex Analysis" by E. Stein and R. Shakarchi, Princeton University Press, 2003 (required).
- Spring: "Riemann Surfaces" by H. Farkas and I. Kra, Springer, 1992 (required) and "Compact Riemann Surfaces" by J. Jost, Springer, 2002 (optional).

**Prerequisites:** Solid command of advanced calculus, linear algebra, and basic point set topology as well as the ability to construct and communicate proofs. More advanced ideas from algebra, analysis, and especially topology (at the level of the Math PhD core) will occasionally appear, but they will not be essential to understanding the main points in the first semester; the Math core will be assumed in the second semester.
**Homework:** There will be substantial homework assignments roughly once per week.
**Project:** There will be a required final project in which students will master an additional topic and write a short expository paper on it, suitable for fellow students.
**Grades:** Grades will be based on homework (65%) and the project (35%).
**Other policies:** Please read my standard policies about other matters.

## Contact Information:

**Instructor:** Douglas Ulmer, Professor of Mathematics
**Office:** Math 204
**Phone:** 621-6861
**E-mail:** ulmer@math.arizona.edu
**Office hours:** Starting 8/29: MW 3-4 in Math 204, F 1-2 in Math East 145. Check my home page for possible changes.