## Professor

John Hunter

Department of Mathematics

University of California

Davis, CA 95616, USA

e-mail: `jkhunter@ucdavis.edu`

Phone:

- (530) 554-1397 (Office)
- (530) 752-6653 (Fax)

Office: 3230 Mathematical Sciences Building

## Course Information

MAT 205B, Spring Quarter, 2018

**Lectures:**
MWF 1:10–2:00 p.m., Wellman 101

**Office hours:**
Th 2:00–3:00 p.m.

**Text:**
*Complex Analysis*, E. M. Stein and R. Shakarchi

**MAT 205A:**
A link to the course website for MAT 205A, taught by Dan Romik, is
here.

## Announcement

Final projects are here:

## Course grade

Course grade will be based on homework (50 %) and a take-home final project (50%) on a topic from complex analysis of your choosing.

Homework will be assigned weekly on this page and is due in clas on Fridays.

## Some books

Here are some further references on complex analysis, Riemann surfaces, and algebraic topology.

**Complex analysis**

- G. A. Jones and D. Singerman, Complex Functions: An Algebraic and Geometric Viewpoint, Cambridge University Press, 1987.

*An approachable and readable account of the geometric aspects of complex analysis.* - W. Schlag, A Course in Complex Analysis and Riemann Surfaces, AMS, 2014.

*A clear and useful recent text that does what the title says.* - R. Narasimhan and Y. Nievergelt, Complex Analysis in One Variable, 2nd Ed., Birkhauser, 2001.

*A concise, rigorous, and elegant presentation of the complex analysis needed for Riemann surfaces and several complex variables.* - G. Sansone and J. Gerretsen, Lectures on the Theory of Functions of a Complex Variable, Vol. II. Geometric Theory, Noordhoff, 1969.

*An old style, leisurely disussion of conformal mapping and Riemann surfaces with interesting examples and insights. (Vol. I. on basic complex analysis is good too.)*

- Terry Tao has notes on conformal mapping, and other aspects of complex analysis.

**Riemann surfaces**

*Excellent introduction (clear and short).*

*Another concise, elegant presentation.*

*Given the author, no further comment is needed.*

**Algebraic topology**

*A concrete introduction which includes a discussion of Riemann surfaces.*

*A standard, well-motivated introduction.*

**Several complex variables**

## Homework

**Set 1** (Fri, Apr 13)

Ch. 8, Exercises, p. 248: 2, 4, 5

Ch. 8, Problems, p. 254: 4

**Set 2** (Fri, Apr 20)

Ch. 8, Problems, p. 256: 3

Additional problems

Here is a visualization of the action of linear fractional transformations on the Riemann sphere.

**Set 3** (Fri, Apr 27)

Ch. 9, Exercises, p. 278: 4, 6, 7

Ch. 9, Problems, p. 281: 3

**Set 4** (Fri, May 11)

Here.

**Set 5** (Fri, May 18)

Here.