Math 205B, Spring 2018

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

A. J. Beardon, A primer on Riemann surfaces, Cambridge University Press, 1984.
Excellent introduction (clear and short).

O. Forster, Lectures on Riemann Surfaces, Graduate Texts in Mathematics 81, Springer 1981.
Another concise, elegant presentation.

S. Donaldson, Riemann Surfaces, Oxford University Press 2011.
Given the author, no further comment is needed.

Algebraic topology

W. Fulton, Algebraic Topology, Graduate Texts in Mathematics 153, Springer 1995.
A concrete introduction which includes a discussion of Riemann surfaces.

A. Hatcher, Algebraic Topology, Cambridge University Press, 2001.
A standard, well-motivated introduction.

Several complex variables

S. G. Krantz, Function Theory of Several Complex Variables, 2nd ed., AMS, 2001.

L. Hormander, An Introduction to Complex Analysis in Several Variables, Elsevier, 1973.

Despite its title, Narasimhan and Nievergelt, Complex Analysis in One Variable, contains an introductory chapter on 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.

Math 205B: Complex Analysis (Spring, 2018)