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, 2015
Lectures: MWF 2:10–3:00 p.m., Physics 130
CRN: 39589
Office hours: TBA W 12:30–1:30 p.m., Th 1:10–2:15 p.m. -->
Text: Complex Analysis, E. M. Stein and R. Shakarchi
MAT 205A: A link to the course website for MAT 205A, taught by Prof. Craig Tracy, is here.
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.)Riemann surfaces
- A. J. Beardon, A primer on Riemann surfaces, Cambridge University Press, 1984.
Excellent introduction (clear and short). A new edition is due out 2016. - 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
A concrete introduction which includes a discussion of Riemann surfaces.
A standard, well-motivated introduction.
Homework
Set 1 (Fri, Apr 10)
Ch. 8, Exercises, p. 248: 1, 4, 5
Ch. 8, Problems, p. 254: 4
Set 2 (Fri, May 1)
Ch. 2, Exercises, p. 64: 11, 12
Ch. 8, Exercises, p. 248: 7, 8
Set 3 (Fri, Jun 5)
here