MATH 8150: Complex Variables I, Spring 2008
Instructor: Dr. Shuzhou Wang
Class Time, Location: MWF 12:20-1:10, Boyd 326
Office Hours: MWF 1:30-2:30pm, Boyd
507, or by appointment.
Phone, E-mail: (706) 542-0884, szwang at math dot uga dot edu
Text: Complex Analysis, by Elias M. Stein and Rami Shakarchi, Princeton University Press, 2003
References:
1. L. V. Ahlfors: Complex Analysis, QA331 .A45
2. J. B. Conway: Functions of One Complex Variable, QA331 .C659
3. Einar Hille, Analytic Function Theory, QA331 .H54
4. W. Rudin: Real and Complex Analysis, QA300 .R82
Problem Books:
1. Ji-Xiu Chen et al, Problems and Solutions in Mathematics, QA43 .P754 (qualifying exam problems in several subjects)
2. G. Polya & G. Szego: Problems and Theorems in Analysis, QA301 .P64413
3. M. R. Spiegel: Complex Variables, QA331 .S6950 (easy)
Prerequisites: Limits, continuity, power series, uniform convergence notions and other theoretical aspects of calculus (math 4100/6100 or equivalent)
Objectives/Topics of the Course: This is a qualifying exam (formerly called prelim) course on the theory of functions of one complex variable. Topics (treated with more rigor than an undergraduate course) include: Cauchy-Riemann Equations, Cauchy's theorems and its consequences including: Morera's theorem, Taylor and Laurent expansions, maximum principle, residue theorem, argument principle, residue theorem, argument principle, Rouche's theorem and Liouville's theorem. Linear fractional transformations and elementary conformal mappings. Additional topics may be included.
Collaboration and Academic Honesty: You are encouraged to form study groups to discuss the material of the course. However, you must write up your own homework with your own understanding. Plagiarism, among other things, is prohibited. Above all, UGA Academic Honesty Policy applies: "All students are responsible for maintaining the highest standards of honesty and integrity in every phase of their academic careers. The penalties for academic dishonesty are severe and ignorance is not an acceptable defense."
Grading Policy: Course grade will be assigned approximately according to: Homework 40%; Midterm 20%; Final 40%. Exam problems will be comparable to complex analysis problems in the analysis written qualifying exam (formerly called the analysis prelim exam). You may find here the mid-term and final exam I gave for this course years ago.