Mathematics 503 -- Introduction to Complex Analysis -- Fall 2017

The study of differentiable functions of one complex variable has applications and extensions to many other areas of mathematics, so that it is a basic tool in diverse situations. Topics to be covered include: differentiability of complex functions, complex integration and Cauchy's theorem, series expansions, calculus of residues, maximal principle, conformal mapping, analytic continuation and time permitting, the Prime Number Theorem. Note: A Problem Session for 503 will be held on Wednesdays, 10:00am-11:40am in room 425 for the Fall semester. There is no need to register for the Problem Sessions.

Prerequisites: Acquaintance with analytic arguments at the level of Rudin's Principles of Mathematical Analysis is necessary. Some knowledge of algebra and point-set topology is useful.

Text: Complex Analysis, Elias M. Stein and Rami Shakarchi, Princeton Lectures in Analysis II, Princeton University Press (April 7, 2003). ISBN-10: 0691113858

Course Format: There will be weekly homework assignments which will be graded.

Homework Assignments and Grading Policy: The grade for the course will be based on graded homework problems, a midterm, and a final exam as follows:

Written homework solutions should be legibly written, with sufficient justification and mathematical details, and are due by the announced deadline, unless with advanced approval. A joint problem session for this course and 501, scheduled for W 10:00 -- 11:40AM, in Hill 425. The session will be led by graduate student Matthew Welch. He will lead discussions on various problems which will be provided in advance of the session for students to work on.

More Information: Contact J. Tunnell in Hill 546, email to tunnell@math