General Information

Instructor: Andreas Seeger

Classes: MWF, 2:25-3:15 p.m., Van Vleck B 115.
This is a introductory course in complex analysis.
It is targeted at advanced undergraduate and beginning graduate students.

Textbook:
Complex Analysis.
By Elias M. Stein and Rami Shakarchi.
Princeton University Press.
ISBN 0-691-11385-8
Errata, released by Princeton University Press.
Comments on the text.

Office hours: MW 3:15-4:15, and by appointment.

Assignments will be sent by email and posted on this page.
There will be 2 Midterm exams in class, dates TBA.
Final exam: Wednesday, December 19, 10:05-12:05.

The main topic in Math 623 is the basic theory of functions of one complex variable:

I. Holomorphic functions and power series, Cauchy's theorem and Cauchy's integral formulas, maximum principle, sequences of holomorphic functions and normal families, Schwarz reflection principle, Runge's approximation theorem, meromorphic functions, argument principle and applications, homotopies and simply connected domains, the logarithm, Fourier series and harmonic functions, elementary theory of conformal mappings, Schwarz lemma, Riemann mapping theorem, series and products (Mittag-Leffler theorem, Weierstrass products), ... .

II. We will have to choose among several possible additional topics:

such as (i) The Laplace and Fourier transforms
(ii) The Gamma and Zeta functions and the prime number theorem.

Additional References:

Classical topics in complex function theory, by Reinhold Remmert.
Translated from the German by Leslie Kay. Graduate Texts in Mathematics, 172.
Springer-Verlag, New York, 1998. ISBN 0-387-98221-3

Complex analysis, by Theodore W. Gamelin
Undergraduate Texts in Mathematics.
Springer-Verlag, New York, 2001. ISBN 0-387-95093-1; 0-387-95069-9