San Jose State University Department of Mathematics

Fall 2013

Math 238: Advanced Complex Variables

Instructor: Slobodan Simic, simic@math.sjsu.edu

Time and place: MW 12:00-1:15 in MH 234

Prerequisite: Math 138 or instructor consent

Textbook: David C. Ullrich, Complex Made Simple, American Math. Society,Graduate Studies in Mathematics, vol. 97, 2008

What this course is about: Complex analysis is a classical branch of math-ematics which studies complex functions of a complex variable. It isboth intrinsically beautiful and useful not only in mathematics but alsoin electrical engineering, physics and elsewhere. Unlike in real analysis,in complex analysis one gets many things for “free”: for instance, if acomplex function is differentiable once, it is differentiable infinitely manytimes (it is, in fact, analytic!). After reviewing the basics, in Math 238we will focus on some beautiful advanced results and concepts such asthe Riemann Mapping Theorem, analytic continuation, Riemann surfaces(depicted above), the Picard theorems, and so on. The text I chose is fullof careful explanations of why the theorems work the way they do. It isaimed directly at students and assumes minimal prerequisites.

Web page: Go to http://www.math.sjsu.edu/ simic/ and click on Math 238.