San Jos´ e State University Department of Mathematics Fall 2013 Math 238: Advanced Complex Variables Instructor: Slobodan Simi´ c, [email protected] 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 is both intrinsically beautiful and useful not only in mathematics but also in electrical engineering, physics and elsewhere. Unlike in real analysis, in complex analysis one gets many things for “free”: for instance, if a complex function is differentiable once, it is differentiable infinitely many times (it is, in fact, analytic!). After reviewing the basics, in Math 238 we will focus on some beautiful advanced results and concepts such as the Riemann Mapping Theorem, analytic continuation, Riemann surfaces (depicted above), the Picard theorems, and so on. The text I chose is full of careful explanations of why the theorems work the way they do. It is aimed directly at students and assumes minimal prerequisites. Web page: Go to http://www.math.sjsu.edu/˜ simic/ and click on Math 238.