MATH 325

COMPLEX ANALYSIS

FALL 1999

 

INSTRUCTOR : CHRIS GOLÉ

OFFICE : BURTON 316

TELEPHONE: (585) 3875

EMAIL & WWW : cgole@math.smith.edu & www.math.smith.edu/~cgole

OFFICE HOURS : Mondays and Wednesdays 2-4

CLASS MEETING : T-TH 10:20-11:50

TEXT: Visual Complex Analysis , by T. Needham, Oxford (available at Grécourt bookshop)

ABOUT THE CLASS: Complex Analysis is a beautifully rich theory (click here for a very short introduction). We will approach the subject in a geometrical way, going through the topics of complex numbers, their algebra and geometry, analytic functions and their conformality, Moebius transformations, Rouché's theorem and the classical theory of complex integration (Cauchy's formula and theorem, Calculus of residue). If time allows, we may touch on Riemann surfaces and complex dynamical systems. We will make occasional use of the program F(z), available on some machines in Burton 301.

PREREQUISITE: MTH 225 or 243 or permission of the instructor

HOMEWORK: It will be due on Thursdays. You will be asked to bring preliminary drafts on Tuesdays that we will discuss in the class. The homework problems from this book are quite challenging, but very exciting. You are strongly encouraged to form groups and submit group homework, at the condition that you make clear arrangements so that each member contributes to each assignment.

CHATROOM: Eric Brewer and Julie Thompson are installing a chatroom for the class. Eventually I will post the homework on it, which will also email it to you automatically. But the main function of the chatroom is to foster your commmunication about mathematical matters with your group, with me and with the rest of the class. We will also have a department wide chat room, called Virtual Math Forum.

EXAMS: There will be one midterm and one final exam, both take-home. The midterm will consist of two stages: the first stage showing your personal work, the second, an improved version with your group. The grade for the midterm will be an average of both versions. The final will be an individual take home.

GRADING:

WHAT

WHEN

%

Homework

Weekly

35

Midterm

Due Thursday November 4

35

Final

Due Tuesday December 21

30

 

ATTENDANCE: Attendance to all the classes is very important. I would appreciate your writing me an email message or calling me if you cannot make it to a class.