Math 60380

Spring 2010

Schedule
Webpage for 60370 (last semester)

Instructor: Jeffrey Diller (click for contact info, general policies, etc.)

Official Time and place: MWF 9:35-10:25 in Hayes-Healy 117 (Note change of room, effective Friday 1/15).

Textbook: I will be drawing from several different textbooks this semester including the one by Greene and Krantz that we used last term. On the schedule page, I'll post appropriate readings to go with my lectures. The other books that I currently plan to use are.

Complex Analysis by Theodore Gamelin.
Lectures on Riemann Surfaces by Otto Forster.
Complex Analysis in one variable by Raghavan Narasimhan.

All these books will be on reserve in the math library. Please be considerate of other students in the class by not taking the books out of the library. All three books are helpful, but if I could own only one of them, I would pick the book by Forster.

Thing's I'd like to cover in this course: more or less in order

Subharmonic functions and the Dirichlet problem
Monodromy, Elliptic modular functions, and the theorems of Picard and Montel
Applications to complex dynamics
Riemann surfaces--introduction and examples
The Uniformization Theorem and applications
Meromorphic functions on compact Riemann surfaces and embedding into projective space
Runge's Theorem, the inhomogeneous Cauchy-Riemann equations and applications
A brief introduction to several complex variables

Homework: There'll be somewhat less homework than in the first semester, with assignments every other week instead of every week. As in the first semester, I'll count homework as 50% of your grade.

Project: Instead of a midterm and final exam, I'll determine the remaining 50% of your grade by having you each do an individual course project. The topic is very flexible as long as it substantially involves complex analysis. I'll ask you to turn in a paper (on the order of ten pages) and give a lecture summarizing what you've learned. You should choose a topic before spring break, and we'll save the last n (=# of students) classes for presentations.