|
Instructor: Matt Kerr Office: Cupples I, Room 114 e-mail: matkerr [at] math.wustl.edu Office Hours: Mon/Wed 1-2 Course Outline:
The second semester course (Math 5122) will finish Ahlfors, covering (among other things) elliptic functions, the Riemann mapping theorem, the big Picard theorem, and the prime number theorem. Additional topics of study will include modular forms and several complex variables. Prerequisites (for undergraduates): Math 4111, 4171, and 4181, or permission of instructor. Class Schedule: Lectures are on Monday, Wednesday and Friday from 12PM--12:50PM in Cupples II Room L015. First class is Monday Aug. 24 and last class is Monday Dec. 7, with holidays on Monday Sep. 7, Monday Oct. 5, and Wed/Fri Nov. 25/27. Midterm Exam 1: Friday Oct. 16 (in class) Midterm Exam 2: Monday Nov. 16 (in class) Final Exam: Wednesday Dec. 16, 10:30AM--12:30PM, in the same classroom. Assignments: There will be a weekly homework due on Thursday by 11:59PM (starting the second week), to be turned in via Gradescope. I am available for help in office hours. (Regarding late homework, see the Grading Policy below.) The assignments will be distributed through Gradescope, and solutions posted on Canvas. Make sure you can do the problems I don't assign. HW 1: (I.A) #3, 4; (I.B) #1, 2, 5 Grader: Calvin Reedy, c.m.reedy [at] wustl.edu Lecture Notes: Will be posted here on the day of the lecture. The hope is that this makes taking notes optional. I. Holomorphic functions A. Complex numbers Books: Lars Ahlfors, Complex Analysis (3rd Ed.); McGraw-Hill is the recommended textbook, which means I will follow it at least half the time and some of the problems I assign will come from it. Buy, check out, or borrow a copy. If you would like to read more adventurously than Ahlfors and/or my lecture notes, here are some suggestions. First, there are many other excellent standard texts, including John B. Conway, Functions of One Complex Variable; Springer Robert Greene and Steven Krantz, Function Theory of One Complex Variable; AMS and the second half of Walter Rudin, Real and Complex Analysis (3rd Ed.); McGraw-Hill. For a point of view based in formal and convergent power series (convenient for locally computing composition inverses and solutions of differential equations) you can consult Henri Cartan, Elementary Theory of Analytic Functions of One and Several Complex Variables; Addison-Wesley Serge Lang, Complex Analysis (3rd Ed.); Springer. For a view toward several complex variables there is Raghavan Narasimhan and Yves Nievergelt, Complex Analysis in One Variable; Birkhauser ; and the beautiful expository monograph Steven Krantz, Complex Analysis: the Geometric Viewpoint; MAA treats theorems in complex analysis through the prism of differential geometry. Finally, Harvey Cohn, Conformal Mapping on Riemann Surfaces; Dover leads (with lots of beautiful pictures and physical intuition) into Riemann surfaces and complex algebraic geometry. A copy of each of these books has been placed on the reserve shelf behind the help/front desk of Olin Library. If you go to the front desk and ask for one of the books, you can check it out for use in the library for 3 hours. Grading Policy: Your final grade for the semester is determined as follows: HW 20%, Midterm 1 20%, Midterm 2 20%, final exam 40%. I will drop the lowest two grades you receive on homework. You may not use AI in any stage of preparation of your homework. On the other hand, I would encourage you to discuss problems with me and with other students. Homework and examination grades will be regularly updated on Canvas. Grades are typically curved in a course like this but will never be less than the following scale:
If you are a graduate student, a letter grade of B is required to pass; if you are an undergraduate taking this class Pass/Fail, you must earn a C- to pass. All work submitted under your name is expected to be your own; please make sure to document any ideas that come from another source. |