MA 224: Complex Analysis, Jan 2024

Basic Information

Class: TuTh, 10:00-11:30AM, LH-4

Instructor: Ved Datar

Email: vv lastname at math.iisc.ac.in, no spaces

Office: X05

Office hours: Tu 11:00-12:00.

TA:

TA office hours:

Textbook: Complex Analysis Lecture Notes (incomplete draft version) This is an incomplete draft version of the lecture notes from when I taught this course at Berkeley in Fall 2016 and IISc in Spring 2020. Please let me know if you find any mistakes. The final chapters will be completed over the course of the next few months.

Other reference books:

Lars Ahlfors, Complex Analysis , McGraw-Hill, 1979.

Pre-requisites: MA 221 or permission from instructor (possible only in exceptional cases).

Topics to be covered: Complex numbers, holomorphic and analytic functions, Cauchy-Riemann equations, Cauchy’s integral formula, Liouville’s theorem and proof of fundamental theorem of algebra, the maximum-modulus principle. Isolated singularities, residue theorem, Argument Principle. Mobius transformations, conformal mappings, Schwarz lemma, automorphisms of the disc and complex plane. Normal families and Montel’s theorem. The Riemann mapping theorem. The Gamma and Zeta functions. If time permits - Zeta function and the primes and/or Picard’s theorem.

Grade Distribution

Assignment - 20%, Midterm - 30%, Final - 50%

Assignments: There will be an assignment due almost every week. We will probably have 11-12 assignments in total. There will be no late submission of the assignment permitted, unless there is a valid medical reason or some other emergency. If you miss a assignment, your score for that particular assignment will be zero. and I will consider your best 10 assignment scores towards the final grade. Though collaboration is allowed on assignments, you have to mention the students that you discussed with and the references used. Also, the final solutions must be written in your own words. If copying is detected on any assignment, you will receive zero points for that assignment Assignments will be posted on MS teams, and you can either hand in the hard copy in class on the due date, or upload a version on MS teams by the due date and time.

Exams: There will be one midterm of 60 points each and a final exam of 100 points. To pass the class, you have to take the final exam.

Tentative schedule, homeworks and lecture notes