Math 213a    Fall 2024
ADVANCED COMPLEX ANALYSIS


Meeting Time: Tuesdays and Thursdays 12:00 noon - 01:15 p.m.

Location: Room 412 of the Science Center

Exam Group: FAS10_D

Instructor: Professor Yum-Tong Siu (email: siu@math.harvard.edu)

Office Hours: Tuesdays and Thursdays 10:30 a.m. to 12 noon (SC 511)

Course Assistant: Jit Wu Yap (email: jyap@math.harvard.edu)
Office Hours: Fridays 2 p.m. to 3 p.m. (SC428g)

Textbooks: "Complex Analysis" by Elias M. Stein & Rami Shakarchi, Princeton University Press 2003                                 

Course Description: Fundamentals of complex analysis, and further topics such as conformal mapping, hyperbolic geometry, canonical products, elliptic functions and modular forms.

Prerequisites: Basic complex analysis, topology of covering spaces, differential forms.

 

LECTURE NOTES: Overview of Math 213a

LECTURE NOTES: Review of Basic Complex Analysis (Part I through Part IV)

HOMEWORK #1: Assigned September 10, 2024 due September 17, 2024

LECTURE NOTES: Review of Basic Complex Analysis (Part V through Part VIII)

HOMEWORK #2: Assigned September 17, 2024 due September 24, 2024

LECTURE NOTES: Elliptic Functions (Approach of Jacobi) Part I

HOMEWORK #3: Assigned September 24, 2024 due October 1, 2024

LECTURE NOTES: Elliptic Functions (Approach of Jacobi) Complete

HOMEWORK #4: Assigned October 1, 2024 due October 8, 2024

LECTURE NOTES: Elliptic Functions (Approach of Weierstrass) Part I

LECTURE NOTES: Elliptic Functions (Approach of Weierstrass) Parts I and II

HOMEWORK #5: Assigned October 8, 2024 due October 15, 2024

LECTURE NOTES: Elliptic Functions (Approach of Weierstrass) Complete

HOMEWORK #6: Assigned October 15, 2024 due October 22, 2024

LECTURE NOTES: Theta Functions of Jacobi (Part I)

LECTURE NOTES: Theta Functions of Jacobi (Complete, appended with a list of theta function identities)

HOMEWORK #7: Assigned October 22, 2024 due October 29, 2024

LECTURE NOTES: Schwarz-Christoffel Transformations

LECTURE NOTES: Gamma Function

LECTURE NOTES: Dirichlet Series

HOMEWORK #8: Assigned October 29, 2024 due November 5, 2024

HOMEWORK #9: Assigned November 5, 2024 due November 12, 2024

LECTURE NOTES: Prime Number Theorem (Part I)

HOMEWORK #10: Assigned November 12, 2024 due November 19, 2024

LECTURE NOTES: Prime Number Theorem (Complete)

LECTURE NOTES: Weierstrass and Hadamard Factorization of Entire Functions

HOMEWORK #11: Assigned November 19, 2024 due November 26, 2024

LECTURE NOTES: Logarithmic Derivative Lemma

LECTURE NOTES: Second Main Theorem of Nevanlinna

LECTURE NOTES: Quadratic Reciprocity

Take-Home Open-Book Final Examination
due December 11, 2022
(Click to Download)