Math 213a Fall 2024 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.
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
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)
Prerequisites:
Basic complex analysis, topology of covering spaces, differential forms.
due December 11, 2022
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