**Math 213a, Fall 2018ADVANCED COMPLEX ANALYSIS**

Office Hours: Tuesdays and Thursdays, 1:30 p.m. - 3 p.m.

Course Meets in Science Center 222

Tuesdays & Thursdays 3 p.m. - 4:15 p.m.

Course Assistant: Karl Winsor (kwinsor@math.harvard.edu)

Office Hours: Mondays, 6 p.m. - 7:15 p.m. in Science Center 109

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

Course Description: Fundamentals of complex analysis, and further topics

such as elliptic functions, canonical products, conformal mappings,

the
zeta function and prime number theorem, and Nevanlinna theory.

LECTURE NOTES: Elliptic Functions (Part 1)

HOMEWORK: Assigned September 6, 2018 due September 18, 2018

LECTURE NOTES: Elliptic Functions (Parts 1 and 2)

HOMEWORK: Assigned September 11, 2018 due September 18, 2018

LECTURE NOTES: Elliptic Functions (Parts 1 to 3)

HOMEWORK: Assigned September 13, 2018 due September 18, 2018

LECTURE NOTES: Elliptic Functions (Parts 1 to 4)

HOMEWORK: Assigned September 18, 2018 due September 25, 2018

LECTURE NOTES: Elliptic Functions (Complete)

LECTURE NOTES: Theta Functions of Jacobi (Part 1)

HOMEWORK: Assigned September 20, 2018 due September 25, 2018

HOMEWORK: Assigned September 25, 2018 due October 2, 2018

LECTURE NOTES: Theta Functions of Jacobi (Complete)

LECTURE NOTES: Uniformization Theorem (Part 1)

HOMEWORK: Assigned October 2, 2018 due October 9, 2018

LECTURE NOTES: Uniformization Theorem (Parts 1 and 2)

HOMEWORK: Assigned October 4, 2018 due October 9, 2018

LECTURE NOTES: Uniformization Theorem (Complete)

LECTURE NOTES: Schwarz-Christoffel Transformation

HOMEWORK: Assigned October 9, 2018 due October 16, 2018

HOMEWORK: Assigned October 11, 2018 due October 16, 2018

LECTURE NOTES: Poisson Kernel

HOMEWORK: Assigned October 16, 2018 due October 23, 2018

LECTURE NOTES: First Main Theorem of Nevanlinna

HOMEWORK: Assigned October 18, 2018 due October 23, 2018

LECTURE NOTES: Second Main Theorem of Nevanlinna (Part 1)

HOMEWORK: Assigned October 23, 2018 due October 30, 2018

LECTURE NOTES: Second Main Theorem of Nevanlinna (Parts 1 and 2)

HOMEWORK: Assigned October 25, 2018 due October 30, 2018

LECTURE NOTES: Second Main Theorem of Nevanlinna (Parts 1 to 3)

HOMEWORK: Assigned October 30, 2018 due November 6, 2018

LECTURE NOTES: Second Main Theorem of Nevanlinna (Complete)

HOMEWORK: Assigned November 1, 2018 due November 6, 2018

LECTURE NOTES: Application of Nevanlinna Theory to the Transcendence of Certain Numbers

HOMEWORK: Assigned November 6, 2018 due November 13, 2018

LECTURE NOTES: Prime-Counting Function and Zeros of Riemann Zeta Function (Part 1)

HOMEWORK: Assigned November 13, 2018 due November 20, 2018

LECTURE NOTES: Prime-Counting Function and Zeros of Riemann Zeta Function (Parts 1 and 2)

HOMEWORK: Assigned November 15, 2018 due November 20, 2018

LECTURE NOTES: Prime-Counting Function and Zeros of Riemann Zeta Function (Parts 1 to 3)

No Homework Assigned on November 20, 2018 due to Thanksgiving Recess

HOMEWORK: Assigned November 27, 2018 due December 4, 2018

LECTURE NOTES: Quadratic Reciprocity as Application of the Third Jacobian Theta Function

HOMEWORK: Assigned November 29, 2018 due December 4, 2018

LECTURE NOTES: Prime-Counting Function and Zeros of Riemann Zeta Function (Complete)

LECTURE NOTES: Infinite Product Expansions of Theta Functions of Jacobi

Take-Home Final Exam |