Math 246B    Fall 2005

Instructor: William Duke
Office: MS 6119
Office hours:  MW 3:15-4:15 and by appointment.

Lecture: MW 2-3:15, MS 6627

General Information

The prerequisite for this course is Math 246A or equivalent.   The textbook is Complex Analysis by Stein and Shakarchi.    Math 246A last term (Spring 2005) covered chapters 1, 2 (except section 5.5), 3 and 8 of the text.  This term will cover most of the rest of the book.

Grades will be based on exercises (most from the text) to be assigned as we go and posted on this web site.  You will be responsible for handing in the solutions of at least 30 of them (your choice) at the end of the term (Friday, December 16).

Syllabus

1. Entire Functions (Chapter 5)
2. Poisson Summation (Chapter 4, Sections 1 and 2)
3. The Gamma and Zeta Functions (Chapter 6)
4. The Prime Number Theorem (Chapter 7)
5. Elliptic Functions (Chapter 9)
6. Applications of the Theta Function (Chapter 10)

Homework Problems

Chapter 4, Page 127
Exercises: 2, 3, 7.

Chapter 5, Page 153
Exercises: 1, 3, 4, 8, 9, 11, 13, 14, 15, 16.
Problems: 1, 3.

Chapter 6, Page 174
Exercises: 1, 3, 5, 7, 9, 10, 13, 14, 15, 16.
Problems: 1, 2, 4.

Chapter 7, Page 199
Exercises: 1, 2, 3, 4, 5, 6, 7, 8, 10.
Problems: 1, 2.

Chapter 9, Page 278
Exercises: 1, 2, 3, 4, 5, 6, 7, 8.
Problems: 1, 2, 3.

Chapter 10, Page 309
Exercises: 1, 4, 5, 6, 7, 9, 10, 11, 12.
Problems: 1, 2, 3, 5, 6.