**Instructor:** Rowan Killip, 6935 Math Sciences Building.

**Office Hours:** Killip: MW 11--12 + by appointment, in 6935 Math Sciences Building.

**Exams:**Three-hour final: Tuesday, March 17, 3pm--6pm.

**Homework:** There will be periodic homework. It is due *in class*.

You are welcome (indeed encouraged) to discuss the problems amongst yourselves and to use whatever human, online, or printed sources you wish. However, you must write up your solutions in your own words; the loaning or copying of solutions is strictly forbidden.

**Grading:** Homework 50%; Final 50%.

**Syllabus:** This course covers the main topics in classical Complex Analysis at the graduate level and provides preparation for the complex analysis part of the Analysis Qualifying Exam. Computational familiarity with the subject, such as is typically covered in undergraduate courses, will be assumed (though can reasonably be gained in parallel with a little extra effort).

There is no formal textbook. Probably the best match for the syllabus is

*Complex Analysis* by Elias M. Stein and Rami Shakarchi.

Other popular volumes on the subject are

*Complex Analysis* by Lars Ahlfors.

*Complex Analysis* by Ted Gamelin.

*Analytic Functions* by Stanislaw Saks and Antoni Zygmund, which is available online.

Our discussion of harmonic functions is strongly influenced by Chapter 2 of

*Elliptic Partial Differential Equations of Second Order* by David Gilbarg and Neil Trudinger.

Notes for last two lectures about the prime number theorem.

**Homework Problems:**

Homework 1. Due Friday, Jan 31.

Homework 2. Due Friday, Feb 21.

Homework 3. Due Friday, Mar 13.