Math 621: Complex analysis
Spring 2018

Instructor: Paul Hacking, LGRT 1235H,


Classes: Mondays, Wednesdays, and Fridays, 9:05AM--9:55AM in LGRT 1322.

Office hours: Mondays 2:00PM--3:00PM and Tuesdays 2:00PM--3:00PM, in my office LGRT 1235H.

Course text: Complex analysis, by E. Stein and R. Shakarchi, Princeton 2003. googlebooks.

Other useful references: Complex analysis by L. Ahlfors. googlebooks.

Prerequisites: Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of Math 421 for example.


We will cover Chapters 1, 2, 3, and 8 of Stein and Shakarchi, and other topics TBD.

Class Log.


Homeworks will be due every 2 weeks at the beginning of Wednesday's class. (First homework due 2/7/18.)

Homework sets.


There will be one midterm exam and one final exam.

The Midterm will be Wednesday 3/7/18, 7:00PM--8:30PM, in LGRT 1322. The syllabus for the midterm is the following sections of Stein and Shakarchi: Chapter 1, Sections 1,2,3; Chapter 2, Sections 1,2,4; Chapter 3, Sections 1,2,3. Please try the review problems here. Solutions pdf.

The final exam will be Tuesday 5/8/18, 8:00AM--10:00AM, in LGRT 1322. The syllabus for the final is the material we've covered since the midterm: Chapter 3, Sections 4,5,6; Chapter 8, Sections 1,2,3; Chapter 9, Section 1; Winding numbers, General form of Cauchy's theorem and the Residue theorem, Harmonic functions (these topics are not covered in our text but a good reference is Lang, Complex Analysis, Chapters IV and VIII.) Please try the review problems here. Solutions pdf.

This course is also assessed via the complex analysis basic qualifying exam. General information. Syllabus.

Grading: Your course grade will be computed as follows: Homework 30%, Midterm 30%, Final 40%.

Overview of course

We will cover the basic theory of functions of one complex variable, at a pace that will allow for the inclusion of some non-elementary topics at the end. Basic Theory: Holomorphic functions, conformal mappings, Cauchy's Theorem and consequences, Taylor and Laurent series, singularities, residues, elliptic functions, other topics as time permits.

See also the syllabus for the complex analysis qualifying exam here.

This page is maintained by Paul Hacking