University of Massachusets, Amherst
Math 621
Complex Analysis
Spring Semester 2011


Instructor: Dr. Farshid Hajir.    Office: Lederle Graduate Research Tower 1118.    Phone: 545-6015. e-mail:
I encourage you to use the email address above to send me questions about the homework or to set up an appointment.

Homepage URL:
You can find a link to this course information sheet from my homepage.

Description: This course 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 and harmonic functions; conformal mappings; Cauchy's Theorem and consequences; Taylor and Laurent series; singularities; residues; Dirichlet Series such as the Riemann Zeta Function and/or other topics as time permits. There will be regular problem assignments, a midterm exam, and a final exam.

Text: E. Stein, and R. Shakarchi, Complex Analysis, Princeton 2003.

Prerequisites: Advanced Calculus. Students are expected to have a working knowledge of complex numbers and functions at the level of M421, for example.

Meeting Time and Place: Tues Thurs 9:30-10:45 am, LGRT 1322.

Office Hours: Tentatively Tue 2-3, Wed 2-3. During the first two weeks, my office hours will be posted on my office door. After the first two weeks, my permanent office hours will be announced in class and posted on my website. You are always welcome to set up an appointment to see me by e-mail or phone.

Homework Problems: They'll be listed separately at The Homework Page.

Exams: There will be a midterm exam, and a comprehensive final, to be scheduled.

Grading: Homework and class participation (30%), Midterm (30%), Final (40%).

Grading Scales


>= 90%


>= 86% and < 90%


>= 82% and < 86%


>= 78% and < 82%


>=74% and < 78%


>= 70% and < 74%


>=65% and <70%


>=60% and < 65%


>=55% and < 60%


below 60%

Homework, Attendance, and Collaboration: Attendance and class participation are important, as are the homework assignments. You may occasionally be asked to present a homework problem on the board. I recommend that you WORK WITH YOUR FELLOW STUDENTS IN GROUPS!! If you are stuck on a problem and seek help from an instructor or a fellow student, you owe it to yourself to aim for an understanding of the concepts and ideas that come up in the discussion (do not just memorize the series of steps leading to the solution). Then, go home and reconstruct the argument for yourself in the privacy of your own brain, to make sure you are not merely reproducing mindlessly something you have not thought through. It is of paramount importance that you do the write-up completely independently. Failure to do so will be cause for disciplinary action.

Course Outline

We will cover the material basically in the same order as in Stein and Shakarchi. This tentative outline assumes that we will be able to cover the basic material at a pace that will allow quite a bit of time for further topics; it will be modified as necessary as the course progresses.
  • Week 1: 1.1, 1.2
  • Week 2: 1.3, 2.1, 2.2
  • Week 3: 2.3, 2.4, 2.5
  • Week 4: 2.5, 3.1
  • Week 5: 3.2, 3.3, 3.4
  • Week 6: 3.5, 3.6, 3.7
  • Week 7: 5.1, 5.2, 5.3
  • Spring Break
  • Week 8: 5.4, 5.5
  • Week 9: 8.1, 8.2
  • Week 10: 8.2, 8.3
  • Week 11: 7.1
  • Week 12: 7.2
  • Week 13: 9.1
  • Week 14: 9.2
  • Week 15: Review