Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 205B: Complex Analysis

Approved: 2021-11-02, Hunter/Romik
4 units
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Complex Analysis, by E. M. Stein and R. Shakarchi (Princeton University Press, 2003)
MAT 205A
Course Description:
A second graduate course in complex analysis covering some of the more advanced topics in the theory. Specific topics will vary depending on the instructor’s preference.
Suggested Schedule:

Any combination of the following topics is suitable to cover; suggested references appear in parentheses:

  • Conformal maps and the Riemann mapping theorem (Chapter 8 in [5])
  • Elliptic functions (Chapter 9 in [5])
  • Modular forms and theta functions; applications to number theory (Chapter 10 in [5])
  • The Fourier transform in complex analysis (Chapter 4 in [5])
  • Entire functions and the Weierstrass-Hadamard theory of infinite products (Chapter 5 in [5])
  • Introduction to Riemann surfaces ([2], [3])
  • Other topics at the instructor’s discretion

The advanced topics covered in MAT205A and MAT205B do not need to be learned in a specific order. In a given year, the instructors teaching those classes may decide to cover some of the advanced topics suggested for MAT205B in MAT205A, and vice versa.


  1. M. J. Ablowitz, A. S. Fokas. Complex Variables: Introduction and Applications, 2nd Ed. Cambridge University Press, 2003.
  2. R. Narasimhan, Y. Nievergelt. Complex Analysis in One Variable, 2nd Ed. Birkhauser, 2001.
  3. O. Forster. Lectures on Riemann Surfaces. Springer, 1981.
  4. D. Romik. Complex Analysis Lecture Notes (version of June 15, 2021). Free online resource.
  5. E. M. Stein, R. Shakarchi. Complex Analysis (Princeton University Press, 2003).