Course Title:	Complex Analysis
Unique Number:	M381D (54010)
Lectures:	PMA 12.166, Mon Wed Fri 10-11 am
Instructor:	Prof. Hans Koch

Brief description: We plan to cover much of Chapters 2-4 in Ahlfors' book, part of Chapters 5 and 6, and some more on elliptic functions (Chapter 7). This includes the topics listed for the Complex part of the Analysis Course Syllabus.

Textbook:   L.V. Ahlfors, Complex Analysis, 3rd Edition, McGraw-Hill, 1979.

Prerequisites: Familiarity with the subject matter of the undergraduate analysis course M365C, a syllabus of which can be found on this page

Consent of Instructor   not required for graduate students

First Day Handout:   Here

Exams:    old:  1, 2, 3    new:  1, 2

Homework:   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Comments by the grader

Disabilities

Some References:
L.V. Ahlfors, Complex Analysis, 3rd Edition, McGraw-Hill, 1979.
S. Lang, Complex Analysis, Graduate Texts in Mathematics 103, Springer, 1999.
E.M. Stein, R. Shakarchi, Complex Analysis, Princeton University Press, 2003.
J.B. Conway, Functions of One Complex Variable, Springer, 1978.
R.E. Greene, S.G. Krantz, Function Theory of One Complex Variable, AMS, 2001.
R. Narasimhan, Y. Nievergelt, Complex analysis in one variable, Birkhäuser 2001.
T.W. Gamelin, Complex Analysis, Springer, 2001.
S.G. Krantz, Complex Analysis: The Geometric Viewpoint, MAA, 1990.
W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987.
O. Forster, Lectures on Riemann Surfaces, Springer, 1981.
A.F. Beardon, A Primer on Riemann Surfaces, Cambridge University Press, 1984.
Z. Nehari, Conformal Mappings Dover, 1990.
R. Remmert, Classical Topics in Complex Function Theory, Springer, 1998.

Some online:
J. Erickson, Complex Analysis.
C. Bennewitz, Complex Analysis Course Notes, Lund (2006).
A. Rainer, Advanced Complex Analysis, Course Notes, Vienna (2017).
D. Romik, Complex Analysis Lecture Notes, 2021.
B. Simon, Advanced Complex Analysis, A Comprehensive Course in Analysis, Part 2B, AMS (2015).
C. McMullen, Advanced Complex Analysis, Course Notes, Harvard University, Math 213a (2017).
A. Thorup, Notes on Automorphic Functions, 1995.
C. Teleman, Riemann Surfaces, course notes 2003.
B. Salvatore, Modular Forms, Eisenstein Series, and a short introduction to elliptic functions, 2006.
H. K, Notes on metric spaces.