Advanced Complex Analysis
Math 213a / Tu Th 10-11:30 / Science Center 216
Harvard University - Fall 2017
Curtis T McMullen
McGraw-Hill, 3rd Edition.
Intended for graduate students.
Prerequesites include differential forms,
topology of covering spaces and a first course in complex analysis.
Undergraduates require Math 113 and 131, or permission of the instructor.
Classical Topics in Complex Function Theory.
- Stein and Shakarchi,
Princeton University Press, 2003.
Visual Complex Analysis.
Oxford University Press, 1997.
- Sansone and Gerretsen,
Lectures on the Theory of Functions of a Complex Variable.
(2 volumes.) P. Noordhoff, Ltd., 1960.
A Course in Arithmetic.
Theory of Functions.
A second course on complex analysis on the plane, sphere and complex tori.
Possible topics include:
Reading and Lectures.
Students are responsible for all topics covered in
the readings and lectures. Lectures may go beyond the
reading, and not every topic in the reading will be
covered in class.
All enrolled students are expected to attend lectures regularly.
Basic complex analysis
Holomorphic functions and forms; Cauchy's formulas
Distributions, the d-bar equation
Hyperbolic, Euclidean and spherical geometry via Lie groups
Schwarz lemma and the Poincare' metric
Entire and meromorphic functions
The Gamma function
Riemann mapping theorem
Local connectivity and boundary values
The area theorem; compactness
Universal cover of plane regions
Graduate students who have passed their
quals are excused from a grade for this course.
Grades for other students will be based on the homework,
which includes a `midterm and final' (see below).
Homework will be assigned every week.
Late homework will not be accepted.
Collaboration between students is encouraged, but you
must write your own solutions, understand them and
give credit to your collaborators.
Midterm and Final.
Two homeworks will be designated the `midterm' and `final'
assignments. These are to be done without collaboration.
Course home page: