Spring Semester - 2018

Graduate Course Description

Course Title: Complex Analysis
Unique Number: M381D (54275)
Time/Location of Lecture: MWF 10-11 am, RLM 12.166
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 on the Preliminary Exam Syllabus in Complex Analysis.

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

Some Other References:
A.F. Beardon, A Primer on Riemann Surfaces, Cambridge University Press, 1984.
J.B. Conway, Functions of One Complex Variable, Springer, 1978.
T.W. Gamelin, Complex Analysis, Springer, 2001.
R.E. Greene, S.G. Krantz, Function Theory of One Complex Variable, AMS, 2001.
S.G. Krantz, Complex Analysis: The Geometric Viewpoint, MAA, 1990.
B.P. Palka, An Introduction to Complex Function Theory, Springer, 1991.
W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987.

Some online:
H. K, Notes on metric spaces.
A. Thorup, Notes on Automorphic Functions, 1995.
B. Salvatore, Modular Forms, Eisenstein Series, and a short introduction to elliptic functions, 2006.

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

Consent of Instructor   not required

First Day Handout:   Here

Exams:    old:  1, 2, 3    new:  1, 2, 3

Homework:   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

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