MAT 542: Complex Analysis I

Spring 2003

SUNY at Stony Brook
Department of Mathematics
SUNY at Stony Brook

Textbook: Comlex Analysis, 3rd edition, by Lars V. Ahlfors, McGraw-Hill Inc., 1979.

You can also consult many other good textbooks such as Function of One Complex  Variable, 2nd edition, by J.B. Conway, as well as classical texts Theory of Functions, by C. Carathéodori, Analytic Function Theory by E. Hille, The Theory of Functions by E.C. Titchmarsh and Theory of Functions of a Complex Variable by A.K. Markushevich.

Schedule: MWF 9:25  - 11:20 am, PHYSICS P123

Instructor: Leon  Takhtajan, Math Tower 5-111, Phone: 632-8287,
email:, office hours: Monday 2:00 - 3:00 pm, Tuesday 4:00 - 5:00 pm, and by appointment.

Assistant/Grader: Jihyeon (Jessie) Yang,  Math Tower 2-112, email:

Topics covered: The course will cover, in a relatively self-contained manner, the basic syllabus. In addition, we will discuss the theory of elliptic functions.

Prerequisites: The foundations from algebra, real analysis and topology (as in Chapter 3.1 in Ahlfors' book).

Howework: Homework will be assigned, collected and graded. Their will be total of ten assignments with problems varying from routine to the very challenging.

HW1 ps /pdf (due January 29, 2003).

HW2 ps /pdf (due February 5, 2003).

HW3 ps /pdf (due February 24, 2003).

HW4  Problems 1-8 on p. 108 and 1-3 on p. 120 in Ahlfors' book (due Monday, March 3, 2003).

HW5 ps /pdf (due March 24, 2003).

HW6 ps /pdf (due April 7, 2003).

HW7 ps /pdf (due April 21, 2003).

HW8 Problems 2, 4 on p. 190; 2,5 on p. 193; 1 on p. 197; 3 on p. 198; 1-3 on p. 227 in Ahlfors' book (due Friday, May 2, 2003).

HW9 Problems 4-6 on p. 171; 1,3 on p. 175 in Ahlfors' book (due Friday, May 9, 2003).

Exams:  Their will be one midterm exam and a final exam on
Thursday, May 15, 5:00 - 7:30 pm, in PHYSICS P-116

Grading: Grades will be assigned on the following basis: Homework 25%, Midterm Exam 25%, Final Exam 50%.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information and documentation of disability is confidential.