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MAT 542: Complex Analysis I

Spring 2003

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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: *leontak@math.sunysb.edu,
*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: *jessie@math.sunysb.edu*

**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.