Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: W 1-3pm
MLC hours: F 2:30-3:30pm
After Spring Break: I am available by e-mail anytime

Grader: Zhuang Tao, e-mail: zhuang.tao@stonybrook.edu
Grader's office: Math Tower 2-114
Grader's office hours: F 9-10am
Grader's MLC hours: Tue 5-7pm

The Instructor may be reached by e-mail at kamenova@math.stonybrook.edu.

Description: Elementary functions, holomorphic functions. Cauchy theory, power series, classification of isolated singularities, calculus of residues, open mapping theorem, Riemann mapping theorem.

After the Spring Break: every week I am going to send an announcement which sections of [Ahlfors] you are going to read. During our scheduled class time, we are going to have a discussion session via Zoom (in Blackboard) on these sections of the book.

Syllabus:

1. The field of complex numbers, geometric representation of complex numbers.

2. Analytic functions.

3. Analytic functions as mappings.

4. Complex integration.

5. Local properties of analytic functions.

6. The calculus of residues.

7. Power series.

8. The Riemann mapping theorem.

9. Harmonic functions.

• HW 1 (due on February 4)
  

• HW 2 (due on February 11)
  

• HW 3 (due on February 18)
  

• HW 4 (due on February 25): Problems 1, 2, 3, 4 and 7 on page 108 from [Ahlfors]
  

• HW 5 (due on March 3): Problems 1, 2, 3 on page 120, Problems 1, 5 on page 123 from [Ahlfors]
  

• HW 6 (due on March 10): Problems 2, 3, 4 on page 130, Problem 1 on page 133, Problem 1(in addition, prove that equality implies that f(z) is a linear transformation) on page 136 from [Ahlfors]
  

• HW 7 (due on April 7): Problems 1, 4, 5 on page 148, Problems 1, 2 on page 154 from [Ahlfors]
  

• HW 8 (due on April 21): Problems 3(e), 4 on page 161, Problem 1 on page 166, Problems 1, 6 on page 171 from [Ahlfors]
  

• HW 9 (due on May 5): Problem 2 on page 178, Problems 1, 5 on page 184, Problem 2 on page 190, Problem 5 on page 198 from [Ahlfors]
  

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