Instructor: Anar Akhmedov
Lectures: MWF 2.30 - 3.20pm in Vincent Hall 209.
E-mail: akhmedov@math.umn.edu
Office Hours: Monday 11.00 - 11.50am and Friday 3.30 - 5.10pm. My office is in room 355 of the Vincent Hall.
Prerequisites: Math 8701 or Instructors permission.
Course Syllabus: Click here to download course syllabus in PDF format.
Textbooks:
Complex Analysis (3rd. Ed., McGraw-Hill), by Lars Ahlfors.
| Title | Author(s), Publ. info | Location |
|---|---|---|
| Complex Analysis | Elias M. Stein and Rami Shakarchi | On reserve in math library |
| Functions of One Complex Variable I (2nd Ed., Springer GTM) | John B. Conway | On reserve in math library |
| Riemann Surfaces | Simon Donaldson | On reserve in math library |
| Algebraic Curves and Riemann Surfaces | Rick Miranda | On reserve in math library |
Notes on Riemann Surfaces, Modular Functions and Modular Forms:
Simon Donaldson, "Riemann Surfaces"
James Milne, "Modular Functions and Modular Forms" .
Course Outline: This is a second course in complex analysis. The spring semester we plan to cover conformal mappings, harmonic functions, Dirichlet problem, the Riemann Mapping Theorem, complex analysis on tori (elliptic functions, modular functions), analytic continuation, Picard's Theorem, and some additional topics if time permits.
Web page: http://www.math.umn.edu/~akhmedov/M8702.html.
Grading: The course grade will be based on homework assignments, in-class midterm and a comprehensive take-home final, with the following weights:
Exams: There will be an in-class midterm on Wednesday, March 13th and a comprehensive
take-home final examinations. The exams worth 30% + 35% = 65% of the final course grade.
Homework: There will be 7 biweekly homework assignments, each worth 50 points, consisting of problems from the textbook and some additional problems. Homework will be a fundamental part of this course, and will be worth 350 points (35% of the course grade). The first homework assignment will be due on February 1. NO LATE HOMEWORK WILL BE ACCEPTED. You may work together on homework problems, but everyone must turn in their own written solutions. Please staple your homework before handing it in.
TAKE HOME FINAL
DUE: by 2.30pm Friday, May 17
Codes
MIDTERM
FINAL
43
58
18
60
26
35
16
47
60
49
72
50
Assignment Problems Homework 1
due 02/01
Homework 1
Homework 2
due 02/15
Ahlfors, Chapter 6, Exercises 6.1.1, 6.1.2 (page 232)
Homework 2 additional problems
Homework 3
due 03/01
Ahlfors, Chapter 6, 6.2.3, 6.2.5, 6.2.6 (page 238)
Homework 3 additional problems
Homework 4
due 03/15
Ahlfors, Chapter 6, Exercises 6.4.1, 6.4.2, 6.4.3, 6.4.5 (pages 247-248)
Homework 5
due date extended to 04/03
Ahlfors, Chapter 7, Exercises 7.3.1, 7.3.2(pages 274-275) and Exercises* 7.3.3 1-6 (pages 276-277)
Homework 5 additional problems
Homework 6
due 04/ 22
R. Miranda, Chapter I, Exercises I.1.G, I.2.C, I.2.J, I.3.A, I.3.C, I.3.E
Homework 7
due 05/03
R. Miranda, Chapter II, Exercises II.1.C, II.3.I, II.3.J, II.4.D, II.4.G, II.4.K
Homework 8
will not be collected
R. Miranda, Chapter III, Exercises III.3.A, III.3.E, III.3.G, III.3.H, III.3.I, III.4.F, III.4.G, III.4.H