Spring 2013 MATH V3007 Complex Variables

Instructor: Name: Eric Urban (Professor)
Email: urban @ math.columbia.edu
Office: 608 Mathematics
Tel: (212) 854-6362
Fax: (212) 854-8962
Office hours: Tuesdays, 3:30 pm - 5:00 pm (room 608)
or by appointment.
Meeting time and location: Day/Time: Tuesdays and Thursdays, 11:40 am-12:55 pm.
Location: 520 Mathematics Building.
Prerequisites: Prerequisites: MATH V1202. Students should be comfortable with rigorous mathematical proofs and elementary topics such as real numbers, limits, series, continuous and differentiable functions, Riemann integration, change of variables.
Textbooks: Stein, Elias M.; Shakarchi, Rami: Complex analysis. Princeton Lectures in Analysis, II. Princeton University Press, Princeton, NJ, 2003. It is put on reserve in the Math. library and some chapters can be accessed here
About the course: This is a theoretical introduction to complex analysis exposing fundamental facts about analytic functions, Cauchy-Riemann equations, Cauchy's integral formula and conformal mappings. Topics covered include holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, meromorphic functions, Laurent series, residue theorem, entire functions, conformal mapping and if time permits the Zeta function and the prime number theorem and/or Elliptic functions.
Teaching Assistant: Karol Koziol karol@math.columbia.edu
Grading policy: Homework: 40%; Midterm: 20%; Final exam: 40 %
Homework: There will be weekly written homework assignments to be handed in. They can be found here along with the due date and time. There will be 11 assignments and your lowest homework grade will be dropped. Late homework will not be accepted. You are encouraged to discuss the homework with other fellow students. However, you must write up the final solutions by yourself. You might also use any resources you like to solve the problems. However, any resource you use other than Stein-Shakarchi's textbook must be cited in your homework.

To receive credit you must
1. Write you name clearly on the front.
2. Staple your work.
3. Justify your work (not just write the answer) and simplify your answers as far as possible.
4. Hand in your work in the designated mail box outside room 410 with my name on it on the 4th flour of the math department.

You can see your grades in the Courseworks Grade Book. Your graded homeworks will be returned in class one week later. Uncollected homework should be retrieved and left in front of 604/605 Math in the receptacle provided for a period of two weeks. It will be discarded after that period of time.; Midterm Exam; There will be one midterm exam during class, which is now scheduled on Tuesday February 26th, 2013. Here is a midterm review that will be corrected in class on Thursday February 21st.; Final exam
There will be a final exam given at the end of the term. All students must take the final exam at the time scheduled by the university, which is projected to be Thursday May 16th from 4: 10 pm to 7:00 pm.
Conflicts: If you have a conflict with any of the exams, please contact the instructor as soon as possible and at least one week before the exam. Make-up exams will not be given. Students can only be excused from the exams because of serious illness; you will need a note from your doctor or dean.
Help Room: 406 Mathematics Building, Columbia Help Room (on Columbia campus). There is more information here.
Academic honesty: Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Permitting someone else to copy your work is also considered cheating. Any cheating during midterms or finals will result in you failing the course and the matter being reported to your dean.