Fall 2023 MATH W4065 Honors 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
- Mondays, 10:00 am - 12:00 pm (room 608)
or by appointment.
- Meeting time and location
- Day/Time: Tuesdays and Thursdays, 11:40 pm- 12:55 pm.
Location: Math 407
- 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.
- 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
- Roy Magen
- Office hours: TBA
- Homework
- There will be weekly written homework assignments to be handed in.
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 and the homework assignment 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.
Exams
- Midterm Exams
- There will be two midterm exams during
class, which are
scheduled on :
- Midterm 1: Oct 5th
- Midterm 2: Nov 12th
- Final exam
The final exam is projected to be on Dec 21st from 4:10pm to 7pm. All students
must take the final exam at the time scheduled by the university. If you have a conflict with the final exam, please contact
me as soon as possible.
-
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 and your dean.
- Grading policy
- Homework: 30%
- Midterms: 20% each
- Final exam: 30 %
- 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
in homeworks, midterms or finals will result in you failing the course and the
matter being reported to your dean.