Spring 2010 Math W 4032 Fourier Analysis
- Instructor
- Name: Nam Q. Le (Ritt Assistant Professor)
Email: namle @ math.columbia.edu
Office: 423 Mathematics
Tel: (212) 854-4306
Fax: (212) 854-8962
- Office hours
- Mondays and Wednesdays, 11: 00 am -noon (room 423)
or by appointment.
- Meeting time and location
- Day/Time: Mondays and Wednesdays, 9:10 am-10:25 am.
Location: 417 Mathematics Building.
Attending the lectures is strongly encouraged.
First lecture: January 20, 2010.
- Prerequisites
- three terms of calculus and linear algebra or four terms of calculus. Students should be comfortable with elementary topics
such as limits, series, differentiable functions, Riemann integration and some linear algebra.
- Textbook
- Stein, Elias M.; Shakarchi, Rami: Fourier analysis. An introduction. Princeton Lectures in Analysis, 1.
Princeton University Press, Princeton, NJ, 2003. The book should be available at the
Columbia bookstore.
- About the course
- This is an elementary introduction to Fourier analysis exposing basic facts about Fourier series,
Fourier transforms and finite Fourier analysis and their applications to a wide range of disciplines such as partial differential
equations and number theory.
Topics covered include Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution, Heisenberg
uncertainty principle. Other selected
topics will be also introduced. The aim, essentially, is to cover Chapters 2-7 of Stein-Shakarchi with a few selected topics of my own choosing.
- Schedule of lectures
- A tentative schedule of lectures can be found here.
- Teaching Assistant
Yifeng Liu
Yifeng has scheduled to work in the Help
room (406 Math Building ): Thursdays 2-4 pm
Also, Yifeng holds a Problem session in Room 405 Math Building, Thursdays 1-2 pm.
- 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
in the schedule of lectures along with the due date and time. There will be 12 assignments and your
lowest two homework grades will be dropped. The homework will mostly be exercises
from Stein-Shakarchi, though a few of them may be my own questions. 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 resourses you like to solve the problems. However, any resourse 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. Write out your work (not just the answer) and simplify your
answers as far as possible.
4. Hand in your work in the designated mail box with my name on it ( The Drop Box ) on the 4th flour
of the math department across from office 410.
You can see your grades in the Courseworks Grade Book. Your graded homeworks will
be returned in class on Mondays. Uncollected homework
should be retrieved and left in 406 Math in the receptacle provided for a
period of two weeks. It will be discarded after that period of time.
Exams
Midterm Exam
There will be one midterm exam during
class, which is tentatively
scheduled as follows
- Midterm: Wednesday February 17th, 2010
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.
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
Wednesday May 12, 2010 from 9: 00 am - noon .
- 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.
- Help Room
-
406 Mathematics Building, Columbia Help Room (on Columbia
campus). There is more information here.
If you would like help with the material, in addition to the
office hours you can take advantage of the
Columbia
Help Room which is designated for students who need help with
their upper-level mathematics courses. No appointment is necessary.
- 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.
- Special dates
- January 29: End of Change of Program Period; Last Day to Add a Class;
Last Day to Receive Tuition Refund for Class Dropped
Feb 23: Last Day to Drop a Class for Barnard, Columbia College,
General Studies, SIPA, GSAS, and Continuing Education
Mar 15- Mar 19: Spring recess
Mar 25: Last Day to Drop a Class for Schools not noted
above. Last day for pass/fail option.