MATH 522

**Meeting times (lectures)**: TTh 9:30
- 10:45 AM at **LeConte (LC)
303B**.

**Instructor**: Dr**. Peter
G. Binev**
http://www.math.sc.edu/~binev/

e-mail: binev@math.sc.edu)

phones: 576-6269 (at LC
425) *or* 576-6304 (at SUM
206H)

**Office hours**:
TTh 10:50 - 12:00 AM at LeConte
425/Sumwalt
206, or by appointment.

**Prerequisites**: The
students should be familiar with vector spaces and complex numbers and should have
experience with at least one upper level (500) mathematical course. Formally,
the prerequisites are MATH 544 or 526**. **The students who have none of
these courses should contact the instructor to seek consent.

**Learning Outcomes**: At
the end of this course students will master concepts of multiresolution
analysis, digital filters, and wavelets. They will be able to interpret the
outcomes of digital wavelet transform (DWT) and to design basic numerical
algorithms for DWT in Matlab.

**Cell Phones**: All cell phones ** must be turned off**
during the class.

**Homework**: A few homework problems will be assigned each class.
Be sure to do these problems before the next class. Some
solutions will be collected.

**Projects**:** **Every
student has to choose a project motivated by the computational or theoretical
problems discussed in the course. Several possible themes for the projects will
be suggested by the instructor in the length of the course. The last few weeks
of the class will be devoted to discussions of the projects and MATLAB
implementations of some of the numerical algorithms. The project in a form of a
poster or short paper should be submitted before **December 2, 2008**.

**Graduate Projects**:** **The graduate students attending the class
should work on larger projects which contain two parts, theoretical and
computational. They should also prepare a 15-minute oral presentation.

**Discussions**: The homework and the projects will be discussed in
class. The participation in the discussions is important part of the course.

**Midterm Exam**: There will be a midterm exam in a form of a test.
The tentative date of the exam is **September 18**, 2008. The problems on
the test will be similar to the ones from the homework and the discussions in
class. You can find a practice exam here.

**Final Exam**: The final exam in a form of a test will take place
on **Monday, December 8 at 2:00 PM**.

**Grading**: The final grade will be determined from the homework and the
participation in the discussions (25%), the midterm exam (20%), the project
(25%), and the final (30%).

**Academic Dishonesty**: Cheating and plagiarism
will not be allowed. The University of South Carolina has clearly articulated
its policy governing academic integrity and students are encouraged to
carefully review the policy on the Honor Code in the Carolina Community (see http://www.jour.sc.edu/pages/academicintegrity/policies.html).

**ADA**: If you have special needs as addressed by
the Americans with Disabilities Act and need any assistance, please notify the
instructor immediately.

**Web Materials**: There
is plenty of information about wavelets on the web. Here is a short list of
some (mostly undergraduate) courses on wavelets:

http://math.gmu.edu/~dwalnut/teach/Math672/672f03.html

http://www.cs.kuleuven.be/~ade/WWW/WAVE/

http://www.engmath.dal.ca/courses/engm6610/notes/notes.html

http://www.amara.com/current/wavebiblio.html

http://www.ifp.uiuc.edu/~minhdo/teaching/wavelets.html

http://faculty.gvsu.edu/aboufade/web/students.htm

http://www.waveletsandsubbandcoding.org/Repository/VetterliKovacevic95_Manuscript.pdf