## Wavelets and Applications, MATH 5750 (6880), Section 2, Spring 2009, 9:10-10:30, JWB 333

• Course Syllabus
• Office Hours: Tuesday and Thursday following class (10:30-11:30) and by appointment.

### Project

The course project is due by 5pm on April 30, 2009. The project proposal is due by 5pm on February 27, 2009. Details for the project proposal can be found here.

Homework: There are three types of problems. If there is just a number, for example 2.1, this corresponds to the associated exercise in the Exercise section of the chapter. If the number is preceded by an E, for example E2.1, this is exercise 2.1 given in class. If the number is preceded by a G, for example G2.1, this question must be answered by students registered for MATH 6880. Students registered for Math 5750 are welcome to answer the G exercises, but they will not affect your homework score. The homework assigned is considered open (i.e. more problems may be added) until "END" is the last bullet and a due date is posted.

• Homework 1 DUE: Tuesday, Feb. 10
• Chapter 2: 2.1, E2.2, E2.3, 2.4, G2.5, G2.6
• Chapter 3: 3.1 Note: I removed G3.17
• The linked pdf has the entire assignment, including exercises from class.
• END
• Homework 2 DUE: Thursday, Mar. 5
• Chapter 3: 3.8, 3.12 E3.1, E3.4, G3.14
• Chapter 4: E4.2
• Chapter 6: 6.4(a), G6.2
• The linked pdf has the entire assignment, including exercises from class.
• END
• Homework 3 Due Thursday, Apr. 16
• END
• Homework 4 Due Thursday, Apr. 30

The goal for the course is to be about 60-70% wavelet theory (i.e. math) and 30-40% wavelet applications, mostly from signal processing (data compression, denoising, sparse representations, etc.). If the class is small enough, it is my intention to tailor the course to the interests of the students.

Textbook: A Wavelet Tour of Signal Processing, 3rd Edition by Stephane Mallat. This is a new edition an will not be available until mid December. The publisher has assured us that the book will be delivered in plenty of time. The new edition incorporates the considerable advances of the past decade and is subtitled The Sparse Way. This edition includes advances such as directional systems (curvelets) and an introduction to compressed sensing. If you have to buy a wavelet book, this one is a standard reference and will be up to date. The book is too robust to cover in its entirety, so there will be plenty for you to learn when the course is finished. A good book to have on your shelf for both a mathematician and one interested primarily in the application of wavelets.

Prerequisites: The main prerequisites are motivation, some mathematical sophistication, MATH 2210 (multivariate calculus), and MATH 2250 or 2270 (linear algebra). You should have taken a proof based course in the past such as 3210-3220 Foundations of Analysis I and II. If you have taken 5210 and/or 5610 that will be very helpful, but I will cover background material that is missing from the audience background. It will also be very helpful if you are familiar with MATLAB, although you can learn Matlab quickly during the course.

Structure: There will be regular homework (probably 5 assignments over the semester). Students will be asked to complete a project in line with their interests. This project could be an implementation of wavelets (or a wavelet like system) or a presentation of some aspect of wavelet theory.

Students with Disabilities
Students needing special accomodations should make reasonable prior coordination with the Center for Disability Services, 162 Olpin Union building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accomodations.