Math 472/572 - Fourier analysis and wavelets


Fall 2009

This class is cross-listed as:

Here are quick links to the homework, and to the textbook.

This course is an introduction to Fourier Analysis and Wavelets. It has been specifically designed for engineers, scientists, statisticians and mathematicians interested in the basic mathematical ideas underlying Fourier analysis, wavelets and their applications.
This course integrates the classical Fourier Theory with its latest offspring, the Theory of Wavelets. Wavelets and Fourier analysis are invaluable tools for researchers in many areas of mathematics and the applied sciences, to name a few: signal processing, statistics, physics, differential equations, numerical analysis, geophysics, medical imaging, fractals, harmonic analysis, etc. It is their multidisciplinary nature that makes these theories so appealing.

Topics will include:

Numerical experiments are necessary to fully understand the scope of the theory. We will let the students explore this realm according to their interests. The use of some Wavelet Toolbox will be encouraged. There exists a WAVELAB 850 package which is Matlab/Octave based software designed by a team at Stanford and available for free on the Internet. MATLAB 7.4.0 is available in the Mathematics and Statistics Department Computer Laboratory.

Grades: Grades will be based on homeworks, projects and/or take-home exams.

Prerequisites: Linear algebra and advanced calculus, or permission from the instructor.

Textbook: We will be using a preliminary version of a book that I am writing with my colleague Lesley Ward from University of South Australia. I will be posting chapters on the course webpage as the semester evolves. The book is called Harmonic Analysis: From Fourier to Haar. I appreciate all the feedback I can get from you, because now is our opportunity to make meaningful changes before the book goes into print.

Recommended Texts:

There are many excellent books devoted to the classical theory of Fourier analysis (starting with A. Zygmund's Trigonometric Series , and following with a long list).

In the last 15-20 years there have been published a number of books on wavelets, as well as countless articles. Here is a limited guide:

More Mathematical More applied/friendlier For a wider audience or emphasis on applications There is a wealth of information available at wavelet digest

Americans with Disabilities Act: Qualified students with disabilities needing appropriate academic adjustments should contact me as soon as possible to ensure your needs are met in a timely manner. Handouts are available in alternative accessible formats upon request.

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: August 24, 2009