Math 472/572 - Fourier Analysis and Wavelets


Fall 2021

This class is cross-listed as:

Here is a quick link to the homework.

Here is a nice video about Fourier series recommended by my former PhD student David Weirich.

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 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 important 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. Matlab is now available for free for all UNM students. It is installed in all pod computers. You can download it onto your laptop or home computer. Follow the instructions on You are allowed to install it on two devices. Once installed on your computer, you run it by clicking on it (Mac,Windows) or typing matlab (Linux).

Textbook: We will use a book that I wrote with my colleague Lesley Ward from University of South Australia. The book is called Harmonic Analysis: From Fourier to Wavelets , Student Mathematical Library Series, Volume 63, American Mathematical Society 2012. I appreciate all the feedback I can get from you in terms of typos, erratas, and possible improvements for the second edition! Here is a list of errata so far compiled.

Recommended Texts: The literature for Fourier Analysis and Wavelets is large, here you will find a commented list of texts

Grades: Grades will be based on homework assignments and a final group project.

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

UNM Administrative Mandate on Required Vaccinations: All students, staff, and instructors are required by Administrative Mandate on Required Vaccinations to be fully vaccinated for COVID-19 as soon as possible, but no later than September 30, 2021, and must provide proof of vaccination or of a UNM validated limited exemption or exemption no later than September 30, 2021 to the UNM vaccination verification site. Students seeking medical exemption from the vaccination policy must submit a request to the UNM verification site for review by the UNM Accessibility Resource Center. Students seeking religious exemption from the vaccination policy must submit a request for reasonable accommodation to the UNM verification site for review by the Compliance, Ethics, and Equal Opportunity Office. For further information on the requirement and on limited exemptions and exemptions, see the UNM Administrative Mandate on Required Vaccinations.

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Accomodation Statement: In accordance with University Policy 2310 and the Americans with Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor's attention, as I am not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Resource Center at (505) 277-3506 or for additional information.
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Last updated: August 14, 2021