Wavelet theory evolved as mathematicians from areas such as harmonic analysis, functional analysis, and approximation theory brought their specialties together to develop the foundational results and construct algorithms for use in applications. Through development of an undergraduate course on wavelets, the organizer came to realize that the very manner in which wavelet theory came into being is an effective way to present the material to undergraduates. Constructing discrete wavelet transforms in an ad hoc manner (1) shows students that real-world problems are typically solved by using different areas of mathematics, (2) solidifies ideas from sophomore calculus and linear algebra, (3) establishes the computer as an effective learning tool, (4) provides strong motivation for taking upper level classes such as real analysis, (5) allows students to learn about a current topic and its uses in real-world applications.
One of the best ways to develop an understanding of how wavelets are utilized in applications is through the use of projects. In this workshop, participants will be given a list of candidate topics and then form into groups of size 2-3 to develop a project about the topic. The project length is large in scope: they can serve as a final project in a wavelets course, a supplemental project for a linear algebra course, or even a standalone research project for summer work. Faculty groups are expected to create the project and then provide resources for students/faculty who might wish to use them. These resources might include a description of goals/outcomes, the project duration, necessary software, and even an "answer key" for the supervising faculty member. Group members are encouraged to post their projects on the University of St. Thomas wavelets web site: http://cam.mathlab.stthomas.edu/wavelets/finalprojects/
On the last day of the workshop, faculty groups will present their developed project (or status thereof) to not only the other participants but also to the participants of the Introduction to Wavelets workshop held concurrently.
It is expected that all participants in this workshop already have a working knowledge of wavelets such as previously attending an introductory wavelet workshop.
Detailed information for past workshops is available at http://cam.mathlab.stthomas.edu/wavelets/pdffiles/MathFest09.pdf. This pdf file gives several topics from which participants can choose for their projects.
There is a maximum of 12 participants. While all university faculty interested in teaching an introductory course on wavelets at their home institutions are encouraged to enroll, we especially encourage new faculty and faculty members from underrepresented groups.