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Wavelets and Applications


Wavelets and Applications: A Multi-Disciplinary Undergraduate Course with an Emphasis on Scientific Computing


Patrick Van Fleet
June 7-10, 2006
University of St. Thomas
St. Paul, MN

With support from NSF Grant DUE-0442684

Registration for this workshop is now closed

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.

In this workshop, we will discuss the basic topics covered in the course as well as ideas for presenting the material.We will begin with applications such as data compression, edge detection, and signal de-noising. Associated labs utilize a package (available in Mathematica or Matlab) of graphical and computational routines. Instructions are provided for developing the latter set of routines from scratch should the instructor so desire. The goal of the applications and software development is to show that the ad hoc construction can be improved using a general mathematical model. The remainder of the workshop is spent developing wavelets in this context.Workshop participants will receive software and lecture materials that can be used to offer the course at their home institution.

More information regarding the workshop can be found online at http://cam.mathlab.stthomas.edu/wavelets.

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