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