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IMA Special Workshop
Wavelets and Applications: A Multi-Disciplinary Undergraduate Course with an Emphasis on Scientific Computing
July 13-16, 2011

 Program Application    Live Streaming    Abstracts and Talk Materials 
  Organizers
Catherine Beneteau Department of Mathematics, University of South Florida
Caroline Haddad Department of Mathematics, State University of New York at Geneseo
David Ruch Department of Mathematical and Computer Sciences, Metropolitan State College of Denver
Patrick J. Van Fleet (Chair) Center for Applied Mathematics, University of St. Thomas
  Description

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 next part of the workshop is spent developing wavelets in this context. During the final day of the workshop, participants from the concurrent Project Building workshop will make presentations that illustrate applications of wavelets and how they might be integrated in not only a wavelets course, but in other courses, or as a standalone research project. Workshop participants will receive software and lecture materials that can be used to offer the course at their home institution.

Past Workshops:

Detailed information for past workshops is available at

http://www.stthomas.edu/wavelets.

Click for example on Tampa, 2009 under the WORKSHOPS link at the upper left of the site.July 13-16, 2011

Participants:

There is a maximum of 15 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.

  Schedule
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