Park City Mathematics Institute Research Project Abstract

Wavelets are Fun!

Authors: Brian Hopkins, Robert Greenblatt, Shira Helft, Leslie Hicks, Manish Parmar, TJ Peacher, Rebecca Poore, Renee Trochet

 

This teacher group participated in the Undergraduate Summer School course on wavelets led by Ed Aboufadel of Grand Valley State University. The group attended the 1pm lecture and then spent an hour debriefing, working on problem sets, discussing supplementary articles supplied by the instructor, etc. Mathematica (available for free to PCMI participants) was the primary tool. Initial classes established the theoretical foundation of wavelets, focusing on the work of Alfréd Haar in the early 20th century and major extensions by Ingrid Daubechies in the 1980s. Applications then became the focus, such as hiding information via steganography, defeating online security CAPTCHAs, simulating the artistic style of Chuck Close, detecting potholes from sensors on cars, analyzing handwriting, and authenticating artwork.

 

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.