ACS-Mellon Technology Fellows Program Application  

The Singular Value Decomposition (SVD) is a topic rarely discussed in undergraduate linear algebra courses and, in fact, surprisingly few faculty members are familiar with the decomposition that Gilbert Strang calls "absolutely a high point of linear algebra." Nowadays, computer algebra systems can painlessly provide the decomposition and as an added benefit display the vivid graphics associated with SVD.  Once understood, SVD can bring to introductory linear algebra exciting applications and a greater understanding of standard results.

In the fall of 1998 I will be teaching introductory linear algebra using the text Matrices, Geometry & Mathematica by Jerry Uhl.  This text uses SVD as a springboard for nearly every elementary topic in matrix theory.  I used a preliminary version of this text the previous time I taught the course and was so enthusiastic about the material that I have since become a contributing author.  Despite my enthusiasm for the material, I doubt this particular text will gain widespread exposure at ACS institutions due to its unrelenting emphasis on SVD and its dependence on Mathematica.  This is a pity as other linear algebra texts, including the more recent reform texts, make little or no mention of SVD.

Instructors of linear algebra here at Davidson have asked me to prepare SVD modules for inclusion in a more traditional course.  I have made only ad hoc responses with an amalgam of lecture notes and unpolished Mathematica notebooks.  I would like to produce a web based introduction to SVD suitable for inclusion in any standard introductory linear algebra course.  I envision the introduction as three lessons on the following topics followed by one or more of several exciting applications.

The lessons would contain relevant exercises and be designed for students to read and complete on their own over a week's time.  Ideally, then, the introduction to SVD will cost the standard course only one day of class which could be used to review concepts from the three lessons and discuss the application.  I feel confident that my colleagues here at Davidson would make use of the materials and I hope that other ACS institutions might use the materials as well.

Technical requirements: Nearly all of the material will be initially written in Mathematica 3.0 notebooks.  These source notebooks will be available for downloading and those with Mathematica 3.0 will be able to edit and experiment with the notebooks.  The goal, however, is to make the introduction available to anyone with a web browser.

The web pages will include mathematical symbols and animations.  Although there are numerous viewers and plug-ins to deal with mathematical symbols, currently it seems most convenient to use embedded gifs.  Fortunately Mathematica 3.0 notebooks can be saved in html format with all of the mathematical symbols automatically converted to gifs.  Currently I plan to store animations as animated gif files.  The file sizes may dictate an alternative method, but I am reluctant to use any format that would require a plug-in.  I would welcome advice from other ACS faculty on this point.

I believe that the Davidson College web server could easily handle the material, but if this becomes unwieldy, as a Math Archives moderator, I could post the materials at UTK.

Dissemination and evaluation: As a member of PKAL, Project NExT, and Project NExT-SE, I plan to initially use the listservers of these organizations to shamelessly self promote the materials.  In addition I plan to advertise the materials during SVD related talks like the one I recently gave on biomedical imaging during the Real Life Applications Special Session at the MAA meeting in Charleston.

The success of this project will be reflected by the use of the materials by individuals, and more importantly, instructors.  The web pages will include a survey intended to monitor this use.  Although individuals perusing the pages may not take the time to complete a survey, I expect that any instructor using the materials for a course would take the time to give some feedback.

Institutional support: I think it is unrealistic to expect a $2500 stipend to cover a course reduction for the fall semester.   But in any case, I would prefer to work on this project while teaching the material.  I expect to discuss what should go into the pages with my students.  I believe this will benefit my students and improve the clarity of the final project.