From 1998 to 2002, I was associated with the Summer Institute in Mathematics for Undergraduates (SIMU) at the University of Puerto Rico, Humacao in different capacities. In the summers of 1998, 1999, and 2001, I was a seminar leader and supervised undergraduate research projects. In the summers of 2000 and 2002, I spoke in the colloquium series.

I lead a Seminar in Coding Theory at SIMU 2001.

Draft materials:

I gave a talk on *Computational Algebra and Digital Filter Design*
in the Colloquium series at SIMU 2000. Here are the
slides for the talk. (The talk also contained
audio and Maple demos.)

Some materials I used in the SIMU 99 Gr"obner Bases seminar

- Week 1 discussions
- Week 2 discussions
- Week 3 discussions
- Week 1 lab
- Week 2 lab
- Week 3 lab
- Possible project topics
- One group of project topics this year includes study of linkages -- the motions of planar assemblies of rigid segments of fixed length joined by rotational joints. Another linkage, this one tracing out an ellipse.

One interesting application of computational algebra is finding the equations
of curves defined by various kinematic constructions. One example is
the *envelope of a parametrized family of curves* in the plane.
The envelope is a curve such that all the curves in the family are tangent
to the envelope at their points of intersection with the envelope. If the
curves in the family are circles, for instance, the envelope describes the
*boundary* of the region swept out by a circle moving along the path
described by the centers as the parameter varies.
Here is an interesting example of the envelope of a family of circles in
the plane we studied at SIMU last summer. Be sure to look at the end of
the following Maple worksheet!