Holy Cross Mathematics and Computer Science

Summer Institute in Mathematics for Undergraduates

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.

SIMU 2002

I gave a talk on Counting Solutions of Systems of Polynomial Equations in several variables -- slides

SIMU 2001

I lead a Seminar in Coding Theory at SIMU 2001.

Draft materials:

SIMU 2000

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.)

SIMU 1999

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

SIMU 1998

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!