the Geometry Center also has a successful summer program for talented undergraduates. The program matches undergraduates with ongoing projects at the Center. Most projects involve aspects of mathematical research, education and curriculum development, communication of mathematics, and the construction of mathematical software.
During the summer of 1995, the Center sponsored 20 undergraduate students who contributed to about a dozen different projects. One team of students is working with inservice high school teachers to create supplementary K-12 curriculum materials which enhance a Center-developed video on shape of surfaces and three-dimensional manifolds. Another team is working on the Center's newest mathematical software: a package designed to compute the solution manifolds of underdetermined systems of nonlinear equations. Another student is creating a graphical database of common geometric objects and using the World Wide Web to disseminate this database. Anyone accessing the database (which we call it the "topological zoo") will have access to both static and interactive pictures of the objects, mathematical facts about the objects, and links to related definitions and ideas that arise in multivariable calculus and differential topology.
One team of two students is engaged in a project that is particularly relevant to engineering education. They are creating a module for the undergraduate engineering calculus that deals with the static and dynamic deformation of beams. The summer students are creating lab exercises on centroids, moments of inertia, and boundary conditions that describe cantilevered, simply supported, and doubly clamped beams.
The summer students are also conducting experiments to investigate the static deformation and dynamic oscillation of beams. They used a video camera to record the oscillations of meter sticks clamped or supported in a variety of configurations, and analyzed each frame of the video in order to tabulate the position of the beam as a function of time. They then solved the fourth-order partial differential equation governing the beams' motion and compared the experimental data with the prediction of the PDE. Along the way they learned how to decompose a function into fundamental modes of oscillation, how boundary conditions delimit families of solutions, and how different materials and cross-sections of beams lead to different dynamics.
In addition to the obvious educational benefit to the team of summer students, this project has an additional benefit that is much larger in scope. We intend to take some of the material that the students produced and incorporate it into a newly developed science and engineering calculus curriculum at the University. We are particularly excited about exposing future engineers to experimental data and asking them to compare the results from a mathematical model to real data. We are equally excited by the opportunity to use engineering problems to motivate the learning of advanced mathematical ideas. We believe that this will not only increase the students' ability to learn and retain the mathematics, but will also increase their willingness to accept that these and many other mathematical ideas are actually useful in engineering.
Author: Frederick J. Wicklin <email@example.com>
Comments to: firstname.lastname@example.org
Created: Fri Aug 18 1995 --- Last modified: Jul 21 1996
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