RESEARCH EXPERIENCES FOR UNDERGRADUATES (REU)
In summer 2000 the School of Mathematics offered for the first time
a Research Experiences for
Undergraduates (REU) program. Seven faculty volunteered to mentor
16 undergraduate students from all around the U.S. The program was promoted
nationally, in print, on our web pages, and by word of mouth. From the
many applicants the participating faculty jointly chose the most promising
applicants whose interests best meshed with our strengths. The students
were in residence here for about 8 weeks. The summer 2000 program was
the first year of our ongoing REU program intended to introduce undergraduates
to genuine research environments and to put them in close contact with
research mathematicians. Working in teams or individually, students carried
out their own projects and wrote reports on their findings. We do hope
to continue this program with NSF support. Details on how to apply for
being accepted to the program for the Summer 2001 can be found on the
department website.
Below are the project titles, the mentors and the student participants
on each project:
*The Use of Symmetries in Euclidean and Non-Euclidean Mechanics.
Mentor: Professor Scot Adams. Students: Pritam Dalal, UC Berkeley, and
Shawn Hermans, St. John's University.
*A Design for Magnetic Heads. Mentor: Professor Avner Friedman.
Student: Phil Mendelsohn, University of Minnesota, Twin Cities.
*Traffic Simulation. Mentor: Professor Lawrence Gray. Students:
Steve Formaneck, University of Minnesota, Morris and Joel Rice, Colorado
College.
*Stochastic Simulation of Exotic Options. Mentor: Professor Rachel
Kuske. Student: Nick Stadtmiller, Northwestern.
*Randomness in Physics and Chemistry. Mentor: Profes sor Rachel
Kuske. Student:Laura Chasman, California Institute of Technology.
*Tree groups of shifted graphs. Mentor: Professor Victor Reiner.
Students:Paul Bendich, Grinnell College and Tristram Bogart, Oberlin College.
*One-parameter families of algebraic curves. Mentors: Professors
Victor Reiner and Joel Roberts. Student: Rory Mulvaney, University of
Minnesota, Twin Cities.
*Cryptology, Coding, and Number Theory. Mentor: Professor Paul
Garrett, Students: Geoff Anderson, Harvard, Dan Biebighauser, Concordia
College, Erin Casey, St. Benedict, Andrew Crabbe, Trinity University,
Chris Davis, Stanford University, and Kaisa Taipale, California Institute
of Technology.
Professor Victor Reiner wrote as follows about the two projects he mentored:
"This past summer I mentored two projects, one jointly with Joel
Roberts, titled 'One-parameter families of algebraic curves' involving
a single U of M undergrad named Rory Mulvaney. Rory's goal was to assimilate
some basic material from elementary algebraic geometry, and then create
some graphics macros usable in MATLAB that do such things as plot implicitly
defined curves in the real plane, compute multiple tangent lines to an
algebraic curve at its singular points, and superimpose these on a plot
of the curve, compute the equation for the envelope of a 1-parameter family
of algebraic curves, and superimpose a plot of the envelope on the plot
of the family."
"Rory did a wonderful job, and his software is being used in the
labs associated with MATH 5385 Introduction to computaalgebraic geometry,
which was taught by Joel Roberts this Fall."
"Another project, titled 'Tree groups of shifted graphs', involved
two undergraduates: Paul Bendich from Grinnell College and Tristram Bogart
from Oberlin College. Paul and Tristram read up on the background for
what I was calling the "tree group" of a graph (network): a
subtle and fairly mysterious isomorphism invariant of a graph, which is
a finitely generated abelian group of order equal to the number of spanning
trees in the graph. For a particularly nice class of graphs (threshold
graphs), where we know a simple product formula for the number of trees,
I had them perform experiments in Maple computing the structure of this
tree group via a Smith normal form computation on the Laplacian matrix
of the graph. They then formulated a conjecture as to what the structure
for general shifted graphs should be, and proved some special cases. I'm
hoping that some future REU students will resolve this conjecture!"
For more information on both of these projects, see the students' reports
at the math REU web page: www.math.umn.edu/arb/reu/.
www@math.umn.edu
URL http://www.math.umn.edu/index.shtml
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