Preface
Technical Reports
This page contains the
technical reports written by the students who participated in the 2002
Summer Institute in Mathematics for Undergraduates
(SIMU) at the University
of Puerto Rico – Humacao. SIMU,
the largest National Science Foundation (NSF) Research Experience for
Undergraduate (REU) in mathematics, is a six-week research program
currently in its fifth year.
The
twenty-four students who participated in SIMU 2002 came from universities
in Arkansas, California, Illinois, Louisiana, Massachusetts, Nebraska, New
York, Oregon, Pennsylvania, Puerto Rico, Texas,
Utah, and Washington. They
worked in groups of three on undergraduate research projects in two
exciting areas in the mathematical sciences.
The projects in the area of Computational Mathematics Applied to
Fluid Motion were directed by Professor Ricardo Cortez from Tulane University.
Professor Cortez was assisted by Angela Gallegos and Alexander
Villacorta, graduate students at the University of California, Davis and
the University of California, Santa Barbara respectively.
The projects in the area of Integrals: An Introduction to
Research in Mathematics were directed by Professor Víctor H. Moll
from Tulane University.
Professor Moll was assisted by Christopher Duncan and Dante V.
Manna, graduate students at Tulane University.
The reports contained herein are the culmination of hundreds of
hours of work by the SIMU 2002 students and staff during the six weeks of
the program. Because the
quantity of work produced by these students during the program is so great
and because of other time constraints, these technical reports perhaps
best can be classified as “not-fully edited”.
SIMU’s
primary target population is Latino and Native American students from the
United States and Puerto Rico. The
goal of SIMU is simple: to increase the number of Chicanos/Latinos
and Native American earning Master’s, Ph.D’s, and pursuing research
careers in the mathematical sciences.
We believe that one way to try to achieve this goal is by
bringing together a group of talented students and challenging them to
engage in quality mathematical research in an intense, supportive and
collaborative environment.
The
2002 SIMU was funded by grants from the National Security Agency (NSA
Grant MDA904-02-1-0006) and the National Science Foundation (NSF Grant
DMS-9987901). Other support
was provided by (of course) the University of Puerto Rico – Humacao and
the National Aeronautics and Space Administration (NASA).
A program like SIMU could not take place without the generous
support of many individuals. We
take this opportunity to thank Barbara Deuink, National Security Agency;
Lloyd Douglas, National Science Foundation; Manuel Gómez, Vice President
for Research and Academic Affairs, University of Puerto Rico; Pablo V.
Negrón, Professor and Chair of Mathematics (and SIMU Co-Founder),
University of Puerto Rico – Humacao; and James Schatz, Chief of
Mathematics Research, National Security Agency.
Herbert
A. Medina and Ivelisse Rubio
2002 SIMU Co-Directors
Humacao, PR, August 2002
Note
on Format: All the reports can be downloaded in
Adobe Portable Document Format (PDF) format.* Each report contains an abstract. Two
of the reports contain bitmap (BMP) graphics that did not convert to
PDF; the graphics also can be downloaded below.
If you would like a paper copy of any of the
reports,
please send your request to simu@cuhwww.upr.clu.edu.
* Adobe Acrobat Reader
is freeware that allows you to view and print PDF files; it can be
downloaded from the Adobe website www.adobe.com. |
High-Order
Blobs and Particle Methods for Dispersive Partial Differential Equations
Jamie
A. Burke, University of California, Los Angeles
Christopher
N. Gallo, University of Chicago
Alejandro
Pérez, University of
California, Santa Barbara
Comparison
of Numerical Methods for Solving the Convection-Diffusion Equation in 2D
Edgar
Lobaton, Seattle University
Ubaldo Rodríguez Bernier,
University of Puerto Rico - Cayey
Leah Shilling, Slippery Rock
University
A
Computational Model of Caudal Fin Undulations Using Impulse Methods
Jamie
N. Bailey, Westminster College, Salt Lake City
Apolinar Gallardo, Los Angeles Valley
College
Tiffany Psemeneki, Boston University
A
Computational Model of the Flagella
Oscar
Del Valle, Cosumnes River College
Heather Flores, University of
Nebraska - Lincoln
Stefan Mendez-Diez,
University of Chicago
A
Symbolic Evaluation of Integrals of Rational Functions
Danielle
Brooker, Keuka College
Aaron
Cardona, Ouchita Baptist University
José
G. Miranda, University of
Puerto Rico - Cayey
Asymptotics
of a Transformation on the Space of Rational Functions
M.
Sage Briscoe, Tulane University
Laura Jiménez, California
State University, Fullerton
Luis A. Medina Rivera,
University of Puerto Rico - Humacao
Coefficients
and Roots of a Family of Polynomials: Divisibility and Asymptotics
Danielle
Heckman,
Keuka College
María Osorio, Mount Holyoke College
Juan Carlos Trujillo, Cosumnes
River College
Dynamic
Properties of a Rational Landen Transformation
Benjamín
Alemán, University of Oregon
Angela Gallegos, University of
California, Irvine
Sandra Moncada, Texas
A&M International University
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