Preface
This page contains the technical reports written by the
students who participated in the 1999 Summer Institute in Mathematics for
Undergraduates (SIMU) at the University of Puerto Rico – Humacao.
SIMU is a six-week summer undergraduate research program whose 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
Americans earning Masters, 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 reports contained herein are the culmination of hundreds of hours
of work by the 1999 SIMU students during the six weeks of the program.
The
twenty-four students who participated in the 1999 SIMU worked in groups of
three on undergraduate research projects in two active and exciting areas in
the mathematical sciences. The
projects in the area of Gröbner basis were directed by Professor John
B. Little from College of the Holy Cross; and those in the area of probability
and statistics were directed by Professor Rudy Guerra from Southern
Methodist University. Because the
quantity of work produced by these students during the six weeks of the
program is so great and because of other time constraints, these technical
reports are for the most part unedited.
The
1999 SIMU was funded by grants from the National Security Agency (NSA Grant #
MDA904-99-1-0041), the National Science Foundation (NSF Grant # DMS-9907887),
the University of Puerto Rico, the National Aeronautics and Space
Administration (NASA), the Alliance for Minority Participation (AMP), and the
Society for Advancement of Chicanos and Native Americans in Science (SACNAS).
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Acknowledgements
Individuals who have
given indispensable assistance in the funding and creation of SIMU include:
Barbara Deuink, National Security Agency; Dennis Fernández, Director, Puerto
Rico Alliance for Minority Participation; Manuel Gómez, Vice-President for
Research and Academic Affairs, University of Puerto Rico; Joe Jenkins, National
Science Foundation; Ivis Aponte, Director, Puerto Rico National Aeronautics and
Space Administration Space Grant Consortium; Roberto Marrero-Corletto,
Chancellor, University of Puerto Rico – Humacao; Wilson Ruiz, Chairman,
Department of Mathematics, University of Puerto Rico – Humacao; James Schatz,
Chief Mathematical Research Division, National Security Agency, and Jimmy
Torres, Dean for Academic Affairs, University of Puerto Rico – Humacao.
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1999 SIMU
Technical Reports
| Note
on Format: All the abstracts and papers can be downloaded in
either PDF or DVI format. The abstracts should download without
any complications. There are some drawbacks to each format for the
papers that contain graphics. Our DVI --> PDF converter, chooses to ignore EPS image
files, so the PDF versions may be missing some graphics. In order
for the DVI file to print correctly, it requires any image files
associated with it to be copied to the same directory on your hard drive
as the DVI file. So if you choose to download the DVI file, make
sure and download any image files associated with the paper to the same
folder/directory on your hard drive.
If you would like a hard copy of any of the papers,
please send your request to simu@cuhwww.upr.clu.edu.
|
The
Maximal Workspace of a Planar Robot: A Gröbner Basis Approach
Jamie
Arellano, Chapman University
Diana
Gómez, University of California, Santa Cruz
Ruby
Vigil, Santa Clara University
| Abstract: |
PDF
File. DVI File. |
| Paper: |
PDF
File. DVI File.
Graphics files needed for DVI version: 1,
2, 3,
4, 5,
6, 7,
8, 9,
10, 11. |
Bi-Symmetric
Invariants
Thomas
José Castillo, Harvard University
Mónica
Castro-Simmons, University of Puerto Rico – Humacao
Emily
R. Puente, Wellesley College
Conformations
of Cyclic Molecules: A Gröbner Basis Approach
Carlos
E. Guillén-Diaz, University of California, Riverside
Everilis
Santana-Vega, University of Puerto Rico – Humacao
Omar E. Zúñiga-Bonilla,
University of California, Riverside
Padé
Approximation in Two-Variables Using Gröbner Basis Techniques
(A
revised version of this paper has been submitted to the Journal of Symbolic
Computation.)
David
J. Ortiz, University of Texas, Austin
Ricardo
Ortiz-Rosado, University of Puerto Rico – Cayey
Karen
R. Ríos-Soto, University of Puerto Rico – Mayagüez
First-Order
Auto-Regressive Time Series Models and the Bootstrap
Esmeralda Cárdenas, Texas A&M International University
Karen
Garrett de Luna, University of Washington, Seattle
Alexander
Villacorta, University of Michigan, Ann Arbor
Bootstrapping
Methods for Estimating Standard Errors for Residual Variance in the One-Way
Fixed Effects Model
Mayteé
Cruz-Aponte, University of Puerto Rico – Humacao
Anthony
C. Moscoso, University of Colorado, Boulder
Roberto
Muñoz-Alicea, University of Puerto Rico – Humacao
Bootstrap
Methods for Genetic Linkage Analysis
Rafael
Del Valle Vega, University of Puerto Rico – Río Piedras
Zoila
Garza, University of Texas at San Antonio
Amy
Katherine Olgin, University of California, Berkeley
Bootstrapping
Regression Models
Carina
Nieves, Kean University
Reyes
Matiel Ortiz Albino, University of Puerto Rico – Mayagüez
Dennis
Rosario Román, University of Puerto Rico – Mayagüez
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