Preface
This
page contains the technical reports written by the students who participated in
the 2000 Summer Institute in Mathematics for Undergraduates (SIMU) at the
University of Puerto Rico – Humacao. SIMU,
a National Science Foundation (NSF) Research Experience for Undergraduate (REU)
site, 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 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 reports contained herein are the culmination of hundreds
of hours of work by the SIMU 2000 students and staff during the six weeks of the
program.
The
twenty-four students who participated in SIMU 2000 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 Computational Algebra were directed by Professor Reinhard
Laubenbacher from New Mexico State University.
Professor Laubenbacher was assisted by Abdul Jarrah and Rebecca E. Pablo
who are graduate students at New Mexico State University.
The projects in the area of Integration of Rational Functions were
directed by Professor Victor H. Moll from Tulane University.
Professor Moll was assisted by Jean Carlos Cortissoz, graduate student at
Cornell University, and Dagan Karp, graduate student at Tulane University.
Because the quantity of work produced by these students during six weeks
of the program is so great and because of other time constraints, these
technical reports can be classified as “not fully edited”.
In fact, before students become fully engulfed in their research, they go
through an intensive pre-research training which lasts almost three weeks; thus,
these technical reports are the culmination of research done by SIMU students in
a little over three weeks.
The
2000 SIMU was funded by grants from the National Security Agency (NSA Grant
MDA904-00-1-0005), the National Science Foundation (NSF Grant DMS-9987901), the
University of Puerto Rico, the National Aeronautics and Space Administration
(NASA), and the Alliance for Minority Participation (AMP).
Herbert
A. Medina
Ivelisse
Rubio
SIMU Co-Directors
August,
2000
Back
to the top.
Acknowledgements
Individuals who have
given indispensable assistance in the funding and creation of SIMU include (in
alphabetical order):
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; Roberto Marrero-Corletto,
Chancellor, University of Puerto Rico – Humacao; Pablo Negrón-Marrero,
Professor of Mathematics, University of Puerto Rico - Humacao; Wilson Ruiz, Chairman,
Department of Mathematics, University of Puerto Rico – Humacao; and James Schatz,
Chief Mathematical Research Division, National Security Agency.
Back
to the top.
2000 SIMU
Technical Reports
|
Note
on Format: All the abstracts and reports can be downloaded in
Adobe Portable Document Format (PDF). (Click here to download
Adobe Acrobat Reader, free software that will allow you to view and
print PDF files.) A couple of the reports contain Postscript
graphics and the Postscript -> PDF converter that we used makes these
files look awkward on a
monitor, but they will print fine.
If you would like a paper copy of any of the
reports,
please send your request to simu@cuhwww.upr.clu.edu.
|
Time
Complexity for Cracking a Gröbner
Basis Cryptosystem
Marian
Hernández-Viera, University of Puerto Rico – Humacao
Ariel
Rivera Torres, University of Puerto Rico – Río Piedras
Ray
Sardo, Loyola Marymount University
Primary
Decomposition of Ideals Arising from Hankel Matrices
Paul
Brodhead, University of Wisconsin, Madison
Malarie
Cummings, Hampton University
Cora
Seidler, University of Texas at El Paso
Binomial
Ideals from Graphs
Danielle
Farrar, University of Washington
Yolanda
Manzano, St. Mary's University Juan
Manuel Torres Acevedo, University of Puerto Rico – Humacao
Initial
Ideals of Generic Ideals and Moreno-Socias Conjecture
(A
revised version of this paper will appear in the Proceedings of the 2001 ISSAC
Conference.)
Edith
Aguirre, University of Texas at El Paso
Juan
Ariel Ortiz-Navarro, University of Puerto Rico – Humacao
Rogelio Torrez, Arizona State University
The
Dynamics of Even-Odd Splitting
(A
revised version of this paper will appear in the Pi Mu Epsilon Journal.)
Emilia Huerta-Sánchez, Mills College
Aida
Navarro-López, University of Puerto Rico - Humacao
David
Uminsky, Harvey Mudd College
Investigating
a Family of Integrals with Three Parameters
Lianette
Passapera-Sánchez, University of Puerto Rico – Humacao
Christian
Roldán-Santos, University of Puerto Rico – Mayagüez
Yvette
Uresti-Ovalle, St. Mary's University
Convergence
of a Landen Transformation of Degree Six
(A
revised version of this appeared in the Electronic Journal of Combinatorics, 8
(2001) R30.)
Encarnación
Gutiérrez, University of California, Los Angeles
Miguel
Rosario-García, University of Puerto Rico – Mayagüez
María
de la Luz Torres, University of California, Riverside
Unimodality
and Log-Concavity of Polynomials
Jenny
Alvarez, University of California, Santa Barbara
Miguel
Amadis, Nyack College
Leobardo
Rosales, University of California, San Diego
Back
to the top
|
