Preface
This
page contains the technical reports written by the students who participated in
the 2001 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 research program.
The reports contained herein are the culmination of hundreds of hours of
work by the SIMU 2001 students and staff during the six weeks of the program.
The
twenty-four students who participated in SIMU 2001 came from universities in
California, Georgia, Indiana, New Mexico, New York, Puerto Rico, and Texas.
They 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 (reports 5 – 8
in below) were directed by Professor Reinhard Laubenbacher from New Mexico State
University. Professor Laubenbacher
was assisted by Luis García and Rebecca E. Pablo, graduate students at New
Mexico State University. The
projects in the area of Coding Theory were directed by Professor John B.
Little from College of the Holy Cross. Professor
Little was assisted by Jean Carlos Cortissoz and Jesús F. Rodríguez, graduates
students at Cornell 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 perhaps best can be classified as “not-fully edited”.
In fact, before students become fully engulfed in their research, they
participate in an intensive pre-research training that lasts two – three
weeks; thus, these technical reports are the culmination of research done by
SIMU students in three – four weeks.
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 2001 SIMU
was funded by grants from the National Security Agency (NSA Grant
MDA904-01-1-0053) 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 Pablo V. Negrón, Professor and Chair
of Mathematics (and SIMU Co-Founder), University of Puerto Rico – Humacao;
Barbara Deuink, National Security Agency; Roberto Marrero Corletto, Chancellor,
University of Puerto Rico – Humacao; James Schatz, Chief of Mathematics
Research, National Security Agency; and Manuel Gómez, Vice President for
Research and Academic Affairs, University of Puerto Rico.
Herbert A. Medina & Ivelisse Rubio
2001
SIMU Co-Directors
Humacao, PR, August 2001
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2001 SIMU
Technical Reports
Note
on Format: All the reports can be downloaded in
Adobe Portable Document Format (PDF) or in Postscript (ps) format. (Click here to download
Adobe Acrobat Reader, free software that will allow you to view and
print PDF files. Click here
to download Ghostview and Ghost script, free software that will allow
you to view and print Postscript flies.) The abstracts for the
reports are available in PDF format only. The
reports were written in LaTeX. A few of them contain Postscript
graphics; the LaTeX code was used to produce a Postscript file first and
then we used a Postscript -> PDF converter to obtain the PDF
file. The converter makes the document look awkward on a
monitor, but it prints well. (The ones that do not contain
Postscript graphics were converted to PDF using PDFLaTeX and these look
fine on the screen and also print well.)
If you would like a paper copy of any of the
reports,
please send your request to simu@cuhwww.upr.clu.edu.
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Lexicographic
and Non-Lexicographic Greedy Codes
Kishion Acosta, University of
California, Los Angeles
Marian
Hernández-Viera, University of Puerto Rico – Humacao
José
E. Lugo Martínez, University of Puerto Rico – Río Piedras
Codes
from n-Dimensional Polyhedra and n-Dimensional Cyclic Codes
Vanessa
Díaz, University of Puerto Rico – Río Piedras
Carlos
Guevara, City College of New York
Michael
Vath, University of Notre Dame
Generalized
Hamming Weights for Linear Codes
Iskra
Núñez, University of Texas at El Paso
Estefan
Ortiz, St. Mary's University Alicia
Urdapilleta, Mills College
Algebraic
Geometry Curves and Elkies Codes
Bárbara
Rivera, University of Puerto Rico – Río Piedras
Eric
Summerville, St. Mary's University
Jessica
Zúñiga, Rice University
Binomial
Ideals from Graphs
Rodolfo
de la Cruz,
University of California, Santa Barbara
Elden Krause, Loyola Marymount University
Patricia Pichardo, Georgia Institute
of Technology
Zero-Dimensional
Gorenstein Ideals
Sarah
Genoway, University of
Texas at Austin
Reyes
M. Ortiz-Albino, University of Puerto Rico – Mayagüez
Venessa
Tavares, University of California, Berkeley
Integral
Closure of Monomial Ideals: The Maximal Case
Carlos
A. Arreola, University of California, Los Angeles
Ricardo
Garza, California State University, Bakersfield
Aida
Yelitza Navarro-López, University of Puerto Rico –
Humacao
Integral
Closure of Monomial Ideals: The Square Case
Sotero
Alvarado, University of California, San Diego
Angela
Esquibel, University of New Mexico
Lianette
Passapera Sánchez, University of Puerto Rico – Humacao
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