Pure mathematics is, in its way, the poetry of logical ideas. Albert Einstein

Coordinates

office: Math Department
e-mail: omar.colon4@upr.edu

Schedule: August-December, 2024:

MATE 3063, Calculus III
MATE 6995, Special Topics (Discrete Dynamical Systems)

Education:

Ph.D. Mathematics, 2005
Virginia Polytechnic Institute and State University
Blacksburg, Virginia, USA
Advisor: Reinhard Laubenbacher
M.S. Mathematics, 2002
New Mexico State University
Las Cruces, New Mexico, USA
B.S. Computational Mathematics, 1999
Universidad de Puerto Rico - Humacao
Humacao, Puerto Rico.

Research:

Steady State Dynamics of non-linear discrete dynamical systems over Finite Fields.

Articles or Proceedings

On the transient of Non Linear Boolean Dynamical Systesm. (with E. Rodriguez ) In Preparation.
Determining steady state behaviour of discrete monomial dynamical systems, Adv. Math. Commun. 11: 2017(2), 283-287 (with D. Bollman)
Problems and Solutions: Mathematics Olympiads in Puerto Rico:2016-2017 with Luis Caceres, Omar Colón, Pedro Torres, Andres Chamorro and Arturo Portnoy, AFAMaC publications 2017.
Problems and Solutions: Mathematics Olympiads in Puerto Rico:2015-2016 with Luis Caceres, Pedro Torres, Andres Chamorro and Arturo Portnoy, AFAMaC publications 2016
Problems and Solutions: Mathematics Olympiads in Puerto Rico:2014-2015 with Luis Caceres, Juan Ortiz and Arturo Pornoy, AFAMaC publications 2016
The problem of the week: A successful online training experience for math olympiad. Proceeding of 13th International Congress on Mathematical Education. Hamburg, 2016 (with L. Caceres and A. Portnoy)
On the transient of Boolean monomial dynamical systems. Congressus Numerantium 222: 215-228. 2014. (with D. Bollman)
Math Olympiads in Puerto Rico: Celebrating 15 years, with Luis Caceres, Juan Ortiz, Arturo Portnoy and Yuri Rojas, OMPR publications, 2014.
A new characterization of the Frobenius Number. Proceeding of CET 2012. Beijing China. (with D. Bollman)
A control theory for Boolean Monomial Dynamical Systems, Journal of Discrete Event Dynamic Systems. 20: 19-35. 2010. (with D. Bollman, V. Ocasio and E. Orozco)
Fixed Points in Discrete Models for Regulatory Genetic Networks. J Bioinform Syst Biol. 2007; 2007(1): 97356. (with D. Bollman and E. Orozco)
Monomial dynamical systems over finite fields. Complex Systems. 16: 333-342. 2006. (with A. Jarrah, R. Laubenbacher and B. Sturmfelds)
Boolean Monomial Dynamical Systems. Annals of Combinatorics. 8: 425-439. 2004. (with Reinhard Laubenbacher and Bodo Pareigis)
Multivariable Polynomial Reduction over Finite Fields. Proceedings of the Computer Research Conference, 1996. University of Puerto Rico, Mayaguez Campus. (with A. Caceres)

Grants, Awards and Scholarships:

Co-Pi, Puerto Rico Mathematical Olympiad, $170,000.00, Mayaguez Goverment.
Pi, Development of a Computer Science Research Laboratory for Undergraduates. Grant given by Lockheed-Martin. $25,000.00
Co-Pi, Development of a Portable, Continuous-mode Quartz Crystal Microbalance Biosensor. Internal Grant by UPR-Mayaguez. $ 74,900.00. (Co-Pi, Abel Baerga, Pi, Rick Valentin)
Co-Pi, PREMUR, Research Experiences for Undergraduates at The University of Puerto Rico, Mayaguez. Grant given by the National Security Agency, $93,000.00. (Co-Pi Damaris Santana and Pi Luis Caceres)
Alliances for Graduate Education and the Professoriate (NSF-AGEP) Scholarship given by the National Science Foundation.
Beca Presidente. Scholarship given by the president of the University of Puerto Rico.
Puerto Rico Alliance for Minority Participation (PR-AMP). Scholarship
Poster awarded at the Undergraduate Research Section at the 1999 Joint Meetings of the American Mathematical Society and Mathematical Association of America, San Antonio, TX, January 1999.
Poster awarded at the Undergraduate Research Section at the 1998 Joint Meetings of the American Mathematical Society and Mathematical Association of America, Baltimore, MD, January 1998. (See FOCUS, 98 Feb issue page 3)

Other Activities:

Trainer, Olimpiadas Matematicas de Puerto Rico, since 2005.
Coordinator, Olimpiada Latinoamericana Matematicas, 2010. Mayaguez, PR.
Deputy Leader, Olimpiada Centroamericana de Matematicas, 2013. Santa Marta, Colombia.
Delegation Leader, Iberoamerican Mathematical Olimpic, 2014. San Pedro Sula, Honduras.
Deputy Leader, Olimpiada Internacional de Matematicas, 2015. Chiang Mai, Thailand.
Deputy Leader, Olimpiada Internacional de Matematicas, 2016. Hong Kong.
Deputy Leader, Iberoamerican Mathematical Olimpic, 2016. Chile.
Deputy Leader, Olimpiada Internacional de Matematicas, 2017. Rio di Janeiro, Brazil.
Deputy Leader, Olimpiada Internacional de Matematicas, 2018. Romania.
Deputy Leader, Olimpiada Internacional de Matematicas, 2019. United Kingdom.
Invited Speaker. XI CIEMAC, TEC Costa Rica. 2019
Deputy Leader, Olimpiada Internacional de Matematicas, 2020. Russia
Deputy Leader, Oiimpiada Iberoamericana de Matematica, 2022, Colombia
Deputy Leader, Olimpiada Centro Americana Matematica, 2022, Costa Ria