My main objective in teaching is to make mathematics accessible to all Trinity students regardless of their background or major. The three important ingredients essential in accomplishing this task are:
Making mathematics relevant to other disciplines such as biology, economics, physics, engineering, etc. This is particularly important in lower division classes such as Calculus I.
Emphasizing mathematical concepts and what the underlying ideas must be and discussing them thoroughly and interactively with my students. The aim here is to make students think creatively and not get unduly bogged down with techniques and details.
Making the learning of mathematics an enjoyable endeavor. I use humor as much as I can in the classroom to make students comfortable and relaxed. The class environment becomes more conducive to learning and the exchange of ideas without any intimidation.
Ph.D., University of Missouri–Columbia
"Towards a theory of periodic difference equations and population biology" with R. Luis and H. Oliveira), Dynamics, Games and Science I, Springer Proceedings in Mathematics (Eds. Peixoto, Pinto, Adrego, Rand), 2011, 287–322.
"Stability of a Ricker-type competition model and the competitive exclusion principle" (with Luis and Oliveira), Journal of Biological Dynamics, to appear.
My research spans a spectrum of topics in mathematics with tools mainly from topology and analysis. In the last twenty years, I have led the efforts to develop the theory of difference equations and discrete dynamical systems.
My efforts involved the founding of the Journal of Difference Equations and Applications in 1995, the establishment of the International Society of Difference Equations in 2001, and the initiation of a series of annual International conferences on difference equations that started at Trinity in 1995.
Recently, I have been doing research on models of populations and their dynamical behavior. As part of Trinity IRBM, an NSF-funded project, I am working with three teams of students and faculty on the distribution of mammals, invasive grass, and a virus infection of bacteria.
Mathematical Models in Life Sciences
Community service & Involvement
I serve as co-editor in chief of the Journal of Difference Equations and Applications, and the Journal of Biological Dynamics. I am an elected member of the Board of Directors of the International Society of Difference Equations (ISDE) and former president of this society (two terms). I serve as the vice-chairman of the European Committee for establishing a Center of Excellence in Mathematics and Theoretical Physics at Birzeit University, (ECCE-Birzeit), 2005.
I coordinated the Trinity folkloric dance group Dabka, which gave performances at Trinity and in the city of San Antonio.