URI URI



Research
sum

My research interests lie mainly in the field of difference equations and dynamical systems. Specifically I investigate the local and global dynamics of second-order difference equations whose transition functions satisfy certain monotonicity characteristics. I have also recently become interested in math education research pertaining to remediation in introductory-level college math courses.

Information regarding current research projects and past presentations may be found below. For a statement on my research, please click here.

Papers
Global Dynamic Scenarios for Competitive Maps in the Plane
(with M.R.S. Kulenović) In preparation.
Generalized Beverton-Holt Equations
(with M.R.S. Kulenović) In preparation.
A Generalization of Lyness' Equation
(with M.R.S. Kulenović) In preparation.
Implementing Online Programs in Gateway Mathematics Courses for Students with Prerequisite Deficiencies
(with D. McArdle, L. Thoma, and L. Wu) In preparation.
Upcoming Presentations
January
2018
 
 
Global Dynamic Scenarios for Competitive Maps in the Plane
AMS Special Session on Bifurcations of Difference Equations and Discrete Dynamical Systems
Joint Mathematics Meetings, San Diego, CA
Presentations
November
2017
 
 
Designing and Implementing Online Programs in Mathematics Courses for Students with Prerequisite Deficiencies (with D. McArdle)
UCONN Mathematics Education Research Seminar
University of Connecticut, Storrs, CT
May
2017
 
 
A Generalization of Lyness' Equation
AMS Spring Eastern Sectional Meeting: Special Session on Asymptotic Properties of Discrete Dynamical Systems
Hunter College, NYC, NY
April
2017
 
 
Generalizing Lyness' Equation: An Investigation of Global Periodicity and an Application of KAM Theory
URI Difference Equations Seminar
University of Rhode Island, Kingston, RI
September
2016
 
 
Generalized Beverton-Holt Difference Equations
AMS Fall Eastern Sectional Meeting: Special Session on Autonomous and Non-Autonomous Difference Equations and Applications
Bowdoin College, Brunswick, ME
April
2016
 
 
Geneveralized Beverton-Holt Difference Equations and Applications of Concavity
URI Difference Equations Seminar
University of Rhode Island, Kingston, RI
November
2015
 
 
Global Dynamics of a Second-Order Quadratic-Fractional Difference Equation
AMS Fall Eastern Sectional Meeting: Special Session on Difference Equations and Applications
Rutgers University, New Brunswick, NJ
November
2015
 
 
Local and Global Dynamics of a Second-Order Quadratic-Fractional Difference Equation
URI Difference Equations Seminar
University of Rhode Island, Kingston, RI