Currently, our department has 16 research faculty members, 9 lecturers, and 16 graduate teaching assistants. Research activities are mainly concentrated in the areas of Combinatorics and Graph Theory, Complex Dynamical Systems, Difference Equations, Numerical Analysis, and Applied Analysis. Also, individual faculty members perform research in other areas.
The math department works in a wide range of areas of discrete mathematics both pure and applied: graph theory, network theory, extremal and probabilistic methods, analytic methods, finite model theory, combinatorial games, combinatorial optimization. You can learn more about discrete mathematics at our department here.
Complex Dynamical Systems
This area covers dynamics in one or more complex variables and related problems for one or more real variables. Recent topics worked on by the members of our department include dynamics of cubic polynomials, attractors in the real or complex projective plane and the dynamics of an infinite sequence of polynomials including holomorphic motions and polynomial-like sequences.
The math department at URI is an internationally recognized center of learning in the area of Difference Equations (DE for short) with a long tradition of substantial contributions in this field. For the most part, we focus on the development of the basic theory of the global behavior of nonlinear Difference Equations of order greater than one, related to the global stability and periodicity of solutions.
Numerical PDE's & Linear Algebra
Focuses on numerical solutions of partial differential equations as well as numerical linear algebra and scientific computation, specifically working in structured problems, deriving fast algorithms. Deals with eigenvalues of large matrices. Popular applications of mathematical modeling and computer simulation include blood flow in an artery, air flow in the human airway, and related applications in the areas of biology, groundwater and population control
Optimization and Control
Professor Kaskosz is currently focused on other areas of research. In the past, she did much research in Optimization and Control Theory, in particular, in H-infinity Control, Nonsmooth Control and Differential Inclusions.