## Research Areas

The Department of Mathematical Sciences has an internationally recognized research faculty active in the following areas:

### Algebra

Rings, modules, groups and their representations; applications to combinatorial designs and cryptology, computational algebra

### Analysis

Harmonic analysis, function and operator theory and their interactions; Sobolev inequalities; inequalities involving the Fourier transform; operators on Banach spaces; ordinary and partial differential equations; stochastic differential systems; vortex and climate dynamics with applications to climatic and financial markets

### Combinatorics and Geometry

Enumerative and algebraic combinatorics; graph theory; design theory and applications; finite projective planes and their automorphisms; finite geometries, and Euclidean geometry

### Cryptology and Information Security (also visit our CCIS website)

Block ciphers, public key cryptography, provable security, group-theoretic cryptography, cryptanalysis, secret sharing, hash functions, secure group communications

### Dynamical Systems and Control Theory

Nonlinear dynamical systems, computational topological methods, complex dynamical systems, fractal geometry, mathematical theory of control systems, stability analysis

### Foundations of Mathematics

Constructive mathematics; set theory; higher computability

### Mathematical Biology

Multi-host multi-strain epidemiological models, host immune response, nested immuno-epidemiological dynamics, spatial temporal dynamics in epidemiology, reaction diffusion systems, cell motility, time-since-infection structured partial differential equations, age structured pde's, avian influenza, Ebola

### Probability and Statistics

Time-series analysis and regression modeling; parametric and nonparametric function estimation; weak convergence of stochastic processes; environmental statistics and biostatistics

### Mathematics Education

Technology in the classroom, integrated curricula, improving performance for pre-calculus mathematics and in mathematics for engineering students