**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**

Constructructive mathematics; set theory; higher computability

**Mathematical Biology**

Medical imaging; computer-aided detection; diagnosis, image-guided therapy and surgery; genomics, proteomics and mathematics in the path from genes to drug design; combinatorics and algorithms in molecular biology and biochemistry; evolutionary trees and algorithms

**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