Below are general descriptions of research areas that are currently represented in the department. For further information about a particular field of mathematics represented in the department, click on the link to that area below. For specific information on a specific faculty member's research, please go to the departmental directory link on the left-hand side and click on that individual's name or personal web page.

Algebra
Algebra may be viewed as an abstraction of the fundamental properties of arithmetic and is central to many other areas of mathematics. Research interests in this department include infinite abelian groups, the interplay between properties of a ring and modules over that ring, representations of finite partially ordered sets over fields and rings, and set theoretic techniques applicable to algebraic structures of large cardinality.

Analysis
Analysis is a vast realm of mathematics which encompasses calculus and its extension into higher mathematics, both in one and higher dimensional settings. Research interests in the department include harmonic analysis, functional analysis, differential equations, and special functions.

Differential Equations
The differential equations group at Baylor conducts research in ordinary and partial differential equations, discrete dynamical systems cast as finite difference equations, and the interaction between hybrid discrete/continuous dynamical systems (dynamic equations on time scales).

Mathematical Physics
Mathematical physics studies conceptual frameworks which (presumably) describe physical phenomena. Research interests of the mathematical physics group include spectral (zeta) functions, quantum field theory under the influence of external conditions, Casimir effect, Bose-Einstein condensation, conical manifolds, and quantum chaos.

Numerical Analysis
Numerical analysis is the study of computer methods for solving math problems that arise in engineering and other scientific areas. Research interests in this department include optimization and iterative methods for large matrix problems, and solving singular partial differential equations via adaptive and/or splitting finite difference methods.

Representation Theory
Representation theory studies how symmetry manifests itself in mathematics and in physics. Research interests of the group at Baylor include representations of Lie groups and Lie algebras, symmetries of differential equations, and algebro-geometric aspects of representation theory.

Topology
Topology is the study of the properties of spaces that are preserved under continuous transformation. The department currently has topologists working on the topology of continua and the topology of spaces that arise from low-dimensional dynamical systems