The study of of algebraic structures, or sets with a finite number of operations that satisfy a number of fixed axioms.

Analysis is the study of functions, continuity and discontinuity, and infinity and the infinitesimal.

Applied Mathematics is the study of applied partial differential equations, dynamical systems, mathematical biology, mathematical finance, and numerical analysis.

Computational Statistics and Data Science is the application of high level techniques to complex data.

Financial Mathematics, or PhiMAC, develops analytical and computational tools for analysis, modeling, and decision making in financial markets.

Geometry & Toplogy is the study of quantitative and qualitative properties of space.

Mathematical Biology focuses on the development and analysis of models of population dynamics and evolution.

Mathematical Logic is the study of underlying patterns of algebraic and geometric structures.

Probability & Statistics is the interdisciplinary study of theoretical probability, applied probaility, mathematical statistics, and applied statistics.