Mathematical analysis covers a wide range of different subjects. Areas currently active at Cornell include: dynamics, harmonic analysis, potential analysis, partial differential equations, geometric analysis, applied analysis, and numerical methods.

In the Cornell Department of Mathematics, the “applied” group includes mathematicians working in dynamical systems theory, PDEs, calculus of variations, computational algebra, applied probability theory, statistics, numerical analysis, and scientific computing.

Combinatorics is the study of finite structures, many of which arise in other branches of mathematics or from problems arising in science or engineering.

Differential geometry is a vast subject that has its roots in both the classical theory of curves and surfaces and in the work of Gauss and Riemann motivated by the calculus of variations.

Mathematical logic is the study of the strengths and limitations of formal languages, proofs, and algorithms and their relationships to mathematical structures.

Topology is the qualitative study of shapes and spaces by identifying and analyzing features that are unchanged when the object is continuously deformed — a “search for adjectives,” as Bill Thurston put it.