Topology is concerned with the intrinsic properties of shapes of spaces. One class of spaces which plays a central role in mathematics, and whose topology is extensively studied, are the n dimensional manifolds. These are spaces which locally look like Euclidean n-dimensional space. Historically, topology has been a nexus point where algebraic geometry, differential geometry […]
Overview Probability is concerned with the mathematical analysis of random phenomena. It is younger than most other areas of Mathematics, as it originated with the study of games of chance by Pascal and Fermat (1654); since then it has become indispensable for dealing with randomness in almost all branches of science. Today, in addition to […]
The objects of study of algebraic geometry are, roughly, the common zeroes of polynomials in one or several variables (algebraic varieties). But because polynomials are so ubiquitous in mathematics, algebraic geometry has always stood at the crossroads of many different fields. Classical questions in algebraic geometry involve the study of particular sets of equations or […]
The combined Columbia-Barnard Mathematics Department currently consists of 51 faculty members (27 senior, 24 junior), 19 adjunct professors, 8 Post-Doctoral Research Fellows and Scientists, and 59 PhD students. In addition, each year we have many short-term and long-term visitors and researchers that contribute to the intellectual life of the department. Research activity in the department […]