The Courant Mathematics and Computing Laboratory (CMCL) is a research center at the Courant Institute of New York University. Our program is devoted to the formulation, analysis and numerical resolution of a broad class of scientific problems, drawn from aerodynamics, multi-phase flow, combustion, electromagnetics, optics and materials science. One component of the CMCL involves the design of new schemes for partial differential equations, particularly those which support adaptive mesh refinement, fast algorithms, and parallel computation. A second component of our effort concerns the modeling and numerical investigation of a variety of questions in materials science, complex fluid dynamics, interface motion, and electromagnetics. The third component of the CMCL involves the mathematical analysis of stochastic problems that arise in physics and Monte Carlo methods for their solution.