Computational applied mathematics studies important scientific problems through a combination of science (experiments and underlying scientific theories), applied mathematics (techniques and theories) and computation (software and hardware). The dominant mathematical modeling technique used in this field is differential equations, and most problems studied arise in the natural sciences and engineering, such as climate modeling or aircraft wing design. However, computational applied mathematics has much wider applicability, as illustrated by its heavy use in modeling derivatives on Wall Street. Computational biology is an area of computational applied mathematics that has split off in the department to become its own separate field of research and graduate training.

The Stony Brook Department of Applied Mathematics and Statistics has one of the country's leading groups in computational fluid dynamics. A particular focus is interaction of nonlinear waves. These waves arise in a variety of settings, such as diffraction of shock waves, enhanced oil recovery, pollution in groundwater, and the design of particle accelerators. High-performance scientific computing is another major focus, especially in computational fluid dynamics simulations. The University has a local 3Tf cluster called Seawulf and a 100Tf Blue Gene in the New York Center for Computational Sciences, a joint Stony Brook-Brookhaven National Laboratory center. For more information about Computational Applied Mathematics research, see Computational Applied Mathematics projects.

There is demand for both M.S. and Ph.D. degrees in computational applied mathematics. The department offers a 30-credit M.S. degree, with no thesis, that prepares students for non-academic careers. The department also offers a Ph.D. degree which starts off with the same courses as the M.S. degree. For more details about requirements for the Ph.D., please see Ph.D. Requirements.

Required Courses for M.S. in Computational Applied Mathematics track (with offering sequences)

First Semester
AMS 501 Differential Equations and Boundary Value Problems

AMS 510 Analytical Methods for Applied Mathematics and Statistics
AMS 526 Numerical Analysis I
AMS 595 Fundamentals of Computing (1 credit)

Second Semester
AMS 503 Applications of Complex Analysis
AMS 527 Numerical Analysis II
AMS 528 Numerical Analysis III

plus four electives chosen from other graduate courses in the department or (with an advisor's approval) graduate statistics courses in other departments.