EMSW21 - RTG: Numerical Mathematics for Scientific Computing

New York University, New York NY

Investigators

Abstract

For at least two decades, high-level reports on the health of mathematical sciences research in the United States have recommended creation of a more direct path between this research and its users. The most obvious means for improving this connection is software, which is ubiquitous in science, engineering, business, medicine, as well as everyday life. Mathematics embodied in software can quickly bring new knowledge, insights, and methods to bear in contexts ranging from detecting tumors to finding the best travel route to deciding how to invest. The role of software as standard-bearer for the mathematical sciences is especially important for industry, where mathematical discoveries tend to be applied only if they have been transformed into software. Successful production of high-quality, timely mathematical software brings an array of complex intellectual challenges requiring training not only in mathematics, but also in software development and the needs of application areas. Accordingly, the goal of this Research Training Group is to produce mathematical scientists with a deep, hands-on understanding of mathematical algorithms and their instantiation in software; in addition, we intend to make the crucial elements of the training program broadly available. The faculty involved with this activity, from the Courant Institute of Mathematical Sciences at New York University, and the Applied Physics and Applied Mathematics Department at Columbia University, represent a variety of experiences in applied and computational mathematics, numerical algorithms and software, and real-world applications. Our belief is that the combined expertise of these researchers will provide a rich source of common insights that currently exist in relative isolation. The Research Training Group will provide, for undergraduates, Ph.D. students, and postdoctoral researchers: (1) training that explores in depth the relationships among mathematical modeling, algorithm design, software choices, and the hardware environment; (2) understanding of how algorithm and software design may be affected, even driven, by the nature of problems and the contexts in which they need to be solved; (3) hands-on experience of designing software that succeeds when it can and fails gracefully when it cannot. At all levels, participants will experience individual and team involvement with mathematical software development. The undergraduate part of the program will include an enhanced curriculum and summer research experiences directly connecting the mathematical sciences with real-world applications. Ph.D. student training will include joint mentoring by faculty with expertise in applied and computational mathematics and scientific software, an enhanced curriculum that builds on the strengths of the two universities, and internships in government and industrial research laboratories. Postdocs will join longer-term projects with emphasis on applications, and will also be involved in undergraduate and graduate student training. Our hope is that the experiences of this Research Training Group will be helpful in developing other programs with similar goals.