Mathematics

The Department of Mathematics provided these comments concerning the CS&E Initiative:

• CS&E Initiative and Departmental Plans and Priorities. The Department of Mathematics has strong and internationally acclaimed research and educational programs in computational mathematics. These activities go beyond the traditional strength in numerical analysis and scientific computation, and have influenced current research in wide areas of mathematics including geometry, topology, analysis, discrete mathematics, and mathematical physics. The main lines developed in the Department's preproposal for Provost Grey's Initiatives have also been incorporated in this year's Academic Plan of the Department. There are two aspects of direct relevance to the CS&E Initiative. The first is discrete mathematics, an area that has gained enormously in importance because of its manifold applications to problems of computing and which has been developing rapidly itself due to the availability of fast computers. The second is a focus on experimental mathematics, i.e., research in mathematics involving novel uses of computing for the discovery and understanding of mathematical structures. Both are a high priority. Mathematics also wishes to further develop existing strength in the Department in the areas of scientific computation, fluid dynamics, image and signal processing, and mathematical biology, which are three more areas explicitly covered by the CS&E Initiative. Thus, the CS&E Initiative is the natural context for the realization of our plans. Moreover, the core areas of mathematics play an increasingly important role in an ever wider range of technological applications. One can hardly imagine a program in the area of CS&E without a strong mathematical component.
• Hiring. Exciting hires in CS&E that would have a strong and positive impact on the Department's programs include Neil Sloane, AT&T (coding theory), John Conway, Princeton (discrete mathematics), Ron Graham, UCSD, and Richard Stanley, MIT (both combinatorics), Peter Shor, AT&T (quantum computation), Hendrik Lenstra, Berkeley (applied number theory), Charles Peskin, Courant Institute, NYU (mathematical biology), and Ronald R. Coifman, Yale, Vladimir Rokhlin, Yale (both computational harmonic analysis). Strong PhD programs in computational sciences exist at Yale, Stanford, Brown, UCLA, MIT, Michigan, Wisconsin, Rice, Cornell, Texas, Maryland, Courant, Illinois, Purdue, and Florida, and in mathematical biology at Utah and Boston University.
• CS&E and its Relation to Teaching. CS&E-oriented appointments are expected to bring wider variety and deeper expertise in related areas into the Department's teaching programs at both graduate and undergraduate levels.
• Resources. The Department has requested to the Dean of MPS seven FTEs in discrete mathematics and 3 three FTEs in scientific computation for the period 2000-2006. The Department has also requested office and additional space for its needs. However, at this point, the Department is not in the position to commit any resources to the Initiative.