MATHEMATICAL SCIENCES $181,870,000

The FY 2003 Budget Request for the Mathematical Sciences (DMS) Subactivity is $181.87 million, an increase of $30.39 million, or 20.1 percent, over the FY 2002 Current Plan of $151.48 million.

(Millions of Dollars)

Advances in science and engineering, driven in part by increasingly sophisticated and readily available computing environments, have lifted the mathematical sciences to the forefront of science and engineering, reshaping modern discovery through quantitative predictions, instrumentation development, modeling, visualization, computational algorithms, and optimization methods. Science and engineering are becoming more mathematical and statistical, not only in the physical, engineering and informational sciences, but also the biological, geophysical, environmental, social, behavioral, and economic sciences.

NSF has a crucial role in the support of academic research in the mathematical sciences, providing nearly 70 percent of all federal academic support. NSF-supported research involves a broader range of infrastructure, fundamental research, and multidisciplinary research topics than that sponsored by other federal agencies that support academic mathematical sciences research. Especially important is the critical function of the mathematical sciences in the education and training of the nation's scientific and engineering workforce.

Mathematical Sciences includes areas such as analysis, geometry, topology, foundations, algebra, number theory, combinatorics, applied mathematics, statistics, probability, biomathematics, and computational mathematics. Awards in these areas support a variety of research projects, multidisciplinary projects, and Focused Research Groups, with some grants including funding for graduate and postdoctoral students as well as for workshops, computing equipment and other research and education needs. In addition, this Subactivity supports infrastructure efforts across the mathematical sciences, including national research institutes, postdoctoral research fellowships, graduate education, broadened career experiences for researchers, research conferences and workshops, shared scientific computing research equipment, and undergraduate investments such as Research Experiences for Undergraduates (sites and supplements).

The pervasive nature of the mathematical sciences in underpinning and enabling much of today's scientific, engineering, commercial, and defense-related activities is illustrated by the following examples:

• Describing the theory of how insects manipulate the flow of air around them, a researcher at Cornell University determined how the rotating motion of insect wings during flapping creates non-linear vortices that permit the insect to hover. These vortex dynamics explained the role of the phase relation between the wing translation and the rotation in generating lift.
  
  
• Researchers on a Focused Research Group Award to several institutions have developed a highly competitive, nonlinear-based approach to optical fiber transmission of light. The mathematical theory produces precise pulse shapes with maximal fiber lifetimes. Effective computational techniques have been added that address the randomness in optical fiber links that has historically limited performance of high-speed optical fiber communications.
  
  
• In an award jointly supported by the Biological Sciences Activity and the Mathematical Sciences Subactivity, researchers at Rockefeller University and the Universidad de Buenos Aires identified improved control tactics for a vexing public health problem in Latin America. Mathematical models, calibrated to detailed household data in northwest Argentina showed that simple and inexpensive methods could prevent Chagas disease - a disease that is often fatal and spread by a blood-feeding bug.
  
  
• Researchers at the University of Texas at Austin have developed a discontinuous Galerkin (DG) finite element method for the two-dimensional, depth-integrated shallow-water equations. The resulting computational methods have been used in the development of a complex shallow-water simulator, called UTBEST (University of Texas Bay and Estuary Simulator). The simulator can model and predict spread of a contamination event in the Houston Ship Channel with the domain being all of Galveston Bay.

The FY 2003 Budget Request of $181.87 million will enhance interdisciplinary research groups and other collaborative mechanisms that integrate the strength of the mathematical sciences with chemistry, materials research, physics, astronomy and other sciences and engineering.

Of special importance in FY 2003 is the Mathematical Sciences priority area investment of $47.39 million, an increase of $17.39 million over the FY 2002 investment in interdisciplinary mathematics. This investment reflects the importance of mathematical and statistical sciences in the kinds of crosscutting science and engineering research areas described above.

The FY 2003 increases will support:

• Research in dynamical systems, structure and geometry of the physical world, and other mathematical and statistical fundamental research necessary to support advances in interdisciplinary research.
  
  
• Focused mathematical sciences research teams, interdisciplinary training groups, and other collaborative mechanisms related to advancing science and engineering. For example, the Division of Mathematical Sciences and the Geosciences Directorate plan a GEO-Math partnership to advance the understanding of problems arising from differences in scales, both time scales and distance scales, in geophysical problems. It is anticipated that the FY 2002 interagency partnerships with DARPA and NIH will be continued.
  
  
• New and continuing national institutes in the mathematical sciences that will address the growing interface between the mathematical sciences and other disciplines and the mathematical and statistical problems whose solutions will contribute to both fundamental knowledge and national needs.
  
  
• An increase of $10.0 million, to approximately $26.0 million, for the Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE). This program supports undergraduate, graduate and postdoctoral education and training activities and curriculum development designed to improve and reform the research and training opportunities in the mathematical sciences.