MATHEMATICAL SCIENCES $141,480,000

The FY 2002 Budget Request for the Mathematical Sciences (DMS) Subactivity is $141.48 million, an increase of $20.0 million, or 16.5 percent, over the FY 2001 Current Plan of $121.48 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, 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 over 66 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 total scientific and engineering workforce.

The Mathematical Sciences Subactivity includes support for 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. Support across the mathematical sciences includes research institutes, postdoctoral research fellowships, graduate education, broadening the career experiences of researchers, providing opportunities that increase participation in the nation's research personnel base, research conferences and workshops, and shared scientific computing research equipment. Support for infrastructure in the mathematical sciences includes undergraduate investments such as Research Experiences for Undergraduates.

The pervasive nature of the mathematical sciences in underpinning and enabling today's science, economics, and engineering disciplines is illustrated by the following examples:

• Addressing the pressing need for increased capacity of communication channels, researchers at University of Colorado at Boulder, Brown University, and Northwestern University have developed new methods for simulating fiber-optic transmission of bit-error probabilities, allowing simulations with significantly fewer computations.

• A researcher at the University of Utah, supported by both the Mathematical Sciences Subactivity and the Office of Polar Programs, has applied methods from percolation theory to investigate the properties of the sea ice that covers a sizeable fraction of the Earth's polar oceans. The research was able to explain the thresholds for porosity, temperature, and salinity, above which sea ice becomes permeable to brine.

At the same time, NSF supported mathematical sciences research probes fundamental theories:

• A mathematical sciences researcher was awarded a Presidential Early Career Award for Scientists and Engineers this past year for introducing modern methods into the ancient art of counting. One of the oldest parts of mathematics concerns enumerating the number of pieces into which a given integer can be broken. The research showed how to associate a "modular L function" with the function that counts the number of pieces. Through this research new and deep formulas including a deeper understanding of the work of the great Indian mathematician Ramanujan were derived.

The FY 2002 Budget Request of $141.48 million, an increase of $20.0 million, will enable both the enhanced participation of the mathematical sciences in interdisciplinary mathematics and the establishment of new interdisciplinary national institutes. These investments reflect the importance of mathematical and statistical sciences in cross-cutting science and engineering research areas such as pattern recognition, managing large data sets, relationships between structure and function, modeling uncertainty, and the geometrization of science. Specifically:

• Special emphasis on Focused Research Group activities that advance areas of mathematical biology, nanotechnology, and new partnerships with the Computer and Information Science and Engineering Activity and the Geosciences Activities within NSF and new interagency partnerships with the National Institutes of Health (NIH) and the Defense Advanced Research Project Agency (DARPA).

• Up to 4 new Mathematical Sciences National Institutes will be established. These new Institutes will address both 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 societal needs.

• The Vertical Integration of Research and Education (VIGRE) program will be increased by $6.0 million to $16 million through redirecting funds from existing programs that are phasing out.