Mathematics in Science and Engineering
The rapid pace of discovery in science and engineering depends on the mathematical and statistical sciences. These sciences are often invisible partners--encapsulated in research tools like algorithms, models and software packages. These tools, for example, help make sense of the complex processes that drive climate change. Topology illuminates how magnetic fields and fluid flows interact in the plasma within stars. And mathematical modeling plays a key role in developing micro, nanoscale and optical devices.
The mathematical sciences are also critical to training a mathematically literate workforce for the future. Technology-based industries rely on large numbers of college graduates well-versed in mathematics, science and engineering. Businesses rely increasingly on computer control systems, electronic data management, business forecasting models and modern economic theory.
The National Science Foundation (NSF) is the primary supporter of U.S. academic research in the mathematical sciences. As the role of mathematics expands in science and society, the resources devoted to three key areas--fundamental mathematical research, collaborations between mathematics and other disciplines, and mathematics education--must expand to support the nation's scientific, technical and commercial enterprises. To address these challenges, NSF has made increased investment in the mathematical sciences a priority area.
NSF's Division of Mathematical Sciences invested $151 million in fiscal 2002, and additional investments came from other NSF programs. The division has requested $182 million in the fiscal 2003 budget. A $60 million NSF-wide investment has been designated for the three key areas of research, collaborations and education. These public investments in mathematical sciences will support nearly 2,000 individual investigators and teams, 300 postdoctoral scholars and 1,300 graduate students, while complementing the Math and Science Partnerships that also seek to improve education and training.
NSF supports three world-class national research institutes: the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis), Institute for Pure and Applied Mathematics (University of California, Los Angeles), and the Mathematical Sciences Research Institute (Berkeley, Calif.). The Institute for Advanced Study (Princeton, N.J.) and the National Center for Atmospheric Research (Boulder, Colo.) provide additional postdoctoral training. NSF also supports the new Banff International Research Station (Alberta, Canada), a US-Canadian center for sharing information, forming collaborations and advancing research in the mathematical sciences in North America.
Vertical Integration in Higher Education
NSF's effort to strengthen math education and training included an investment of almost $16 million in fiscal year 2002 for the Vertical Integration of Research and Education (VIGRE) in the mathematical sciences. VIGRE awards help math departments carry out innovative programs in which undergraduates, graduate students, postdoctoral fellows and faculty support each other in research and educational activities.
The increasing integration of scientific disciplines has led to numerous partnerships in the mathematical sciences. In fiscal 2002, NSF teamed with the Defense Advanced Research Projects Agency to enable research in Computational and Algorithmic Representations of Geometric Objects. Computational geometry has proven to be a rich area of research with numerous applications in computer graphics, robotics and computer-aided design (CAD). Research in this area is expected to improve engineering design, the modeling of physical systems and cartography.
NSF has also joined the National Institute for General Medical Sciences, of the National Institutes of Health, in a program to employ the mathematical sciences in medical-related biological research. The opportunities include advances in evolutionary theory, statistical approaches to the search for genes, predictive models of the cellular state, improved algorithms for use in medical imaging, and simulations of systemic responses to burns and other injury.
Within NSF, the Division of Mathematical Sciences has teamed with the Directorate for Geosciences to increase collaborations in areas of mutual interest. Initial projects will focus on problems of scale, such as how mathematical models of physical phenomena differ at different time scales or distance scales.
The National Science Foundation (NSF) is an independent federal agency that supports fundamental research and education across all fields of science and engineering. In fiscal year (FY) 2016, its budget is $7.5 billion. NSF funds reach all 50 states through grants to nearly 2,000 colleges, universities and other institutions. Each year, NSF receives more than 48,000 competitive proposals for funding and makes about 12,000 new funding awards. NSF also awards about $626 million in professional and service contracts yearly.
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