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Mathematical Sciences
February 2002
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.
NSF Priority
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.
Budget Details
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.
Research Institutes
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.
Partnerships
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.
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