Purpose
This research areawhile embracing mathematics and statisticswill advance research across disciplines and train a mathematically literate workforce.
Background
Today's discoveries in science, engineering and technology are intertwined with advances across the mathematical sciences. New mathematical tools are needed to understand scores of subjects, from the complex processes that drive the climate system to interactions of magnetic fields and fluid flows in the hot plasmas within stars. Mathematical modeling plays a key role in research on microscale, nanoscale and optical devices. Furthermore, for the United States to remain competitive among other nations with strong traditions in mathematics education, we must attract more young Americans to careers in the mathematical sciences.
Potential Impact
 Improved analysis of huge amounts of data from scientific instruments (e.g., genetic research, earthquake sensors and weather observations)
 Better models for complex phenomena (e.g., electrical patterns in the brain and heart, economic activity in society and information flow in computer networks)
 Improved forecasting of extremely complicated outcomes (e.g., climate patterns, air traffic control and electrical power grids)
 Improved decisionmaking tools for Internetbased business information systems
 More competitive U.S. workforce underscored by mathematics and statistics education
Example: Automatic Segmentation and Virtual Endoscopy
A group at the University of California, Berkeley, has developed computational algorithms to perform virtual endoscopy, allowing noninvasive examination of arterial and vascular structures, virtual colonoscopies and guidance for surgical navigation and procedures. Starting with various types of scans, the goal of their algorithms is to provide a complete reconstruction of the internal structures, complete with examination of pathways, interconnectedness and identification of abnormal pathologies and regions. Why is this research important? The answer lies partly in the delicate nature of some of the structures. Probes and invasive testing to map out structures of aortas, colons and vasculatures carry an intrinsic risk: these procedures can themselves cause tearing and blockages, and induce more serious problems. Advance knowledge about the unknown terrain provides insight about accessibility and areas requiring detailed examination. The algorithms developed by the group are accurate, robust and reliable in practical computation and are now in use in a variety of medical imaging software.
LongTerm Goals
 Foster significant advances in fundamental mathematics and statistics
 Foster interdisciplinary research partnerships that integrate mathematics with other science and engineering disciplines and recognize mathematicians and statisticians as full partners
 Integrate the most appropriate stateoftheart statistical principles and mathematical tools and concepts into ongoing research
 Train a new generation of researchers in interdisciplinary approaches applicable for future science and engineering challenges
 Increase the number and diversity of U.S. students trained in the mathematical and statistical sciences
 Develop a framework to improve the image and understanding of mathematics in the general population
FY 2006 Areas of Emphasis
 Fundamental Mathematical and Statistical Sciences
 Advancing Interdisciplinary Science and Engineering
 Mathematical and Statistical Challenges Posed by Large Data Sets
 Managing and Modeling Uncertainty
 Modeling Complex Nonlinear Systems
 Advancing Mathematical Sciences Education
Activities and Existing Competitions
The Mathematical Sciences Priority Area consists of the following activities with their solicitations.
 Collaboration in Mathematical Geosciences (CMG). This is a joint program of the Directorate for Geosciences, the Division of Mathematical Sciences, and the Office of Polar Programs.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf05535
 Enhancing the Mathematical Sciences Workforce in the 21st Century (EMSW21). This is a program of the Division of Mathematical Sciences.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf05595
 Focused Research Groups in the Mathematical Sciences (FRG). This is a program of the Division of Mathematical Sciences.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf02129
 Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences (UBM). This is a joint program of the Division of Mathematical Sciences, the Division of Emerging Frontiers of the Directorate for Biological Sciences, and the Division of Undergraduate Education of the Directorate for Education and Human Resources.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf04546
 Joint DMS/BIO/NIGMS Initiative to Support Research in the Area of Mathematical Biology. This is a joint program of the Division of Mathematical Sciences, the Directorate for Biological Sciences, and the National Institute of General Medical Sciences of the National Institutes of Health.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf04572
 Mathematical Sciences: Innovations at the Interface with the Physical and Computer Sciences and Engineering. This encompasses three joint programs of the Division of Mathematical Sciences with the Directorate for Computer and Information Science and Engineering, the Directorate for Engineering, and the Directorate for Mathematical and Physical Sciences.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf05622
 Mathematical Social and Behavioral Sciences (MSBS). This is a joint program of the Division of Mathematical Sciences and the Division of Behavioral and Cognitive Sciences and Division of Social and Economic Sciences of the Directorate for Social, Behavioral, and Economic Sciences.
http://www.nsf.gov/publications/pub_summ.jsp?ods_key=nsf05542
Related Resources
Division of Mathematical Sciences (DMS)
http://www.nsf.gov/div/index.jsp?div=DMS
Mathematical Sciences (DMS) Active Funding Opportunities
http://www.nsf.gov/funding/pgm_list.jsp?org=DMS
Directorate for Mathematical and Physical Sciences
http://www.nsf.gov/dir/index.jsp?org=MPS
Mathematics Classroom Resources
http://www.nsf.gov/news/classroom/mathematics.jsp
Mathematics Discoveries
http://www.nsf.gov/discoveries/index.jsp?prio_area=9
Mathematics News
http://www.nsf.gov/news/index.jsp?prio_area=9
Mathematics Overview
http://www.nsf.gov/news/overviews/mathematics/index.jsp
Mathematics in FY 2006 Budget Request (pages 409412)
http://www.nsf.gov/about/budget/fy2006/pdf/9NSFWideInvestments/35FY2006.pdf
Mathematics Research Overview Related Web Sites and Other Resources
http://www.nsf.gov/news/overviews/mathematics/resources.jsp
