Mathematics is the key to opportunity. No longer only the language of science, mathematics is now essential to business, finance, health, and defense. Yet because of the lack of mathematical literacy, many students are not prepared for tomorrow's jobs. Everybody Counts suggests solutions. Written for everyone concerned about our children's education, this book discusses why students in this country do not perform well in mathematics and outlines a comprehensive plan for revitalizing mathematics education in America, from kindergarten through college. single copy, $8.95; 2-9 copies, $7.50 each; 10 or more copies, $6.95 each (no other discounts apply) Table of Contents <ul>
<li>FRONT MATTER</li>
<li>OPPORTUNITY</li>
<li>HUMAN RESOURCES</li>
<li>MATHEMATICS</li>
<li>CURRICULUM</li>
<li>TEACHING</li>
<li>CHANGE</li>
<li>ACTION</li>
<li>REFERENCES</li>
</ul>

Everybody Counts: A Report to the Nation on the Future of Mathematics Education

Science & Math

Mathematical Sciences Education Board

Board on Mathematical Sciences and Their Applications

National, Research Council

Mathematics

National Academies Press

Mathematical sciences play a key role in many important areas of Homeland Security including data mining and image analysis and voice recognition for intelligence analysis, encryption and decryption for intelligence gathering and computer security, detection and epidemiology of bioterriost attacks to determine their scope, and data fusion to analyze information coming from simultaneously from several sources. This report presents the results of a workshop focusing on mathematical methods and techniques for addressing these areas. The goal of the workshop is to help mathematical scientists and policy makers understand the connections between mathematical sciences research and these homeland security applications.

The Mathematical Sciences' Role in Homeland Security: Proceedings of a Workshop

Computers & Technology

Division on Engineering and Physical Sciences

Networking & Cloud Computing

The exponentially increasing amounts of biological data along with comparable advances in computing power are making possible the construction of quantitative, predictive biological systems models. This development could revolutionize those biology-based fields of science. To assist this transformation, the U.S. Department of Energy asked the National Research Council to recommend mathematical research activities to enable more effective use of the large amounts of existing genomic information and the structural and functional genomic information being created. The resulting study is a broad, scientifically based view of the opportunities lying at the mathematical science and biology interface. The book provides a review of past successes, an examination of opportunities at the various levels of biological systemsâ€" from molecules to ecosystemsâ€"an analysis of cross-cutting themes, and a set of recommendations to advance the mathematics-biology connection that are applicable to all agencies funding research in this area. Table of Contents <ul>
<li>Front Matter</li>
<li>Executive Summary</li>
<li>1 The Nature of the Field</li>
<li>2 Historical Successes</li>
<li>3 Understanding Molecules</li>
<li>4 Understanding Cells</li>
<li>5 Understanding Organisms</li>
<li>6 Understanding Populations</li>
<li>7 Understanding Communities and Ecosystems</li>
<li>8 Crosscutting Themes</li>
</ul>

Mathematics and 21st Century Biology

Committee on Mathematical Sciences Research for DOE's Computational Biology

Biological Sciences

The U.S. Air Force is developing new force capabilities appropriate to an emerging array of threats. It is clear that advances in information science and technology (IS&amp;T) are essential for most of these new capabilities. As a consequence, the Air Force is finding it necessary to refocus its IS&amp;T basic research program to provide stronger support for reaching these goals. To assist this effort, the AFOSR asked the NRC for a study to create a vision and plan for the IS&amp;T-related programs within the Officeâ€™s Mathematics and Space Science Directorate. This report provides an assessment of basic research needs for Air Force systems and communications, software, information management and integration, and human interactions with IS&amp;T systems. The report also offers a set of priorities for basic IS&amp;T research, and an analysis of funding mechanisms its support. Table of Contents <ul>
<li>Front Matter</li>
<li>Executive Summary</li>
<li>1 Introduction</li>
<li>2 Background</li>
<li>3 Basic Research for Air Force Network Systems and Communications</li>
<li>4 Basic Research for Air Force Software</li>
<li>5 Basic Research for Air Force Information Management and Integration</li>
<li>6 Basic Research for Human Interactions with Air Force IS&amp;T Systems</li>
<li>7 Priorities in Basic IS&amp;T Research for the Air Force</li>
<li>8 Funding Mechanisms</li>
<li>9 Future Considerations</li>
<li>Appendix A: Meeting Agendas</li>
<li>Appendix B: Acronyms</li>
</ul>

Basic Research in Information Science and Technology for Air Force Needs

Committee on Directions for the AFOSR Mathematics and Space Sciences Directorate Related to Information Science and Technology

Modeling, simulation, and analysis (MS&A) is a crucial tool for military affairs. MS&A is one of the announced pillars of a strategy for transforming the U.S. military. Yet changes in the enterprise of MS&A have not kept pace with the new demands arising from rapid changes in DOD processes and missions or with the rapid changes in the technology available to meet those demands. To help address those concerns, DOD asked the NRC to identify shortcomings in current practice of MS&A and suggest where and how they should be resolved. This report provides an assessment of the changing mission of DOD and environment in which it must operate, an identification of high-level opportunities for MS&A research to address the expanded mission, approaches for improving the interface between MS&A practitioners and decision makers, a discussion of training and continuing education of MS&A practitioners, and an examination of the need for coordinated military science research to support MS&A. Table of ContentsFront MatterExecutive Summary1 Introduction2 The Changing Landscape3 New Challenges and Directions for MS&amp;A4 MS&amp;A and Decision Making5 Education, Training, and Professional Practice in Defense-Related MS&amp;A6 Moving ForwardAppendix A Serious Games and Their Role in Defense Modeling, Simulation, and AnalysisAppendix B Social Behavioral ModelingAppendix C ComposabilityAppendix D Committee Membership BiographiesAppendix E Acronyms

Defense Modeling, Simulation, and Analysis: Meeting the Challenge

History

Committee on Modeling and Simulation for Defense Transformation

Military

The stability of the financial system and the potential for systemic events to alter its function have long been critical issues for central bankers and researchers. Recent events suggest that older models of systemic shocks might no longer capture all of the possible paths of such disturbances or account for the increasing complexity of the financial system. To help assess these concerns, the Federal Reserve Bank of New York and the NRC cosponsored a conference that brought together engineers, scientists, economists, and financial market experts to promote better understanding of systemic risk in a variety of fields. The book presents an examination of tools used in ecology and engineering to study systemic collapse in those areas; a review of current trends in economic research on systemic risk, the payments system, and the market of interbank funds; and for context, descriptions of how systemic risk in the financial system affects trading activities. Table of ContentsFront Matter1 Introduction2 Current Trends in Economic Research on Systemic Risk3 Systemic Risk in Ecology and Engineering4 The Payments System and the Market for Interbank Funds5 Concluding ObservationsAppendixesAppendix A: Conference ProgramAppendix B: Background PaperAppendix C: About the Rapporteurs

New Directions for Understanding Systemic Risk: A Report on a Conference Cosponsored by the Federal Reserve Bank of New York and the National Academy of Sciences

Business & Money

Economics

Great advances have been made in our understanding of the climate system over the past few decades, and remotely sensed data have played a key role in supporting many of these advances. Improvements in satellites and in computational and data-handling techniques have yielded high quality, readily accessible data. However, rapid increases in data volume have also led to large and complex datasets that pose significant challenges in data analysis. Uncertainty characterization is needed for every satellite mission and scientists continue to be challenged by the need to reduce the uncertainty in remotely sensed climate records and projections. The approaches currently used to quantify the uncertainty in remotely sensed data lack an overall mathematically based framework. An additional challenge is characterizing uncertainty in ways that are useful to a broad spectrum of end-users.  In December 2008, the National Academies held a workshop, summarized in this volume, to survey how statisticians, climate scientists, and remote sensing experts might address the challenges of uncertainty management in remote sensing of climate data. The workshop emphasized raising and discussing issues that could be studied more intently by individual researchers or teams of researchers, and setting the stage for possible future collaborative activities. Table of ContentsFront Matter1 Introduction2 Cross-Cutting Issues3 Concluding ThoughtsReferencesAppendix A: Workshop AgendaAppendix B: Summaries of Workshop PresentationsAppendix C: Planning Committee andRapporteur Biographies

Uncertainty Management in Remote Sensing of Climate Data: Summary of a Workshop

Division on Earth and Life Studies

Space Studies Board

Board on Atmospheric Sciences and Climate

Climate Research Committee

Committee on Applied and Theoretical Statistics

Committee on Earth Studies

Earth Sciences

The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries. Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment. Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences. Table of Contents <ul>
<li>Front Matter</li>
<li>Introduction</li>
<li>Compressed Sensing / Through the Kaleidoscope</li>
<li>Eigenvectors / From the Mathematical Sciences to . . . an IPO</li>
<li>Mathematical Simulations / When the Lab Isn't Big Enough</li>
<li>Bayesian Inference / Not an Enigma Anymore</li>
<li>Diffusion Tensor Imaging / A New View of the Brain</li>
<li>Fast Multipole Method / A Long-Term Payoff</li>
<li>Cellular Automata / Sublimely Complex</li>
<li>Graph Spectra / Sparsest Cuts in Minimum Time</li>
<li>Bioinformatics / Interpreting the Human Genome</li>
<li>Geometry and Physics / Endlessly Intertwined</li>
<li>Probability and Statistical Physics / Connecting Microscopic and Macroscopic</li>
</ul>

Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century

Humor & Entertainment

Committee on the Mathematical Sciences in 2025

Puzzles & Games

Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners. Table of Contents <ul>
<li>Front Matter</li>
<li>Summary</li>
<li>1 Introduction</li>
<li>2 Sources of Uncertainty and Error</li>
<li>3 Verification</li>
<li>4 Emulation, Reduced-Order Modeling, and Forward Propagation</li>
<li>5 Model Validation and Prediction</li>
<li>6 Making Decisions</li>
<li>7 Next Steps in Practice, Research, and Education for Verification, Validation, and Uncertainty Quantification</li>
<li>Appendixes</li>
<li>Appendix A: Glossary</li>
<li>Appendix B: Agendas of Committee Meetings</li>
<li>Appendix C: Committee Biographies</li>
<li>Appendix D: Acronyms</li>
</ul>

Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification

Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification

Research

The United States is in the midst of a major demographic shift. In the coming decades, people aged 65 and over will make up an increasingly large percentage of the population: The ratio of people aged 65+ to people aged 20-64 will rise by 80%. This shift is happening for two reasons: people are living longer, and many couples are choosing to have fewer children and to have those children somewhat later in life. The resulting demographic shift will present the nation with economic challenges, both to absorb the costs and to leverage the benefits of an aging population. Aging and the Macroeconomy: Long-Term Implications of an Older Population presents the fundamental factors driving the aging of the U.S. population, as well as its societal implications and likely long-term macroeconomic effects in a global context. The report finds that, while population aging does not pose an insurmountable challenge to the nation, it is imperative that sensible policies are implemented soon to allow companies and households to respond. It offers four practical approaches for preparing resources to support the future consumption of households and for adapting to the new economic landscape. Table of Contents <ul>
<li>Front Matter</li>
<li>Summary</li>
<li>1 Introduction</li>
<li>2 Overview</li>
<li>3 Demographic Trends</li>
<li>4 Health and Disability in the Working-Age and Elderly Populations</li>
<li>5 Labor Force Participation and Retirement</li>
<li>6 Aging, Productivity, and Innovation</li>
<li>7 Saving and Retirement Security</li>
<li>8 Capital Markets and Rates of Return</li>
<li>9 The Outlook for Fiscal Policy</li>
<li>10 Research Recommendations</li>
<li>References</li>
<li>Appendixes</li>
<li>Appendix A: Population and Related Projections Made by the Committee</li>
<li>Appendix B: Biographical Sketches of Committee Members</li>
</ul>

Aging and the Macroeconomy: Long-Term Implications of an Older Population

Division of Behavioral and Social Sciences and Education

Committee on Population

Robert Pool

Committee on the Long-Run Macro-Economic Effects of the Aging U.S. Population

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