The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.
The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.
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.
Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance. To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration.
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.
Over the next decade, the mathematical community and the nation's colleges and unversities must restructure fundamentally the culture, content, and context of undergraduate mathematics. Acknowledging the weaknesses in the present college mathematics curriculum and the ways in which it is taught, this book cites exemplary programs that point the way toward achieving the same world-wide preeminence for mathematics education that the United States enjoys in mathematical research. Moving Beyond Myths sets forth ambitious goals for collegiate mathematics by the year 2000 and provides a sweeping plan of action to accomplish them. It calls on mathematics faculty, their departments, their professional societies, colleges and universities, and government agencies to do their parts to implement the plan, help the public move beyond commonly held myths about mathematics, and bring about a revitalization of undergraduate mathematics.
The goal of this book is to determine what makes certain doctoral/postdoctoral programs in mathematical sciences successful in producing large numbers of domestic Ph.D.s, including women and underrepresented minorities with sufficient professional experience and versatility to meet the research, teaching, and industrial needs of our technology-based society. Educating Mathematical Scientists describes the characteristics of successful doctoral/postdoctoral programs, based on the diverse set of 10 universities at which site visits were made.
As requested by the National Science Foundation (NSF) and the Interagency Committee for Extramural Mathematics Programs (ICEMAP), this report updates the 1984 Report known as the "David Report." Specifically, the charge directed the committee to (1) update that report, describing the infrastructure and support for U.S. mathematical sciences research; (2) assess trends and progress over the intervening five years against the recommendations of the 1984 Report; (3) briefly assess the field scientifically and identify significant opportunities for research, including cross-disciplinary collaboration; and (4) make appropriate recommendations designed to ensure that U.S. mathematical sciences research will meet national needs in coming years. Of the several components of the mathematical sciences community requiring action, its wellspring--university research departments--is the primary focus of this report. The progress and promise of research--described in the 1984 Report relative to theoretical development, new applications, and the refining and deepening of old applications--have if anything increased since 1984, making mathematics research ever more valuable to other sciences and technology. Although some progress has been made since 1984 in the support for mathematical sciences research, the goals set in the 1984 Report have not been achieved. Practically all of the increase in funding has gone into building the infractructure, which had deteriorated badly by 1984. While graduate and postdoctoral research, computer facilities, and new institutes have benefited from increased resources, some of these areas are still undersupported by the standards of other sciences. And in the area of research support for individual investigators, almost no progress has been made. A critical storage of qualified mathematical sciences researchers still looms, held at bay for the moment by a large influx of foreign researchers, an uncertain solution in the longer term. While government has responded substantially to the 1984 Report's recommendations, particularly in the support of infrastructure, the universities generally have not, so that the academic foundations of the mathematical sciences research enterprise are as shaky now as in 1984. The greatet progress has been made in the mathematics sciences community, whose members have shown a growing awareness of the problems confronting their discipline and increased interest in dealing with the problems, particularly in regard to communication with the public and government agencies and involvement in education. (AA)
This book reviews the evaluation research literature that has accumulated around 19 K-12 mathematics curricula and breaks new ground in framing an ambitious and rigorous approach to curriculum evaluation that has relevance beyond mathematics. The committee that produced this book consisted of mathematicians, mathematics educators, and methodologists who began with the following charge: Evaluate the quality of the evaluations of the thirteen National Science Foundation (NSF)-supported and six commercially generated mathematics curriculum materials; Determine whether the available data are sufficient for evaluating the efficacy of these materials, and if not; Develop recommendations about the design of a project that could result in the generation of more reliable and valid data for evaluating such materials. The committee collected, reviewed, and classified almost 700 studies, solicited expert testimony during two workshops, developed an evaluation framework, established dimensions/criteria for three methodologies (content analyses, comparative studies, and case studies), drew conclusions on the corpus of studies, and made recommendations for future research.
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