U.S. Research Institutes in the Mathematical Sciences


Book Description

This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: 1. What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? 2. What kinds of institutes should there be in the United States, and how many does the nation need? 3. How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?




U.S. Research Institutes in the Mathematical Sciences


Book Description

This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? What kinds of institutes should there be in the United States, and how many does the nation need? How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?







Braid Foliations in Low-Dimensional Topology


Book Description

Offers a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centres around a key theorem or theorems.




The Mathematical Sciences in 2025


Book Description

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


Book Description




Educating Mathematical Scientists


Book Description

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.




Strengthening the Linkages Between the Sciences and the Mathematical Sciences


Book Description

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.




Experiments in International Benchmarking of US Research Fields


Book Description

How can the federal government gauge the overall health of scientific researchâ€"as a whole and in its partsâ€"and determine whether national funding adequately supports national research objectives? It is feasible to monitor US performance with field-by-field peer assessments. This might be done through the establishment of independent panels consisting of researchers who work in a field, individuals who work in closely related fields, and research "users" who follow the field closely. Some of these individuals should be outstanding foreign scientists in the field being examined. This technique of comparative international assessments is also known as international benchmarking. Experiments in International Benchmarking of U.S. Research Fields evaluates the feasibility and utility of the benchmarking technique. In order to do this, the report internationally benchmarks three fields: mathematics, immunology, and materials science and engineering, then summarizes the results of these experiments.