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E-grāmata: Mathematical Sciences in 2025

  • Formāts: 222 pages
  • Izdošanas datums: 13-May-2013
  • Izdevniecība: National Academies Press
  • Valoda: eng
  • ISBN-13: 9780309284585
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  • Formāts: 222 pages
  • Izdošanas datums: 13-May-2013
  • Izdevniecība: National Academies Press
  • Valoda: eng
  • ISBN-13: 9780309284585
Citas grāmatas par šo tēmu:

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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.
Summary 1(14)
1 Introduction
15(12)
Study Overview
15(4)
Nature of the Mathematical Sciences
19(2)
Everyone Should Care About the Mathematical Sciences
21(4)
Structure of the Report
25(2)
2 Vitality Of The Mathematical Sciences
27(31)
The Topology of Three-Dimensional Spaces
28(4)
Uncertainty Quantification
32(1)
The Mathematical Sciences and Social Networks
33(2)
The Protein-Folding Problem
35(2)
The Fundamental Lemma
37(2)
Primes in Arithmetic Progression
39(1)
Hierarchical Modeling
40(2)
Algorithms and Complexity
42(2)
Inverse Problems: Visibility and Invisibility
44(2)
The Interplay of Geometry and Theoretical Physics
46(4)
New Frontiers in Statistical Inference
50(3)
Economics and Business: Mechanism Design
53(1)
Mathematical Sciences and Medicine
54(1)
Compressed Sensing
55(3)
3 Connections Between The Mathematical Sciences And Other Fields
58(35)
Introduction
58(1)
Broadening the Definition of the Mathematical Sciences
59(7)
Implications of the Broadening of the Mathematical Sciences
66(5)
Two Major Drivers of Expansion: Computation and Big Data
71(11)
Contributions of Mathematical Sciences to Science and Engineering
82(1)
Contributions of Mathematical Sciences to Industry
82(5)
Contributions of Mathematical Sciences to National Security
87(6)
4 Important Trends In The Mathematical Sciences
93(23)
Increasing Importance of Connections for Mathematical Sciences Research
93(6)
Innovation in Modes for Scholarly Interactions and Professional Growth
99(7)
The Mathematical Sciences Should More Thoroughly Embrace Computing
106(1)
Funding Implications of Increasing Connectivity of the Mathematical Sciences
107(3)
A Vision for 2025
110(6)
5 People In The Mathematical Sciences Enterprise
116(29)
Introduction
116(1)
Changing Demand for the Mathematical Sciences
117(7)
The Typical Educational Path in the Mathematical Sciences Needs Adjustments
124(4)
Attracting More Women and Underrepresented Minorities to the Mathematical Sciences
128(9)
The Critical Role of K-12 Mathematics and Statistics Education
137(3)
Enrichment for Precollege Students with Clear Talent in Mathematics and Statistics
140(5)
6 The Changing Academic Context
145(10)
APPENDIXES
A Past Strategic Studies
155(4)
B Meeting Agendas and Other Inputs to the Study
159(4)
C Basic Data about the U.S. Mathematical Sciences
163(12)
D Examples of the Mathematical Sciences Support of Science and Engineering
175(15)
E Illustrative Programs Aimed at Increasing Participation in the Mathematical Sciences by Women and Underrepresented Minorities
190(7)
F Biographical Sketches of Committee Members and Staff
197