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1 Introduction
Pages 15-26

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From page 15...
... Too many mathematical scientists remain unaware of the expanding role for their field, and this in turn will limit the community's ability to produce broadly trained students and to attract larger numbers of students. A community-wide effort to rethink the mathematical sciences curriculum at universities is needed.
From page 16...
... Details of federal funding are given in Appendix C While the mathematical sciences community and its sponsors regularly hold meetings and workshops to explore emerging research areas and assess progress in more mature areas, there has been no comprehensive strategic study of the discipline since the so-called Odom study1 in the late 1990s.
From page 17...
... This was done so the report would not veer into advocacy and also so it would be steered by someone with a broad view of how the mathematical sciences fit within broader academic and research endeavors. The breadth of the current committee -- only half of the members sit in academic departments of mathematics or statistics -- enabled the study to assess the actual and potential effects of the mathematical sciences on the broader science and engineering enterprise.
From page 18...
... Similar questions were discussed with several dozen community members at open sessions the committee held at the Joint Mathematics Meetings in New Orleans, January 2011; the International Congress of Industrial and ­ ­ A ­ pplied Mathematics in Vancouver, July 2011; and the Joint Statistical Meetings in Miami, August 2011. In addition, helpful discussions were held in March 2011 with the AMS Committee on Science Policy, in April 2011 with the SIAM Science Policy Committee, and in October 2011 and April 2012 with the Joint Policy Board for Mathematics.
From page 19...
... Such work -- for example, the compressed sensing research highlighted in Chapter 2 -- usually goes far beyond routine application of an existing idea, tending to be instead very innovative and deep. A large fraction of mathematical science work is not motivated by external applications, and the reader who focused only on applications would be misled about something central to the culture of the mathematical sciences: the importance of discovery for its own sake and the quest for internal coherence, both common drivers of research.
From page 20...
... A strong core in the mathematical sciences -- consisting of basic concepts, results, and continuing exploration that can be applied in diverse ways -- is essential to the overall enterprise because it serves as a common basis linking the full range of mathematical scientists. Researchers in farflung specialties can find common language and link their work back to common principles.
From page 21...
... That is, important applications are the rule rather than the exception.4 Over and over, research that was internally motivated has become the foundation for applied work and underlies new technologies and start-ups. And often questions that arise because of our inability to mathematically represent important phenomena from applications prompt mathematical scientists to delve back into fundamental questions and create additional scaffolding of value both to the core and to future applications.
From page 22...
... Whether they know it or not, their lives depend intimately and deeply on the mathematical sciences; they are wrapped in an intricate and elegant net woven with strands from the mathematical sciences. Here are some examples.
From page 23...
... • Alice's office building consumes energy to run electric lights, tele phone landlines, a local computer network, running water, heating, and cooling. Mathematical optimization and statistical techniques are used to plan for efficient energy delivery based on information about expected energy consumption and estimated safety factors to protect against unusual events such as power outages.
From page 24...
... • When Alice and Bob order products online, the processes used for inventory management and control, delivery scheduling, and pricing involve ingredients from the mathematical sciences such as random matrices, scheduling and optimization algorithms, decision theory, statistical regression, and machine learning. • If Alice or Bob borrows money for a house, car, education, or to pay off a credit card or invest savings in stocks, bonds, real estate, mutual funds, or their 401(k)
From page 25...
... Mathematical scientists can change course during their careers. Because the mathematical sciences deal with methods and general principles, researchers need not maintain the same focus for their entire careers.
From page 26...
... Chapter 5 discusses the pipeline that prepares people for mathematical science careers, while Chapter 6 discusses the ramifications of emerging changes in the academic environment.


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