The Mathematical Sciences: A Report (1968) / Chapter Skim
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Pages 13-42
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From page 13... ...
They utilize the ideas and techniques of core mathematics and the methods and results of physical mathematics, statistics, and other applied mathematical sciences. Most of these technologies depend, often in a crucial way, on effective use of electronic computers.
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From page 14... ...
Our recommendations, to be stated and discussed below, fall under six main heads: Improvement in the quality of education in the mathematical sciences at the undergraduate level through expanded federal support, especially at key points. There is a growing shortage calf college teachers in the mathematical sciences.
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From page 15... ...
1. We recommend that, as a national policy, federal support for basic research and research apprenticeship in the mathematical sciences and in each of their major subdivisions including the areas of core mathematics-continue to grow in proportion to the number of appropriately qualif ed investigators and graduate students.
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From page 16... ...
The ratio of the national investment in basic research to the investment in fields of application is so small, and the benefits from basic research so large, that the goal of programs for the support of basic mathematical research, in core mathematics and in the applied mathematical sciences, should be limited only by the availability of high-quality investigators. We estimate that at present about one out of every six PhD's in the mathematical sciences is consistently active in research.
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From page 17... ...
Despite the large sums available to finance computing service on campus, the money available for research in computer science has been, with the exception of a few spectacular projects, seriously inadequate. ~# The role of computers in higher education across the board has recently been studied in the Pierce reports of the President's Sci
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From page 18... ...
. DISCUSSION There is a significant distinction between such applied mathematical sciences as physical mathematics and the mathematics underlying operations research and such partly mathematical sciences as statistics and computer science.
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From page 19... ...
Support of such work for its own sake is now clearly justified and need not interfere with other work in these areas supported because of its more immediate usefulness. Sources of Support The major federal support of research and higher education in the mathematical sciences comes from a variety of agencies, the most important being the National Science Foundation and certain of the mission-oriented agencies, as indicated in more detail in Chapters 10 and 11.
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From page 20... ...
6. We recommend that mission-oriented agencies that expect to derive significant benefits from the use of mathematical sciences continue and expand their partnership with the community of mathematicians by: (:aJ participating in the sponsorship, not only of research that promises predictable returns in applications, but also of basic investigations that enlarge the intellectual foundations of the field, and (bJ evolving organized plans for bringing their unsolved scientific problems to the attention of the mathematical-sciences community and for provid ing the opportunity to qualified research mathematicians to further, at times and in the depth of their choosing,, the mathematization of major realms of scientific and technical eff ort of national concern.
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From page 21... ...
This support should increase at rates that will enable these agencies to share responsibly in maintaining at least the natural growth rate and that provide for higher rates of expansion in areas with long-term relevance to the agency's mission. DISCUSSION At issue here for the most part is basic research, conducted at universities, government laboratories, and industrial establishments in the areas of applied mathematics and statistics, computer science, and operations research and management science.
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From page 22... ...
~ik ~ We believe, however, that project grants and contracts are not always best suited for fulfilling several necessary tasks: assisting departments of quality and promise to become truly outstanding, developing new centers of leadership in the applied mathematical sciences, and providing centers of research and graduate education in geographical regions so far deprived of them. # This committee is aware that authoritative voices have proposed very radical revisions of the whole federal system for supporting academic research and university education, abandoning the present forms of support in favor of direct federal subsidy to universities.
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From page 23... ...
In the mathematical sciences these have usually tended to be better suited to the needs of computing, statistics, and traditional applied mathematics than to those of core mathematics. The departmental grants should extend such opportunities to core mathematics, as well as permitting other areas of the mathematical sciences to develop their identities and programs.
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From page 24... ...
Computer science, applied mathematics, and statistics support a higher than average proportion of their students through research assistantships. Core mathematics, on the other hand, employs a higher proportion of graduate students as teaching assistants; 38
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From page 25... ...
We deplore the fact, however, that at present some graduate students teach throughout their graduate careers, while others do no teaching at all. We suggest that universities, in cooperation with relevant government agencies, strive toward a system in which every graduate student acquires teaching experience during some years In graduate school (whether by teaching a section, leading recitation groups, or doing informal instruction)
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From page 26... ...
DISCUSSION A much smaller proportion of women than of men go beyond the master's degree to the PhD degree in the mathematical sciences. Because of social pressures and family obligations, it is generally much harder for a woman than for a man to qualify for support, which usually demands full-time graduate study.
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From page 27... ...
We recommend that graduate departments in the mathematical sciences be encouraged to make special efforts to admit talented college graduates with weak or inadequate preparation in the mathematical sciences and to provide suitable educational programs f or such stud en is af ter their ad mission. DISCUSSION The faculties of many colleges are too small or too poorly prepared to offer their students adequate preparation for modern graduate work in the mathematical sciences.
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From page 28... ...
For the mathematical sciences these challenges have been underlined by an extraordinary growth in the number of student majors, by rapid and extensive developments in subject matter, and by increases in numbers of majors in other fields who elect courses in the mathematical sciences, sometimes for cultural reasons but more often for their usefulness in those other fields (see discussions of The Increase in Mathematical Majors, page 122; Total Enrollments in the Mathematical Sciences, page 124; and The College Teacher, page 147~. If these challenges are even partially to be met, it is imperative that, along with educating new college teachers of the mathematical sciences, special efforts be made to upgrade and update present college faculties, with special emphasis on current developments in the mathematical sciences and their penetration into new areas of application.
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From page 29... ...
See the discussion of The College Teacher on page 147, references 4 and 5, and the reports of our Panel on Undergraduate Education. Undergraduate Education in AbLlied Mathematical Sciences 1 1 Applied mathematics as a science and an art with its own objectives, attitudes, and skills has lagged badly.
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From page 30... ...
an undergraduate program offering an additional route to graduate study in any of the particular, more specialized mathematical sciences or in the partly mathematical sciences. At present, in many universities and colleges, students receive an excellent preparation for graduate work in core mathematics, but a traditional mathematics major program may not be the only way or the best way of attracting and motivating an undergraduate for further work in the partly mathematical sciences.
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From page 31... ...
Mathematical Sciences in Government Research and Development Establishments Examples from major industries, notably the Bell Telephone Laboratories and the Boeing Aircraft Company, have shown how the imaginative employment of mathematical techniques contributes to the development of new capabilities based on sophisticated technology. In the early 1950's, the Mathematics Division of the National Bureau of Standards very effectively served this role
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From page 32... ...
IMPLICATIONS FOR PROGRAM AND RESOURCES PLANNING Most of the recommendations of the previous sections make budgeting and policy demands on the conduct of the federally sponsored research and advanced education programs in the mathematical sciences. Relevant information and data have been developed
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From page 33... ...
No long-term rates of growth have been projected for this remainder item; its future level will be established by the needs and opportunities as they are identified by the individual agencies. Returning to the allocation of $45 million to basic research in 1966, we have estimated that about $35 million of this went for the support of academic research, leaving a remainder of roughly $10 million for the conduct of basic mathematical-sciences research under programs administered at the local level by the major federally sponsored research and development centers.
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From page 34... ...
The funding of applied research in the mathematical sciences by the mission-oriented agencies of the federal government; (c) Manpower demands in certain of the applied mathematical sciences, especially computer science and those intervening in the field of operations research.
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From page 35... ...
call for an expansion in the support of basic academic research and research apprenticeship in the mathematical sciences at least at a rate that will not interpose economic barriers to the achievement of competence in research and research education. In the absence of much of the necessary information, only relatively crude planning factors can be established.
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From page 36... ...
, a total of 4,800 will have to be accommodated by fellowship and traineeship programs if one third of them are to be given research apprenticeship support, in accordance with Recommendation 11. The corresponding figure for 1966 is 1,834, and the at least 4 percent per year increase in cost of research also affects the rate per research apprentice in these programs.
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From page 37... ...
In addition to the need for a basic policy that maintains the present momentum of research and research apprenticeship in the mathematical sciences across the board, our recommendations recognize certain critical areas in which more than ordinary efforts are needed if the mathematical-sciences community is to render the required services in today's social fabric. These are Recommendations 2, 3, and 4 relating to the support of research and research education in computer science and in the applied mathematical sciences as such.
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From page 38... ...
If, however, the doubling time of the number of eligible departments should be two years, rather than the three years estimated above, these projections would represent gross underestimates for the latter years. In contrast, the support of a few research and research training programs of exceptional quality in the applied mathematical sciences for their own sake will be of low cost.
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From page 39... ...
The program of special fellowships or forgivable loans to promising students, emerging from colleges with inadequate departments in the mathematical sciences, would be gauged to make 200 awards per year at a total program cost of $1 million. The development, finally, of undergraduate programs in the applied mathematical sciences is largely an internal decision of university administrations, which might be expedited only peripherally by the possibility of federal support.
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From page 40... ...
It is proposed that project support remain pre-eminent and, among the various forms of broader support, areas as well as departmental grants be given increased utilization as against interdepartmental and institution-wide grants for the development of quality in the mathematical sciences. Cautionary Remarks The mathematical sciences, perhaps more than any other major discipline of modern science, play a pivotal role in a wide variety of contexts, both in opportunities for application and in requirements of education.
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From page 41... ...
Each of the contexts for implementation of these programs has its own scale of benefits relative to which the programs must be weighed. Since a number of these programs will be funded by agencies that share in their implementation as parts of other, broader activities, often of a more applied nature, a good deal of support calf the mathematical sciences may be termed "implicit." In particular, this implies that the federal government must be alert to the impact on the mathematical sciences of abrupt shifts in criteria for support · · .
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