The Mathematical Sciences: A Report (1968) / Chapter Skim
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8 Graduate Education
8 Graduate Education
Pages 135-146
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From page 135... ...
This has been reflected in increased international recognition of the research accomplishments of Americantrained American mathematicians (see the section on The Position of the United States in Mathematics, page 10~. It would also be widely agreed by professionals in the field that the number of truly distinguished university centers for mathematical research in the United States has roughly tripled during the postwar period, from approximately three to approximately nine (see Appendix E)
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From page 136... ...
Amp `~.=J. alla Grille IS lrUe at tne factors of gain projected for 1965-1975: for mathematics and statistics this is 3.5, while for engineering, the physical sciences, and the biological sciences these projected factors are 2.6, 2.1, and 2.3, respectively.
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From page 137... ...
is required; in some programs a master's thesis is required; and in some departments a master's degree is awarded as a kind of "consolation prize" to those who try and fail to complete the requirements for a doctorate. For the mathematical sciences, about 60 percent of the master's degrees currently being awarded are granted by departments of mathematics that also offer a doctorate, and for these departments the CBMS survey furnishes a bit more information.
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From page 138... ...
At about one fourth of these departments a thesis is definitely required for a master's degree; at about one half there are two alternative master's programs, one involving a thesis and one not; at the others no thesis is required, the requirement tending to consist of course work plus various kinds of comprehensive ex aminations. On the average, about one full year of course work is required for a master's degree in the mathematical sciences, and the median elapsed time from bachelor's to master's degree is between one and two years.
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From page 139... ...
Once of Education,~7 shown in Table 10, do not show any such decisively stronger gains for mathematics and statistics. The factors of gain in these numbers of doctoral degrees for the period 1955-1965 are: mathematics and statistics, 2.8; engineering, 3.6; physical sciences, 1.7; and biological sciences, 1.9.
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From page 140... ...
As noted above in our discussion of the master's degree, even in mathematics departments offering the PhD degree this currently amounts to approximately 63 percent of those studying for graduate degrees; and presumably it includes a much larger percentage of those studying in graduate mathematics departments in which only a master's degree is offered. Another reason may be simply that doing research acceptable for the PhD degree is harder in mathematics than in other fields, leading fewer to try for this degree in mathematics and leading to a higher attrition rate among those who do.
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From page 141... ...
His sense of participation as a contributor to his subject will give him a greater authority and involvement as a teacher. The attainment of a PhD degree is an excellent scheme for making students gain the insight that comes from doing research.
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From page 142... ...
In the face of this situation, the Committee on the Undergraduate Program in Mathematics has discussed and evaluated several lower levels of preparation in its report, Qualifications for a College Faculty in Mathematics.29 It concludes that a teacher with what it calls the "Advanced Graduate Component" has the subject-matter background to teach all the undergraduate mathematics except specialized courses intended for students who are going to be research mathematicians. This Advanced Graduate Component is essentially the present-day training for the PhD degree except for the thesis.
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From page 143... ...
As for the question of formal recognition of the Advanced Graduate Component level of training, there is widespread agreement in the mathematical community that training to this level should be formally recognized in some way beyond the mere award of the master's degree. According to the CBMS survey, about 70 percent of the mathematics departments that grant the PhD degree are of this
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From page 144... ...
The general effectiveness of the mathematical teaching in colleges would be increased if demonstrably competent people without PhD degrees could be retained on faculties instead of being dismissed in order to satisfy technical requirements about the numbers of doctorate holders on faculties. If an intermediate degree at the Advanced Graduate Component level in the mathematical sciences were to be given only by departments that already have strong PhI)
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From page 145... ...
The CBMS survey found that in academic year 1965-1966 universities with PhD programs in the mathematical sciences used large lecture sections in elementary calculus to varying degrees: approximately 55 percent of these universities used no large lecture sections at all; approximately 18 per cent made some use of large lecture sections but for fewer than three fourths of their students; and approximately 27 percent used large lecture sections for three fourths or more of their students. Our Panel on Undergraduate Education has pointed out advantages of large lecture sections, both for the students and for the graduate assistants, and has recommended that more teaching be done in this way (see the section on Methods Used to Relieve the Shortage of Teachers in Chapter 4 of reference 1~.
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From page 146... ...
We feel it is best for a graduate student in the mathematical sciences to acquire this teaching experience during his middle graduate-study years. He should not be burdened with teaching during his initial year of graduate study, when he must adjust to especially demanding and intensive course work; and during his final year of studying for his PhD degree, he may need to devote his full energies to research and thesis writing.
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