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11
Federal Support of Education
In this chapter we survey federal support of higher education in
the mathematical sciences, considering separately graduate educa-
tion, postdoctoral research education, and the continuing education
of college teachers. Under this last heading we also note briefly the
National Science Foundation's support of certain other activities
designed to improve undergraduate education, notably the valuable
studies and conferences of the CUPM. As observed in the introduc-
tory paragraphs of Part III, our report does not concern itself
directly with the extensive activities in support of curriculum re-
vision and continuing teacher training for the elementary and
secondary school levels.
GRADUATE EDUCATION
Where graduate students are concerned, federal support of research
merges directly into support of education. In fact, one form of
graduate-student support, research assistantships, has already been
noted above in our discussion of project grants. More important,
the intellectual activities central to research and advanced graduate
education are literally inseparable, a point that has also been
emphasized in the preceding chapter.
The CBMS survey found that in academic year 1965-1966 some
750 research assistants were supported on project grants in the
mathematical sciences. We observe that, since some 900 senior
mathematical scientists (associate and full professors) were on
179

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180
[eve! and Forms of Support
federal research grants for the summer of 1966, this gives an average
ratio of less than one research assistant to each senior research
grantee. We feel that the research assistantship is a valuable form
of graduate-student support, especially because of the local control
and flexibility in the appointment of research assistants. As a goal
for the immediate future, an average ratio of one research assistant
to each senior research grantee would seem reasonable, with the
ratio continuing to be highest in such mathematical sciences as
computer science and statistics, as is the case now.
Apart from research assistantships, federal support of graduate
students assumes two principal forms: fellowships and traineeships.
With the exception of fellowships awarded under the National
Defense Education Act (NDEA), fellowships are awarded by the
granting agencies directly to students. Traineeships and NDEA
fellowships are awarded in blocks to institutions, which in turn
award them to students. For fiscal 1966 the CBMS survey found that
some 1,200 graduate students in the mathematical sciences were
supported on federal fellowships and some 630 on federal trainee-
ships. The total magnitude of this support was slightly over $10
million, as shown in Table 15.
TABLE 1 5 Federal Fellowships and Traineeships in the Mathe-
matical Sciences for Fiscal Year 1966
FORM OF SUPPORT
$ MILLIONS
NSF predoctoral fellowships
NDEA graduate fellowships
Other federal fellowships
. .
NSF trainees. llpS
Other federal traineeships
SF summer fellowships for teaching assistants
TOTAL
3.
3.1
a.:
To
1.6
0.2
0.2
Altogether, federal fellowships, traineeships, and research as-
sistantships supported about 28 percent of the approximately 9,400
full-time mathematical-science graduate students in U.S. universities
in academic year 1965-1966, as Table 16 shows in more detail.
As noted in the preceding section, we feel that it is federal sup-
port of graduate students together with federal project-grant sup

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Federal Support of Education
181
TABLE 16 Sources of Support of Graduate Students in the Mathe-
matical Sciences in Academic Year 1965-1966
NUMBER
SOURCE OF SUPPORT
PERCENTAGE
SUPPORTED SUPPORTED
Federal fellowships1,203 13
Federal traineeships632 7
Federal research assistantships;~4 8
Private fellowships366 4
Teaching assistantships3,625 38
Self-supporting2,782 30
~iOTALS9,362 100
port that has been decisive in the rise of the United States to a pos~-
tion of world pre-eminence in the mathematical sciences, and that
these forms of support will be decisive for the maintenance of this
U.S. position in the future. Furthermore, in the face of the inten-
sibed shortage of qualified college teachers of the mathematical
sciences discussed in Chapter 7, we are especially concerned that
federal fellowship and traineeship programs at least keep pace with,
and support, the projected 10 percent per year growth in mathe-
matical-science PhD production. Thus we would recommend that
federal fellowships and traineeships combined continue to support,
as Table 16 shows they did in academic year 1965-1966, about 20
percent of the expanding full-time graduate-student population in
the mathematical sciences (see Chapter 2, Recommendation 11~.
In accordance with recommendations of our Panel on Under-
graduate Education, we also propose two special-purpose programs
for support of graduate students in the mathematical sciences.
Their aim is to broaden and improve opportunities for graduate
study by women and by graduates of weaker or less well-known
colleges.
The first of these programs, for women, is designed to offset to
some degree the dropout rate of women between receipt of the
BA and PhD degrees, a rate which postwar figures suggest is perhaps
six times as high as the rate for men. The program recognizes that
a woman's graduate study may have to be part time or may have to
involve retraining after several years' absence. The specific recom-
mendation to federal funding agencies is for 100 special part-time
graduate fellowships for women. Accompanying this is a recommen

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182
Level and Forms of Support
cation to academic institutions to provide more opportunities for
part-time employment of women and in particular to remove
nepotism rules that prohibit or restrict teaching in the same insti-
tution by husband and wife.
The second of these programs, for graduates of weaker or less
well-known colleges, is designed to afford such students the oppor-
tunity to prove themselves in their early graduate years and to
encourage them, if successful, to enter college teaching. The pro-
gram recognizes that such students represent a "higher risk" and
that they may require extra preparatory courses prior to full grad-
uate work. The proposal calls for tuition scholarships, perhaps 200
a year, supplemented by "forgivable loans" to cover the initial years
in graduate school, with a portion of the loan, perhaps 20 percent,
to be forgiven for each year the student subsequently spends in
college teaching.
More details concerning these two special proposals and the
problems they are designed to meet are given in the Report of our
Panel on Undergraduate Education, Chapters 1 and 5.
POSTDOCTORAL RESEARCH EDUCATION
A limited number of research mathematical scientists are supported
under various federal postdoctoral fellowship programs. The CAMS
survey found that during academic year 1965-1966 approximately
100 U.S. mathematical scientists were in residence at U.S. univer-
sities under postdoctoral fellowships and research instructorships.
About one third of these were holding awards under the National
Science Foundation's regular and senior postdoctoral fellowship
programs. Such awards have remained fairly steady in number over
recent years, as Table 17 shows.
We feel that, especially for the young research investigator, more
such support is needed. In all sciences, and certainly in the mathe-
matical ones, the immediate postdoctoral years are crucial for
firmly launching young PhD's on research careers. At the same
# Added in proof: Owing to lack of funds, the National Science Foundation has
entirely suspended for academic year 1968-1969 its program of senior postdoctoral
fellowships. See Fellowships and Research O pportunities in the Mathematical
Sciences, Division of Mathematical Sciences, National Research Council, Septem-
ber 1968, p. 3.

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Federal Support of Education
~3
TABLE 17 National Science Foundation Regular and Senior Post-
doctoral Fellowships in the Mathematical Sciences
REGULAR
SENIOR
FISCAL YEAR POSTDOCTORALS POSTDOCTORALS
1962 17 ~
1963 29 5
1964 26 7
1965 21 8
1966 27 7
time many feel that capable young PhD's at academic institutions
should be doing some teaching as well as research during these
years and should be encouraged to seek teaching positions in a
broader range of colleges and universities.
Research instructorships and postdoctoral fellowships are pres-
ently available for no more than 100 young mathematicians each
year; but we feel that by 1969, which is as early as new programs
could be implemented, such opportunities could profitably be
offered to 200 or 300. This would be about 20 to 30 percent of the
1,000 PhD degrees that we may reasonably anticipate will be
awarded in the mathematical sciences in 1969. (Young's PhD
study in the CBMS Survey Report16 suggests that in recent years
only approximately 15 percent of the PhD's in the mathematical sci-
ences have become consistently productive research mathematicians;
it is this percentage that we believe can be improved.) For this
situation we would like to recommend to federal funding agencies
two new programs of teaching fellowships for the immediate post-
doctoral years.
The first proposal, coming from our Panel on Undergraduate
Education, calls for approximately 50 two-year teaching fellowship
awards for young PhD's who would carry out research activities at
a major mathematical center while teaching a course or two at a
nearby smaller college. The purpose is the dual one of helping to
launch young PhD's on academic careers of research and teaching
while encouraging the distribution of such research and teaching
talent to a broader range of colleges.
Another proposal deserving serious study would offer two-year
teaching fellowships for postdoctoral training at regional centers

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184
Level and Forms of Support
located at well-established mathematical centers around the country.
Beyond the objective of further training in research and acquisition
of teaching experience, there would be the hope that, after two
years of working together, small groups of these trained PhD's
might be willing to go together to form research nuclei in a uni-
versity or in a geographical cluster of smaller colleges.
CONTINUING EDUCATION FOR COLLEGE TEACHERS
The report) of our Panel on Undergraduate Education and
Chapter 9 of the present report have emphasized the importance
of keeping college teachers of the mathematical sciences profes-
sionally alive and knowledgeable about new developments.
The principal academic-year program with this objective is the
National Science Foundation Science Faculty Fellowship Program.
Table 18 shows the numbers of mathematical awards under this
program in recent years.
TABLE 1 8 National Science Foundation Science Faculty Fellow-
ships in the Mathematical Sciences
FISCAL YEAR
POSTDOCTORAL PREDOCTORAL
FELLOWSHIPS FELLOWSHIPS
962 18 49
963 19 57
964 23 59
965 16 60
1966 16 73
The Science Faculty Fellowship Program offers an excellent way
to upgrade and update college and university faculty in the mathe-
matical sciences. In view of the continuing and seriously growing
need for such upgrading and updating, this NSF program merits very
considerable expansion. As a minimal objective, the Science Faculty
Fellowship Program should be expanded gradually to provide for
about 150 awards in the mathematical sciences by 1971, roughly
double the number in recent years. Fiscally this would amount to

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Federal Support of Education
1LS5
an expansion from $1 million to perhaps $~.5 million by 1971. Our
Panel on Undergraduate Education has estimated that a program
of this expanded size would offer opportunity for awards to approxi-
mately one quarter of the doctorate faculty and one half of the non-
doctorate faculty at least once in their teaching careers.
Only a very limited number of the more than 10,000 college
teachers of the mathematical sciences can be on leave in any given
academic year to take advantage of fellowship programs. The most
favorable time for training activities for larger numbers of college
teachers is during the summer. The NSF already sponsors limited
programs of such summer activities for college teachers in the form
of summer institutes, research-participation projects, and short
courses, conferences, and seminars. For college mathematical-science
teachers in the summer of 1966 the total magnitude of these pros
grams was approximately $1.4 million, the major item being sum
. . ~ .
mer institutes ot various sorts.
The Mathematical Association of America has urged a greatly
exported program in this direction in a resolution addressed to the
Congress of the United States and the officers of the NSF.4 In addi-
tion, the Association's Committee on Institutes and the Panel on
College Teacher Preparation of CUPM have issued a joint report on
summer institutes5 which says, in part, ". . . a greatly expanded
effort in the direction of summer institutes of all types is urgently
needed . . . Even if summer institutes are to reach only 10 percent
of all college mathematics teachers each summer, the number of
institutes will need to be approximately tripled."
The NSF also supports, at a modest level, certain other activities
designed to improve undergraduate education in the mathematical
sciences. Support of these activities encompassing course content
improvement programs, curriculum conferences, acceleration of
student development, instructional equipment, and visiting scien-
tists amounted in 1966 to approximately $2.7 million. An espe-
cially important item here has been support of the Committee on
the Undergraduate Program in Mathematics. The published cur-
riculum studies and recommendations of CUPM have formed valu-
able guidelines for college curriculum development in the mathe-
matical sciences; these have, in fact, been used extensively by our
Panel on Undergraduate Education in writing its report. We feel
that continued support of CUPM, as well as of the college visiting
lecturer program and these other NsF-funded activities, is justified,

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]:eve! and Forms of Support
and we heartily endorse the resolution of the Mathematical Asso-
ciation of America to this effects
In concluding this section we invite attention to the reports of
our Panel on Undergraduate Eduction, and particularly Chapters
~ and 6 of that report, in which the special problems and needs
of the undergraduate teacher of the mathematical sciences are dis-
cussed in detail.