Appendix D
The Mathematical Sciences Since 1998

The nature of higher education in the mathematical sciences is not static. Identifying the impact of the National Science Foundations (NSF’s) Grants for the Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) program is made more difficult because this nature continued to evolve during the lifetime of the VIGRE program. This appendix looks briefly at how the field has changed since the VIGRE program began.

Federal funding in mathematics, both by the National Science Foundation and by federal agencies in general, continued to grow from 1999 through 2005, the most recent year for which data are available. The NSF’s share of federal funding to academic institutions has oscillated, as shown in Table D-1, but it remains the dominant source of funding for the mathematical sciences.

Although the overall amount of federal funding has grown, NSF’s fraction of the total federal obligations to institutions is similar during the VIGRE period and the period prior to the program (see Figure D-1). Note that the NSF’s responsibility for graduate student support has gone up from the pre-VIGRE period to the VIGRE period (VIGRE was established in 1998), as shown in the figure.

The average percentage of support provided by NSF to full-time graduate students in mathematics and statistics at doctorate-granting institutions from 1980 to 1998 was 34 percent of all federal funding. During the 1999 to 2006 period it was 55 percent.

Considering the mechanisms of support that NSF uses with respect to graduate students, there is some growing reliance on teaching assistantships. Comparing Table D-2 with Table 2-3 in Chapter 2, one sees that the percentage of graduate students supported by NSF research assistantships has declined somewhat in the years since the establishment of the VIGRE program, while the fraction of students supported by NSF-sponsored teaching assistantships has increased. Of course, most teaching assistantships are provided by universities, so looking at NSF support gives only a partial picture.

Turning from funding to an assessment of the number of students in mathematics and statistics, the committee is pleased to see that the number of full-time graduate students has grown during the VIGRE period, after falling somewhat from 1992 to 1998, and that the number of students is now higher than at any time since 1980. Figure D-2 shows the reversal.



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Appendix D The Mathematical Sciences Since 1998 The nature of higher education in the mathematical sciences is not static. Identifying the impact of the National Science Foundations (NSF’s) Grants for the Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) program is made more difficult because this nature continued to evolve during the lifetime of the VIGRE program. This appendix looks briefly at how the field has changed since the VIGRE program began. Federal funding in mathematics, both by the National Science Foundation and by federal agencies in general, continued to grow from 1999 through 2005, the most recent year for which data are available. The NSF’s share of federal funding to academic institutions has oscillated, as shown in Table D-1, but it remains the dominant source of funding for the mathematical sciences. Although the overall amount of federal funding has grown, NSF’s fraction of the total federal obligations to institutions is similar during the VIGRE period and the period prior to the program (see Figure D-1). Note that the NSF’s responsibility for graduate student support has gone up from the pre- VIGRE period to the VIGRE period (VIGRE was established in 1998), as shown in the figure. The average percentage of support provided by NSF to full-time graduate students in mathematics and statistics at doctorate-granting institutions from 1980 to 1998 was 34 percent of all federal funding. During the 1999 to 2006 period it was 55 percent. Considering the mechanisms of support that NSF uses with respect to graduate students, there is some growing reliance on teaching assistantships. Comparing Table D-2 with Table 2-3 in Chapter 2, one sees that the percentage of graduate students supported by NSF research assistantships has declined somewhat in the years since the establishment of the VIGRE program, while the fraction of students supported by NSF-sponsored teaching assistantships has increased. Of course, most teaching assistant - ships are provided by universities, so looking at NSF support gives only a partial picture. Turning from funding to an assessment of the number of students in mathematics and statistics, the committee is pleased to see that the number of full-time graduate students has grown during the VIGRE period, after falling somewhat from 1992 to 1998, and that the number of students is now higher than at any time since 1980. Figure D-2 shows the reversal. 0

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06 EVALUATION OF NSF’S VIGRE PROGRAM TABLE D-1 National Science Foundation (NSF) Share of Federal Funding to Universities and Colleges for Research in the Mathematical Sciences, 1999-2005 (in thousands of dollars) Year NSF Share Total Percent 1999 84,975 131,264 65 2000 99,625 211,490 47 2001 105,251 169,702 62 2002 142,298 200,758 71 2003 162,546 230,156 71 2004 184,037 322,989 57 2005 185,390 365,756 51 NOTE: Data are collected by NSF from NSF’s “Survey of Federal Funds for Research and Development.” Data contained in the survey are provided by agencies. SOURCE: National Science Foundation-National Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. FIGURE D-1 National Science Foundation support to full-time graduate students in mathematics and statistics at doctorate-granting institutions as a percentage of federal support, 1980-2006. SOURCE: National Science Figure D-1.eps Foundation-National Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via bitmap image WebCASPAR, http://webcaspar.nsf.gov. Data from the American Mathematical Society also show a rise in graduate students over the more recent period, as shown in Figure D-3. As Figure D-4 shows, the percentage of graduate students in mathematics and statistics who are U.S. citizens or permanent residents has unfortunately not rebounded, although more and more graduate students fall into this category from 2000 to 2006. The percentage of female graduate students, which had been rising between 1980 and 1998, appears to have leveled off. The same is true for underrepresented minorities. This is of concern, and additional research could be directed toward a deeper understanding of changes in the composition of the graduate student body in the mathematical sciences.

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0 APPENDIX D TABLE D-2 Percentage of National Science Foundation Support for Full-Time Graduate Students in Mathematics and Statistics, 1999-2006, by Mechanism of Support Research Teaching Other Mechanisms of Year Fellowships Traineeships Assistantships Assistantships Support 1999 24 4 68 2 2 2000 37 6 54 3 1 2001 37 5 54 4 0 2002 33 4 59 3 1 2003 30 3 62 5 1 2004 26 4 65 5 0 2005 26 1 63 9 1 2006 28 3 60 8 1 SOURCE: National Science Foundation-National Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. FIGURE D-2 Full-time graduate students in mathematics and statistics at doctorate-granting institutions in the Figure D-2.eps United States, 1980-2006. SOURCE: National Science Foundation-National Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” bitmap image accessed via WebCASPAR, http://webcaspar.nsf.gov. AMS data show similar results. The percentage of U.S. citizens among total full-time graduate stu - dents in mathematics dropped from 55 percent in 1998 to 49 percent in 2001, then rose to 56 percent in 2007. The percentage of females has remained flat, ranging between 29 and 32 percent between 1998 and 2007. The percentage of underrepresented minorities has also remained flat—at about 10 percent—from 2003 to 2007 (Phipps et al., 2008b). Digging a bit deeper into data on graduate study, the committee notes that the median time to degree seems not to have changed much during the first 5 years of the VIGRE program, as noted in Table D-3.

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0 EVALUATION OF NSF’S VIGRE PROGRAM 12000 10000 8000 Full-time 6000 First-year 4000 2000 0 2000 2006 2004 2005 2002 2003 2007 2001 1998 1999 FIGURE D-3 Full-time and first-year graduate students in Groups I, II, III, and Va (departments granting degrees in applied mathematics), fall 1998 to fall 2007. SOURCE: Phipps et al. (2008b). Figure D-3.eps 70% 60% 50% 40% 30% 20% 10% 0 FIGURE D-4 Percentage of full-time graduate students in mathematics and statistics at doctorate-granting insti - tutions in the United States who are U.S. citizens/permanent residents, underrepresented minorities, or female, 1980-2006. SOURCE: National Science Foundation-National-Institutes of Health, “Survey of Graduate Students Figure D 4.eps bitmap image and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov.

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0 APPENDIX D TABLE D-3 Median Years Elapsed from Bachelor’s to Doctoral Degree in Mathematics, 1999-2003 Year Median Years 1999 8.0 2000 7.6 2001 8.0 2002 7.6 2003 7.7 SOURCE: Adapted from NSB (2006), Appendix Table 2-34. FIGURE D-5 Number of degrees awarded in the mathematical sciences in the United States, 1980-2006, by degree Figure D-5.eps level. SOURCE: Adapted from NSF, Division of Science Resources Statistics (2008), Table 35. bitmap image Figure D-5 looks at degree production in the mathematical sciences. The falling number of bachelor’s degrees awarded from 1980 to 1998 has been reversed since 2001 and is almost back to the peak of degrees awarded in the mid-1980s. Likewise, the number of master’s degrees and PhDs awarded has also grown during the VIGRE period. Turning to doctorates, the committee notes that the percentage of doctorates awarded to U.S. citi - zens and permanent residents, although rising during the early 1990s, is declining overall, as shown in Figure D-6. By contrast, the percentage of female and underrepresented minorities who received doctor- ates has generally been growing.

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0 EVALUATION OF NSF’S VIGRE PROGRAM FIGURE D-6 Percentage of mathematics and statistics doctorates in the United States, by gender, race, and citi - zenship, 1980-2006. NOTE: The percentage female is the numbers females divided by the number of females Figure D-6.ep of plus the number of males. In some cases gender was unknown.age same is true for citizenship. Underrepresented bitmap im The minorities include black, non-Hispanic; American Indian or Alaska Native; and Hispanic. The percentage of underrepresented minorities is divided by total doctorates, which include some people for whom race/ethnicity is “other/unknown.” SOURCE: National Science Foundation, “Survey of Earned Doctorates/Doctorate Records File,” accessed via WebCASPAR, http://webcaspar.nsf.gov. Looking at recent doctorates and where they were planning to go after receiving their doctorate, the committee sees similar trends during the VIGRE program (Table D-4) and the earlier period repre - sented in Table 2-5 in Chapter 2. For all years, about one-third of new PhDs in mathematics planned to go directly into a postdoctoral appointment. (Because the total number of PhDs is rising, this translates into more postdoctorals.) As might be expected given the goals of the VIGRE program, the number of postdoctoral fellows in mathematics and statistics has risen quite a bit since the VIGRE program started, as shown in Figure D-7. Finally, the committee collected some information on VIGRE-like activities taking place in recent years in departments that did not receive a VIGRE award. Those data are presented in Table D-5. All of the trends discussed above need to be considered as background or context when assessing the impact of the VIGRE program.

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 APPENDIX D TABLE D-4 New Doctorate Recipients with Definite Commitments to Postdoctoral Study or Research, by Broad Field of Doctorate, 1999-2005 Field of Doctorate 1999 2000 2001 2002 2003 2004 2005 Number Total recipients with commitments, all fields 25,975 26,711 26,889 25,984 26,167 26,280 27,383 Total planning postdoctoral study 7,090 6,978 7,109 7,195 7,784 8,210 8,786 Science and engineering, total 6,485 6,386 6,346 6,445 6,988 7,405 7,952 Mathematics 215 213 217 239 258 269 298 Percentage Total planning postdoctoral study 27 26 26 28 30 31 32 Science and engineering, total 39 38 37 40 43 45 45 Mathematics 30 29 31 36 37 36 36 SOURCE: National Science Foundation, Science and Engineering Doctorate Awards, Arlington, Va., various years. FIGURE D-7 Number of postdoctoral fellows in mathematics and statistics at doctorate-granting institutions in the United States, 1980-2006. SOURCE: National Science Foundation-National Institutes of Health, “Survey of Figure D-7.eps Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. bitmap image

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 EVALUATION OF NSF’S VIGRE PROGRAM TABLE D-5 “VIGRE-like” Activities of Departments That Did Not Receive a VIGRE Award Topic Number Outreach to K-12 students 40 Outreach to K-12 teachers 53 Summer camps in mathematics/statistics 30 Postdoctoral fellowships 44 Graduate traineeships 57 Undergraduate research experiences 71 Mentoring by faculty 95 Mentoring of students by postdoctorals or graduates 31 Teaching collaborations with other departments outside of mathematics or statistics 67 Research collaboration with other departments outside of mathematics or statistics 92 Group activities that include undergraduates, graduates, postdoctorals, and faculty 50 Other activities 11 SOURCE: Committee request for information. Total number of departments responding was 122.