September 10, 1997

Dear Colleague:

In the summer of 1995, the Directorate for the Mathematical and Physical Sciences (MPS) hosted a workshop on Graduate Education and Postdoctoral Training in the Mathematical and Physical Sciences1. This workshop recommended moving from research assistantships provided through individual investigator grants to departmental traineeships and that students receive a broader education in a shorter time. Subsequently, the MPS Advisory Committee endorsed these recommendations. The Douglas Report (1992)2 earlier made the same recommendations with regard to the Mathematical Sciences.

In 1994, the Division of Mathematical Sciences (DMS) initiated the Group Infrastructure Grants (GIG) Program to provide funding for infrastructure needs of the Mathematical Sciences. Those needs, as evidenced by the proposals received and awarded by the GIG Program, were primarily focused on the support of graduate students, postdoctorates, and the development of innovative graduate programs. The David Report of 19843 made a compelling case for increased funding for graduate students and postdoctorates in the Mathematical Sciences and the responses to the GIG Program demonstrated in a conclusive manner that those needs remain paramount for the Mathematical Sciences community.

In the last decade, the time to degree for a Ph.D. in the Mathematical Sciences has significantly increased from four to seven years. This partially reflects that entering students, especially native born students, are less well prepared than before. But also involved is the heavy dependence by the Mathematical Sciences graduate students and postdoctorates on time consuming teaching assignments for financial support. At the same time the doctoral programs have become quite narrowly focused with an emphasis on producing academicians. Consequently the new Mathematical Sciences Ph.D.s are not as well prepared to take advantage of the rapidly growing demand for mathematicians by industry and commerce as might be desired. These facts suggest graduate faculty need to examine their degree programs so as to expand career opportunities, to seek alternative methods of support for graduate students, and to provide postdoctoral training for future research university faculty.

Over the last decade, foreign students have received over half the Ph.D.s in mathematics awarded by U.S. universities4. Consequently, the U.S. mathematical community, both academic and industrial, has become increasingly dependent on immigrants. Since so many factors could interrupt the influx of foreign students, it is highly risky for the nation to continue this heavy dependence. Since U.S. graduate schools are highly attractive to the international student, the lack of native born mathematical students almost certainly has its roots in the undergraduate mathematical science programs in U.S. post secondary institutions and at the K- 12 level. This suggests a need to reexamine the undergraduate programs with special attention to the education of K-12 teachers.

In recent years, the National Science Foundation, under the leadership of its Director, Dr. Neal Lane, has promoted the concept of the integration of research and education. The Research Experiences for Undergraduates (REU) Program is one example of this integration of research and education, and anecdotal feedback suggests that it has been successful in producing some excellent graduate students and young researchers.

Given the facts and situations described above, DMS has decided to replace its GIG Program with a program that would increase funding for graduate students and postdoctorates and which would encourage a restructuring of both the undergraduate and the graduate programs to meet today's needs. A Special Emphasis Panel was assembled to provide guidance and direction. At the request of the Chair of that Panel, a draft description of a program named VIGRE was provided as a means of focusing the Panel's discussions. The report of that Special Emphasis Panel is attached. The Division anticipates that a program along the lines discussed in this report will be announced shortly.


Donald J. Lewis
Division of Mathematical Sciences


1For the report of this and related workshops, see: the NSF report, Graduate Education and Postdoctoral Training in the Mathematical and Physical Sciences (1995); the SIAM report, Mathematics in Industry (1995); the National Research Council (NRC) report, Mathematical Sciences, Technology and Economic Competitiveness (1991)

2Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States (1992) NRC

3Renewing U.S. Mathematics (1984) (NRC) Notices of the American Mathematics Society, December 1996, Vol. 43

4Notices of the American Mathematics Society, December 1996, Vol 43

This is a report of a special emphasis panel. The opinions,findings, conclusions or
recommendations expressed in this report are those of the participants

Report of the Special Emphasis Panel on VIGRE

The DMS special emphasis panel met on May 19 - 20 to consider the proposed program entitled Vertically Integrated Grants for Research and Education in the Mathematical Sciences (VIGRE). Panel members included: Mary Ellen Bock (Purdue), John Garnett (UCLA), Tom Gerig (North Carolina State), Philip Hanlon (Michigan), Ray Johnson (Maryland), Nancy Kopell (Boston), Morton Lowengrub (Chair, Indiana), Calvin Moore (U. of California, Berkeley), Tinsley Oden (Texas, Austin), Peter Sarnak (Princeton) and Shmuel Winograd (IBM).

The panel strongly endorses the concept of vertical integration, that is, constructing undergraduate, graduate and postdoctoral programs to be mutually supportive. We recommend that the solicitation make clear to the mathematical community the notion of vertical integration. The community must recognize that the purpose of this program is to provide quality experiences for undergraduate and graduate students while also continuing professional development at the postdoctoral level. The funding provided by these grants should enable departments to carry out innovative educational programs at all levels not possible through present departmental resources. The panel sees this as a program that can achieve a change of culture in a department, one that results in broadening opportunities for undergraduate and graduate students both through innovative curriculum development and research experiences. The panel strongly recommends that this program be sustained for at least five years in order to bring about necessary systemic change. The duration of an award should be three to five years and if possible the award should be renewable.

We strongly recommend that the core components of every proposal include the following: graduate traineeships, undergraduate research experiences, and postdoctoral fellowships.

The VIGRE program should aim to increase the participation of underrepresented groups, i.e., women, racial and ethnic minorities, and persons with disabilities, at all levels of the mathematical sciences. No proposed project should negatively impact minority participation. Those proposed projects for which increased minority participation is a major component should describe their existing programs or the basis on which their new project is founded.

Undergraduate education is where the future mathematical sciences professionals are first exposed to the mathematical sciences as they will see it throughout their careers. It is a time the students should be exposed to, and begin to develop the skills for, the various demands and opportunities of their future careers. These include the breadth and the rigor of the mathematical sciences and its use in solving problems which arise in other scientific disciplines and industry.

Graduate education is that phase in which students deepen their knowledge of the mathematical sciences culminating in the carrying out of independent research. It is also the time when the student is mature enough to develop some of the skills such as teaching and communication which he/she will be using as a professional.

The postdoctoral program must be one that allows continued professional development as a scholar and teacher. It should be viewed as a natural extension of graduate education that provides the individual with the skills to become a full-fledged professional mathematical scientist. Hence, the fellow must be an integral part of the intellectual life in a department, fully participating in all its activities.

We want to emphasize again that the purpose is to increase the quality and breadth of mathematical sciences education, not the size of graduate programs.

In the rest of the report we will elaborate on the particular sections in the proposed program.


For undergraduate students, VIGRE has three closely related objectives: preparing mathematical science majors for a wider variety of career opportunities; improving the communication skills of mathematics students; and increasing the number of students who major in the mathematical sciences.

The panel believes that an undergraduate research experience should stimulate interest and give life to learning, and that undergraduate research should be broadly interpreted to include all activities that introduce undergraduates to the joy of discovery and excite them about the mathematical sciences.

Examples of research experiences may include faculty directed projects (REUs), cooperatives in industry, practice teaching in schools and participation in interdepartmental teams or in departmental educational innovations such as workshops or construction of web pages. While undergraduates may lack depth of knowledge, they may contribute to a research effort by providing freshness of outlook.

Mentoring is a key component of the research experience. The mentoring and group work associated with such programs provide a more supportive environment than the classroom setting. Well run honors programs provide the additional benefit of attracting and retaining students from underrepresented groups in the mathematical sciences.

The panel endorses the need to improve the communication skills of undergraduate students. In particular, they should develop the ability to speak and write about mathematics, and to communicate ideas to their peers and to non-mathematicians. Enhanced communication skills will give mathematical science majors even greater employment opportunities.

Costs associated with the undergraduate component of VIGRE may include items besides student stipends. Funds may be required to gain access to the laboratories of other disciplines or to provide release time for faculty who organize coop opportunities and oversee the undergraduate research program. Student stipends for summer projects are expected to be at least $1,000 per month with academic year stipends comparable on a pro rata basis.


The panel felt that the graduate traineeships have great potential for effecting positive changes in graduate programs in the United States. These traineeships provide a mechanism for broadening graduate education; shortening the average time to doctoral degree; improving communications skills; and improving the opportunities for employment.

The traineeships are intended for doctoral degree programs and would provide stipends for 11 months of support. This would ensure that the student participate in the program in the summer as well as the academic year. The summer months would provide time for experiences in industry, business, national laboratories, or science/engineering departments as well as additional course work to deepen the student's knowledge. The twelfth month is available for other opportunities. These experiences should broaden graduate education without sacrificing rigor.

The panel supports graduate students having a significant teaching experience. This should include a minimum of one year of supervised teaching with at least one semester in which the student has substantial responsibility for the class. Since every graduate student should have this teaching experience, an individual student should have at most three years of non-teaching support from a VIGRE award. Other methods of enhancing the teaching experience might include the participation of the graduate student in undergraduate curriculum development.

As with the undergraduates, the panel endorses the need to improve communications skills. In addition to teaching, giving seminar talks and learning to write proposals, the panel encourages experiences working in teams and as part of the undergraduate research experiences.

Shortening the average time for the doctoral degree is an important aspect of this program. It is desirable that the average time to degree be no more than five years. It is understood that interdisciplinary or special programs may take longer. However, since the students involved in this program would have fewer teaching obligations than students supported as teaching assistants and since the program would involve year round participation by students, this goal seems reasonable.

The panel realizes that the graduate traineeship program presents challenges for universities in covering courses and recitation sections. Since it is explicitly state that the program is not intended to increase the size of the graduate program, the traineeship program would mean a decrease in the students available as teaching assistants. Possible substitutes for graduate student teachers include postdoctoral, visiting and tenure-track faculty.


The program for postdoctoral fellows should be designed to produce professionals ready to begin an academic career. At the conclusion of the postdoctoral program, fellows should have developed an independent research program, developed teaching skills at various program levels, and begun to develop a broad perspective of their field. The structure of the postdoctoral program should be flexible and could include an interdisciplinary research experience in other academic departments and programs, industry, or national laboratories. While the intent is to train fellows for academic positions, industrial experience involving practical problem solving or interdisciplinary research involving the integration of other disciplines into the fellows' research may provide invaluable experience for an academic career. The postdoctoral fellow is expected to prepare and submit a proposal to secure summer salary support during the third year of his/her program.

The program should provide opportunities for the fellows to interact with their peers in national meetings and symposia so as to expose them to the broader community of scholars in their fields. The proposed program should include features designed to recruit members of underrepresented groups for postdoctoral fellows.

The scope of individual postdoctoral programs must be broader than a teaching experience and must provide ample opportunity to develop a viable research effort with the help of a senior faculty member of the department as a mentor.

The panel agrees that the postdoctoral fellowships should be three year positions. This provides the fellow with sufficient time to develop the desired skills before having to begin the search for a new position.

The proposal should clearly indicate how the postdoctoral program develops the skills and reputation of the fellows as professional mathematical scientists.

We recommend that under the section on allowable costs, the paragraph referring to postdoctoral fellows be replaced by the following: For the first year of the program, the postdoctoral fellow will be paid a salary stipend from grant funds at the full- time equivalent rate of $38K per academic year. The percentage time appointment on grant funds can vary from 25 % to 50%. The host university will provide an academic appointment paid by university funds for the balance of the percentage of time adding up to 100% time. The full time rate for the university appointment will be at least $38K for the first academic year. The teaching duties assigned to the postdoctoral fellow will be prorated based on percentage time appointment on university funds and will not exceed an average of seven classroom contact hours per week for a full-time appointment. In addition, the Foundation will provide summer support for two summers at the rate of $8K per summer. Each postdoctoral fellow will receive a total of $7,500 for the three years to cover travel, equipment, and supplies. The university is expected to provide for health care benefits for the postdoctoral fellows and other fringe benefits that are provided employees with 50% or more time appointments.


We support the inclusion of curriculum development in the program as an optional component. New materials may be desirable particularly when the goal of the project is to prepare students and postdoctoral fellows in areas that are not part of the traditional curriculum, as in interdisciplinary subjects. Such curriculum development should mesh with the overall research and education goals of the project and could include efforts of junior members of the project team such as graduate students and postdoctoral fellows. We expect that, in some cases, the appropriate materials may not impact a large number of students. However, it would be important to develop materials that are portable to other institutions. Curriculum development can be supported by means of release time for regular faculty or postdoctoral fellows.


We recommend that outreach to industry, national laboratories, other academic areas and K-12 education be included as optional components. Resources could be provided for collaboration with industrial and national laboratory partners, particularly when the participants are graduate students and postdoctoral fellows. We also support resources for other kinds of training by industrial partners.

We encourage providing resources to stimulate interactions with other academic departments. This might include support for laboratories that help train students or postdoctoral fellows in a project and travel money for junior members of the team to collaborate outside the institution. We encourage creative new models of collaborations with industry, national laboratory, and academic partners.

We also recommend support for an optional component aimed at teacher enhancement and the development of K-12 instructional materials, as described in the draft proposal. Such a component must be coherent with the subject and goals of the rest of the project.


We strongly recommend that the following criteria be addressed in the preparation of proposals:

The Foundation provides awards for research and education in the sciences and engineering. The awardee is wholly responsible for the conduct of such research and preparation of the results for publication. The Foundation, therefore, does not assume responsibility for the research findings or their interpretation.

The Foundation welcomes proposals from all qualified scientists and engineers and strongly encourages women, minorities, and persons with disabilities to compete fully in any of the research and education related programs described here. In accordance with federal statutes, regulations, and NSF policies, no person on grounds of race, color, age, sex, national origin, or disability shall be excluded from participation in, be denied the benefits of, or be subject to discrimination under any program or activity receiving financial assistance from the National Science Foundation.

Facilitation Awards for Scientists and Engineers with Disabilities (FASED) provide funding for special assistance or equipment to enable persons with disabilities (investigators and other staff, including student research assistants) to work on NSF projects. See the program announcement or contact the program coordinator at (703) 306-1636.

The National Science Foundation has TDD (Telephonic Device for the Deaf) capability, which enables individuals with hearing impairment to communicate with the Foundation about NSF programs, employment, or general information. To access NSF TDD dial (703) 306-0090; for FIRS, 1-800-877-8339.

NSF 97-170 (Electronic Dissemination Only)