Educating Mathematical Scientists: DOCTORAL STUDY AND THE POSTDOCTORAL EXPERIENCE IN THE UNITED STATES

Committee on Doctoral and Postdoctoral Study in the United States

Board on Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council


National Academy Press
Washington, D.C.
1992



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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States Educating Mathematical Scientists: DOCTORAL STUDY AND THE POSTDOCTORAL EXPERIENCE IN THE UNITED STATES Committee on Doctoral and Postdoctoral Study in the United States Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1992

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Robert M. White is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Frank Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board is designed to conduct studies for federal agencies and maintain liaison with the mathematical sciences communities and academia, professional societies, and industry. Support for this project was provided by the Alfred P. Sloan Foundation. Library of Congress Catalog Card Number 92-60165 International Standard Book Number 0-309-04690-4 Additional copies of this report are available from: National Academy Press 2101 Constitution Avenue, N.W. Washington, D.C. 20418 S546 Printed in the United States of America

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States COMMITTEE ON DOCTORAL AND POSTDOCTORAL STUDY IN THE UNITED STATES RONALD DOUGLAS, State University of New York at Stony Brook, Chair HYMAN BASS, Columbia University AVNER FRIEDMAN, University of Minnesota PETER GLYNN, Stanford University RONALD GRAHAM, AT&T Bell Laboratories RHONDA HUGHES, Bryn Mawr College RICHARD JACOB, Arizona State University PATRICIA LANGENBERG, University of Maryland DONALD LEWIS, University of Michigan J. SCOTT LONG, Indiana University at Bloomington JOHN RICE, University of California at San Diego DONALD RICHARDS, University of Virginia KAREN UHLENBECK, University of Texas at Austin MARY WHEELER, Rice University Staff JOHN E. LAVERY, Director JAMES A. VOYTUK, Senior Staff Officer

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States BOARD ON MATHEMATICAL SCIENCES SHMUEL WINOGRAD, IBM T.J. Watson Research Center, Chair RONALD DOUGLAS, State University of New York at Stony Brook, Vice-Chair LAWRENCE D. BROWN, Cornell University SUN-YUNG A. CHANG, University of California at Los Angeles JOEL E. COHEN, Rockefeller University AVNER FRIEDMAN, University of Minnesota JOHN F. GEWEKE, University of Minnesota JAMES GLIMM, State University of New York at Stony Brook PHILLIP A. GRIFFITHS, Institute for Advanced Study DIANE LAMBERT, AT&T Bell Laboratories GERALD J. LIEBERMAN, Stanford University RONALD F. PEIERLS, Brookhaven National Laboratory JEROME SACKS, National Institute of Statistical Sciences Ex Officio Member WILLIAM F. EDDY, Carnegie Mellon University Chair, Committee on Applied and Theoretical Statistics Staff JOHN E. LAVERY, Director JO NEVILLE, Administrative Secretary RUTH E. O'BRIEN, Staff Associate HANS OSER, Staff Officer JOHN R. TUCKER, Staff Officer JAMES A. VOYTUK, Senior Staff Officer SCOTT T. WEIDMAN, Senior Staff Officer BARBARA WRIGHT, Administrative Assistant

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS NORMAN HACKERMAN, Robert A. Welch Foundation, Chair PETER J. BICKEL, University of California at Berkeley GEORGE F. CARRIER, Harvard University (retired) GEORGE W. CLARK, Massachusetts Institute of Technology DEAN E. EASTMAN, IBM T.J. Watson Research Center MARYE ANNE FOX, University of Texas-Austin PHILLIP A. GRIFFITHS, Institute for Advanced Study NEAL F. LANE, Rice University ROBERT W. LUCKY, AT&T Bell Laboratories CLAIRE E. MAX, Lawrence Livermore Laboratory CHRISTOPHER F. MCKEE, University of California at Berkeley JAMES W. MITCHELL, AT&T Bell Laboratories RICHARD S. NICHOLSON, American Association for the Advancement of Science ALAN SCHRIESHEIM, Argonne National Laboratory KENNETH G. WILSON, Ohio State University NORMAN METZGER, Executive Director

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States PREFACE Although the United States is considered a world leader in mathematical sciences research and in doctoral and postdoctoral education, concern is growing about whether the needs of the profession and of an increasingly technological society are being met. Many doctoral students are not prepared to meet undergraduate teaching needs, establish productive research careers, or apply what they have learned in business and industry. This inadequate preparation, continuing high attrition, and the declining interest of domestic students, the inadequate interest of women students, and the near-absent interest of students from underrepresented minorities in doctoral study are problems that transcend the current difficult job market. One of the principal strengths of the American educational system is its diversity. No single paradigm for education at any level—doctoral/postdoctoral, undergraduate, secondary, or elementary—is imposed. Different programs can all be successful in accomplishing the same goals. This system encourages innovation and the development of local solutions that satisfy the needs of the profession and the country. Such local solutions can then spread, improving education everywhere. A consequence of this system is that there are at present doctoral and postdoctoral programs that succeed in preparing their students for careers in teaching and industry as well as in academic research and succeed also in attracting large numbers of domestic students, including women and students from underrepresented minorities. But these programs have remained largely unnoticed by both the community and students. In an educational system that encourages innovation, the spread of successful innovative methods now seems to be stymied. This observation was the starting point of this study. A study of the American doctoral and postdoctoral system of education in the mathematical sciences was proposed at a meeting of the Board on Mathematical Sciences in April 1990. With the support of the Alfred P. Sloan Foundation, the Committee on Doctoral and Postdoctoral Study in the United States was established in July 1990. Its charge was to determine what makes certain programs successful in producing large numbers of domestic PhDs with sufficient professional experience and versatility to meet the research, teaching, and industrial needs of our technology-based society and then to make this information available to the mathematical sciences community. The committee members were chosen to be broadly representative of the mathematical sciences. Since the committee had neither the charge nor the resources to do a complete quantitative and qualitative study of all of the mathematical sciences doctoral/postdoctoral programs in the United States, it proceeded differently. In a two-day meeting in

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States September 1990, the committee reviewed data on these programs, clarified the definition of a successful program, and selected a diverse set of programs in 10 universities for two-day site visits, which were carried out in October-November 1990 and January-February 1991. These programs were in both small and large, and in both public and private, universities. They were also geographically diverse. They were all in the “top 100” and included four departments in the “top 20.” Achieving unanimity on the selections was no small task since the committee members had widely divergent opinions—some based on philosophical differences between the disciplines of the mathematical sciences—about what was important in doctoral and postdoctoral programs. To minimize bias in the site visits, a uniform plan was prepared in advance for two days of observation and discussion by teams consisting of two (three for larger departments) members of the committee. Before the site visits began, a field test of this plan was conducted at a university not among the 10 universities chosen for the study, and, as a result, adjustments to the plan were made. Information to be collected before the site visit included the information packet sent to prospective graduate students, orientation material sent to new graduate students, orientation material sent to new faculty, completion rates for the different programs (with separate breakdowns for women and minorities), information on first-year courses, sample qualifying and candidacy examinations, a description of the duties and responsibilities of teaching assistants, a breakdown of funding sources for graduate students, and list for the previous five years of doctoral students, postdoctoral associates, and junior faculty appointments with information on their advisors, career tracks, and so forth. The allocation of time during the visits was 50% for students, 25% for faculty, and 25% for administrators. At the beginning and end of the visit, the team held discussions with the chair(s) of the mathematical sciences department(s). The team also spoke separately with the following people and groups: director of the graduate programs, members of the graduate committee, graduate students (in small groups and in informal settings), women and underrepresented minority students (if enrolled in sufficient numbers), thesis advisors, junior faculty, postdoctoral associates, graduate secretary, supervisors of teaching assistants and of the teaching assistant orientation program, and the person(s) responsible for admissions and recruitment. The team visited the departmental and institutional libraries, the computing facilities for students, and students' office space and their space for socializing. It observed the opportunities for social interaction among students and between students and faculty. Since the committee was not in any sense evaluating the programs at the universities it visited and because it wished to receive the full and open cooperation of the departments, no program identification is made in this report, nor are the site visit reports included. However, quotes from site visit reports are incorporated to illustrate the committee's findings. The statistical data presented during the site visits are not presented in this

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States report, since an extensive statistical portrait of a restricted number of departments would not serve the committee's purpose. After the site visits were completed, the committee met in March 1991 to analyze the results. At the end of two days of discussion, the committee was unanimous in concluding that the widely differing programs that had been visited by different teams did indeed have common characteristics that produced success. Moreover, the committee decided that one report was appropriate for all of the mathematical sciences. The committee recognizes the limitations of this methodology. The result is a report that is often impressionistic in nature, but one that represents unanimous impressions of committee members with widely varying disciplinary and intellectual backgrounds. Within these limitations, the committee believes that it has a strong message to deliver in favor of adjusting the American doctoral and postdoctoral system of education in the mathematical sciences so that it responds better to the needs of the profession, students, and the society. The audience to which the report speaks is all U.S. doctoral and postdoctoral programs in the mathematical sciences, and, in particular, those programs that have limited human and financial resources. The report suggests that even with limited resources success can be achieved if, among other things, a program focuses its energies rather than trying to implement a “standard” or traditional program that covers too many areas of the mathematical sciences. It also notes that departments with the best faculty do not necessarily have the most successful doctoral and postdoctoral programs. A quality faculty is necessary for a good program, but of equal importance are students and researchers that can benefit from the program. The committee was assisted in preparing this report by many people at the National Research Council and in the mathematical sciences community. The cooperation and assistance of the faculty, students, postdoctoral associates, and administrators at the 10 institutions visited by the committee were invaluable. While the committee wishes that these people and universities could be identified, this study was structured to keep their identities anonymous, since the intention was not to certify or advertise these programs but rather to use them as examples of what is possible. The Board on Mathematical Sciences gratefully acknowledges support from the Alfred P. Sloan Foundation for this report.

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States CONTENTS     EXECUTIVE SUMMARY   1 1   INTRODUCTION   5     Purpose and Scope of This Report   6     Contents of This Report   8 2   HISTORICAL PERSPECTIVE   9     The Early Years   9     The Era of Growth   11     The Era of Contraction   12     The Recent Past   14 3   THE PRESENT SYSTEM AND SUCCESSFUL PROGRAMS   15     Characteristics of Successful Programs   17 4   HUMAN RESOURCE ISSUES   18     Recruitment   18     Admission   21     Domestic Students   21     Women and Underrepresented Minorities   23     Foreign Students   25     Placement   25 5   FOCUSED, REALISTIC MISSION   27     Standard Model   27     Specialized Models   29 6   POSITIVE LEARNING ENVIRONMENT   32     Communication and Cooperation   32     Effective Advising   34     Course Work and Specialized Study   35     Early Research Experience   36     Master's Degree Programs   36     Qualifying Examinations   37     Research and Thesis   38     Postdoctoral Fellowships   40     A Positive Learning Environment for All Programs   41

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Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States 7   RELEVANT PROFESSIONAL DEVELOPMENT   42     Teaching Skills   42     Communication Skills   43     Teaching Assistantships   44     The Non-academic Market   45     The Postdoctoral Experience   46 8   TOWARD MORE SUCCESSFUL PROGRAMS   47     Faculty and Departments   48     Professional Societies   49     Federal Agencies   49     The Key to Action   51     BIBLIOGRAPHY   52 APPENDIX A:   DOCTORAL AND POSTDOCTORAL PROGRAM SELF-EVALUATION   57 APPENDIX B:   ADVICE TO POTENTIAL GRADUATE STUDENTS IN THE MATHEMATICAL SCIENCES   62 APPENDIX C:   PROFESSIONAL MASTER'S DEGREE PROGRAMS IN THE MATHEMATICAL SCIENCES   64