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Notices of the American Mathematical Society NUMERICAL ANALYSIS edited by Gene H. Golub and Joseph Oliger Lecture Notes from the Short Course sponsored by the AMS, Atlanta, january 3-4, 1978 This is the collection of texts prepared by the lec­ corporate the classical notions and realistic costs turers of the Numerical Analysis Short Course of producing the desired result. The discussion of given at the A. M.S. meeting in Atlanta, Georgia in good vs. best approximation is an example. More January 1978. Computational linear algebra, opti· attention is being given to providing not only an mization and the solution of nonlinear equations, answer, but a computed guarantee that it is a good the approximation of functions and functionals, answer-or a poor one. Easily computed and sharp and approximations for initial and boundary value a posteriori estimates are needed. The discussion problems for ordinary and partial differential equa­ of estimates of condition numbers is an example. tions are discussed. Methods such as the QR fac­ There is progress being made in algorithm design torization, singular value decomposition, quasi­ based on operator splittings which allow one to Newton and secant methods, finite difference, fi· take advantage of being able to solve simpler sub­ nite element and collocation methods are included problems very efficiently. Updating strategies for in these discussions. · optimization and splitting methods for differential equations are examples. The subject matter was chosen to emphasize prom­ inent research areas and attitudes in numerical These texts should be useful to the practicing users analysis. These are introductory lectures on the of numerical methods, programmers, scientists, subject matter for presentation to an audience of and engineers who would like to know what prog· scientists from other areas or disciplines. Typically, ress is being made on the theoretical and develop­ there Is an introduction to a given problem area mental side of the subject. They should be useful and to techniques used, an application to applied to numerical analysts to review progress in areas problems, and a discussion of current research other than their own, and to mathematicians in questions or directions. general who would like to understand what the concerns of numerical analysts are. The teXts Several trends in modern numerical analysis are should be useful for the development of seminars discussed in these lectures. There has always been and reading courses in the academic environment. the quest to find the best way to do things. More Many will probably find the bibliographies of cUt· realistic notions of "best" are evolving which in- rent work most useful. THE LECTURERS AND TITLES CLEVE MOLER, Three Research Problems in Numerical Linear Algebra J. E. DENNIS, J R., A Brief Introduction to Quasi-Newton Methods CARL De BOOR, The Approximation of Functions and Linear Functionals: Best vs. Good Approximation JAMES M. VARAH, Numerical Methods for the Solution of Ordinary Differential Equations JOSEPH E. OLIGER, Methods for Time Dependent Partial Differential Equations GEORGE J. FIX, Variational Methods for Elliptic Boundary Value Problems Publication: November 1978, iv + 135 pages Hard Cover: List $14.00, AMS Member $10.50. CODE: PSAPM/22 Soft Cover: List $10.00, Individual $7.50. CODE: PSAPMS/22 ORDERS MUST BE PREPAID, PLEASE SPECIFY CODE American Mathematical Society, P. 0. Box 1 571 , Annex Station Providence, Rl 02901 OF THE AMERICAN MATHEMATICAL SOCIETY Ed Dubinsky, Rob ion C. Kirby, EDITORIAL COMMITTEE Arthur P. Mattuck, Barbara L. Osofsky, George Piranian, Everett Pitcher (Chairman), Scott W. Williams MANAGING EDITOR Lincoln K. Durst ASSOCIATE EDITOR Hans Samelson CONTENTS December, 1978 STATEMENT, Committee on Employment and Educational Policy . • 522 ASSISTANTSHIPS and FELLOWSHIPS in the MATHEMATICAL SCIENCES in 1979-1980 FOREWORD .... 523 I. GRADUATE STUDY AT UNIVERSITIES. 525 Departments with Graduate Programs 525 Departments Accepting Critical, Historical or Expository Theses for Doctoral Degrees 583 II. STIPENDS FOR STUDY AND TRAVEL 585 Graduate Support . 585 Postdoctoral Support . 588 Travel and Study Abroad 595 Study in U. S. for Foreign Nationals 589 Sources of Fellowship Information 600 INDEX OF ABSTRACTS, Volume 25 A-737 INDEX, Volume 25 . A-772 SUBSCRIPTION INFORMATION: c}/otiai) of the American Mathematical Society is published eight times a year (January, February, April, June, August, October, November •. and December). Subscription prices for Volume 26 (1979) are $19.00 list, $9.50 member. The subscription price for members is included in the annual dues. Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, R. 1. 02901. All orders must be accompanied by payment. OTHER CORRESPONDENCE with the Society should be sent to the Society at P. 0. Box 6248, Providence, R.I. 02940. Please affix one of the peel­ off labels from copies of the c}/otiai) to any correspondence with the Society. Second class postage paid at Providence, Rhode Island, and additional mailing offices. U.S. Postal Service Publication Number: 398520. Copyright© 1978 by the American Mathematical Society Printed in the United States of America Current and prospective graduate students in mathe­ matics and their advisors should be aware of employment prospects in the profession. Historically, the vast majority of Ph. D. mathematicians have pursued academic careers. In recent years, new Ph. D.'s in mathematics have typically had difficulty in finding academic employment. This is particularly true for those who studied "pure" mathematics. Because many departments are close to being fully tenured, it has become increasingly common for young mathemati­ cians to find themselves looking for jobs again a few years after receiving their degrees. These nonretained Ph. D. 's often have great difficulty trying to find a second academic position. Careful studies made under the auspices of the AMS Committee on Employment and Educational Policy indicate that for a number of years to come, the number of openings for traditional academic employment in mathe­ matics will be considerably smaller that the rate at which Ph. D.'s in pure mathematics are currently entering the job market. Talented young people should not be discouraged from becoming mathematicians. Some academic positions will, of course, become available every year. In addition, there are career opportunities for mathematicians outside of the traditional academic environment. However, im­ portant career decisions should be based on a realistic assessment of employment prospects. More information will be found in the following articles: "Future Job Pros­ pects for Ph. D. 's in the Mathematical Sciences" by Wendell Fleming, these cifoticeD, December, 1975; "21st Annual AMS Survey, First Report," these cJ{oticei), October, 1977; "21st Annual AMS Survey, Second Report," these c)loticeD, February, 1978; and "22nd Annual AMS Survey, First Report," these c){oticeD, October, 1978. Committee on Employment and Educational Policy Lida K. Barrett Hugo Rossi Alan J. Goldman Martha K. Smith Arthur P. Mattuck Robert J. Thompson FOREWORD The December issue of the cNOtictiJ regularly contains an extensive report on de­ partments with graduate programs in the mathematical sciences. This report customarily includes data on the number of degrees awarded, and information on support available for graduate students through fellowships and assistantships. Beginning with the 1978 issue, the information about departments has been aug­ mented in two ways over that given in earlier years. Just below the deadline for applications, the number of full-time faculty members in the department is reported, as well as the number of those who have published a mathematical paper or book within the past three years. (These data extend the reports formerly published in the Mathematical Association of America's Guidebook to Depart­ ments in the Mathematical Sciences, which ceased publication following the 1975 edi­ tion.) This information was added to the listings at the request of the Data Subcom­ mittee of the Society's Committee on Employment and Educational Policy (CEEP) in the belief that current figures on faculty size and mathematical publication may be useful to prospective graduate students. Another recommendation of the CEEP Data Subcommittee was that this issue of the cNOtiaiJ contain a list of the departments which accept critical, historical, or ex­ pository theses for doctoral degrees in addition to, or in place of, the more traditional re­ search theses. This list appears on page 583, following the list of assistantships and fel­ lowships. Both of these lists are arranged in alphabetical order by states, followed by a listing of Canadian departments. A postal strike in Canada appears to be at least partially responsible for the fact that fewer Canadian departments are listed than in past issues of this report. Further in­ formation on Canadian departments may be anticipated in the supplement to be pub­ lished in the February 1979 issue of the cNOtictiJ. In addition to information for graduate students supplied by departments, this issue contains information on support for graduate study available from other sources, and information on support of postdoctoral study and research available from a variety of sources. The fmal part of this issue contains, as usual, the annual index of abstracts of papers presented to the Society, as well as an index of the other
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