Calendar of AMS Meetings and Conferences

This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub­ and annual meetings are joint meetings of the Mathematical Associ­ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet­ mathematics and from the headquarters office of the Society. Ab­ ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as­ at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub­ additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. Meetings

Abstract Program Meeting # Date Place Deadline Issue 840 March 18-19, 1988 East Lansing, Michigan Expired March 841 March 25-26, 1988 Knoxville, Tennessee Expired March 842 April 8-9, 1988 Las Cruces, New Mexico Expired March 843 * April 23-24, 1988 College Park, Maryland Expired April 844 August8-12, 1988 Providence, Rhode Island May 19 July I August (AMS Centennial Celebration) October 28-30, 1988 Lawrence, Kansas August 24 October January 11-14, 1989 Phoenix, Arizona October 12 December (95th Annual Meeting) January 17-20, 1990 Louisville, Kentucky (96th Annual Meeting) January 16-19, 1991 San Francisco, California (97th Annual Meeting) *Please refer to page 441 for listing of special sessions.

Conferences

April 21-23, 1988: Symposium on the Interface of Computing July 3-23, 1988: Summer Research Institute on Operator Science and Statistics, Reston, Virginia (see news item, Theory /Operator Algebras and Applications, University of page 42, January issue) New Hampshire, Durham, New Hampshire May 4, 1988: Symposium on Some Mathematical Questions July 18-29, 1988: AMS-SIAM Summer Seminar on in Biology: The Dynamics of Excitable Media, Las Vegas, Computational Solution of Nonlinear Systems Equations, Nevada Colorado State University, Fort Collins, Colorado May 29-June 4, 1988: Symposium on The Legacy of John August 6-7, 1988: AMS Short Course: Chaos and Fractals: von Neumann, Hofstra University, Hempstead, New York The mathematics behind the computer graphics June 4-August 11 , 1988: Joint Summer Research September 6-10, 1988: International Neural Network Society, Conferences in the Mathematical Sciences, Bowdoin 1988 Annual Meeting, Boston, Massachusetts (see news College, Brunswick, Maine item, page 269, February issue) Deadlines

MayjJune Issue July 1August Issue September Issue October Issue Classified Ads* Apr18, 1988 May 30, 1988 Aug 1, 1988 Aug 31, 1988 News Items Apr 22, 1988 Jun 10, 1988 Aug 5, 1988 Sept 6, 1988 Meeting Announcements** Apr 14, 1988 Jun 3, 1988 Jul 28, 1988 Aug 24, 1988 * Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. ** For material to appear in the Mathematical Sciences Meetings and Conferences section. OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

ARTICLES DEPARTMENTS

253 Geometry-Supercomputer Project Inaugurated 251 Letters to the Editor A group of 13 leading mathematicians and computer scientists for the U.S., 266 News and Announcements England and France have joined forces to use the Supercomputer facility at 273 NSF News and Reports the University of Minnesota to study fundamental problems in geometry. 275 AMS Meetings and Confer- ences 255 Advisory Committee Examines Future Directions 307 Mathematical Sciences Meet- At the fall meeting of the NSF Advisory Committee for the OMS the discus­ ings and Conferences sion focused on the NSF budget, the status of new programs instituted in 314 New AMS Publications 1987, and on five issues that will affect future planning for the OMS. 315 Queries 316 AMS Reports and Communica­ 259 Computational Mathematics Program Takes Shape tions Established by the NSF one year ago, the Computational Mathematics Recent Appointments, 316 Program in the OMS is now providing research support for a wide range of Reports of Past Meetings, 316 topics in the mathematical sciences and is a good source of funding for interdisciplinary projects with a computational aspect. Reports from the Committee on Human Rights of Mathematicians, 319 320 Miscellaneous Personal Items, 320 FEATURE COLUMNS Deaths, 320 321 New Members of the AMS 328 Assistantships and Fellow­ ships in the Mathematical 263 Mathematical Text Processing Sciences in 1988-1989 This month, Richard Palais has turned his column over to Timothy Wallstrom, (Supplement) who in an article, "The Equation Processor in Word 3.0", examines various 338 Critical, Historical, or Exposi­ features of a new version of Microsoft Word for the Macintosh. tory Theses (Supplement) 339 Postdoctoral Positions Re­ search or Research Teaching 1988-1989 (Supplement) 339 Foreign Language Require­ ment for Ph.D. (Supplement) 340 Classified Advertising 369 Forms AMERICAN MATHEMATICAL SOCIETY 1988 is a very important year for the mathematical community. It repre­ sents the 1OOth anniversary of the American Mathematical Society and is highlighted by a series of events that celebrates the achievements of our community and previews the future with mathematics. This special year was EDITORIAL COMMITTEE launched at the Joint Mathematics Meeting in Atlanta with a Banquet: "1 00 Robert J. Blattner, Ralph P. Boas Years of American Mathematics" and a Special Session: "Forces for Change Lucy J. Garnett, Mary Ellen Rudin in Mathematics Education." The year-long celebration will continue through Nancy K. Stanton, Steven H. Weintraub Everett Pitcher (Chairman) 1988 with: MANAGING EDITOR February 11-15 James A. Voytuk "American Mathematics Entering its Second Century" - American As­ ASSOCIATE EDITORS sociation for the Advancement of Science Annua1 Meeting, Boston, MA Stuart Antman, Queries Hans Samelson, Queries April24-30 Ronald L. Graham, Spec/a/ Articles National Mathematics Awareness Week- JPBM Annual Event Jeffrey Lagarias, Spec/a/ Articles April24-27 SUBSCRIPTION INFORMATION Subscription prices for Volume 35 (1988) are "A Century of American Mathematics" - National Academy of Sci­ $1 05 list; $84 institutional member; $63 individual ences Annual Meeting, Washington, DC member. (The subscription price for members is included In the annual dues.) A late charge of April 28 or 29 10% of the subscription price will be imposed "The Impact of Mathematics"- Board on Mathematical Sciences Event, upon orders received from nonmembers after Washington, DC January 1 of the subscription year. Add for post­ age: Surface delivery outside the United States May 1988 and lndia-$10; to lndia-$20; expedited deliv­ "Mathematics Education: Wellspring of U.S. Industrial Strength" ery to destinations in North America-$15; else­ where-$38. Subscriptions and orders for AMS Mathematical Sciences Education Board Symposium, Irvine, CA publications should be addressed to the Amer­ May 29-June 4 ican Mathematical Society, P.O. Box 1571, An­ nex Station, Providence, Rl 02901-9930. All or­ "The Legacy of John von Neumann" - Hofstra/AMS/SIAM Interna­ ders must be prepaid. tional Symposium, Hempstead, NY ADVERTISING July 11-15 Notices publishes situations wanted and classi­ fied advertising, and display advertising for pub­ "Applied Mathematics: Foundations for Science & Technology"- SIAM lishers and academic or scientific organizations. Annual Meeting, Minneapolis, MN Copyright @ 1988 by the American Mathemat­ ical Society. All rights reserved. Printed in the August 8-12 United States of America. Mathematics into the 21st Century - AMS Centennial Celebration, The paper used in this journal is acid-free and Providence, RI falls within the guidelines established to ensure October 1988 permanence and durability. e [Notices of the American Mathematical Society is "The Future of Mathematics Education in the U.S." - MSEB/BMS published ten times a year (January, February, Report to the Nation March, April, MayfJune, July/August, Septem­ ber, October, November, December) by the Amer­ The goal of these events will be to increase public understanding and to ican Mathematical Society at 201 Charles Street, stimulate a dialogue in the mathematical community. Participation at the Providence, Rl 02904. Second class postage paid Atlanta meeting was outstanding and it is hoped that the other events will at Providence, Rl and additional mailing offices. generate an equal reaction. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Sponsored by the Joint Policy Board for Mathematics (American Mathemat­ Membership and Sales Department, American ical Society, Mathematical Association of America, Society for Industrial Mathematical Society, P. 0. Box 6248, Provi­ and Applied Mathematics) with the cooperation of two National Research dence, Rl 02940.] Publication here of the Soci­ Council boards (Board On Mathematical Sciences, Mathematical Sciences ety's street address, and the other information in brackets above, is a technical requirement of the Education Board). U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street address.

250 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Elections form of presentation be suggested but not imposed. Thus the information is requested I have recently submitted my ballot to twice but not sought more forcefully. The "elect" officers of the American Mathe­ absence of information in some instances matical Society. I am concerned about how represents the fact that the Secretary was the Society conducts its elections. For some not sufficiently adroit in locating the candi­ positions, only one candidate is nominated. date or had too short a time interval in The Selection Commmittee has effectively Letters which to do so. chosen the winner. In other cases, we are asked to choose between candidates know­ to the Editor ing little or nothing about them or their views. This does not allow us to make intelligent, informed decisions. It is very surprising to me when only one candidate is nominated for a position. In that case, there is no election and the Policy on Letters to the Editor "winner'' does not necessarily have the Letters submitted for publication in support of a majority of (even) the voting Notices are reviewed by the Editorial members of the Society. I think it is sad that Committee, whose task is to determine we do not elect our president-and that he which ones are suitable for publication. or she cannot assume our support. The publication schedule requires from In this past election, there were several two to four months between receipt of the candidates who did not have any biographi­ letter in Providence and publication of the cal information included with the ballot. I earliest issue of Notices in which it could do not know if this was due to the candi­ appear. Publication dates, the Society, or both. However, any decisions are ultimately made by majority vote of the Editorial reason is upsetting. Without a biographical COMMENT BY THE SECRETARY OF THE Committee, with ample provision for prior sketch, a candidate is at a terrible disadvan­ AMS: There is only one candidate named discussion by committee members, by tage-as is the voter. by the Council for positions of editor, asso­ mail or at meetings. Because of this discus­ Many candidates chose to make no ciate secretary, secretary, associate treas­ sion period, some letters may require as statement. These statements give me some urer, treasurer, and president elect as a much as seven months before a final deci­ indication of what a candidate wants to do matter of considered Council policy. One sion is made. Letters which have been, or for the mathematical community; I cannot reason is the expertise that some of these may be, published elsewhere will be con­ get this from a list of publications and talks. positions require. Another is that one sidered, but the Managing Editor of No­ When a candidate fails to make a statement, should not ask an individual to rearrange tices should be informed of this fact when I cannot conclude that person has any ideas his schedule in anticipation of a job that the letter is submitted. The committee reserves the or interest in serving. This is our only may not materialize. As a related policy, right to edit letters. opportunity to find out what these people the voting strength of persons elected in the Notices does not ordinarily publish think is important. I voted for no candidate contested elections for member-at-large complaints about reviews of books or ar­ who failed to make a statement. and vice president exceeds that of persons ticles, although rebuttals and correspon­ People earn awards based on the quality chosen in uncontested elections. [Because dence concerning reviews in Bulletin ofthe of their work. I do not believe that becom~ of a change in the bylaws, the year 1987 is American Mathematical Society will be ing an official of the American Mathemati­ a transition year in which the last sentence considered for publication. cal Society should be an award. In my does not apply.] Letters should be typed and in legible mind, the job ofthe Selection Committee is Candidates have the opportunity but not form or they will be returned to the sender, to offer us a slate of candidates from which the obligation to provide biographical in­ possibly resulting in a delay of publication. to choose. Further, before having one's formation and a statement. Some choose to Letters should be mailed to the Editor of Notices, American Mathematical Society, name placed on a ballot, a candidate should provide one or both. It was a matter of P.O. Box 6248, Providence, RI 02940, and be asked to express an interest in serving policy, debated in the Council, that such will be acknowledged on receipt. (not just a willingness to serve). information not be required and that the DouglasS. Kurtz New Mexico State University (Received October 26, 1987)

FEBRUARY 1988, VOLUME 35, NUMBER 2 251 The Mathematical Heritage , of Elie Cartan

, ELIE CARTAN ET LES MATHEMATIQUES D'AUJOURD'HUI

This special issue of the journal Asterisque is devoted to the Proceedings of a joint NSF-CNRS seminar. This conference was centered around important areas of contemporary research in mathematics and mathematical physics which Elie Cartan pioneered. The variety of subjects treated in this volume show the great depth of Cartan's work, and cover topics as different as the theory of systems of PDEs, (Lie) group theory, Riemannian geometry, symplectic mechanics, and general relativity.

CONTENTS: Une lettre d'Andre Weil a Henri Cartan. M. Berger: La geometrie metrique des varietes riemanniennes (variations sur la formule a 2 = b2 + c2 - 2bc cos a). S. S. Chern: Moving frames. Yvonne Choquet-Bruhat: Causalite des theories de supergravite. C. Feffer­ man, C. R. Graham: Conformal invariants. I. M. Gelfand, A. V. Zelevinsky: Representation models for classical groups and tLeit higher symmetries. M. Gromov: Isometric immersions of Riemannian manifolds. V. Guillemin: The integral geometry of line complexes and a theorem of Gelfand-Graev. S. Helgason: Fourier transform on symmetric spaces. V. G. Kac, D. H. Peterson: Defining relations of certain infinite dimensional groups. B. Kostant: The McKay correspondence, the Coxeter element and representation theory. J-L. Koszul: Crochet de Schouten-Nijenhuis et cohomologie. M. Kuranishi: Cartan connections and CR structures with non-degenerate Levi-form. G. D. Mostow: Discrete subgroups of Lie groups. W. Schmid: Boundary value problems for group invariant differential equations. I. M. Singer: Families of Dirac operators with applications to physics. J-M. Souriau: Un algorithme generateur de structures quantiques. A. Trautman: Optical structures in rela­ tivistic theories. A. Weinstein: Poisson structures and Lie algebras. Annexe: Resumes des autres conferences de R. Bryant, M. Dufio et J. Tits.

1980 Mathematics Subject Classifications: 51, 53, 83, 20, 43, 22, 17 and others 444 pages, 1986, Hardcover List Price: $4 7, Indiv. mem $33 To order, please specify ASTCARTAN/NA PREPAYMENT REQUIRED. Add shipping and handling.* In the U.S., Canada, or Mexico, order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-9930 or call 800-556-7774 to use Visa or MasterCard. Orders from other countries should be sent to the SMF, B.P. 126-05, 75226 Paris Cedex 05, France or to OFFILIB, 48 rue Gay-Lussac, 75240 Paris Cedex 05, France. * AMS shipping and handling: 1st book $2, each add'l $1, max $25; by air, 1st book $5, each add'l $3, max $100. GEOMETRY-SUPERCOMPUTER PROJECT INAUGURATED

On December 14, mathematicians gathered at the complex. The investigation will require deep theoretical University of Minnesota to inaugurate the Geometry­ analysis not only in geometry itself, but also in the Supercomputer Project, which will use the power of a development of algorithms to produce the software to Cray 2 supercomputer to illuminate certain basic ques­ perform the large-scale computations required. tions in geometry. The project will combine the diverse One of the questions the group will pursue is how knowledge and expertise of 13 eminent mathemati­ best to represent a 3-manifold in a computer. One cians artd computer scientists from the U.S., England, method is to decompose the manifold into hyperbolic and France. At the inauguration, four members of the tetrahedra and give the computer a description of how group-William P. Thurston, Robert E. Tarjan, Benoit the tetrahedra are glued together to obtain the mani­ B. Mandelbrot, and Adrien Douady-presented talks fold. "This approach is successful in many cases," says about research relating to the project. Thurston, "but in certain extreme cases, the tetrahe­ "The project will bring together people from all dra essentially get turned inside out." To avoid this over the world to communicate and work jointly," said difficulty, the group will try to substitute for the tetrahe­ Thurston, whose pioneering ideas in geometry form a dral boundaries 2-dimensional minimal surfaces, which major impetus of the group. Members of the group "yield flexible, smoothed-off tetrahedra that can slide acknowledge that it is impossible to predict the exact against each other," says Thurston. These methods may direction the research will take simply because this kind be useful in randomly generating 3-manifolds on which of interdisciplinary, collaborative approach has been to test conjectures. rare in mathematics. "It's not really a single, coherent One of the group members, Fred Almgren, is inves­ project," Thurston explained, "but rather a coherent tigating 2-dimensional surfaces. He is developing algo­ collection of closely related projects." rithms to compute and display surfaces spanning closed Nonetheless, certain problems have emerged as cen­ curves and minimizing area among surfaces of varying tral to the group's efforts. One of these is the elusive topological structure. He is also studying the evolution question of the classification of 3-manifolds. The clas­ of regions driven by free energies which are in part sification problem has long been solved for 1- and 2- 2-dimensional and in part 3-dimensional. Almgren says, dimensional manifolds. In 1960, Stephen Smale proved "We will be seeing surfaces that have never been seen the Poincare Conjecture for n-manifolds for n ~ 5, and before!" in 1981, Michael Freedman established the case of n = 4. The proposed catalog of 3-manifolds will also require That the case of n = 3 remains unsolved is in some sense a study of the properties of certain groups described by not surprising. For dimensions one and two, visualiza­ generators and relations. The work of James W. Cannon tion plays a fundamental role in pointing the way to a and David B. A. Epstein will lay the foundation for proof, and for n ~ 4, space is just ~·roomier." a "calculator" for computing with the infinite groups One of the main tools the group will use to investigate of low-dimensional topology. Such a calculator would the classification problem is hyperbolic geometry. The be useful, for example, in recognizing when pictures of group plans to test the "geometrization conjecture" which seemingly different knots really represent the same knot Thurston made about 10 years ago. The conjecture says viewed from different perspectives. that every 3-manifold either has a standard geometric structure, typically a hyperbolic structure, or can be built up from such geometric manifolds. This conjecture Unexpected Connections contains the Poincare Conjecture as a special case. One of the benefits of this kind of collaboration is the Thurston has verified his conjecture in many specific unexpected connections that arise when researchers from cases, but the general case still appears staggeringly different branches of mathematics start talking to one

FEBRUARY 1988, VOLUME 35, NUMBER 2 253 Geometry-Supercomputer Project another. For example, Tarjan explained how he and Fractals also have deep connections to the topology Thurston were working with a data structure problem of 3-manifolds. In general, a 3-manifold that admits a which Thurston interpreted as a problem in hyperbolic hyperbolic structure gives rise to a particular fractal set geometry. on the 2-sphere. Information about the entire structure The original question centered on finding the simplest of the mainfold is hidden in this fractal set. way to transform one binary tree into another. It turns Using the Cray 2 to draw pictures of the fractals out that this problem translates into the question of that arise in the group's investigations will help them finding the simplest way to transform a triangulation to better understand the properties of the fractals. The of the 2-sphere into a decomposition of the 3-ball study of dynamical systems will benefit in another way into hyperbolic tetrahedra. The number of tetrahedra in from the computational power of the supercomputer: the decomposition provides a measure of the "distance" in many cases, the best way to represent dynamical between the two trees. According to Thurston, hyperbolic information is through movies, which require a great geometry is useful in this situation because it brings deal of computational power. together information about the large- and small-scale aspects of the problem. "Hyperbolic space captures the complexity of the two-dimensional case on all scales," he Computer Vision remarked. Project member David Mumford will be conducting Tarjan, who specializes in the theory of algorithms, is research in computer vision. His research is linked to investigating the fundamental questions underlying some other problems in the project in that many of the of the computational problems the project raises. "Com­ techniques and underlying geometric constructions are putational geometry is a rich source of computational similar. and algorithmic problems, and geometric methods can "We want to program computers to analyze pictures as be used to analyze algorithms. There is a real exchange of an animal does, by separating the picture into identifiable ideas between the two fields." The other computer scien­ objects, and separating the objects from the background," tists in the group, David P. Dobkin and Allan Wilks, will Mumford explained. "Existing computer programs can contribute their special expertise in computer graphics. do this in situations in which the lighting and many other factors are closely controlled, but real pictures present Fractal Geometry great complications." Mumford says that the theorems and algorithms appropriate for computer vision are not Project member Benoit B. Mandelbrot will be investi­ yet known, but the process appears to be amenable to gating fractals, which are sets of fractional dimension. mathematical analysis. Although such mathematicians as Hausdorff, Poincare, One aspect of vision that is difficult to program is and Besicovitch worked on the subject, it was Mandel­ a data structure to represent a commonality of shape. brot who developed and popularized fractals and coined For example, forks come in many different shapes, sizes, the term. Fractals arise in a great many areas within and colors, but people easily recognize all forks as being and outside mathematics and have applications ranging in some sense the same. Programming this recognition from physics to cinematography. Pictures of fractals­ capacity is a great challenge. Remarked Epstein, "If you convoluted, complicated shapes which often resemble asked a computer to go out and find you a fork, it the jagged edge of a coastline-are costly to produce but would have a very difficult time." Even the mathematical contain a great deal of information. viewpoint appropriate to shape recognition is unclear. Many of the problems the group will be investigating Mumford explained that, to a topologist, all forks are the have connections to fractal geometry. For example, same because they are all homeomorphic to the ball in Douady, John H. Hubbard, and John W. Milnor will 3-space. But if one fork has rounded edges and another be examining dynamical systems governed by iteration has sharper comers, a differential geometer would find of complex polynomials. Iterating a complex polynomial the two very different. "There should be a common gives rise to a Julia set, which is generally a fractal set ground between topology and geometry that identifies and is consequently difficult to understand because of shapes more in the way that people do," says Mumford. its complexity. Douady and Hubbard have developed a method of storing the minimal amount of information about the topology of the Julia set in a binary tree. The Support for the Project resulting combinatorial information illuminates certain The project is supported by a $1.5 million, 3-year grant properties of the original polynomial. The process works from the National Science Foundation (NSF). The work­ backward as well: one can construct polynomials with stations of the U.S. researchers will be linked through particular dynamical properties by starting with the NSFNET, a large-scale "internet" which provides ac­ appropriate combinatorial tree. cess to many other smaller networks. The University

254 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Geometry-Supercomputer Project

of Minnesota and its Supercomputer Institute are also brings with it a responsiblity to the larger professional supporting the project by sponsoring visiting scientists, community. There has been a great deal of grassroots contributing office space, paying all administrative costs, support for the project, and we have a responsiblity to waiving most of the overhead, and donating 600 hours share our work with others. This is not intended to be a of time on its Cray 2 supercomputers. The university private club." Mumford summarized the feeling of the estimates the value of these contributions to be about $1 group when he remarked that what brings them together million. In addition, Cray Research and Sun Microsys­ is "a love of geometry and a desire to understand its tems have provided generous corporate support. computational aspects." Thurston emphasizes that while the amount of the grant may seem large, the funds are divided among 13 investigators and will support junior investigators, Geometry Computing Group postdoctoral associates, and graduate students, as well as Frederick J. Almgren, Princeton University; James W. the purchase of computer hardware. Cannon, Brigham Young University; David P. Dobkin, The Geometry-Supercomputer Project has been in Princeton University; Adrien Douady, Ecole Normale the planning stages for several years now. Albert Marden Superieure, Paris, France; David B. A. Epstein, Univer­ began discussing the idea with members of the group sity of Warwick, Coventry, England; John H. Hubbard, about three years ago, and two years ago organized a Cornell University; Benoit B. Mandelbrot, IBM and Yale workshop at the University of Minnesota during which University; Albert Marden, University of Minnesota; the group laid the groundwork for the project. Although John W. Milnor, Institute for Advanced Study; David Marden is modest about his role as organizer, the group Mumford, Harvard University; Robert E. Tarjan, AT&T acknowledges that he has been the main driving force Bell Laboratories and Princeton University; William P. behind the project. "The research ideas have been around Thurston, Princeton University; Allan R. Wilks, AT&T a long time," says Thurston, "but the project is really the Bell Laboratories. brainchild of Marden." It is clear that the group sees itself in the context Allyn Jackson of the larger scientific community. "The group has Staff Writer great scientific power," says Marden, "and this power

ADVISORY COMMITTEE EXAMINES FUTURE DIRECTIONS

The latest meeting of the NSF Advisory Committee for Science and Technology Centers. After the presentations, the Mathematical Sciences, held November 2-3, 1987, the committee met in subgroups focused on five issues: was marked by a sharp focus and a sense of purpose. In an • documenting opportunities and needs, atmosphere of cooperation, the committee's active and • long-range plan, lively discussions led to some concrete recommendations • science and technology centers, for action. • education and human resources, Previous meetings usually began with several presen­ • directions of research in the mathematical sciences. tations by various NSF staff members from the Division The committee met after the subgroup discussions of Mathematical Sciences (DMS) and other divisions. and endorsed various subgroup recommendations, which At this meeting, though, only DMS staff members gave were presented during the committee's session with NSF formal presentations, and they kept them brief. The pre­ Director Erich Bloch. The meeting closed with an open­ sentations concerned the NSF budget and plan, and four ended discussion and planning for the next meeting. new programs: Computational Mathematics, Research Experiences for Undergraduates, Calculus Reform, and

FEBRUARY 1988, VOLUME 35, NUMBER 2 255 Advisory Committee

How the DMS Fits In clear that certain problems remain, such as the declining number of American Ph.D.s in mathematics. One source In one of the presentations, DMS Director Judith S. of this problem lies at the undergraduate level. For Sunley provided some interesting background on how example, according to Jerome Goldstein, some schools the DMS fits into the NSF and into the government in encourage students to complete a double major of math­ general. She explained that each year, the DMS .actually ematics with another field, but often these double majors works with several different budgets. For example, at have very few mathematical requirements. Lynn Arthur the time of this writing, the DMS was operating with Steen cited a study which said that 25% of mathemat­ a provisional budget, because its 1988 budget had not ics majors were actually receiving double majors with yet been approved by Congress. By August 1987, the computer science. NSF had submitted its 1989 budget to the Office of Another reason for a follow-up to the David Report Management and Budget (OMB), and, by February is the need to indicate new scientific opportunities that 1988, the budget will have gone to Congress. In addition, have surfaced since the report came out. As an example, for long-range planning, the DMS must consider its Goldstein pointed to the potential impact of mathematics budgetary needs for 1990 through 1994. The DMS budget in the health sciences. He said that the Centers for passes through many hands within the NSF before it even Disease Control have been using a mathematical model reaches the OMB-the Directorate of Mathematical to predict the spread of the AIDS virus. Recently, and Physical Science, the Controller's Office, and the researchers at Los Alamos National Laboratory have Executive Council. Jane Stutsman of the Controller's improved the model by using a more realistic and Office described the budget formulation as a "consensus­ sophisticated analysis and have obtained very different building process," in which, at each level, compromises results. are made and priorities established. The group agreed that the new report may take about Sunley also pointed to some examples of initiatives 18 months to prepare, should reassemble some of the that originated within the DMS and the mathematical people from the original David committee, and should be community, but have had an impact on the NSF as conducted under the auspices of the National Academy a whole. For example, she described how several years of Sciences or another group outside the mathematical of policy studies by the mathematical community had community. They also felt it should emphasize exciting resulted in the establishment of the Computational Math­ new research opportunities and the contributions that ematics program in the DMS. This program eventually mathematics can make to science and to the nation. formed the core of a much-expanded, NSF-wide initia­ tive in computational science and engineering which was designed to encourage the use of scientific computation Long-Range Planning in all areas of science and engineering. The long-range planning subgroup, chaired by Thomas Kurtz, focused on the idea of building strong links Subgroup Discussions between the DMS and other disciplinary divisions within the NSF. One such link has already been proposed: Documenting Opportunities and Needs the initiative entitled "Innovative Interactions Between The subgroup on documenting opportunities and needs, Mathematics and Biology," which was also discussed at chaired by M. Susan Montgomery, addressed the idea the meeting last April. of a follow-up to the David Report. Because of the Recent examples of fruitful interactions between importance of the David Report, Bloch said he would mathematics and biology have revealed the potential like to see it updated and encouraged the committee to richness of collaboration between these fields. This ini­ do so. The subgroup identified several reasons for such a tiative would seek to tap that potential by providing reassessment. new funds to promote the exchange of ideas between First, the group agreed that progress on various mathematicians and biologists. The intent is not only recommendations of the David Report needs to be to bring new mathematical tools to the frontiers of bi­ evaluated. The David Report made recommendations not ological research, but also to provide impetus for the only to the federal agencies, but to academic institutions development of new mathematics. and to the mathematical sciences community itself. The The subgroup felt this initiative would address the improvement in the federal agencies is clear: between needs for direct stimulation of collaborative research 1982 and 1987, federal support ofmathematical research and for training new scientists familiar enough with has almost doubled. However, progress on the other both fields to make significant contributions in a cross­ recommendations is less clear. disciplinary setting. The potential impact on biological Second, the critical needs of the mathematical com­ research and on the public perception of mathematics munity may have changed since the David Report. It is were seen as important assets of the initiative.

256 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Advisory Committee

The subgroup recommended the initiative be put a center based in another science such as biology, forward as "Phase I" of a broader program of "Innova­ engineering, or computer science. tive Interactions" to develop and strengthen connections Because of the fundamental role that mathematics between mathematics and other scientific fields. They plays in all of science and engineering education, the pointed out that the proposals the NSF receives for educational component of the STCs provides another its Science and Technology Centers (STCs) competition avenue for participation. Gnanadesikan said that actively may contain viable ideas for "Phase II." In addition, the involving students in research shows them the excitement interest which Washington policymakers have recently of mathematics. In addition, industrial linkages with the expressed in mathematical modeling of the spread of the STCs could provide work experience which he says AIDS virus could have implications for the first phase of is "very much treasured by students." Alan C. Newell the initiative. The full committee agreed that the DMS offered a different twist on the educational component: should ask the heads of the Directorates of Mathematical the idea of continuing education in the use of current and Physical Sciences and of Biological and Behavioral mathematical tools for users of mathematics. Sciences to explore ways to implement this initiative. The subgroup also discussed the idea of Research Education and Human Resources Groups in the mathematical sciences. Smaller and more focused than the large-scale STCs that the NSF is ini­ During the meeting of the subgroup on education and tiating in 1988, groups were seen as a natural way human resources, chaired by Steen, Gnanadesikan said for mathematicians to increase collaboration with other that the mathematical community must overcome its disciplines and integrate research and education. In "research-education dichotomy" if it is to be effective in addition, groups may provide an excellent vehicle for addressing education and pipeline questions. While this the "Innovative Interactions" initiative. Although they dichotomy is still strong, there is evidence of change. The reached no firm consensus on a model, the subgroup felt calculus reform initiative at the DMS, in addition to the that the diversity of ideas discussed affirmed the advan­ Mathematical Sciences Education Board and the MS2000 tages to collaborative research modes and to retaining a project (Mathematical Sciences in the Year 2000) at the flexible approach to their implementation. National Research Council, are likely to spur further efforts. The subgroup's lively discussion testified to their concern Science and Technology Centers with such issues. Part of the group's discussion focused on the under­ Ramanathan Gnanadesikan chaired the subgroup on representation of minorities and women in mathematics Science and Technology Centers (STCs). The subgroup and science. David Sanchez suggested the idea of a and the full committee agreed that centers may provide "matching" program to build linkages between mathe­ an excellent opportunity, as well as a challenge, to the matical sciences departments at historically black colleges mathematical community. The STCs are intended to and at research universities. Steen noted mutual benefits: combine basic collaborative research with technology the universities could stimulate research efforts and the transfer and education. Advantages of scale, "vertical colleges could contribute their expertise in dealing with integration" of research and education, and development the special needs and concerns of minority students. The of ties with other disciplines were seen by the subgroup subgroup felt the DMS should take an active role in as some of the key benefits of the STCs. initiating such linkages. Deputy DMS Director Andre Manitius, who is also Underrepresentation of women continues to be a an STC coordinator, noted that "it is obvious that there significant problem in the mathematical sciences. The can be no serious effort in STCs without the contribution subgroup discussed ideas for addressing this problem, of the mathematical community." In addition, he said, again focusing on the possibility of an assertive role mathematical scientists can play a ,crucial role in the for the DMS. Because women now comprise 15% of evaluation of centers' proposals, because many STC all mathematical scientists, it may be feasible to initiate proposals are likely to have a mathematical or statistical new programs to encourage female students through the component. Later, the full committee told Bloch that the use of role models, new fellowship opportunities, etc. STC reviewing panels should have more mathematicians Statistics was suggested as one area in which to begin and statisticians, and Bloch appeared very receptive to developing such ideas. the idea. The subgroup also discussed the problems associated Manitius also explained that mathematicians can with educational proposals that mathematicians have participate in the STCs in more than one way. For submitted to the DMS and to the NSF's Directorate example, a center might focus on a single mathematical for Science and Engineering Education. Several program topic, but have outreach to other departments on campus. officers said that mathematicians often have excellent Or, mathematics might function as an enabling tool for ideas for educational programs, but are unfamiliar with

FEBRUARY 1988, VOLUME 35, NUMBER 2 257 Advisory Committee the ways in which such proposals differ from scientific encouraged by the work you have done these two days," proposals. It was suggested that the professional societies he said. During a discussion on some of the issues raised, could hold seminars on writing educational proposals. Bloch remarked that mathematics is and will remain one ofthe areas of emphasis at the NSF. Bloch also spoke of the importance of international Scientific Directions in the Mathematical Sciences · collaboration and told the committee, "you need to be The subgroup on scientific directions, chaired by Alan concerned with that." He had just returned from France, Weinstein, focused on new and promising developments where he had visited the National Institute for Research in research in the mathematical sciences. The discussion in Computer Science and Automation (INRIA). Bloch ranged over a wide array of mathematical topics and has supported the idea of joint projects between NSF displayed a great vitality. For example, Andrew Odlyzko grantees and INRIA researchers. Manitius was involved described how the methods of ergodic theory and group in generating interest and support for such projects representation theory are now being used for codes for within the NSF, and in linking key people at the NSF high-speed modems. The time lag between theoretical de­ and at INRIA. What resulted was a new initiative called velopments and applications is shortening: mathematical "NSF-INRIA Collaborative Research," which will be papers written in 1983 or 1984 have led to products that announced early this year. The program will provide are already on the market. He also said that attempts Jl'~~oney and computer equipment for joint U.S.­ to understand the geometry of the Karmarkar algorithm (French 1projects in computer science, engineering, and have revealed that the trajectories used are geodesics in mathertlatics. a particular Euclidean geometry. Another topic touched upon during the committee's Interconnections between fields emerged as a theme free-form discussion was the problem of mathematicians of the subgroup's discussion. Examples cited included who do high-quality research but who have stopped ap­ the use of dynamical systems in robotics, connections plying for NSF grants. Sunley suggested that data from between logic and model theory, the use of continuous the NSF on declinations of grant proposals could provide methods in numerical analysis, and the trend toward some insight into how many active research mathemati­ nonsmooth methods in geometry. The group felt that the cians are unsupported. In addition, universities might be richness of the topics discussed testified to the health able to provide data on those who are writing papers but and unity of the discipline. have no grant support. The area of geometry frequently surfaced during Richard Nicholson, Assistant Director for Mathemat­ the discussion. The group noted that there have been ical and Physical Sciences, said that he personally reads important recent strides not only in geometry itself, selected "best declinations" from all divisions in his but also in the applications of geometry to other areas directorate. He indicated that the quality of declined of mathematics and to other fields of science. The proposals in mathematics is comparable to that in other full committee endorsed the group's recommendation disciplines in his directorate, and that in mathematics, that the NSF explore the possibility of a "geometrical as in all disciplines, the quality seems to have risen mathematics" initiative emphasizing both research in in the past few years. While this situation may appear geometry and applications. at odds with the recent increases in the DMS budget, Such an initiative could have important connections he explained that, in order to increase grant size, the to education. Many geometers must learn about the NSF has maintained a policy of limiting increases in other disciplines that drive many geometrical problems, the number of grants. Increasing the number of grants and, conversely, those in other fields need to learn by reducing average grant size would be shortsighted, he the tools and methods of geometry for applications. said, especially since grants in mathematics are not large. A geometry initiative could provide special training Nonetheless, some committee members felt that the for graduate students and postdoctoral researchers. In situation in the mathematical sciences is anomalous. addition, increased use of geometry and visualization Kurtz noted that in many other sciences, almost every using computer graphics could be an important means researcher is supported, but the same is not at all of revitalizing college and precollege mathematics. true in mathematics. Steen pointed out that while the nation's small colleges have the greatest potential of producing students who go on to graduate school, very Discussions of the Full Committee few mathematicians at such institutions receive NSF Bloch's session with the committee began with a persua­ grants. Said Steen, "This sends a clear signal to the sive description by Newell of the ideas and recommen­ students: don't go into mathematics." dations the committee had formulated. After listening patiently and with interest, Bloch complimented the committee for having "done a lot of work." "I am very

258 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Advisory Committee

Meeting Seen as Successful they demonstrated at this meeting, it will be a strong voice for the mathematical sciences The word around the NSF was that the meeting had been in the NSF. highly successful. NSF staff members who had attended Allyn Jackson the meeting as observers were reportedly impressed with Staff Writer the committee's focused discussion and sense of purpose, and the exchange with Bloch was seen as productive and positive. Much of the credit for the success goes NSF Advisory Committee to Sunley, who reorganized the meeting by breaking for the Mathematical Sciences the committee up into the topical subgroups. Sunley, Robert D. Edwards, University of California, Los An­ Manitius, and the DMS program officers contributed geles; Ramanathan Gnanadesikan, Bell Communications a great deal of effort to the meeting by preparing Research; Jerome A. Goldstein, Tulane University; Julia extensive background materials to lay the groundwork Knight, University of Notre Dame; Thomas G. Kurtz, for substantive discussion. As chairman, Newell provided University of Wisconsin, Madison; Andrew J. Majda, the confidence and enthusiasm which gave the committee Princeton University; M. Susan Montgomery, University a sense of direction. of Southern California; Alan C. Newell, Chairman, Uni­ The committee itself seemed to be pleased with the versity ofArizona; Andrew M. Odlyzko, AT&T Bell Lab­ effectiveness of the meeting. Their enthusiasm was clear oratories; David N. Sanchez, Lehigh University; Lynn as they discussed the preparations they would make Arthur Steen, St. Olaf College; Stephen M. Stigler, before the next meeting, on March 24-25. A report University of Chicago; Chuu-Lian Temg, Northeastern will be written to carry the recommendations of this University; Alan D. Weinstein, University of California, latest meeting formally to Bloch and Nicholson. If the Berkeley; Floyd L. Williams, University ofMassachusetts, committee sustains the level of interest and commitment Amherst.

COMPUTATIONAL MAmEMATICS PROGRAM TAKES SHAPE

In the area of computation, the main role of mathematics history, in its objectives, and in the projects it supports, has been to provide that essential link between the scien­ this program recognizes not only the pervasive and tist and the computer. Now mathematicians themselves fundamental role of mathematics in computation, but are beginning to find that present-day computers offer also the potential of present-day computers to reach into solutions to problems, provide new insights, and present all areas of mathematics. unexpected challenges. For example, results in number theory and statistical matrix theory have been proved with computers guiding the researchers through the in­ History tricate theoretical work. The understanding of chaos in The Computational Mathematics program has its roots in dynamical systems has depended in an essential way a series of recommendations made by the mathematical on numerical simulations. Computers have been used to community over the past five years. In 1982, a report by generate new families of minimal surfaces whose ana­ a panel headed by Peter D. Lax put forth several recom­ lytical form was intractable without the computer. And mendations, including making supercomputers available computational investigations of partial differential equa­ to academic researchers and increasing support for com­ tions relating to fluid dynamics are now being conducted putational mathematics. The NSF responded to the first on supercomputers. recommendation with the establishment of the Divi­ One year ago, the National Science Foundation (NSF) sion of Advanced Scientific Computing, but the second established a program in Computational Mathematics in recommendation required further effort. the Division of Mathematical Sciences (DMS). In its

FEBRUARY 1988, VOLUME 35, NUMBER 2 259 Computational Mathematics Program

The 1984 David Report reiterated the importance he did research in the numerical solution of partial of computational mathematics. In that same year, the differential equations. NSF Advisory Committee for the Mathematical Sciences discussed the idea of increasing support for compu­ Objectives of the Program tational mathematics with NSF Director Erich Bloch, who expressed interest in the idea. Shortly afterward, Since its beginning, the formulation of the program a panel headed by Werner C. Rheinboldt produced a and its objectives have changed and have become more report that expanded on the third recommendation of focused. The program presentlY has three main purposes: the Lax Report. The Rheinboldt Report emphasized that • to promote innovative uses of computers in mathe­ the interdisciplinary nature of computational endeavors matical research by an individual or a team necessitates a group or team approach. • to encourage the development and implementation The Rheinboldt Report lent strength to the efforts of critical computational techniques from inception to of the NSF's main proponents of the computational algorithm to software mathematics program, John C. Polking, then Director of • to support research opportunities for mathemati­ the DMS, and Melvyn Ciment, then a Program Officer cians and scientists in applying mathematics to large-scale for Applied Mathematics. Kent Curtis and Bruce Barnes scientific computation. of the Division of Computer and Computation Research Chin says that the main difference between this pro­ were also involved in the establishment of the program, gram and computational mathematics programs at the for originally it was envisioned as a joint initiative defense agencies and at the Department of Energy is between their division and the DMS. The combined the explicit goal of encouraging the use of computation effort persuaded key officials in the NSF's Directorate of in all areas of mathematics. Generally, other programs Mathematical and Physical Sciences of the merit of the focus only on the second and third objectives. Also, this proposed program. program differs from others such as the DMS's SCREMS In fact, the case was so persuasive that the idea grew program (Scientific Computing Research Equipment for into an NSF-wide initiative in Computational Science the Mathematical Sciences), which provides only equip­ and Engineering. This initiative, begun in 1986, provided ment, or the NSF supercomputer access program, which new resources for computation in all areas of science provides only computing resources. and engineering. Some divisions within the NSF have In fact, Computational Mathematics will generally distributed the new funds from the initiative to existing not support requests just for hardware or for computer programs, while others, like the DMS, have used the time. Ann Boyle, Program Director for Algebra and funds to establish new programs. Number Theory, handled the program for two months Initially, there was some question within the DMS before Chin arrived. She says, "If you're developing as to whether the funds should be distributed to the ex­ some software that others can use too, if you're going to isting programs. It was decided that a separate program make computation more accessible to others, or if you're could better provide the focus and visibility needed to formulating a new idea of how to use computers, then make a significant impact. In addition, one of the goals Computational Mathematics may consider split-funding of the program is to encourage interactions between the research." mathematicians in different areas and between mathe­ Implicit in the objectives of the program is its inter­ maticians and scientists in other disciplines. Pursuing disciplinary component. Increasing the use and useful­ this goal would have been difficult had the funds been ness of scientific computing requires more than simply distributed to all the different DMS programs. However, additional funding for individual investigators. Many all of the DMS programs have benefitted: in fiscal1987, important research problems in science and technology every other DMS program split-funded projects with the require an interdisciplinary approach which necessitates Computational Mathematics program, which spent 22% not only the collaboration of scientists, engineers, math­ of its $3 million budget in this way. ematicians, statisticians, and computer scientists, but The program has had more than its share of staffing also access to suitable hardware and software and the difficulties. Shortly after the program began, Ciment, who associated support personnel. was serving as program officer, left to accept a position In addition, says Chin, the program is intended to as deputy director of the Division of Advanced Scientific stimulate interactions within mathematics itself. Chin Computing. Paul Swarztrauber of the National Center for sees computation as a means of "enhancing the current Atmospheric Research took his place, but could remain trend of cross-fertilization between different areas of with the program for less than a year. His successor is mathematics." Computation becomes a common ground the present program officer, Raymond C. Y. Chin, who on which mathematicians from various areas can meet joined the DMS staff in September 1987 from Lawrence to exchange not only ideas about computing but about Livermore Laboratory in Livermore, California, where mathematics as well. "So many unexpected and exciting

260 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computational Mathematics Program

results have come out of collaborations between mathe­ Examples of Projects Funded maticians in different areas," says Chin, "but too often During fiscal 19 87, the Computational Mathematics pro­ they are isolated from one another. We have to start gram funded 24 out of 44 proposals with its bu~ge~ of talking to each other more." $3 million. The program supported not only prmcipal According to Swarztrauber, another effect this pro­ investigators, but also graduate students, postdoct?ral fel­ gram can have is to help attract and keep more young lows, programming and secretarial services, eqUipme.nt, people in mathematics. "The computational aspects of and computer time. The projects funded covered a wide mathematical disciplines are relatively new develop­ range of topics; a few of the projects are described b~low. ments, and the people doing this research are young J. Glimm and 0. McBryan of the Courant Institute and vibrant," he says. "The Computational Mathematics of Mathematical Sciences received a grant to investigate program is helping to support the young people attracted the area of nonlinear waves in hyperbolic systems and in to these rapidly developing areas." hyperbolic-elliptic systems. An interesting feature of the One of the reasons mathematics plays such a crucial project is the simultaneous development of the ma~he­ role in computation is that developments in hardware matical theory and the computational implementation. require constant updating and even rethinking of the The proposal says, "The goal of this work is to develo~ software. Indeed, developments in software have trailed the mathematical theory and to utilize it to the maxi­ those in hardware: the machines continue to become mum extent possible within the computational process." faster, but it is not always clear how to exploit the The project received split funding with the Division of increased speed. The NSF has seen this problem in their Advanced Scientific Computing. National Supercomputing Centers, which are reaching J. Guckenheimer of Cornell University received a the saturation point. Now the centers must make sure group grant for computational researc~ in dynamical that the users' codes are as efficient as possible. systems. The project has the broad aim of develop­ But increasing the efficiency of the codes is difficult. ing algorithms and efficient computing environments for "Physicists and chemists burn up a lot of supercomputer studies in dynamical systems, but encompasses several time," says Chin. "But if they have codes that work, specific problems. For example, Hilbert's 16th pro~­ they have to use them. They don't have time to worry lem will be investigated using numerical and symbohc about whether they're optimally efficient-they have computations to obtain certain bounds associated with to focus on the science." Mathematicians will use the polynomial vector fields. Another aim is to use ~AC­ insights gained from such calculations to develop more SYMA to implement perturbation methods for ordmary efficient algorithms. Says Chin, "Mathematicians can differential equations. In addition, the group will sym­ make enormously important contributions to large-scale bolically compute polynomial knot invariants associated scientific computing, for improvements in efficiency are with periodic orbits of 3-dimensional flows. . often just as important as increases in computer speed." A project headed by Charles Sims of Rutgers Um­ versity was split-funded with the Algebra and Number Interdisciplinary Proposals Theory program. Among other things, Sims is exp!or­ ing the possibility of constructing a solvable quo~Ient Probably the greatest challenge facing the program is its algorithm which will be useful in the s.tudy. of fimtely interdisciplinary aspect. For one thing, it is often difficult presented groups which may have an mfim~e number to find reviewers who can competently evaluate inter­ of elements. His project is unusual because, m algebra, disciplinary proposals. Not only must each disciplinary using the computer to investigate finite p~enoi?ena is contribution be evaluated, but also the merit of the en­ often straightforward, but moving to the mfimte case tire project must be weighed. Chin recommends writing usually requires a new approach. proposals in a "simpler" manner. "Investigators should One of the largest grants in Computational write proposals that are addressed M~th­ to nonspecialists, that ematics went to the Geometry-Supercomputer anyone can read." Project, organized by Albert Marden of the University. of Min­ Interdisciplinary proposals received by Computa­ nesota. Combining research in geometry, numencal tional Mathematics have not always adequately explained a~al­ ysis, computer science, and computer vision, the project how the different parts of the project will be integrated. brings together 13 mathematicians from the U.S., Eng­ "Often investigators propose to get a group of people land, and France to develop algorithms and comp~ta­ together, but don't explain how the research will form tional techniques in order to pursue important questw~s a unified whole," says Chin. Successful interdisciplinary in geometry. In addition, they will conduct. research. m proposals make a case for why the research would fractals and dynamical systems. (For more mformatlon proceed more slowly or not at all without collaboration. on this project, see the article in this issue of Notices.)

FEBRUARY 1988, VOLUME 35, NUMBER 2 261 Computational Mathematics Program

Future of the Program foundations of computation. In addition, Chin says he would like to see the program be influential in stimu­ The program could take several different directions in lating thought about curriculum issues in computation~! the coming years. Chin says the program will try to mathematics. For example, an undergraduate program m strengthen its ties with other computational programs computational mathematics might be very attractive to in the NSF. The NSF-wide initiative in computational students interested in careers in industry or government science and engineering increased resources for comput­ laboratories. With the increased importance of computa­ ing, but the overall effort remains somewhat fragmented. tion, this program stands at the center of scientific and Workshops to bring people together from different dis­ technological development. ciplines might help strengthen the ties. DMS Director Judith S. Sunley said that a future objective of the Allyn Jackson program is to support research in the mathematical Staff Writer

The first published Colloquium Lectures were those of E. B. van Vleck, H. S. White, and F. S. Woods in 1903.

AMERICAN MATHEMATICAL SOCIETY •'PROVIDENCE • AUGUST 8-12, 1988

262 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematical Text Processing

Richard S. Palais

Several years ago, as I wrote the markup language style of input nesses become apparent, and I had first article in this series on TWP for mathematical text. I had heard no time for that kind of test. So (technical word processing) for of this eminently sensible strategy it was a stroke of good luck that personal computers, the picture long in advance from beta testers, Timothy Wallstrom wrote to me was one of rapid development and and was anxious to test it out my­ last September. Tim is a Prince­ flux. But now the situation has self. When I did try it, my first ton graduate student who started stabilized and it seems an appro­ impressions were quite positive; I out writing his thesis with Word priate time to bring the column found the equation processor both 3.0 and later switched to T£X. I to a close. In fact I had originally easy to use and easy to learn. But I found his description of his expe­ planned to finish the series in this have learned that first impressions riences so interesting that I asked issue, with a final article bringing of software obtained by working him to rewrite it for this column, up to date my discussion of TWP toy examples can be deceptive. and he kindly took time out from software for writing mathematics Only by exercising a program over his thesis to write the report below. on the Macintosh family of com­ many weeks in a real application puters. But, of course, this week do its true strengths and weak- of the Notices deadline turned out to be not only the week I received significant updates of three impor­ tant pieces of software (MacEqn, WriteNow, and MacT£X), but it is also exam week here at Brandeis, The Equation Processor in Word 3.0 and I have decided to put off that final review until next month. Timothy Wallstrom One of the more significant events in Macintosh word process­ ing this past year has been the long awaited appearance of Mi~rosoft Word 3.0. This turned out to be an embarrassing fiasco for Microsoft; the original release was riddled Among Macintosh word proces­ any personal computer." Word 3.0 sors, Microsoft with bugs, some fairly serious. But Word has long was almost three times the size of by now these have been pretty been the most popular alterna­ Word 1.05, even without the dic­ tive well eliminated and there is little to Apple's MacWrite. For al­ tionary, and its dizzying array of most doubt that it will become one of two years, Word faced min­ features required over 500 pages the staples of high-end word pro­ imal competition, and remained of documentation to describe. stuck cessing for the Mac. For me Word in its version 1.05 incar­ Included among these features 3.0, whatever its flaws, is an im­ nation, first released in April of was one of particular interest for 1985. In February of 1987, portant milestone from the TWP Micro­ technical word processing (TWP), soft standpoint. For Microsoft had the released version 3.0, which it and a first among Macintosh word touted idea of marrying WYSIWYG word as "the most powerful word processors: Word 3.0 had its own processing processing of normal text with a software available for integrated formula processor. No

FEBRUARY 1988, VOLUME 35, NUMBER 2 263 Mathematical Text Processing

longer would you need to create formula is essentially a graphic. principle and what it can do conve­ your equations in a separate desk To create a formula, one toggles niently in practice. In principle, it accessory (DA) or application, and Word into "Show ~, mode, and can handle just about any equation then paste them into your man­ enters a series of commands, to­ you are likely to run across. The uscript. Aside from the formula gether with their arguments. The set of formula commands include processor, however, most of Word following equation, for example, is those for matrices, brackets, frac­ 3.0's other features, such as mail well known (though not, perhaps, tions, integrals, radicals, and over­ merge or form generation, were in this guise): strike. Some of these commands designed with the business com­ take modifiers, that enhance their munity in mind, and are of little x1.2 =. \F( -b ±. \R(b2 - 4ac), 2a). versatility. Formulas need not be use for TWP. Is the formula pro­ "displayed"; they can be accom­ As you may have guessed, a " . \" cessor an efficient tool for TWP, or modated "in-line," though Word (obtained by typing "\" with the a viable alternative for desk acces­ is poor at adjusting interline spac­ command and option keys de­ sory equation processors? Is it a ing in such cases. pressed), readies Word for a for­ good reason for a mathematician In practice, the limiting factor mula command, such as "F" (for to buy Word 3.0? in creating formulas with Word "fraction"), or "R" (for "root"). If your needs are light and is the difficulty in reading and Parentheses are used to group the occasional-your equations are usu­ evaluating the "source code." This list of arguments, and commas to ally short and elegant, you are not can actually be much harder in separate them. Formulas can be concerned about the correct use of Word than in TEX. Several factors used as arguments of other for­ italic, and your output will usually contribute to this problem: mula commands. An expression be printed on the ImageWriter­ • The characters of the source involving the "root" formula com­ you may find the formula proces­ code can be formatted just like mand, for example, was used as sor quite handy. It is certainly a any other text in the document. the first argument of the "fraction" great improvement over creating This is useful and necessary­ formula command. By nesting for­ equations in MacPaint or Mac­ you may need to italicize your mulas in this way, one can build Draw, and then pasting them in expressions, or use characters up formulas of considerable com­ as graphics. But if you need to from a symbol font. But it plexity. Word automatically ad­ write technical manuscripts of any tends to make a mess, and can justs fraction bars, brackets, in­ length or complexity, you will al­ lead to confusion. Since each tegral signs, and other characters, most certainly find yourself turn­ character automatically inher­ for the size of the expressions in­ ing to more powerful tools that are its the formatting of volved. the pre­ simultaneously easier to use, such vious character, formula com­ To see the formula as it will as the Expressionist DA, or one of mands and their companions­ print, hold your breath and tog­ the Macintosh implementations of commas, parentheses, and the gle Word into "Hide ~" mode. If TEX, such as TEXtures. (Yes, once " . \" character-tend to be­ you have entered the formula cor­ you have mastered it, TEXtures is come italicized, subscripted, or rectly, the tangle of formula com­ easier to use than Word, partic­ even encrypted into a symbol mands, parentheses, and commas ularly if you have long or com­ font. This doesn't affect the fi­ will evaporate, and the remaining plicated equations that employ an nal formula, but it can vastly characters will fold up into the assortment of mathematical sym­ complicate debugging and edit­ formula you intended. The code bols.) Word 3.0 accommodates in­ ing. above, for example, will produce line graphics, so it can be used • The "Show ~" mode shows not effectively in conjunction with an only the formula commands equation processor DA, but so do and characters, but also spaces other word processors, such as (as dots), tabs, paragraph mark­ WriteNow, that cost half as much. If you've made a mistake, the ers (of course), and everything Word's formula processor is a formula may fold up partially or else, and these frequently over­ hybrid between the powerful but incorrectly, but usually it will just lap. The result can be visual intimidating "mark-up languages" sit there. There are no diagnostics. chaos. such as TE)(, and less powerful In discussing the formula pro­ • Pairing off left and right paren­ but more easily learned WYSIWYG cessor, it is important to distin­ theses in a complicated for­ approaches to TWP, in which the guish between what it can do in mula is a tedious and time-con-

264 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematical Text Processing

suming exercise, particularly if in-line formulas, Word will spare usually quite adequate. I am con­ they have contracted exotic for­ you the tedium of "cut and paste." cerned, rather, with problems of mats. Of course, some diffi­ The printed results of the for­ character placement and spacing. culty of this kind is inevitable, mula processor are quite adequate Such problems, for example, al­ but Word maximizes the prob­ on the ImageWriter and for in­ most always accompany the use of lem by minimizing its reserved formal work. When printing to italic. In every WYSIWYG equa­ symbols. Just the comma and the LaserWriter, however, it shares tion processor I have seen, the parentheses are used, and these all the problems suffered by other spacing of italic characters is quite are required everywhere. Even WYSIWYG approaches to TWP on inaccurate, leading to gaps and the "Displace" command, that the Mac. A number of problems, collisions with sub- and super­ takes no argument, must be in fact, seem inherent to current scripts, among other things. TEX followed by an empty pair of WYSIWYG techniques, and since handles italic (and everything else) parentheses. these problems are not shared brilliantly, and will produce truly • The formula processor has no by TEX typesetting software, now typeset results. built-in intelligence about what available for the Macintosh, it may • Can you really see what you should and should not be ren­ be useful to discuss some of them. will get? The Macintosh screen, dered in italic. It's quite a • Fonts. Mathematical docu­ with a resolution of 72 dpi, sim­ nuisance to go through and ments use a wide variety of sym­ ply cannot render accurately what change the formatting charac­ bols, and while excellent Macin­ you will get on the 300 dpi Laser­ ter by character. What's worse, tosh symbol fonts have been de­ Writer. The difference is signifi­ such alteration can make the veloped, such as the Maine and cant for mathematical work-an document virtually unreadable Princeton fonts, there is still the equation that looks fine on screen on the screen, particularly when inevitable tedium of memorizing may print out poorly on the Laser­ viewing the source code. The that "v"' is "option-shift-_", or Writer. In fact, if you are using italic algorithm, which yields that "E" is "option-shift-q", or at LaserWriter fonts, the dot pat­ somewhat illegible results even least of consulting a table for this terns you see on your screen are on isolated characters, tends to information. In TEX, you simply not even used by the LaserWriter, push a character into the next type a control sequence such as which instead employs character character's personal space, ob­ "\phi", "\psi", or "\in", using shapes stored in its own ROM. scuring them both. the roman alphabet (whose key There is no way, therefore, to • In contrast to TEX. Word has locations you already know), and magnify the screen image so as no macro capability. It has a obtain ¢, 'If, E, and so forth. This to obtain a more accurate view user-defined glossary, but this involves more typing, but I'm con­ of what will be printed. Fonts are is hardly comparable. The use vinced that it is faster and less handled differently by the Macin­ of macros greatly simplifies the draining, even if you do use a lot tosh TEX programs, however, and appearance of the source code of \epsilons. you are able to preview exactly, at in a complicated formula, and • "Near-typeset" quality. While 300 dpi, the way the TEX fonts makes debugging easier. there is much justifiable enthusi­ will print on the LaserWriter. Word's integrated approach does asm over WYSIWYG methods of It is, of course, blatantly unfair confer some advantages to its for­ document preparation, it must be to compare Word's formula pro­ mula processor. Some applications clearly stated that at present, none cessor to the mathematical type­ and DAs produce equations that, of these methods will lead to re­ setting capabilities of such state­ once pasted into your manuscript, sults of true typeset quality. The of-the-art machinery as TEX. In­ become uneditable graphics. You discrepancy between typeset and stead, Word's formula processor is can always edit the equations in "near-typeset" quality, moreover, rather like the screwdriver in the a Word document. Since the char­ is most noticeable in mathematics, Swiss army knife that is Word 3.0. acters in your formula are part of which is the hardest kind of mate­ It is handy in a pinch, and with your text, any global font changes rial to typeset, and can have a con­ some ingenuity, you can do quite you make (through use of style siderable impact on the ease with a bit with it. For any major under­ sheets, for example), will auto­ which a manuscript can be read. I taking, however, it is simpler and matically apply to the equations. am not talking about printer reso­ better to get the right tool for the If you tend to use a lot of short, lution here; the LaserWriter's 300 job. dots-per-inch (dpi) resolution is

FEBRUARY 1988, VOLUME 35, NUMBER 2 265 News and Announcements

New MathSci Service Available charge will be assessed for each ad­ In order to apply for travel and ditional reference sent. Requests for subsistence support, graduate stu­ A new service is now available on the full text of articles can be made dents must submit basic mathemati­ MathSci, the electronic index which online through DIALORDER with cal biographical data (school, degree provides online access to Mathemat­ the Mathematical Reviews Document program, major professor, expected ical Reviews and several other math­ Delivery Service, MATHDOC. graduation date, etc.,) plus two let­ ematical and statistical indexes. For more information, contact ters of recommendation (one from DIALOG Information Services DIALOG at 1-800-3-DIALOG. the major professor). Young Ph.D.s Inc. has announced that its Selective must submit a curriculum vitae, one Distribution of Information (SDI) Centennial Celebration Travel letter of recommendation, and a list Service is available on MathSci. SDI and Subsistence Support of current grant support. is similar in concept to the Mathe­ Applications and references must matics Offprint Service that the AMS It is anticipated that the Society will be received by Mrs. Tricia Cross, ran in the early 1970s. With SDI, receive funds from one or more fed­ Centennial Coordinator, American users describe the kinds of articles eral agencies for travel and subsis­ Mathematical Society, P.O. Box 6248, in which they are interested, and tence support for senior graduate Providence, Rhode Island 02940, no SDI automatically sends each user students and young Ph.D.s to attend later than April 5, 1988. The selec­ any new MathSci entries fitting that the AMS Centennial Celebration to tion panel will notify all applicants user's description. be held in Providence, Rhode Is­ of its decision on May 15, 1988. The user's description is stored land from August 8 through August Preregistration deadline is June 1, in an "SDI profile," a computer 12,~1988. The Centennial program, 1988. file which contains MathSci com­ built around 21 Invited Addresses mands specifying various attributes by an extraordinary group of U.S. International Neural Network of the articles in which the user mathematicians, is likely to influ­ Society 1988 Annual Meeting is interested-author, subject, key­ ence the direction of mathematics words, journal name, publisher, year research internationally for the next The International Neural Network published, English or non-English ten to fifteen years. Such a program Society (INNS) will hold its annual language, etc. Users can also specify will be particularly valuable to this meeting at the Park Plaza Hotel in whether they want only bibliographic new generation of mathematicians. Boston on September 6-10, 1988. references or the full MathSci records Applicants eligible for support The planned conference program in­ containing the abstracts of the pa­ will include graduate students in the cludes symposia on selected topics, pers. With each monthly update of mathematical sciences at U.S. insti­ contributed oral and poster presenta­ MathSci, the user is automatically tutions of higher learning and Ph.D.s tions, tutorials, commercial and pub­ sent, in the U.S. mail, a list of the who are less than three years from lishing exhibits, a placement service references fitting the user's profile. their degrees. The selection commit­ for employers and educational insti­ The cost for the service is $12.95 tee will establish a selection crite­ tutions, government agency presen­ per profile per month. For this price, rion aiming at the broadest possible tations, and social events. Plenary the user will receive up to 25 refer­ distribution of support. These selec­ lectures will be given by Stephen ences with each monthly update of tion requirements may undergo slight Grossberg, Carver Mead, Terrence MathSci. If, for a particular update, modification pending exact amount Sejnowski, Nobuo Suga, and Bernard there are more than 25 references of awards. Widrow. fitting the user's profile, an extra

266 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Individuals from fields as diverse paper sessions. Abstracts accepted 40 Washington Street, Wellesley Hills, as engineering, psychology, neuro­ for presentation at the meeting will Massachusetts 02181, 800-521-5144 science, mathematics, and physics are be published as a supplement to the or 617-235-7500. now engaged in neural network re­ INNS journal, Neural Networks. Pub­ Advance Registration Fee Schedule search. This diversity is reflected in lished abstracts will be available to INNS Member: both the 1988 INNS Annual Advi­ the conference participants until March 31, 1988, $125; sory Committee and in the Editorial Tutorials will consist of one-hour until July 31, 1988,$175. Board of the INNS journal, Neural introductory lectures by distinguished Nonmember: Networks. To enhance the effective­ scientists. The lectures will help pre­ until March 31, 1988, $170*; ness of these multidisciplinary events pare the audience for· the more ad­ until July 31, 1988, $220*. and to inform a wide audience, this vanced presentations at the meeting. Full-time student: meeting will be carried out with the The tutorial topics include: member $$0; nonmember $85*. active participation of several profes­ • Vision and image processing *Includes the option of electing sional societies, including AMS and • Pattern recognition, associative one-year INNS membership and sub­ SIAM. learning, and self-organization scription to the INNS journal, Neural Special Sessions, with a distin­ • Cognitive psychology for informa- Networks free of charge. guished group of invited lectures, tion processing The conference registration fee will be given in: • Local circuit neurobiology schedule has been set to cover ab­ • Vision and Pattern Recognition • Adaptive filters stract handling costs, the book of • Motor Control and Robotics • Nonlinear dynamics for brain the­ abstracts, a buffet dinner reception, • Cognitive and Neural Systems ory (competition, cooperation, equi­ coffee breaks, informational mail­ • Combinatorial Optimization and libria, oscillations, and chaos) ings, and administrative expenses. Content Addressable Memory • Applications and combinatorial op­ Anticipated financial support by gov­ • Applications and Implementations timization ernment and corporate sponsors will The INNS has announced an open • Implementations (electronic, VLSI, cover additional basic meeting costs. call for abstracts to be considered and optical neurocomputers) Tutorials and other special pro­ for oral or poster presentation on Tutorials will be held on Tuesday, grams will require payment of addi­ biological and technological models September 6, 1988, from 8:00 a.m. tional fees. of: until 6:00 p.m. The general confer­ • Vision and image processing ence will begin with a reception at Manin Selected • Speech and language 6:00 p.m., followed by the conference as Brouwer Lecturer • Sensory-motor control and robotics opening and a plenary lecture. • Pattern recognition Tutorial Registration Fee Schedule Yurii I. Manin has been selected • Associative learning Note: Tutorial Attendees must as the 1987 Brouwer Lecturer and • Self-organization also register for the conference. Medalist of the Netherlands Mathe­ • Cognitive information processing INNS Regular Member: matical Society in the area of number • Local circuit neurobiology until March 31, 1988, $100; theory. To commemorate the Dutch • Analysis of network dynamics until July 31, 1988, $150. mathematician L.E.J. Brouwer, the • Combinatorial optimization INNS Student Member: Society regularly designates a special • Electronic implementation (VLSI) until March 31, 1988, $30; area of mathematics as the current • Optical implementation until July 31, 1988, $60. Brouwer area. • Neurocomputers Students are encouraged to join Manin is associated with the • Applications the INNS and to participate in the Steklov Mathematical Institute of . To be considered for presenta­ Annual Meeting. For full-time stu­ the Soviet Academy of Sciences. He tion, abstracts must be typed on the dents, reduced registration and mem­ is known for his outstanding work INNS abstract form in camera-ready bership rates are available. Addi­ on arithemetic algebraic geometry, format and be submitted by March tional financial support is anticipated logic, and theoretical physics. Al­ 31, 1988. An abstract form and in­ for stud_ents and meeting volunteers. though Manin was unable to deliver structions may be obtained from To apply, attach a letter of request the Brouwer Lecture in person (nor­ Dr. Harold Szu-INN, NRL Code and a brief description of interests to mally a condition for the award), 5756, Washington, DC 20375-5000 the conference registration form and highlights of his work were presented USA. Acceptance notifications will send to the address given below. in his absence. be mailed by June 30, 1988. An in­ For further information and Previous Brouwer Lecturers and dividual may make at most one oral an application form, contact Medalists include Rene Thorn (1970), presentation during the contributed UNIGLOBE-Neural Networks 1988, Abraham Robinson (1973), Armand

FEBRUARY 1988, VOLUME 35, NUMBER 2 267 News and Announcements

Borel (1978), Harry Kesten (1981) ciate professor of mathematics, Cal­ Yugoslavia, and Zambia. In addi­ and Jiirgen Moser (1984). ifornia State University, Hayward: tion, other countries are open to Brazil; CAROL N. HARRISON, assis­ applications in any discipline and International Exchange of Scholars tant professor of mathematical sci­ mathematics is among their preferred ences, Susquehanna University: fields. The Council for International Ex­ Liberia; THOMAS C. HOLYOKE, pro­ Scholars in all academic ranks, change of Scholars has announced fessor emeritus of mathematics, An­ including emeritus, are eligible to ap­ that more than 900 scholars, aca­ tioch College: Botswana; PAUL D. ply and must have a Ph.D., college or demics, and professionals have re­ HuMKE, professor of mathematics, university teaching experience, and ceived awards under the Fulbright Saint Olaf College: Hungary; STEVE evidence of scholarly productivity. Scholar program to travel, lecture, A. KosciUK, professor of mathemat­ U.S. citizenship is required. In a consult and conduct research abroad ics and statistics, National Autono­ few countries (of Central and South in 1987-1988. The council, an af­ mous University, Nicaragua: Nicara­ America and Francophone Africa), filiate of the American Council of gua; MARC S. MANGEL, professor of knowledge of the host country lan­ Learned Societies, cooperates with mathematics, University of Califor­ guage is required. the United States Information Agen­ nia, Davis: United Kingdom; MAR­ For information, contact CIES, cy in administering the Fulbright pro­ IALUISA N. McALLISTER, professor Eleven Dupont Circle NW, Suite gram. of mathematics, Moravian College: 300, Washington, DC; 202-939-5401. Included in the list of those se­ Italy; SHELDON E. NEWHOUSE, pro­ When inquiring, indicate countries of lected for these awards are twenty­ fessor of mathematics, University of interest. -CIES News Release five in the fields of mathematics North Carolina, Chapel Hill: Brazil; and computer science. The names HENRY 0. POLLAK, independent Second Annual Courant Institute of these recipients, with their home scholar, Summit, New Jersey: Aus­ Prize for Mathematical Talent institutions and countries in which tralia; EDWARD L. ROBERTSON, pro­ they will be teaching or doing re­ fessor of computer science, Indiana In 1986-1987, the Courant Insti­ search, are given below University: Kenya; JoHN F. Rossi, tute held its second annual com­ CHRISTINE W. AYOUB, professor assistant professor of mathematics, petition for undergraduate scientists. of mathematics, Pennsylvania State Virginia Polytechnic Institute and Students were invited to submit orig­ University: Morocco; DALE W. State University: Finland; DAVID inal solutions to mathematical prob­ BEHRENS, associate professor of ScHMITZ, mathematician, Golden lems of their own choosing. mathematics, Pennsylvania State Uni­ Software, Golden, Colorado: Czecho­ The first prize of $1,000 was versity: Morocco; ELIZABETH D. slovakia; CHANCHAL SINGH, profes­ awarded to Andrea Bertozzi, a se­ BEHRENS, associate professor of math­ sor of mathematics, Saint Lawrence nior at Princeton University, for her ematics and business administration, University: India; PATRICIA SIPE, as­ entry, "Perturbed heteroclinic orbits Hastings College, Nebraska: Malawi; sistant professor of mathematics, in planar fluid flow." The second DAVID BELLIN, assistant professor of Smith College: Chile; CASLAV V. prize of $7 50 was awarded to Mark computer science, William Paterson STANOJEVIC, professor of mathemat­ Christopher Haase, a freshman at College: Honduras; DAVID W. CLAY, ics and statistics, University of Mis­ Ohio State University, for his entry, assistant professor of mathematical souri, Rolla: Yugoslavia. "Quadratic reciprocity over Zp[x]." and computer science, Florida Insti­ -Chronicle of Higher Education The deadline for this year's com­ tute of Technology: Lesotho; petition is April 1, 1988. Information KENNETH L. COOKE, professor of 1988-1989 Fulbright Grants and a complete set of rules can be ob­ mathematics, Pomona College: Brazil; in Mathematics Still Available tained by writing to Robert V. Kahn, CHARLES M. CRITTENDEN, professor Courant Institute of Mathematical of computer science, Weber State The Council for International Ex­ Sciences, New York Univeristy, 251 College: Jamaica; MARK G. DAVID­ change of Scholars (CIES) has an­ Mercer Street, New York, NY 10012. SON, assistant professor of mathe­ nounced that a number of 1988-1989 matics, Louisiana State University, Fulbright Grants remain available to Weizmann Institute of Science Baton Rouge: Iceland; REBECCA DER­ U.S. faculty in the field of mathe­ Announces SIMONIAN, assistant professor of epi­ matics. Postdoctoral Fellowships demiology and public health, Yale There are specific openings in University: USSR; DAVID D. DEx­ Austria, Congo, Czechoslovakia, The Feinberg Graduate School of TER, director of the department of Egypt, Gabon, Hungary, Jordan, Le­ the Weizmann Institute of Science computer science, Alma College: sotho, Morocco, Romania, Turkey, is now offering Postdoctoral Fellow­ Turkey; RICHARD L. EPSTEIN, asso- ships in the fields of biology, chem-

268 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

istry biochemistry-biophysics, phys­ Concentration Year gram committee to assess the merit ics ~athematics, and science teach­ in Nonlinear Elasticity of the paper. Twenty-minute pre­ in~. The fellowships, intended for sentations will be given on the ac­ young scientists who have re~ently A year of concentrated study (Octo­ cepted papers. A compilation of all received Ph.D. degrees, provide a ber 1987-July 1988) is taking place abstracts accepted will be available at twelve-month stipend (with COL ad­ in Rome at the Instituto perle Appli­ the conference, and complete confer­ justments), a relocation allowance cazioni del Calcolo "M. Picone" of ence proceedings will be published and airfare to Israel. If the fellowship the Italian Research Council (CNR). at a later date. Authors are encour­ is renewed for a second year, return The general topic of the year is Math­ aged to bring complete camera-ready airfare is provided. ematical Problems in Engineering, versions of their papers to the confer­ Application forms and additional with special emphasis on Mathemat­ ence for inclusion in the proceedings. information may be obtained from ical Methods and Models in Nonlin­ For further information, please con­ The Feinberg Graduate School, The ear Elasticity. Activities on this sub­ tact Harold Fredricksen, Department Weizmann Institute of Science, Re­ ject are being coordinated by a scien­ of Mathematics, Code 53, Naval hovot, 7 6100 Israel. Applications are tific committee including F. Brezzi, Postgraduate School, Monterey, Cal­ reviewed twice each year: January 1 A. DiCarlo, G. Geymonat, P. Podio­ ifornia 93943. and May 15. Guidugli and M. Rosati. Funds are being made available by CNR and Argentine Winter Weizmann Institute of Science the Universities of Rome. Mathematics Laboratory Announces Openings for Scientists An important purpose of the year is to enhance the interactions be­ The Argentine National Research The Weizmann Institute of Science tween mathematicians, scientists, and Council has given its support to is now offering a limited number of engineers. One or more workshops a Winter Mathematics Laboratory temporary appointments for the po­ are being held during the year, as (LAMAIN), to be held each year at sition of scientist. To qualify, candi­ well as individual lectures, seminars, the Regional Center for Scientific and dates must have completed two years discussion groups, and several lecture Technological Research (CRICYT) of postdoctoral work. series. To participate or gain further in Mendoza, Argentina, from June Appointments will be made in the information, contact the Secretariat: 1 to September 30. areas of biology, chemistry, biochem­ Mrs. G. Castellini or Mrs. G. Sil­ LAMAIN is organized into re­ istry-biophysics, physics, mathemat­ veri, lAC, Viale del Policlini co 13 7, search units, consisting of groups of ics, and science teaching for a period 1-00161 Roma (ph. (39 6)853502). specialists doing research on a spe­ of one year. The appointments, how­ cific subject. The units meet for not ever, may be extended for a period Crypto '88 Conference less than one month and conduct not to exceed five years from the courses, short preparatory courses, candidate's receipt of a Ph.D. de­ The annual CRYPTO conference, seminars, and workshops. The main gree (or equivalent). Successful ap­ sponsored by the International As­ purpose is research, but sometimes pointees will be eligible to apply for sociation for Cryptologic Research the specialists teach newcomers about a promotion to the position of senior (IACR) in cooperation with the IEEE the research topics. scientist. Financial remuneration for Computer Society Technical Com­ The facilities of CRICYT in­ a scientist is at the level of lecturer mittee on Security and Privacy, and clude conference rooms, classrooms, and includes all the associated bene­ the Computer Science Department of a dozen individual offices for fits. In addition, a relocation stipend the University of California, Santa LAMAIN participants, a mathemat­ is provided. Barbara, will be held in Santa Bar­ ical library, and bilingual secretarial Application forms and additional bara, California, on August 21-25, services. information may be obtained from 1988. Original papers are sought on For more information, contact E. The Feinberg Graduate School, The all theoretical and practical aspects H. Zarantonello, CRICYT, Casilla Weizmann Institute of Science, Re­ of cryptography. de Corereo 131, Mendoza 5500 Rca, hovot, 7 6100 Israel. Applications are Ten copies of the abstract should Argentina. reviewed twice each year: January 1 be mailed by March 1 to Shafi Gold­ and May 15. wasser, Program Chairperson, MIT Travel Support for Laboratory for Computer Science, Foreign Graduate Students NE43-307, 545 Technology Square, Cambridge, Massachusetts 02139. The Society is pleased to announce Abstracts should provide sufficient that travel support for foreign grad­ detail (4-6 pages) to allow the pro- uate students attending 1988 AMS

FEBRUARY 1988, VOLUME 35, NUMBER 2 269 News and Announcements

conferences is expected to be avail­ Distinguished Service Award. The butions to ACM publications, having able again this year through a grant award, which is given each year served on the Editorial Board of the from the STEP program of the Insti­ on the basis of value and degree Journal of the Association for Com­ tute of International Education. An of service to the computing com­ puting Machinery from 1969 through application has been filed by the So­ munity, ·was presented to Professor 1985, four of these years as editor-in­ ciety for foreign students attending Brooks "for lasting contributions as chief." The ACM Outstanding Con­ the International Symposium on the a teacher and researcher in com­ tribution Award is given each year Legacy of John von Neumann to puter architecture, interactive com­ on the basis of value and degree of be held May 29-June 4 at Hofstra puter graphics and software engineer­ service to ACM. Professor Coffman University, Hempstead, New York; ing and for dedicating his personal is presently a member of the Tech­ the Summer Institute on Operator and professional life to public ser­ nical Staff, Department of Mathe­ Theory/Operator Algebras and Ap­ vice." Brooks established the Univer­ matical Foundations of Computing plications to be held July 3-23 at sity of North Carolina Computer Sci­ at AT&T Bell laboratories, Murray Bowdoin College, Brunswick, Maine; ence Department in 1964 and served Hill, New Jersey. Coffman has au­ the Summer Seminar on Computa­ as its chairman until 1984. He is thored or co-authored more than a tional Solution of Nonlinear Systems widely known for his design contri­ hundred published research papers of Equations to be held July 18-29 butions to the IBM 7030 (Stretch) on data structures and algorithms, at Colorado State University, Fort and Harvest Computers in the late mathematical models of computer Collins, Colorado; the Joint Sum­ 19 50s and his management of the organizations and operating systems mer Research Conferences to be held IBM Systems/360 project during the and queueing theory. In 1984 he was June 11-August 5 at Bowdoin Col­ early 1960s. Among his honors are elected a Fellow of the IEEE and was lege, Brunswick, Maine; and the AMS the National Medal of Technology recognized as a Distinguished Mem­ Centennial Symposium to be held (1985), the MacDowell Award from ber of the Technical Staff by AT&T August 8-12 in Providence, Rhode the IEEE Computer Society (1982), Bell laboratories. Island. and the Thomas Jefferson Award John K. Ousterhout, Associate To be eligible for these grants from the University of North Car­ Professor, Department of Electrical the foreign student must be enrolled olina, Chapel Hill (1986). He is the Engineering and Computer Sciences, in full-time graduate studies at a author of numerous research papers, University of California, Berkeley, U.S. institution of higher education. as well as two books, The Mythical has received the 1987 ACM Grace Students are ineligible if they are Man-Month (1975), and Automatic Murray Hopper Award. The award, receiving any U.S. government funds Data Processing, with Kenneth Iver­ which is given annually to an indi­ for academic support or if they are son (1962). vidual who has made an outstanding on refugee, immigrant, or tourist visa Kent K. Curtis, Senior Scien­ contribution to the computer indus­ status. Previous recipients of STEP tist, Computer and Information Sci­ try while thirty years of age or un­ awards are ineligible for a second ence and Engineering Directorate of der, was given to Ousterhout for his grant. the National Science Foundation, "contribution to very large-scale inte­ To apply, send a letter stating has received the ACM President's grated circuit computer-aided design. your name, home country, student Award "for sustained support of His systems, "Caesar" and "Magic," status, the name of the institution computer research and education, for have demonstrated that effective at which you are enrolled, the name enlightened research administration CAD systems need not be expensive, of an official at the institution who and support policies, and for appli­ hard to learn, or slow." can verify your status and financial cation of computers to research and Adele Goldberg, Daniel Ingalls, situation, and the name of the AMS education." This award, which was and Alan Kay received the 1987 conference you plan to attend to: Dr. presented by Paul Abrahams, ACM ACM Software System Award. The James W. Maxwell, Associate Exec­ President, on October 29, 1987, at award, which recognizes the devel­ utive Director, American Mathemat­ the ACM/IEEE Computer Society's opers of a system that has signifi­ ical Society, P.O. Box 6248, Provi­ Fall Joint Computer Conference in cantly influenced fundamental con­ dence, Rhode Island 02940. Dallas, Texas, was established in cepts of software system design or 1985 to give special recognition to commercial software products, was 1987 ACM Awards individuals~or exemplary leadership presented on October 29, 1987, at in achieveme111s in the computer sci­ the ACM/IEEE Computer Society's Frederick P. Brooks, Jr., Kenan Pro­ ences. Fall Joint Computer Conference in fessor of Computer Science at the Edward G. Coffman, Jr., has re­ Dallas, Texas. The 1987 Award com­ University of North Carolina, Chapel ceived the 1987 ACM Outstanding mends Goldberg, Ingalls, and Kay Hill, has received the 1987 ACM Contribution Award for his "contri- or "seminal contributions to object-

270 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements oriented programming techniques. the point where continuation of this this symposium is given on page 14 7 The series of languages and devel­ feature no longer seems effective. of Notices, January 1988. opment systems known as Smalltalk The Notices Editorial Committee has laid the foundation for explorations reluctantly decided to discontinue Errata to 1987 Index in new software methodologies, graph­ the publication of this column. Re­ ical user interface designs, and forms sponses to published Queries will still The following are corrected and com­ of on-line assistance to the software be considered for publication in a fu­ plete entries for the 1987 Index to development process." The Small talk ture issue, but no new Queries will the Notices: system was developed by the three be accepted. Any Queries now under AMS REPORTS & COMMUNICA­ computer scientists while working as consideration may be published in a TIONS a team at the Xerox Palo Alto Re­ future issue, but it is expected that Business Meetings of the Society search Center (PARC). the February 1988 issue will contain January, San Antonio, 398; -ACM Press Release the last official Queries Column. August, Salt Lake City, 1014 The Notices Editorial Committee Council Meetings of the Society Queries Column would like to thank Professors Flem­ January, San Antonio, 397; April, to be Discontinued ing, Samelson, and Antman for their Newark, 699; August, Salt Lake services as editors of this column and City, 1013 The Queries Column first appeared the mathematical community for the BACKLOG OF MATHEMATICS in the October 1972 issue of No­ queries and the responses they have RESEARCH JOURNALS, 373, tices as the result of a suggestion submitted over the past 16 years. 825 from the AMS Committee to Mon­ BUSINESS MEETINGS OF THE itor Problems in Communications. Errata SOCIETY In the original announcement of the January, San Antonio, 398; column, readers were invited to sub­ Inadvertently the article "The AMS August, Salt Lake City, 1014 mit questions regarding mathemat­ Centennial 1888-1988" in the Jan­ BYLAWS OF THE AMS, 1155 ical matters, such as details of, or uary issue of Notices which contained COUNCIL MEETINGS references to, vaguely remembered a description of the AAAS Sympo­ January, San Antonio, 397; April, theorems, sources of exposition of sium on American Mathematics En­ Newark, 699; August, Salt Lake folk theorems, or the state of cur­ tering the Second Century did not list City, 1013 rent knowledge concerning published the Plenary Speaker, Raoul H. Bott NEW AMS MEMBERS, 145, 559, conjectures. The column was edited of Harvard University, with the other 693, 819, 1005, 1146 by Wendell H. Fleming until Febru­ lecturers at this special event. Pro­ OBITUARIES ary of 197 5 when Hans Samelson fessor Bott will lecture on Sunday, Chen, K. T., 1100 assumed the editorship. In August February 14 at 1:00 p.m. in Exhibit Dunford, Nelson, 287 1985 Stuart Antman joined Samel­ Hall B of The Hynes Convention Grad, Harold, 494 son in editing the column to provide Center in Boston and the lecture is Lunford, Geoffrey S. S., 288 a wider coverage of fields in the entitled "Mathematics and Physics: Ostrowski, Alexander M., 288 mathematical sciences. An uneasy but pre-ordained collab­ Pollard, Harry, 289 Unfortunately, in recent years the oration". The complete program for Reiner, Irving, 287 number of Queries has declined to

FEBRUARY 1988, VOLUME 35, NUMBER 2 271 TERNATIONAL URAL ORK IETY 1988 ANNUAL MEETING september 6·10, 1988 Boston, MA

The International Neural Network society Call for Abstracts: The INNS welcomes nNNSl is an association of scientists, engineers, abstracts for oral or poster presentation at its students, and others seeking to learn about 1988 Annual Meeting. session topics include: and advance our understanding of the modelling of behavioral and brain processes • Vision and image processing and the application of neural modelling o Speech and language concepts to technological problems. The INNS • sensory-motor control and robotics invites all those interested in the exciting and o Pattern recognition of neural networks to o Associative learning rapidly expanding field • Self-organization attend its 1988 Annual Meeting at the Boston • Cognitive information processing Park Plaza Hotel. o Local circuit neurobiology The meeting includes plenary lectures, • Analysis of network dynamics poster o combinatorial optimization symposia, contributed oral and • Electronic implementation 235-7500 or !BOO> 521-5144. registration rates at the 1988 meeting. MEMBERSHIP FEES (1988) Regular $45.00, student $35.00 National Science Foundation News & Reports

Program Officer Search vestigators in computer science, en­ and image processing, computer vi­ gineering, and mathematics. The ini­ sion, fluid flow and turbulence, op­ The Division of Mathematical Sci­ tiative will focus on critical issues at timization, algebraic and symbolic ences at the National Science Foun­ the interface of these fields, where the computation. dation will need to replace a large U.S. and French strengths are com­ • Development of knowledge­ portion of its current staff by next plementary and likely to produce a based systems, involving interface be­ fall. It is likely that program officers synergistic effect. On the French side, tween numerical and symbolic com­ will be needed in Algebra and Num­ the research resources will be concen­ putation and computer graphics. ber Theory, Applied Mathematics, trated at INRIA, the French National • Manufacturing systems, auto­ Statistics and Probability, Computa­ Institute for Information Science and mation and control. tional Mathematics, Geometric Anal­ Automation with locations in Roc­ Awards in this initiative are in­ ysis, and Special Projects (particu­ quencourt, Rennes and Sophia An­ tended for small teams that will in­ larly undergraduate activities). De­ tipolis. INRIA will also serve as a clude several U.S. and French in­ pending on the outcome of discus­ focal point for other French research vestigators with common research sions with current staff, between 6 institutes and universities who wish objectives. In general, NSF awards and 10 program officers may be to participate in this initiative. The in this initiative will be intended to needed. joint efforts will involve coordination cover costs of U.S. investigators only. In general, the program officers of research, joint projects and pub­ Awards under this initiative are likely are rotators, holding their positions lications, short and long-term visits, to fall in the range from $10,000 to for one to three years and then re­ joint workshops, and communication $50,000 per year, but smaller and turning to their (usually academic) and exchange of data, software and larger grants may be awarded if ap­ institution. Additional information messages through a high-speed elec­ propriate. on these positions may be obtained tronic network. U.S. computer scientists, engi­ from Dr. Judith Sunley, the Division This initiative is designed to max­ neers, and mathematicians in related Director. She can be reached at (202- imize the potential benefits of com­ areas from universities or other non­ 357-9669) by telephone or by elec­ plementary U.S. and INRIA strengths profit research institutions may sub­ tronic mail at [[email protected]]. in the areas of scientific software, net­ mit proposals for support under this Applications or suggestions are wel­ working, computational and applied initiative. There is no deadline for come. mathematics, and systems control. proposal submission under this ini­ Please consider, both personally Topics to be emphasized include: tiative. and among your professional con­ • Performance evaluation of su­ For additional information, con­ tacts, who could and would fill these percomputers and other computing tact International Programs, U.S.­ positions effectively. It is a matter systems, by both mathematical and France Program, 202-357-7554. of significance to the entire profes­ experimental research. sion that these positions be filled by • Networking: development of Multimillion-Dollar Project competent mathematicians. communication networks and study to Upgrade and Expand NSFNET of standardization protocols. NSF-INRIA Collaborative Research • Software systems, software engi­ The NSF has announced a multi­ neering, and computer architectures. million dollar agreement for the up­ The NSF has announced an initiative • Parallel algorithms, computa­ grading, expansion, and management to support new international research tional and applied mathematics. Ar­ of NSFNET, a network for high­ efforts involving U.S. and French in- eas of interest include control, signal speed data communication among

FEBRUARY 1988, VOLUME 35, NUMBER 2 273 NSF News & Reports national research institutions. vices worth approximately $5 to $8 erators, and radiotelescopes, to name NSFNET will connect the founda­ million. MERIT officials plan to have a few. By making it easier for aca­ tion's five national supercomputer the network operational by mid- demic, industrial, and government centers and the National Center for 1988. researchers to work together, the en­ Atmospheric Research in Boulder, MERIT officials estimate that hanced NSFNET will speed the pace Colorado, with seven regional NSFNET will be 20 to 30 times at which basic knowledge is applied academic-research networks. faster than the present links to the for the development of new technol­ MERIT, Inc., a consortium of foundation's supercomputer centers. ogy." eight Michigan universities, will re­ For example, communications lines ceive $50 million over the next five will transmit more than 1.5 million FY 1988 Federal Budget years to manage all operations and bits of data per second, or the equiv­ services on the network. Members alent of 50 single-spaced typewritten On December 22, the U.S. Congress of this consortium include Central pages. A scientist who uses NSFNET passed the 1988 fiscal year budget Michigan University, Eastern Michi­ will be able to send experimental data and substantially reduced appropri­ gan University, Michigan State Uni­ quickly to a collaborator on another ations in many areas. In particular versity, Michigan Technological Uni­ campus, watch the graphic result of a the NSF budget request for 1988 versity, Oakland University, The Uni­ simulation on a supercomputer thou­ received severe cuts. The extent of versity of Michigan, Wayne State sands of miles away, or send a pa­ these cuts on the mathematical com­ University, and Western Michigan per to a publisher with camera-ready munity will not be known until mid University. MERIT currently man­ page layouts and graphics. The super­ January when the NSF completes its ages Merit Computer Network, Mich­ network will also make it easier for allocation to the various divisions igan's higher education network. scientists to share software and other and projects. What is known at this In addition to a $14 million grant tools and products of their research, time is that the NSF budget increased from the NSF, the project will in­ and will encourage cooordinated re­ by only 5.8 percent to $1.717 billion volve government, industry, and aca­ search efforts by experts in diverse and that a substantial portion of this demic participation. The state of fields. increase was designated for science Michigan will contribute $5 million Stephen Wolff, Director of NSF's education. The effect of these cuts to the project. International Busi­ Division of Networking and Com­ on the budgets of the divisions and ness Machines Corporation will con­ munication Research and Infrastruc­ directorates of interest to the mathe­ tribute hardware and software worth ture said, "With its increased capac­ matical community will be reported approximately $20 to $30 million, ity, NSFNET will give scientists and in Notices as soon as they are avail­ and MCI Communications Corpora­ engineers better access to supercom­ able. tion will contribute fiber optic com­ puters and other unique scientific munications lines and support ser- resources-data bases, particle accel-

274 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

FUTURE MEETINGS East Lansing, Michigan March 18-19 276

Knoxville, Tennessee March 25-26 279

Las Cruces, New Mexico Apri18-9 282

College Park, Maryland April23-24 286

Invited Speakers and Special Sessions 288

FUTURE CONFERENCES

Symposium on Some Mathematical Questions in Biology Las Vegas, Nevada, May 4 291 Symposium on the Legacy of John von Neumann Hofstra University, May 29-June 4 291

Joint Summer Research Conferences in the Mathematical Sciences Bowdoin College, June 11-August 5 298

Summer Research Institute University of New Hampshire, July 3-23 300

Summer Seminar in Applied Mathematics Colorado State University, July 18-29 301

Call for Topics 303

IL ______I - FEBRUARY 1988, VOLUME 35, NUMBER 2 275

I East Lansing, Michigan Michigan State University March 18-19

Third Announcement

The eight-hundred-and-fortieth meeting of the American Dan Phillips, Jean-Michel Rakotoson, Paul Sacks, Mar­ Mathematical Society will be held at Michigan State shall Slemrod and Joel Smoller. University in East Lansing, Michigan on Friday, March Algebraic combinatorics, BRUCE SAGAN, Michigan 18 and Saturday, March 19, 1988. This meeting will be State University. Tentative speakers include: George in conjunction with a meeting of the Association for Andrews, Lynne Butler, Paul Edelman, Francis Garvan, Symbolic Logic. Ira Gessel, Ian Goulden, Richard Grassl, Curtis Greene, David Jackson, Gilbert Labelle, Pierre Leroux, Kathy Invited Addresses O'Hara, Saul Stahl, John Stembridge, Sheila Sundaram, Michelle Wachs, and Dennis White. By invitation of the Committee to Select Hour Speakers for Central Sectional Meetings, there will be four invited otle-hour addresses. The speakers, their affiliations, and Contributed Papers titles when available are as follows: There will also be sessions for contributed ten-minute BARBARA L. KEYFITZ, University of Houston, Systems papers. of conservation laws that change type. BRIAN PARSHALL, University of Illinois at Urbana­ Champaign. Registration KARL RuBIN, Ohio State University, Elliptic curves The registration desk will be open on Friday, March 18 and the Birch and Swinnerton-Dyer conjecture. and Saturday morning, March 19 in the C-Wing lobby WILLIAM P. ZIEMER, Indiana University, Fine regu­ of Wells Hall. The registration fees are $30 for members larity in partial differential equations. of the AMS, $45 for nonmembers, and $10 for students or unemployed mathematicians. Special Sessions By invitation of the same committee, there will be several Petition Table special sessions of selected twenty-minute papers. Topics A petition table will be set up in the registration area. atld the names and affiliations of the organizers and Additional information about petition tables can be partial lists of tentative speakers are: found in a box in the Atlanta meeting announcement on Algebraic groups and related topics, WILLIAM page 68 of the January issue of Notices. HABOUSH and BRIAN PARSHALL, University of Illinois. Groups and geometries, JONATHAN HALL and BERNT S'l'ELLMACHER, Michigan State University. H. Bender, A. Accommodations Delgado, D. Frohardt, R. L. Greiss, P. R. Hewitt, U. Blocks of rooms are being held at the following locations. Meierfrankenfeld, A. Rybat, Y. Segev, S. D. Smith, G. Participants should make their own reservations and Stroth, and F. G. Timmesfeld. mention the AMS meeting to obtain rates listed below. Phase transition and connection matrices, Please note that the rates are subject to change and KONSTANTIN MISCHAIKOW and AMY NOVICK-COHEN, do not include appropriate taxes. The deadline to make Michigan State University. reservations is March 1, 1988. Nonlinear partial differential equations, DAN Kellogg Center (on P:HILLIPS, Purdue University. Tentative speakers include campus) Michigan State Christoph Borgers, Kuo-Shung Cheng, Amy Novick­ University, East Lansing 48824-1027 Telephone: 517-355-5090 Cohen, David Hoff, Bradley Lucier, Nicholas Owen,

216 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETy

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Single $49 Double $54 Travel University Inn (.5 mile) The East Lansing area is serviced by Capital City Airport 1100 Trowbridge, East Lansing 48823 and by the following airlines: Piedmont, American Eagle, Telephone: 517-351-5500 Northwest Orient, United Express and ComAir. There is taxi service available Single $39.50 to the campus and area motels from the All rooms have two (2) single beds airport. East Lansing and Michigan State University are lo­ Red Roof Inn (2 miles) cated off of Interstate 96 and Interstate 69. From the Dunkel, East Lansing East take I-96 from Detroit; from the West take I-94 to Telephone: 517-332-2575 I-69: from the South take I-69 or Highway 127. Each of the above routes leads you to Interstate 496 Single $27.95 Double $34.95 from which you should take the exit for Trowbridge Comfort Inn ( 4 miles) Road to the edge of the MSU campus. At the end of the 2209 University Park, Mason 48854 exit take a left on Harrison Road, and take a right onto Telephone: 517-349-8700 Kal~mazoo Road. Follow the signs for the parking lots at the north end of the football stadium. Single $43.20 Parking Food Service There is public parking available at the north end of The cafeteria in the International Center adjacent to the football stadium which participants should use on Wells Hall is open on Friday from 7:00 a.m. to 4:00 Friday, which is a short walk from the C-Wing of Wells p.m. There is a cafeteria and dining room in the Kellogg Hall where registration and all sessions are scheduled. Center and fast food restaurants in the student union On Saturday, participants can park in available spaces and adjacent to campus. A list of nearby restaurants will around Wells Hall as well as the north and south public be available at registration. parking lots of the football stadium. Robert M. Fossum Associate Secretary Urbana, Illinois

'~CENTENNIAL CELEBRATION

The Combined Membership List, joint with MAA, first appeared in 1952.

AMERICAN MATHEMATICAL SOCIETY • PROVIDENCE • AUGUST 8-12, 1988

278 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Knoxville, Tennessee Knoxville Hilton March 25-26

Second Announcement

The eight-hundred-and-forty-first meeting of the Ameri­ Commutative algebra, MATTHEW MILLER, Univ~rsity can Mathematical Society will be held at the Knoxville of South Carolina. The list of tentative speakers includes Hilton in Knoxville, Tennessee on Friday, March 25 David Anderson, David E. Dobbs, Melvin Hochster, and Saturday, March 26, 1988. The meeting will be Evan G. Houston, Sam W. Huckaba, Andrew R. Kl.lstin, hosted by the Department of Mathematics, University Budh Singh Nashier, Bernd Ulrich, Wolmer Vasconcelos, of Tennessee at Knoxville. T. M. Viswanathan, and Dana Weston. Topics in stochastic processes, BALRAM RAJPUT, Uni­ Invited Addresses versity of Tennessee. Tentative speakers include Ishwar Basawa, Richard C. Bradley, Kurt Helmes, Itaru Mitoma, By invitation of the Committee to Select Hour Speak­ Joanna B. Mitro, Arunava Mukherjea, Magda Peligrad, ers for Southeastern Sectional Meetings, there will be Loren D. Pitt, Murali Rao, Jan Rosinski, Jerzy Szulga, four invited one-hour addresses. The speakers and their and Bob Taylor. affiliations are as follows: J. ALAN GEORGE, University of Tennessee and Oak Ridge National Laboratories, Solutions of large sparse Contributed Papers equations. There will also be sessions for contributed ten-minute LoUis N. HowARD, Florida State University, Some papers. aspects of double-diffusive convection. CRAIG HuNEKE, Purdue University, Applications of Froebenius in commutative algebra. Other Activities S. JAMES TAYLOR, University of Virginia, The mea­ In conjunction with the AMS sectional meeting, the sure theory of random fractals. University of Tennessee will host a conference on Prob­ ability and stochastic processes, coordinated by BALR.AM Special Sessions RAJPUT. The conference will be held on Thursday, March 24 and Friday, March 25. There will be four one-hour By invitation of the same committee, there will be invited addresses. The speakers and their affiliations are: several special sessions of selected twenty-minute papers. BURGESS DAVIS, Purdue University. A partial listing of topics and the names and affiliations ALEJANDRE DE AcosTA, Case Western Reserve Uni­ of the organizers is as follows: versity. Numerical linear algebra,. JAMES -BUNCH, University OLAV KALLENBERG, Auburn University. of California, San Diego. The list of tentative speakers MALCOLM R. LEADBETTER, University of North includes Randy Bank, Ralph Byers, Jim Demmel, Howie Carolina-Chapel Hill. Elman, Pat Eberlein, Bill Gragg, Anne Greenbaum, Persons interested in participating should contact Mike Heath, Joseph Liu, Tom Manteuffel, Esmond Ng, Balram Rajput, Department of Mathematics, University Bob Plemmons, Chuck Romine, Dan Sorensen, G. W. of Tennessee, Knoxville, TN 37996-1300. Stewart, and Margaret Wright. Finite field theory and applications, RoBERT Mc­ CoNNEL, University of Tennessee-Knoxville. Tentative Registration speakers are Jacob T. B. Beard, Joel B. Brawley, Javier The meeting registration desk will be located on the Calderon Gomez, Robert McConnel, Gary L. Mullen, second floor lobby of the Knoxville Hilton. The session David R. Richman, Peter Shiue, and Theresa P. Vaughan. rooms will be adjacent to the lobby. The desk will be open from 8:00 a.m. to 5:00 p.m. on Friday, and from

FEBRUARY 1988. VOLUME 35, NUMBER 2 279 RIVER

AV 1 KNOXVILLE HILTON 2 TRAI LWAYS BUS DEPOT 3 UNIVERSITY OF TENNESSEE 4 WELCOME CENTER

280 Meetings

8:00 a.m. to noon on Saturday. The registration fees Holiday Inn-Central (2.5 miles) are $10 for members, $16 for nonmembers, and $5 for Dale Avenue, Knoxville 37921 students or unemployed mathematicians. Telephone: 615-525-5371 or Toll Free: 800-238-8000 Single: $38 Double: $40 Social Event Days Inn Merchants (7 miles) A party is planned for Friday evening, March 25 at the Merchants Center Boulevard, Knoxville 37912 Knoxville Hilton. The menu includes beer, soft drinks Telephone: 615-687-8989 and snacks. The cost of the party is $6.50 per person. Double: $35 Tickets may be purchased at the meeting registration Single: $33 desk, at the door, or in advance by sending your check to Barbara Jendrucko, Department of Mathematics, Uni­ Food Service versity of Tennessee, Knoxville, TN 37996-1300. The Hilton, both Holiday Inns, the Quality Inn, and the Best Western Campus Inn have restaurants for break­ Petition Table fast, lunch and dinner. Downtown Knoxville and the including A petition table will be set up in the registration area. surrounding area have many fine restaurants Chesapeake's Additional information about petition tables can be Regas, the Copper Cellar, Ruby Tuesday's, The Butcher found in a box in the Atlanta meeting announcement on (seafood), Naple's and Pero's (Italian), house), Casa Gallardo (Mexican) and many page 68 of the January issue of Notices. Shop (steak others. The downtown and campus areas also have many diners and national fast food chains. Information on Accommodations the downtown and area restaurants will be included in registration Blocks of rooms are being held at the following hotels. a welcome packet available at the meeting Participants should make their own reservations directly desk. with the hotel of their choice and be sure to identify themselves with the AMS meeting at the University. Travel Please make reservations by February 24, 1988. After that of Tennessee campus is located approx­ date, reservations· will be accepted on a space available The University McGhee-Tyson basis. Rates do not include applicable taxes and are imately 10 miles from the Knoxville airlines (includ­ subject to change. Airport which is served by most major ing Delta, Northwest, American, United, Eastern, TWA) The Knoxville Hilton and other regional and commuter airlines. Participants 501 West Church Street, Knoxville 37902 can also arrive by Greyhound and Trailways buslines. Telephone: 615-523-2300 Participants traveling by car may reach Knoxville via Interstate 40 from the east and west, and Interstate 7 5 Single $51 Double $51 from the north and south. Best Western Campus Inn (1 mile from Hilton) Knoxville 37916 1706 West Cumberland Ave, Parking and Local Travel Arrangements Telephone: 615-524-4681 Complimentary parking will be available in the Hilton Single $32 Double $36 garage for guests and conference participants. Please Although rooms have not been blocked at any of these obtain a complimentary parking pass at the hotel regis­ locations, they are included for information purposes. tration desk at the time of your departure. Holiday Inn World's Fair (3 blocks) Knoxville is served by a mass transit system of buses. Henley Street, Knoxville 37902 Bus stops are located near the Best Western Campus Inn Telephone: 615-522-2800 or Toll Free: 800-238-8000 and Holiday Inn at Dale Avenue. The standard fare is 75 cents. Single: $48 Double: $58 Frank T. Birtel Quality Inn Hotel Downtown ( 6 blocks) Associate Secretary Summit Hill Drive, Knoxville 37902 New Orleans, Louisana Telephone: 615-522-2600 or Toll Free: 800-223-7778 Single: $40 Double: $40

FEBRUARY 1988, VOLUME 35, NUMBER 2 281 Las Cruces, New Mexico New Mexico State University AprilS-9

Second Announcement

The eight-hundred-and-forty-second meeting ofthe Amer­ Goodman, Ron Iman, Benjamin Kedem, Hung Nguyen, ican Mathematical Society will be held at the New Mexico Eugene Schuster, Sidney Yakowitz, and Lu Zhang. State University in Las Cruces, New Mexico on Friday, Mathematics of computer vision, computer graphics April 8 and Saturday, April 9, 1988. and robotics, KEITH L. PHILLIPS, New Mexico State University. The tentative speakers include Peter Alfeld, John Canny, Invited Addresses Peter Doyle, Warren Krueger, Rastislav Telgarsky and Zhi Zhao. By invitation of the Committee to Select Hour Speak­ Non-commutative rings and their applications, RoBERT ers for Far Western Sectional Meetings, there will be B. WARFIELD, JR. three invited one-hour addresses. The speakers and their affiliations are as follows: Contributed Papers JoHN L. CANNY, University of California, Berkeley, Robot motion planning and real geometry. There will also be sessions for contributed ten-minute DAVID LEIGH DONOHO, University of California, papers. Late papers will be accepted for presentation at Berkeley, Geometrizing rates of convergence. the meeting but will not appear in the printed program. ROBERT B.WARFIELD, JR., University of Washington, Representation theory of Noetherian rings. Registration The meeting registration Special Sessions desk will be located in the main lobby at the east end of Science Hall, and will be open By invitation of the same committee, there will be from 7:30 am to 4:30pm on Friday, April 8 and 8:00am six special sessions of selected twenty-minute papers. A to 1:30 pm on Saturday, April 9. The registration fees listing of topics and the names and affiliations of the are $30 for members, $45 for nonmembers, and $10 for organizers follows: students and unemployed mathematicians. Algebraic topology and algebraic K-theory, GERALD J. DUNN, REINHARD LAUBENBACHER, GERALD M. LOD­ Social Events DER, DAVID J. PENGELLEY, CLAYTON C. SHERMAN, and FRANCIS D. WILLIAMS, New Mexico State University. There will be an informal welcome reception with a cash Tentative speakers include Gerald J. Dunn, Zbigniew bar on Thursday evening, April 7 in the Plaza Suites at Fiedorowicz, Yutaka Hemmi, James P. Lin, Jerry M. the Holiday Inn de Las Cruces. A banquet will be held at Lodder, Charles A. McGibbon, Stephen A. Mitchell, Les the Holiday Inn on Friday evening, April 8. The banquet Reid, Clayton C. Sherman, and Francis D. Williams. speaker will be WILLIAM J. LEVEQUE, Executive Director Hypercube theory, FRANK HARARY, New Mexico State of the AMS. Advance payment of $15 per person will University. Tentative speakers include Fan R. K. Chung, be necessary. Reservations and payment should be sent Paul Erdos, Geoffrey Exoo, Neil Graham, Ron L. Gra­ to arrive by April 4 to Gerald Rogers, Department of ham, Frank Harary, Larry Harper, J. P. Hayes, Martin Mathematics, New Mexico State University, Las Cruces, Lewinter, M. Malek and Edgar Palmer. NM 88003. Applications ofparallel computing, MARY A. MAHER, An outing/walk/hike on the Pine Tree Loop Trail New Mexico State University. at Aguirre Springs in the nearby Organ Mountains is Probability and statistics, H. T. NGUYEN, New Mex­ being planned for Sunday morning, April 10, following ico State University. The tentative speakers are I. R. the meeting. The Organ Mountains rise dramatically with organlike spires to 9,000 feet just east of Las

282 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

cruces. The Aguirre Springs area encompasses diverse Sales Manager, Millie Folberg, by mail or telephone and vines and creeks at just over 6,000 feet underneath identify themselves as attending the AMS meeting. ~e spires. Interested participants should arrange their El Howard Johnson's Motor Paso air departures for the afternoon, and be prepared Lodge (1 mile) South Valley Drive, Las Cruces for an early start on Sunday, especially if they have an 88005 Telephone: 505-526-4441 arly afternoon departure. Good walking shoes, sunhat, :unglasses and sunscreen are advised. ~he weather will Single: $28.25 Double: $30.00 probably not be bot, but the sun can be mtense. In order to be guaranteed the rates quoted above, The outing will be coordinated with direct trans­ participants need to identify themselves as attending the portation to the El Paso airport. How~ver, . the local meeting at NMSU and ask for the NMSU rate. organizers must have ample advance notificatiOn of the air departure times of those interested. Interested par­ Motel 6 (1 mile) La Posada Lane, Las ticipants should notify David Pengelley, Departme~t of Cruces 88005 Mathematics, NMSU, Las Cruces, NM 88005 by mall or Telephone: 505-525-1010 phone 505-646-3901. Single: $20.95 Double: $25.95 Anyone who may wish to visit Juarez, Mexico should bring appropriate papers for regaining entry into the Super 8 Motel (1 mile) United States. La Posada Lane, Las Cruces 88005 Telephone: 505-523-8695 Toll Free: 800-843-1991 Petition Table Single: $24.95 Double: $27.65 A petition table will be set up in the registration area. The Howard Johnson's, Motel 6 and Super 8 are Additional information about petition tables can be within walking distance to the Holiday Inn Las Cruces. found in a box in the Atlanta meeting announcement on page 68 in the January issue of Notices. Hilton Las Cruces ( 4 miles) South Telshor Boulevard, Las Cruces 88001 Telephone: 505-522-4300 Accommodations Single: $50 Double: $55 Participants should make their own reservations directly with the motel of their choice. Except as noted, rates are subject to possible change and do not include any Food Service applicable local taxes. The Holiday Inn, Howard Johnson's and the Hilton Special rates for AMS participants have been arranged have full service restaurants. Information at the Holiday Inn de Las Cruces, on other restaurants where an informal will be available at registration. reception will be held on Thursday evening, April 7 and a banquet dinner on Friday evening, April 8. Special scheduled transportation will also be provided between Travel the Holiday Inn and the NMSU campus. Most participants coming from afar should use the El Holiday Inn de Las Cruces (1 mile) Paso (Texas) International Airport, which is less than one 201 East University Avenue, comer of Valley Drive, hour from Las Cruces. El Paso is served by several airlines Las Cruces 88005 including: American, America West, Continental, Delta, Telephone: 505-526-4411 Southwest, and United. Scheduled limousine service is available from the airport to Las Cruces, with stops at Plaza Suites Single: $34 the Holiday Inn and Hilton. The limousine will stop at Plaza Suites Double: $37 other locations by advance arrangement. Reservations Central Rooms Single: $46 are required and a special rate of $10 each way has been Central Rooms Double: $50 arranged for meeting participants. To make advance Plaza suites surround the courtyard and outdoor pool. reservations, call Super Shuttle at 505-525-1784 Central and Rooms surround courtyard dining and indoor mention the special AMS agreement. pool. Rates for the Plaza Suites include complimentary Some participants may wish to rent a car at the El continental breakfast and free happy hour. Paso Airport. All major companies are represented. There To receive the special guaranteed meeting rates, par­ are Avis and Hertz rental car agencies in Las Cruces, at ticipants should make their reservations directly with the the Holiday Inn and Howard Johnson's respectively.

FEBRUARY 1988, VOLUME 35, NUMBER 2 283 Telshor Blvd .

.-To Albuquerque To El Paso-

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It is possible to fly directly to Las Cruces with Mesa Local Information Airlines. This service is availab~e ~rom_ Albuquerque ~nd Las Cruces, with a smaller cities served by Mesa Auhnes m the surroundmg population over 50,000, lies near the foot of the Organ Mountains, southwestern states. in the Mesilla Valley of . southern New Mexico Las Cruces is also served by Greyhound bushnes and on the Rio Grande. The valley is rich El Paso has Amtrak rail service. farmland, with the country's largest pecan farm, chile, cotton and other For those participants arriving by car directions are crops. The surrounding mesas represent the northern as follows. edge of the Chihuahuan desert, and nearby From the east (El Paso) on Interstate 10: Follow nountain ranges, the southern edge of the Rockies that rise to over 12,000 feet. signs for Tucson u~til the .New Mexico .stat~ University exit. Turn immediately nght onto Umvers1ty Avenue, then turn right at the second light on Espina into the Weather University. At the second stop sign, turn left on to Las Cruces Stewart. Continue for one block to Sweet Street. You will lies at an altitude just under 4,000 feet. The climate see street parking to the right and Science Hall is visible is typical of the northern edge of the Chihuahuan across the far left corner of the intersection. It is a long desert: low humidity, much sunshine and building with tinted windows. large daily temperature fluctuation. In April, the average midday From the west on Interstate 10: Exit at Main Street. high is 77 degrees F and the nighttime low averages 41 degrees Turn right at the end of the exit onto Main Street and F. right at the traffic light onto University Avenue. Continue Lance W. Small on University Avenue and take a right turn at the third Associate Secretary traffic light onto Espina and then proceed as above. La Jolla, California From the north on Interstate 25: Exit at University Avenue and turn right. At the third traffic light, turn left on Espina and proceed as above.

Parking There is free on-street parking approximately one block south of Science Hall. Park only where curbing is WHITE. Lot restrictions do not apply on evenings or weekends in University parking lots.

CHARACTERIZING K-DIMENSIONAL EXISTENCE THEOREMS FOR MINIMAL UNIVERSAL MENGER COMPACTA SURFACES OF NON-ZERO GENUS Mladen Bestvina SPANNING A CONTOUR In the past few years, H. Torunczyk, J. W. Cannon, and R. Friedrich Tomi and Anthony J. Tromba D. Edwards have characterized manifolds which satisfy a In 1931 Jesse Douglas and Tibor Rado simultaneously solved homotopy-theoretical local property and a certain .. general the famous problem of Plateau, which states that every positioning .. property. Following this pattern, the author of the Jordan wire in Rn bounds at least one disk type surface of present work proves that certain compact metric spaces are least area. In this paper, the authors approach this classical homeomorphic to the k-dimensional universal Menger space problem using purely differential geometric concepts. In f.lk. Different constructions of the universal k-dimensional addition to reproving the results of Douglas, the authors compactum have appeared in the literature, and the author develop a new geometric criterion on a given finite system of shows that these constructions yield the same space. In disjoint Jordan curves in 3-dimensional Euclidean space. This addition, the author proves theorems that strongly resemble criterion guarantees the existence of a minimal surface having the well-known facts about Q-manifolds, such as the Z-set a prescribed genus and having these curves as boundary. unknotting theorem. In particular, f.lk is proved to be strongly 1980 Mathematics Subject Classifications: 53A10; 49F10 homogeneous. ISBN 0-8218-2445-7, LC 87-31849 1980 Mathematics Subject Classifications: 54F65; 55Ml0, 57Nl5 ISSN 0065-9266 ISBN 0-8218-2443-0, LC 87-28829, ISSN 0065-9266 92 pages (softcover), January 1988 120 pages (softcover), January 1988 Individual member $8, List price $13, Individual member $9, List price $15, Institutional member $12 Institutional member $10 To order, please specify MEM0/380NA To order, please specify MEM0/382NA

Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added.

FEBRUARY 1988, VOLUME 35, NUMBER 2 285 College Park, Maryland University of Maryland April23-24

First Announcement

The eight-hundred-and-forty-third meeting of the Amer­ Qualitative theory of nonlinear partial differential ican Mathematical Sociey will be held at the University equations, TAI-PING Lm. of Maryland in College Park, Maryland on Saturday and Most of the papers to be presented at these special Sunday, April 23 and 24, 1988. sessions will be by invitation. However, anyone submit­ ting an abstract for the meeting who feels that his or her paper would be particularly appropriate for one of Invited Addresses these special sessions should indicate this clearly on the By invitation of the Committee to Select Hour Speakers abstract form and submit it by February 8, 1988, three for Eastern Sectional Meetings, there will be four invited weeks before the deadline for contributed papers, in one-hour addresses. The speakers, their affiliations, and order that it may be considered for inclusion. Partici­ titles when available, are as follows: pants are reminded that a charge of $16 is imposed for KENNETH S. BROWN, Cornell University, Piecewise retyping abstracts that are not in camera-ready form. linear homeomorphisms of the line. THOMAS G. GooDWILLIE, Brown University, Fixpoint Contributed Papers sets and traces in algebraic K-theory. TAI-PING LIU, University of Maryland, College Park, There will also be sessions for contributed ten-minute Recent progress in nonlinear hyperbolic waves. papers. Abstracts should be prepared on the standard LEONARD L. SCOTT, University of Virginia, Char­ AMS form available from the AMS office in Provi­ lottesville, The isomorphism problem for finite group dence or in the Departments of Mathematics. Abstracts rings: progress and philosophy. should be sent to the Editorial Department, American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940, so as to arrive before the February Special Sessions 29, 1988 abstract deadline. Participants are reminded By invitation of the same committee, there will be eight that a charge of $16 is imposed for retyping abstracts special sessions of selected twenty-minute papers. The that are not in camera-ready form. Late papers will not topics and names and affiliations of the organizers are: be accommodated. Several complex variables and applications, CARLOS BERENSTEIN, University of Maryland and BERNARD Council Meeting SHIFFMAN, Johns Hopkins University. Measurable dynamics, MIKE BoYLE and JoNATHAN The Council of the Society will meet at 7:00 p.m. on KING, University of Maryland. Saturday, April 23, at the Quality Inn College Park. Elliptic equations and geometry, DENNIS DETURCK and JERRY KAzDAN, University of Pennsylvania. Other Activities Combinatorial group theory, BEN FINE, Fairfield Uni­ versity, ANTHONY M. GAGLIONE, United States Naval In conjunction with the AMS sectional meeting, the Uni­ Academy, and F. C. Y. TANG, University of Waterloo. versity of Maryland will host a conference on nonlinear Geometric methods in group theory, Ross GEOGHE­ partial differential equations in honor of the 70th birth­ GAN, State University of New York at Binghamton. day of Avron Douglis on Thursday and Friday, April 21 Algebraic K-theory, THOMAS G. GOODWILLIE. and 22. Invited speakers include LUIS A. CAPPARELLI, Model theory, DAVID KUEKER, University of Mary­ Institute for Advanced Study; MICHAEL G. CRANDALL, land. University of Wisconsin; RoNALD J. DIPERNA, Univer­ sity of California, Berkeley; EuGENE B. F ABES, University

286 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

of Minnesota; PETER D. LAx, Courant Institute of Math­ Comfort Inn (1 mile) ematical Sciences; CATHLEEN S. MoRAWETZ, Courant 9020 Baltimore Avenue, College Park 20740 Institute of Mathematical Sciences; and HANS F. WEIN­ Telephone: 301- 441-8110 BERGER, University of Minnesota. For further information, contact the conference or­ Single $51.70 Double $53.90 ganizers: L. C. EVANS, P. M. FITZPATRICK, or T.-P. LIU, Maryland Inn-Best Western (.5 mile) Department of Mathematics, University of Maryland, 8601 Baltimore Avenue, College Park, 20740 College Park, MD 20742. Telephone: 301-454-2834. Telephone: 301-474-2800 Single $56.10 Double $61.60 Registration College Park Motor Inn The meeting registration desk will be located in the 5043 Branchville Road, College Park 20740 central lobby of the Mathematics Building. The desk will Telephone: 301-441-3 707 be open from 8: 15 a.m. to 1:45 p.m. on both Saturday and Sunday April 23 and 24. The registration fees are Single $44 Double $55 $30 for members of the AMS, $45 for nonmembers, and $10 for students and unemployed mathematicians. Travel The University of Maryland is located on Petition Table Baltimore Boulevard, U.S. Route 1, approximately 8 miles north­ A petition table will be set up in the registration area. east of Washington, D. C. The three major airports Additional information about petition tables can be serving the College Park area are Baltimore-Washington found in a box in the Atlanta meeting announcement on International, approximately 25 miles north of College page 68 of the January issue of Notices. Park; Washington National, 10 miles south; and Dulles International, 35 miles west. From Baltimore-Washington Accommodations International: Take limou­ sine directly to the University of Maryland Campus. The Rooms have been blocked at the following hotels and cost is $15- $22. Taxi service is also available and would motels. Participants should make their own reservations cost approximately $34. directly with the hotel of their choice, identifying them­ From Washington National: Take the Washington selves as attending the American Mathematical Society's Flyer Limousine Service to the campus ($12) or take meeting at the University of Maryland. Rates quoted the metro from the airport to Brookland ($2.60) and include applicable tax but are subject to change. Reserva­ transfer at Brookland to the Campus Bus. You may tions should be made before April 1 except at the Holiday purchase transfers at the Metro entrance at the Airport. Inn which has a reservation deadline of March 22. From Dulles International: Take the limousine service to the Sheraton Hotel, Silver Spring and then a local taxi Adult Education Center (on campus) to the campus. The total cost is approximatiely University College $30. By train: Amtrak trains stop at Union Station in University of Maryland, College Park 20742 Washington, D. C. and at the Capitol Beltway Telephone: 301-985-7310 Station in Lanham. Cab fare from either Amtrak station to the Single $52.50 Double $68.25 campus is approximately $13. By bus: The Greyhound Terminal is located at 1005 Quality Inn (.5 mile) First Street, N.E. in Washington, D. C. Taxi fare to the 7200 Baltimore Avenue, College Park 207 40 campus is approximately $13. Telephone: 301-864-5820 By car: The major highway servicing College Park is Single $52.80 Double $59.40 Interstate 95. From the north or south, take Exit 25B (Route 1 South); the University is located approximately Holiday Inn-Straw Boss (2 miles) 2 miles south of this exit. The Mathematics Department 10000 Baltimore Avenue, College Park 20740 is the large, domed building near the north gate. Telephone: 301-345-6700 W. Wistar Comfort Single $60.50 Double $60.50 Associate Secretary Although rooms have not been blocked at the fol­ Middletown, Connecticut lowing locations, they are included here for information purposes.

FEBRUARY 1988, VOLUME 35, NUMBER 2 287 Invited Speakers and Special Sessions

Information

Invited Speakers Organizers and Topics at AMS Meetings of Special Sessions The individuals listed below have accepted invitations The list below contains all the information about to address the Society at the times an~ places in­ Special Sessions at meetings of the Society available dicated. For some meetings, the list of speakers is at the time this issue of Notices went to the printer. incomplete. The section below entitled Information for Organizers describes the timetable for announcing the existence East Lansing, March 1988 of Special Sessions. Barbara L. Keyfitz Karl Rubin Brian Parshall William P. Ziemer March 1988 Meeting in East Lansing Central Section Knoxville, March 1988 Deadline for organizers: Expired Craig L. Huneke S. James Taylor Deadline for consideration: Expired J. Alan George Louis N. Howard William Haboush and Brian Parshall, Algebraic groups and related topics Las Cruces, April 1988 Jonathan Hall and Bernt Stellmacher, Groups and John L. Canny Robert B. Warfield, Jr. geometries David Leigh Donoho Konstantin Mischaikow and Amy Novick-Cohen, College Park, April 1988 Phase transition and connection matrices Kenneth S. Brown Tai-Ping Liu Dan Phillips, Nonlinear partial differential equations Tom Goodwillie Leonard L. Scott, Jr. Bruce Sagan, Algebraic combinatorics AMS Centennial Celebration March 1988 Meeting in Knoxville Providence, August 1988 Southeastern Section Michael Aschbacher Victor G. Kac Deadline for organizers: Expired Raoul H. Bott Peter D. Lax Deadline for consideration: Expired (AMS-MAA) (AMS-MAA) Balram S. Rajput, Topics in stochastic processes Luis A. Caffarelli Saunders Mac Lane James R. Bunch, Numerical linear algebra Persi Diaconis (AMS-MAA) Robert M. McConnel, Finite field theory and applica­ Charles L. Fefferman Andrew Majda tions Michael H. Freedman Charles S. Peskin Matthew Miller, Commutative algebra Harvey M. Friedman Dennis P. Sullivan Benedict H. Gross Robert E. Tarjan April 1988 Meeting in Las Cruces Joseph Harris William P. Thurston Far Western Section Deadline for organizers: Expired Roger E. Howe Karen K. Uhlenbeck Deadline for consideration: Expired Vaughan F. R. Jones Edward Witten Gerald J. Dunn, Reinhard Laubenbacher, Gerlad M. Lawrence, October 1988 Lodder, David J. Pengelley, Clayton S. Sherman, Bjarn Dahlberg Peter Scott and Francis D. Williams, Algebraic topology and Steven E. Herder Sidney M. Webster algebraic K-theory Frank Harary, Hypercube theory

288 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions

other proposals. (Specific deadlines for requesting approval for Special Sessions at national meetings are given above.) If necessary, the numerical limitation is enforced. Proposals for Special Sessions should be submitted di­ rectly to the Associate Secretary in charge of the meeting (at the address given below). If such proposals are sent to the Providence office, addressed to Notices, or directed to anyone other than the Associate Secretary, they will have to be forwarded and may not be received before the quota is filled. In accordance with an action of the Executive Committee of the Council, no Special Session may be arranged so late that it may not be announced in Notices early enough to allow any member of the Society who wishes to do so to submit an abstract for consideration for presentation in the Special Session before the deadline for such consideration. Special Sessions are effective at Sectional Meetings and can usually be accommodated. They are arranged by the Associate Secretary under the supervision of the Committee to Select Hour Speakers for the section. The limitation on the number of sessions depends on the space and time available. The same restriction as for national meetings applies to the deadline for announcing Special Sessions at sectional meetings: no Special Session may be approved too late for its announcement to appear in time to allow a reasonable interval for members to prepare and submit their abstracts prior to the special early deadline set for consideration of papers for Special Sessions. The Society reserves the right of first refusal for the publication of proceedings of any special session. These October 1988 Meeting in Lawrence proceedings appear in the book series Contemporary Math­ Associate Secretary: Andy Roy Magid ematics. Deadline for organizers: April 15, 1988 Deadline for consideration: August 3, 1988 Send Proposals for Special Sessions to the Associate Secretaries January 1989 Meeting in Phoenix The programs of sectional meetings are arranged by the Associate Associate Secretary: Lance W. Small Secretary for the section in question: Deadline for organizers: March 15, 1988 Far Western Section (Pacific and Mountain) Deadline for consideration: September 21, 1988 Lance W. Small, Associate Secretary Department of Mathematics University of California, San Diego Information for Organizers La Jolla, CA 92093 619-534-3590) Special Sessions at Annual and Summer Meetings are held (Telephone under the general supervision of the Program Committee. Central Section They are administered by the Associate Secretary in charge Andy Roy Magid, Associate Secretary of the meeting with staff assistance, from the Society office Department of Mathematics of Oklahoma in Providence. University Elm PHSC 423 arise from an invitation to a 601 Some Special Sessions Norman, OK 73019 Associate Secretary. proposed organizer issued through the (Telephone 405- 32S-2052) proposed by interested organiz­ Others are spontaneously Eastern Section ers or participants. Such proposals are welcomed by the W. Wistar Comfort, Associate Secretary Associate Secretaries. of Mathematics Annual Department The number of Special Sessions at a Summer or Wesleyan University Meeting is limited to twelve. Proposals, invited or offered, Middletown, CT 06457 that are received at least nine months prior to the meeting (Telephone 203-347-9411) are screened for suitability of the topic and of the proposed list of speakers, and for possible overlap or conflict with

FEBRUARY 1988, VOLUME 35, NUMBER 2 289 Invited Speakers and Special Sessions

Southeastern Section the special early deadline announced above and in the Frank T. Birtel, Associate Secretary announcements of the meeting at which the Special Session Department of Mathematics has been scheduled. Contributors should know that there Tulane University is a limitation in size of a single special session, so that New Orleans, LA 70 118 it is sometimes true that all places are filled by invitation. (Telephone 504-865-5646) Papers not accepted for a Special Session are considered as As a general rule, members who anticipate organizing Special ten-minute contributed papers. Sessions at AMS meetings are advised to seek approval at least Abstracts of papers submitted for consideration for pre­ nine months prior to the scheduled date of the meeting. No Special sentation at a Special Session must be received by the Sessions can be approved too late to provide adequate advance Providence office (Editorial Department, American Mathe­ notice to members who wish to participate. matical Society, P. 0. Box 6248, Providence, RI 02940) by the special deadline for Special Sessions, which is usually Information for Speakers three weeks earlier than the deadline for contributed papers for the same meeting. The Council has decreed that no A great many of the papers presented in Special Sessions paper, whether invited or contributed, may be listed in the at meetings of the Society are invited papers, but any program of a meeting of the Society unless an abstract of the member of the Society who wishes to do so may submit paper has been received in Providence prior to the deadline. an abstract for consideration for presentation in a Spe­ cial Session, provided it is received in Providence prior to

CURRENT TRENDS IN Contents ARITHMETICAL ALGEBRAIC Introduction GEOMETRY A. Beilinson, Height pairing between algebraic Kenneth A. Ribet, Editor cycles (Contemporary Mathematics, Pierre Deligne, Dale Husemoller, Survey of Volume 67) Drinfef d modules Jean-Marc Fontaine, William Messing, p-adic periods and p-adic etale cohomology Henri Gillet, An introduction to higher dimensional This volume contains papers presented at Arakelov theory the AMS-IMS-SIAM Joint Summer Research Conference on Current Trends in Arithmetical Serge Lang, Diophantine problems in complex Algebraic Geometry, held in August 1985 at hyperbolic analysis Humboldt State University in Arcata, California. Ron Livne, Cubic exponential sums and Galois The conference focused on hyperbolic geometry, representations Arakelov theory, and connections between etale J.-F. cohomology and crystalline cohomology. The J.-P. Serre, Lettre a Mestre book is accessible to both graduate students and Joseph H. Silverman, A survey of the theory of mathematicians interested in current topics in height functions arithmetical geometry, particularly those readers in Lucien Szpiro, Presentation de Ia theorie neighboring fields who wish to acquire an overview d'Arakelov of some topics in which research is now intensely active. Some of the introductory papers will be 19110 Mathematics Subject Classifications: 11G, 14F, 19E. 32H of interest to the nonspecialists, while others are ISBN 0-8218-5074-1, LC 87-11506 directed at researchers and advanced graduate ISSN 0271-4132 students familiar with the area. Portions of this 304 pages (softcover), June 1987 Individual member 118. List price $30. book are likely to become fundamental references Institutional member $24 and will be of permanent value to researchers. To order, please specify CONM/67NA

Shipping/Handling: 1st book $2, each additional S1. maximum $25; by air, 1st book S5. each additional $3, maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-9930, or call toll free 800-556-7774 to charge with VIsa or MasterCard

280 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Symposium on Some Mathematical Questions in Biology Las Vegas, Nevada May 4, 1988

The twenty-second annual Symposium on Some Math­ Program ematical Questions in Biology on The dynamics of Chairman: Hans G. Othmer excitable media will be held on Wednesday, May 4, during the annual meeting of the Federation of Amer­ 9:00 a.m.- Presiding: HANS G. 0THMER, Univer­ ican Societies for Experimental Biology, May 1 - 6, sity of Utah 1988. The symposium is sponsored by the American An analysis of bursting in excitable cells. JAMES C. Mathematical Society, the Society for Industrial and ALEXANDER, University of Maryland Applied Mathematics, and the Society for Mathemat­ ical Biology. Cardiac pacemaking: A consensus of sinus node The AMS-SIAM Committee on Mathematics in cells. JosE JALIFE, SUNY Upstate Medical Center the Life Sciences serves as the Organizing Committee Aspects of propagation failure in excitable media. for the symposium. The committee consists of Gail JAMES KEENER, University of Utah A. Carpenter (Northeastern University); Kenneth L. Lange (Massachusetts Institute of Technology); Hans 1:30 p.m.- Presiding: HANS G. 0THMER, Univer­ G. Othmer (University of Utah); Alan S. Perelson sity of Utah (Los Alamos National Laboratory); Richard E. Plant, Wave propagation in aggregation fields of "Dic­ chairman (University of California, Davis); and John tyostelium discoideum': PETER MONK, University of Rinzel (National Institutes of Health). Professor Oth­ Delaware mer is the organizer of the symposium. The use ofa bidomain model for propagation studies The theme of the symposium is The dynamics of in cardiac tissue. ROBERT PLONSEY, Duke University excitable media. There will be two half-day sessions, each including three one-hour lectures. Collective behavior in the hippocampus. RoGER TRAUB, Thomas J. Watson Research Center and New York University

Symposium on The I~egacy of John von Neumann Hempstead, New York May 29-June 4, 1988

With the anticipated support of the National Science Summer Institutes and Special Symposia whose mem­ Foundation and the Alfred P. Sloan Foundation, a bers at the time of selection were: Albert Baernstein II, symposium on The legacy of John von Neumann will Eric Friedlander, H. Blaine Lawson, Jr., Linda Preiss take place Sunday through Saturday, May 29-June 4, Rothschild, Robert B. Warfield, Jr., and John Wermer. 1988 at Hofstra University in Hempstead, New York. The symposium will be sponsored by the Amer­ The topic was selected by the AMS Committee on ican Mathematical Society, Hofstra University and

FEBRUARY 1988, VOLUME 35, NUMBER 2 291 Meetings

the Society for Industrial and Applied Mathematics. H. GoLDSTINE, American Philosophical Society; PAUL Proceedings will be published by the AMS. R. HALMOS, Santa Clara University; ISRAEL HALPERIN, The organizing committee for the symposium in­ University of Toronto; UFFE HAAGERUP, Odense cludes JAMES G. GLIMM, Courant Institute of Mathe­ University, Denmark; EDWIN HEWITT, University of matical Sciences, HERMAN H. GoLDSTINE, American Washington; W. DANIEL HILLIS, Thinking Machines Philosophical Society, JoHN IMPAGLIAZZO, Hofstra Corporation; ARTHUR M. JAFFE, Harvard Univer­ University, GEORGE W. MACKEY, Harvard Univer­ sity; RICHARD B. KADISON, University of Pennsylva­ sity, I. M. SINGER, MIT (co-chair), MARSHALL H. nia; SHIZUO KAKUTANI, Yale University; GEORGE W. STONE, Emeritus, University of Chicago/University MACKEY, Harvard University; FRANCIS J. MURRAY, of Massachusetts (co-chair), and SHMUEL WINOGRAD, Emeritus, Duke University; MICHAEL J. NEUMANN; T. J. Watson Research Center, IBM Corporation. DONALD ORNSTEIN, Stanford University; STEVEN A. John von Neumann is considered one of the ORSAZG, Princeton University; NICHOLAS PIPPENGER, foremost mathematicians of the twentieth century. IBM Almaden Research Center; I. I. RABI, Columbia Born in Hungary on 28 December, 1903, he excelled University; IRVING E. SEGAL, Massachusetts Institute brilliantly in his studies, and at the age of twenty­ of Technology; MARSHALL H. STONE, Emeritus, Uni­ two had received his doctorate in mathematics from versity of Chicago/University of Massachusetts; En­ the University of Budapest with extensive studies in WARD TELLER, Lawrence Livermore National Labora­ experimental physics and chemistry. Von Neumann tory; NICHOLAS A. VONNEUMAN; MARINA VON NEU­ soon was recognized as a mathematical genius and by MANN WHITMAN, General Motors Corporation; and 1933 he was accepted into the Institute for Advanced EDWARD WITTEN, Princeton University. Study at Princeton, New Jersey. John von Neumann, often called "Johnny" by his colleagues and associates, was a man of great warmth, Preregistration presence and humor. Possessing an incredible memory, The deadline for preregistration is April 4, 1988. The he could recite verbatim the contents of a book after preregistration fee is $60. After April 4, 1988 the just one reading. His genius touched many fields of registration fee will be $75. study in mathematics, physics, computability, and The Organizing Committee invites all participants economics. Computer science, logic, ergodic theory, to a reception and dinner on Thursday, June 2 from fluid mechanics, quantum mechanics, atomic energy, 6:00 p.m. until 8:00 p.m. in the East Wing of the algebra, measure theory, econometrics and ordnance Student Center. MARSHALL H. STONE will speak on are just a few areas that were deeply influenced the life of von Neumann. Tickets for the event will by von Neumann's work. Known as the "father of be available through preregistration until April 4 at a the modem computer", von Neumann was a leader in cost of $20. Seating is limited to 400 persons. many organizations and agencies such as the American Forms for preregistration and housing are found Philosophical Society, National Academy of Sciences, at the back of this issue. Atomic Energy Commission, Los Alamos Scientific Laboratory and, in 19 51, President of the American Mathematical Society. Registration Von Neumann died on February 8, 1957 at a The symposium registration desk will be located in relatively young age. In spring 1988, on the occasion the Daniel I. Monroe Lecture Hall. The desk will be of the 85th anniversary of his birth, and during staffed from 2:00 p.m. until 8:00 p.m. on Sunday, May the 1OOth anniversary of the American Mathematical 29; and from 8:00 a.m. until 5:00 p.m. from Monday, Society, it is only fitting that a symposium of this May 30 through Friday, June 3. Registration will not scope and magnitude be given in his honor, reviewing be opened on Saturday, June 4. The onsite registration his many contributions to science and to discuss the fee will be $75. current state of research in the mathematical fields he developed. A tentative list of invited speakers includes EN­ Petition Table RICO CLEMENTI, IBM; ALAIN CONNES, l.H.E.S., Uni­ A petition table will be set up in the registration area. versity of Paris IV; JOHN CoNWAY, Princeton Univer­ Additional information about petition tables can be sity; JACK D. CowAN, University of Chicago; HARRY found in a box in the Atlanta meeting announcement FURSTENBERG, Hebrew University; JAMES G. GLIMM, on page 68 of the January issue of Notices. Courant Institute of Mathematical Sciences; HERMAN

292 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Visual Index and one drinking glass. Towels are exchangeable daily upon request at the check-in desk. Participants are includ­ An alphabetical list of registered participants, advised to bring their own washcloths and hangers. ing local addresses, arrival and departure dates, will There is no daily maid service in the sleeping rooms. be maintained in the registration area. Each residence hall is equipped with clothes wash­ ers ($.50) and dryers ($.50); however there is no pro­ Book Exhibit and Sale vision for purchasing detergents. Vending machines are available for soft drinks, candy, and miscellaneous mathematics There will be an exhibit of assorted snacks in each residence hall. and a sale at books offered by various publishers, No pets are allowed in the residence halls. Res­ discounts of recent books published by the substantial idence halls will have designated smoking and non­ book exhibit and American Mathematical Society. The smoking areas. Rooms and hallways are equipped with I. Monroe Lecture sale will be located in the Daniel heat sensors. Hall, adjacent to registration and sessions, and will be open during the same hours as registration Sunday Check-In Locations and Times through Friday. The residence hall check-in desk will be located at the Service Desk in the Student Center. The desk is open Accommodations on a 24-hour basis. For directions to the residence halls and the Student University Housing Center, see the section on travel. Participants desiring confirmed reservations for on­ At the time of check-in, participants assigned campus housing must preregister and send payment in rooms during preregistration through the Mathematics full for housing to the Mathematics Meetings Housing Meetings Housing Bureau will present their receipt at Bureau prior to the April 4, 1988 deadline. Participants the Service Desk in the Student Center which will in the symposium may occupy residence hall rooms at enable them to receive a key. Those participants being Hofstra University during the period May 28 through assigned a room directly by the check-in desk will June 5 only. All must check out by June 5. A limited be required to fill out a housing form, thus enabling number of rooms on campus will be available for them to receive same key. Spouses desiring a room those participants who do not preregister but plan on key must follow this procedure also. Please note that, attending the meeting and registering on site. Rooms although there is no deposit required for keys, a penalty will be assigned at the Service Desk located in the of $15 will be imposed for each key lost or not returned. Student Center. All payments, however, must be made It is the responsibility of the Mathematics Meetings at the Symposium Registration Desk during scheduled Housing Bureau to collect this penalty. Therefore, it registration hours. As a room is assigned at the Service is requested that proper caution be exercised to avoid Desk, each person will be given a form to hand to this charge. At checkout, all keys must be returned the AMS Housing Coordinator at the registration desk to the check-in desk. Should the clerk not be present, along with the payment. Onsite payments can be made please ensure that your name is left at the check-in by cash, personal checks, travelers' checks, VISA or desk with the key. MasterCard. Room and Board Rates Participants requesting housing on the Hofstra University campus will be assigned to halls within the The following rates apply for residence hall accommo­ Colonial Square Complex. (Please refer to the section dations at Hofstra University. Please note that there below titled Room and Board Rates.) is no room tax applicable to these rates. Residence halls within the Colonial Square Com­ Children 18 years and younger may stay in the plex have two floors. Each complex has 14 suites, same room as their parents at no charge. each suite consisting of two bedrooms and a shared Singles Doubles bath with shower. Residence halls are air-conditioned Colonial Square $28.00 $44.00 and equipped to accommodate handicapped persons. Residence Halls (or $22.00 pjp) Sleeping rooms are comfortable, very well maintained, Hotels and contain two single beds, desks, chairs, reading Participants wishing to reside off campus should lamps, and closets. Rooms will be prepared for occu­ make their own reservations directly with the ho­ pancy in advance. In addition to bed linen, pillow, tel/motel of their choice. Although rooms have not and blanket, participants will receive a towel, soap,

FEBRUARY 1988, VOLUME 35, NUMBER 2 293 Meetings

been blocked at any of these locations, they are in­ Netherlands cluded for informational purposes. Please note that Monday-Thursday 7:30a.m.- 10:00 a.m. rates do not include applicable taxes and are subject 4:30 p.m. - 7:00 p.m. to change. Friday 7:30a.m.- 10:00 a.m. 11 :00 a.m. - 2:00 p.m. Long Island Marriott (1 mile) 101 James Doolittle Blvd, Uniondale 11553 The Netherlands offers healthy lighter fare entrees Telephone: 516-794-3800 or Toll Free: 800-228-9290 and salads including breakfast bar with yogurt, fresh Single occupancy $121-140 fruit, bagels, breads; quiches and salads of the day; Double occupancy $141-160 char-broiled burgers, salad plates and BBQ, in season. The Rathskellar Grand Royal Hotel ( 1 mile) Monday - Friday 11:00 a.m.- 7:00p.m. 80 Clinton Street Saturday and Sunday 4:30p.m.- 7:00p.m. Telephone: 516-486-4100 Single occupancy $70 This pub features homemade pizza, heros, grilled Double occupancy $80. items and sandwiches. Music is featured. Bits & Bytes The Garden City Hotel (2.5 miles) Monday--Friday 11:00 a.m.- 3:00p.m. Garden City, Long Island Telephone: 516-747-3000 or Toll Free: 800-547-0400 Located on South Campus. Enjoy burgers, chicken Single occupancy $135 bits, hot and cold sandwiches, soups, salad and bread Double occupancy $150 bar, Hebrew National Hot Dogs, Snapple Juices and desserts in a hi-tech setting. Howard Johnson Plaza Hotel (5 miles) 150 Sunnyside Boulevard, Plainview, Long Island Hofstra USA Dutch Treats 11803 Monday - Friday 11:00 a.m.- 3:00p.m. Telephone: 516-349-9100 or Toll Free: 800-654-2000 4:30p.m.- 7:00p.m. Single occupancy $91-109 Saturday and Sunday 11:00 a.m.- 2:00p.m. Double occupancy $101-119 4:30p.m.- 7:00p.m. Food Service Kate & Willys Monday - Friday 11:00 a.m. - 3:00 p.m. The Food Service at Hofstra offers a wide selection 4:30p.m.- 7:00p.m. of choices from fast foods to full dinners on a cash Saturday and Sunday 4:30 p.m. - 7:00 p.m. basis. The average prices for meals are: $3.50 for breakfast, $5.50 for lunch, and $7.50 for dinner. Eatery There are seven food service operations that will be Monday - Sunday 4:30 p.m. - 7:00 p.m. open during the symposium. The recommended site Hofstra USA, Kate & Willys and the Eatery are for all meals is the Student Center, located on the located in the USA Complex on North Campus. south campus. Dutch Treats features carry out items. Kate & Willys Student Center - Main Level has a pub style menu. The Eatery serves buffet dinner Monday through Friday nightly. Hot Breakfast 7:30a.m.- 10:15 a.m. For those participants who wish to go off campus Continental Breakfast 10:00 a.m. - 10:45 a.m. to get their meals, please be advised that there are Lunch 11 :00 a.m. - 2:00 p.m. only a few restaurants within walking distance of the Dinner 4:30 p.m. - 7:00 p.m. Hofstra campus. Saturday and Sunday Social Events Brunch 11:00 a.m. - 2:00 p.m. Dinner 4:30p.m.- 6:30p.m. There will be a complimentary welcoming wine and cheese reception on Sunday, May 29 from 7:30 Located in the heart of the Student Center build­ p.m. until 9:00 p.m. in the Multi-Purpose Room in ing, the facility offers a complete menu including the Student Center. hot deli sandwiches, grill, cold sandwiches, a 25 item The Organizing Committee invites all participants salad bar, hot entrees, and frozen yogurt with top­ to a reception and dinner on Thursday, June 2 from pings. Vegetarian and Kosher meals are available upon 6:00 p.m. until 8:00 p.m. in the East Wing of the request. Student Center. MARSHALL H. STONE will speak on

294 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

the life of von Neumann. Tickets for the event will be Marriott Hotel which is one mile from the Hofstra available through preregistration until April4 at a cost campus. With advance reservations, you may request of $20. Seating is limited to 400 persons. If space is to be dropped off at the Student Center on the available after the preregistration deadline, tickets will Hofstra Campus. For reservations please call 718-995- be sold at the registration desk on Sunday, May 29 5592. On arrival at either airport, proceed to the and Monday, May 30 ONLY. NO TICKETS CAN BE Ground Transportation Counter for limousine service SOLD AFfER THE CLOSE OF REGISTRATION to Hempstead. ON MONDAY. For those participants arriving by car: Recreation From upstate New York or New England: Proceed south to the New England Thruway (Interstate 95) The Hofstra Swim Center will be available for use and take this to the Throgs Neck Bridge. Take Cross by symposium participants. Membership at the Swim Island Parkway to Grand Central Parkway heading Center is complimentary for symposium participants. to Eastern Long Island. The Grand Central Parkway Upon room registration at the Hospitality Service becomes the Northern State Parkway. Follow the Office (Room 112 Student Center), participants will Northern State Parkway to Meadowbrook South to be given an identification card that will allow for Hempstead Turnpike which is exit M5 West. Follow admittance into the Hofstra Swim Center. Participants Hempstead Turnpike west for approximately 1.5 miles must show their identification card for admittance. to the campus. Travel From Northwestern New Jersey, Northern Pennsyl­ vania and the Middle States: Take either Interstate Meetings, Incentives, Conventions of America, Inc. 78, Interstate 80, U.S. Route 22, New Jersey Route (MICA, Inc.) has been designated the official travel 4, or New Jersey Route 17 to the George Washington management firm for the symposium in an effort to Bridge. Proceed over the bridge to the Cross Bronx ensure that everyone attending the meeting is able to Expressway onto the Throgs Neck Bridge. Follow the obtain the best possible airfare. Although any travel directions in the preceding paragraph from the Throgs agent can obtain Supersaver or other such published Neck Bridge. promotional fares, only MICA can obtain the special From Southern New Jersey, Southeastern Pennsyl­ additional 5% discount over and above these fares vania, Maryland, Washington, D.C. and Virginia: Take and the 45% discount off of regular coach fares. The the New Jersey Turnpike to exit 13; then Route 278 to latter, of course, is financially beneficial only when the Verrazano-Narrows Bridge. From the bridge, take one does not qualify for one of the promotional fares. the Belt Parkway east to the Southern State Parkway. Participants should pay particular attention to the Follow the Jones Beach signs as far as Meadowbrook cancellation policies stated in MICA's advertisement Parkway, and go north (exit 22) on the Meadowbrook found elsewhere in this announcement. Parkway to Hempstead Turnpike West (exit M5) and Hofstra University is located 25 miles east of New continue west for approximately 1.5 miles to campus. York City in Hempstead, Long Island. The John F. To the Student Center: Follow the Hempstead Kennedy and LaGuardia International Airports are 30 Turnpike until you see the campus signs for Hofstra minutes from the campus by car or airport limousine University. Take a right (from the east) on to Oak service. The Long Island Railroad provides regular Street then your first right into the public parking area. commuter service from the Pennsylvania Station lo­ The Student Center is located at the southern end of cated at 34th Street and 7th Avenue in New York the parking lot. City and the Flatbush Avenue Station in Brooklyn, To the Residence Halls from the Student Center New York to the Hempstead Station. It is a short (check-in desk): Exit the public parking lot taking a cab ride from the Hempstead station to campus. The right onto Oak Street. Take your first right and the Metropolitan Suburban Bus Authority provides pub­ Colonial Square Residence Halls will be on your left. lic bus service to Hofstra from various points. For Please refer to the campus map. information call the Bus Information Center at 516- Campus Shuttle 222-1000, Monday through Saturday. The local taxi service is Larry's Taxi at 516-481-1111. For the convenience of participants, Hofstra Uni­ The Long Island Connecticut Limousine Service versity will operate a shuttle bus service that will provides direct service to Hempstead from JFK and stop at the Daniel I. Monroe Lecture Center, Colonial LaGuardia. If no reservations are made in advance, Square Residence Complex and the Student Center. the limousine service will drop off at the Long Island

FEBRUARY 1988, VOLUME 35, NUMBER 2 295 HOFSTRA. UNIVERSITY

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MAP LEGEND

1 COLONIAL SQUARE 40 COMPUTER CENTER 11 STUDENT CENTER (Weller Annex) 13 UNIVERSITY CLUB 43 DANIEL I. MONROE 14 PHYSICAL FITNESS CENTER LECTURE CENTER 15 SWIM CENTER 47 HOFSTRA INFORMATION 25 LIBRARY CENTER 35 HOFSTRA HALL P-PUBLIC PARKING LOT

296 Meetings

The shuttle is free and will operate daily from 7:30 persons. Hofstra University security monitors park­ a.m. until 11:30 p.m. ing areas regularly and will enforce the towing of Parking improperly or illegally parked vehicles. There is ample parking adjacent to the Colonial Weather Square Residence Halls and the Daniel I. Monroe Lec­ The weather on Long Island during late spring ture Center where all sessions will be held. Participants is usually quite pleasant with daytime temperatures are urged to obey all parking restrictions, especially averaging 70 degrees F and nighttime lows averaging fire zones and parking areas reserved for handicapped 55 degrees F.

AIRLINE INFORMATION SPECIAL AIRFARES 1-800-888-MICA

MICA, Inc., the official travel management firm for the AMS-Hofstra University-SIAM Symposium on the Legacy of John von Neumann to be held May 29- June 4, 1988, has arranged for special discounts aboard United Airlines.

Save 5% off published promotional airfares (meeting all restrictions) or 45% off roundtrip coach fares. Only through MICA can you receive these substantial discounts on United Airlines. It may be possible to receive an even lower airfare depending on your individual circumstances.

The lowest published promotional fares require a Saturday night stay, are subject to an airline change/cancellation penalty and must be purchased at least 30 days prior to departure.

Make your reservations today! For reservations on all airlines, call MICA directly on their nationwide toll-free number 1-800-888-MICA. MICA reservationists will advise you of the most convenient flights and lowest airfares available. You may pay be credit card or ask to be invoiced. Your airfare is guaranteed when your ticket is written!

Call Today Toll-Free 1·800-888-MICA and Save! (UJ UniTED Monday - Friday 9:00 am - 6:00 pm EST Meetings, Incentives, Conventions of America, Inc. (MICA, Inc.) Suite 303, 195 Farmington Avenue, Farmington, CT 06032 (203) 678-1040

FEBRUARY 1988, VOLUME 35, NUMBER 2 297 Joint Summer Research Conferences in the Mathematical Sciences Bowdoin College, Brunswick, Maine, June 11 to August 5, 1988

The 1988 Joint Summer Research Conferences in Kohanski, Summer Research Conference Coordina­ the Mathematical Sciences will be held at Bowdoin tor, American Mathematical Society, Post Office Box College, Brunswick, Maine, from June 11 to August 6248, Providence, RI 02940. 5. It is anticipated that the series of conferences will Please type or print the following: be supported by grants from the National Science 1. Title and dates. of conference desired Foundation and other agencies. 2. Full name There will be ten conferences in ten different 3. Mailing address areas of mathematics. The topics and organizers for 4. Telephone number and area code for office and the conferences were selected by the AMS-IMS-SIAM home Committee on Joint Summer Research Conferences in 5. Your scientific background relevant to the topic of the Mathematical Sciences. The selections were based the conference on suggestions made by the members of the committee 6. Financial assistance requested; please estimate cost and individuals submitting proposals. The committee of travel considered it important that the conferences represent 7. Indicate if support is not required, and if interested diverse areas of mathematical activity, with emphasis in attending even if support is not offered. on areas currently especially active, and paid careful The deadline for receipt of applications is February attention to subjects in which there is important 19, 1988. After that date the Organizing Committee for interdisciplinary activity at present. each conference will consider the requests (selection of The conferences are similiar in scientific structure the participants and the allocation of support is made to those held throughout the year at Oberwolfach. by the Organizing Committee.) You will be notified These conferences are intended to complement the by the AMS of the committee's decision no later than Society's program of annual Summer Institutes and May 1, 1988. Requests received past the deadline will Summer Seminars, which have a larger attendance and be returned. Funds available for these conferences are are substantially broader in scope. The conferences are limited and individuals who can obtain support from research conferences, and are not intended to provide other sources should do so. Women and members an entree to a field in which a participant has not of minority groups are encouraged to apply and already worked. participate in these conferences. It is expected that funding will be available for Any questions concerning the scientific portion of a limited number of participants in each conference. the conference should be directed to the chairman or Others, in addition to those funded, will be welcome, any member of the Organizing Committee. within the limitations of the facilities of the campus. The Joint Summer Research Conferences in the In the spring a brochure will be mailed to all who Mathematical Sciences are under the direction of are invited to attend the conferences. The brochure the AMS-IMS-SIAM Committee on Joint Summer will include information on room and board rates, the Research Conferences in the Mathematical Sciences. residence and dining hall facilities, travel and local The following Committee members chose the topics information and a Residence Housing Form to use for the 1988 conferences: William B. Arveson, James for on-campus housing accommodations. Information Daniel, Martin Golubitsky, Ronald L. Graham, James on off-campus housing will also be included in the I. Lepowsky, John R. Martin, Tilla Klotz Milnor, brochure. Participants are required to make their own Evelyn Nelson, and Ingram Olkin. housing and travel arrangements. Each participant will Descriptions of the subject matter of each of the be required to pay a fee of $25 to cover the cost of 1988 Conferences appeared in the November Notices, social events and refreshments served at breaks, in pages 1133- 1136; they were accompanied by lists of addition to a $15 registration fee. members of the respective organizing committees. Those interested in attending one of the confer­ ences should send the following information to Carole

298 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences

June 11 to June 17 July 23 to July 29 The mathematics and physics of order and disorder Mathematical problems posed by anisotropic materials CHARLES RADIN (University of Texas), Chairman JEAN E. TAYLOR (Rutgers University), Chair

June 18 to June 24 July 23 to July 29 Spatial statistics and imaging Geometric and topological invariants STUART GEMAN (Brown University), Co-Chairman of elliptic operators ANTONIO PosSOLO (University of Washington), JEFF CHEEGER (SUNY, Stony Brook), Co-Chairman Co-Chairman ALAIN CoNNES (College de France), Co-Chairman JEROME KAMINKER (Indiana-Purdue University­ June 25 to July 1 Indianapolis), Co-Chairman Mathematical developments arising from linear programming July 30 to August 5 JEFFREY C. LAGARIAS (AT&T Bell Laboratories), Elliptic genera and elliptic cohomology Co-Chairman PETERS. LANDWEBER (Rutgers University), MICHAEL J. TODD (Cornell University), Chairman Co-Chairman July 30 to August 5 July 2 to July 8 Control theory 8 multibody systems Geometric Problems in Fourier Analysis P.S. KR.ISHNAPRASAD (University of Maryland), WILLIAM BECKNER (University of Texas, Austin), Co-Chairman Co-Chairman JERROLD E. MARSDEN (University of California, D. H. PHONG (Columbia University), Co-Chairman Berkeley), Co-Chairman J. C. SIMO (Stanford University), Co-Chairman July 9 to July 15 Computational number theory CARL POMERANCE (University of Georgia), Chairman

July 16 to July 22 Current progress in hyperbolic systems: Riemann problems and computations BARBARA LEE KEYFITZ (University of Houston), Co-Chairman BRENT LINDQUIST (New York University, Courant Institute), Co-Chairman

FEBRUARY 1988, VOLUME 35, NUMBER 2 299 1988 Summer Research Institute Operator Theory /Operator Algebras and Applications University of New Hampshire, Durham, New Hampshire, July 3-23

The thirty-sixth Summer Research Institute spon­ provided striking insight into the behavior of operators sored by the American Mathematical Society will be under similarity transforms. The classical perturbation devoted to Operator theory /operator algebras and ap­ theory for Schrodinger operators has been transformed plications and will take place at the University of and simplified by the use of path integrals and the New Hampshire, Durham, New Hampshire. Mem­ Feynman-Kac formula. A rich theory of completely bers of the Organizing Committee include: WILLIAM positive and completely bounded maps of C*-algebras B. ARVESON, University of California, Berkeley (co­ has emerged, and this has had significant implications chair), RoNALD G. DouGLAS, SUNY at Stony Brook for operator theory, including dilation theory, the (co-chair), CIPRIAN I. FoiAs, Indiana University, I. characterization of operators having annular spectral C. GoHBERG, Tel Aviv University, PETER D. LAX, sets, and the partial solution of Sz.-Nagy's problem. Courant Institute of Mathematical Sciences, DoNALD The C*-algebras of Toeplitz operators associated with SARASON, University of California, Berkeley, BARRY a large class of domains in en are now clearly un­ SIMON, California Institute of Technology, and DAN­ derstood. Finally, the structure of broad classes of VIRGIL VOICULESCU, University of California, Berke­ reflexive operator algebras has been penetrated and ley. It is anticipated that the institute will be partially put into the context of "noncommutative" harmonic supported by a grant from the National Science Foun­ analysis. dation. Proceedings of the institute will be published These algebraic methods are diverse, and they in the AMS series Proceedings of Symposia in Pure touch upon a broad area of mathematics. In addi­ Mathematics. tion to the interrelations alluded to above, there have This topic was selected by the 1986 Committee on been direct applications to systems theory, complex Summer Institutes and Special Symposia whose mem­ variables, and statistical mechanics. Moreover, signif­ bers were ALBERT BAERNSTEIN II, ERIC FRIEDLANDER, icant problems and motivations have arisen from the H. BLAINE LAWSON, JR., LINDA PREISS ROTHSCHILD, subject's traditional underpinnings with partial differ­ ROBERT B. WARFIELD, JR. and JOHN WERMER. ential equations. While it would not be possible or During the last twenty years operator theory has perhaps even desirable to attempt to unify these re­ come of age. The subject has developed in several sults and methodology, it is time to pause, summarize directions, using new and powerful methods that have progress and examine the common points of view that led to the solutions of basic problems thought to be now run through the subject. inaccessible in the sixties. Some of these developments The three weeks of the Summer Research Institute have made mutually enriching contacts with other are planned to cover various aspects of operator areas of mathematics, including algebraic topology theory j operator algebras and applications with roughly and index theory, complex analysis in one and several the following schedule: variables, and probability theory. The period has seen the full characterization of WEEK ONE: Mathematical physics, Schrodinger op­ quasitriangular operators in terms of the Fredholm erators, scattering theory, path integral methods, dif­ index, the classification of families of essentially nor­ ferential operators, symmetric and selfadjoint opera­ mal operators via C*-algebraic extensions, and the tors. One and several complex variables, Toeplitz and subsequent development of the latter subject culmi­ Wiener-Hopf operators, Hankel operators, integral nating in the unification of C*-algebraic K-homology operators, algebraic and complex geometric methods. and K-cohomology in the Kasparov KK-bifunctor. Invariant subspaces, subnormal operators, hyponor­ The invariant subspace problem has been solved for mal operators, spectral operators, noncommutative subnormal operators and related classes. The classical approximation theory, non-selfadjoint operators. Weyl-von Neumann theorem has been vastly general­ ized to separable C*-algebras. The Ringrose problem WEEK TWO: Dilation theory and operator maps, has been solved, using algebraic methods that have model theory, spectral and functional calculus

300 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Summer Research Institute

theories. Engineering, systems theory and control, Those interested in receiving an invitation to par­ operator-valued polynomials and functions, interpo­ ticipate in the institute should send the following lation of operators, spaces with an indefinite metric. information to John Balletto, Summer Institute Con­ Partial differential operators, numerical analysis, ellip­ ference Coordinator, American Mathematical Society, tic operators, heat equation asymptotics. Post Office Box 6248, Providence, RI 02940 prior to April 1, 1988. WEEK THREE: Index theory, K-theory, non­ Please type or print the following: commutative topology and geometry, cyclic coho­ 1. Full name mology. Selfadjoint operator algebras, non-selfadjoint 2. Mailing address operator algebras, similarity of nests. 3. Telephone number and area code for office and Accommodations will be available in the campus home residence halls for participants and their families; 4. Your scientific background relevant to the institute cafeteria style meals will be available. All facilities topic will be accessible to the handicapped. 5. Financial assistance requested Information on housing, dining, travel and the 6. Indicate if support is not required, and if interested local area will be sent to invited participants in the in attending even if support is not offered. spring. Each participant will pay a registration fee Requests for invitations will be forwarded to the and a social fee to cover the costs of social events Organizing Committee for consideration. Requests scheduled during the institute. will be considered after April 1, 1988 and applicants selected will receive formal invitations and notification of financial assistance beginning in mid-May.

1988 Summer Seminar in Applied Mathematics Computational Solution of Nonlinear Systems of Equations Colorado State University, Fort Collins, Colorado, July 18-29

The nineteenth AMS-SIAM Summer Seminar in Ap­ level research aspect. Throughout, the emphasis will plied Mathematics will be held July 18-29, 1988, be placed upon the computational aspects and applica­ at Colorado State University, Fort Collins, Colorado. tions. A significant number of anticipated participants The seminar will be sponsored jointly by the American will be scientists and mathematicians employed in Mathematical Society, the Society for Industrial and national and industrial research laboratories. It is Applied Mathematics, and the Department of Mathe­ also planned to gain participants from several foreign matics at Colorado State University. It is anticipated countries. that it will be supported by grants from federal agen­ Among the currently active topics to be treated will cies. The proceedings of the seminar will be published be continuation methods, quasi-Newton and nonlinear by the Society in the Lectures in Applied Mathematics conjugate gradient methods, piecewise-linear methods, series. mesh refinement and multigrid methods, and complex­ The aim of the conference is to provide a wide­ ity of nonlinear methods. The Organizing Committee ranging survey of current major thrusts in the numer­ consists of E. L. ALLGOWER, Colorado State Univer­ ical solution of nonlinear systems of equations. The sity; H. B. KELLER, California Institute of Technology; conference will be of two weeks duration. The con­ H.-0. PEITGEN, Universitat Bremen and University of ference will simultaneously have entry-level Summer California at Santa Cruz; W. C. RHEINBOLDT, Uni­ School aspects for young researchersand a frontier- versity of Pittsburgh; and S. SMALE, University of

FEBRUARY 1988, VOLUME 35, NUMBER 2 301 Summer Seminar

California, Berkeley. The principal speakers will be 4. Anticipated arrival and departure dates; announced in a future issue of the Notices. 5. Your scientific background relevant to the topic of A brochure will be available from the AMS of­ the seminar; fice which will include a description of the scientific 6. Financial assistance requested (please estimate cost program, information on accommodations, and local of travel); information. Each participant will pay a $15 reg­ 7. Indicate if support is not required, and if interested istration fee and a social fee in an amount to be in attending even if support is not offered. determined. Participants who wish to apply for a grant-in-aid Those interested in attending the seminar should should so indicate; however, funds available for the send the following information to Betty A. Verducci, seminar are very limited and individuals who can Summer Seminar Conference Coordinator, American obtain support from other sources should do so. Mathematical Society, P. 0. Box 6248, Providence, Graduate students who have completed at least one RI 02940, E-Mail: [email protected]. before May year of graduate school are encouraged to participate. 6, 1988. Please type or print the following: 1. Full name; 2. Mailing address; 3. Telephone number and area code for office and home;

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E-RADIAL PROCESSES AND RANDOM FOURIER SERIES Michael B. Marcus (Memoirs of the AMS. Number 368)

Gaussian processes can be represented as random Contents Fourier transforms of time changed Brownian Representing ~-radial processes motion. The more general class of ~-radial processes is the focus of this memoir. which Necessary conditions for continuity extends the work of R. Dudley and X. Fernique on Sufficient conditions for continuity stationary Gaussian processes and of G. Pisier and the author on p-stable processes. By providing Processes for which the Levy transforms or the a methodology for studying questions about the logarithms of the characteristic functions are sample path properties of ~-radial processes. this regularly varying with index 1 < p < 2 work would lead to further study of infinitely Processes for which the Levy transforms or the divisible processes on abstract structures. The logarithms of the characteristic functions are author also provides recent results about infinitely regularly varying with index 1 or 2 divisible processes which are of interest even in the case of real valued random variables. Suprema of ~-radial processes and random Fourier series The book is directed at probabilists interested in 1980 Mathematics Subject Classifications: sample path properties of stochastic processes. as 60G10, 60G17, 60G15, 60E07, 42A61, 42A20, well as at harmonic analysts having an interest 43A50 in random structures. Readers will gain insight ISBN 0-8218-2432-5, LC 87-12569 into the way the entropy approach to the study of ISSN 0065-9266 192 pages (softcover), July 1987 continuity of strongly stationary processes extends Individual member 111. List price $19, to those processes which are naturally associated Institutional member $15 with Orlicz space metrics. To order. please specify MEM0/368NA

Shipping/Handling: 1st book S2, each additional S1. maximum $25; by air, 1st book S5. each additional $3, maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-9930, or call toll free 800-556-7774 to charge with VIsa or MasterCard

302 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Call For Topics For 1990 Conferences

Suggestions are invited from mathematicians, either Sciences, a one-, two-, or three-week conference may singly or in groups, for topics of the various confer­ be proposed. ences that will be organized by the Society in 1990. The deadlines for receipt of these suggestions, as well as some relevant information about each of the con­ 1990 AMS Symposium in Pure Mathematics ferences, are outlined below. An application form to This symposium in pure mathematics has traditionally be used when submitting suggested topic(s) for any been conducted in the spring of even numbered of these conferences (except the Short Course Series) years in conjunction with a sectional meeting. The may be obtained by writing to the Meetings Depart­ symposium can be held independently of a sectional ment, American Mathematical Society, P.O. Box 6248, meeting and serves to honor great accomplishments Providence, RI 02940, or telephoning 401-272-9500. in mathematics. Proceedings are normally published Individuals willing to serve as organizers should by the Society as volumes in the series Proceedings of be aware that the professional meeting staff in the Symposia in Pure Mathematics. Society's Providence office will provide full support Topics in recent years have been: and assistance before, during, and after each of these 1982-Several complex variables, organized by YuM­ conferences. Organizers should also note that for all TONG SIU of Stanford University conferences, except Summer Research Conferences, it 1984-Pseudodifferential operators and Fourier inte­ is required that the proceedings be published by the gral operators with applications to partial differential Society, and that proceedings of Summer Research equations, organized by FRANCOIS TREVES of Rutgers Conferences are frequently published. A member of University the Organizing Committee must be willing to serve as 1987- The mathematical heritage of Herman Weyl, editor of the proceedings. organized by R. 0. WELLS, JR. of Rice University. All suggestions must include ( 1) the names and Deadline For Suggestions: September 1, 1988 affiliations of proposed members and chairman of the Organizing Committee; (2) a two- or three-page de­ tailed outline of the subject( s) to be covered, including the importance, timeliness of the topic, and estimated 1990 AMS Summer Institute attendance; (3) a list of the recent conferences in the same or closely related areas; (4) a tentative list Summer institutes are intended to provide an un­ of names and affiliations of the proposed principal derstandable presentation of the state of the art in speakers; (5) a list of likely candidates who would be an active field of research in pure mathematics and invited to participate and their current affiliations; and usually extend over a three-week period. Dates for (6) any other observations which may affect the size of a summer institute must not overlap those of the the conference and the amount of support required. Society's summer meeting, which at the time of this Any suggestions as to sites and dates should be made printing have not yet been determined. There should as early as possible in order to allow adequate time for be a period of at least one week between them. Pro­ planning. By action of the AMS Board of Trustees, the ceedings are published by the Society as volumes in the Meetings Department of the Society is responsible for series Proceedings of Symposia in Pure Mathematics. the final selection of the site for each conference and Topics in recent years have been: for all negotiations with the host institution. Individ­ 1986-Representations of finite groups and related uals submitting suggestions for the conferences listed topics, organized by JONATHAN L. ALPERIN of the below are requested to recommend sites or geographic University of Chicago. areas which would assist the Meetings Department in 1987- Theta functions, organized by LEON EHREN­ their search for an appropriate site. In the case of Joint PREIS of Yeshiva University and ROBERT GUNNING of Summer Research Conferences in the Mathematical Princeton University.

FEBRUARY 1988, VOLUME 35, NUMBER 2 303 Call for Topics

1988- Operator theory /Operator algebras and applica­ 1988- Computational solution of nonlinear systems tions, organized by WILLIAM B. ARVESON of University of equations, organized by EuGENE ALLGOWER of of California, Berkeley, and RONALD G. DOUGLAS of Colorado State University. State University of New York at Stony Brook. 1989- The mathematics ofrandom media organized by 1989 -Several complex variables and geometry, orga­ WERNER KoHLER of Virginia Polytechnic Institute and nized by STEVEN G. KRANTZ of Washington Univer­ BENJAMIN WHITE of Exxon Research & Engineeering sity. Company. Deadline For Suggestions: September 1, 1988 Deadline For Suggestions: September 1, 1988

1990 AMS-SIAM-SMB Symposium 1990 Joint AMS-IMS-SIAM Summer Some Mathematical Questions in Biology Research Conferences in the Mathematical Sciences This one-day symposium now under joint sponsorship with the Society for Mathematical Biology is usually These conferences are similar in structure to those held in conjunction with the annual meeting of a held at Oberwolfach and represent diverse areas of biological society closely associated with the topic. mathematical activity, with emphasis on areas cur­ Papers from the symposia are published by the Society rently especially active. Careful attention is paid to as volumes in the series Lectures on Mathematics in subjects in which there is important interdisciplinary the Life Sciences. activity at present. Topics for the sixth series of Topics in recent years have been: one-week conferences, being held in 1988, are The 1985-Plant biology, organized by ROBERT M. MIURA mathematics and physics of order and disorder, Spa­ of the University of British Columbia. tial statistics and imaging, Mathematical developments 1986-Modeling circadian rhythms, organized by GAIL arising from linear programming, Geometric Problems A. CARPENTER of Northeastern University. in Fourier Analysis, Computational number theory, 1987-Models in population biology, organized by Current progress in hyperbolic systems: Riemann prob­ ALAN HASTINGS of the University of California, Davis. lems and computations, Mathematical problems posed 1988-Dynamics of excitable media, organized by by anisotropic materials, Geometric and topological HANS G. OTHMER of the University of Utah. invariants of elliptic operators, Elliptic genera and 1989-Sex allocation and sex change: Experiments and elliptic cohomology, Control theory 8 multibody sys­ models organized by MARC MANGEL of the University tems. If proceedings are published by the Society, they of California, Davis. will appear as volumes in the series Contemporary Mathematics. Deadline For Suggestions: September 1, 19 8 8 Deadline For Suggestions: February 1, 1989

1990 AMS-SIAM Summer Seminar Call for Topics for The goal of the summer seminar is to provide an 1990 AMS Short Course Series mathematics environment and program in applied The AMS Short Courses consist of a series of in­ latest ideas and in which experts can exchange the troductory survey lectures and discussions ordinarily Proceedings are newcomers can learn about the field. extending over a period of one and one-half days in the series published by the Society as volumes starting immediately prior to the Joint Mathematics Lectures in Applied Mathematics. Meetings held in January and August each year. Each Topics in recent years have been: theme is a specific area of applied mathematics or chemical reac­ 1985-Reacting flows: Combustion and mathematics used in the study of a specific subject or of Cornell Univer­ tors, organized by G.S.S. LUDFORD collection of problems in one of the physical, biologi­ sity. cal, or social sciences, technology, or business. Topics Aspects of VLSI Design with 1987- Computational in recent years have been Computation Complex­ Device Simulation, an Emphasis on Semiconductor ity Theory (January 1988), Moments in Mathemat­ University of organized by RANDOLPH BANK of the ics (January 1987), Approximation Theory (January California, San Diego. 1986), Actuarial Mathematics (August 1985), Fair Al­ location (January 1985). Proceedings are published by

304 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Call for Topics

~------~------~ the Society as volumes in the series Proceedings of Submit suggestions to: Professor Stefan A. Burr, Chair­ symposia in Applied Mathematics, with the approval man, Short Course Subcommittee, Department of of the Editorial Committee. Computer Science, CUNY, City College, New York, Deadline for Suggestions: Suggestions for the January NY 10031. 1990 course should be submitted by July 1, 1988; suggestions for the August 1990 course should be submitted by December 1, 1988.

THE MAXIMAL SUBGROUPS OF The maximal rank theorem CLASSICAL ALGEBRAIC The classical module theorem GROUPS Modules with 1-dimensional weight spaces Gary M. Seitz The rank 1 theorem (Memoirs of the AMS, Number 365) Natural embeddings of classical groups Aimed at researchers in group theory, this book Component restrictions classifies the maximal closed connected subgroups VIX is usually basic of the classical algebraic groups over algebraically closed fields of positive characteristic, with the X= An main result being a description of all closed X = Bn. Cn. Dn. n :j:. 2 connected overgroups of the irreducible closed connected subgroups of the classical algebraic X = 82. C2. and G2 groups. These results extend Dynkin's earlier X= F4 (p > 2), E6. E1. E8 work with groups over fields of characteristic 0. By presenting a detailed analysis of group Exceptional cases for p = 2 or 3 embeddings, the author seeks to overcome the Embeddings and prime restrictions various difficulties present in the representation theory of algebraic groups in positive characteristic. The main theorems Therefore, readers witt obtain an understanding 1980 Mathematics Subject Classification: 20 not only of the maximal subgroups of the classical ISBN 0-8218-2427-9. LC 87-1161 algebraic groups, but also of methods for studying ISSN 0065-9266 292 pages (softcover), May 1987 embeddings of linear groups. Because the Individual member 117, List price $28, arguments involve both representation theory and Institutional member $22 group theory, readers should be familiar with the To order, please specify MEM0/365NA structure and representations of algebraic groups. Confents Shipping/Handling: 1st book $2, each add'l $1, $25 max. By air, 1st book $5, each add'l $3, Preliminary lemmas $100 max. Q-levels and commutator spaces Prepayment required. Order from AMS, P.O. Box 1571, Annex Station. Providence. Rl 02901-9930, Embeddings of parabolic subgroups or call 800-556-7774 to use VISA or MasterCard. I il ~= -a

FEBRUARY 1988, VOLUME 35, NUMBER 2 305 Daniel Gordon, Douglas Grenier, and Audrey DANIEL SHANKS, DEDICATION Terras, Heeke operators and the fundamental Special Issue domain for (SL(3, Z)) Mathematics of Computation Marie-Nicole Gras, Special units in real cyclic sextic fields R. K. Guy, C. B. Lacampagne, and J. L. Selfridge, Primes at a glance This special issue of Mathematics of Computation Neal Koblitz, Elliptic curve cryptosystems (Volume 48, Number 177, January 1987) is D. H. Lehmer and Emma Lehmer, Cyclotomic of his dedicated to Daniel Shanks on the occasion resultants 70th birthday. Since 1959, when Shanks joined H. W. Lenstra, Jr. and R. J. Schoof, Primitive the Editorial Committee for this journal, he has normal bases for finite fields been a guiding force in shaping the computational R. A. Mollin, Class numbers of quadratic fields number theory component of the journal, and has determined by solvability of diophantine equations had an immense influence in the field. This volume Peter L. Montgomery, Speeding the Pollard and contains papers by some of the top researchers in elliptic curve methods of factorization the field and covers such topics as elliptic curves, Morris Newman and Robert C. Thompson, primality testing, congruences, class groups, and Numerical values of Goldberg's coefficients in the cyclotomic fields. Although a numbered issue series for log( ex eY) of the Mathematics of Computation journal, it A. M. Odlyzko, On the distribution of spacings will serve as a stand alone reference work for between zeros of the zeta function computational number theory. M. Pohst, On computing isomorphisms of Contents equation orders William W. Adams, Characterizing Pseudoprimes Carl Pomerance, Very short primality proofs for third-order linear recurrences Herman J. J. te Riele, On the sign of the Leonard M. Adelman, Dennis R. Estes, and difference 1r(x)- Ji(x) Kevin S. McCurley, Solving bivariate quadratic Robert D. Silverman, The multiple polynomial congruences in random polynomial time quadratic sieve Richard Blecksmith, John Brillhart, and Irving Jonathan W. Tanner and Samuel S. Wagstaff, Gerst, Parity results for certain partition functions Jr., New congruences for the Bernoulli numbers and identities similar to theta function identities Heinz M. Tschope and Horst G. Zimmer, Johannes Buchmann, The computation of the Computation of the Neron- Tate height on elliptic fundamental unit of totally complex quartic orders curves Johannes Buchmann and H. C. Williams, On Lawrence C. Washington, Class numbers of the principal ideal testing in totally complex quartic simplest cubic fields fields and the determination of certain cyclotomic H. C. Williams, Effective primality tests for some constants integers of the forms A5n - 1 and Ar - 1 Nicholas Buck, Lones Smith, Blair K. H. C. Williams and M. C. Wunderlich, On the Spearman, and Kenneth S. Williams, The parallel generation of the residues for the continued cyclotomic numbers of order fifteen fraction factoring algorithm Duncan A. Buell, Class groups of quadratic Don Zagier, Large integral points on elliptic curves fields. II David G. Cantor, Computing in the Jacobian of a 1980 Mathematics Subject Classification: 11 ISSN 0025-5718 hyperelliptic curve 448 pages (softcover), January 1987 H. Cohen and A. K. Lenstra, Implementation of Individual member $29, List price $48, a new primality test Institutional member $38 /NA H. Cohen and J. Martinet, Class groups of To order, please specify SHANKS number fields: numerical heuristics Harvey Cohn and Jesse Deutsch, Application of Shipping/Handling: 1st book $2, each add'l $1, symbolic manipulation to Heeke transformations of $25 max. By air, 1st book $5, each add'l $3, modular forms in two variables $100 max. T. W. Cusick and Lowell Schoenfeld, A table Prepayment required. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901-9930, of fundamental pairs of units in totally real cubic or call 800-556-7774 to use VISA or MasterCard. fields * 1988-1989. Academic Year Devoted to Mathematical Sciences Operator Algebras, Mittag-Leffler Insti­ tute, Djursholm, Sweden. Meetings and Conferences PROGRAM: Emphasis will be mainly on the theory of C* and Von Neu­ mann algebras. DEADLINE FOR APPLICATION: April1, 1988. Send to the Mittag-Leffler In­ stitute, Auravagen 17, S-18262, Djur­ sholm, Sweden. INFORMATION: U. Haagerup, Odense Universitet, Department of Mathe­ matics, Campusvej 55, 5230 Odense M, Denmark, or E. St0rmer, Oslo Universitet, Department of Mathe­ THIS SECTION contains announcements of meetings and conferences of interest to matics, P.O. Box 1053 Blindern, 0316 some segment of the mathematical public, including ad hoc, local, or regional meetings, and meetings or symposia devoted to specialized topics, as well as announcements Oslo 3, Norway. of regularly scheduled meetings of national or international mathematical organizations. 1987-1988. Academic Year Devoted to (Information on meetings of the Society, and on meetings sponsored by the Society, will Differential Geometry, University of be found inside the front cover.) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, North Carolina, Chapel Hill, North Car­ and specifies the place, date, subject (when applicable}, and the speakers; a second olina. full announcement will be published only if there are changes or necessary additional PROGRAM: There will be a dual em­ information. Once an announcement has appeared, the event will be briefly noted in each month, phasis on topics related to manifolds issue until it has been held and a reference will be given in parentheses to the year, and page of the issue in which the complete information appeared. Asterisks (*) sectional curvature and of non positive mark those announcements containing new or revised information. to exterior differential systems and IN GENERAL, announcements of meetings and conferences held in North America carry control theory. A workshop format only date, title of meeting, place of meeting, names of speakers (or sometimes a general with short tertn visitors will be typi­ statement on the program), deadlines for abstracts or contributed papers, and source cal. of further information. Meetings held outside the North American area may carry more INFORMATION: P. Eberlein or R. detailed information. In any case, if there is any application deadline with respect to Gardner, Department of Mathemat­ participation in the meeting, this fact should be noted. All communications on meetings ics, University of North Carolina, and conferences in the mathematical sciences should be sent to the Editor of Notices, Chapel Hill, North Carolina 27514. care of the American Mathematical Society in Providence. DEADLINES for entries in this section are listed on the inside front cover of each issue. In 198 7-19 8 8. Academic Year Devoted to order to allow participants to arrange their travel plans, organizers of meetings are urged Several Complex Variables, Mittag-Leffler to submit information for these listings early enough to allow them to appear in more than Institute, Djursholm, Sweden. (January one issue of Notices prior to the meeting in question. To achieve this, listings should be the scheduled date of the meeting. 1987, p. 131) received in Providence SIX MONTHS prior to September 14, 1987-June 25, 1988. Pro­ gram on Applied Combinatorics, Institute in Exploration INFORMATION: For further details, see for Mathematics and its Applications, 3-6. Model Optimization Republic of the Meetings section of this issue of University of Minnesota, Minneapolis, Geophysics, Berlin, Federal p. 1138) Notices. Minnesota. (April1987, p. 548) Germany. (November 1987, 7-11. 1988 Australian Applied Mathe­ January-July 1988. Symposium on Rep­ 15-19. The Nineteenth Southeastern matics Conference, Leura, Australia. (Feb­ resentation Theory and Group Theory, International Conference on Combina­ .ruary 1987, p. 363) Manchester, England. (April1987, p. 548) torics, Graph Theory and Computing, of April 17, 1988-December 24, 1988. 8-12. Workshop on Representations Louisiana State University, Baton Rouge, to Au­ Mathematiscbes Forschungsinstitut Ober­ p-adic Groups and Applications Louisiana. (October 1987, p. 997) tomorphic Forms, Mathematical Sciences wolfach (Weekly Conferences), Federal * 15-19. William H. Roever Lectures in Research Institute, Berkeley, California. Republic of Germany. (October 1987, Geometry, Washington University, Saint (August 1987, p. 813) p. 995) Louis, Missouri. 11-15. 154th National Meeting of the American Association for the Advance­ PROGRAM: J. W. Morgan, Colum­ February 1988 ment of Science (AAAS), Boston, Mas­ bia University, will give five lectures sachusetts. (January 1988, p. 156) on the Yang-Mills Equations and the 1-5. Fourth International Conference on Topology of 4-Manifolds. Data Engineering, Los Angeles Airport 13-14. Symposium on American Mathe­ matics Entering its Second Century, Bos­ INFORMATION: G. R. Jensen, Wash­ Hilton, Los Angeles, California. (January ington University, Campus Box 1146, 1988, p. 156) ton, Massachusetts.

FEBRUARY 1988, VOLUME 35, NUMBER 2 307 Meetings and Conferences

Saint Louis, Missouri 63130, 314-889- 18-19. 840th Meeting of the AMS, 11-13. 1988 Computer Networking Sym­ 6750. East Lansing, Michigan. (January 1988, posium, Sheraton National Hotel, Arling­ p. 156) ton, Virginia. (October 1987, p. 998) March 1988 INFORMATION: For further details, see 11-15. Institute of Electrical and Elec­ tronics Engineers Computer Society's lOth 4-5. Illinois Number Theory Conference, the Meetings section of this issue of Notices. International Conference on Software En­ University of Illinois, Urbana-Champaign, gineering, Raffles City, Republic of Sin­ Illinois. (January 1988, p. 156) 20-24. International Conference on Al­ gapore. (October 1987, p. 998) 7-10. Second International Conference gebraic Topology, Northwestern Univer­ 14-16. John H. Barrett Memorial Lec­ on Computer Workstations, Santa Clara, sity, Evanston, Illinois. (November 1987, ture, University of Tennessee, Knoxville, California. (October 1987, p. 997) p. 1138) Tennessee. (January 1988, p. 157) 7-11. Period of Concentration on q-Series 21-25. International Conference on The­ 15-16. Fifth Annual Auburn Miniconfer­ and Partitions, Institute for Mathematics ory and Applications of Differential Equa­ ence on Real Analysis, Auburn Univer­ and its Applications, University of Min­ tions, Ohio University, Athens, Ohio. sity, Auburn, Alabama. (January 1988, nesota, Minneapolis, Minnesota. (August (August 1987, p. 814) p. 157) 1987, p. 814) 21-25. Workshop on Invariant Theory 17-27. The First Canadian Number The­ 8-11. 1988 International Zurich Semi­ and Tableaux, Institute for Mathematics ory Association Meeting, Banff, Alberta, nar on Digital Communications, Zurich, and its Applications, University of Min­ Canada. (Note date and title changes Switzerland. (October 1987, p. 997) nesota, Minneapolis, Minnesota. (August February 1987, p. 364) * 9-15. International Conference on Alge­ 1987, p. 814) 21-23. Symposium on the Interface of braic Geometry, Berlin, German Demo­ 25-26. 841st Meeting of the AMS, Computing Science and Statistics, Reston, cratic Republic. (January 1988, p. 156) Knoxville, Tennessee. (January 1988, Virginia. (January 1988, p. 157) * 11-12. Piedmont Mathematics Confer­ p. 157) INFORMATION: H. Daly, American ence: Smooth Dynamical Systems Pro­ INFORMATION: For further details, see gram, Where. Mathematical Society, Post Office Box the Meetings section of this issue of 6248, Providence, Rhode Island 02940. PROGRAM: A number of 50-minute Notices. lectures, both invited and contributed, 23-24. 843rd Meeting of the AMS, 28-31. Nineteenth Iranian Mathematical with ample time for individual inter­ College Park, Maryland. (January 1988, Conference, Rasht, Iran. (August 1987, action. Invited participants include C. p. 157) p. 814) Chicone, S. Newhouse, Z. Nitecki, S. INFORMATION: For further details, see 28-April I. Conference on Harmonic Schecter. the Meetings section of this issue of Analysis, Mathematical Sciences Research INFORMATION: D. S. Shafer, Math­ Notices. ematics Department, University of Institute, Berkeley, California. (January North Carolina, Charlotte, North Car­ 1988, p. 157) 24-28. International Council on Math­ olina 28223. 28-April 3. Complex Analysis Days in ematics in Developing Countries' Sympo­ Guadeloupe, Pointe a Pitre, Guadeloupe. sium on Mathematics of Computation, Ho * 11-12. 1988 SEAS-SIAM Meeting, Uni­ (October 1987, p. 998) Chi Minh City, Vietnam. (October 1987, versity of Tennessee Space Institute, Tul­ p. 998) lahoma, Tennessee. Apri11988 * 24-May 3. Twenty-sixth International SPEAKERS: J. Ford, Georgia Tech and Symposium on Functional Equations, Sant A. Stanley, Los Alamos. 7-9. 1988 Spring Topology Confer­ Feliu de Guixols, Spain. INFORMATION: ence, University of Florida, Gainesville, S. Shankle, 615-455- INFORMATION: C. Alsina, Department 0631, ext. 276 or T. Florida. (November 1987, p. 1138) H. Moulden, ext. of Mathematics, Universitat Politec­ 279. 7-9. The Schwarz Function and its Gen­ nica Catalunya, Avgda Diagonal, 649. eralization to Higher Dimensions, Univer­ 13-18. Second International Conference E08028 Barcelona, Spain. Those wish­ sity of Arkansas, Fayetteville, Arkansas. ing to be invited should describe their on Hyperbolic Problems, Aachen, Federal (January 1988, p. 157) Republic of Germany. (February 1987, interest and work in functional equa­ p. 363) 8-9. Conference on Applied Mathemat­ tions. ics, Central State University, Edmond, 14-18. Fourth International Conference Oklahoma. (January 1988, p. 157) 25-30. Table Ronde Analyse et Agrega­ on Artificial Intelligence Applications, tion des Preferences et Modelisation des Sheraton Harbour Island, San Diego, Cal­ 8-9. 842nd Meeting of the AMS, Las Cruces, New Mexico. Choix, Marseille, France. (January 1988, ifornia. (October 1987, p. 997) p. 157) 16-18. Twenty-first Annual Simulation INFORMATION: J. Balletto, American * 27-May 5. NATO Advanced Studies Symposium, Tampa, Florida. (August Mathematical Society, Post Office Box Institute on Number Theory and Ap­ 1987, p. 814) 6248, Providence, Rhode Island 02940. plications, Banff Centre, Banff, Alberta, Canada.

308 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

INFORMATION: Interested number the­ 1000 Centennial Drive, Berkeley, Cal­ 29-31. Eighteenth International Sympo­ orists may write for detailed informa­ ifornia 94 720. sium on Multiple-Valued Logic, Madrid, tion to R. A. Mallin, Mathematics Spain. (October 1987, p. 998) * 23-25. Noncommutative Ring Theory, Department, University of Calgary, 29-June 4. Symposium on the Legacy of Northern Illinois University, DeKalb, Calgary, Alberta, Canada T2N 1N4. John von Neumann, Hofstra University, Illinois. Hempstead, New York. (January 1988, * 28-29. Idaho State University Spring INFORMATION: W. D. Blair, Depart­ p. 158) on Applied and Computational conference ment of Mathematical Sciences, INFORMATION: J. Balletto, American Linear Algebra, Pocatello, Idaho. Northern Illinois University, DeKalb, Mathematical Society, Post Office Box INVITED SPEAKERS: C. R. Johnson, Illinois 60115, 815-753-6772. 6248, Providence, Rhode Island 02940. College of William and Mary, and 23-26. Economie Mathematique, Mar­ S. F. McCormick, University of Col­ 30-June 3. Canadian Applied Math­ seille, France. (January 1988, p. 158) orado. ematics· Society Conference on Contin­ INFORMATION: L. Ford, Department 23-26. Third SIAM Conference on Ap­ uum Mechanics and its Applications, Si­ of Mathematics, Idaho State Univer­ plied Linear Algebra, Concourse Hotel, mon Fraser University, British Colum­ sity, Pocatello, Idaho 83209, 208-236- Madison, Wisconsin. (November 1987, bia, Canada. (Note changes from October 3465 or 3350. p. 1139) 1987, p. 998) 23-27. Conference on Mathematical 30-June 3. International Conference on Methods and Applications, Chiangmai, May 1988 Numerical Mathematics, Kent Ridge, Re­ Thailand. (June 1987, p. 685) public of Singapore. (April1987, p. 553) 4. Symposium on Some Mathematical * 26-27. Tenth Symposium on Mathe­ 30-June 3. Sixth International Con­ Questions in Biology: The Dynamics of matical Programming with Data Pertur­ ference on the Theory and Applications Excitable Media, Las Vegas, Nevada. bations, George Washington University, of Graphs, Western Michigan Univer­ (January 1988, p. 157) Washington, District of Columbia. sity, Kalamazoo, Michigan. (June 1987, INFORMATION: B. Verducci, Ameri­ PROGRAM: This symposium is de­ p. 685) can Mathematical Society, Post Office signed to bring together practitioners 30-June 3. Theorie des Nombres, Mar­ Box 6248, Providence, Rhode Island who use mathematical programming seille, France. (January 1988, p. 158) 02940. optimization models and deal with 30-June 4. Conference on Hyperplane questions of sensitivity analysis, with 5-6. Nineteenth Annual Pittsburgh Con­ Sections and Related Topics, L' Aquila, researchers who are developing tech­ ference on Modeling and Simulation, Uni­ Italy. (January 1988, p. 158) niques applicable to these problems. versity of Pittsburgh, Pittsburgh, Penn­ * 31-June 3. Conference on Reaction- CALL FOR PAPERS: Abstracts of pa­ sylvania. (October 1987, p. 998) Diffusion Equations, Heriot-Watt Univer­ pers intended for presentations at the sity, Edinburgh, United Kingdom. 9-13. Algorithmique et Programmation, Symposium should be sent in tripli­ Marseille, France. (January 1988, p. 157) cate to A. V. Fiacco at the address PROGRAM: This conference forms part 16-20. Ninth Australian Statistical Con­ listed below. Abstracts should provide of a special program in reaction­ ference, Canberra, Australia. (August a good technical summary of key re­ diffusion equations at Heriot-Watt 1987, p. 814) sults, avoid the use of mathematical University in 1987-1988. 16-20. 1988 Mathematical Sciences Con­ symbols and references, not exceed INFORMATION: K. J. Brown, Heriot­ gress and 32nd Annual General Meeting 500 words, and include a title and the Watt University, Department of Math­ of the Australian Mathematical Society, name and full mailing address of each ematics, Riccarton, Edinburgh EH 14 Canberra, Australia. (June 1987, p. 685) author. The deadline for submission 4AS, United Kingdom. 16-20. Workshop on Harmonic Maps of abstracts is March 11, 1988. INFORMATION: A. V. Fiacco, School and Minimal Surfaces, Mathematical Sci­ June 1988 ences Research Institute, Berkeley, Cali- · of Engineering and Applied Science, fomia. (January 1988, p. 158) · The George Washington University, * 1-4. Algebraic Logic and Universal Al­ 16-2 I. Theorie des Representations des Washington, District of Columbia gebra in Computer Science, Iowa State Groupes Finis, Marseille, France. (Jan­ 20052, 202-994-751 I. University, Ames, Iowa. uary 1988, p. 158) * 26-28. Third Lehigh University Geome­ CONFERENCE THEMES: Algebraic Spec­ * 23-25. Workshop on Differential Geom­ try and Topology Conference, Bethlehem, ification of Data Type, Relational etry, Calculus of Variations, and Com­ Pennsylvania. Database Theory, Logic of Programs, puter Graphics, Mathematical Sciences Specification of Programming Lan­ Research Institute, Berkeley, California. INFORMATION: D. Davis or D. John­ guages. son, Department of Mathematics, SPEAKERS: J. Berman, D. Kazen, V. ORGANIZERS: P. Concus, R. Finn, D. Lehigh University, Bethlehem, Penn­ Pratt, B. Jonson, E. Nemeti. A. Smith. Hoffman, sylvania 18015, 215-758-3730. INFORMATION: C. Bergman, Depart­ INFORMATION: I. Kaplansky, Math­ ment of Mathematics, Iowa State Uni­ Research Institute, ematical Sciences versity, Ames, Iowa 50011.

FEBRUARY 1988, VOLUME 35, NUMBER 2 309 Meetings and Conferences

4-August 11. Joint Summer Research site de Montreal, Montreal, Canada. (Jan­ CALL FOR pAPERS: The deadline for Conferences in the Mathematical Sci­ uary 1988, p. 158) abstracts of contributed papers is May ences, Bowdoin College, Brunswick, 11-14. International Conference on Al­ 1, 1988. Maine. (January 1988, p. 158) most Everywhere Convergence in Prob­ INFORMATION: T. Lyche, Institutt for Informatikk, Post Office Box 1080 Kohanski, Ameri­ ability and Ergodic Theory, Columbus, INFORMATION: C. Blindern, 0316 Oslo 3, Norway; o; Office Ohio. (October 1987, p. 998) can Mathematical Society, Post L.L. Schumaker, Center for Approxi­ Rhode Island 12-18. Workshop on Coding Theory and Box 6248, Providence, mation Theory, Texas A&M Univer­ Applications, Institute for Mathematics 02940. sity, College Station, Texas 77843- and its Applications, University of Min­ 5-8. Statistical Society of Canada's nesota, Minneapolis, Minnesota. (August 3368. Meeting, University of Victo­ Annual 1987, p. 814) 16-23. Annual Seminar Canadian Math­ Columbia, Canada. ria, Victoria, British 13-1 7. Nonlinear Hyperbolic Problems ematical Society-Banach Spaces and Ge­ p. 1139) (November 1987, Conference, Talence, France. (October ometry of Convex Bodies, Banff, Alberta, 5-9. Institute of Electrical and Electron­ 1987, p. 999) Canada. (January 1988, p. 159) Society's Con­ ics Engineers Computer * 13-1 7. Program Design and Data Ab­ 19-24. 1988 IEEE International Sympo­ Vision and Pattern ference on Computer straction, Salisbury State College, Salis­ sium on Information Theory, Kobe, Japan. University of Michigan, Ann Recognition, bury, Maryland. (October 1987, p. 999) Arbor, Michigan. (October 1987, p. 998) 19-25. Workshop on Design Theory and Symposium on PRINCIPAL SPEAKER: W. J. Collins, 5-12. Third International Applications, Institute for Mathematics Peftiscola, Spain. Radford University, Virginia. Differential Geometry, and its Applications, University of Min­ (October 1987, p. 998) PURPOSE: This meeting is designed to give college teachers an opportunity nesota, Minneapolis, Minnesota. (August * 6-8. Fourth Annual ACM Symposium to deepen their knowledge of the con­ 1987, p. 814) on Computational Geometry, University cepts and techniques required to teach 20-24. Fifth International Conference on of Illinois, Urbana-Champaign, Illinois. an introductory programming course. Boundary and Interior Layers: Computa­ INFORMATION: B. Chazelle, Depart­ INFORMA noN: B. A. Fusaro, Depart­ tional and Asymptotic Methods, Shang­ ment of Computer Science, Prince­ ment of Mathematical Sciences, Sal­ hai, China. (June 1987, p. 685) ton University, Princeton, New Jersey isbury State College, Salisbury, Mary­ 20-24. International Algebra Conference, 08544. land 21801, 301-543-6471 or 914- Lisbon, Portugal. (February 1987, p. 364) 938-5285. on Matrix Spectral 6-10. The Second International Confer­ * 20-24. Conference The Johns Hopkins Univer­ ence on Vector and Parallel Computing * 13-1 7. Gordon Conference on Theoret­ Inequalities, Issues in Applied Research and Develop­ ical Biology and Biomathematics, Tilton sity, Baltimore, Maryland. ment, Troms0, Norway. (January 1988, Academy, Tilton, New Hampshire. INVITED SPEAKER: R. C. Thompson. p. 158) The principal lecturer, R. INFORMATION: H. G. Othmer, De­ PRoGRAM: C. Thompson, will give ten lectures * 6-1 0. Fractals and the Microcomputer partment of Mathematics, University inequalities for eigenvalues, sin­ Salisbury State College, Salisbury, Mary~ of Utah, Salt Lake City, Utah 84112, on values, and invariant factors land. 801-581-3901 or M. C. Mackey, De­ gular with applications to control theory SPEAKER: W. D. Withers, partment of Physiology, McGill Uni­ PRINCIPAL and functional analysis. Maryland. versity, 3655 Drummond Street, Mon­ U.S. Naval Academy, INFORMATION: R. Horn, Department This meeting is designed to treal, Quebec, Canada H3G 1Y6. PuRPOSE: of Mathematical Sciences, The Johns an operational Telephone: 514-398-4336. give college teachers Hopkins University, Baltimore, Mary­ grasp of chaos theory and fractals. 15-1 7. Ninth National Educational Com­ land 21218. Apply now, but no later INFORMATION: B. A. Fusaro, Depart­ puting Conference (NECC '88), Anatole than April 8, 1988, to ensure con­ ment of Mathematical Sciences Sal­ Hotel, Dallas, Texas. (October 1987, sideration for on-campus housing and isbury State College, Salisbury, Mary­ p. 999) financial support. land 21801, 301-543-6471 or 914- Pacific Coast Re­ 938-5285. 15-1 7. The Seventh 20-25. Geoffrey J. Butler Memorial Con­ Modeling Conference, Ensenada, source ference on Differential Equations and Pop­ Twelfth International Conference 1988, p. 159) * 6-16. Mexico. (January ulation Biology, University of Alberta, on Operator Theory, Romania. * 16-22. Mathematical Methods in Edmonton, Alberta, Canada. (January INFORMATION: 12 Operator Theory Computer-Aided Design, Oslo, Norway. 1988, p. 159) Conference, INCREST, Department PROGRAM: The meeting will focus on 25-30. International Conference on Bio­ of Mathematics, Bd. Pacii 220, 79622 curve and surface methods. There will mathematics, Xian, China. (October 1987, Bucharest, Romania. be sessions for contributed twenty-five p. 999) minute papers. International Col· 6-24. SMS-NATO ASI: Methods in * 27-July 2. Seventeenth Theoretical Methods in Field and Superstring Theories, Univer- loquium on Group Physics, Ste-Adele, Quebec, Canada.

310 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

ORGANIZERS: Y. Saint-Aubin and L. 20-31. Ninth Latin American School of Georgia World Congress Center, Atlanta, Vinet, Universite de Montreal. Mathematics, Santiago, Chile. (Novem­ Georgia. (October 1987, p. 999) CALL FOR PAPERS: The deadline for ber 1987, p. 1140) * 1-7. International Symposium on Num­ abstracts of contributed posters is 23-August 3. Sixth International Con­ ber Theory and Analysis, Tsing Hua March 1, 1988. gress on Mathematical Education, Bu­ University, Beijing, People's Republic of INFORMA noN: M. Bergevin, XVII dapest, Hungary. (February 1987, p. 364) China. ICGTMP, Departement de Physique, 24-30. International Conference on Rad­ Universite de Montreal, C.P. 6128, ORGANIZERS: Y. Wang, Q. K. Lu, S. icals - Theory and Applications, Sapporo, Kung. succ. A, Montreal, Quebec, Canada Japan. (October 1987, p. 999) H3C 3J7. Telephone: 514-343-6670. INFORMATION: W. Yin, Department 25-28. First International Conference on of Mathematics, University of Science 27-July 15. Microprogram on the Struc­ Optimal Design and Analysis of Experi­ and Technology of China, Hefei, An­ ture of Banach Spaces, Mathematical Sci­ ments, Neuchatel, Switzerland. hui, People's Republic of China and ences Research Institute, Berkeley, Cali­ PROGRAM: This conference-workshop Guangshan Xu, Institute of Math­ fornia. (June 1987, p. 685) is designed to bring together the scien­ ematics, Academia Sinica, Beijing, tists from the four corners of the globe People's Republic of China. July 1988 actually working on Optimal Designs 4-11. Algebraic Logic Conference, Bu­ and Analysis of Experiments to dis­ dapest, Hungary. (October 1987, p. 999) 3-23. Summer Research Institute on cuss the most updated progress in the 5-8. Second Boston Workshop for Math­ Operator Theory /Operator Algebras and field, to develop new ideas and new ematics Faculty, Wellesley College, Applications, University of New Hamp­ fields of applications, and to show the Wellesley, Massachusetts. (January 1988, shire, Durham, New Hampshire. (Jan­ importance of optimally choosing a p. 159) uary 1988, p. 159) design of experiment in different area 6-7. AMS Short Course on Chaos and INFORMATION: J. Balletto, American of experimental sciences. ORGANIZERs: Y. Dodge, V. Fedorow, Fractals: The Mathematics Behind the Mathematical Society, Post Office Box Computer Graphics, Providence, Rhode 6248, Providence, Rhode Island 02940. H. P. Wynn. CALL FOR PAPERS: Those wishing Island. 4-8. Infinite Dimensional Lie Algebras to present papers at the conference INFORMATION: M. Foulkes, Ameri­ and Groups, Marseille, France. (Novem­ should submit an abstract in English can Mathematical Society, Post Office ber 1987, p. 1139) (limited to one typed page) no later Box 6248, Providence, Rhode Island 5-8. Tenth Dundee Conference on the than February 15, 1988 to Y. Dodge 02940. Theory of Ordinary and Partial Differen­ at the address given below. Notifica­ tial Equations, Dundee, Scotland. (Octo­ tion of acceptance of abstracts will be 8-12. AMS Centennial Celebration, Prov­ ber 1987, p. 999) given by March 15, 1988. Contributed idence, Rhode Island. (April1987, p. 553) 10-16. Representation Theory and Group papers may be orally presented on any INFORMATION: For further details, see Theory, Manchester, England. (February topic related to the conference theme. the Meetings section of this issue of 1987, p. 364) INFORMATION: For further informa­ Notices. tion, registration materials and pro­ 13-20. Edinburgh Mathematical Soci­ gram details, please contact Y. Dodge, * 8-13. Spaces of Self-Homotopy Equiv­ ety's 1988 Saint Andrews Colloquium, St. Universite de Neuchatel, Groupe d'ln­ alences, Centre de recherches mathema­ Andrews, Fife, Scotland. (February 1987, formatique et de Statistique, Pierre-a­ tiques, Universite de Montreal, Montreal, p. 364) Mazel7, CH-2000Neuchatel, Switzer­ Quebec. 17-27. Ninth Congress of the Interna­ land. Telephone: (038) 25 72 05. tional Association of Mathematical Phys­ ORGANIZERs: P. Booth and R. Pic­ ics, Swansea, Wales. (February 1987, 25-30. Third International Congress on cinini. p. 364) Computational and Applied Mathematics, INFORMATION: F. H. Clarke, Director, 18-22. Twelfth IMACS World Congress University of Leuven, Belgium. (August Centre de recherches mathematiques, on Scientific Computation, Paris, France. 1987, p. 814) Universite de Montreal, C.P. 6128-A, (February 1987, p. 364) 31-August 6. Nonstandard Analysis, Montreal, Quebec H3C 317 Canada. 18-29. AMS-SIAM Summer Seminar University of Massachusetts, Amherst, * 8-14. Conference on Algebraic Logic, on Computational Solution of Nonlinear Massachusetts, and Smith College, North­ Budapest. Systems Equations, Colorado State Uni­ ampton, Massachusetts. (January 1988, versity, Fort Collins, Colorado. (January p. 159) ORGANIZER: The Janos Bolyai Math­ 1988, p. 159) ematical Society. PROGRAM: The conference will focus INFORMATION: B. Verducci, Ameri­ August 1988 on algebraic logic with an emphasis on can Mathematical Society, Post Office 1-5. Fifteenth Annual Conference and its connections with universal algebra, Box 6248, Providence, Rhode Island Exhibition on Computer Graphics and model theory, classical logic, nonclas­ 02940. Interactive Techniques (SIGGRAPH '88), sical logics, and abstract model theory. Connections with logics and seman-

FEBRUARY 1988, VOLUME 35, NUMBER 2 311 Meetings and Conferences

tics in computer science, categories, INFORMATION: C. McCrory, Depart­ ment of Mathematics, University of and semigroups will also be consid­ September 1988 ered. Georgia, Athens, Georgia 30602. INFORMATION: Write to Janos Bolyai * 6-10. International Neural Network So­ Mathematical Society, Budapest, 20-26. Groups, Pusan, Republic of Ko­ ciety 1988 Annual Meeting, Boston, Mas­ Anker koz 1-3. 1.111., H-1061, Hun­ rea. (June 1987, p. 686) sachusetts. gary. Telephone: 427-741. * 21-25. Crypto 88 Conference, Santa Bar- bara, California. INFORMATION: For further details, see 9-12. International Symposium in Real the News and Announcements section Analysis, University of Ulster, Coleraine, INFORMATION: For further details, see of this issue of Notices. Northern Ireland. (February 1987,p. 364) the News and Announcements section of this issue of Notices. 13-16. Workshop on Arboreal Group 9-13. First International Symposium on Theory, Mathematical Sciences Research Algebraic Structures and Number Theory, 21-27. Seventeenth International Con­ Institute, Berkeley, California. (January Hong Kong. (November 1987, p. 1140) gress of Theoretical and Applied Mechan­ 1988, p. 160) * 12-14. International Conference on Math­ ics, Grenoble, France. (January 1987, * 13-23. Heyting Summer School and Con­ ematical Modelling in Sciences and Tech­ p. 135) ference on Mathematical Logic, Chaika nology, Madras, India. (Note date change, 21-27. International Conference on Gen­ near Varna, Bulgaria. October 1987, p. 999) eral Algebra, Krems/Donau, Austria. (November 1987, p. 1140) TOPics: Recursion theory, modal and INFORMATION: P. Achuthan, Indian nonclassical logics, intuitionism and Institute of Technology, Madras-600 22-25. 1988 Joint Statistical Meetings, constructivism, related applications to 036, India. New Orleans, Louisiana. (June 1987, computer science, life and work of p. 686) Arend Heyting (1898-1980). 14-18. Institute of Mathematical Statis­ 22-26. Conference on Categorical Topol­ CALL FOR PAPERS: Submit five copies tics Annual Meeting, Fort Collins, Col­ ogy and its Relations to Algebra, Analysis orado. (October 1987, p. 999) of a draft full paper, in English, of and Combinatorics, Prague, Czechoslo­ no more than 15 double-spaced pages, 14-27. Harmonic Analysis on Reduc­ vakia. (October 1987, p. 1000) accompanied by a camera-ready one­ tive Groups, Bowdoin College, Bruns­ 22-26. International Conference on Op­ page abstract, to reach the address wick, Maine. (This conference has been erator Theory: Advances and Applications, given below by March 15, 1988. postponed. For further details, see the University of Calgary, Alberta, Canada. INFORMATION: Write to Heyting 1988, announcement for July 30-August 12, (November 1987, p. 1140) Sector of Logic, Mathematics Faculty, 1989, in this section of Mathematical 22-26. 20th Nordic Congress of Mathe­ Sofia University, boul. Anton Ivanov Sciences Meetings and Conferences) maticians, Trondheim, Norway. (Novem­ 5, Sofia 1126, Bulgaria. 15-19. New Directions in Dynamical ber 1987, p. 1140) Systems, Brown University, Providence, * 19-23. Sixth International Colloquium 23-30. 1988 Association for Symbolic Rhode Island. (October 1987, p. 999) on Differential Geometry, Universidad Logic European Summer Meeting, Padova, de Santiago de Compostela, Santiago de * 15-19. International Symposium on Ap­ Italy. (January 1988, p. 160) proximation, Optimization and Comput­ Compostela, Spain. 29-September 2. ICO Topical Meeting ing, University of Regina, Saskatchewan, on Optical Computing, Orsay, France. SPEAKERs: J. Eells, A. Gray, G. Hec­ Canada. (October 1987, p. 1000) tor, A. Lichnerowicz, F.J. Turiel, D. Sullivan L. Vanhecke. INFORMATION: Conference and ac­ 29-September 2. Orbit Method in Repre­ CALL FOR PAPERS: Participants wish­ commodation information, and guide­ sentation Theory, Copenhagen, Denmark. ing to present papers are asked to sub­ lines for submitting papers, may be (October 1987, p. 1000) mit an extended summary of about obtained from: A. G. Law or C.-L. * 29-September 2. Workshop on Sym­ Wang, University of Regina, Saskatch­ 500 words with completed registra­ plectic Topology, Mathematical Sciences tion cards by May 1, 1988. For more ewan, Canada S4S OA2. Telephone: Research Institute, Berkeley, California. 306-584-4148. information, write to the address be­ PROGRAM: This workshop forms part low. 16-19. Institute of Mathematical Statis­ of the Institute's yearlong 1988-1989 INFORMATION: Departamento de Ge­ tics Symposium on Probability and its program on symplectic geometry and ometria y Topologia, Facultad de Applications, Colorado State University, mechanics. Matematicas, Universidad de Santi­ Fort Collins, Colorado. (October 198 7, INFORMATION: I. Kaplansky, Math­ ago de Compostela, 15705 Santiago p. 999) ematical Sciences Research Institute, de Compostela, Spain. * 19-24. Georgia Topology Conference, 1000 Centennial Drive, Berkeley, Cal­ * 25-30. International Symposium in Honor University of Georgia, Athens, Georgia. ifornia 94 720. of Rene Thorn, Paris, France. PROGRAM: Intersection homology and INFORMATION: M. Chaperon, A. its applications. Chenciner, U D.T., or R. Moussu, Colloque Rene Thorn, IHES, 35, route

312 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

de Chartres, 91440 Bures-sur-Yvette, ORGANIZERS: G. Baumslag, F. Can­ C. Miller. France. nonito, December 1988 INFORMATION: I. Kaplansky, Math­ 26-0ctober 1. Fifth International Confer­ 6-8. First International Conference on ematical Sciences Research Institute, ence on Complex Analysis, Halle, German Matter Elements Analysis, Guangzhou, 1000 Centennial Drive, Berkeley, Cal­ Democratic Republic. (October 1987, Guangdong, People's Republic of China. ifornia 94720. p. !000) (October 1987, p. 1000) July 1989 October 1988 January 1989 5-19. Microprogram on Noncommutative 28-30. Fall Sectional Meeting, Lawrence, 8-11. First Caribbean Conference on Rings, Mathematical Sciences Research Kansas. Fluid Dynamics, Saint Augustine, Trini­ Institute, Berkeley, California. (June !987, p. 686) INFORMATION: J. Balletto, American dad, West Indies. (June 1987, p. 686) on Re­ Mathematical Society, Post Office Box 11-14. Joint Mathematics Meetings, 30-August 12. Harmonic Analysis Bruns­ 6248, Providence, Rhode Island 02940. Phoenix, Arizona. (April 1987, p. 553) ductive Groups, Bowdoin College, wick, Maine. (January 1988, p. 160) INFORMATION: H. Daly, American November 1988 Mathematical Society, Meetings De­ partment, Post Office Box 6248, Prov­ September 1989 * 13-17. French-Israeli Conference on idence, Rhode Island 02940. on Combinatorics and Algorithms, Israel. * 25-29. Third International Conference * 23-27. Workshop on Algorithms, Word the Theory of Groups and Related Topics, FOR PAPERS: Abstracts of up to CALL Problems, and Classification in Combina­ Canberra, Australia. (June 1987, p. 686) words are due by July 1, 1988, 200 torial Group Theory, Mathematical Sci­ should be sent to A. S. Fraenkel and ences Research Institute, Berkeley, Cali­ at the address given below. January 1990 fornia. INFORMATION: C. Weintraub, Depart­ 17-20. Joint Mathematics Meetings, is the sec­ ment of Applied Mathematics and PROGRAM: This workshop Louisville, Kentucky. (April1987, p. 553) Computer Science, Weizmann Insti­ ond of three workshops that form part tute of Science, Rehovot, 7 6100, Israel of the Institute's yearlong 1988-1989 INFORMATION: H. Daly, American or J. Bond, LRI, Universite de Paris­ program on Combinatorial Group Mathematical Society, Meetings De­ Sud, bat. 490, 91405 Orsay, Cedex, Theory and Geometry. partment, Post Office Box 6248, Prov­ France. idence, Rhode Island 02940.

FEBRUARY 1988, VOLUME 35, NUMBER 2 313 New AMS Publications

given. In addition, the volume contains interpolation methods which extend the usefulness of the tables. MATHEMATICAL SCIENCES Contents PROFESSIONAL DIRECTORY Equicoordinate percentage points This directory, published annually, lists key personnel­ Earlier tables of the percentage points and of the probability officers and committee members (together with their current integral of the multivariate t and multivariate normal addresses and telephone numbers in many cases) of over distributions thirty professional mathematical organizations and a selected group of government agencies. Editors of over 100 journals Construction of the present tables are represented. The directory also contains academic Applications of the tables departments in the mathematical sciences and mathematical Examples illustrating applications of the tables units in nonacademic organizations. Terms of office and other pertinent information for some professional organizations are Tables also included. One-sided Percentage Point (g) for Equal Correlations (Case 1980 Mathematics Subject Classification: 00 I With Correlation p) ISBN 0-8218-0116-3 ISSN 0737-4356 Two-sided Percentage Point (h) for Equal Correlations (Case 196 pages (softcover), January 1988 I With Correlation p) Individual member $26, List price $26, Institutional member $21 One-sided Percentage Point (g1) for Block Correlations (Case To order, please specify ADMDIR/88N II With P1 = P2 = 0.5, P3 = 0.0) One-sided Non-equicoordinate Percentage Point (g2) for Block Correlations (Case II With P1 = P2 = 0.5, P3 = 0.0) FOUR SETS OF TABLES. 1980 Mathematics Subject Classifications: 62005, 62F07, 62F25, PERCENTAGE POINTS OF MULTIVARIATE 62H10, 62J15 STUDENT t DISTRIBUTIONS ISBN 0-8218-1911-9, LC 74-6283 ISSN 0094-8837 Robert E. Bechhofer and Charles W. Dunnett 384 pages (hardcover), January 1988 (Selected Tables in Mathematical Statistics, Volume 11) Individual member $28, List price $46, Institutional member $37 To order, please specify TABLES/11 N This volume presents tables dealing with the central multivariate student t distribution in which there is a common variance estimate in the denominators of the variates and the numerators are equicorrelated. The tables contain one-sided and two-sided upper equicoordinate percentage points for this distribution. In addition, the volume provides tables based on the assumption that the variates have a certain block correlation structure. The entries have been computed to an accuracy of 5 decimal places. ·

These tables, prepared under the aegis of the Institute for Mathematical Statistics, are considerably more comprehensive than previously published tables of this type. They have applications in many statistical settings, including selection among normal means using either the indifference-zone or the subset approach and in multiple comparisons involving contrasts among means. These and other applications are described in detail, and examples of the uses of the tables are

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314 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Queries

Edited by Hans Samelson and Stuart Antman

THIS IS THE LAST TIME the Queries column will be published on a formal basis. ply: L~ q(n)xn = TI~(l + xn) = see the News and Announcements section of this issue of Notices for further TI~(l-xn) mod 2 = I:~:(-1)k· information. xk(3k+I)f2 (Euler), so q(n) is even REPLIES from readers will, when appropriate, be edited into a composite answer except for the pentagonal num­ and published in a future issue of Notices. All answers received will be forwarded bers. In more detail: Put E(n), to the questioner. resp O(n), =#partitions into an RESPONSES should be typewritten if at all possible and sent to Queries Column, even, resp odd, number of unequal American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940. parts. Then E(n)- O(n) = (-1)k if n = k(3k + 1)/2, = 0 other­ Queries der). Does this imply that the se­ wise. See Hardy and Wright, In­ quence {A(n) ·B(n)}n=O.l.2 .... is PF? troduction to the Theory of Num­ 389. Francesco Brenti (Room 2- bers, Oxford, 1938, p. 284 ff. One 032, Department of Mathemat­ proof uses the argument above, ics, M. I. T., Cambridge, Mas­ Responses the other, due to F. Franklin, A(x) and sachusetts 02139). Let The editors would like to thank all CR Acad. Sci. Paris 92 ( 18 81), with real B(x) be two polynomials those who sent in replies. 448-450, is called by Hardy and coefficients. Suppose that the two Wright "a very beautiful elemen­ infinite sequences {A( n )}n=o.u.... 383. (vol. 34, p. 926, October 1987, tary proof, which uses no alge­ and {B ( n)} n=O.I.2 .... are PF ( = P6lya Moshe Lotan) Why is q(n) (= # braical machinery." (Contributed frequency sequences of infinite or- partitions of n into unequal parts) by G. E. Andrews, F. Garvan, J. so often even (empirically)? Re- T. Ward, J.-P. Serre, M. Lotan)

I HAVE A PHOTOGRAPHIC MEMORY REVIEWS IN NUMERICAL ANALYSIS Paul Halmos 1980-86

Paul R. Halmos, eminent mathematician and brilliant expositor, These five volumes bring together a wealth of bibliographic is also a snapshot addict. For the past 45 years, Halmos has information in the area of numerical analysis. Containing snapped mathematicians, their spouses, their brothers and over 17,600 reviews of articles, books, and conference sisters and other relatives, their offices, their dogs, and their proceedings, these volumes represent all the numerical carillon towers. From 6000 or so photographs in his collection, analysis entries that appeared in Mathematical Reviews Halmos has chosen about.600 for this book. The pictures are between 1980 and 1986. Classified according to the 1980 candid shots showing mathematicians just being themselves, Mathematics Subject Classification scheme, the reviews are and the accompanying captions, in addition to identifying the listed in each subsection according to their MR classification subjects, contain anecdotes and bits of history that reveal number. Accompanying each entry is a list of all subsequent Halmos' inimitable wit, charm, and insight. This delightful reviews that cite the entry as a reference. In addition, author collection of mathematical memorabilia is certain to become a and key indexes appear at the end of volume 5. book as well as a valuable historical record. favorite browsing 1980 Mathematics Subject Classifications: 65XX, 76XX, 41XX, 35XX 1980 Mathematics Subject Classifications: 00, 01 ISBN 0-8218-0102-3, LC 87-25478 ISBN 0-8218-0115-5 3750 pages, 5 volumes (softcover), January 1988 336 pages (hardcover), January 1988 Individual member $150, List price $250, Individual member $35, List price $58, Institutional member $200, Reviewer $125 Institutional member $46 To order, please specify REVNANf86NA To order, please specify PHOMEM/NA

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FEBRUARY 1988, VOLUME 35, NUMBER 2 315 AMS Reports and Communications

Recent Appointments Dorian Goldfeld (1989) has been Philip C. Curtis, Jr. (MAA, 1990) has appointed to the Committee on Re­ been reappointed and D. 0. Loftsgaarden (MAA, 1990) has been ap­ Committee members' terms of office on search Fellowships by President G. D. pointed by President Leonard Gillman standing committees expire on Decem­ Mostow. Continuing members of the ber 31 of the year given in parentheses committee are Frederick J. Almgren, Jr. (MAA) to the AMS-MAA Committee on following their names, unless otherwise (1989), Philip C. Kutzko ( 1988), chair­ Employment and Educational Policy. specified. man, George Lusztig (1988), John W. Continuing members of the committee Morgan (1989), M. Beth Ruskai ( 1988), are Morton Brown (MAA ,1989), Stefan George A. Hagedorn (1990) has been and Nancy K. Stanton (1988). Terms A. Burr (AMS, 1989), Edward A. Connors (AMS, 1988), chairman, David appointed to the Program Committee expire on June 30. J. Lutzer (MAA, 1989), and Audrey A. for National Meetings by President G. David Mumford ( 1989) has been Terras (AMS, 1988). D. Mostow. Continuing members of the appointed by President G. D. Mostow to committee are Peter B. Gilkey (1990), the Committee on National Awards and Presidents Leonard Gillman (MAA), LindaKeen(1988),HughL. Montgom­ Public Representation. Continuing Charles William Gear (SIAM), and G. D. ery (1989), Everett Pitcher (ex officio), members of the committee are William Mostow (AMS) have appointed Ronald Paul H. Rabinowitz (1988), chairman, Browder (ex officio), G. D. Mostow (ex M. Davis (MAA, 1990) and reappointed Donald C. Rung (AMS, 1990) to the AMS­ and Nolan R. Wallach (1988). officio), chairman, and Everett Pitcher Thomas G. Kurtz ( 1990) and Barbara (ex officio). MAA-SIAM Joint Committee on Employ­ L. Osofsky (1990) have been appointed President G. D. Mostow has ap­ ment Opportunities. Brian J. McCartin by President G. D. Mostow to the pointed Luis A. Caffarelli ( 1990) to the (SIAM, 1989) has been appointed chair­ Committee on Academic Freedom, Committee to Select the Winner of the man. Continuing members of the Tenure and Employment Security. Steele Prize. Continuing members of the committee are Calvin T. Long (MAA, Continuing members of the committee committee are Frederick J. Almgren, Jr. 1988), John W. Petro (AMS, 1988), and are Jerome A. Goldstein (1989), Robert (1989), Hermann Flaschka ( 1988), John Robert S. Stepleman (SIAM, 1988). R. Phelps (1989), Halsey L. Royden P. Hempel (1988), William S. Massey (1989), chairman, Frank A. Raymond (1988), chairman, and Gail S. Young Reports of Past Meetings (1989). ( 1989), Neil J. A. Sloane ( 1990), Louis Solomon (1989), Richard P. Stanley President G. D. Mostow has ap­ 1987 Symposium on Some (1989), and Michael E. Taylor (1990). pointed Michael I. Brin (1990) and Joel Mathematical Questions in Biology L. Lebowitz ( 1990) to the Committee on Terms expire on June 30. William B. Arveson (AMS, 1989) has Human Rights of Mathematicians. Models in Population Biology Continuing members of the committee been reappointed to the AMS-IMS-SIAM Committee on Joint Summer Research are Bettye Anne Case ( 1989), Patrick X. The twenty-first annual Symposium on Conferences in the Mathematical Sci­ Gallagher (1989), Herman R. Gluck Some Mathematical Questions in Biol­ ences by President G. D. Mostow. Con­ (1989), Leon A. Henkin (1988), and ogy was held on Wednesday, February tinuing members of the committee are Neil I. Koblitz (1988). 18, 1987, in the Acapulco Room of the John A. Burns (SIAM, 1988), Martin FrankL. Gilfeather (1990) has been Hyatt Regency. Golubitsky (SIAM, 1988), Daniel J. Kle­ appointed and C. Edmund Burgess The symposium was held in conjunc­ itman (AMS, 1989), James I. Lepowsky (1990) has been reappointed by Presi­ tion with the annual meeting of the (AMS, 1988), Ingram Olkin (IMS 1988), dent G. D. Mostow to the Committee on American Association for the Advance­ Mary Ellen Rudin (AMS, 1989), Lesley Professional Ethics. Continuing mem­ ment of Science (AAAS). The sympo­ Sibner (AMS, 1990), and Stephen G. bers of the committee are Paul R. Hal­ sium was sponsored by the American mos (1988), Linda Keen (1989), and Simpson (AMS, 1988). Terms expire on Mathematical Society, the Society for Anneli Lax (1988). June 30.

316 FEBRUARY 1988, VOLUME 35, NUMBER 2 AMS Reports and Communications

Industrial and Applied Mathematics, There were 15 invited addresses. A applied mathematics in which theta and Section A (Mathematics) of the total of 74 mathematicians registered functions play an important role. The AAAS. The AMS-SIAM Committee on for the seminar. According to the regis­ program consisted of thirty-four com­ Mathematics in the Life Sciences served tration cards of those who attended, 6 prehensive, seventy-five minute ex­ as the Organizing Committee for the stayed only during the first week, 8 only pository lectures and sixty-five research symposium. The committee consists of during the second week and 60 for up to reports. Gail A. Carpenter (Northeastern Uni­ the full period of the seminar. Lecture Notes. Twenty-four papers versity); Kenneth L. Lange (Massachu­ Six countries not in North America were reproduced and distributed to par­ setts Institute of Technology); Hans G. were represented by the following ticipants during the Institute, totaling Othmer (University of Utah); Alan S. numbers of participants: Austria (2), 744 pages of lecture notes. Perelson (Los Alamos National Labora­ France (I), Holland (1), Italy (4), Portu­ Participants. There were 175 regis­ tory); Richard E. Plant, chairman (Uni­ gal (1) and Federal Republic of Ger­ tered mathematicians, 27 of which were versity of California, Davis); and John many(!). students. Accompanying members in­ Rinzel (National Institutes of Health). As with previous summer seminars, cluded 19 spouses and 11 children. Of The theme of the symposium was the Society will publish formal proceed­ all registered, the length of attendance at Models in Population Biology. There ings in the series Lectures in Applied the Institute was: were two half-day sessions, each includ­ Mathematics. Less than one week 11 6.3% ing three one-hour lectures. Nineteen One week 60 34.3% people registered for the symposium. 1987 Summer Research Institute on Two weeks 41 23.4% Support was provided by a grant from Theta Functions Three weeks 63 36.0% the National Science Foundation. 175 100.0% The thirty-fifth Summer Research Insti­ Twenty-two countries in addition to tute of the American Mathematical the United States were represented by 1987 AMS-SIAM-IMA Summer Society was held at Bowdoin College, the following numbers of participants: Seminar Computational Aspects of Brunswick, Maine, from July 6-24, Argentina (1), Australia (2), Brazil (2), VLSI Design with an Emphasis on 1987. The Institute was supported by Bulgaria (1), Canada (4), China (2), Semiconductor Device Simulation Grant No. DMS-8611435 from the England (2), France (6), W. Germany National Science Foundation. (4), India (3), Iran (2), Israel (1), Italy The American Mathematical Society, The topic was selected by the 1985 (6), Jamaica (1), Japan (12), Mexico (1), the Society for Industrial and Applied Committee on Summer Institutes and the Netherlands (2), New Zealand (1), Mathematics, and the Institute for Special Symposia whose members at Norway (1), Spain (4), Taiwan (1) and Mathematics and Its Applications co­ the time were ALBERT BAERNSTEIN II, the USSR (4). sponsored the 1987 AMS-SIAM-IMA ERIC FRIEDLANDER, HUI-HSIUNG Huo NSF grant support was awarded to Summer Seminar at the University of (chairman), H. BLAINE LAWSON, JR., 133 mathematicians, which represents Minnesota, Minneapolis, from April 30 JuDITH D. SALLY, and JoHN WERMER. 76% of the total of registered partici­ to May 7, 1987. The seminar was sup­ Organizing Committee. The mem­ pants. To maximize the number of par­ ported by the Air Force Office of Scien­ bers of the organizing committee for the ticipants receiving travel and/or subsis­ tific Research and the National Science Institute were: ENRICO ARBARELLO, Uni­ tence reimbursement, partial support Foundation. versity of Rome; DAVID CHUDNOVSKY, was offered in most cases. The AMS-SIAM Committee on Columbia University; GREGORY CHu­ Conference Site. Bowdoin College Applied Mathematics selected the topic DNOVSKY, Columbia University; LEoN proved to be an adequate site for con­ for this conference. Members of the EHRENPREIS, Temple University (co­ ducting the Institute. The close proxim­ committee at the time were C. K. Chu, chairman); RoBERT C. GuNNING, Prince­ ity to the Portland Jetport and reason­ Constantine M. Dafermos, James M. ton University (co-chairman); able service to and from the major port Hyman, Alan G. Konheim, George C. TAKAHIRO KAWAI, Research Institute of of entry, Boston and Logan Interna­ Papanicolaou (chairman), and Robert F. Mathematical Sciences, Kyoto Univer­ tional Airport, allowed relatively easy Warming. sity; and HENRY McKEAN, New York access to the site. The climate was comfortable, The Organizing Committee for the University. albeit humid. The town of seminar included Randolph Bank Program. The Institute was devoted Brunswick provided limited social and (chairman), William Coughran, Eric to the presentation and extension of recreational opportunity and therefore Grosse, R. Kent Smith, and Mitchell research on the topic of theta functions limited distraction from the conference Luskin. and the variety of areas in both pure and itself.

FEBRUARY 1988, VOLUME 35, NUMBER 2 317 AMS Reports and Communications

Conclusion. The organizing Transformation groups in geometry, Robert McFadden, K.S.S. Namboori­ committee did an outstanding job in CAROLYN S. GoRDON and Quo-SHIN CHI, pad, Francis Pastijn, Dominique Perrin, arranging for a scientific program that Washington University. The speakers J.-E. Pin, Mohan S. Putcha, Lex E. was intense, significant and challenging were Chal Benson, B. E. Blank, Robert Renner, John Rhodes, Jacques Sakaro­ for the participants. The quality of lec­ A. Blumenthal, Quo-Shin Chi, Josef vitch, Boris M. Schein, Imre Simon, tures and research presented was exem­ Dormfeister, Robert J. Fisher, Jr, Joseph B. Stephen, Howard Straubing, plary. Samuel I. Goldberg, James J. Hebda, Denis Therien, and Pascal Weil. Gary R. Jensen, H. Turner Laquer, Diophantine problems, RoBERT E. The October Meeting in Lincoln Maung Min-oo, John Mitchell, Phil­ TUBBS, University of Colorado, Boul­ lippe Topndeur, Kichoon Yang and der. Speakers were RichardT. Bumby, The eight hundred and thirty-seventh Yunbo Zheng. W. Dale Brownawell, T. W. Cusick, meeting of the American Mathematical Cellular automata and nonlinear David Easton, James Fennell, Mike Society was held at the University of dynamics, ERICA JEN, Los Alamos Na­ Fried, Andrew M. W. Glass, Julia Nebraska in Lincoln, Nebraska, on Fri­ tional Laboratory. Speakers included Mueller, Cameron L. Stewart, Kenneth day, Saturday and Sunday October 30-- Karel Culik, Peter Gacs, Yu He, How­ B. Stolarsky, Robert E. Tubbs, Jeffery 31 and November 1, 1987. There were ard Gutowitz, Erica Jen, and Stephen J. D. Vaaler, Paul Vojta, and Jing Yu. 268 registrants including 224 members Willson. Commutative algebra and algebraic of the Society. Finite geometries and combinatorial geometry, ROGER A. WIEGAND and BRIAN Invited Addresses. By invitation of designs, SPYROS S. MAGLIVERAS, EARLS. HARBOURNE, University of Nebraska, the committee to Select Hour Speakers KRAMER, and DALE MEsNER, University Lincoln. The speakers included D. D. for Central Sectional Meetings there of Nebraska, Lincoln. The speakers Anderson, Susan Jane Colley, Bruce were four invited addresses as follows: were Bruce A. Anderson, M. D. Atkin­ Crauder, FrankR. DeMeyer, S. P. Dutta, CAROLYN S. GoRDON, University of son, Ronald D. Baker, Eiichi Bannai, E. Graham Evans, Carl Faith, Robert Pennsylvania and Washington Univer­ Lynn M. Batten, Frank E. Bennett, Fossum, A. V. Geramita, Charles C. sity, St. Louis, When you can't hear the Albrecht Beutelspacher, Julia M. N. Hanna, William J. Heinzer, Melvin shape of a manifold; DAVID GRIFFEATH, Brown, Aiden A. Bruen, A. R. Calder­ Hochster, Craig Huneke, Sheldon Katz, University of Wisconsin, Madison, bank, William Cherowitzo, Charles J. Pablo Lejarraga, Lawrence S. Levy, Random cellular automata: A survey; Colbourn, Huw Davies, Marialuisa de Rick Miranda, M. Pavaman Murthy, Ira DAVID W. MASSER, University of Michi­ Resmini, John F. Dillon, Jeffrey H. J. Papick, Igor Reider, Christel gan, Ann Arbor, Transcendence with­ Dinitz, Jean Doyen, David A. Drake, Rotthaus, Judith D. Sally, David J. out transcendental numbers; and DAN Alan Hartman, Katherine Heinrich, Saltman, Robert Speiser, Bernd Ulrich, VmcULEscu, University of California, J.W.P. Hirschfeld, Chat Yin Ho, Daniel Marie A. Vitulli, and David Wright. Berkeley, Hilbert space operators R. Hughes, Norman W. Johnson, Dieter Contributed Papers. There was one modulo normed ideals. Jungnickel, David Klamer, Donald L. session for contributed ten-minute pa­ Special Sessions. By invitation of Kreher, E. Mendelsohn, N. S. Mendel­ pers on Saturday afternoon that con­ the same committee, there were seven sohn, R. Padmanabhan, Antonio Pasini, sisted of 9 papers. special sessions of selected papers. The Stanley E. Payne, VeraS. Pless, D. K. Robert M. Fossum topics, organizers and speakers follow. Ray-Chaudhuri, Alexander Rosa, Paul Associate Secretary Operator algebras and operator J. Schellenberg, J. J. Seidel, Johannes Urbana, Illinois theory, FRANK L. GILFEATHER, Univer­ Siemons, Edward Spence, Douglas R. sity of Nebraska, Lincoln. Speakers Stinson, Luc Teirlinck, Joseph A. Thas, The November 1987 Meeting included William B. Arveson, Larry Vladimir D. Tonchev, Tran Van Trung, in Los Angeles Baggett, Hari Bercovici, John W. Scott A. Vanstone, Walter D. Wallis, and Michael A. Wertheimer. Bunce, Raul E. Curto, Domingo A. The eight hundred and thirty-fifth meet­ Semi-groups and connections with Herrero, Palle E. T. Jorgensen, Victor ing of the American Mathematical Soci­ automata and formal languages, JoHN Kaftal, PaulS. Muhly, C. Pearcy. costel ety was held at the University of Califor­ C. MEAKIN and STUART W. MARGOLIS, Peligrad, Justin Peters, Bernard Russo, nia, Los Angeles, Los Angeles Califor­ University of Nebraska, Lincoln. Norberto Salinas, Albert J.-L. Sheu, nia, in conjunction with the Southern Speakers were David Barrington, Jean Roger R. Smith, Harald Upmeier, Beli­ California Section of the Mathematical Berstel, Jean-Camille Birget, Karl sario A. Ventura, Bruce H. Wagner, Association of America on November Byleen, Arthur Gerhard, Simon M. Martin Walter, Gary Weiss, and Derek 14-15,1987. Therewere241 registrants Goberstein, Karsten Henckell, Peter R. Westwood. including 152 members of the Society. Jones, David Klamer, Michael Kunze,

318 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Invited Addresses. By invitation of Michael Nadel, Vladimir Oliker, R. C. Ulrich Oertel, James T. Rogers, Dale M. the Committee to Select Hour Speakers Penner, Mark Pinsky, Y. S. Poon, Mar­ Rohm, Martin Scharlemann, Michael for Far Western Sectional Meetings, tin Ross, Leslie Saper, Bruce Solomon, Starbird, Morwen B. Thistlethwaite, F. there were three invited addresses: Mark Stem, Johan Tysk, S. Walter Wei, C. Tinsley, Keith Wolcott and Raymond BJORN ENQUIST, University of Califor­ Howard Weiss, Brian White, Jon G. Y. Wong. nia, Los Angeles, Computation ofoscil­ Wolfson, Pit-Mann Wong, Youyu Xu, Contributed Papers. There were latory solutions to hyperbolic differen­ Kichoon Yang, Chi-Ming Yau and two sessions for contributed ten minute tial equations; HENRYK HECHT, Univer­ StephenS. T. Yau. papers on Saturday, November 14, that sity ofUtah,Harish-Chandra modules, Geometric methods in representa­ consisted of 10 and 11 papers, respec­ globalizations, and geometry ofthe flag tion theory, HENRYK HEcHT. Speakers tively. variety; and PAUL C. YANG, University included Dan Barbasch, Mladen Hugo Rossi of Southern California, Conformal de­ Bozicevic, Luis Casian, Jen-Tseh Associate Secretary formations of metrics. Additionally, Chang, Devra Garfinkle, Joseph F. Salt Lake City, Utah there were two joint invited addresses: Johnson, Lisa Mantini, Dragan Milicic, THEODORE E. HARRIS, University of Cali­ Tomasz Przebinda, Brad Shelton and fornia, Los Angeles, Stochastic flows of Joseph A. Wolf. Report from the Committee mappings; and LLoYD S. SHAPLEY, Uni­ Game theory, WILLIAM LucAs, Clare­ on Human Rights of versity of California, Los Angeles, mont Graduate School. Speakers were Mathematicians Utility categories and applications. Harrison H. C. Cheng, lrinel Dragan, Special Sessions. By invitation of Thomas S. Ferguson, William Geller, Update on the Situation the same committee, there were five Johannes G. C. Heijmans, Dov Mon­ in Chilean Universities special sessions. Organizers and speak­ derer, T. E. S. Raghavan, Eric Ras­ ers were: musen, and L. S. Shapley. In the January 1988 issue of Notices, Differential geometry, RoBERT Stochastic processes, SIDNEY PoRT, Herbert Clemens, Chair of the AMS GREENE, University of California, Los University of California, Los Angeles Committee for Human Rights, reported Angeles, S.-Y. CHENG, University of and Ruth Williams, University of Cali­ on the situation of mathematicians and California, Los Angeles, and H.-Y. fornia, San Diego. Speakers included other academics in Chile. To that report, CHOI, University of Utah. Speakers were Kenneth Alexander, P. J. Fitzsimmons, he recently added the following update: Robert Brooks, Shaoping Chang, Shiu­ Dick Holley, Thomas S. Mountford, After an outpouring of international Yuen Cheng, S. S. Chern, Kevin Cor­ Charles M. Newman, and Thomas S. concern, the recently appointed rector of lette, Dennis DeTurck, T. Duchamp, Salisbury. the University of Chile, responsible for Wei-Qui Gao, Peter B. Gilkey, C. Robin Geometric topology, JoHN WALSH, carrying out many of the firings, was Graham, Robert E. Greene, Detlef Gro­ University of California, Riverside. himself dismissed in October. The new mol, David Hoffman, Ralph Jenne, The speakers were Stephen Brick, rector, Juan de Dios Vial, is an academic Gary R. Jensen, Kang Tae Kim, Nicho­ Robert Edwards, Dennis J. Garrity, Jim with real support in the university com­ las J. Korevaar, Rob Kusner, Gary Hoste, W. Kazez, D. D. Long, Darryl munity. So there is now reason to be Lawlor, Guojun Liao, E. B. Lin, Alan McCullough, Andy Miller, K. C. Millet, hopeful.

FEBRUARY 1988, VOLUME 35, NUMBER 2 319 Miscellaneous

Personal Items Jerome Sacks, of the Univer­ November 23, 1987, at the age sity of Illinois at Urbana-Cham­ of 56. He was a member of the paign, has been named a Fellow Society for 27 years. Sir Michael Atiyah, FRS, has been of the American Statistical Asso­ Ruel V. Churchill, Professor appointed by the LMS Council as ciation. Emeritus at the University of Mich­ the 1989 Forder Lecturer. In this Rae Michael Shortt has been igan, died on October 31, 1987, at position, he will be visiting a num­ promoted to associate professor the age of 8 7. He was a member ber of universities in New Zealand of mathematics at Wesleyan Uni­ of the Society for 56 years. in early 1989. The LMS Forder versity, effective July 1988. Edward W. Suppiger, of Pen­ Lectureship, which is awarded bi­ Grace Wahba, Bascom Profes­ sacola, Florida, died on November ennially, was instituted in conjunc­ sor of the University of Wisconsin, 26, 1987, at the age of 80. He was tion with the New Zealand Mathe­ Madison, is visiting the Depart­ a member of the Society for 39 matical Society in 1985, as a result ment of Statistics at Yale Uni­ years. of a generous bequest made to the versity as the Clare Booth Luce London Mathematical Society in Professor of Statistics. 1983 by the late H.G. Forder. Leslie Piegl, AvH Research Fel­ Deaths low, will serve as CAD Mathe­ matics Consultant for Structural James R. Baugh, California State Dynamics Research Corporation. University, Long Beach, died on

I (CENTENNIAL CELEBRATION

The first book published by the Society was the Proceedings of the International Congress of 1893 at the Chicago World's Columbian Exposition

AMERICAN MATHEMATICAL SOCIETY • PROVIDENCE • AUGUST 8-12, 1988

320 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

ORDINARY MEMBERS Clara S Chan Ronald W Fechter International House of Chicago Flushing, New York Adrian Adascalitei Chicago, Illinois Iasi, Romania Frederick Ferguson Daniel K Chan Brooklyn, New York Mary Almas University of Colorado Mount Sinai Medical Center Franc Forstneric Boulder, Colorado Levy Place, New York Institiit Mittag-Leffler Thierry J Chaussalet Djursholm, Sweden Nikos P Andrianos North Carolina State University Pittsburgh, Pennsylvania Thomas Michael Foy Raleigh, North Carolina Golden Valley, Minnesota Kenichiro Aoki Ryland D Crews Princeton University Margaret Napolitano Freije Amelia, Virginia Princeton, New Jersey Holy Cross College Charles W Culmer Worcester, Massachusetts Muharem Husein Avdispahic Philadelphia, Pennsylvania Pijade, Yugoslavia Margo Galson Robert C Dalang Maspeth, New York Esther Badt University of California, Berkeley Wayne State University Tunc Geveci Berkeley, California Detroit, Michigan San Diego State University James W Daniel San Diego, California Wolfgang Walter Bein University of Texas at Austin Duke University Weibang Gong Austin, Texas Durham, North Carolina Qufu Normal University Tarun Kumar Das Shandong, People's Republic of D L Berman Allahabad, India China Leningrad, U S S R Michael W Davis Richard Eugene Griffin Raymond Thomas Bevilacqua Ohio State University Georgia Institute of Technology Ellensburg, Washington Columbus, Ohio Atlanta, Georgia Nicu Boboc Paul Joseph DesRoche Albert Groenenboom University of Bucharest Tampa, Florida Hengelo, Netherlands Bucharest, Romania S H Doong Rami P Grossberg Stephen Dale Boeh Minneapolis, Minnesota Rutgers University Cranston, Rhode Island . New Brunswick, New Jersey Aly Abd Rahman El Sabbagh William S Boyd University of Groningen Jeffrey Bennett Hamlin Rhodes College Groningen, Netherlands Pittsburgh, Pennsyl,vania Memphis, Tennessee Henry Epstein Marvin Edwin Harrell Lowell Edwin Bush Bures-sur-Yvette, France Emporia, Kansas Arlington, Texas Raisa Epstein Tian-Xiao He Zhenfu Cao University of California, Berkeley Texas A & M University Harbin Institute of Technology Berkeley, California College Station, Texas Harbin, People's Republic of China Ron Faerber Steffen Heinze Angel Capellan Sacramento, California Heidelberg, Federal Republic of Jamaica Hills, New York Germany Florence D Fasanelli Roberto Jose Cauvi Washington, District of Columbia Lima, Peru

FEBRUARY 1988, VOLUME 35, NUMBER 2 321 New Members of the AMS

Haruzo Hida Mary Elizabeth Koban R Morkvenas University of California, Los Angeles Johnstown, Pennsylvania Lithuanian Academy of Science Los Angeles, California Vilnius, U S S R L A Kurdachenko Kevin John Howat Dnepropetrovsk, U S S R Ian L Morrison Wadsworth Publishing Company Fordham University Stanislaw Kus Belmont, California Bronx, New York Lublin, Poland Liqun Huang Yukio Otsu Mark T Lane Kalamazoo, Michigan Kyushu University Massachusetts Institute of Technology Fukuoka, Japan Guenther P Huck Lexington, Massachusetts Northern Arizona University Steve Randall Overton Namyong Lee Flagstaff, Arizona Knoxville, Tennessee Seoul, Korea Jen lng G Hwang Sangeeta Pahuja Mary Ann Leggett Norfolk, Virginia New Delhi, India Jackson, Mississippi E Infeld Vassilis Papageorgiou An-Min Li Warsaw, Poland Clarkson University Sichuan University Potsdam, New York Sergey lvashkovich Sichuan, People's Republic of China L'vov, USSR Michael John Papaik Shangzhi Li Woburn, Massachusetts Nigel Jefferies University of Science & Technology London, England of China Marvin C Papenfuss Mingchang Jiang Hefei, People's Republic of China Loras College Dubuque, Iowa Brandeis University Chongchao Liang Waltham, Massachusetts Shandong College of Oceanography Bozenna J Pasik-Duncan Qingdao, People's Republic of China University of Kansas James Sherman Johnson Lawrence, Kansas Garden Grove, California Chao-Qiang Lin Jennifer M Johnson Northwestern Polytech University V Pestov Xi'an, People's Republic of China Tomsk, USSR University of Utah Salt Lake City, Utah L Loone Tuyet D Pham Tartu, Estonia, U S S R Akron, Ohio Jason Andrew Jones Pennsylvania State University Eduardo A Luna Gaston E Phillips University Park, Pennsylvania Santiago, Dominican Republic Elmhurst, New York Zoran Kadelburg Nicolaie Lungu Despina Polemis Belgrade, Yugoslavia Cluj-Napoca, Romania Jamaica, New York Jerzy Kakol 0 A Malafeev Walter M Potter A Mickiewier University Leningrad, U S S R University of Wisconsin Poznan, Poland Madison, Wisconsin Adamantios Stylianos Mattheos Hilbert J Kappen Athens, Greece Imelda Yeung Powers Eindloven, Netherlands Franklin & Marshall College Steven Matthysse Lancaster, Pennsylvania Najafabadi A Karshenas Sudbury, Massachusetts Teheran, Iran Robert H Price Sergej V Matveev Addison-Wesley Publishing Company Harvir Singh Kasana Cheljabinsk, U S S R University of Roorkee Reading, Massachusetts Eleanor May Roorkee, India Jan Pruss Princeton University Gesamthochschule Paderborn Sikander Hayat Khiyal Princeton, New Jersey UMIST Paderborn, Federal Republic of Sergey Merkulov Manchester, England Germany U S S R Academy of Science Shaukatullah Qazi Yoshio Kitazawa Moscow, U S S R Pomona, California Kano, Nigeria Walter Miller Sun Qi Matthias P Klay Washington, District of Columbia Stanford University Sichuan University Stanford, California Antonio C Monteiro Chengdu, People's Republic of China Mathematics Institute Tie Hu Qin AU Klimyk Oxford, England Kiev, USSR Fudan University Shanghai, People's Republic of China

322 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

,-- Monica Radivoiovici-Tatoiu Stuart A Wilkinson New Zealand Mathematical Society Bucharest, Romania University of Lancaster Ting On To England Lancashire, Norsk Matematisk Foreningros Brian W Ridgely Merrillville, Indiana John Wolfskill Johan F Aarnes University Northern Illinois Polskie Towarzystwo Matematyczne Anne Drinkwater Roberts DeKalb, Illinois University of Utah Waclaw Pawel Nieuwazny Xu Salt Lake City, Utah Xu Hai Real Sociedad Matemdtica Espanola Wuhan University Maria L Fernandez-Rodriguez Domingo Rodriguez Wuhan, People's Republic of China New York, New York Societe Mathematique Suisse Hongcang Yang Claude Cibils Rita V Rodriguez-Anger Academia Sinica Florida Institute of Technology Chengdu, People's Republic of China Societe Mathematique de Belgique Melbourne, Florida Christian Michaux Hong-Ming Yin Sholom S Rosen Washington State University Sociedad Colombiana de Matemdticas Baltimore, Maryland Pullman, Washington Alberto S Schotborgh Markus Rost Qing Zhang Sociedade Portuguesa de Matemdtica University of Regensburg Providence, Rhode Island Isabel Salgado Labouriau Regensburg, Federal Republic of Germany Frank Zizza Suomen Matemaattinen Yhdistys University of Washington Aatos 0 Lahtinen James WRoth Seattle, Washington Maynard, Massachusetts Svenska M atematikersamfundet Sergej M Zverev J Rikard Bogvad Mary M Schroth Academy of Science Torsten Ekedahl Charlotte, Michigan L'vov, USSR Unione Matematica Italiana David H Sharp L Maria Abatangelo Los Alamos National Laboratory Gian-ltalo Bischi Los Alamos, New Mexico RECIPROCITY MEMBERS Maurizio Falcone Peter Shenkin Australian Mathematical Society Filippo Notarnicola John Jay College (CUNY) Gerhard Huisken Diego Massimo Palara New York New York, Deutsche Mathematiker-Vereinigung e. V. Wiskundig Genootschap Andrzej Skowron J Bemelmans NicoM Temme University of Warsaw U Jannsen Osterreichische Mathematische Warsaw, Poland Israel Mathematical Union Gesellschaft Khudadino K D Soomro Hanna Moscovitz Maximilian Ganster Sind University Korean Mathematical Society Khairpur, Pakistan Young Wook Kim NOMINEE MEMBERS Andreas Stahel London Mathematical Society Adelphi University University of Utah Alfred W Goldie City, Utah Al Sheik Salt Lake Gerard Franciscos Helminck James R Stoker T S Taha American University Pasadena, California J D Maitland Wright Vittorio Boria Louis Theodore Mariano Michael A Trick Mathematical Society of Japan Minneapolis, Minnesota Kazuo Augustine Hashimoto Amherst College Toshiyuki lwamiya Peter H Anspach Vadim Z Tsalyuk Yuichi Kanjin Steven E Mutchnik R Krasnodar, U S S Inoue Masaaki Marc D Sanders Emile Volcheck Shoichi Nakajima Jeremy M Schofield Vaals, Netherlands Takahiko Nakazi Angelo State University Masafumi Okumura Sanjay Subhash Mehta Sebastian Walcher Fumio Sakai University of California, San Diego Shizuka Sato Armstrong State College La Jolla, California Mitsuo Sugiura Stephanie Stevens Dirk Werner Naoyoshi Suzuki Bates College Freie University Takeshi Tokuyama Jay H Reichgott Berlin, Federal Republic of Germany Yoshihito Tomita Geoffrey B Shilling Morimasa Tsuchiya Masao Yamazaki

FEBRUARY 1988, VOLUME 35, NUMBER 2 323 New Members of the AMS

Beloit College Joe A Francis James Madison University Joan Frances Kelley Jesse K Lee Judith A Phillippi Xiaolong Luo John Carroll University Bloomsburg University ofPennsylvania Antonio J Machiavelo Darrell J Horwath Boon L Cheng John Edward Meier Dale J Snyder J Edward Kerlin Yuim-Chung Sheu John Thomas Wade Boston University Arthur A Small Mark Turpin Li-Min Song Johns Hopkins University, Baltimore Piotr Ludwik Szafranski Thomas Lewis Gibson Bowling Green State University Colum MWatt William W Hall John A Maroli Chen-LiPan D Reidel Publishing Company Tamas Varga Ursula Porod David J Lamer Brandeis University Kefeng Ying Duke University James R Hughes Kansas State University Jacek B Poznanski Brock University Celeste I Card Eastern New Mexico University Elizabeth Jane Pattison Kent State University, Kent Kim L Luna Brown University Chandra R Asthagiri Hon-Ming Lau Eastern Washington University Per Enflo Gayle Lynn Smith Xiezhang Li Bryn Mawr College Ann M Heath George Mason University Knox College Timothy C Kearns Robert Scott Villegas California State University, Long Beach Jeffrey George Seyfert Hardin-Simmons University Louisiana State University, Baton Rouge William Lee Baker Elisa M Allgood California State University, Sacramento Robert J Kingan Harvard University Scott A Douglas John D Liter Dan Abramovich Cornel G Ormsby Fatemah F Mohammed Henri R Darmon Angeline Todino Zafra Carleton University David Allan Kotz Abdunnabi M Ali Michael James McGrath Louisiana Tech University Diane M Stukel Eric P Twietmeyer Grayling Bernard Williams Fan Zhang Wenxiang Wang Maca/ester College Carnegie-Mellon University Herbert H Lehman College, CUNY Charles A Amundson Sea-Mean Chiou Jan A Plaza David L Ehren Steve Earth Charley Kerning Wang Howard University Mankato State University Bruce Harvey Clark John F Close Catholic University ofAmerica Maureen H Fenrick Frans A Susilo Illinois State University Wichai Chumni Memorial University of Newfoundland City College, CUNY Haifa N Konkar Roland H Eddy Jean Cadet Daniel C Fisherman Indiana University at Bloomington Memphis State University Timothy Mooney Gendron Akira Abe Raymond A Clapsadle Wolfgang Brueggemann Mahendra Nauth Singh Miami University, Oxford Wenhan Chen Robert G Lowery Clemson University JunMu Eugene Yongbao Wang Julie B Lassiter Swatee Naik Colorado College Clet Niyikiza Michigan State University Nara Sherman Thacher Shan Sun Luan Cong Owen P Thomas Zeljko Cuckovic Colorado State University Daoping Xu Jose H Giraldo Barbara K D'Ambrosia Jun Yan Richard J Hensh Christopher Hiu Jing Zhao Liangjiao Huang Bruce N Lundberg Keng-Huat Kwek Iowa State University Mia Poje Kuiyuan Li WaelAAmin Steven Z Zhou Joseph J Spencer Simonthy Renaldin Fuad Peter P Springer Concordia University Swie T Lie Steve Hardy Kathryn Ann Mack Michigan Tech University Felice duBerger Jon D Phillips Robin Lynne Byrd Cornell University Xuehuang Qiu Anne Marie LaHaie Shuh-Jye Chern Laura J Smith Charles E Southwell Yong YaoDu Zhiming Sun Hasan Naveed Zaidi

324 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

,.-- Mississippi State University Petter F Mostad Santa Clara University Zeather N Gladney M J Radzikowski Michael A Jones Oded Schramm Sharon K Sheehan Monmouth College Richard Evan Schwartz Seton Hall University Thomas J Smith John W Simpson John C Marques Montana State University John Martin Steinke Thomas L Marsh Jennifer M Wilson Shippensburg University of Pennsylvania Ralph C Smith Otis C Wright Scott Michael Fabbri New .Mexico State University, Las Cruces Purdue University Southern Illinois U, Carbondale Min-Hyung Cho Shamim Ismail Ansari Geeta B Joshi Mansor M Losta Fabio Antonelli Hetao Liu Ricardo L Soto Hung-Chieh Chang Marcin Schroeder Zhangxin Chen Tingxiu Wang North Carolina State University Johnny Chow Bo Zhang Hongwei Chen Chun-Tak Fan Dong-Ming Hwang Southwest Missouri State University Xiaobing Feng Douglas James Sally D Vestal Anna Guerrieri Zhongshan Li Sandeep Harishchandra Holay StJohn's University Kevin D Yeomans Yue Huang Arturo Giscombe North Georgia College Belgin Karaman Mohamed A Hafez Deborah Ann Adams Pradipkumar H Keskar St Louis University Allyson Lee Wilson Vijay Kodiyalam Fuziyah Ishak Shikang Li Northwestern University Mary Carolyn Thomas Anand Pralhad Masur Anetta M Bajer Nickolas John Michelacakis Stanford University Jon C Howell Phillip L Mitchell Kenneth D Dutch Lisa A Langsetmo Zhijian Qiu Edward Emmett Jenvey Hyeonggi Lee KN Raghavan Suheil Afif Khoury Kevin D Woerner Gregory S Rhoads Matthew James Nicol Oberlin College Pugi Tang Ioannis Nicolaos Petridis Judith Esther Goldberg Asurumuni A Waidyaratne Dong Zhang Warren T Wood George V Wegele Syracuse University Yuing Wei Ohio Wesleyan University Peter C Brown Danny Scott Wendt John Patrick Lawrence Qazi M Dawood Ngai-Ching Wong Cynthia L Milligan Pennsylvania State University, University Changsheng Xu Mary Kathleen Porter Park Jianming Xu Hualin Xing Paul Joel Brunetto Zhuan Ye Qing Chang Temple University Queens College, CUNY Martin I Funk W P Abeysinghe Olen Tiga Ajchara Harnchoowong M W Chandrakantha Tianshan Hu Reed College Zijun Zhao Shan Hwai-Ling William L Bloch Texas Christian University Anjali Vasant Kalvade Brooks K Roberts H G Dollar III WuLi Irena Swanson Xiaoye Li United States Naval Academy Rensselaer Polytechnic Institute Yi Li Daniel B Widdis Steven P Clay Yong Li Bruce Kaemper Geist University Laval Andrew E McNerney Caroline N Haddad Yves Bourgault Arup Mukherjee Denise T Maurais Alain Charbonneau Paolo Piccione Bohdan P Szanc Sylvie Martel JuRao Paul A Roncevich Rice University University ofAlabama-Birmingham Carlos Alberto Torre Oscar Garcia-Prada Richard B Davidson Bo Zhou Steven Duane Underwood SUNY at Albany Princeton University Kenneth A Schwartz University ofBritish Columbia Amit Badiani Teresa Maureen Hofstedt Sacred Heart University Dror Bar-Natan Raymond M Lam Barbara J Elliott Andrea L Bertozzi Maria Lardas Koutsoukos University of Calgary Martin Jude Bridgeman Bonaventure Anani Anthonio Ze Li Dou Jean-Michel Pierre Brouchet GabrielE Fractman

FEBRUARY 1988, VOLUME 35, NUMBER 2 325 New Members of the AMS

Wenhua He Debra S Shure Xiaoming Zhllu Denis Joseph Keroack University of Maine, Orono University ofMissouri, Columbia Semkowicz Krzysztof Christopher B Nichols Hegang Chen Digby M Smith Francis Twolyongut University of Maryland, Baltimore County L'niversitv of Missouri, Kansas City Kam Chuen Yuen V Michael Boyle Deyue Wei Paul M Grden University of California, Irvine ['niversitv of Missouri, Rolla Victor Acosta University a.( Maryland. College Park Philip J Gloor A Drumm Mark K Davis Todd Cniversity ofMonrana E Faulkenberry Paul McGill Richard James F Robmson-Cox Foster Kuo-Tong Thau Dean P Steven E Rummel Kyril Tintarev Meihui Guo Jean Bernard Nestor [ 'niversity of North Carolina at Chapel University of California, Riverside Kwang SPark Hill T Clegg Matthew Philip W Steitz Bruce Edwin Jimeuez Harrell John M Masako Takagi Anne Louise Miller Susan Rose Mills Ching Wah Woo [ niversity a.{ Nebraska at Lincoln William D Turner You Zhiping Steven P Haataja of California, Santa Barbara University University o.f liJassachusetts, Amherst Upali Jayantha Karunaratne Geoffrey M Boynton Cornelius Pillen Matt David I .unsford Gwyn Harney James F Riordan Troy Darin Riggs Jeff N Kidder Guozhang Sun Lih-Chyun \\ ang Stephen Robert Lines Kongming Wang A Papadopoulos [ niversity of Nebraska at Omaha Caroline Sheng Wang John A Luca~h Gary A Ropp Wei Fusheng Mike Pulverenti Wasin So Fernando Zalamea Peggy J Thomassin l 'niversity of Nevada, Las Vegas University Michigan o.f Patnck Alan Todd University of Cincinnati Benjamin V Collins Fan Guangwei Carolyn S Dee l'niversity o.f Orepon Kim Seong-A Linwood T Early Karin M Deck Xiaotong Shen Jeanine A Esmacher Jens Erwin Harlander Wu Zhiqin Rodrigo P Gomez Junjiang Lei University of Dallas Michael J Kantor Terry Reilly Paul H Ladehoff Nancy C VanNess [ 'niversity of Pennsylvania Leonard Leung Man Chun Oliver J Golden University of Florida Barbara E Nimershiem Catanzano Sheri Ann Eric R Purohit ( 'niversity of Pitt.1burgh, Pittsburgh Chambers Kelly Ann Thomas M Richardson Song-Ying L1 Miller Julie M Alyssa D Sankey Zhijun Liu Pennington Robin Arnie Alexander J Shiffer Shixian Qian W Reiter Robert Nathan R Soderberg Huiman Xie Wilhelm Kurt Schwab Diana L Watson Ning Xu Zoran Vondracek University o.f Minnesota-Duluth University of Puerto Rico, Mayaguez University of Idaho Marcia A Rowell Antonio Acevedo Young Sook Do Veronica Cecilia Celis Minnesota-Minneapolis University of Svarez Luisa Leonardo University of Kansas Lu Cheng W Kangas George Jaeduck Jang University of Regma J LaBerge Timothy Jinghua Kuang Ping Wang Ramanujackhary Kumanduri University of Lethbridge University of Rhode Island Kwak Jacqueline R Knight Minkyu Eleftherios 1\taragakis Hwei-Ting Lin Tinh V Le Susan C Mosher Darryl C Rae Ling Ma Gloria Mari-Beffa I 'niversity of Rochester University of Louisville Libin H Mou Luisa Ares De Parga Lutz Martha Kay Roberto Murillo Yoounggi Choi Edward O'Connor George Jin Keun Seo Ricardo Fajardo L Robertson Roland Shiah-Sen Wang In-Suk Kim University of Lowell Xuefeng Wang Josue Ortiz Lewis D Grasso Baisheng Yan Janice L Pearce Richard L Hickey Yin Yan Shiaohui Wang

326 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

..- University of South Carolina, Aiken University of Virginia Western Illinois University Jane C Beattie Steven Neil Evans Sung Yong Cha Jacek Szmigielski Min Zeng University of South Carolina Bruce F Torrence Jun Qin Western Michigan University Kenneth F Yarnall University of Winnipeg Hector G Hevia-Soto Shiying Zhao Diane J Vuignier Ewa M Kubicka Grzegorz M Kubicki University of Southern Colorado University of Wisconsin, Milwaukee Reza Rashidi John W Walker Brian S King Thomas B Sprague John J Koker University of Southwestern Louisiana Ignatios E Vakalis Anthony K Bourque University of Wisconsin, Parkside Wichita State University Judith L Couington Dennis E Miller John David Besser Michael Jay Thielen University of Tennessee, Chattanooga Russell Shuttleworth Walt M Mobley Utah State University William Paterson College Eric T McQueen University of Texas at Austin Sandeep Maheshwari Rich Wellman Guohui Feng Xavier University Linguo Gong Vanderbilt University Dianne R Elsaesser Xingping Sun Ariyadasa Aluthge Paul Arnold Sundheim Marvin Edward Glover Jr Yale University Carlin J Sappenfield Donghun Han University of Toronto Amy S Kiuchi Peter Danziger Villanova University Karl L DePaepe Carla A Monticelli York College, CUNY Andrew Edward Dobrowolski Tuval S Foguel Wake Forest University Gayathri Duvvuri Oumar Kaba Lanie Barry Ehlinger Fantahun K Gelenchi Doris Ann Hepler York University Ardeshir Guran Helen Stergiopoulou John Cadualadr Owen Washington University Howard D Troughton Dashan Fan Luigi Fontana University of Tulsa Nong Lin INSTITUTIONAL Karen E Cleary Daowei Ma Kevin R Gehringer Bradley University He Ouyang Peoria, Illinois University of Utah Javier Soria Timothy C Bratten Hesheng Zhao College of Staten Island Marc A Cremer Staten Island, New York Wayne State David J Eyre University Jiaming Du David Tod Fullwood Min-Xiang Hu Ming He TWO-YEAR COLLEGES Yuan-Ping Hu Manfred Kotter He Li Burlington County College Ronald S Lundstrom Ying Wu Pemberton, New Jersey Yonghao Ma Michael James Myers Wesleyan University Clark Technical College Michael John O'Reilly Ann Kizanis Springfield, Ohio University of Vermont West Virginia University Mohawk Valley Community College Wendy M Fenwick Maria R Brunett Utica, New York Helen P Read Fangjun Hsu Normandale Community College University of Victoria Bloomington, Minnesota Richard C Brewster Nolan W Evans Alison R Nishihara Jingzhi Tie

FEBRUARY 1988, VOLUME 35, NUMBER 2 327 Mathematical Sciences Assistantships and Fellowships Supplementary List

Graduate Study at Universities Under the DEGREES AWARDED column the following terms have in 1988-1989 been used: Bachelor's by inst. Number of bachelor's degrees awarded by the institution The entries below supplement the December 1987 Special Issue of Bachelor's by dept. Number of bachelor's degrees awarded the Notices. by the department In the section on "number anticipated," the first number refers to the Master's by dept. Number of master's degrees awarded total number of assistantships and fellowships in the program. The by the department second number following the colon is the number available to NEW Ph.D. (84/87) Doctoral degrees awarded during the last students (first year or above). A dash is used to indicate "information three years (1984-85, 1985-86 and 1986-87) not supplied by the department." Abbreviations used The number following "Faculty" is the number of faculty members in ANT Algebra or Number Theory S Statistics the department who are full-time employees in the institution and at AFA Analysis or Functional CS Computer Science least half-time in the department; the number following "Published" is Analysis OR Operations Research the number of those reported who have published a technical paper GT Geometry or Topology AM Applied Mathematics or book in the last three years. L Logic ME Mathematics Education The section on "Graduate Students" refers to the number of graduate P Probability students in the department who are full-time (including teaching as­ sistants), full-time first year, and part-time. Information not supplied Under the SERVICE REQUIRED column, hours per week section, "c" in any of these categories is indicated by a dash. denotes contact hours.

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated} paid to student paid by hours type Academic year dollars months student ($) 1986-1937

Alabama

Alabama A&M University, Normal 35762 MATHEMATICS Applications due: 8/17/88 Bachelor's by inst. 345 Jerry R. Shipman, Chairman Faculty 13; Published 2 Bachelor's by dept. 5 Graduate Students: full-time 2; full-time first year-; part-time 10 Teaching Assistantship (1:1) 4250 20 Teaching

328 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student ($) 1986-1987

Arizona

University of Arizona, Tucson 85721 MATHEMATICS Applications due: 3/5/88 Bachelor's by inst. 3100 Alan C. Newell, Head Faculty 58; Published 45 Bachelor's by dept. 18 Graduate Students: full-time 62; full-time first year 23; part-time 0 Master's by dept 5 Fellowship* 8000-10000 9 1255 Ph. D. (84/87) ANT 4, GT 1. Teaching Assistantship (36:20) 8400-9300 9 1255 4 Teaching Total: 5 Research Assistantship (25:25) 8400-9300 9 1255 10 Research Tuition Scholarship (4:4) 1255 Registration Scholarship (2:2) 3604 *Fellowships awarded on competitive basis. Applicants within the Faculty of Science compete for the award. Total of 8 awards available.

California

Stanford University, Stanf<>rd 94305 COMPUTER SCIENCE* Applications due: 1/1/88 Bachelor's by inst. 1628 Nils Nilsson, Chairman Faculty 25; Published - Bachelor's by dept. 8 Graduate Students: full-time 294; full-time first year 94; part-time 82 Master's by dept. 122 Fellowship (51:-) 8816-15000 9 ** Research Ph. D. (84/87) CS 41. Total: 41 Teaching Assistantship (38:-) 8730-9369 9 ** 20 Teaching, grading Research Assistantship (91:-) 8730-9369 9 ** 20 Research Course Assistantship (7:-) 7410 9 ** W G~d~g *Financial assistance below for 1987-1988. **Minimal student fees.

University of California, Santa Cruz 95064 MATHEMATICS Faculty 15; Published 15 Bachelor's by inst. 1289 Gerhard Ringel, Chairman Graduate Students: full-time 35; full-time first year 7; part-time 3 Bachelor's by dept. 29 Master's by dept. 8 Ph. D. (84/87) ANT 1, AFA 3, Fellowship (3:3) 6500 9 4086 AM 1, Other 2. Total: 7 Teaching Assistantship (27: 7) 1118 9 16-20 Grading, teaching

FELLOWSHIPS $15,000

The University of Arizona's Department of Mathematics and Program in Applied Mathematics are looking for outstanding graduate students. The stipend will be $15,000 for twelve months and will be available for at least three years. Applications should be received by March 15, 1988. For more information please write to: Dr. Alan C. Newell Department of Mathematics University of Arizona Tucson, Arizona 85721

Equal Employment Opportunity/Affirmative Action Employer.

FEBRUARY 1988, VOLUME 35, NUMBER 2 329 Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated). paid to student paid by hours type Academic year dollars ·months student ($) 1986-1987

District of Columbia

George Washington University, Washington 20052 OPERATIONS RESEARCH Applications due: 3/1/88 Bachelor's by inst. 1272 Donald Gross, Chairman Faculty 9; Published 9 Bachelor's by dept. 7 Graduate Students: ful~time 50; ful~time first year 11; part-time 128 Master's by dept. 30 Fellowship (3:3) 3430 9 3430 Ph. D. (84/87) OR 10. Total: 10 Teaching Assistantship (2:1) 2200-4400 4.5-9 175-375 15 Teaching Research Assistantship (1-4:1-3) 9000-13000 9-12 6860 20 Research

Florida

University of Florida, Gainesville 32611 MATHEMATICS Applications due: 3/15/88 Bachelor's by inst. 5728 Gerard G. Emch, Chair Faculty 46; Published 41 Bachelor's by dept. 72 Graduate Students: full-time 57; full-time first year 20; part-time 5 Master's by dept. 13 Fellowship (4:2) 8000-11000 9 Ph. D. (84/87) AFA 1, AM 1. Teaching Assistantship (75:30) 8000-9000 9 200 4' Teaching Total: 2 Research Assistantship (4:2) 8000-9000 9 200 12 Research

Illinois

Sangamon State University, Springfield 62708 MATHEMATICAL SCIENCES Applications due: 4/30/88 G. A. lasby, Convenor Faculty 7; Published 0 Graduate Students: full-time 30; full-time first year 20; part-time 40 Graduate Assistantship (2:2) 20

Indiana

Indiana University, Bloomington 47405 COMPUTER SCIENCE Applications due: 2/1/88 Bachelor's by inst. 4625 Franklin Prosser, Chairman Faculty 24; Published 18 Bachelor's by dept. 85 Graduate Students: full-time 130; full-time first year 50; part-time 0 Master's by dept. 45 Fellowship (5:5) 2000 9 14/hr. Ph. D. (84/87) CS 8. Total: 8 Teaching Assistantship (35:15) 8250 9 14/hr. 20 Grading, teaching Research Assistantship (10:0) 8250 10 14/hr. 20 Research System Assistantship (5:0) 7425 9 14/hr. 20 Research

Louisiana

Southern University, Baton Rouge 70813 MATHEMATICS Applications due: 5/88 Bachelor's by inst. 1200 lovenia OeConge-Watson, Chairperson Faculty 41; Published 5 Bachelor's by dept. 3 Graduate Students: ful~time 23; full-time first year 10; part-time 3 Master's by dept. 5 Teaching Assistantship (4:3) 2500-4000 9 3

Maryland

Johns Hopkins University, Baltimore 21205 BIOSTATISTICS Applications due: 12/2/87 Bachelor's by inst. 596 Charles A. Rohde, Chairman Faculty 14; Published 9 Master's by dept. 1 Graduate Students: full-time 26; ful~time first year 6; part-time 4 Fellowship (10:6) 5000 9 11000 Ph. 0. (84/87) Other 3. Total: 3

330 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student (S) 1986-1987

Massachusetts

Harvard University, Cambridge 02138 STATISTICS Applications due: 1/15/88 Bachelor's by inst. 1568 Donald B. Rubin, Chairman Faculty 6; Published 6 Bachelor's by dept. 0 Graduate Students: ful~time 17; ful~time first year 3; part-time 0 Master's by dept. 6 Fellowship (3:3) 13000 9 Ph. D. (84/87) S 6. Total: 6 Teaching Fellowship (12:S-8) 9900 9 Varies 8 Teaching, grading Research Assistantship (12:5-8) 9900 9 Varies 10-15 Research

Massachusetts Institute of Technology, Cambridge 02139 SLOAN SCHOOL OF MANAGEMENT SCIENCE* Faculty 36; Published 36 Bachelor's by inst. 1159 Tom Magnanti, Chairman Graduate Students: ful~time 62; ful~time first year 13; part-time- Bachelor's by dept. 43 Master's by dept. 66 Ph. D. (84/87) OR 10, Other 4. *Total of 62 assistantships-and fellowships in the program with an estimated 16 available to new students Total: 14 (first year or above). Any further information is available upon request from Sharon Cayley, Ph.D. Program Coordinator.

Michigan

Michigan State University, East Lansing 48824 MATHEMATICS Applications due: 4/1/88 Bachelor's by inst. 6488 Kyung Whan Kwun, Chairman Faculty 90; Published 65 Bachelor's by ~ept. 82 Graduate Students: full-time 113; full-time first year 38; part-time- Master's by dept. 29 Fellowship (1:1) 9 2320.50 Ph. D. (84/87) AFA 2, GT 1, Teaching Assistantship (90:39) 8600-9600 9 2320.50 4-8 Grading, teaching AM 5. Total: 8 Research Assistantship (7:7) 2500 3* *Summer before first year.

University of Michigan, Ann Arbor 48109 STATISTICS Applications due: 4/15/88 Bachelor's by inst. 4993 Edward D. Rothman, Chairman Faculty 13; Published 13 Master's by dept. 8 Graduate Students: full-time 37; full-time first year 16; part-time - Regents Fellowship (1:2) 10000 8 Ph. D. (84/87) S 6. Total: 6 Teaching Assistantship (22:varies) 1532-7652 88 4-25 Grading, teaching Research Assistantship (Varies:-) 3826-7652 8 10-25 Research Block Grant (7:Varies) 400-1050 8

Wayne State University, Detroit 48202 MATHEMATICS Applications due: 2/88 Bachelor's by inst. 2270 Betram Schreiber, Chairman Faculty 42; Published 35 Bachelor's by dept. 15 Graduate Students: full-time 37; ful~time first year 12; part-time 17 Master's by dept. 7 Fellowship (3:-) 5500 9 Ph. D. (84/87) AFA 1, GT 2, Teaching Assistantship (26:-) 6600-9000 9 6' AMl. Total: 4 Research Assistantship (2:-) 7500 12

FEBRUARY 1988, VOLUME 35, NUMBER 2 331 Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student ($) 198&-1987

Minnesota

University of Minnesota, Minneapolis 55455 STATISTICS Applications due: 3/15/88 Bachelor's by inst. 5525 Seymour Geisser, Director Faculty 19; Published 19 Bachelor's by dept. 15 Graduate Students: full-time 67; full-time first year 17; part-time - Master's by dept. 7 Ph. D. (84/87) S 11. Total: 11 Fellowship (3:-) 5250 Teaching Assistantship (25:-)** 7650 Research Assistantship (8:-)** 7650 Graduate School Fellowship (-:-) 8000 Statistics Alumni Scholarship (1:-) 5250 *7-15 credits: resident $850, nonresident $1700. **All student appointments of at least 25% will receive tuition fellowships equal to twice the percent of their appointment.

Missouri

University of Missouri-Columbia 65211 STATISTICS Applications due: 3/1/88 Bachelor's by inst. 3494 John E. Hewett, Chairperson Faculty 12; Published - Bachelor's by dept. 5 Graduate Students: full-time 17; full-time first year 15; part-time 5 Master's by dept. 4 Fellowship (4:-) 1000-8000 9 870.33 Ph. D. (84/87) S 7. Total: 7 Teaching Assistantship (19:-) 7210--7577 9 870.33 20 Teaching Research Assistantship (1:-) 7200-8000 9 870.33 20 Research

Montana

Montana State University, Bozeman 59717 MATHEMATICAL SCIENCES Applications due: 4/1/88 Bachelor's by inst. 1500 K. Tiahrt, Chairman Faculty 26; Published 20 Bachelor's by dept. 40 Graduate Students: full-time 31; full-time first year 10; part-time 0 Master's by dept. 8 Teaching Assistantship (31:15) 6000--9000 9 450 13 Teaching Ph. D. (84/87) AFA 3. Total: 3 Research Assistantship (2:1) 6000--9000 9 450 13 Research

New Jersey

Rutgers University, New Brunswick 08903 STATISTICS Applications due: 3/15/88 Bachelor's by inst. 6640 Robert Berk, Chairman Faculty 18; Published 14 Bachelor's by dept. 12 Graduate Students: full-time 42; full-time first year 9; part-time 38 Master's by dept. 23 Fellowship (4:1) 6000--10000 9 139 Teaching Assistantship (9:0) 8245-8445 9 139 15 Grading, teaching Research Assistantship (3:0) 8245-8445 9 139 15 Research

Stevens Institute of Technology, Hoboken 07030 PURE AND APPLIED MATHEMATICS Applications due: 4/1/88 Bachelor's by inst. 274 Milos Dostal, Head Faculty 10; Published 6 Bachelor's by dept. 7 Graduate Students: full-time 22; full-time first year 8; part-time 129 Master's by dept. 5 Teaching Assistantship (9:1) 7020--7965 9 Ph. D. (84/87) Total: 6 Research Assistantship (1:-)

332 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student ($) 1986-1987

New York

Adelphi University, Garden City 11530 MATHEMATICS AND COMPUTER SCIENCE Applications due: 4f15f88 Bachelor's by inst. 1310 William Steinmetz, Chairman Faculty 14; Published 6 Bachelor's by dept. 19 Graduate Students: full-time 15; full-time first year 6; part-time 34 Master's by dept. 15 Teaching Assistantship (4:-) 3600 9 20 Ph. D. (84f87) ANT 1, s 1, CS 1, AM 4. Total: 7 Full Tuitionship Scholarship (8:-) Half Scholarship (5:-)

Hofstra University, Hempstead 11550 MATHEMATICS Applications due: 3f15f88 Bachelor's by inst. 1500 Harold M. Hastings, Chairman Faculty 20; Published 14 Bachelor's by dept. 25 Graduate Students: full-time 1; full-time first year 1; part-time 11 Master's by dept. 1 Fellowship (8:4) 500-3000 9 237 fer. Teaching Assistantship (6:3) 600-5600 9 237/cr. 2-15 Teaching, tutoring Internship (2:2) 5000-8000 9 237 fer. Varies Research

Rochester Institute of Technology, Rochester 14623 QUALITY AND APPLIED STATISTICS Applications due: 5f1f88 Master's by dept. 22 Edward G. Schilling, Chairperson Faculty 8; Published 3 Graduate Students: full-time 8; ful~time first year 6; part-time 130 Research Assistantship (8:6) 2900-8700 12 8800 10 Research

State University of New York at Albany 12222 COMPUTER SCIENCE Applications due: 3f15f88 Bachelor's by inst. 2165 Richard E. Stearns, Chair Faculty 15; Published 14 Bachelor's by dept. 80 Graduate Students: full-time 55; full-time first year 33; part-time 34 Master's by dept. 26 Fellowship (2:-) 10000 9 Research Ph. D. (84f87) CS 1. Total: 1 Teaching Assistantship (25:4) 6400-7400 9 20 Grading, teaching Research Assistantship (4:-) 9720-10000 12 20 Research

North Carolina

Duke University, Durham 27706 MATHEMATICS Applications due: 1f31f88 Bachelor's by inst. 1615 Michael C. Reed, Chairman Faculty 33; Published 25 Bachelor's by dept. 40 Graduate Students: full-time 41; full-time first year 11; part-time 0 Master's by dept. 2 Ph. D. (84f87) ANT 1, GT 2, Fellowship (3:2) 15502-19888 9 6888 P 1, AM 5. Total: 9 Teaching Fellowship (7:5) 14130 6-9 5680 6-10 Grading, teaching Teaching Assistantship (20:-) 14130 8 5680 6-10 Grading, teaching Research Assistantship (3:-) 14130 6-9 5680 6-10 Research

Ohio

Kent State University, Kent 44242 MATHEMATICAL SCIENCES Applications due: 2f88 Bachelor's by inst. 2502 Olaf P. Steckelberg, Chairman Faculty 35; Published 25 Bachelor's by dept. 84 Graduate Students: full-time 70; full-time first year 15; part-time 15 Master's by dept. 21 Ph. D. (84f87) ANT 1, AFA 7, Fellowship (1:1) 7250 9 20 Teaching 1. Total: 9 Teaching Fellowship (4:5) 6900 9 20 Teaching Other Teaching Assistantship (14:-) 6300 9 20 Teaching Research Assistantship (5-8:-) Varies 20 Research Part-time Instructorship (25:-) Varies

FEBRUARY 1988, VOLUME 35, NUMBER 2 333 Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student (S) 198~1987

Oklahoma

University of Oklahoma Health Sciences Center, Oklahoma City 73190 BIOSTATISTICS AND EPIDEMIOLOGY Faculty 7; Published 7 Bachelor's by inst. 2455 Daniel Schneider, Chairman Graduate Students: full-time 30; full-time first year 5; part-time 25 Master's by dept. 13 Ph. D. (84/87) Other 4. Total: 4 Teaching Assistantship (1:-) 300-500/mo. 9 Varies 20 Grading Research Assistantship (5:-) 500-800/mo. 12 Varies 20-30 Reseimh

Pennsylvania

Shippensburg State University, Shippensburg 17267 MATHEMATICS AND COMPUTER SCIENCE Applications due: 3/88 Bachelor's by inst. 1083 Howard T. Bell, Chairman Faculty 25; Published 5 Bachelor's by dept. 105 Graduate Students: full-time 25; full-time first year 22; part-time 53 Master's by dep.t. 16 Graduate Assistantship (9:9) 3.38-3.55/hr. 9 2

South Dakota

South Dakota State University, Brookings 67007 MATHEMATICS Applications due: 4/15/88 Bachelor's by inst. 1403 Kenneth L. Yocom, Head Faculty 17; Published 3 Bachelor's by dept. 32 Graduate Students: full-time 12; full-time first year 2; part-time 1 Master's by dept. 2 Teaching Assistantship (9:5) 3000-6000 9 47 fsem.cr.hr. 3-6'

Tennessee

East Tennessee State University, Johnson City 37614. MATHEMATICS Applications due: 1/3/88 George D. Poole, Chairman Faculty 17; Published 5 Graduate Students: full-time 15; full-time first year -; part-time - Teaching Assistantship (2:-) 4600 9 20 Research Assistantship (3:1) 4600 9 20

GRADUATE STUDY IN MATHEMATICS AT DUKE The Department of Mathematics of Duke University offers courses and thesis direction leading to the degrees ofMaster ofArts, and Doctor of Philosophy. The Department and University offer fellowships, teaching assistantships, and research assistantships. There are 29 graduate faculty mem- bers representing many areas of mathematics, especially nonlinear partial differential equations and geometry. Excellent library facilities as well as office space are available in the mathematics building. For further information write to: Professor Stephanos Venakides Director of Graduate Studies, Department of Mathematics Duke University Durham, North Carolina 27706

334 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student (S) 1986-1987

Texas

University of Texas at Arlington 76013 MATHEMATICS Applications due: 3/31/88 Bachelor's by inst. 3454 George Fix, Chairman Faculty 35; Published 25 Bachelor's by dept. 95 Graduate Students: full-time 79; full-time first year 10; part-time 20 Master's by dept. 10 Teaching Assistantship (45:10) 8400-12000 12 9 Ph. D. (84/87) ANT 1, AFA 10, Research Assistantship (10:6) 12000-14000 12 9 GT 2, P 2, S 3. Total: 18

University of Texas at Dallas, Richardson 75083 MATHEMATICAL SCIENCES Applications due: • Bachelor's by inst. 985 John W. Van Ness, Head Faculty 11; Published 10 Bachelor's by dept. 11 Graduate Students: ful~time 51; full-time first year 9; part-time 80 Master's by dept. 18 Teaching Assistantship (23:-) 8400-12000 12 20 Grading, teaching Ph. D. (84/87) S 6. Total: 6 Research Assistantship (1:-) 7464-10344 12 20 Research *Sixty days prior to registration.

Vermont

University of Vermont, Burlington 05405 COMPUtER SCIENCE AND ELECTRICAL ENGINEERING* Applications due: 3/1/88 Bachelor's by inst. 1675 Kenneth Golden, Chairperson Faculty 9; Published 6 Bachelor's by dept. 56 Graduate Students: full-time 16; full-time first year 10; part-time 2 Master's by dept. 10 Teaching Assistantship (9:5) 7200 9 100 20 Teaching Research Assistantship (1:1) 10400 11 100 •• Research *Information is for Computer Science only. **Hours per week: 20 academic year, 40 in summer.

Virginia

George Mason University, Fairfax 22030 MATHEMATICAL SCIENCES Faculty 25; Published 18 Bachelor's by inst. 1800 Stephen H. Saperstone, Chairman Graduate Students: full-time 6; ful~time first year 3; part-time 15 Bachelor's by dept. 23 Master's by dept. 3 Fellowship (1:1) 4850-5200 9 756-1512 Teaching Assistantship (6:5) 4850-5850 9 756-1512 6' Grading, teaching Research Assistantship (1:1) 4850-5200 9 756-1512 10 Research

Hampton University, Hampton 23668 MATHEMATICS Application~ due: 3/1/88 Bachelor's by dept. 19 Ram B. Ram, Chairperson Faculty 16; Published 5 Graduate Students: ful~time 6; full-time first year 4; part-time 2 Research Assistantship (10:7) 7200· 12 20 Other (6:4) 5400 9 20

Wisconsin

Marquette University, Milwaukee 53233 MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE Applications due: 2/15/88 Bachelor's by inst. 1843 Douglas Harris, Chairman Faculty 27; Published 19 Bachelor's by dept. 54 Graduate Students: full-time 42; ful~time first year 20; part-time 24 Master's by dept. 15 Teaching Assistantship (18:8) 6300-6600 9 20 Teaching Research Assistantship (2:2) 6300 9 20 Research

FEBRUARY 1988, VOLUME 35, NUMBER 2 335 Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student (S) 1986-1987

University of Wisconsin, Madison 53706 STATISTICS Applications due: 2/1/88 Bachelor's by inst. 6002 Robert B. Miller, Chairman Faculty 22; Published 22 Bachelor's by dept. 22 Graduate Students: full-time 96; full-time first year 24; part-time 17 Master's by dept. 13 Fellowship {1:1-3) 10251 9 2484 Ph. D. {84/87) S 26. Total: 26 Teaching Assistantship (33:10) 6884-10830* 9 2484 20** Research Assistantship (20:2-4) 11460 12 2484 *1986-1987 figures. Rate range from one-third time for inexperienced to half-time for experienced. ••so% time.

Canada

Queen's University, Kingston, Ontario K7L 3N6 MATHEMATICS AND STATISTICS Applications due: 2/88 Bachelor's by inst. 2741 L. L. Campbell, Head Faculty 45; Published 33 Bachelor's by dept. 45 Graduate Students: full-time 29; full-time first year 17; part-time 6 Master's by dept. 6 University Scholarship (-:15) 6500-7000 12 Ph. D. (84/87) ANT 3, s 2, Research/Teaching Other 1. Total: 6 Assistantship (25:-) 2400-10000 8-12 Teaching, grading, research Q.G.A. (-:-) 500-6000 12 Tuition Bursary** 5700 *Canadian and landed immigrants: approximately $1,715 per year; foreign students: approximately $7, 400 per year. **Visa students only.

Simon Fraser University, Burnaby, British Columbia V5A 186 MATHEMATICS AND STATISTICS Faculty 34; Published 30 Bachelor's by inst. 1635 A. R. Freedman, Chairman Graduate Students: full-time 57; full-time first year 19; part-time 3 Bachelor's by dept. 35 Mastlf's by dept. 10 Fellowship (-:-) 3200-3800 4 Ph. D. (84/87) ANT 3, AFA 3, Teaching Assistantship (100:100) 3200-3700 4 186-648/ sem. 20 Teaching, grading L 2, S 8, AM 2, Other 4. Research Assistantship(-:-) 4000 4 186-648/sem. 20 Research Total: 22 Stipend (5:0) 3800 4 186-648/sem. NSERC Postgraduate (5:Varies) 12000 12 186-648/sem.

Universite Laval, Quebec, Quebec GlK 7P4 MATHEMATIQUES, STATISTIQUE, ET ACTUARIEL Applications due: 2/1/88 Bachelor's by inst. 3435 Robert Cote, Directeur Faculty 37; Published 28 Bachelor's by dept. 60 Graduate Students: full-time 39; full-time first year 18; part-time 9 Master's by dept. 4 Ph. D. (84/87) ANT 1, AFA 5, L 1, P 1, AM 4. Total: 12 Students getting financial aid receive a minimum of $6000 for mixed duties. Knowledge of French required.

University of New Brunswick, Fredericton, New Brunswick E3B 5A3 COMPUTER SCIENCE Applications due: 3/1/88 Bachelor's by inst. 1300 W. D. Wassson, Director Faculty 22; Published 18 Bachelor's by dept. 90 Graduate Students: full-time 35; full-time first year 15; part-time 10 Master's by dept. 12 Teaching Assistantship (20:10) 800/mo. 12 1600/yr. 8 Grading, lab sup. Research Assistantship (30:10) 800/mo. 12 8 Research

University of Toronto, Toronto, Ontario M5S 1A4 INDUSTRIAL ENGINEERING* Applications due: 1/31/88 Bachelor's by dept. 66 A. K. S. Jardine, Chairman Faculty 16; Published 12 Master's by dept. 11 Graduate Students: full-time 33; full-time first year 15; part-time 20 Ph. D. (84/87) P 2. Total: 2 *Financial assistance not yet known.

336 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Assistantships and Fellowships

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (Total no. : no. anticipated) paid to student paid by hours type Academic year dollars months student (S) 1986-1987

University of Western Ontario, London, Ontario N6A 5B9 APPLIED MATHEMATICS Faculty 25; Published 20 Bachelor's by inst. 3636 James D. Talman, Chairman Graduate Students: full-time 21; ful~time first year 3; part-time 1 Master's by dept. 1 Teaching Assistantship (21:-) 11500-17735 12 2250.43 10 Marking, tutoring Ph. D. (84/87) AM 4. Total: 4

University of Western Ontario, London, Ontario N6A 5B7 COMPUTER SCIENCE Applications due: 4/30/88 Bachelor's by inst. 3636 I. Gargantini, Chairman Faculty 23; Published 20 Bachelor's by dept. 118 Graduate Students: full-time 31; ful~time first year 28; part-time 24 Master's by dept. 9 Teaching Assistantship (19:20) 8500-12000 12 10 Grading, teaching Research Assistantship (2:2) 8500-10000 12 10 Research Other (7:7) 1500 4 OGS (1:-) 9105 12 NSERC (2:-) 11600 12

Errata

For CARNEGIE-MELLON UNIVERSITY, Department of Statistics, there are no fees or tuition paid by the student.

The number of Ph.D.s granted in the last three years at the UNIVERSITY OF ALBERTA, Department of Statistics and Applied Probability was omitted. It should have been S 1. Total: 1.

PROCEEDINGS OF THE 1985 lwasawa theory, and arithmetic algebraic geometry. Included are papers by H. Stark and B. Gross MONTREAL CONFERENCE IN based on lectures they gave at the conference. NUMBER THEORY In his paper, Stark presents a new point of view H. Kisilevsky and J. labute, Editors regarding modular forms and Dirichlet series. {Conference Proceedings of the Canadian Gross's paper presents a geometric approach to Mathematical Society, Volume 7) Eichler's arithmetic theory of definite quaternion algebras and to Waldspurge's results on the central This volume contains the proceedings of the critical values of L-series. Canadian Mathematical Society's Summer Seminar 1980 Mathematics Subject Classifications: in Number Theory, held in June 1985 at the 11F55, llR, 11F41, 11F30. 12A70. 11G05, Loyola Campus of Concordia University. Directed 11G40, 11531, 14L05 at advanced graduate students and research ISBN 0-8218-6012-7, LC 87-1307 ISSN 0731-1036 mathematicians, this book requires a background 472 pages (softcover), June 1987 of graduate study in number theory and modular Individual member 132, List price $54, functions and will provide readers with a survey Institutional member $43 of current research topics in number theory. The To order, please specify CMSAMS/7NA papers range over a variety of areas, including local and global number fields, L-series, modular forms,

Shipping/Handling: 1st book S2. each additional S1, maxim12m S25; by air, 1st book SS, each additional S3, maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-9930, or call toll free 800-556-7774 to charge with VIsa or MasterCard

FEBRUARY 1988, VOLUME 35, NUMBER 2 337 Critical, Historical, or Expository Theses Supplementary List

The list below supplements the list pub­ Massachusetts Inst of Tech New Jersey lished on pages 1305-1306 of the De­ cember 1987 Notices. These additional de­ Management Science * Rutgers Univ partments gave affirmative responses to Statistics Ph.D. the question: Will your department accept a critical, historical or expository thesis Michigan of sufficiently high quality for the Ph.D. Michigan State Univ New York degree? D.A. degree? or other degree? Ph.D. Affirmative responses to this question are Mathematics Adelphi Univ listed below. Mathematics and Montana Computer Science Ph.D.,D.A. California Montana State Univ Mathematical Sciences Ed. D. Canada Stanford Univ Univ of Western Ontario Computer Science Ph.D. Applied Mathematics Ph.D. *Judgement of quality of thesis at the Massachusetts discretion of a committee of three faculty. Harvard Univ Statistics Ph.D.

Postdoctoral Positions Research or Research/Teaching 1988-1989 Supplementary List

The list below supplements the list pub­ Maryland Texas lished on pages ·1307 -1308 of the Decem­ ber 1987 Notices. The first number refers Johns Hopkins Univ Univ of Texas at Arlington to the total number in the department. The Biostatistics Mathematics 4:2 second number following the colon is the number available for 1988-1989. An aster­ isk is used to indicate that no information Massachusetts Virginia was supplied by the department. Harvard Univ Hampton Univ Statistics 1:0 Mathematics 1:1 California Michigan Wisconsin Stanford Univ Computer Science 4:* Michigan State U niv Univ of Wisconsin, Madison Univ of California, Santa Cruz Mathematics 4:2 Statistics Mathematics 19: 19 Ohio Canada Florida Kent State Univ Univ Laval Univ of Florida Mathematical Sciences 30:15 Mathematiques, Statistique, Mathematics and Actuariel University of Western Ontario Applied Mathematics 1:*

338 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Foreign Language Requirement for Ph.D. Supplementary List

The list below supplements the list pub- Maryland Ohio lished on pages 1309-1312 of the Decem- ber 1987 Notices. These additional depart- Johns Hopkins Univ Kent State Univ ments gave affirmative responses to the question: Does your department have, as Biostatistics 1 Mathematical Sciences a requirement for Ph.D., reading know!- edge of a foreign language? How many? one or two? Affirmative responses to this Massachusetts Wisconsin question are listed below. A dash is used to indicate that no information was sup- Harvard Univ Marquette Univ plied by the department. Statistics 1 Mathematics, Statistics and Computer Science 2 Michigan California Canada Michigan State Univ Univ of California, Santa Cruz Mathematics 2 Univ Laval Mathematics Univ of Michigan Mathematiques, Statistique, 1 Statistics and Actuariel Florida Wayne State Univ Univ of Florida Mathematics 2 Mathematics New Jersey Indiana Stevens Inst of Tech Indiana Univ Pure and Applied Mathematics 1 Computer Science

FEBRUARY 1988, VOLUME 35, NUMBER 2 339 Classified Advertisements

SUGGESTED USES for classified advertising are books or lecture notes for sale, books being MATH TEACHER sought, positions available, exchange or rental of houses, and typing services. QUALIFIED ETHNIC MINORITIES ARE THE 1988 RATE IS $.85 per word with a minimum of $42.50. The same ad in 6 consecutive ENCOURAGED TO APPLY issues is $4.00 per word. The same ad in 10 consecutive issues is $7.00 per word. Type will be set solid unless centering and spacing are requested. A centered line of any length SUNY Plattsburgh has a vacancy in the or the equivalent in white space is $10.00 (one-time charge). A word is defined as a group Math Department for September 1988. of characters with space at each end. Prepayment is required of individuals but not of The position is full-time tenure-track at institutions. For an additional $10.00 charge, announcements can be placed anonymously. ranks of all levels. Correspondence will be forwarded. Primary responsibility is undergradu­ DEADLINES are listed on the inside front cover. ate teaching, research and service to the U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, College. religion or national origin. "Positions Available" advertisements from institutions outside the Qualifications: Ph.D. in mathematics U. S. cannot be published unless they are accompanied by a statement that the institution or statistics required. does not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific wording may be found following the Classified Advertisements in the January and SUNY Plattsburgh is a public four­ July/August issues of the Notices. year college with approximately 5600 SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians undergraduates and 11 0 math majors. are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and We will start to consider applications speak to Paula Montella for further information. on January 20, 1988 and will accept SEND AD AND CHECK TO: Advertising Department, AMS, P.O. Box 6248, Providence, applications until position is filled. Rhode Island 02940. Individuals are requested to pay in advance, institutions are not required Submit letter of application, current to do so. resume and three current letters of reference to: Chairman, Search Committee POSITIONS AVAILABLE Harvey Mudd College Department of Mathematics Department of Mathematics SUNY Plattsburgh DIRECTOR, SCHOOL A tenure track position in the mathe­ Box 1494 OF MATHEMATICS matics department is available at the Plattsburgh, New York 12901 GEORGIA INSTITUTE SUNY IS AN EQUAL OPPORTUNITY/ OF TECHNOLOGY Assistant Professor level. Qualifications include a Ph.D. in mathematics and a AFFIRMATIVE ACTION EMPLOYER We are seeking a person of professo­ strong interest in research and in un­ rial rank who has a record of research dergraduate teaching. Responsibilities excellence and is desirous of directing include teaching, research, curriculum McMASTER UNIVERSITY an ambitious mathematics department development, and possibly supervision DEPARTMENT OF with a faculty of about 45. Please ad­ of industrially-sponsored projects in the MATHEMATICS & STATISTICS dress inquiries and a resume to: Director Mathematics Clinic program pioneered Search Committee, School of Mathe­ by the college. Harvey Mudd College, The Department of Mathematics & Sta­ matics, Georgia Institute of Technology, one of the nation's most selective un­ tistics, McMaster University, invites ap­ Atlanta, GA 30332. Georgia Institute of dergraduate colleges, offers degrees plications for a tenure track Assistant Technology is a Unit of the University in mathematics, engineering, chemistry, Professorship starting July 1 , 1988. System of Georgia and is an Equal and physics. The forty mathematicians Candidates should have a Ph.D. and Opportunity and Affirmative Action Em­ and computer scientists at the five Clare­ proven research ability in some area of ployer. mont Colleges and the Claremont Grad­ Mathematics related to Analysis, as well uate School together with the site in as capability in teaching. Salary based Southern California provide an attractive on qualifications and experience. This POST-DOCTORAL POSITION IN professional setting. There are strong position is subject to final budgetary STOCHASTIC ANALYSIS active research groups in several areas approval. of pure and applied mathematics, espe­ In accordance with Canadian Immi­ The Department of Mathematics at cially Differential Equations, Algebra, and gration requirements, in the first stage Carnegie Mellon University expects to Functional Analysis. The computer facil­ of this competition priority is given to have a one-year post-doctoral position ities at the college are outstanding and Canadian Citizens and permanent resi­ in stochastic analysis beginning in the the mathematics department operates dents. fall of 1988. To apply, send a curricu­ its own Computer Laboratory. Reply to: Please send curriculum vitae and lum vitae, a brief description of your Robert L. Borrelli, Mathematics Depart­ arrange for three letters of reference to: research interests, and have three let­ ment, Harvey Mudd College, Claremont, I. Hambleton, Chairman ters of reference sent to Prof. Steven CA 91711, 714-621-8023. An equal op­ Mathematics & Statistics E. Shreve, Department of Mathematics, portunity/affirmative action employer. McMaster University Carnegie Mellon University, Pittsburgh, Hamilton, Ontario PA 15213. Carnegie Mellon is an equal LSS 4K1 Canada opportunity/affirmative action employer.

340 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE - UNIVERSITY OF NORTH FLORIDA THE AMERICAN UNIVERSITY Department of Mathematical Sciences ASSISTANT PROFESSORS MATHEMATICAL SCIENCES of MATHEMATICS DEPARTMENT Applications are invited for anticipated THE UNIVERSITY OF TEXAS AT tenure-track positions at the Assistant Two positions available for the 1988- EL PASO and Associate Professor levels. Candi­ 1989 academic year as Assistant Profes­ CHAIRPERSON SEARCH dates must have a Ph.D. in mathemat­ sors of Mathematics, one tenure track, ics or statistics, strong teaching ability, one temporary in the Department of Applications are invited for the position and continuing scholarly activity. Can­ Mathematics and Statistics. of Chairperson of the Mathematical Sci­ didates for Associate Professor must Qualifications: For the tenure track po­ ences Department of the University of sition a Ph.D. in Mathematics; evidence Texas at El Paso. The Chairperson is have a record of outstanding teaching and substantial research. Duties include of scholarship and research in numeri­ responsible to the Dean of the College teaching major, graduate, and service cal analysis or real or complex analysis of Science for the administration of and (other areas will be considered). For the planning for the department. The Univer­ courses. The Department offers the B.A. temporary position a Ph.D. in Mathemat­ sity is seeking a mathematician or statis­ and B.S. degrees in mathematics and ics or Mathematics Education; evidence tician, with a broad view of the discipline, statistics and the M.A. degree with tracks in mathematics, statistics, and computer of scholarship and research. an outstanding research record and a Responsibilities: Undergraduate dedication to excellence in teaching, to science. The university, a growing insti­ teaching, advising, and university ser­ provide leadership to a department with tution in the State University System, cur­ vice. 25 full-time faculty members. Candidates rently has over 7000 students enrolled. Send resume, three letters of recommen­ Salary competitive and commensu­ should also have previous administrative rate with experience. Position available experience, a record of leadership and dation, and transcript by February 15, August 1988, subject to final budgetary the ability to communicate effectively 1988, to Leonard J. Lipkin, Chairperson, approval. Send curriculum vitae and across the campus. The new chairper­ Department of Mathematical Sciences, names of three references by March 1 , son will be instrumental in developing University of North Florida, Jacksonville, to Austin Barron, Chair, Department of and expanding the research capabilities Florida 32216. An EOE/AA employer. Mathematics and Statistics. The Ameri­ of the department. can University, 4400 Massachusetts Ave. The Mathematical Sciences Depart­ The NW, Washington, DC 20016 ment offers the B.S. and B.A. degrees in University of California The American University is an EEO 1AA Mathematics and the B.S. degree in Ap­ Department of Mathematics University. Women and minorities are en­ plied Mathematics. At the graduate level and Computer Science couraged to apply. the department offers the M.S. degree in Mathematics and in Statistics and also Applications are invited for one or the M.A.T. degree for high school math­ more Visiting Professorships beginning ematics teachers. There are about 55 in September 1988. Positions are funded THE UNIVERSITY OF ~ndergraduate and 20 graduate majors in the Assistant Professorship salary MISSOURI-ST. LOUIS 1n the department. range and have a maximum duration of Applications are invited for a tenure­ Candidates must possess a doctorate two years. Candidates possessing the track assistant professorship in statis­ in Mathematics or Statistics. Salary is Ph.D. and significant accomplishments tics. Qualifications include a Ph.D. de­ competitive and will be commensurate or high potential in both teaching and research are sought. No restriction as gree, evidence of good teaching skills, Y:'ith the successful candidate's expe­ and strong research potential. The pri­ nence. The position will be available to area of specialization in Mathemat­ mary duties of the position are teaching from September 1, 1988 and, in order ics or Computer Science. Minority and women candidates are particularly urged and conducting a high quality research t? be assured of consideration, applica­ program in statistics. The current teach­ tions should be received by February 15, to apply. ing load is two courses per semester. Applications (including a resume Applicants should send a curriculum 1988. The ability to teach one or more com­ listing names, addresses, and telephone· vitae and see that at least three letters puter science courses would be advan­ numbers of at least three references) of recommendation are sent to: tageous to a candidate. Send resume should be submitted to: Chair and at least three letters of reference to Dr. James E. Nymann, Chair Computer Science Search Committee Grant Weiland, Chairman of the Search Mathematical Sciences Search Committee, Department of Mathemat­ Committee Department of Mathematics and Computer Science ics and Computer Science, University of University of Texas at El Paso Missouri-St. Louis, 8001 Natural Bridge El Paso, Texas 79968-0514 University of California Riverside, CA 92521 Road, St. Louis, Missouri 63121-4499. An Equal Opportunity1 Affirmative Action The University of Missouri-St. Louis is Institution. University of California, Riverside, is an Affirmative Action/Equal Opportunity an Equal Opportunity1 Affirmative Action Employer. Employer.

FEBRUARY 1988, VOLUME 35, NUMBER 2 341 Classified Advertisements

POSITIONS AVAILABLE University of Toronto Rice University Department of Mathematics Department ST. MARY'S of Mathematical Sciences COLLEGE OF (Opening CALIFORNIA· for Tenure-Track Applied Applications are invited for a tenure­ Analysis) Department of Mathematical Sciences stream position in Applied Mathematics Moraga, CA 94575 at the level of Assistant Professor. This The Department of Mathematical Sci­ position Two tenure-track assist. professorships is subject to final budgetary ences seeks applications for a tenure­ approval and is to track opening beginning fall 1988. A Ph.D. and a com­ begin July 1 , 1988. in Applied Analysis for the The University mitment to both liberal arts education of Toronto encourages ~all, 1988. Applications at all levels and both men and women 1n all areas of Applied and continued research are expected of to apply. Analysis will be Candidates considered, candidates to join a young and growing must have a Ph.D. and however preference will be demonstrate given department. For 1 of the 2 positions, clear strength in both re­ to junior applicants with interests in search partial differential preference will be given to candidates and teaching. Priority will be given equations, particularly to candidates f~uid dyna.mics with computer science expertise. St. of exceptional promise andjor wave propaga­ working on fundamental tiOn. Candidates Mary's is a coeducational college of problems in are sought with demon­ their field. strated potential about 3300 students, located 10 miles in both teaching and Applicants should research. Applications east of Berkeley. Current salary range is send their complete should be sub­ $26,234-$31 ,223. curriculum vitae, together with a list of mitted to Professor William W. Symes, publications Department Send resume and 3 letters of recom­ and arrange to have at least of Mathematical Sciences three recent P.O. Box mendation, at least 1 of which must letters of reference sent 1892, Houston, Texas 77251~ directly to: 1892. Application materials speak to teaching ability, to J. R. should in­ clude a statement Sangwine-Yager, Chair, Dept. of Math­ Professor D. R. Masson of research interests Associate and the names of ematical Sciences, P.O. Box 517, St. Chairman at least three indi­ viduals Mary's College, Moraga, CA 94575. Department of Mathematics to serve as references. (Rice is University an Affirmative Deadline, February 5, 1988. An EO/AA of Toronto Action/Equal Opportunity employer. Toronto, Canada M5S 1A1 Employer.) To insure full consideration, applications and letters of reference should be re­ ceived by February 15, 1988. NORTH TEXAS STATE UNIVERSITY (THE UNIVERSITY 0F NORTH The TEXAS) University of California The Mathematics Department antici­ Department of Mathematics pates authorization to make several new and Computer Science MATHEMATICS FACULTY faculty appointments for 1988-89. Salary Applications are invited for a tenure­ Two tenure track positions available and rank will be commensurate with track or tenure position in Computer September, 1988. One position will most qualifications and experience. The focus Science beginning Fall1988. Candidates likely be filled by a statistician, while of the department is on pure and appli­ must have demonstrated excellence in the second one will be in the area of cable mathematics. Hence we seek to appoint research and teaching. Research spe­ applied mathematics. Applicants must mathematical research scholars cialities in all areas of Computer Science possess Ph.D. A strong commitment to of the highest possible caliber who will will be considered but we are particularly undergraduate teaching required. Estab­ also be very good teachers. interested in research areas in Computer lishment of an active research program North Texas State University has been Systems and Computer Methodology expected. Current reslrtirch interests in designated by the State Legislature as and Applications. The position is open the Department include discrete math­ an emerging national research university, as to the level of appointment. ematics, statistics, differential geometry and its name will become the University Applicants should send a curriculum and topology. Computer facilities are of North Texas in May, 1988. Interested vitae and see that at least three letters available for teaching and research pur­ persons are asked to see our full page ad of recommendation are sent to: poses. Salary and rank are based on in the December issue of the No­ Chair background and experience. Please sub­ tices for additional information about the Computer Science Search mit letter of application, curriculum vitae department and the University. Committee and three (3) letters of reference con­ Applicants should submit a vita and Department of Mathematics and cerning teaching and research abilities letters of reference to Dr. John Ed Allen, Chairman, Computer Science by February 15, 1988 to: E. Phadia, Department of Mathematics, University of California Chairperson, Department of Mathemat­ North Texas State University, Denton, Riverside, CA 92521 ics, WILLIAM PATERSON COLLEGE, Texas 76203-5116. University of California, Riverside, is Wayne, New Jersey 07470. WPC is NTSU IS AN EQUAL OPPORTUNITY/ an Affirmative Action/Equal Opportunity an Equal Opportunity I Affirmative Action AFFIRMATIVE ACTION EMPLOYER. Employer. Employer.

342 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE SHEPHERD COLLEGE Yale University SHEPHERDSTOWN, WV 25443 Department of Mathematics UNIVERSITY OF MASSACHUSETTS AT AMHERST Ph.D. required for tenure-track appoint­ YALE UNIVERSITY anticipates making oept. of Mathematics & Statistics ment beginning fall 1988. Commitment a tenured appointment (Professor or to quality undergraduate teaching at Associate Professor) in pure mathemat­ Applications are invited for one or more a growing, competitive, undergraduate, ics in 1988. In addition to distinguish­ anticipated visiting position~ ~urin~ the state-supported college with over 3900 ing themselves in research, candidates academic year 1988-89. Pnonty w111 be students, located on the banks of the should be recognized as successful given to candidates whose research Potomac River, 90-minute drive from teachers of graduate and undergraduate interests interact broadly with current Washington, DC, and close to an East students. Yale is an Equal Opportu­ faculty interests in the department. Rank Coast "software corridor." Successful nity/Affirmative Action Employer. and salary commensurate with qualifica­ candidate will teach a variety of math­ Submit vita, copies of publications, tions and experience. Submit curriculum ematics courses in a department of and names of three references (not vitae and have three letters of recom­ seven faculty; secondary field in engi­ letters) to mendation sent to: Hiring Committee, neering or an applied mathematics area Professor R. R. Coifman, Dept. of Mathematics & Statistics, Led­ is an advantage. Applications reviewed Chairman erie Graduate Research Tower, U. of beginning February 15 and received un­ Department of Mathematics Massachusetts, Amherst, MA 01003. For til position is filled. Send curriculum Yale University full consideration, applications should be vitae and have three letters ·of recom­ Box 2155, Yale Station complete by April 1, 1988. The Univer­ mendation sent to: Dr. Donald Henry, New Haven, Connecticut 06520 sity of Massachusetts is an Affirmative Shepherd College, Shepherdstown, WV, Closing date for applications is Action/Equal Opportunity Employer, and 25443. AA/EOE. February 28, 1988. encourages women and minorities to apply.

University of Wyoming NATIONAL SCIENCE Rocky Mountain Mathematics Consortium FOUNDATION (NSF) Regional Summer School Washington, D.C. TOPICS IN COI\ffiiNATORICS NSF's Office of College Science Instrumen­ July 18- August 5, 1988 tation (proposed change in organizational title: Topics of current interest in combinatorics will be covered: latin squares Office of Undergraduate Science, Engineering including the solution of the Evans' conjecture; (0,1)-matrices and various and Mathematics Education) is seeking qualified packing and covering problems connected with them, including problems candidates for three positions: (1) Program that arise in coding theory where the matrices are considered to be over the Director, mathematics, (2) Program Director, biology and (3) Program Director, chemistry. binary field; classes of combinatorially defined matrices; doubly stochastic These positions are excepted from the compe­ matrices including their application to satellite communication and the titive civil service and will be filled on a per­ graph isomorphism problem; permanents of (0,1)-matrices (counting per­ manent, rotator, or temporary basis, in early mutations with restricted positions, rook polynomials) and their possible 1988. The salary range is from $45,763 to evaluation by determinants of (0,1,-1)-matrices, with application to sign­ $72,500 per annum. solvable linear systems; permanents of doubly stochastic matrices, includ­ The Program Director is assigned a program ing the solution of the van der Waerden conjecture and generalizations. In with responsibility for providing leadership in each area progression will be made to some unsolved problems of research undergraduate education in his/her respective discipline; and must possess sufficient teaching interest. experience to decide whether a proposed project PREREQUISITES: No previous graduate course in combinatorics is re­ is likely to meet the needs of students and faculty. quired, but some basic knowledge of combinatorics, linear algebra, and Applicants must have a Ph.D. or equivalent abstract algebra is necessary. experience in mathematics, biology or chemistry. LECTURERS: Richard A. Brualdi, Department of ::'\fathematics, Univer­ In addition, 6 or more years of successful sity of Wisconsin, ::'\fadison, Wisconsin, and Vera Pless, Department of experienCE! as a science faculty member involved in teaching and research, and/or managerial Mathematics, University of Illinois, Chicago, Illinois. experience is required. ADl\-fiSSION AND SCHOLARSHIPS: Entry into the summer school is Applicants should send resume or SF-171, restricted, but is without charge to those who are qualified and are admit­ Application for Federal Employment to: National ted. A limited number of scholarships, covering living costs, are available Science Foundation, Division of Personnel and for qualitied graduate students. For further information and application Management, 1800 G St., NW., Washington, DC forms, please write to: 20550. Attn: Catherine Handle. For further information call 202/357-9529. Hearing impaired Professor A. Duane Porter- ::'\fathematics Department individuals should call TDD 202/357-7492. NSF Box 3036- University of Wyoming is an Equal Opportunity Employer. Laramie, Wyoming 82071

FEBRUARY 1988, VOLUME 35, NUMBER 2 343 Classified Advertisements

POSITIONS AVAILABLE Institute for Computer Applications in KEENE STATE COLLEGE Science and Engineering (ICASE). A Keene, New Hampshire 03431 THE UNIVERSITY OF limited number of visiting appointments MISSOURI-ST. LOUIS are available for both junior- and senior­ Fall 1988. Applications are invited for level researchers at the Institute for at least one tenure-track position at the The Department of Mathematics and assistant/associate professor level. Ap­ Computer Science seeks applicants for Computer Applications in Science and Engineering (!CASE) which is operated plicants must have a clear commitment two, possibly three tenure-track posi­ to excellence in teaching and hold a by the Universities Space Research As­ tions in computer science beginning in Ph.D. in mathematics. Candidates who Fall1988. sociation. !CASE serves as a center for interaction between Langley Research are in the late stages of their dissertation It is our intention to fill these positions will be considered. Prior full-time college with people having overlapping research Center staff and the academic commu­ nity in the areas of applied and numerical teaching experience preferred. The se­ interests that are also shared by one or lection procedure will begin January 20 mathematics, applied computer science, more members of our present faculty. and continue until position(s) are filled. and development of mathematical mod­ Areas that are presently under consid­ Applicants should submit a current eration are Algorithms and Complexity, els in a variety of application areas. Applications for partial support while on resume and three letters of reference to: Database Design, Numerical Analysis, Gaynelle Pratt sabbatical leave are encouraged as are and Denotational Semantics of Program­ Personnel Office applications from Ph.D.'s for two-year re­ ming Languages. Keene State College newable appointments. Inquiries should Applicants who have an active in­ Keene, NH 03431 be addressed to the Director, ICASE, terest in both teaching and research An EOE employer. are encouraged to apply. Please send Mailstop 132C. NASA Langley Research all applications, resumes and letters of Center, Hampton, Virginia 23665. An reference to Jerrold Siegel, Chairman, Equal Opportunity Employer. Department of Mathematics and Com­ puter Science, University of Missouri-St. Louis, 8001 Natural Bridge Road, St. Courant Institute of UNIVERSITY OF Louis, Missouri 63121-4499. The Univer­ Mathematical Sciences HOUSTON-CLEAR LAKE DIVISION OF MATHEMATICS sity of Missouri-St. Louis is an Equal Op­ Applications are invited for visiting posi­ AND SYSTEM DESIGN portunity I Affirmative Action Employer. tions and staff researchers in the fields of applied mathematics, numerical anal­ Applications are invited for a tenure ysis, and scientific programming, espe­ track position at the rank of Assistant OAKLAND UNIVERSITY cially as related to parallel processing. Professor or above, commencing Au­ Chairperson, Department of Short term positions for visiting faculty gust 15, 1988. Applicants should have a Mathematical Sciences as well as multiyear ~ositions for staff Ph.D. in any field of mathematics with· Applications and nominations are invited researchers are available. competence to teach courses in our un­ for the position of Chairperson. Minimum Research areas currently active at dergraduate computer science program. qualifications: earned PhD in a mathe­ Courant include linear algebra, fluid dy­ The division is especially ·interested in matical science; ten years of post-PhD namics, Monte Carlo methods, inverse establishing a group in computational academic experience (or comparable); problems, simulation of computers and mathematics over the next five years. substantial research record and an active networks, and parallel software. This last Candidates should have a strong com­ commitment to research; demonstrated area includes the LAPACK project, de­ mitment to teaching and scholarship. academic or professional leadership ex­ veloping new versions of the UNPACK The Division of Mathematics offers the perience. The department has about 30 and EISPACK libraries to be portable B.A., B.S., and M.S. degrees in mathe­ regular faculty members and 20 part­ and efficient across all current super­ matics. Application, detailed resume and time faculty and graduate assistants. An computers. This is a joint project with three letters of recommendation should applicant should send a letter, vita and Jack Dongarra at Argonne National Lab­ be send to: the names, addresses and telephone oratory. Michael J. Mezzino, Jr., Chair numbers for at least three references. Interested parties should contact ei­ Division of Mathematics and Send nominations and applications to ther Prof. Malvin H. Kalas (kalos@nyu. System Design Professor James H. McKay, Chairper­ arpa, [email protected], 212-998-3342) University of Houston-Clear Lake son Search Committee, Department of or Prof. James W. Demmel (demmel 2700 Bay Area Blvd. Mathematical Sciences, Oakland Uni­ @acf8.nyu.edu, 212-998-3470), for fur­ Houston, Texas 77058 versity, Rochester Ml 48309-4401. To ther information. Mail may be addressed AFFIRMATIVE ACTION/EQUAL OPPOR­ ensure full consideration, nominations to Courant Institute, New York Univer­ TUNITY EMPLOYER or applications should be received by sity, 251 Mercer Str., New York, NY MINORITIES AND WOMEN ARE EN­ February 15, 1988. OU is an AA/EO 10012. New York University is an equal COURAGED TO APPLY. employer. opportunity employer.

344 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

AVAILABLE - POSITIONS The Mathematics Department at NORTHEAST MISSOURI Wheaton College invites applications for STATE UNIVERSITY ROLLINS COLLEGE, DEPT OF a two-year tenure-track assistant pro­ DIVISION OF MATHEMATICS MATHEMATICAL SCIENCES, fessorship beginning September 1988. AND COMPUTER SCIENCE Winter Park, FL 32789 Requirements are the Ph.D. in the math­ The division seeks applicants for four one tenure track position, preferably at ematical sciences, a commitment to qual­ or more tenure-track positions available the Assistant Professor level, is available ity teaching, and active scholarly activity. August, 1988. Candidates in the areas tor Sept 1988. The area of specializa­ Preferred areas: analysis, computer sci­ of algebra, analysis, applied mathemat­ tion is open, but a doctorate, strong ence. Send a letter of application, vita, ics (especially modeling) and statistics commitment to teaching undergraduates transcripts, and three letters of recom­ are of particular interest. Teaching loads and continued professional activity are mendation to: Rochelle Leibowitz, Chair, for faculty engaged in research aver­ required. The Department offers majors Mathematics Department, Wheaton Col­ age 9 hours per semester. A successful in mathematics and computer science lege, Norton, MA 02766. AA/EOE. candidate must be able to contribute and an ability to teach in both areas is significantly to the division's teaching viewed as a plus. The Department also and research program including sub­ has a strong interest in the instructional stantial interaction with undergraduate use of computers, particularly computer UNIVERSITY OF THE WEST INDIES majors and graduate students. North­ algebra systems. The teaching load is CAVE HILL CAMPUS-BARBADOS east is a public, liberal arts and sciences 8-10 hours per week. Winter Park, a university with selective admissions and are invited for the posts delightful city of 40,000, is located in Applications an enrollment of over 6,000. Applica­ Lecturer /Lecturer and Lec­ the greater Orlando area. To insure of Senior tions will also be accepted for about Lecturer in Computer full consideration, applications must be turer1 Assistant four renewable, temporary instructor­ in the Department of Mathe­ complete by 15 Feb 1988. Send resume, Science ships. Candidates for these positions are at the Cave Hill Campus of the transcripts and 3 letters of recommen­ matics not required to hold a Ph.D. Teaching of the West Indies. dation (at least one of which must University load averages 12 hours per semester. Lecturer/Lecturer: Appli­ comment on teaching) to: David Kurtz, 1) Senior A complete application consists of a be competent to teach Chair. Please indicate availability for in­ cants should letter, resume, transcripts of all under­ Languages ii) Design terviews at the AMS-MAA meetings in i) Programming graduate and graduate study and three Algorithms AND/OR Atlanta. Rollins is committed to equal and Analysis of letters of reference. These should be Networks ii) Data Base opportunity I affirmative action. i) Computer sent to: Systems. Other areas of Management Dr. Lanny Merely, Head operating systems; soft­ interest include Division of Mathematics and interactive computer Applications are invited for tenure-track ware engineering; Computer Science and simulation; com­ positions at the Assistant or Associate graphics; modelling Northeast Missouri State compiler design and Professor level beginning August, 1988. puter architecture; University Preferences will be given to applicants numerical analysis. Kirksville, MO 63501 areas of Lecturer: Ap­ in numerical analysis or other 2) Lecturer1 Assistant EQUAL OPPORTUNITY/ AFFIRMATIVE be competent to teach applied mathematics and in mathemat­ plicants should ACTION EMPLOYER ics education. Responsibilities will in­ two or more of the above areas but appli­ clude a maximum three course, 12-hour cants with other active interests in Com­ teaching load and continuing research puter Science will also be considered. activity. Internal grants for support of Successful applicants to assume duties WELLESLEY COLLEGE research and other scholarly activities by September 1 , 1988 or as soon as WELLESLEY, MASS. 02181 SALARY SCALES: are available. Selection will be based on possible thereafter. Temporary (or visiting) position for 1988- x 1644- evidence of teaching effectiveness and Senior Lecturer: BDS $50,712 89 or 1988-90. Requirements include a X 1776-69,456 research potential. A Ph.D. in Mathemat­ 60,576x 1776-65,904 (B) Ph.D. in Mathematics, excellence in and ics is required. Salary will be competitive. p.a. Lecturer: BDS $38,208,x1644-48,072 commitment to mathematical research p.a. Assistant Lec­ Screening will begin January 1 ,1988 and (B)x1644-57,936 and undergraduate teaching in a lib­ p.a. Detailed continue until positions are filled. Send turer:BDS $31,548-34,644 eral arts environment. Applicants should and resume and three letters of recommen­ applications including qualifications send a curriculum vitae and at least three dation to: experience, date of birth, marital status letters of recommendation that address Gary Jones, Chairman and the names and addresses of three both teaching and research. Contact as Search Committee referees should be sent as soon Chair, Department of Mathematics. Department of Mathematics possible to the CAMPUS REGISTRAR, Wellesley College is an equal opportu­ Murray State University UNIVERSITY OF THE WEST INDIES, nity affirmative action employer and par­ Murray, KY 42071 P.O. BOX 64, BRIDGETOWN, BARBA­ ticularly encourages applications from Murray State University is an EO/AA DOS. women and minority candidates. employer.

FEBRUARY 1988, VOLUME 35, NUMBER 2 345 Classified Advertisements

POSITIONS AVAILABLE UNIVERSITY OF NORTH William Paterson College CAROLINA AT CHARLOTTE Mathematics Department UNIVERSITY OF NORTH FLORIDA DEPARTMENT OF Department of Mathematical Sciences . COMPUTER SCIENCE Two tenure track positions available September, 1988. One position will most Applications are invited for anticipated Several tenure-track positions in all ar­ likely be filled by a statistician while the tenure-track positions at the Assistant eas at Assistant, Associate, or Full second one will be in the area of applied and Associate Professor levels. Candi­ Professor level in Computer Science/ mathematics. Applicants must possess dates must have a Ph.D. in mathemat­ Computer Engineering. Salary and rank the Ph.D. degree. A strong commitment ics or statistics, strong teaching ability, dependent on qualifications and expe­ to undergraduate teaching required. Es­ and continuing scholarly activity. Can­ rience. Salary is competitive. Ph.D. in tablishment of an active research pro­ didates for Associate Professor must CS/CE preferred. Ph.D. in a related gram is expected. Current research in­ have a record of outstanding teaching area to CS/CE considered. Applications terests in the Department include dis­ and substantial research. Duties include accepted until the positions are filled. crete mathematics, statistics, differential teaching major, graduate, and service The Department of Computer Science is geometry, and topology. Computer fa­ courses. The Department offers the B.A. housed in the College of Engineering and cilities are available for teaching and and B.S. degrees in mathematics and offers both undergraduate and graduate research purposes. Salary and rank are statistics and the M.A. degree with tracks degrees in computer science. Active re­ based on background and experience. in mathematics, statistics, and computer search areas in the department include An additional one year appointment is science. The university, a growing insti­ artificial intelligence, computer architec­ also available at the rank of Instructor. tution in the State University System, cur­ ture, computer visionjrobotics, database For this position, a Master's degree in rently has over 7000 students enrolled. systems, data communication, theoreti­ mathematics is required. Submit a letter Send resume, three letters of recom­ cal CS, VLSI design. On-campus Ph.D. of application, current vitae, and three mendation, and transcript by March 15, level research and study are available letters of reference concerning teaching 1988, to Leonard J. Lipkin, Chairperson, through cooperation with other partici­ and research abilities .by February 15, Department of Mathematical Sciences, pating institutions of the Microelectronics 1988 to E. Phadia, Chairperson, Depart­ University of North Florida, Jacksonville, Center of N.C. (MCNC). A wide variety ment of Mathematics, William Paterson Florida 32216. An EOE/ AA employer. of excellent computing facilities includ­ College, Wayne, New Jersey, 07470. ing IBM, VAX, Burroughs, Harris, Xerox, WPC is an Equal Opportunity I Affirmative Sun, and others are available to support Action Employer. UNIVERSITY OF CENTRAL FLORIDA educational and research activities. Also, Department of Mathematics as a participant in MCNC, UNCC has ac­ cess to state-of-the-art computing, VLSI WILKES COLLEGE Applications are invited for a tenured design, and fabrication facilities. Char­ Faculty Position track and visiting positions at Associate, lotte is the largest city in the Carolinas The Department of Mathematics and Assistant Professor or instructor level with excellent housing, good schools Computer Science invites applications beginning in August 1988. Ph.D. de­ and mild climate. for a tenure-track position beginning fall gree with strong research potential or Vita, transcript and four letters of 1988. PhD (or ABO) in MIS or computer experience and dedication to teaching reference should be sent to Chairperson, science or a PhD in mathematics and required for appointment at Associate Faculty Search Committee, Department substantial interest in computing is re­ or Assistant Professor level. Candidate of Computer Science, The University quired. Teaching responsibilities include with substantial completion of Ph.D. re­ North Carolina at Charlotte, Charlotte, a mix of mathematics and computer sci­ quirements will be considered for the NC 28223. ence, both undergraduate and graduate. instructor level. The positions are un­ UNCC is an EOE/AA Employer. Wilkes College has 1750 undergradu­ restricted as to area of specialization ates; the department has 13 · full-time within mathematical sciences. Candidate faculty and 160 majors. Computing facil­ should send a detailed resume and ar­ WILLIAMS COLLEGE ities include a Data General MV1 0000, range to have at least three letters of DEPARTMENT OF MATHEMATICS an H P3000-6800 and about 100 mi­ recommendation and a transcript sent Anticipated opening for a three-year ap­ crocomputers. Send resume and three to: Dr. Lokenath Debnath, Department pointment. Statistics or related field pre­ letters of recommendation to Richard E. of Mathematics, University of Central ferred. Start Fall '88 with Ph.D. or equiv­ Sours, Chairman, Department of Math­ Florida, Orlando, Florida 32816, post­ alent. Includes long-term possibilities. ematics and Computer Science, Wilkes marked by April 15, 1988. The University Teach 5 courses per year plus alternate College, Wilkes-Barre, PA 18766. Wilkes is an equal opportunity affirmative action Januaries. Send vita and reference let­ College is an Affirmative ActionjEqual employer. As an agency of the State of ters to Robert M. Kozelka, Chaircreature, Opportunity Employer. Florida, UCF makes all application mate­ Dept. of Mathematics, Williams College, rials and selection procedures available Williamstown, MA 01267. Equal Oppor­ for public review. tunity1 Affirmative Action Employer.

346 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE - Northern Michigan University DePaul University Department of Mathematics THE WICHITA STATE UNIVERSITY, The Department of Mathematics and Chicago, Illinois 60614 WICHITA, KANSAS 67208 Computer Science invites applications PROFESSOR STEPHEN W. BRADY, for two tenure-track positions in com­ A tenure-track position is available be­ SEARCH COMMITTEE CHAIRMAN puting. A Ph.D. in computer science or a ginning in September, 1988. The position DEPARTMENT OF MATHEMATICS AND Ph.D. in mathematics with significant ex­ will probably be at the assistant profes­ STATISTICS perience in computer science is required. sor level, but associate professors may Senior and Junior level tenure eligible All specialities will be considered. Inter­ apply. A PhD in mathematics is required. positions starting August, 1988. Special ests in the department include: heuristic Candidates should show potential for consideration given for Prob. and Stat., search, artificial intelligence, computer continuing mathematical research and POE, or Complex Analysis. All areas of graphics, and mathematical software. have a strong commitment to good applied mathematics C9f:!Sidered. Ph.D. NMU is primarily an undergraduate in­ teaching. The official teaching load is in Math. or Stat. required. Candidates stitution, and a commitment to teaching nine quarter courses/year, but a reduc­ expected to be active in research, par­ is an essential expectation of the posi­ tion to seven quarter courses/year for ticipate in doctoral program and have tion._ Research and professional activity sustained research is typical. Summer strong interest in teaching. Applicants are both encouraged and supported. teaching is often available. for Associate or Full Professor positions Applicants should send transcripts, Applicants should send a vita and 3-4 should have significant research record. three letters of recommendation and a letters of recommendation at least one Salary competitive. Send letter, detailed resume to Dr. Terrance L. Seethoff, De­ of which comments on their teaching to: resume and names of three references. partment of Mathematics and Computer Hiring Committee, Department of Math­ Assistant Professor candidates should Science, Northern Michigan University, ematics, 2323 N. Seminary, Chicago, arrange to have three reference letters Marquette, Ml 49855. NMU is an equal Illinois 60614. DePaul University is an sent. Deadline February 15, 1988, then opportunity, affirmative action employer. AA/EOE. monthly until positions filled. AA/EOE

: ~=:THE SALEM STATE COLLEGE U UNIVERSITY .... OF CALGARY R

FACULTY Position in the Division of POSITIONS Applied Mathematics The University of Calgary Department of Mathematics and MATHEMATICS: Assistant Professor, tenure-track. Ph.D. Statistics invites applications for a position in the Division of Applied and college-level teaching. experience required. Interest Mathematics. Preference will be given to applicants with expertise in research and publication desired. Position is nine-month, in areas of modern analysis which reinforce existing areas of research in the Division. The position is expected to be at the subject to availability of funding. Salary is open, highly Assistant Professor level and commences July 1, 1988. competitive, and commensurate with qualifications and ex­ peri~_nce. Se~d resume and letter of app.lication indicating In accordance with Canadian immigration requirements, priority pos1t1on des1red to: Affirmative Action Office Salem will be given to Canadian citizens and permanent residents of State College, Salem, MA 01970 by March 1, '1988. Canada. Applicants should send their complete curriculum vitae including SSC is an Equal Opportunity/Affirmative Action a list of publications and the names and addresses of three Employer and actively seeks the candidacy of references, prior to March 15, 1988, to: minorities and women. Dr. Eugene Couch Division of Applied Mathematics Department of Mathematics and Statistics S:llem State The University of Calgary 2500 University Drive N.W. College Calgary, Alberta, Canada T2N 1N4 The University of Calgary does not discriminate in its employment on a basis of color, age, sex, race, religion or national origin.

FEBRUARY 1988, VOLUME 35, NUMBER 2 347 Classified Advertisements

POSITIONS AVAILABLE ST. CLOUD STATE UNIVERSITY The mathematics department of the Col­ DEPARTMENT OF lege of William and Mary anticipates UNIVERSITY OF QUEENSLAND MATHEMATICS AND STATISTICS authorization for one or more tenure Equal Opportunity in Employment ST. CLOUD, MN 56301 track positions, at the assistant profes­ Policy is University sor level or above, to begin August 16, CHAIR OF COMPUTATIONAL The Department invites applications for 1988. Applicants should hold a Ph.D. MATHEMATICS three or more tenure track positions in mathematics and exhibit capability for DEPARTMENT OF MATHEMATICS at the rank of Assistant or Associate strong sustained research and a commit­ Professor to begin 9/6/88. One position The University is seeking a mathemati­ ment to effective teaching. Candidates requires specialization in mathematics cian with an outstanding research record whose research interests lie in matrix education, the other positions are open and with considerable experience in the analysis or a related specialization are to all areas of specialization. Applicants practical applications of mathematics. particularly encouraged to apply. Letters must have a commitment to under­ Specialisation is expected in at least of application accompanied by a curricu­ graduate education, excellent teaching one major area of applied computational lum vitae and names of at least three credentials, and a record of or strong mathematics such as numerical analy­ references should be addressed to: potential for scholarly and professional sis, operations research or mathematical Chair, Mathematics Search activity. A doctorate is preferred but programming. Committee ABDs are encouraged to apply. Send The Professor will lead the compu­ Department of Mathematics resume, graduate transcripts, and three tational mathematics group within the The College of William and Mary letters of reference to Gail Earles, Chair­ department and will be required to en­ Williamsburg, Virginia 23185 person. Applications will be accepted gage in teaching of undergraduates and Initial screening of applications will until position is filled; first screening is the promotion of research and postgrad­ begin February 15, 1988, and applica­ 2/1/88. St. Cloud State University is an uate studies. Consultation with industry tions will be accepted until the position(s} equal opportunity employer. is strongly encouraged. are filled. EOE/ AA The University provides prescribed travel and removal expenses, superan­ UNIVERSITY OF SOUTH CAROLINA nuation, housing assistance and special Department of Mathematics studies programs. The Center for Research in Scientific Salary: $A58,870 per annum. Closing Applications are invited for anticipated Computation at North Carolina State Uni­ date: 29 February 1988. Reference No. tenure-track faculty positions at all ranks. versity invites applications for a tenure 48187. Applications in all areas of mathemat­ track position in the area of scientific Additional information and applica­ ics will be considered; the Department computing. The successful candidate will tions forms are available from the Di­ particularly wishes to strengthen its pro­ have a mutually agreeable joint appoint­ rector, Personnel Services, University of grams in applied and computatio~al ment in the departments of mathematics Queensland, St. Lucia 4067, Queens­ mathematics. The Ph.D. degree or 1ts and computer science. All areas of sci­ land, Australia. equivalent is required, and all appoint­ entific computing will be considered. ments will be consistent with the De­ However, we especially solicit applicants partment's commitment to excellence in capable of research in parallel computing research and teaching at both the un­ and numerical linear algebra. Applicants Several tenure-track positions at all lev­ dergraduate and graduate levels. Faculty will be expected to receive a PhD. in ap­ els will be available beginning September research is strongly supported through or computer science 1988. Applicants showing significant re­ plied mathematics funding for visitors and travel, and ex­ before their fall 1988 appointment. They search accomplishments or exceptional cellent library and computing facilities. should have a strong interest in both re­ research promise, as well as evidence The Department operates its own VAX Resumes including of good teaching ability, are invited to search and teaching. computation center which will access a research interests along with names of apply. Initial tenure-track appointment is planned DEC high performance comput­ at least three references should be sent for four years. There is no restriction as ing complex to be installed by mid-1988. to field. In addition to a curriculum vitae, to A detailed resume containing a sum­ Carl Meyer, Director candidates should send a summary of Professor mary of research accomplishments and Center for Research in Scientific research plans, available preprints or re­ goals, and four letters of recommenda­ Computation prints, and have at least three reference tion sould be sent to: letters sent to: Box 8205 Dr. Colin Bennett, Chairman North Carolina State University Samuel Gitler, Chairman Department of Mathematics Mathematics Department Raleigh, NC 27695-8205 University of South Carolina status of non-US citizens University of Rochester Immigration Columbia, South Carolina 29208 application. NCSU Rochester, New York 14627 must be stated in the The University of South Carolina is an action An equal opportunity/affirmative ac­ is an equal opportunity/affirmative Affirmative Action/Equal Opportunity em­ employer. tion employer. ployer.

348 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE LAMAR UNIVERSITY, DEPARTMENT LECTURER, MATHEMATICS OF MATHEMATICS, Argonne National BOX 10047, BEAUMONT, TX 77710 Several one or two year appointments. Laboratory-Mathematics and Teach 18 credits of courses per year at Computer Science Division The Department of Mathematics of both graduate and undergraduate levels. Lamar University invites nominations and Do research and collaborate with other Argonne National Laboratory is seek­ applicants for a Department Head, start­ faculty members in areas of applied ing a research associate to partic­ ing August 25, 1988. Minimal qualifica­ mathematics, including differential equa­ ipate in a new project to produc~ tions include a Ph.D. in Mathematics or tions, control theory, approximation the­ a portable, high performance numen­ Mathematical Sciences and a record of ory, probability combinatorics, ergodic cal software library for supercomputers professional accomplishments. Adminis­ theory. Masters degree in Mathematics and shared memory parallel proces­ trative experience is desirable. Salary required; Ph.D. preferred. Demonstrated sors. The library will replace the widely commensurate with experience. Send a excellence in teaching and research. used LINPACK and EISPACK libraries. detailed resume and 3 letters of recom­ Submit letter of application and resume This multiyear position will involve nu­ mendation to: Dr. J. R. Hopper, Chairman by March 15, 1988 to Pan Tai Liu, Search merical analysis and scientific program­ of Search Committee. Deadline for ap­ Committee Chair, Lecturer, Mathemat­ ming on vector and parallel processors. plications: March 18, 1988. (Subsequent ics (020321) Position, The University of The project is being conducted jointly deadlines at 30 day intervals thereafter Rhode Island, P. 0. Box G, Kingston, with the Courant Institute of Mathe­ until position is filled.) An Affirmative Rl, 02881. AA/EOE matical Sciences. For further informa­ Action/Equal Opportunity Employer. tion contact Jack Dongarra, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 ((312)972- 7246, [email protected]). EOE/AA ROSE-HULMAN INSTITUTE OF TECHNOLOGY GLASSBORO STATE COLLEGE DEPARTMENT OF MATHEMATICS MATHEMATICS. Assistant Professor, A tenure-track assistant or associate (tenure track position). Responsible for OPEN POSITION professorship will be available Septem­ teaching advanced undergraduate math Department of Mathematical Sciences ber 1, 1988. Applicants should have a courses particularly in the area of ge­ Roosevelt University Ph.D. in mathematics or statistics and ometry and applied math. Ph.D. required Chicago, Illinois 60605 a strong commitment to teaching and and evidence of excellent undergraduate teaching should be available. Applications are invited for one tenure­ scholarly activity. Send letter of applica­ COMPUTER SCIENCE. 'Assistant track position starting August 15, 1988. tion, resume, three letters of recommen­ Professor, (two tenure track positions). Requirements are a Ph.D. in computer dation and graduate transcripts to Roger Responsible for teaching undergraduate science or in mathematics with evidence Lautzenheiser, Chairman, Department of courses in Computer Science. Ph.D. in of interest and ability in computer sci­ Mathematics, Rose-Hulman Institute of Computer Science preferred, candidates ence. Duties consist primarily of teach­ Technology, Terre Haute, IN 47803. with Master's degrees invited to ap­ ing, but research is expected for tenure Rose-Hulman Institute of Technology ply. Evidence of excellent undergraduate and for promotion. The normal teach­ is an equal opportunity employer. teaching required should be available. ing load is four courses each semester. Begin: September 1, 1988. Salary: Salary is negotiable, based on qualifica­ competitive. Send resume by March tions and experience. 1, 1988 to: Mr. Seth Bergmann, Hir­ Applicants should send their complete ASSISTANT PROFESSOR, ing Committee, (Pool #3, Mathematics) curriculum vitae, together with a list of MATHEMATICS (Pools #4 & #5, Computer Science), De­ any publications and arrange to have Tenure-track position. Teach courses partment of Mathematics and Comptuer at least three letters of reference sent at graduate and undergraduate level. Science, Glassboro State College, Glass­ directly to: Do substantial research in mathemat­ boro, NJ 08028 (609) 863-6050. Glass­ Dr. J. L. Johnson, Chair ics. Participate in normal department boro State College is a comprehensive Department of Mathematical business. Ph.D. in Mathematics. Demon­ institution with a present enrollment of Sciences strated excellent potential in teaching 8,000 undergraduate and 1 ,200 gradu­ Roosevelt University and research. Submit letter of applica­ ate students located in southern New 430 S. Michigan Avenue tion and resume by March 15, 1988 to: Jersey approximately 20 miles south­ Chicago, IL 60605 Pan Tai Liu, Search Comittee Chair, As­ east of Philadelphia. It is an affirmative Applications completed by February 28, sistant Professor, Mathematics (020322) actionjequal opportunity employer. Ap­ 1988 will be given first consideration. Position, The University of Rhode Is­ plications from women, minorities and Roosevelt University is an Equal Oppor­ land, P. 0. Box G, Kingston, Rl 02881. the handicapped are encouraged. tunity Employer. AA/EOE

FEBRUARY 1988, VOLUME 35, NUMBER 2 349 Classified Advertisements

POSITIONS AVAILABLE CARNEGIE MELLON UNIVERSITY Zeev Nehari Assistant Professorship UNIVERSITY OF PUERTO RICO in Mathematics Mathematical Department of Mathematics This position has been instituted in the Research Faculty position at the Instructor or As­ Department of Mathematics of Carnegie Pure and applied mathemati­ sistant Professor level in the area of Mellon University to honor the memory cians in all areas of speciali­ Computer Science. Responsibilities in­ of Professor Zeev Nehari, a member of zation are invited to apply for clude research and teaching courses the Department from 1954 to his death technical staff positions. The in Mathematics and Computer Science primary responsibilities are to in 1978. Applicants are expected to conduct independent both at the undergraduate and graduate show exceptional research promise as research as part of MITRE's level. Applicants for the Assistant Profes­ well as clear evidence of achievement. mathematical research proj­ sor position must possess a Doctorate The appointment is for two academic ect, and to collaborate on (Ph.D.) in Computer Science (preferably years, beginning in September 1988 and interdisciplinary research and in the area of Operating Systems). Ap­ development projects in such extendable for one further year when areas as signal and image plicants with only a master's degree and mutually agreeable. It carries a reduced processing, radar, communi­ willing to pursue a Ph.D. degree will academic year teaching load of six hours cations, concurrent process­ be considered. Fluency in spoken and per week during one semester and three ing, and VLSI design. written Spanish and English is required. hours per week during the other. The Salary: $16,224 annually for Instructor Present staff have diverse applicant should have research inter­ research interests in algebra, position and $21,120 annually for the ests which intersect those of current combinatorics, computing the­ Assistant Professor position. Applicant faculty of the Department. Applications ory, geometry, and analysis. should send a complete resume and should include vita, list of publications, three letters of recommendation to Dr. Qualifications for these posi­ a statement describing current research tions include a Ph.D. degree Rafael Martinez, Acting Director, Depart­ achievements and plans for research in or equivalent in mathematics ment of Mathematics, U.P.R., P. 0. Box the near future, and at least three letters or a related field, demon­ 5000, Mayaguez, P.R. 00709-5000. An of recommendation to be requested by strated research potential, and the ability to represent affirmative actionjequal opportunity em­ the applicant, all to be sent to Professor ployer. ideas clearly. A desire to col­ David R. Owen, Chairman, Zeev Ne­ laborate actively in interdisci­ hari Assistant Professorship Committee, plinary research is essential. Department of Mathematics, Carnegie U.S. citizenship is required. Mellon University, Pittsburgh, PA 15213, McMASTER UNIVERSITY Applicants should submit a DEPARTMENT OF as soon as possible. AA/EOE. curriculum vitae by 1 March MATHEMATICS AND STATISTICS 1988, and have letters of ref­ erence sent directly to us. The Department of Mathematics and University of California at Riverside To obtain further informa­ Statistics, McMaster University, invites tion, or to apply, write to applications for a tenure track Assistant Applications are invited for a tenure­ Signal Processing and Mathematical Research Professorship starting July 1, 1988. track or tenure position in Mathematics beginning Fall 1988. Candidates must Group, E025, MITRE, Bed­ Candidates should have a Ph.D. and ford, MA 01730. Address proven research ability in some area of have demonstrated excellence in re­ electronic mail to linus! Mathematics related to Algebra, as well search and teaching. The department is math@ mitre-bedford, arpa. especially interested in the research area To apply for positions in the as capability in teaching. Salary based Washington DC area, write on qualifications and experience. This of analysis but candidates in all areas will be considered. Applicants should to M.X. Mason, MITRE, position is subject to final budgetary 7525 Colshire Drive, approval. send a curriculum vitae and see that Mclean, VA 22102 at least three letters of recommendation In accordance with Canadian Immi­ An Equal Opportunity Employer gration requirements, in the first stage are sent to: of this competition priority is given to Chair, Mathematics Search Canadian Citizens and permanent resi­ Committee dents. Department of Mathematics and MITRE Please send curriculum vitae and Computer Science arrange for three letters of reference to: University of California I. Hambleton, Chairman Riverside, CA 92521 Mathematics & Statistics University of California, Riverside, is McMaster University an Affirmative Action/Equal Opportunity Hamilton, Ontario Employer. L8S 4K1 Canada

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POSITIONS AVAILABLE -- Texas A&l University UNIVERSITY OF PITISBURGH Department of Mathematics AT GREENSBURG THE OHIO STATE UNIVERSITY AT OFFICE OF THE DEAN NEWARK The Department of Mathematics at OF INSTRUCTION UNIVERSITY DRIVE, Texas A&l University invites applica­ APPLIED MATHEMATICIAN NEWARK, OHIO 43055 tions for a tenure-track position at the ASSISTANT PROFESSOR Assistant Professor level. Duties to be­ The University of Pittsburgh at Greens­ OF MATHEMATICS gin in the Fall of 1988. Candidates must burg has a full-time teaching position Assistant Professor of Mathematics have a Ph.D. in mathematics. Tangible available September 1, 1988. Ph.D. required. starting September 1988. This is a evidence of scholarly publications and Teaching experience and a full-time, tenure track position involving a strong commitment to superior teach­ strong interest in Applied Mathematics teaching (presently six quarter courses ing is required. Normal teaching load is are essential. Duties include 12 credit annually), research and service. Ph.D. twelve {12) semester hours with associ­ hours of instruction per Fall and Winter and documentation of teaching excel­ ated academic duties. Send resume and Terms. Rank and salary commensurate lence required. Salary: $24,000-$28,080. three letters of recommendation to: with qualifications. Attractive package of OSU-N is a two-year regional campus Professor Genaro Gonzalez, Chair fringe benefits. Applicants selected for 40 miles east of Columbus. Classes are Department of Mathematics interview must pay all costs. Success­ small. Curriculum vitae and three let­ Texas A&l University ful applicant fully reimbursed. Send CV, ters of reference, written to the search Campus Box 172 transcripts, three letters of recommenda­ committee, should be sent to: Chairman, Kingsville, TX 78363 tion, and a letter of interest;teaching phi­ Math Search Committee, c/o Personnel Deadline is March 15, 1988, or until po­ losophy to: Dr. Estrella Z. Ang, Chair, Di­ Officer at the above address. To be as­ sition is filled. Applications from women vision of Natural Sciences & Engineering, sured of consideration, application must and minority candidates are encouraged. University of Pittsburgh at Greensburg, be received by March 15, 1988. Texas A&l University is an Equal Oppor­ Greensburg, PA 15601 before February The Ohio State University at Newark tunity I Affirmative Action Employer. 29, 1988. AA/EOE is an EEO I AA Employer

The mathematics department has an opening at the senior level. Candidates FLORIDA INTERNATIONAL must show evidence of continuing re­ UNIVERSITY search, which should include recent pub­ Miami, Florida 33199 lications. Strong undergraduate teaching The Department of Mathematics announces tenure track posi· and some administrative experience is tions at the assistant professor level beginning August 1988. preferred. Salary is dependent upon qualifications and will be competitive. Candidates must have a Ph.D. in Mathematics and a commitment Applications should include a vita and to research and quality teaching. Preferred areas of specialization names and addresses of at least three are harmonic analysis, logic, representation theory and several references. Application should be made complex variables. Qualified candidates in other areas will be by February 15, 1988 or until filled to: considered. Dr. B. G. Hodges, Chair, Department Teaching load consists of 5 courses o~ Mathematics, Winthrop College, Rock per academic year. Send H1ll, SC 29733. resume and 3 letters of recommendation to Recruitment Com­ Winthrop College is an Affirmative mittee, Department of Mathematics, Florida International Action/Equal Opportunity Employer. University, Miami, FL 33199.

Florida International University is the State University of Florida at Miami. The University is an Equal Opportunity/Affirmative Action Employer. bn'~"""-' "'~"~'

FEBRUARY 1988, VOLUME 35, NUMBER 2 351 Classified Advertisements

POSITIONS AVAILABLE VIRGINIA TECH-INTERDISCIPLINARY DEPARTMENT HEAD CENTER FOR APPLIED MATHEMAT­ MATHEMATICAL SCIENCES CHAIR OF THE DEPARTMENT ICS. Several anticipated postdoctoral DEPARTMENT OF MATHEMATICS positions for new or recent Ph.D.'s CLEMSON UNIVERSITY ROSE-HULMAN INSTITUTE OF TECHNOLOGY in control theory, continuum mechan­ Applications and nominations are invited POSITION AVAILABLE ics, integral equations or related area, for the position of Department Head. BEGINNING JULY 1, 1988 with interest in boundary control and Qualifications include a Ph.D. degree stabilization problems. Experience with teaching experience, proven research Applications and nominations are invited numerical methods for partial differential ability, and leadership capacity. Adminis­ for the position of Chair of the Depart­ equations or equations with delays, or trative experience is highly desirable but ment of Mathematics at Rose-Hulman In­ a strong mechanics background is de­ not required. The Mathematical Sciences stitute of Technology. Candidates should sirable. Full-time research appointment Department has 46 faculty members and have a Ph.D. degree, administrative po­ beginning June 1988 or as negotiated. over 100 graduate students. It offers tential, a record of scholarly activity and Appointment is for up to one year but a broad program in the mathematical excellence in teaching. Responsibilities may be renewed. Search ends when sciences including B.A., B.S., M.S., and include scheduling classes, budgeting, positions are filled. Send vita and one Ph.D. degree programs for its majors; recruiting, making promotion, tenure and letter of reference to ICAM, Attn: Ken­ provides service courses for students retention recommendations and teaching neth B. Hannsgen, Virginia Tech, Blacks­ in science, engineering, and education one course per quarter. burg, VA 24061-0123. Virginia Tech is curricula; and jointly administers a Ph.D. Rose-Hulman is a small (1300 stu­ an Equal Opportunity1 Affirmative Action program in Management Science with dents) science and engineering college Employer. the Management Department. noted for its well-qualified and highly Clemson's Department of Mathemati­ motivated undergraduates. The median cal Sciences has pioneered the concept SAT scores for the 1991 class are 660 UNIVERSITY OF TORONTO of integrating major areas of the math­ in mathematics and 540 in verbal. There Department of Mathematics ematical sciences-algebrajcombinator­ are no remedial courses and mathemat­ Scarborough Campus ics, analysis, computational mathemat­ ics students are encouraged to present ics, operations research, and probability/ papers at undergraduate conferences Applications are invited for a limited statistics-into balanced educational pro­ and to compete in mathematical con­ term Assistant Professorship, beginning grams at both the undergraduate and tests. July 1, 1988, for a term of two years. graduate levels. A candidate is sought The mathematics department con­ Applications from male and female can­ who is committed to working with the sists of twelve active (writing, research, didates in any branch of pure or applied faculty to foster these programs and consulting) full time faculty members mathematics are welcome. Duties con­ who will provide leadership for the fu­ with interests and expertise in mathe­ sist of research and teaching, and candi­ ture development of the Department. matics, operations research and statis­ dates must demonstrate clear strength in Initial screening of applicants will be­ tics. both. Applications should be sent to Pro­ gin in early March 1988 but applications Fringe benefits include TIAA-CREF fessor J. M. Perz, Chairman, Physical will be accepted until March 28, 1988. health and life insurance, tuition benefit Sciences Division, Scarborough Cam­ The position will be available August for children, and a personal computer in pus, University of Toronto, 1265 Mili­ 1 , 1988. Salary will be commensurate each faculty member's office. tary Trail, Scarborough, Ontario, Canada with credentials and experience. Vitae To apply, send a letter of application, M1C 1A4, and should include a complete (with names and telephone numbers of a curriculum vitae and the names, ad­ curriculum vitae, and the names of at three references who will be contacted dresses and telephone numbers of at least three referees. The deadline is Feb­ after the initial screening of applicants), least three people who are willing to ruary 15, 1988. In accordance with Cana­ nominations, and requests for further serve as references for you, to dian Immigration requirements, this ad­ information should be sent to: Mathematics Chair Search vertisement is directed to Canadian citi­ Professor James P. Jarvis, Committee zens and permanent residents. Chairman Department of Mathematics Department Head Search Rose-Hulman Institute of Committee Technology THE UNIVERSITY OF Department of Mathematical Terre Haute, IN 47803 TENNESSEE/KNOXVILLE Rose-Hulman Institute of Technology is Sciences an equal opportunity employer. Senior position available in Differen­ 0-1 02 Martin Hall tial Equations. Preference for specialty Clemson, SC 29634-1907 in Dynamical Systems. Contact John Clemson University is an AA/EO Em­ S. Bradley, Head, Mathematics Depart­ ployer ment. AN EEO TITLE IX/SECTION 504 EMPLOYER.

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POSITIONS AVAILABLE - Howard University MILLSAPS COLLEGE DEPARTMENT OF MATHEMATICS THE COOPER UNION FOR THE Howard University expects to have two JACKSON, MS 39210 ADVANCEMENT OF tenure track positions available at any SCIENCE AND ART level in the Department of Mathematics Applications are invited for a tenure track SCHOOL OF ENGINEERING in August 1988. Each position requires position starting Fall 1988. Candidates must possess a PhD in Mathematics Applications are invited for a tenure the teaching of undergraduate and grad­ and a dedication to quality teaching. track position as Assistant Professor uate courses, particularly those in the Rank is open and salary will be com­ of Mathematics, to begin September 1 , Ph.D. program in Mathematics. One po­ petitive. Candidates from all areas of 1988. A doctorate in mathematics or one sition demands a Ph.D. in Mathematical mathematics are encouraged to apply. of the mathematical sciences is required. Statistics, with some teaching obliga­ Submit a letter of application, resume, The Cooper Union, located in lower tions in this area. There is no restriction and three letters of recommendation to Manhattan, offers tuition-free programs in the area of specialization for the sec­ Dr. Cecil E. Robinson, Jr., Chair, Depart­ leading to degrees in architecture, art ond position. Please reply to Chairman: ment of Mathematics, Millsaps College, and engineering. Almost all mathemat­ Department of Mathematics, Howard Jackson, MS 39210. Applications will be ics courses are oriented towards the University, Washington, D.C. 20059. considered until the position is filled. needs of undergraduate and master's Howard University is an Equal Oppor­ Millsaps College is an Equal Opportunity level graduate students in chemical, civil, tunity Employer. Employer and encourages applications electrical and mechanical engineering. from women and minorities. These students are admitted on the ba­ sis of previous high academic achieve­ BRYN MAWR COLLEGE ment in science and mathematics and Applications are invited for a tenure are unusually well-prepared to undertake track position as Assistant college-level work in mathematics. Professor of Mathematics with responsibilities in Although research activity is encour­ computer science, starting September aged at Cooper Union, and substantial SOUTHWESTERN UNIVERSITY 1988. Research in mathematics or com­ opportunity exists for collaborative re­ puter science and ability and desire to search with engineering faculty, the prin­ Applications are invited for a tenure-track teach in both fields expected. Ph.D. cipal responsibility of the mathematics in position in Mathematics and a tenure­ mathematics or computer science to be faculty is for high quality undergraduate track position in Computer Science at completed by September 1988. Women teaching of required courses in ana­ the Assistant Professor level beginning and minority candidates especially en­ lytic geometry, calculus, vector calculus, Fall semester, 1988. Successful candi­ couraged to apply. Send application and probability and differential equations, as dates will have a strong commitment to three letters of recommendation to: F. well as undergraduate and graduate teaching excellence at the undergradu­ Cunningham, Jr., Department of Mathe­ electives in such areas as linear algebra, ate level, to maintain an active interest matics, Bryn Mawr College, Bryn Mawr, functions of a complex variable, oper­ in scholarly pursuits, and to possess an PA 19010. Closing date Feb. 15, 1988. ations research, statistics, partial differ­ appreciation for the role of liberal arts Bryn Mawr is an AA/EO employer. ential equations and numerical analysis. education. Ph.D. required. A lively interest in teaching and in stu­ The Department of Mathematics and dents is essential. Some background in Computer Science, which offers a major the applications of mathematics to sci­ BRYN MAWR COLLEGE in computer science, has seven full­ ence and engineering (and in the use of time and several adjunct members. The Applications are invited for an appoint­ computers in such applications) is highly University has a Sequent Balance 8000 ment in mathematics at rank up to desirable. computer designed for parallel process­ Professor. Tenure or tenure track as Please send all inquiries, including · ing available for use, as well as direct appropriate, starting September 1988. a detailed resume and the names of access to the University of Texas com­ Strong research record and commitment several references to: puter system. The position in Computer to excellence in teaching expected. All Prof. Sholom Arzt Science is supported through an endow­ fields will be considered, with preference Department of Mathematics ment provided by Mr. Grogan Lord. for algebra, geometry or applied mathe­ The Cooper Union Send letter of application, vita, and matics. Women and minority candidates 51 Astor Place three letters of reference to: Dr. Theodore are especially encouraged to apply. Se­ New York, N.Y. 10003 D. Lucas, Associate Provost, South­ lection will be made after February 15, The Cooper Union is an equal opportu­ western University, Georgetown, Texas 1988. Please direct inquiries or applica­ nity /affirmative action employer. 78626. Southwestern University is an Af­ tion to: F. Cunningham, Jr., Department firmative Action/Equal Opportunity Em­ of Mathematics, Bryn Mawr College, ployer. Bryn Mawr, PA 19010. Bryn Mawr is an AA/EO employer.

FEBRUARY 1988, VOLUME 35, NUMBER 2 353 Classified Advertisements

POSITIONS AVAILABLE KENNESAW COLLEGE MATH DEPT. Korea Institute of Technology PO BOX444 Department of Mathematics CLARKSON UNIVERSITY MARIETTA, GA 30061 Department of Mathematics Positions in Analysis and Geometry for and Computer Science The Dept. of Math. seeks applications Fall 1988 andjor Spring 1989. Qualifica­ for the position of Dept. Chair. Appli­ tions for the positions include a Ph.D. The Clarkson University Mathematics cants must have a Ph.D. in mathematics, in Mathematics, strong evidence of re­ and Computer Science Department is in­ a record of effective teaching at the search, and ability of speaking Korean. terested in hiring a faculty member in the college or university level, and success­ Send vita and direct three letters of areas of pure and applied mathematics ful administrative experience. Published recommendation to: and computer science. Teaching load is mathematical research beyond the dis­ Professor Dong Youp Suh six hoursjweek. Rank and salary are sertation, a strong commitment to a qual­ Department of Mathematics open. ity curriculum, and support for teaching, Korea Institute of Technology Interested applicants should send re­ service, research and creative activities 400 Kusongdong, Chung-gu, sume and three letters of recommenda­ are required. Vitae and three letters Taejonshi, tion to Professor Athanassios S. Fokas. should be sent to C. B. Schaufele, Chair, Chung chong nam-do, 300-31, Chariman, Department of Mathematics Search Committee, by March 1, 1988. KOREA and Computer Science. Clarkson Univer­ Appointment date is September 1988. Deadline for application: April 15, 1988. sity. Potsdam, NY 13676. The Dept. has 13 full-time faculty and of­ Clarkson University is an Affirmative fers the B.S. degree in math and support Action/Equal Employment Opportunity courses for the master's degree in edu­ LEHMAN COLLEGE (CUNY) Employer MFVH (Minority, Female, Vet­ cation. In addition to major courses, the Department of Mathematics eran, Handicap). dept. offers core and service courses, and Computer Science and is involved in community and in­ Tenure track positions anticipated in stitutional service. Kennesaw College is mathematics and computer science. a nonresidential college, located in a Candidates must have an earned doc­ rapidly growing area of suburban At­ torate, a strong commitment to teach­ lanta. Minority applicants are strongly ing and a demonstrated outstanding re­ urged to apply. EOE/AA search potential. Rank and salary com­ mensurate with qualifications. Send re­ sume and names of three references to: XAVIER UNIVERSITY Prof. Robert Feinerman, Chairman DEPARTMENT OF MATHEMATICS Department of Mathematics and CINCINNATI, OHIO 45207 Computer Science Lehman College Applications are invited for a tenure track Bronx, N.Y. 10468 position in mathematics at the rank of AN EQUAL OPPORTUNITY/ AFFIR­ Assistant Professor beginning Septem­ MATIVE ACTION EMPLOYER ber 1988. Candidates must have an earned doctorate and a strong commit­ ment to teaching a wide variety of under­ LA SALLE UNIVERSITY graduate courses within the framework of a Jesuit liberal arts institution. The A faculty position is available September, position also requires advising majors 1988. Candidate should have a Ph.D. in and assisting in course and curriculum Mathematics. Candidates with a back­ revision while continuing a program of ground in Computer Science and some scholarly development. Ability to teach interest in research preferred. Salary discrete mathematics is desirable, but competitive. EOAA. Please send resume candidates from all areas are encour­ and letters of recommendation to Dr. aged to apply. Send resume, transcripts Samuel Wiley Department of Mathemati­ and three letters of reference to D. C. cal Sciences La Salle University Philadel­ Trunnell, Chair, Dept. of Mathematics. phia, PA. 19141 AA/EOE.

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POSITIONS AVAILABLE PUBLICATIONS the search committee. Screening of ap­ plications will begin on February 1 , 1988. CHRISTOPHER NEWPORT COLLEGE Christopher Newport College employs MATH SCI PRESS, 53 Jordan Rd., MATHEMATICS POSITION FOR only United States citizens and aliens Brookline, MA 02146, 617-738-0307. 1988-1989 New: TOPICS lawfully authorized to work in the United IN PHYSICAL GEOME­ TRY, by Robert Hermann. $80. Vol. 24 in Christopher Newport College invites ap­ States. Applications from women and "ln~erdisciplinary Mathematics". Among plications for a full-time faculty position minorities are encouraged. top1cs: Geometry of vortex filaments a in mathematics. The appointee will be EEO/AA relation between ergodic and control the­ expected to teach a wide variety of ory, and translation of forgotten article undergraduate courses. Area of special­ by ~elmholtz on geometry of thermody­ ization is open. namics. Either tenure-track or restricted (one­ year) positions may be offered, depend­ FOR SALE ing upon the needs of the College. A GEOMETRIZATION PROCEEDINGS OF FIRST SOVIET­ OF STATISTICAL master's degree in mathematics is re­ THEORY JAPAN JOINT SYMPOSIUM OF TOPOL­ quired for consideration; a doctorate is Proceedings OGY (1986), 208 pp., $30. Write to Jun-iti of the GST Workshop, preferred. Appointments will be effective Lancaster 29-31 October Nagata, Department of Mathematics, Os­ 1987. August 22, 1988. Editor C T J Dodson Christopher Newport College is an aka Kyoiku University, Tennoji, Osaka, 543 JAPAN. Includes papers by S-1 Amari, 0 E urban, four-year, undergraduate, state­ Barndorff-Nielsen, P Blaesild, c T J supported college located in the City Dodson, P S Eriksen, B L Foster, B of Newport News, Virginia. The College Hanzon, P E Jupp, W S Kendall, S L offers 49 different majors and concentra­ GALOIS ALGEBRA MICROCOMPUTER Lauritzen, J Lyons, D B Picard, R w tions under eight baccalaureate degree PACKAGE Tucker, G Tunnicliffe-Wilson programs. It enrolls 4400 students, has for IBM PC or compatibles. The GALOIS Also a detailed account of the discussion a full-time faculty of 11 0 (70% of whom package can be used for teaching or sessions. hold earned doctorates or other appro­ research in algebra, number theory and 260 pages Softcover, ISBN 0 901272 40 priate terminal degrees), and a part-time applications in computer science, combi­ X, December 1987. and adjunct faculty of nearly 100. Within natorics and engineering with emphasis AMS Classifications 53B, 53C, 62A, 62E. the context of liberal learning, the Col­ on modular arithmetic, and matrices and Price Postfree, Prepaid: £12 Europe, US lege is committed to meeting the needs polynomials over finite fields or integers $25 elsewhere. of its constituencies through excellence mod n. ULDM Publications, Department of Math­ in instruction and through public service GALOIS for single use $US115; site ematics, University of Lancaster, UK. and research. license for department $US440 (includes Because the College serves an area, postage). the demographics of which reflect a pop­ Order from: Department of Mathe­ ulation with a much higher percentage matics, University of Tasmania, Hobart, SITUATIONS WANTED of minority individuals than the national Tasmania 7001, AUSTRALIA. average, the College seeks faculty mem­ Doctor of Mathematics, Mathematician bers with extensive experience in teach­ and physicist immediately available for ing, advising, and counseling minority teaching andjor research instructorship students. . in his speciality: geometry and mathe­ Interested parties are requested to matical physics. send a letter of application, vita; gradu­ Many years of teaching and research ate transcript, and four letters of recom­ experience at college and university. mendation to: Multi-lingual. Dr. Dennis R. Ridley Dr. S. Pavlovic, 2 Hamburg 55, Assistant to the Vice President for Mohlmannweg 3, W. Germany. Academic Affairs Christopher Newport College 50 Shoe Lane Newport News, VA 23606 At least two of the four letters of ref­ erence should be from individuals with direct knowledge of the applicant's ex­ perience in assisting minority students. ~pplicants will receive a complete posi­ tion description and further details from

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The American Mathematical Society has made special arrangements for AMS members to receive a reduced subscription rate on the new Applied Mathematics Letters. Special Rate for individual members of the American Mathematical Society AMS individual members may subscribe at 50% discount. 1988: Volume 1, (4 issues) Annual Subscription (1988) $120 Special rate for AMS individual members $60

To order: Send your prepaid order to the American Mathematical Society, Annex Station, P. 0. Box 1571, Providence, Rl 02901-9930. Credit card orders cannot be accepted for subscriptions to Applied Mathematics Letters. NOW AVAILABLE AUTHOR AND SUBJECT INDEXES OF MATHEMATICAL REVIEWS, 1980-84

This comprehensive 12-volume set contains both author and subject listings for all of the reviews that appeared in Mathematical Reviews during the years 1980 to 1984. Containing approximately 9,600 pages, it is an important addition to any mathematics library.

With this set of indexes at hand, readers can:

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• discover listings for approximately 200,000 papers, books, and conference proceed­ ings-all the items reviewed in Mathematical Reviews during these years

• obtain information about approximately 8,000 additional items that were not re­ viewed individually, but which are fully classified and cross-referenced in these indexes

• find complete bibliographic information for each article under any author associ­ ated with the article, and cross-references for the names of editors, translators, and other persons associated with an item

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PREPAYMENT REQUIRED. Order from American Mathematical Society, Annex Station, P.O. Box 1571, Providence, RI 02901-9930 Telephone: (401) 272-9500 or (800) 556-7774 A Gourmet Guide to Typesetting with the Jl.MS -T EX macro package M.D. SPIVAK

The Joy of TEXis the user-friendly user's accuracy and still have control over the fin­ guide for A,MS-'JEX, an extension of 'JEX, ished product, even novice technical typists Donald Knuth's revolutionary program for will find the manual easy to use in helping typesetting technical material. A.MS-'lEX them produce beautiful technical 'JEXt. was designed to simplify the input of math­ This book is designed as a user's guide ematical material in particular, and to for­ to the A.MS -'lEX macro package and details mat the output according to any of various many features of this extremely useful text preset style specifications. processing package. Parts 1 and 2, entitled There are two primary features of the "Starters" and "Main Courses " teach the . ' 'lEX system: it is a computer system for reader how to typeset most normally en- typesetting technical text, especially text countered text and mathematics. "Sauces containing a great deal of mathematics; and Pickles," the third section, treats more and it is a system for producing beautiful exotic problems and includes a 60-page dic­ text, comparable to the work of the finest tionary of special '.IEXniques. printers. Exercises sprinkled generously through Most importantly, 'JEX's capabilities are each chapter encourage the reader to sit not available only to 'JEXperts. While down at a terminal and learn through ex­ mathematicians and experienced technical perimentation. Appendixes list summaries typists will find that 'lEX allows them to of frequently used and more esoteric sym­ specify mathematical formulas with great bols as well as answers to the exercises.

ISBN 0-8218-2999-8, LC 85-7506 PREPAYMENT REQUIRED. Order from 290 pages (softcover), 1986 American Mathematical Society AMS Indiv. Memb. $26, AMS Inst. PO Box 1571 ~ Memb. $30, List price $33 Annex Station ..,.• • To order specify JOYT /NA Providence, RI 02901-9930 0 ;(> lrNoED \'@' Shipping/Handling: 1st book $2, each or call 800-556-7774 to use VISA or MasterCard. add'l $1, max. $25; by air, 1st book Prices subject to change. $5, each add'l $3, max. $100 ANNOUNCING Volume 1 • 1988 Journal of the American Mathematical Society

Editors The new Journal of the American Mathematical Society will Michael Artin be published quarterly beginning in January 1988. It will H. Blaine Lawson, Jr. contain research articles of the highest quality in all areas of Richard Melrose pure and applied mathematics. Selected articles scheduled to Wilfried Schmid appear in Volume 1 include: Homology of the zero set of a Robert E. Tarjan unipotent vector field on a flag manifold by C. De Concici, G. Lusztig, and C. Procesi; Reduced Hausdorff dimension and the concentration-cancellation law for 2-dimensional incom­ pressible flows by Ronald J. DiPerna and Andrew Majda; Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem by David Jerison and John M. Lee; p-adic Hodge theory by G. Faltings; Flip theorem and the existence of minimal models for 3-folds by Shigefumi Mori; Zero-one laws for sparse random matrices by Saharon Shelah and Joel Spencer; and Arithmeticity of holonomy groups of Lie foliations by Robert J. Zimmer.

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This year the American Mathematical Society is celebrating its lOOth Anniversary. It is a time to look back with pride to our historic past and to look forward to a future of growth and increased service to the mathematical community. PROBABILITY THEORY SUBJECT INDEXES FROM MATHEMATICAL REVIEWS 198G-84, 1973-79, 195~72, 194G-58 Many mathematicians have expressed a desire to have a compilation of articles, books and conference proceedings that have been reviewed in Mathematical Reviews available by subject area. Together with the companion index on statistics listed below, this volume is the first such compilation. This volume gives a listing· of author names and review numbers of all the items having primary or secondary classifications in probability theory for the entire 45-year span of Mathematical Reviews from 1940 through 1984, conveniently collected in one volume. The titles are also given for items beginning in 1959. Full bibliographic information is not provided here, but can readily be obtained using the information given here by consulting either the appropriate author indexes, the issues of MR, or Math\Sci (for items beginning in 1959). The classification schemes used during these years are also included at the end of the index. This convenient index should be of great value to researchers working in the area of probability, or persons who need to consult the literature in this active field.

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A three-volume set of proceedings of the Solomon Lefschetz Centennial Conference. held in 1984 in Mexico City to celebrate Lefschetz's 100th birthday. The conference focused on the three main areas of Lefschetz's research: algebraic geometry. algebraic topology. and differential equations. • The Lefschetz Centennial Conference, Part I: Proceedings on Algebraic Geometry D. Sundararaman, Editor This volume contains many of the papers in the area of algebraic geometry presented at the Conference. The proceedings begin with two interesting articles: A Page of Mathematical Autobiography. that has been reprinted from an early edition of the Bulletin of the AMS. and "Solomon Lefschetz. a biography" by William Hodge. that is reprinted from the Bulletin of the London Mathematical Society. 1980 Mathematics Subject Classification: 14 ISBN 0-8218-5061-X. LC 86-14040, ISSN 0271-4132 288 pages (softcover). 1986 Individual member $17, List price $29. Institutional member $23 To order. please specify CONM/58.1NA (Part 1) • The Lefschetz Centennial Conference, Part II: Proceedings on Algebraic Topology Samuel Gitter, Editor Part II contains papers in the fields of algebraic and differential topology. Some of the topics covered are: fixed points and the Segal conjecture. continuous cohomology. immersion of manifolds. vector fields on manifolds. BP-obstruction theory. K-theory. homotopy groups of spheres. diffeomorphism groups of surfaces. normed bilinear maps. surgery theory. cohomology of BO. and the Atiyah-Hirzebruch spectral sequence. 1980 Mathematics Subject Classifications: 55, 57, and others ISBN 0-8218-5063-6, LC 86-14040, ISSN 0271-4132 152 pages (softcover). 1987 Individual member $12, List price $20, Institutional member $16 To order, please specify CONM/58.2NA (Part II) • The Lefschetz Centennial Conference, Part Ill: Proceedings on Differential Equations A. Verjovsky, Editor The third volume contains papers presented in differential equations and dynamical systems. Some of the topics covered are dynamical systems and bifurcation. complex differential equations. homology applied to dynamics. and harmonic maps. Aimed at graduate students and researchers in dynamical systems and geometric dynamics. the book requires a knowledge of differential equations. differential topology. complex manifolds. and algebraic topology. 1980 Mathematics Subject Classifications: 58. 34, 35, 53 ISBN 0-8218-5064-4 LC 86-14040. ISSN 0271-4132 264 pages (softcover). 1987 Individual member $17, List price $29. Institutional member $23 To order, please specify CONM/58.3NA (Part Ill)

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Fasten PAYMENT securely CWI Monographs The CWI, Centrum voor Wiskunde en Informatica (Centre for Mathematics and Computer Science), is a research institute of the Stichting Mathematisch Centrum, which was founded in 1946 as a non-profit institution. Its aim is the promotion of mathematics, computer science and their applications.

One-Parameter Semigroups singular kernels. The book covers linear methods and Runge-Kutta methods, collocation methods based on By Ph. Clement, H.J.A.M. Heijmans, S. Angenent, polynomial spline functions, stability of numerical C.J. van Duijn and B. de Pagter methods, and it surveys computer programs for CWI Monographs, 5 Volterra equations. The purpose of this book is to illustrate the richness of 1986 xvi+588 pages Price: US $73.25/Dfl. 150.00 the theory of one-parameter semigroups by examining ISBN 0-444-70073-0 some of its various aspects. The main subjects are: semigroups of linear and nonlinear contractions, analytic semigroups and maximal regularity, positive semigroups including spectral theory and asymptotic behaviour. Two Stability of Runge-Kutta Methods for whole chapters are devoted to applications, the one to nonlinear diffusion and the other to structured Stiff Nonlinear Differential Equations population dynamics. By K. Dekker and J.G. Verwer 1987 x + 312 pages Price: US $51.25/Dfl. 105.00 CWI Monographs, 2 ISBN 0-444-70284-9 Presents a unified account of all developments concerning stability of Runge-Kutta methods for stiff nonlinear differential equations, which began in 1975 with Dahlquist's G-stability paper and Butcher's a­ Mathematics and Computer stability paper. Designed for the reader with a background in numerical analysis, the book contains Science II numerous theoretical and practical results aimed at Fundamental Contributions in The Netherlands giving insight into the treatment of nonlinear problems. since 1945 1984 x + 308 pages Price: US $46.25/Dfl. 95.00 ISBN 0-444-87634-0 Edited by M. Hazewinkel, J.K. Lenstra and L.G.L.T. Meertens CWI Monographs, 4 Contents: The Numerical Solution of Partial Differential Mathematics and Computer Equations (A.O.H. Axelsson). Dynamics in Bio-Mathematical Science Perspective (0. Diekmann). The Arch-Enemy Attacked Mathematically (L. de Haan). Process Algebra: Specification and Proceedings of the CWI Symposium, November Verification in Bisimulation Semantics (J.A. Bergstra and J.W. 1983 Klop). Codes from Algebraic Number Fields (H.W. Lenstra, Jr.). Edited by J.W. de Bakker, M. Hazewinkel and Infinite-Dimensional Normed Linear Spaces and Domain lnvariance (J. van Mill). Geometric Methods in Discrete J.K. Lenstra Optimization (A. Schrijver). Archirithmics or Algotecture? (P.M.B. CWI Monographs, 1 Vitanyi). 1986 viii+ 352 pages Price: US $73.25/Dfl. 150.00 1986 x + 162 pages Price: US $34.25/Dfl. 70.00 ISBN 0-444-70024-2 ISBN 0-444-70122-2 North-Holland The Numerical Solution of Volterra In the U.S.A. and Canada: Equations Elsevier Science Publishing Co. Inc., P.O. Box 1663, Grand Central Station, By H. Brunner and P.J. van der Houwen New York, NY 10163, U.S.A. CWI Monographs, 3 In all other countries: This monograph presents the theory and modern Elsevier Science Publishers, numerical analysis of Volterra integral and integra­ Book Order Department, differential equations, including equations with weakly P.O. Box 211, 1000 AE Amsterdam, The Netherlands.

US $ prices are valid only in the USA and Canada. In all other countries the Dutch Guilder (Off.) price is definitive. Customers in the Netherlands, please add 6% B. T. W. In New York State applicable sales tax should be added. All prices are subject to change without prior notice. NH/MATH/BK/22848 An Indispensable Resource forE very Library- 0-Bibliography of Mathematical Logic (in 6 Volumes) Edited by GertH. Muller, University of Heidelberg, FRG, in collaboration with W. Lenski

The D-Bibliography presents the literature of mathematical logic from its origin as a recognized discipline in the late 19th century to the present. Articles and books are classified by subject according to the standard classi­ fication scheme of Mathematical Reviews and Zentrallblatt fur Mathematik, slightly modified to accommodate earlier literature. The 6 volumes repre­ sent the major categories of logic as listed below. Part I of each volume contains author, titles and classification listings of the relevant literature arranged in sections by subject matter and chronolog­ ically within each section. Part II provides full bibliographic data and other information, i.e., translations, reprints and reviews, arranged alphabetically by author. Parts III and IV provide information about the sources, e. g., jour­ nals and proceedings, as well as a variety of technical indexes which enhance the bibliography's utility. Then-Bibliography will be useful to everyone interested in any aspect of mathematical logic, from beginning graduate students to advanced research workers. Students and scholars in other fields will find in Part I a useful historical overview and a guide to the literature necessary for a deeper understanding of each category. Logicians will be able to collect ref­ erences for their articles and lectures, find specific papers and books for their research, and refresh their knowledge of aspects of logic tangential to their main interests. For the first time, the entire literature of an important area of mathematics is made accessible to the full spectrum of scholars. Volume 1: Classical Logic, edited by W. Rautenberg 1987/485 pp./hardcover $170.00 ISBN 0-387-17321-8 Volume 2: Non-classical Logics, edited by W. Rautenberg 1987/469 pp./hardcover $170.00 ISBN 0-387-15521-X Volume 3: Model Theory, edited by H.-D. Ebbinghaus 1987/617 pp./hardcover $200.00 ISBN 0-387-15522-8 Volume 4: Recursion Theory, edited by P.G. Hinman 1987/697 pp./hardcover $200.00 ISBN 0-387-15523-6 Volume 5: Set Theory, edited by A.R. Blass 1987/791 pp./hardcover $230.00 ISBN 0-387-15525-2 Volume 6: Proof Theory; Constructive Mathematics edited by J.E. Kister, D. van Dalen, A.S. Troelstra 1987/405 pp./hardcover $155.00 ISBN 0-387-15524-4 The n-Bibliography is part of the series Perspectives in Mathe­ matical Logic To Order: call TOLL FREE 1-800-526-7254 (inN], 201-348-4033) or send payment, including $2.50 for postage and handling, to Springer-Verlag New York, P. 0. Box 2485, Secaucus, NJ 07094. Residents of NY, N], and CA please add sales tax for books. Personal checks, money orders and Ameri­ can Express, VISA, and MC are acceptable.

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