OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

Richard M. Schoen Awarded 1989 Bacher Prize page 225

Everybody Counts Summary page 227

MARCH 1989, VOLUME 36, NUMBER 3

Providence, Rhode Island, USA ISSN 0002-9920 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 848 • April 15-16, 1989 Worcester, Massachusetts Expired March 849 • May 19-20, 1989 Chicago, Illinois Expired April 850 • August 7-10, 1989 Boulder, Coloradot May 16 JulyI August (92nd Summer Meeting) 851 • October 21-22, 1989 Hoboken, New Jersey August 16 October 852 • October 27-28, 1989 Muncie, Indiana August 16 October 853 November 18-19, 1989 Los Angeles, California August 16 November** 854 January 17-20, 1990 Louisville, Kentucky October 11 December (96th Annual Meeting) March 16-17, 1990 Manhattan, Kansas August 8-11 , 1990 Columbus, Ohio (93rd Summer Meeting) November 2-3, 1990 Denton, Texas January 16-19, 1991 San Francisco, California (97th Annual Meeting) August 8-11, 1991 Orono, Maine (94th Summer Meeting) January 8-11 , 1992 Baltimore, Maryland (98th Annual Meeting) June 29-July 1 , 1992 Cambridge, England (Joint Meeting with the London Mathematical Society) January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) January 5-8, 1994 Cincinnati, Ohio (100th Annual Meeting) • Please refer to page 294 for listing of special sessions. •• Please note a change in this date making it later than previously published. t Preregistration/Housing deadline is June 1

Conferences

May 26- May 30, 1989: AMS Pure Mathematics Symposium July 10-30, 1989: AMS Summer Research Institute on on Complex Geometry and Lie Theory, Sundance Resort, Several Complex Variables and Complex Geometry, Sundance, Utah University of California, Santa Cruz, California May 29- June 9, 1989: AMS-SIAM Summer Seminar on the August 6- 7, 1989: AMS Short Course on Cryptology and Mathematics of Random Media, Virginia Polytechnic Computational Number Theory, Boulder, Colorado Institute and State University, Blacksburg, Virginia August 7, 1989: AMS-SIAM-SMB Symposium on Some June 3- August 5, 1989: Joint Summer Research Mathematical Questions in Biology, Sex Allocations and Conferences in the Mathematical Sciences, Humboldt Sex Change: Experiments and Models, University of State University, Arcata, California Toronto. Deadlines

May/June Issue July I August Issue September Issue October Issue Classified Ads* April 21, 1989 June 12, 1989 July 31, 1989 Aug 28, 1989 News Items April 27, 1989 June 12, 1989 Aug 3, 1989 Aug 29, 1989 Meeting Announcements•• April 20, 1989 June 5, 1989 July 27, 1989 Aug 22, 1989 • 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

221 Marshall Harvey Stone (1903-1989) George W. Mackey 219 Letters to the Editor Marshall H. Stone's contributions to twentieth century mathematics are 266 News and Announcements highlighted. 275 Funding Information for the 225 Richard M. Schoen Awarded 1989 Bocher Prize Mathematical Sciences Richard M. Schoen is cited for his work on the application of partial 277 1989 AMS Elections differential equations to differential geometry. (Nominations by Petition) 279 Meetings and Conferences 227 Everybody Counts: A Report to the Nation on the Future of of the AMS (Listing) Mathematics Education Summary 303 Mathematical Sciences The official National Research Council summary of the report outlines Meetings and Conferences the bold agenda for change in mathematics education over the next two decades. 317 New AMS Publications 321 AMS Reports and 237 Mathematics: A Challenge for Business, Government, and Academia Communications The text of the talk given by Vice Admiral William 0. Studeman at the Recent Appointments, 321 Phoenix, Arizona meeting is presented. Reports of Past Meetings, 321 326 Miscellaneous FEATURE COLUMNS Personal Items, 326 Deaths, 326 241 Computers and Mathematics Jon Barwise 327 New Members of the AMS Herman and Mark This month's column features two articles by Gene 333 Classified Advertising Sands which address the problems associated with establishing a computational environment for work in mathematics. Barwise's 345 Forms commentary follows.

257 Inside the AMS: Elections Robert M. Fossum Robert Fossum's report highlights the recommendations presented to the Council at the Phoenix, Arizona meeting by the Committee on Election Scheduling. Allyn Jackson's article about the Council meeting follows.

263 Washington Outlook Kenneth M. Hoffman In this month's column, Hans J. Oser reports on the Washington press conference, during which Everybody Counts, A Report to the Nation on the Future of Mathematics Education, was released to the public.

MARCH 1989, VOLUME 36, NUMBER 3 217 AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Since Notices has taken on its new format, the Managing Editor has been responsible for the various commentaries which have appeared in this sec­ tion, referred to in-house as "page 2." The Managing Editor then was James EDITORIAL COMMITTEE Robert J. Blattner, Michael G. Crandall A. Voytuk, who in January took a new position as Director of Project MS Robert M. Fossum (Chairman) 2000 at the National Academy of Sciences. For the next few issues, I will be Lucy J. Garnett, D. J. Lewis providing commentaries for "page 2." Nancy K. Stanton, Robert E. L. Turner While thinking about the various items I might bring to the attention of the INTERIM MANAGING EDITOR readers of Notices, I kept returning to a fact that has made a very big impres­ James W. Maxwell sion on me in the short time I have been working with the Society. I have been a member of the Society for many years and have served on some of the ASSOCIATE EDITORS Ronald L. Graham, Special Articles more active Society committees; however, I had no perception of the breadth Jeffrey C. Lagarias, Special Articles of the Society's activities nor the scope of the operations of the Providence and Ann Arbor offices. Also, there is the "Washington presence of the Soci­ SUBSCRIPTION INFORMATION ety" through the activities of the Joint Policy Board for Mathematics and its Subscription prices for Volume 36 (1989) are Office of Governmental and Public Affairs. Most members are aware of the $108 list; $86 institutional member; $65 individual "Washington presence" but may not be familiar with the exact nature of the member. (The subscription price for members is included in the annual dues.) A late charge of Society's involvement in these activities. In sharing these early impressions 10% of the subscription price will be imposed with colleagues and the staff, it was clear that my experience as a member upon orders received from nonmembers after was not unique. January 1 of the subscription year. Add for post­ age: Surface delivery outside the United States To better acquaint members with the Society, the Notices column "Inside and lndia-$1 0; to lndia-$20; expedited deliv­ ery to destinations in North America-$15; else­ the AMS" will begin a series of articles about the operations and plans of where-$38. Subscriptions and orders for AMS the Society. Readers of Notices can expect to see articles giving an overview publications should be addressed to the Amer­ of the publication program as well as articles detailing some of the most ican Mathematical Society, P.O. Box 1571, An­ important operations in the publication area. If you have ever wondered what nex Station, Providence, Rl 02901-9930. All or­ was involved in the production of Mathematical Reviews and the creation of ders must be prepaid. the MR Database, you will find this in future Notices articles, and I think you ADVERTISING will be very pleased with the efforts of the Society in the development and Notices publishes situations wanted and classi­ maintenance of this important bibliographic data base. In the latter stages fied advertising, and display advertising for pub­ of planning is a system for the electronic exchange of information among lishers and academic or scientific organizations. mathematicians. I find the Society's plans for this system very exciting. Copyright@ 1989 by the American Mathemat­ ical Society. All rights reserved. Printed in the I could go on listing activities of the Society in which members have expressed United States of America. interest and which will be reported on in future articles in Notices; however, The paper used in this journal is acid-free and falls within the guidelines established to ensure I think I will close by saying that we do want the members to know about permanence and durability.@ the Society and to be involved in its activities. I hope that future articles (Notices of the American Mathematical Society is featured in the column "Inside the AMS" will help in our communication published ten times a year (January, February, with members and the readers of Notices. March, April, MayfJune, July/August, Septem­ ber, October, November, December) by the Amer­ William Jaco ican Mathematical Society at 201 Charles Street, Executive Director Providence, Rl 02904. Second class postage paid at Providence, Rl and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Membership and Sales Department, American Mathematical Society, P. 0. Box 6248, Provi­ dence, Rl 02940.] Publication here of the Soci­ ety's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street address.

218 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Notices listed an agenda of items independent publication. The intention of the mathematical community should the ECBT in approving this change was Letters pursue. One of these items is to "find not to raise revenue nor to reduce signif­ better ways to attract the young" to icantly the general availability of the in­ to the Editor mathematics. While it is true that formation. money alone will not suffice, I have This year's distribution arrangement provides for five free copies to the math­ found that students have been very ematics department at colleges and uni­ surprised and impressed with the versities which are institutional members, Assistantships and Fellowships amount of financial assistance avail­ two free copies to each department listing in Notices able to graduate students. We need its program in the publication, and from to continue to make this informa­ three to five free copies to each depart­ I wish to protest the decision to no tion readily available to interested ment advertising its program in the pub­ longer include the listing of "As­ undergraduates. lication. The motivation for this particu­ sistantships and Graduate Fellow­ In the last several years I have lent lar distribution arrangement was to pro­ ships in the Mathematical Sciences" my copy of the December Notices to vide copies to institutional members as a in the December issue of Notices. a number of undergraduates, both to benefit of their memberships, to offer an By publishing this listing separately seniors who have already decided to incentive for participation in the survey which gathers the data needed to produce and charging $9 or $15 for it the pursue the study of mathematics and Society is doing a major disservice a departmental listing, and to encourage to sophomores who were uncertain advertising in the publication." to the mathematical community by but perhaps interested in mathemat­ limiting access to this information. ics as a career. It think that this in­ With the current and projected short­ formation on the available levels of age of mathematicians, the American financial assistance encouraged them Policy on Letters to the Editor Mathematical Society should be at to seriously consider mathematics as Letters submitted for publication in Notices the forefront of the effort to attract a career. I hate to think that a short­ are reviewed by the Editorial Committee, and encourage talented undergradu­ sighted decision on the part of the whose task is to determine which ones are ates to pursue graduate studies in Society to decrease circulation and suitable for publication. The publication mathematics. The one avenue most schedule requires from two to four months increase revenue will have a nega­ between receipt of the letter in Providence undergraduates have to receive in­ tive impact on the future supply of and publication of the earliest issue of formation and advice on a career mathematicians. Notices in which it could appear. in mathematics is through their col­ Publication decisions are ultimately lege professors. If we do not receive David G. Hartz made by majority vote of the Editorial information on what's available, we College of Wooster Committee, with ample provision for prior (Received November 28, 1988) discussion by committee members, by mail cannot pass it on to our students. or at meetings. Because of this discussion It is ironic that the same issue period, some letters may require as much of Notices [November 1988] which EDITOR's NoTE: "The decision to re­ as seven months before a final decision is announces this change in format also move the information on assistantships made. Letters which have been, or may be, contains the AMS-MAA Annual Sur­ and fellowships from Notices was made published elsewhere will be considered, but by the Executive Committee of the Coun­ the Managing Editor of Notices should be vey. This article by Edward A. Con­ cil and the Board of Trustees (ECBT) at informed of this fact when the letter is sub­ nors contains the statement: "We their joint meeting in May 1987, and was mitted. again express our deep concern at the part of their general consideration of The committee reserves the right to low number of American citizens re­ changes in Notices. The ECBT felt that edit letters. ceiving doctorates in the mathemati­ the information on assistantships and fel­ Notices does not ordinarily publish complaints about reviews of books or arti­ cal sciences. Tables 4 and 5, and the lowships was of serious interest to only cles, although rebuttals and correspondence accompanying graphs, provide cause a fraction of the full membership, pri­ concerning reviews in Bulletin of the Amer­ for alarm within the mathematical marily those engaged in advising under­ ican Mathematical Society will be consid­ community and the many groups it graduate mathematics majors interested ered for publication. All published letters services. American business, indus­ in graduate study in mathematics. The must include the name of the author. Letters should be typed and in legible try, government, and academe must consensus was that the December issue of Notices would be more valuable to the full form or they will be returned to the sender, be prepared for the severe effects of membership if it were a regular issue and possibly resulting in a delay of publication. this drought." [pg. 1306] carried the standard features, columns, Letters should be mailed to the Editor Edward David's Keynote Address and news items. Furthermore, they felt of Notices, American Mathematical Soci­ given at the Centennial Meeting and ety, P.O. Box 6248, Providence, RI 02940, that those interested in the information and will be acknowledged on receipt. printed in the October issue of could be equally well served by an

MARCH 1989, VOLUME 36, NUMBER 3 219 Letters to the Editor

More on Typesetting any side, I think it is wiser to let particularly marked words, such as people have the equation numbers THEOREM. Of course it is the au­ This is an open reply to a Letter to where they want to! thor, who should decide which words the Editor, printed in the November (3), the use of unreasonably small should be marked like this! 1988 AMS Notices on p. 1299. second order subscripts and super­ (6) the use of extra space around I found George Bergman's letter scripts: Agreed on this one! formulas in text. I very strongly dis­ on Uniform Style for Papers most (4), the use of very thin strokes in agree on this one! I think it is cov­ interesting. However, I don't share some calligraphic letters. He is right ered by my comment on point (4) all his views in these matters. again!-But I would like to comment above; it is just a habit from type­ I have been using TEX for seven a little more here. I think that a writing, where you cannot distinguish years now, writing a big book, some quite bad habit has evolved, trying between a one-letter word, such as journal articles and lots of smaller to mimic in fonts various notations 'I' or 'a' and a math symbol I or papers with it. used in handwriting or in ordinary a. But in typesetting, the latter are On point ( 1), having your for­ typing. I am aiming at the doubly italicized, and so the difference is mulas distorted by an ignorant type­ written letters, which in type prefer­ noticeable to the reader. I think an setter, he is perfectly right of course! ably could be replaced by boldface. extra space here disturbs the reading I think one of the advantages of us­ Nowadays you can even see under­ more than it helps the reader! ing TEX or some similar system is scored portions of computer typeset, (7). The adding of your electronic that your formulas appear in print printed text, instead of italicized. If mail address is a good idea! exactly as you want them, and not a sort of standard recommendation differently. could be issued, covering some such Hans Riesel On point (2), if equations should cases of text editing, I think a cer­ Royal Institute of Technology, be numbered on the right or on the tain effort to achieve this would be Stockholm left, I disagree with him. I don't think worthwhile. (Received December 30, 1988) it matters at all, and since there are (5), the influence of stubborn text provisions to get the numbering at editors on the author's choice of

tn~~~ AMS Centennial Publications • Volume I ~-~~-:;; A History oftlie Second Fi+h' Years VNDED ~ ~ ';)' American MatliematicaC Socie~ • 1939-1988 it grew in membership, in volume and history is volume one of American Everett Pitcher diversity of its publications, in the Mathematical Society Semicentennial number of meetings and conferences it Publications. This is volume one of a two-volume set organizes, and in the range of services it which is being published to commemorate provides to the mathematical community. the AMS Centennial. (Volume 2 will The book presents a picture of the AMS 1980 Mathematics Subject Classification: 01 contain the Proceedings of the AMS in 1938 and delineates the political ISBN 0-8218-0125-2 Centennial and will be published and social influences that shaped its 360 pages (hardcover), August 1988 at a later date.) Professor Everett subsequent development. Some of List price $40, Institutional member $32, Pitcher served as an AMS Associate the key personalities in the Society's Individual member $24 Secretary for 8 years and as the Society history, notably the Presidents, are also To order, please specify HMPITCHER/NA Secretary for the past 22 years. His long described. This book is the crowning association with the Society, his detailed achievement in Professor Pitcher's years knowledge of its workings, and his of dedication and service to the Society. historical perspective on the American Shipping/Handling: 1st book $2, each add'l mathematical community make him the This book complements the history of the $1, $25 max. By air, 1st book $5, each add'l ideal author for such a work. Society's first fifty years, written in 1938, $3, $100 max. Prepayment required. the Society's semicentennial year, by Order from AMS, P. 0. Box 1571, Annex Professor Pitcher chronicles the Society's Raymond Clare Archibald, who was the Station, Providence, Rl 02901-1571, or call activities over the past fifty years, as AMS librarian at that time. Archibald's 800-556-7774 to use VISA or MasterCard.

220 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY MARSHALL HARVEY STONE 1903-1989

Marshall Stone was born in New York City on April 8, of the great classics of twentieth century mathematics. It 1903. He was the son of Harlan Fiske Stone and Agnes was entitled "Linear transformations in Hilbert space and Harvey Stone. Harlan Stone was a prominent jurist who their applications to analysis". This comprehensive and served on the U.S. Supreme Court from 1925 to 1946 beautifully written book has been enormously influential. and as chief justice from 1942 to 1946. The family lived Modern functional (or abstract) analysis began with the in Englewood, New Jersey, during Stone's school days ideas of Volterra on "functionals" in the late nineteenth and he attended the local public schools. In 191 9 at century and was transformed and given considerable the age of only 16 he entered Harvard University from impetus in the first two decades of the twentieth century which he was graduated, summa cum laude, in 1922. by the work of Hilbert and F. Riesz. The very different Although it had been assumed that Marshall would books of Banach ( 1922) and Stone set the stage for the follow his father into the law, a growing fascination extensive developments of the past half century. with mathematics led to an extraordinary arrangement in which he spent the academic year 1922-1923 as a part time instructor at Harvard to find out whether he liked teaching. It turned out that he did and proceeded quickly to write a Ph.D. thesis under the direction of G.D. Birkhoff. The degree was awarded in 1926 but the work was completed rather earlier. The very distinguished mathematical career of Marshall Stone was under way. Before settling down at Harvard for the thirteen year period 1933-1946 Stone held a variety of positions. He was at Columbia from 1925 to 1927, at Harvard from 1927-1931, at Yale from 1931 to 1933 and at Stanford for the summer of 1933. He became a full professor at Harvard in 193 7. These early years were enormously fruitful ones for Stone's career as a research mathematician-so much so that he was elected a mem­ ber of the National Academy of Sciences in 1938 at the unusually early age of 35. His first paper was a short note on normal orthogonal sets of functions published in 1925 and by 1928 had published ten more papers on various aspects of the theory of orthogonal expansions-special emphasis being placed on expansions in terms of eigenfunctions of linear differential operators. This was one of the principal interests of G. D. Birkhoff and Stone's work was in the same tradition. Then in 1929 he began to work on the abstract theory of possibly unbounded self adjoint In his introduction Stone freely acknowledges his operators in Hilbert space, announcing his results with scientific debt to J. von Neumann. Von Neumann pub­ three notes published in the Proceedings of the National lished a long paper on the same subject in 1929 and it Academy of Sciences in 1929 and 1930. This work is not easy to disentangle their respective contributions. culminated in a six hundred page book which is now one What is clear is that Stone was originally stimulated by

MARCH 1989, VOLUME 36, NUMBER 3 221 Marshall Harvey Stone preliminary work of von Neumann but had many key the irreducible solutions of the Heisenberg commuta­ ideas quite independently. Moreover the whole last half tion relations in integrated form. It may be interpreted of the book, including the chapter on spectral multiplicity as giving a complete determination of all unitary ir­ theory and the extensive applications to differential and reducible representation of a certain non compact non integral operators, has no counterpart in von Neumann's commutative locally compact group-now well known writings. The central point of the work of both men as the Heisenberg group. So interpreted, it is the first was the extension of Hilbert's spectral theorem from example of such a determination by about a decade. bounded to unbounded operators. This extension was Finally a series of natural generalizations of the Stone­ made necessary by the problem of making mathemati­ von Neumann uniqueness theorem culminated in the cally coherent sense of the newly discovered refinement imprimitivity theorem and the extension of the notion of classical mechanics known as quantum mechanics. of induced representation from finite groups to general Here an important part of the problem was discovering locally compact groups. the "correct" definition of self adjointness for unbounded In 1934 and 1935 Stone published two more notes in operators. This correct definition is rather delicate and the Proceedings of the National Academy which seemed the extension of the older theory of Hilbert and others at first to represent a completely new departure. They was a major task. were entitled "Boolean algebras and their applications to The last of the three notes mentioned above was topology" and "Subsumption of Boolean algebras under entitled "Linear transformations in Hilbert space III. the theory of rings". Actually, just as Stone's work on Operational methods and group theory". The material it spectral theory may be regarded as a natural outgrowth of summarized was originally meant to be included as an his earlier work on concrete eigenfuntion expansions, so extra chapter of the book but was omitted for reasons of can his work on Boolean algebras be regarded as a natural space. The two theorems it announces are of sufficient outgrowth of his work on spectral theory. This is because importance to be discussed here in some detail. of the role played in spectral theory by Boolean algebras Three years earlier, in 1927, Hermann Weyl and of projections. In an entirely characteristic attempt to get Eugene Wigner had introduced group theoretical methods to the bottom of things Stone undertook a thoroughgoing into the new quantum mechanics in quite different ways. study of Boolean algebras and made a number of far Weyl's idea was to use group theory to help clarify the reaching discoveries relating Boolean algebras to general foundations. His paper, written in physicists' language, topology on the one hand and to the theory of rings and implicitly conjectured two theorems about one parameter ideals on the other. groups of unitary operators in Hilbert space. Stone's note The discovery of these connections has had signifi­ states these conjectures as carefully formulated theorems, cant consequences for all three subjects. One beautiful announces that he is in possession of proofs and gives result is the celebrated Stone-Weierstrass theorem vastly some indication of their nature. Detailed proofs of generalizing the theorem of Weierstrass concerning the both theorems were published in 1932-one by Stone uniform approximability of arbitrary continuous func­ and one by von Neumann. Both theorems were not tions on a finite interval by polynomials. Another is the only important for quantum mechanics, in the manner natural one to one correspondence between all compact indicated by Weyl, but were also highly significant early Hausdorff spaces on the one hand and certain rings on steps in the then nascent unitary representation theory of the other. Stone's studies of the relationship between non compact locally compact groups. One of them also compact spaces and rings of continuous funtions an­ played an important role in the chain of events leading ticipated important elements in the modern theory of through a note of B.O. Koopman to the ergodic theorems commutative Banach algebras. The detailed development of von Neumann and Birkhoff and on to modern ergodic of Stone's ideas on Boolean algebras, general topology, theory. etc. were published in three lengthy papers in 1935, At this point it is useful to distinguish between 1936 and 1937 respectively. The first appeared in the two versions of one of Stone's theorems. The version American Journal of Mathematics and the second and suggested by Weyl's paper (and which stimulated Koop­ third in the Transactions of the American Mathematical man) asserts that for every one parameter unitary group Society. Applications of the new ideas to spectral theory t -+ U1 there is a unique self adjoint operator H such were announced in notes published in 1940 and 1941. that U1 = eiHt. The version emphasized in Stone's note Soon after the entry of the United States into World is an analogue of the spectral theorem for one parameter War II the character of Stone's work underwent a unitary groups. This version has the great advantage considerable change. For several years he was engaged in that it can be generalized almost verbatim to arbitrary secret work for the U.S. government. A year after the end (separable) locally compact commutative groups. of the war he resigned his position at Harvard to take The other theorem-the celebrated Stone-von Neu­ on the chairmanship of the mathematics department at mann uniqueness theorem-states the uniqueness of the University of Chicago. This once great department

222 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Marshall Harvey Stone had been declining in quality and Stone's mission was His skill with the English language also manifested to strengthen it and bring it up to its former stature. itself in his lectures which were models of clarity and In this he succeeded admirably. Before very long it was organization. Stone was only moderately active in super­ regarded by many as the best mathematics department vising Ph.D. theses. Indeed there are anecdotes about his in the country and, while a position like that is hard to reluctance to do this sort of teaching. On the other hand keep indefinitely, it has remained one of the strongest he did turn out a respectable number of new Ph.D.s departments ever since. He brought in Andre Weil, S.S and influenced many other young mathematicians by his Chern, Saunders Mac Lane and a number of promising writings and through informal personal contact. younger men. Moreover in the words of one of the Stone married young (in 1927) and he and his first latter "Marshall devoted himself with both intensity wife Emmy raised three daughters. Reports have it that he and breadth,-from the largest issues to the smallest was serious about fatherhood in a rather old fashioned details-to the Department's welfare and development". way. His daughters had regular chores to do and in In 1952, Stone turned the chairmanship of the financial matters were kept on strict allowances. On the Chicago department over to Saunders Mac Lane but other hand he also believed in family fun and one of his continued to be occupied with administrative matters. many side interests was gourmet cookery. This marriage He was a strong force in reestablishing the International dissolved in divorce in 1962 but Stone soon remarried. Mathematical Union-was much involved in the drafting His second marriage, to Ravijojla Kostic, lasted the rest of its constitution and served as its president from 1952 of his life. to 1954. He also interested himself actively in the prob­ Of all Stones's many interests his love of travel was lems of mathematical and scientific teaching-especially surely dominant. He began to travel when he was quite at the international level-and served on various boards young and was on a trip to India when he died. He and commissions. travelled frequently and extensively and was interested While his various administrative concerns and ac­ in seeing all parts of the globe. For example he visited tivities prevented him from working on mathematical the Pacific islands and (while travelling with Ravijojla) problems with his former intensity Stone continued to was shipwrecked in Antartica. It is very hard to think of work and to publish results rather steadily until the a place that he has not come fairly close to at some time early 1960's. At the same time his mathematical interests or another. tended more and more toward the elucidation of ques­ Stone, of course, was the recipient of many honors. tions of great generality and and profundity about the We have mentioned his early election to the National true nature of mathematics and mathematical concepts. Academy of Sciences. He was also elected, at an early There is reason to believe that his publications of the age to the American Academy of Arts and Sciences and last thirty years give a very incomplete picture of his to the American Philosophical Society. He was president mathematical activity. At a conference in honor of his of the American Mathematical Society ( 1943-1944) and second retirement (see below) Stone gave a remarkable received many honorary doctorates, both domestic and two hour lecture outlining his rather unusual and original foreign. In 1982 he was awarded the National Medal of views on the nature and structure of mathematics. Science. According to Edwin Hewitt, two extra honors Stone remained at the University of Chicago until he that gave him special pleasure were his election to an retired as Professor Emeritus in 1968. At this time there Honorary Professorship at Columbia Teachers College was a week long conference in his honor the proceedings and to membership in the Explorers Club of New York of which were published in 1970 by Springer-Verlag. City. Felix Browder was the editor. He did not wish to stop Marshall Stone was a man with a very broad outlook teaching however and forthwith began a new career as and wide range of interests who seems to have thought George David Birkhoff professor of mathematics at the rather deeply about a number of issues. One had only University of Massachusetts in Amherst. No doubt the to talk to him at length or read his non mathematical fact that Amherst, Massachusetts had been his father's writings to come away with the impression that here childhood home added to the attractiveness of this move. was an unusually thoughtful man with a high degree of He taught there for the next twelve years and among penetration and insight. More than most he seemed well other activities supervised two Ph.D. theses. During his endowed with a quality which I can only describe as final year he was honored with a second retirement wisdom. conference. While on a visit to Madras, India he died quickly of One of the many striking accomplishments of Mar­ a sudden illness on January 9, 1989. shall Stone was a truly extraordinary command of the George W. Mackey English language. This gave a special flavor to his book, Harvard University his mathematical papers and his many writings on other subjects.

MARCH 1989, VOLUME 36, NUMBER 3 223 Look whafs new in Mathematical Surveys and Monographs The Mathematical SUIVeys and Monographs series is one you're already familiar with. It's been around since 1943, when The Problem of Moments by J. A Shohat and J. D. Tamarkin was pub­ lished. The series has grown over the years and includes important mathematical monographs that cover a broad spectrum of areas such as function theory, analysis, approximation theory, algebra, and topology. Each of the books is designed to gtve a survey of the subject and a brtef introduction to its recent developments and unsolved problems. The editorial conunittee.•• Victor W. Guillemin M. Susan Montgomery (Chainnan) David Kinderlehrer ------... invites you to participate in the development of this classic series by

• consulting them as reference books • using books in this sertes in your courses • recommending them to your library • submitting manuscrtpts for publication to begin a standing order to the Director of Publication at the .AMS

New and Recent Publications in Mathematical Surveys and Monographs Each new title is exceptional. All are the high quality mathematical publications you've grown to expect in the Mathematical Surveys and Morngraphs series. Yet the variety of topics and areas of mathematical interest make them perixt reference books or possible textbooks for graduate level oourses.

0 .AmenabDity by Alan I.. T. Paterson, 1988, 416 pp. 0 Introduction to various aspects of degree theory in (ISBN 0-8218-1529-B). Ust $90, Inst mem. $72, Banach spaces by E. H. Rothe, 1900, 254 pp. (LC 00- Jn:liv. mem. $54, Code SURV/29NA 8038; ISBN 0-8218-1522-9). Ust $62, Inst mem. $50, Jn:liv. trem $37, Code SURV/23NA 0 Direct and inverse scattering on the line 1y Rk:hard Beals, Percy Deift, and Carlos Tonri, 1988, 0 Noncommutative harmonic analy&ia by Mk:hael E. Taylor, 209 pp. (LC 88-14487; ISBN 0-8218-1530-X). Ust 1900, 344 pp. (LC 00-10924; ISBN 0-8218-1523-7). Ust $53, Inst mem. $42, Indiv. mem. $32, Code SURV/28NA $70, Inst mem. $56, Indiv. mem. $42, Code SURV/22NA

0 Basic hypergeometric series and applications by 0 1be Bieberbach coqlecture: Proc«wwi"'P' of the Nathan J. Flne, 1988, 144 pp. (LC 88-6235; ISBN 0-8218- symposium on the occasion of the proof, edited by 1524-5). Ust $39, Inst mem. $31, Indiv. trem $23, Albert Baernstein, David Drasin, Peter Duren, and Code SURV/27NA Albert Marden, 1900; reprinted 1987, 260 pp. (LC 00-10843; ISBN 0-8218-1521-0). Ust $46, Inst mem. $37, Indiv 0 Operator theory and arithmetic in H by Hart l3errovici. mem. $28, Code SURV/21NA 1988, 275 pp. (LC 88-10344; ISBN 0-8218-1528-8). Ust $37, Inst mem. $54, Indiv. trem $40, Code SURV/26NA 0 PartiaDy ordered abelian groups with interpolation by Kenneth R Goodearl, 1986, 358 pp. (LC 00-7876; 0 Asymptotic behavior of dissipative systems 1y ISBN 0-8218-1520-2). Ust $70, Inst mem. $56, Indiv. Jack K Hale, 1988, 198 pp. (LC 87-33495; ISBN 0-8218- mem. $42, Code SURV/20NA 1527-X). Ust $54, Inst mem. $43, Indiv. trem $32, Code SURV/25NA

0 Noetherian rings and their applications, edited by For infonnation on numbers 1-19, please see the AMS Lance W. Small, 1987, 118 pp. (LC 87-14997; ISBN Catalogue of Publications. 0-8218-1525-3). Ust $38, Inst trem $30, Indiv. mem. $23, Code SURV/24NA

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PREPAYMENf REQUIRED. Order from the American Mathematical Society, P. 0. Box 1571, Armex Station, Providence, RI 02901-1571, or call 800-556-7774 from within the oontinental U. S. (401-272-9500, elsewhere) to use VISA or MasterCard. Prices subject to change. Please add K>r SHIPPING AND HANDUNG: first book $2, each additional $1, $25 maximum By air, first book $5, each additional $3, $100 maxinrum RICHARD M. SCHOEN AWARDED 1989 BOCHER PRIZE

The Bacher Prize is awarded every five years for a notable research memoir in analysis which has appeared in the previous five years. The prize honors Maxime Bacher (1867-1918) who was the Society's second Colloquium Lecturer ( 1896) and tenth President ( 1909, 191 0), and one of the founding editors of the Transactions. The sixteenth award was made at the Society's ninety-fifth Annual Meeting, in Phoenix, Arizona, on January 12, 1989. The 1989 recipient is RICHARD M. ScHOEN of Stan­ ford University. The Bacher Prize is augmented by awards from the Leroy P. Steele Fund and currently amounts to $4,000. The Prize was awarded by the Council of the Society acting on the recommendation of the Committee to Select the 1989 Recipient of the Bacher Prize, consisting of Paul J. Cohen, Richard B. Melrose, Chairman, and Louis Nirenberg. The text below includes the Committee's citation, the recipient's response on presentation of the award and a brief biographical sketch of the recipient. Citation The 1989 Bacher Prize is awarded to Richard M. Schoen of Stanford University for his work on the application of partial differential equations to differential geome­ try, in particular his completion of the solution to the Yamabe Problem in "Conformal deformation of a Rie­ mannian metric to constant scalar curvature". Journal of Differential Geometry 20 ( 1984) pages 479-495. Response It is a great honor for me to receive the Bacher prize to certain estimates which were later obtained by Niren­ of 1989, and I thank the A.M.S. and the Bacher Com­ berg and Pogorelov for smooth metrics. In the meantime mittee for recognizing my work in this way. There is Lewy had solved the problem for analytic metrics. This a long tradition of interaction between the cited areas example is typical in that it often happens that a geo­ of Differential Geometry and Partial Differential Equa­ metric problem can be formulated as a specific problem tions. I will discuss the interaction which centers around in P.D.E.; thus from the geometer's point of view P.D.E. nonlinear problems. An early example which illustrates often provides the framework necessary to attempt a this tradition is H. Weyl's formulation, in 1916, of solution as well as a body of knowledge (estimates, reg­ the isometric embedding problem for closed surfaces of ularity results, and such) and more importantly methods positive curvature. The geometric problem was reduced of attack. The interaction benefits both areas because

MARCH 1989, VOLUME 36, NUMBER 3 225 1989 Bocher Prize

Differential Geometry provides a rich class of nonlinear A common feature of both the fields of nonlinear problems which serve as model problems from which a P.D.E. and global Differential Geometry is that our body of knowledge may emerge. The geometric meaning knowledge in both areas is very primitive, and there are of the solution may lead one toward the correct analytical many more unsolved problems than there are theorems. estimates and theorems. Specific areas in which new results would be impor­ The Yamabe Problem should be viewed as a part tant are quasi-linear elliptic systems (hopefully including of the variational theory for the Einstein-Hilbert varia­ the elliptic Einstein equations), nonlinear parabolic and tional problem; the elliptic version of the action principle hyperbolic evolution equations, and singularities of non­ governing the motion of the gravitational field in Gen­ linear equations. The problems involving singularities eral Relativity. Yamabe viewed this general problem as which are important include the study of singular sets an analytic approach to solving the three dimensional for elliptic problems such as those of least area subman­ Poincare conjecture. He formulated the problem which ifolds as well as singularity development in nonlinear bears his name as a semilinear scalar P.D.E. around 1960 evolution equations. I am confident that the long tradi­ and it was solved in special cases by Trudinger and Aubin tion of interaction between Differential Geometry and over the next 15 years. In its strongest form the solution nonlinear P.D.E. will continue to be fruitful to both asserts that critical points of the variational problem fields for many years to come. which are predicted by Morse theory do, in fact, exist. The proof of this general result involves consideration Sketch of large energy solutions, and, in fact, one must consider Biographical singular weak solutions of the P.D.E. The structure of Richard M. Schoen was born October 23, 1950, in weak solutions is an intricate topic about which we have Celina, Ohio. He received his B.S. degree from the limited knowledge. Additionally, an important role in University of Dayton in 1972 and his Ph.D. from the derivation of the necessary estimates is played by Stanford University in 1976 under the direction of Leon results from General Relativity involving gravitational Simon and Shing-Tung Yau. He was a lecturer at the energy. Thus we return full circle to the origins of the University of California, Berkeley from 1976-1978 and problem. an assistant professor at the Courant Institute from Another problem which arises from Differential Ge­ 1978-1980. From 1980-1987 he was a professor at the ometry and has had substantial impact on the devel­ University of California; in Berkeley from 1980-1985 opment of P.D.E. is the Plateau problem, or the study and in San Diego from 1985-1987. Since 1987 he has of minimal submanifolds. The nonparametric minimal been Professor of Mathematics at Stanford University. surface equation provided a strong impetus for the de­ Professor Schoen has been a visiting member at the velopment of the theory of quasi-linear elliptic equations Institute for Advanced Study on two occasions, during in the fifties and sixties. A successful higher dimensional the 1979-1980 academic year and during the spring parametric theory was begun approximately 30 years ago semester of 1984. He was a visiting professor at the through the work of DeGiorgi, Federer, and Fleming. University of Melbourne in Australia during the fall of A major outgrowth of this work was the introduction 1980 and a visiting professor at Stanford University of partial regularity theory into P.D.E. The partial regu­ during the fall of 1983. In the fall of 1985 he was a larity method has become a powerful tool applicable to visitor at the Mittag-Leffler Institute in Sweden and at a variety of nonlinear problems. Finally, the theory of the Institut des Hautes Etudes Scientifiques in France. minimal hypersurfaces has been applied to obtain results Professor Schoen was awarded an NSF Graduate about manifolds of positive scalar curvatures by S.T. Fellowship in 1972, a Sloan Foundation Fellowship in Yau and myself. This application uses the analytic the­ 1979, and a MacArthur Prize Fellowship in 1983. He was ory (existence and regularity) in an important way. Thus elected to the American Academy of Arts and Sciences the theory of minimal submanifolds is of substantial in 1988. importance for both geometry and P.D.E.

226 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY EvERYBODY COUNTS

A Report to the Nation on the Future of Mathematics Education Summary

As the 1980s began, an inattentive nation began stirring In January, the National Research Council (NRC) released a in response to alarming problems in its educational major authoritative report on the state of U.S. mathematics ed­ system. Since then, dozens of reports have analyzed ucation. Presenting a compelling analysis of the problems and virtually every aspect of U.S. education. Some call for challenges in this area, ""Everybody Counts: A Report to the changes in curricula, others for changes in the structure Nation on the Future of Mathematics Education·· treats mathe­ of schools; some cite deficiencies in the ways that teachers matics education as all one system, from kindergarten to grad­ are educated, while others examine signs of decay in the uate school. Not merely a plea for reform, ""Everybody Counts"" charts a bold agenda for change over the next two decades. social and economic structures of society. All agree that The report, three years in preparation, is the joint work of two the present educational system must change. NRC boards, the Mathematical Sciences Education Board and The concern here is with mathematics, which is­ the Board on Mathematical Sciences, together with the Com­ apart from English-the most widely studied subject mittee on the Mathematical Sciences in the Year 2000, a joint in our nation's schools and colleges. Mathematics ed­ activity of the two Boards. ucation is an immense enterprise involving 35 million What follows is the official NRC summary of ""Everybody students and over a million and a half teachers, account­ Counts;· consisting of a condensation of the last two chapters ing for more than 10 percent of the nation's educational of the report, which delineate the challenges of mathematics expenditures-about $25 billion annually. It is an enter­ education, current responses to those challenges, and a na­ prise rooted in antiquity, with some of today's curricula tional plan of action. The quotes appearing in the body of the matching very closely educational patterns of 500 years summary are extracted from the report. The NRC produced only a limited number of copies of this summary, but reprints ago. Yet, paralleling the larger system of which it is a part, of it are available from the AMS. The summary is reprinted in mathematics education has entered a period of significant Notices with the permission of National Academy Press, Wash­ change, certain to last well into the next century. ington, DC. Notices readers are urged to obtain copies of the full re­ National Needs port, which are available from National Academy Press, 2101 Constitution Avenue, Washington, DC 20418; telephone 202- Not only in mathematics but also in every other school 334-3313. Prices are as follows: $7.95 for a single copy, $6.50 subject, educators are faced with significant demographic each for 2-9 copies, and $4.95 each for 1 0 or more copies. No changes and rising expectations for preparing the kind other discounts apply. Shipping and handling are included, and of work force the country will need in the future. orders must be prepaid. Information-age technology will continue to grow in importance. Pressed by rising international competition, American industry will demand improved quality and increased productivity. The world of work in the twenty­ first century will be less manual but more mental; less Opportunity . . • tapping the power of mathematics mechanical but more electronic; less routine but more verbal; and less static but more varied. Communication has created a world economy in "Changing demographics have raised the stakes for which working smarter is more important than just all Americans. Never before have we been forced working harder. Jobs that contribute to this world econ­ to provide true equality in opportunity to learn. omy require workers who are mentally fit-workers who The challenge we face today is to achieve what we are prepared to absorb new ideas, to adapt to change, believe." to cope with ambiguity, to perceive patterns, and to solve unconventional problems. It is these needs, not just

MARCH 1989, VOLUME 36, NUMBER 3 227 Everybody Counts the need for calculation (which is now done mostly by Opportunity for the Nation machines), that make mathematics a prerequisite to so The focus in what follows is on a bold but realistic many jobs. More than ever before, Americans need to approach to reforming mathematics education as schools think for a living; more than ever before, they need to and colleges work toward the demanding objectives now think mathematically. before them. Means must be found for significantly improving student achievement while simultaneously making changes in mathematics education in response Schools to the demands of an increasingly mathematical society. Historically, schools in the United States were designed The changes proposed here are: with a dual mission: to teach all students the basic skills • rooted in traditional values, yet reflect the greatly required for a lifetime of work in an industrial and agri­ increased applicability of mathematics to prob­ cultural economy and to educate thoroughly a small elite lems faced almost daily by scientist, engineer, who would go to college and then pursue professional worker, and citizen; careers. As the needs of society have changed, the balance • guided by national goals, but respect state and of these two goals has shifted. Although schools have local autonomy; adapted somewhat, today's schools continue to labor un­ • built on the educational reform effort already der the legacy of a structure designed for the industrial under way; age misapplied to educate children for the information • to be carried out locally by the only people who age. can bring about meaningful and lasting reform­ The changing nature of work will make continuing the teachers. education a lifelong reality for adults. Schools, therefore, will have to provide all students with a strong foundation Among the several insights and messages that this for continuous learning; colleges and universities will report is intended to convey is this uniquely impor­ have to educate both young adults and older workers; tant one: because of emerging general agreement within and industry will have to focus its continuing education the mathematics, mathematics education, and related on areas that extend, rather than repeat, what schools professional communities on the goals for mathematics provide. Education in the future must build continually, education and the means for achieving them, the stage from childhood to retirement, on a versatile and unbroken is set for the nation to push ahead boldly in this area of foundation provided by school education. education. In the next decade, the United States has a historic opportunity to revitalize mathematics education.

Literacy and Numeracy Change • . . mobilizing for reform Literacy and numeracy-that is, proficiency in language and in mathematics-are the primary sources of strength and versatility in school education. Schools and col­ ·~s technology has 'mathematicized' the workplace leges will have to meet goals now widely held to be and as mathematics has permeated society, a com­ unattainable: placent America has tolerated underachievement as the norm for mathematics education. We have in­ • The level of literacy formerly associated with the herited a mathematics curriculum conforming to the few who entered college must become a goal for past, blind to the future, and bound by a tradition of all. minimum expectations." • The degree of facility with mathematics formerly required only of those preparing for scientific careers is now an essential ingredient in the Mathematics education in the United States is facing foundation for working careers in the informa­ major challenges on nearly every front: tion age. • Far too many students, including a disproportion­ Mathematical and scientific literacy form the basis of ate number from minority groups, leave school technological expertise in the workplace. In tomorrow's without having acquired the mathematical power world, the best opportunities for jobs and advancement necessary for productive lives. will go to those prepared to cope confidently and com­ • The shortage of qualified mathematics teachers petently with mathematical, scientific, and technological in this country is serious, more serious than in issues. As the foundation of science and technology, math­ any other area of education, and affects all levels ematics provides the key to opportunity. from elementary school to graduate school.

228 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Everybody Counts

• At a time when the percentage of minority stu­ the burgeoning service sector are called upon regularly to dents is increasing, the shortage of new minority operate complex machines and to interpret graphs, data, teachers of mathematics is particularly acute. and probabilities. • On average, U.S. students do not master math­ Parental and legislative pressures in the past few ematical fundamentals at a level sufficient to years, driven largely by frustration over declining test sustain our present technologically based society. scores, have led to some rash actions: students of other nations, • When compared with • Increased numbers of required courses-where lag far behind in level of math­ U.S. students there is no agreement on what the added courses the resulting educa­ ematical accomplishment; should contain or where capable teachers are to our ability to compete in tional deficit reduces be found to teach them. areas. international • Increased reliance on standardized tests-where are reflected and magni­ • Public attitudes, which there is very little understanding of what the tests low expectations in fied by the media, encourage contain or what they are capable of testing. mathematics is poor school mathematics. Only in • Increased use of test scores, especially for teacher socially acceptable. performance and school accountability-where there is little in our schools and • Curricula and instruction recognition that the tests reflect only a small part the times; they reflect colleges are years behind of curricular objectives. neither the increased demand for higher-order thinking skills, nor the greatly expanded uses Too often, the results of such actions are unreliable of the mathematical sciences, nor what we now tests, watered-down curricula, and diminished morale. know about the best ways for students to learn The nation is in the grip of a testing mystique that has mathematics. led to widespread misuse of standardized tests. Public • Calculators and computers have had virtually no pressures for "back-to-basics" stem from a very limited impact on mathematics instruction in spite of understanding of the challenges we face. Carried to the their great potential to enrich, enlighten, and extreme, these pressures could rob our children of the expand students' learning of mathematics. opportunity to learn what they will need to know of • Commonly employed methods of evaluation­ mathematics in their adult lives. especially standardized, paper-and-pencil, multiple-choice tests of "basic skills"-are them­ Public Understanding selves obstacles to the teaching of higher-order thinking skills as well as to the use of calculators and computers. • Undergraduate mathematics is intellectually stag­ "As children become socialized by school and society, nant, overgrown with stale courses that fail to they begin to view mathematics as a rigid system stimulate the mathematical interests of today's of externally dictated rules governed by standards students. of accuracy, speed, and memory. Their view of mathematics shifts gradually from enthusiasm to apprehension, from confidence to fear." Counterproductive Beliefs Appropriate response to the challenges of mathemat­ ics education will require a systematic effort to develop "As mathematics is more than calculation, so educa­ in the public a deeper understanding of the changes and tion in mathematics must be more than mastery of the improvements needed. This will be a formidable arithmetic." task. Often, public discussion about mathematics education masks a hidden agenda of values that have traditionally It is mistakenly thought by many otherwise well­ been carried forward by the school study of mathematics. informed adults that the mathematics they learned in Since the demise of Latin as a required school subject, it school is adequate for their children. But mathematics is to mathematics that many look as a vehicle to instill has changed. It is significantly more diverse than it was such qualities as precision, discipline, neatness, and several decades ago when most of today's adults went to accuracy. Mathematical truth-in popular caricature­ school. The mathematics commonly used today goes far is certain, absolute, unchanging, eternal. Mathematics beyond arithmetic and elementary geometry. Members of appears to many to be a safe harbor of calm in a the armed forces as well as workers in manufacturing and turbulent sea of social and educational change.

MARCH 1989, VOLUME 36, NUMBER 3 229 Everybody Counts

In spite of the fact that it is constantly expanding curricula current. In today's climate, in which technol­ and changing, mathematics more than any other science ogy and research are causing unprecedented changes in has been taught as an ancient discipline. A nation that the central methods and applications of mathematics, persists in this antiquated view of mathematics is destined present U.S. practice is totally inadequate. International to fall behind scientifically and economically. Parents comparisons of student performance in mathematics show who persist in this view are denying their children the that U.S. students lag far behind their counterparts in opportunity to develop and prosper in the information age. other industrialized countries. The "top-down" systems have beaten us hands down. The American Way Lessons from the Past "Why Not Just Imitate Japan? International studies Because of vast differences in both tradition and con­ of mathematics and science education show that, stitution, a "top-down" approach will not work in the when compared with students in other countries, United States. Experience has much to teach us on that U.S. students do very poorly while Japanese students score. do very well. One natural response, therefore, is to Few traces remain of the expensive, major curricu­ think that we could improve our educational system lum development projects so prominent in the 1960s by imitating Japan. and 1970s. These projects tried to develop, on a na­ tional scale, complete curricula (including instructional the These same studies, however, document that materials) that could be adopted as a whole by school social context of education has a greater influence districts. But the theorists and planners who developed on student performance than does actual classroom these curricula were naive about the process of change; student expectations, practice. Parental attitudes, big curricular projects failed to take root in American and teacher self-respect are among the most signif­ schools because they were transplanted fully grown into icant factors in quality education and they depend an environment better suited to locally grown methods. uniquely on culture. Where teachers were not directly involved in devel­ Imitating others is no solution. The United States opment, where their identification with the product was must find a strategy that builds on the traditions of not ensured, where they considered district acceptance this country, one whose strength lies in this nation 's of new curricula as a "top-down" imposition, the revised unique tradition of local initiative and decentralized programs did not last. Where parents could not (or did authority." not) understand the need for change or the reasons new curricular emphases were chosen, resentment and anger resulted and a conviction set in that if "the old math" The development of more effective strategies for was good enough for them, it was good enough for their revitalizing mathematics education must be based in children. part on an understanding of why it is so difficult to bring about change in education in the United States. The truth we shrink from confronting is that most previous A New Approach reform efforts have failed. A skeptical public will rightly As our country enters a new period of change in math­ ask why any new effort is more likely to succeed. Part ematics education, we can benefit from several lessons of the difficulty we face in mathematics education is a drawn from these previous attempts: natural reflection of our constitutional dilemma: how to reconcile local authority with national need. • Free-standing, full-service curriculum develop­ In many countries, all children in the same grade ment projects adopted intact by school districts study essentially the same material in almost the same do not work. way. Such practice, common around the world, reveals a • A superficial, district-by-district approach to cur­ strong tradition of a "top-down" approach in education. ricular overhaul is potentially disastrous, given The process of curricular reform prevalent in Amer­ the demanding nature of what schools face in ica might be described as a weak type of grass-roots mathematics education today. approach. With little or no outside help, teacher teams • Any successful effort to improve mathematics at the local level work over the summer in efforts to keep curricula and instruction in the schools will re­ mathematics curricula up to date. quire an extensive public information campaign In static times, in periods of unchanging demands, that reaches all the varied constituencies of math­ perhaps our grass-roots efforts could suffice to keep ematics education.

230 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Everybody Counts

Effective change requires a great deal of the public: Transition 2: The teaching of mathematics is shifting from an authoritarian model based on "transmission change; • conviction of the need for of knowledge" to a student-centered practice featuring of high-quality • consensus on the importance "stimulation of learning." for everyone; mathematics education In both schools and colleges, classrooms of passive • skepticism about "quick fixes" and simplistic students who are expected to sit and absorb rules that solutions; appear as arbitrary dicta are gradually giving way to • awareness of the general nature of the changes learning environments that: needed; • support for investment of the necessary resources; • encourage students to explore; • recognition of the need for continuing leadership • help students to verbalize their mathematical at the national level. ideas; • show students that many mathematical questions The time is ripe for a new approach to curricular reform have more than one right answer; in the United States-one that establishes appropriate • provide evidence that mathematics is alive and national expectations based upon broad public support by exciting; all of the constituencies concerned. • teach students through experience the importance of careful reasoning and disciplined understand­ ing; Transitions ... bridges to the 21st century • build confidence in all students that they can learn mathematics. In order to meet the challenges of our time, mathematics education is beginning already to negotiate several diffi­ Transition 3: Public attitudes about mathematics are cult transitions that will dominate the process of change shifting from indifference and hostility to recognition of during the remainder of this century. the important role that mathematics plays in today's society. Transition 1: The focus of school mathematics is Although the burden of unfavorable school experi­ shifting from a dualistic mission-minimal mathematics ences continues to color public opinion about mathemat­ for the majority, advanced mathematics for a few­ ics, contemporary events are sending different messages to a singular focus on a significant common core of which are gradually being heard: mathematics for all students. • in other nations where more is expected, more mathematics is learned; • as the roles of science and technology expand, so "Everyone depends on the success of mathematics does the importance of mathematics; education; everyone is hurt when it fails. Mathemat­ • for an informed citizenry, mathematical literacy ics must become a pump rather than a filter in the is as important as verbal literacy. pipeline of American education." As attitudes about the importance of mathematics improve, so will expectations for mathematics education. Transition 4: The teaching of mathematics is shifting The needs of industry for a mathematically and from preoccupation with inculcating routine skills to technically literate work force compel schools to provide developing broad-based mathematical power. more mathematical education to more students than ever before. Accomplishing this will pose significant challenges to: • develop a core of mathematics appropriate for "Evidence from many sources shows that the least ef all students throughout each year of school; fective mode for mathematics learning is the one that • educate well a significantly larger proportion of prevails in most of America's classrooms: lecturing the population; and listening." • stimulate able students with the excitement and challenge of mathematics; • differentiate instruction by approach and speed, Broad mathematical power requires that students be not by curricular goals; able to discern relationships, reason logically, and use a • select topics and approaches of broad interest range of mathematical methods to solve a wide variety of and effectiveness. nonroutine problems. The repertoire of skills which now

MARCH 1989, VOLUME 36, NUMBER 3 231 Everybody Counts undergird mathematical power includes not only some traditional paper-and-pencil skills, but also many broader and more powerful capabilities. Today's students must '~s a practical matter, mathematics is a science of be able to: pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and • perform mental calculations and estimates with change." proficiency; • decide when an exact answer is needed and when an estimate will serve the purpose; • know which mathematical operations are appro­ Mathematics teachers at all levels-from elementary priate in particular contexts; school to university-are adapting their teaching meth­ • use a calculator correctly, confidently, and appro­ ods to include both new approaches to instruction and priately; new subject matter appropriate to future-oriented cur­ • estimate orders of magnitude to confirm mental ricula. Calculators and computers make new modes of or calculator results; instruction feasible at the same time that they inject into • use tables, graphs, spreadsheets, and statistical the learning environment the special sense of wonder techniques to organize, interpret, and present which goes with the healthy development of mathemati­ numerical information; cal power. • judge the validity of mathematical and technical Calculators and computers should be used in ways information presented by others; that anticipate continuing rapid change due to technologi­ • use computer software for mathematical tasks; cal developments. Technology should be used not because • formulate specific questions from vaguely defined it is seductive, but because it can improve mathemat­ problems; ical learning by extending each student's mathematical • select effective problem-solving strategies. power. Calculators and computers are not substitutes for hard work or precise thinking, but challenging tools to be used for productive ends. Transition 5: The teaching of mathematics is shifting from emphasis on preparation for future courses to greater emphasis on topics that are relevant to students' present and future needs. Transition 7: The public perception of mathematics is Most mathematics should be presented in the context shifting from that of a fixed body of arbitrary rules to a of its uses, with appreciation of mathematics as a vigorous active science of patterns. deductive logical system built up slowly through the Mathematics is a living subject that seeks to under­ rising levels of education. Examples of areas deserving stand patterns which permeate both the world around greater emphasis are: us and the mind within us. Although the language of • probability, which facilitates reasoning about un­ mathematics is based on rules that must be learned, certainty and assessment of risk; it is important that students move beyond rules to be • exploratory data analysis and statistics, which able to express things in the language of mathematics. facilitate reasoning about data; This transformation suggests change in both curricular • model-building, which facilitates systematic struc­ content and instructional style. It involves renewed effort tured understanding of complex situations; to focus on: • operations research, which facilitates planning • searching for solutions, not just memorizing pro- complex tasks and achieving performance objec­ cedures; tives; • exploring patterns, not just learning formulas; • discrete mathematics, which facilitates under­ • formulating conjectures, not just doing exercises. standing of most applications of computers. As teaching begins to reflect these emphases, students These new topics imply that observation and ex­ will have opportunities to study mathematics as an perimentation will be important in future mathematics exploratory, dynamic, evolving discipline rather than as programs and that school mathematics will draw closer a rigid, absolute, closed body of laws to be memorized. to other school subjects, especially to science. They will be encouraged to see mathematics as a science, Transition 6: The teaching of mathematics is shifting not as a canon, and to recognize that mathematics is from primary emphasis on paper-and-pencil calculations really about patterns and relationships and not merely to full use of calculators and computers. about numbers.

232 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Everybody Counts

Action ... a new national strategy New plans for the renewal of school mathematics must be founded on what we have learned about making changes in the extremely decentralized U.S. system in "All students should study mathematics every year which local and state agencies control education. Two they are in school. Secondary school mathematics special strengths of American mathematics education should provide for all students a core of mainstream should underpin any movement for renewal: mathematics in which different student groups are • The creative efforts of many individuals, schools, distinguished not by curricular goals, but only by and projects around the country, which have speed, depth, and approach." begun to move mathematics education through the transitions just described here. • The unique form of coordinated national leader­ Over the next two decades, all of the major com­ ship, which has evolved within the communities ponents of mathematics education-curricula, teaching, of mathematicians and mathematics educators. education, testing, textbooks, and software­ teacher Together, these resources provide an "augmented must change significantly and in some reasonably co­ grass-roots" model of curricular development, coupling manner. National leadership is needed to ordinated national leadership with the flexibility and initiative of efforts by the primary agents for change and coordinate the decentralized U.S. tradition. support for them by government, business, to garner A national strategy for revitalization which is well and the public. industry, suited to the unique strengths and weaknesses of U.S. mathematics must have several major components: National Goals National goals and local implementation. The key to success is voluntary acceptance by school districts of Our national goal must be to make U.S. mathematics common goals that provide a framework to guide local education the best in the world. Nothing less will be choices and the construction of detailed programs. adequate to fulfill American aspirations. To achieve this goal will require significant actions in response to a • National Standards. School mathematics pro­ three-tiered challenge to: grams across the nation need to share a common philosophy and framework-a universal set of education effective for all • make mathematics interrelated concepts and methods held together Americans; by a simple workable philosophy, yet flexible significantly students' mathematical • improve enough to allow for local and regional variations. achievement; In a highly mobile society, the basic framework in place new curricula appropriate to the • put should be transportable and adaptable. mathematical needs of the twenty-first century. • Local Implementation. Changes in mathematics Actions taken to achieve these broad goals must be curricula must be proposed and undertaken freely based upon an understanding of the total American sys­ by those who bear direct responsibility for curric­ tem of mathematics education, especially understanding ula in the schools. A deep sense of identification of the nature of the changes under way. Unless action is with those changes must be developed within based upon a systematic overview of all of the pertinent the entire school community. In particular, lo­ issues, it will have very little chance of achieving national cal teachers and parents need to be involved in impact. adaptation and decision-making in a thorough and comprehensive way. National Strategy National discipline-based leadership, such as that now being supplied by the mathematics and mathemat­ with leaders from "Few teachers in today 's schools have the authority ics education communities-working mathematics education-is or resources necessary to carry out this agenda. the diverse constituencies of But as schools evolve from a model with teachers needed to: as hired hands to one in which teachers function • lay out the consensual framework, including pro­ as professional educators, schools should welcome posed national standards; the challenge to implement national standards for • coordinate an effort to build and sustain national mathematics education." consensus on goals and the approach to be used to achieve them;

MARCH 1989, VOLUME 36, NUMBER 3 233 Everybody Counts

• provide a continuing national overview and as­ plan for school mathematics. This is needed not only sessment capability for mathematics education. because there must be consistency at the school-college interface, but also because college and university faculty State and local coalitions, collaboratives, and teacher influence heavily who become teachers, how they teach, support networks will be needed to provide similar and what they teach. Undergraduate mathematics is leadership at these levels. the bridge between research and the schools and holds National, state, and local leadership-provided by the the power of reform in mathematics education. The President, Congress, federal officials, governors, chief National Research Council (NRC) Committee on the state school officers, mayors, legislators, school boards, Mathematical Sciences in the Year 2000 (Project MS school superintendents, principals, teachers, and college 2000) is developing such a plan. and university faculty and administration-will be of Significant movement to implement this seven-part critical importance to the consensus-building effort and national strategy is under way through the combined ef­ to local adoption of the national standards. National forts of national organizations, including those concerned and state education-related organizations, parent groups, directly with mathematics and mathematics education, business, and industry can also play important leadership as well as foundations, national education organizations, roles. parent groups, and agencies of government. National support structures are needed to enable the primary participants-teachers, schools, state and local education authorities-to work successfully toward na­ Building Consensus tional goals in their continuous efforts to upgrade math­ The Curriculum and Evaluation Standards for School ematics programs. Local, state, and federal resources Mathematics, developed by the National Council of should be used cooperatively to provide the variety of Teachers of Mathematics (NCTM) and being released materials, teacher support, and increased public aware­ in March 1989, is the linchpin of the strategy. It fo­ ness necessary to enable teachers to adapt curricula and cuses national attention on specific objectives for school instructional practices within the nationwide consensual mathematics in the 1990s. These standards from the framework. teaching profession provide guides to what constitutes Teacher professionalism must be strengthened through excellence in school mathematics programs designed a concerted national effort. This is an essential element to serve all students, from kindergarten through high of any effective strategy for reforming mathematics edu­ school. Already reviewed extensively in draft form by cation in the United States. It is the teachers on whom mathematics teachers and the public, the standards have the real burden of reform rests. The task we are set­ received widespread support in the mathematical and ting before them is very demanding and will take many educational communities. They represent the very first years. Teachers need to approach this task in a highly effort to establish national goals for school mathematics. professional way and they need to be given the sustained The nation has a unique opportunity to build consensus support and working environments that will make it around these goals. possible for them to carry out their vital mission. Initi­ ation of the National Board for Professional Teaching Generating Dialogue Standards is an important step toward enhancing teacher professionalism. Criteria for excellence in mathematics teaching being developed by the mathematics education community should provide part of the foundation for "Implementation will require more than good will the standards developed by the board as it undertakes and community dialogue; it will need professional the certification of professional teachers. leadership of teachers operating in a transformed Leadership in assessment is needed to align state and school environment. No one should underestimate national testing programs with the goals of mathematics the complexity of the challenge; effective reform will education and enable assessment to be a constructive be truly difficult to accomplish." force in the national revitalization effort. Test designers and test-makers are well aware of the general problems in this area. They need to join together with the leadership The development and publication of the NCTM Stan­ of mathematics education in support of a cooperative dards are part of the national, discipline-based leadership national board or other mechanism for promoting use of referred to in the strategy. The NRC took two other steps: significantly improved types of assessment by localities, the establishment in 1985 of the Mathematical Sciences states, and national assessment organizations. Education Board (MSEB), to provide continuing national A national plan for college and university mathematics oversight and coordination in mathematics education at must be developed, one which is closely allied with the all levels, and the formation in 1988 of the Committee

234 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Everybody Counts on the Mathematical Sciences in the Year 2000, to rec­ Parents ommend a revitalization plan for college and university • Demand that schools meet the new NCTM Cur­ mathematics. Both of these steps were taken at the re­ riculum and Evaluation Standards for School quest of the professional societies in mathematics and Mathematics. mathematics education in the United States. • Encourage children to continue studying mathe­ The NCTM Standards report is one of a series matics. of major reports appearing in 1989, to which Everybody • Support teachers who seek curricular improve­ Counts is a public preface. Others are MSEB's Philosophy ments. and Framework for School Mathematics and Strands of • Expect homework to be more than routine com­ the Mathematics Curriculum. putation. A related report comes from the American Associ­ ation for the Advancement of Science's Project 2061. Principals Called Science for All Americans, it sets forth a vi­ • Provide opportunities for teachers to work to­ sion of what every young person should learn about gether. mathematics, science, and technology. • Become educated on issues in mathematics edu­ These reports could join hundreds of other well­ cation. meant reports on the nation's bookshelves or they could • Support innovation. make a difference. To bring their messages to the many • Encourage paired teaching in elementary school. "attentive publics" of mathematics education and help build consensus on their goals, the Mathematical Sciences Superintendents Education Board plans to coordinate an intensive Year • Stimulate public discussion of mathematics edu­ of National Dialogue that will accompany publication cation. of these reports-a dialogue carried directly to teachers, • Provide resources for curricular innovation. administrators, policymakers, business, industry, govern­ • Support a climate of change. ment, and the general public. Professional organizations in the mathematical sciences are making plans for active School Boards involvement in this dialogue. Numbers of other national, • Establish appropriate standards for mathematics. state, and local organizations will participate. • Align assessment with curricular goals. • Support innovation and professional develop­ ment.

Taking Action Community Organizations Current efforts to forge national consensus will not • Enrich mathematical opportunities for all stu­ in themselves transform what happens in schools or dents. colleges. Change in the institutions of education must • Support local efforts to improve mathematics come about as the result of intensive debate within each education. institution. There is plenty of work for everyone: • Explain to the public the need for change.

Students State School Officers • Promote adoption of NCTM's Curriculum and • Study mathematics every school year. Evaluation Standards for School Mathematics. • Discover the mathematics that is around us all. • Encourage use of elementary mathematics spe­ • Use mathematics in other classes and in daily cialists. life. • Speak out publicly about mathematics education. • Study a broad variety of mathematical subjects. • Stress assessment of higher-order thinking.

Teachers College and University Faculty • Talk with each other about mathematics. • Make introductory courses attractive and effec- • Examine current practice and debate new pro­ tive. posals. • Restore integrity to the undergraduate program. • Engage students actively in the process of learn­ • Lecture less; try other teaching methods. ing. • Link scholarship to teaching.

MARCH 1989, VOLUME 36, NUMBER 3 235 Everybody Counts

College and University Administrators The President • Reward curricular innovation and good teaching. • Meet with state governors to affirm the national • Recognize that mathematics classes need com­ agenda. puter laboratories. • Focus public attention on mathematics educa­ • Diminish reliance on underprepared, part-time tion. faculty. • Stress education as crucial to national security. • Emphasize and improve teacher education. Conclusion . . . it is time to act Business and Industry This is just the beginning. Several decades of work lie • Encourage students to study mathematics and ahead if we are to translate the ideas put forth here into science. classroom practice. During that time, continuous change • Do not steal good teachers by hiring them away. in mathematics programs should be the norm in most of • Support local efforts to secure funds for educa­ the nation's school districts. Strong national, state, and tion. local leadership will be needed all along the way. • Support strong continuing education, not reme­ Efforts to bring about lasting change must proceed diation. steadily for many years, on many levels simultaneously, • Provide internship opportunities for teachers. with the broad involvement of all of the constituencies at each stage. First comes serious discussion; then, State Legislators compromise and consensus; finally, action and change. • Work with school leaders to support effective At national, state, and local levels, significant efforts are programs. under way to improve curricular standards, the teaching • Recognize that mathematics education is an in­ profession, and assessment practices. Major projects are vestment. being started to help the diverse efforts of business, • Resist pressures for simplistic cures. industry, government, volunteer groups, and educational organizations to focus on common objectives. As there is no royal road to geometry, so there are no "quick fixes" Governors for mathematics education. • Provide resources to encourage change. Both for reasons of international competitiveness and • Demand new standards for mathematics educa­ scientific leadership, the United States must move quickly tion. to improve the state of mathematics education. It takes • Lead the public to make wise choices among a generation to complete the mathematical education of priorities. a single individual. The first high school graduates of • Create enrichment programs for able students. the next century entered elementary school in 1988. No longer can we afford to sit idly by while our children Congress move through school without receiving the mathematical • Stress education as an essential investment. preparation appropriate for the twenty-first century. • Support mathematics education at all levels. The challenges are clear. The choices are before us. It • Reward effective programs. is time to act.

236 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY MATHEMATICS: A CHALLENGE FOR BUSINESS, GOVERNMENT, AND ACADEMIA

NSA's Role in Mathematics The following is the text of the talk given by Vice Admiral Years of military training have prepared me for many William 0. Studeman, Director of the National Security Agency, complex operational and management roles, but it was at the Thursday evening, January 1a._ open session entitled still surprising to become the leader of the largest and "Mathematics in the American Agend( .Jt the Joint Mathemat­ perhaps the most diversely talented group of math­ ics Meetings in Phoenix, Arizona. The- event, which was pre­ ematicians in the United States. As you may know, ceded by an open reception with a Southwestern theme, was mathematics is the fundamental basis of our work at the American Mathematical Society, the Mathe­ sponsored by NSA, the sine qua non fundamental foundation bedrock matical Association of America, and the Mathematical Sciences Education Board of the National Research Council. of our business. Mathematics is the one aspect of NSA which makes us different from other Defense and execu­ tive branch departments and agencies, and we are proud of both the documented and unrecorded contributions which our mathematicians (our invisible heroes) have After six months in my job, I can honestly say that I made to the history of national and alliance security over am extremely humbled to be present in this assemblage the past half a century and longer. We are America's of august intellectual ability. To paraphrase President largest employer of mathematicians, and we really are Kennedy: No Director of NSA has been with this much employing mathematicians to be mathematicians. We mathematical talent in one room, since our first Director use your theorems, not just your problem solving abil­ met privately with John von Neumann. ities. NSA must provide more care, feeding, attention, I almost changed the topic of my talk this afternoon. and job satisfaction (particularly job satisfaction) for As I was studying my notes and flying to Phoenix, along mathematicians than anyone else, and I believe that this with other NSA employees, we suddenly had a great gives us a unique perspective and responsibility on the idea to patch up Miyaoka's recent attempted proof of future of mathematics in the U.S. Fermat's Last Theorem, but it fit in the margin of the notes, so we didn't think it could be correct. The Evidence of Decline Thank you for inviting me to speak to you this evening. It is a privilege for me to be at the annual meet­ Two recent publications have emphasized the decline ings of the math societies, and a wonderful opportunity that has occurred in American mathematics research for me to share with you some issues and concerns on the and education. The National Academy of Sciences 1984 role of mathematics in the future of American business, study, Renewing U.S. Mathematics (popularly known as government, academia, and, of particular interest to me, the "David Report"), pointed out the dangerous decline its role in the future of American defense. in support to university mathematics research, a decline Many of you are concerned about the proper role that may soon drive our nation's most able researchers of mathematics in defense-supported research. This is into other disciplines that provide adequate resources for an important topic that has been debated at length and their work. The "David Report" spurred my predecessor, which can be divisive, but it is one which I will leave General Odom, to make a commitment to mathematics for another time. Tonight I want to tell you about NSA's research through the expansion and redirection of our role in mathematics and to discuss issues which I believe grants program, and by the encouragement of greater should unite all who are interested in the future of involvement on the part of our mathematicians in the American mathematics. national community. This is a commitment I firmly

MARCH 1989, VOLUME 36, NUMBER 3 237 Mathematics: A Challenge support and would like to build upon. In fact, I am proud sides, new forces are emerging, overpowering military that the NSA Mathematical Sciences Program has agreed force is appearing less useful than before, and communist to help support the following study, known colloquially countries are clearly concerned about what their poor as "David II." economic condition holds for their long term power and The 1987 report, The Underachieving Curriculum, status. The American system is coping with complex highlighted the poor achievement of 8th and 12th grade fiscal and technical efficiency problems which challenge American students in an international comparison. It is our work and market ethics and our competitive abilities. ironic that the United States attracts the brightest minds The challenges NSA face are no less daunting. They from around the world to study mathematics at our include dealing with vast quantities of data in an efficient universities, and yet we fail so miserably in providing manner, pulling targets out of complex backgrounds, a basic mathematics education to our own high school distinguishing the important from the unimportant, sup­ students. We have become a Mecca for international porting decision making in time-critical environments, students seeking the finest training possible, but we converting complex situations and problems into simpli­ cannot seem to motivate and propel our own citizens fied, understandable ideas, and improving the security of into pursuing research in mathematics. I am deeply communications and information management. concerned over the implications of these trends, not only These changes cannot be understood nor these chal­ for national security reasons, but also for their portents lenges met by relying solely on the theories of the past, for American technological research and applications. but rather we must have fresh insights, new ideas, and a deeper understanding of the way the world works. These, The Need for Mathematics I propose, are tasks uniquely suited for the mathemati­ cally trained mind. Changes, Challenges, and Opportunities We are now in a period of vast global, political, economic, Achievements of Mathematicians military and technological change; change that presents NSA with unique challenges and opportunities. Secure The ability to deduce the rules of nature from empirical data systems and communications, the availability of observation has been the hallmark of mathematicians for timely, accurate intelligence, and information handling millennia. From Euclid's axioms of geometry to New­ and display capabilities are essential to maintaining the ton's laws of motion and gravity to Einstein's theories fragile peace. Consumer-driven capitalism seems again of relativity-all have contributed in bringing order from to have passed the test of time, as countries have become chaos. And yes, there are the elite disciplines of mathe­ superpowers on the basis of economics alone, and as the matical cryptanalysis and crytography-for cryptanalysis, economic engines of one after another communist state finding the order of human communications from the have failed miserably. Much of this change is driven by chaos of encrypted signals, and for cryptography, creat­ or itself influences the pace and direction of technology. ing and reconstructing chaos for secure transmissions. Of particular interest to NSA and defense, the nature These are vital disciplines that have served our country of the modem military battlefield is changing. Low in peace, have helped save it in war, and could equally intensity conflicts are more likely than superpower war, doom the nation if their respective successes were to and the technology of war itself is rapidly changing. become the order of the day for the other side (as was These changes include the increasing availability of the case in the heyday of the recent espionage cases). long range (even short time of flight) precision guided munitions supported by highly accurate targeting means, The Mathematical Workplace new and renewed forms of threatening lethality, and other complex factors which impact significantly on the The American workplace has become more mathematical kinematics of modem battle space. The application of in recent years, and this change can only accelerate. stealth is but one example of these modern technologies­ Modern technology and an effective, informed voting but in its purest form, it is a modern warfare approach public demand a comfortable command of discrete wherein partial or periodic invisibility nets advantages in mathematics, statistics, and mathematical modeling-and surprise, tempo, and timing and creates highly stressful these are just the entry-level requirements. When we threat detection and response problems. Stealth systems cannot find mathematically literate entry-level workers, such as today's modern submarine or airplane are the when American government and high technology can no technical analogues of the guerrilla or terrorist which longer recruit the mathematically skilled, and when we have had such a powerful impact on today world stage. must finally rely on the scientific insights and advances Similarly, the world geo-political polarity is shifting. of other nations, then we will have entered a sad period Old alliances are moderating on both the Soviet and U.S. of technological stagnation and decline.

238 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematics: A Challenge

The Blurring of Pure and Applied Math be done without lowering our standards. Overall, math­ ematics is becoming even more essential to our defense, There is a great need to move beyond the artificial to our industrial competitiveness, and to our nation's divisions of mathematics: pure versus applied; defense unquestioned leadership in academic research. versus civilian; industrial versus academic; research ver­ sus teaching. We must realize that what is good for mathematics in its broadest sense benefits every user, no The Challenge for Action matter how narrowly focused their application may be. The Decline Must Stop As an example of the broad application of math­ ematics, my staff assures me that the solution to one The role of mathematics m the future of American of our important problems critically depended upon an business and government will be central, crucial, and application of Tychonoff's Theorem. inescapable. Mathematics will be one of the skills that A little over 40 years ago G. H. Hardy wrote in his separates service careers from those requiring imagi­ masterful book, A Mathematician's Apology. nation, creativity, and originality. Supporting and im­ I have never done anything 'useful.' No discovery proving mathematics can no longer be merely a slogan, of mine has made, or is likely to make, directly or goal or platitude, but rather it must now be an essen­ indirectly, for good or ill, the least difference to the tial objective of any enterprise-business, government, amenity of the world. or academia-that expects to remain competitive for the I wonder how surprised Hardy would be to learn that future. We simply must insure that adequate support his beloved Number Theory, which he was so proud for mathematics research is an accepted norm, that our to say had done nothing 'useful,' is today one of the standards for pre-college education are equal to our capa­ foundation stones of computer science, cryptography, bilities and needs, and that the definition of "acceptable and communications? Just as the true utility of the mathematics activity" is expanded at our universities Conics of Appolonius was not appreciated until centuries and even at our high schools to include mathematics later, so too the pure mathematics of yesterday becomes education. The decline must stop now , and we each the foundation of new applications tomorrow. have a role to play.

Mathematics at NSA The Role of Business and Government The National Security Agency has a long history of American business and government have been accused, demonstrating that mathematicians are the best people with some justification, of taking a limited, narrow ap­ to employ in new interdisciplinary initiatives, especially proach to mathematics. If the work in question is not when the problems are very technical, very new, very "mission oriented," if it does not increase the next quar­ hard, and not very well understood. For example, our ter's profits, if it does not have an obvious application, mathematicians have provided fundamental ideas for our then it is not worthy of support. We can fall back on work in communications, engineering, speech research, the demands of the Congress or of the stockholders, but signals processing, and the design and implementation these answers beg the question. Pure mathematics re­ of powerful, specialized computers. But for our primary search benefits everyone, because it creates a fertile field mission, it is most important that our mathematicians of ideas from which we can draw the solutions to our be mathematicians. problems. Mathematics education is the only hope that The "tools" that we employ to do our job are we have to continue our work-if there is not a sufficient mathematical. The theories that we need to develop mathematically educated labor pool in the future, then to understand what we are doing are mathematical. our work today is for naught. Despite the restrictions we NSA has scaled to a vast plateau where there are more believe may limit our actions, we must insure the future application problems than ever before. There is a great of mathematics. need for us to develop new theoretical frameworks for a complex problems that we face, and number of broad, The Role of Academia this need is not unique to us. From a Defense resources and manpower point of Business and government cannot alone face and solve view, we are heading into a significant austerity period the problems of American mathematics, academia must where no growth at NSA will be the order of the day. shoulder its share of the burden. For mathematicians Nevertheless, as the largest employer of mathematicians to believe that they deserve unrestricted support simply in the United States, I have instructed my personnel because they prefer it that way is arrogance, and to office to hire 100 new mathematicians this year, with think that some special federal dole is appropriate for priority at the masters and doctoral level, if this can mathematicians solely because they do good work is

MARCH 1989, VOLUME 36, NUMBER 3 239 Mathematics: A Challenge conceit. If mathematics is to be properly supported funding for pure mathematics research in those areas by society, then mathematicians must not forget their that best support our mission. obligations. Universities must move beyond measuring Through our grants program, we are providing core success only in terms of grants or publications, and support to the Mathematical Sciences Education Board researchers must recognize their larger obligations. These for their study and revision of the K through twelve changes should not be seen as "add-ons" but rather must mathematics curriculum for American schools. Our be an integral part of the job. If we cannot convince our mathematicians have actively participated in a num­ greatest minds to tackle the vital problems of education ber of national conferences in these areas: "Calculus for and the government as well as business then society will a New Century" last year, "Mathematics Education-A invest elsewhere and everyone will be the loser in the Wellspring of U.S. Industrial Strength" this past Decem­ long term. ber, and, as previously stated, we are also supporting Additionally, mathematics suffers from a significant the follow-on study to the "David Report." NSA and public relations problem. American researchers yearly affiliated mathematicians are attending this forum in solve critical problems, advance theory on every frontier, some numbers as well. and stretch the capabilities of the human mind, but For decades, NSA has worked closely, profitably, the general public (and often the Congress) does not and quietly with university mathematicians-faculty and appreciate these achievements. To address this problem, students, both graduate and undergraduate. We have you are supporting a successful public information effort formal sabbatical programs for visiting and for our own in Washington which must be not only continued but mathematicians. Our academic interactions are assisted also expanded. I might add that NSA's larger public by the Institute for Defense Analyses' Communications participation in mathematics was greatly influenced by Research Division in Princeton, which works closely the Joint Policy Board on Mathematics. If you cannot with us. In 1952 we started holding summer workshops convince the public that you are doing good work and for university mathematicians, and since 1959 they have are solving problems that directly affect them, then your been very successfully conducted in Princeton by C.R.D. other efforts will be in vain. Our mathematicians have been actively supporting the Maryland State Department of Education's sum­ mer Gifted and Talented program in mathematics for NSA's Response to the Challenge students in elementary through high school. We are es­ It would not be fair for me to stand up here and suggest tablishing a Speakers Bureau to bring the excitement tasks for you without telling you what we have done to of mathematics to local high school and middle school meet the challenge. In 1987 at NSA we held two very students. Finally, we are working with The George Wash­ successful meetings with American mathematics leaders ington University to conduct a summer workshop for to explain our uses of and needs for mathematics. We regional high school mathematics teachers. It is not explained, as best we could, what types of mathematics possible for us to support all mathematics everywhere, are important to us and we sought advice on how we but we believe that we have a particular obligation to could better participate in the larger math community. encourage mathematics in schools near us. The technical presentations were published in the Pro­ I hope that our first, halting steps to increase support ceedings of the NSA Mathematical Sciences Meetings, to mathematics will be taken as a challenge by each which is available from our grants office. At that time institution represented here-a challenge that you will our grants program was expanded and redirected to sup­ soon meet and surpass to insure that mathematics will port almost exclusively pure mathematics research. We indeed have a role in the future of American business, believe that our grants program, the NSA Mathemati­ government, and academia. cal Sciences Program, will become an important source of

240 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Edited by Jon Barwise

Editorial notes Sands, of Augusta College, of a commercial product around which Augusta's mathematics department has Environments: a Tale that Wags the Dog Computational built its local area network (LAN). At the end of this Department at the Uni­ In 1983 I left the Mathematics month's column, I exercise my editorial prerogative versity of Wisconsin, Madison, to direct the then new with a commentary on these models. This is not Center for the Study of Language and Information. meant as a criticism of the decisions made in either CSLI is an interdisciplinary research institute devoted department, but to point out a few of the decisions to mathematical and computational approaches to one might want to question, especially in a different understanding language, meaning, information, and sort of institutional setting. I hope that these articles representation. I directed it for two years, before and commentary will prompt others to write of their returning to research, teaching and less demanding experiences, especially those that differ markedly from administrative responsibilities. During that time, es­ that of Grinnell. Write to me at: tablishing a suitable computational environment for the Center was one of the responsibilities that weighed Center for the Study of Language and Information most heavily, absorbing countless hours of thought, Ventura Hall worry, and discussion, and far too much money. Stanford University Last week was a poignant one in this regard. I Stanford, CA 94305 came back from lunch one day to discover many Email: [email protected] of the workstations around which we had built our Another reason for running articles of this kind is plans lined up by the back door, waiting to be to provide mathematicians around the country with taken off to computer heaven (we'll assume, for ammunition. Take these articles to your administra­ charity's sake). Five years after being state-of-the­ tion and say "Look what the competition is up to. art computers, these machines had become jokingly We are falling far behind." From this point of view, referred to as space heaters and door stops. And the both models are quite useful since the computational uniform computational environment we worked so environments they have established are ahead of what hard to create has gradually evolved into something most departments have managed to create. quite different. In addition to the two articles just mentioned, This experience has left me with a keen interest this issue contains a review, by Herbert Holden, of in the problems associated with establishing a com­ FITLIB by PC-Scientific, a program that generates putational environment for work in mathematics, and splines for fitting given data. This is the first of several some pretty definite opinions on these matters. In­ PC-Scientific programs that are in the works. deed, one of my motives in agreeing to create and edit this column was to try to drag out of other mathemati­ 1FX, IDEX, and A.MS -'IFX cians their experiences in creating such environments, In spite of repeated disclaimers, many readers assume so that we do not all have to make the same mistakes. that I must be an expert in everything connected In this month's issue I present what I hope will with computers and mathematics, or at least with be the first two of many articles addressing the some things so connected. In particular, over the questions associated with these problems. The first past few months, I have been asked by several people is by Gene Herman, and describes the computational around the country about the differences between TEX, environment in place in the mathematics department Jb.TEX, and A.MS-T£X. These mathematicians were all at Grinnell College. The second is a review by Mark somehow involved in choosing among these programs,

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either at a personal or departmental level. I have provide good support either for complex mathematics tried unsuccessfully to find someone who would do a or for the difficult task of preparing a long and comparative review. So what I have done instead is complicated document (e.g. , a thesis or multi-chapter to ask a number of people for their opinions on the book with a table of contents, an index, a bibliography, relative merits of these three systems, mix this with and forward and backward references to numbered my own experience, and write it up as a short note. I theorems and equations). And this is where other would like to express my thanks to Ilan Vardi and my macro packages enter the picture. other informants, who prefer to remain nameless, for advice and comments. And I should say, right off, that IDEX for the past four years my own mathematical writing ~TEX is a program written by Leslie Lamport on has been done almost exclusively with ~TEX, though I top of plain TEX. It adds to TEX a rich collection have ventured out into TEX from time to time. I have of macros which make using TEX easier in most never used AMS-TEX at all. Everything I know about situations. Rather than being a typesetting program, it is from my informed sources. it is a full-fledged document preparation system. In fact, it was designed to implement a SCRIBE-like 1FX environment within TEX. In case there are any Rip van Winkles reading this Its most important feature is that it provides a column, TEX is Donald Knuth's typesetting program family of ready made document styles (article, report, that has literally revolutionized the typesetting of book, letter, memo, etc.) for you to use, in the form mathematical text. The stress here is on typesetting. It of ".sty" files. Most of my own writing uses article.sty. is not an editor; rather it can be used with any editor. These styles set a host of parameters for you, like Nor is it a typographic designer. It leaves the decisions the way things get numbered, spacing, margins, and usually made by the typesetter (like how much space the like. Most of these can be modified, though. For to put below a section heading) up to you. Nor does example, sections and subsections are usually numbers, it generate particular document styles. Creating those but I can leave them unnumbered by simply adding an is also up to the user. What it does is to provide a asterisk in the appropriate command. ~TEX excels in powerful set of computational tools that allow you such things as automatic creation of tables of contents to custom design and typeset your own mathematical and indexes, footnotes, the handling of automatic documents. And it is a masterpiece. forward and backward references to numbered text Actually "lEX" is ambiguous. On the one hand items (theorems, definitions, etc.), bibliographies, and it refers to the raw TEX program, which only knows so forth. about low-level typesetting primitives. Using this TEX to typset anything would be almost hopelessly difficult; AMS-'JFX somewhat akin to setting lead type by hand! To make AMS-TEX is also a package of TEX macros. It was TEX a convenient tool one must add to this primitive developed by Mike Spivak for the AMS. But its version of TEX a collection of so-called "macros" that goals are quite different from ~TEX's. It is aimed at teach it some of the higher level concepts of typesetting providing macros which simplify typesetting complex and also instruct it to use a particular output format mathematics in TEX. Its forte is things like matrices style. Knuth has provided an excellent vanilla macro and complicated alignments of equations. The AMS package that is variously refered to as "the basic finds it very useful in this regard. But it does not control sequences", "the plain macro package", or provide the kinds of facilities provided by ~TEX "the plain lEX format". The second, more common described above. usage of "TEX" is to refer to this enhanced "plain" version of TEX. This is what we will usually mean by Relative Advantages TEX in what follows. Which of these programs should you learn and use? Many experienced TEX users find the plain format That will depend on your personality and the kind of an ideal envoironment for most simple typesetting mathematics you want to write. If you are a person tasks; they can easily add themselves the few extra who likes to build your own stereo, or write your macros needed to adapt plain to the use at hand. own programs, then probably TEX is for you. It gives However, for beginners, using even this enhanced you maximum power and leaves you unconstrained TEX is hard going. And experienced TEX users too by anyone else's design decisions. And it is maximally find plain insufficient when they are faced with more flexible. ~TEX, by contrast, is pretty rigid. This can demanding typesetting tasks. For. plain TEX does not be an advantage, in that it keeps you from making all

242 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

kinds of mistakes, but it can also feel like a straight Why not simply combine the :Jb.TEX and AMS-TEX jacket if you bump up against something it won't let macros? Unfortunately, two different macro packages you do easily, like turn footnotes into endnotes, or as complicated as these are unlikely to be compatible create a one page document without a page number. with each other unless they were created with careful But most mathematicians want a program that joint planning. And, sad to say, :Jb.TEX and AMS-TEX puts as little between them and writing mathematics were created independently and are incompatible. as possible. For such mathematicians, I think :Jb.TEX However, I understand that Spivak is at work on a is the current system of choice. It takes care of so package called AMS-TEX that combines the best fea­ many details for you. Especially if you are writing a tures of :Jb.TEX and AMS-TEX. This was demonstrated long article or book. In such cases AMS-TEX is not at the recent annual meeting in Phoenix, and although particularly useful and :Jb.TEX has much to recommend I missed it, I hear that it looks very promising. it. On the other hand, if you are writing a short article In addition, AMS has chosen to create a :Jb.TEX style with lots of displayed equations, AMS-TEX is probably file embodying AMS-TE,X's mathematical formatting more useful. In between it is a matter of taste. abilities while retaining :Jb.TEX's easy-to-use document Another main point in favor of :Jb.TEX is the manual formatting strengths. The Society plans to make an which is extremely well written and is designed to AMS-TEX :Jb.TEX style file available to the mathematical teach you about how to use the program, not to teach and TEX communities this spring. The AMS will you all about typesetting. This is extremely helpful continue to use AMS-TEX for its publications but it for anyone who wants to get something done within a will also accept authors' electronic files prepared with short time of starting with the program. The AMS-TEX :Jb.TEX's AMS-TEX style file. manual (The Joy of TEX) and the TEX manual (The So my recommendation to mathematicians who TEXbook) are also very well-written, but the TEXbook do not want to pay a lot of attention to typesetting suffers from trying to be both a users guide for plain nitty-gritty: start with :Jb.TEX. It will let you do 99% of TE,X, but at the same time a reference manual for what you want to do, and you can always write your the extremely complex TEX program. These two roles way around the other I%. After you have been using are often incompatible. There has long been a good it for a few months and start bumping up against its elementary introduction to plain TEX available from limitations, get the TEX book and add that extra 1%. TUG, the TEX Users Group, ("First Grade TEX: A Beginner's TEX Manual", by Arthur L. Samuel), but true to its name it will only barely get you going and has almost no information about typing mathematics. Very recently Michael Doob of the University of Grinnell College's MathLAN Manitoba ([email protected]) has written a first rate seventy page users manual for plain TEX (A Gene Herman Introduction to TEX), and very generously Gentle Grinnell College placed it in the public domain. Macro packages such as AMS-TEXand :Jb.TEX are almost always add-ons to plain TEX, that is they are built "on top" of it. But the author of any given package may either choose to remain compatible with The Setting plain TEX (as AMS-TEX does) or he may choose Grinnell College is a private, four-year, undergrad­ to redefine certain macros in ways incompatible with uate, liberal arts institution of 1200 students. The plain TEX (as :Jb.TEX does). Aside from displaying really department of mathematics has approximately 8 full­ complicated mathematics, the one clear advantage of time equivalents, including the mathematics faculty AMS-TEX over :Jb.TEX is that the former is a strict extension of TEX, the latter is not. Lamport has *Gene Herman is Professor of Mathematics at Grinnell College. removed part of TEX from :Jb.TE,X, so you cannot He received his Ph.D. in functional analysis from the University learn :Jb.TEX first and then simply add various TEX of California at Berkeley in 1964. He is the author of MAX, the commands as you need them. For very complicated MAtriX Algebra Calculator, which was named in the 1988 EDU­ things that can't be done in :Jb.TEX, you have to figure COM/NCRIPTAL awards as "Distinguished mathematical soft­ College TEXcommands you can use, and which you ware." He is currently editor of "Computer Corner" in the out which Mathematics Journal, and a member of the MAA Committee on can not. Computers in Mathematics Education.

MARCH 1989, VOLUME 36, NUMBER 3 243 Computers and Mathematics

who teach computer science and statistics. We gradu­ spreadsheet and graphing package (Research System ate between 15 and 25 mathematics majors each year 1), a matrix analysis package (MAC, later renamed and also teach a large number of nonmajors. Our MAX), a computer algebra system (MACSYMA), and greatest enrollments are in Calculus I ( 1 75 students a number of Apple II packages that we used primarily in 1987-88), Calculus II ( 170), Linear Algebra and for displaying graphics in the classroom. Differential Equations (95), Series and Differential Then in the fall of 1985, we learned we would Equations ( 46), Computer Programming with Pascal be moved to a new wing of the science building. For (90), and Introduction to Statistics ( 175), although several reasons, this was the perfect opportunity for the enrollment figures for Statistics include sections us to plan a new computer system for the department. taught by faculty in other departments. The scholarly Most obviously, we would be able to design our activities of the faculty include mathematical research, new quarters to house computers comfortably rather reviewing and editing for journals, expository writing, than continue to struggle with the inadequate wiring, textbook writing, and software development. lighting, temperature control, and physical space in our Our physical facilities are new. We occupy the top old building. Also, for the preceding year the College floor of a wing of the science building, where we have had been studying the possibility of installing a local 10 offices, 4 classrooms, a computer lab, and a small area network (LAN) on campus. So the administration unstaffed department office. On the floor below is our was ready to consider a department-size LAN, and secretary whom we share with another department. On we were ready because we had been involved in the the floor below that is our machine room. We moved study. into the building in June, 1987, and the first phase of Another set of reasons for our interest in a new our computer network, which we call MathLAN, was computer system were our existing system's inade­ installed in October, 1987. quacies, which had become more obvious as our use increased. For example, the Apple lis in our class­ The Impetus rooms were incompatible with both the Rainbows in We have used computers in our department for years, our offices and the central minicomputer. The number but our use accelerated rapidly in the early 1980s, of microcomputers on campus was so small that most when we first got computing equipment in our offices of our classes could not be asked to use them to and classrooms. In 1982, we got computer terminals do assignments, and file transfer between micros or in our offices, which connected us to a central PDP between a micro and the mini was tedious. The screen minicomputer. Then, in the summer of 1984, our resolution on both types of micros was low and their terminals were upgraded to Rainbow microcomputers computational speed was slow, which made them un­ which doubled as terminals. A year later we got dot­ satisfactory machines for much of our graphical use. matrix printers for our offices, and some of us got Graphics on the central minicomputer was no better, graphics boards and color monitors for our micros. as timesharing slowed its responses. Also, the response Although we had one classroom with a terminal time of the mini sometimes slowed our classroom as early as 1975, few of us did any computing in the presentations. Most frustrating of all, interesting new classroom until the fall of 1981, when we installed an software was coming out that would not run on our Apple II in each of two classrooms. We added two small, outdated micros and would either run slowly or terminals in the summer of 1983. However, we went not at all on the timesharing mini. In short, our exist­ several years with inadequate projection equipment, ing computer system lacked local power, uniformity, until December of 1985, when we installed high accessibility, and interconnectedness. quality Electrohome monitors in our classrooms and a switch box that let us choose whether the monitors The Plan would display output from the microcomputer or the During the 1985-1986 academic year and part of terminal. the next, we planned a new computer system, wrote Even in the early years of our computer use, we grant proposals to the National Science Foundation had quite a variety of software. By 1985, we had both and several private foundations, and worked with an a simple word processing package and one that could architect to design our new space so it would support produce fairly good mathematical output (MASS-11), the kind of computing we envisaged. Our plan called an electronic mail system for on-campus communica­ for workstations with central fileservers, so we could tion (DREAMS), programming languages, a graphics have both local power and the convenience of a single subroutine package (the Core System), several sta­ location for all software. These would be connected tistical packages (including MINITAB and SAS), a together by a local area network to which peripherals

244 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

would also be attached. Furthermore, the network system and about 40% of our students did. Average would be bridged to the central minicomputer (now a faculty use was about 6 hours a week, with about VAX 8600), so we could continue to use its facilities. three-fourths of that related to teaching, and average A principal criterion in the choice of a vendor was student use was somewhat over 1 hour per week. the availability of appropriate software, especially Our system's hardware is working very well, al­ software for mathematics and computer science. though a few problems remain. The principal one We settled on a network of 50 Sun 3/50 mono­ involves our computer-equipped classroom; the work­ chrome workstations and three file servers, plus two stations are so bulky that they interfere with lines of Apple LaserWriter printers, a high-speed Printronix sight. On the other hand, all the major benefits that line printer, and a Hewlett-Packard 8-pen spooled we expected of our new hardware have indeed come plotter. These are linked by an Ethernet, which is about. Wherever we are-in our offices, a classroom, bridged to the VAX by a fiberoptic cable. The work­ or the lab-we have enormous local power at our fin­ stations are distributed as follows: one in each of the gertips. Complex graphics and long computations are 10 mathematics faculty offices, one in each of our 4 completed quickly; multiple processes are carried out classrooms, 18 in a public terminal room that doubles simultaneously (or so it seems) and results easily trans­ as a lab for math courses, 15 in a computer-equipped ported between them; and heavy use of the system has classroom, two that drive printers, and one for our no noticeable effect on response time. The uniformity, secretary. The file servers are in the basement machine accessibility, and interconnectedness of the system room, one LaserWriter is in our department office so have made instructional use particularly effective. We faculty alone can use it, and the remaining peripherals can prepare computer-based assignments in the pri­ are in the public terminal room. We also continue to vacy of our offices, demonstrate them in class without use our old dot-matrix printers, which are now driven any need to move equipment or files, and have our by our office workstations. Projection equipment for students carry them out in the lab. Since the equip­ the classrooms was again hard to find, but eventually ment is identical in all three locations, compatibility Moniterm came out with monitors that can keep up problems never arise. with the Sun's high scan rate. In a typical 40-student Most of our software is working as well as expected classroom, we have four 25" monitors overhead. to. We will probably switch to a different computer The mathematical software on MathLAN consists algebra system, and some of our other packages of MATLAB (for graphics and numerical linear alge­ (S, SunLink DNI) await updates that promise to bra), SMP (computer algebra), MAX (matrix analysis), cure their most serious deficiencies. MATLAB, MAX, and S (statistics). We also have TEX for mathematical TEX, electronic mail, and the language compilers-the word processing. For programming, we have C, Pascal, software we use most heavily-have been excellent. LISP, FORTRAN, and a few more exotic languages. MATLAB is not easy for a computer novice to use, Finally, we have SunLink DNI (Sun's implementation but, because it is programmable, Emily Moore of of DECNET) for communicating with the VAX, which our department has been able to create a number we use for electronic mail and for its various special­ of special-purpose front ends that are indeed easy ized packages that would be wasteful or impossible to to use. As a result, MATLAB is now our most duplicate on our system. heavily used graphical and numerical package. MAX, The computer center pays the maintenance con­ the MAtriX Algebra Calculator, is a package that tracts for our hardware, and their technicians provide I designed on our previous computer system and routine maintenance. Their staff also hires and pays moved over to our new one. We use it extensively student User Consultants, who help others in our in teaching linear algebra. For mathematical word public terminal room. We, however, provide much of processing, many in our department are so comfortable the system maintenance. That is, a member of the with TEX that they use it themselves all the time, department creates accounts, installs software, does while others have our secretary do most of their backups, writes supplementary documentation, runs TEXing. One use of electronic mail and SunLink DNI, workshops, and troubleshoots software problems. then, has been to exchange files between ourselves The Current State and our secretary. SunLink's terminal emulator has This past semester, the fall of 1988-1989, was the also allowed us to continue using MINITAB in our first one in which we completely moved over from Statistics course, even though we have this statistics our old computer system to MathLAN. During that package only on the central VAX. Thus, we can still semester, all of the mathematics faculty used the new demonstrate MINITAB in our classrooms and have

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students practice it in a supervised lab. However, we planning their computations, interpreting the results, expect to make increasing use of S in the future. and trying to understand the concepts. Underlying all of our software, of course, is Sun's The succeeding semester, in Series and Differential Unix-based SunOS operating system and SunView Equations, we have students use the graphical and windowing system, which have their good and not­ numerical capabilities of MATLAB to aid them in so-good aspects. On the one hand, this is powerful understanding convergence in many of its guises. software that supports multiple windows, multiple The course covers both the pure mathematics, such as processes in each window, and easy communication uniform convergence, Taylor series, and Fourier series, between processes. On the other hand, not all of us and numerical aspects, such as numerical solution of are sufficiently interested in either the details or the differential equations and numerical summation. Such sophisticated concepts of Unix to learn to use it well. a course is hardly conceivable without the computer. Also, SunView does not hide enough of the Unix But with MATLAB, students are able to carry out details from us, nor does it provide as uniform and projects and exercises that help them gain insight into easily understood an environment as, for example, analytic processes. the Macintosh windowing system does. We hope that We also use MATLAB, at least for its graphics, Sun's new Open Look system will be a significant in Calculus. However, in most sections last semester, improvement. this simply meant that the instructor used it for Perhaps the most intimidating problem for us has classroom demonstrations. In only 3 of our 8 sections been the amount of time we have had to invest in did instructors have the students carry out graphical managing our computer system. Fortunately, the Col­ exercises using MATLAB. Still, it is clear that the lege has provided a few short-term reduced teaching computer is rapidly changing our attitude toward loads for us and has tentatively agreed to a substantial graphing in calculus, inclining us to treat graphing as long-term teaching reduction for one member of our a tool for analyzing functions and not as an end in department, John Stone, to be system manager. Also, itself. we hope to tum over the more routine technical as­ On the other hand, we are less certain of the pects of system management, such as doing backups, role of computer algebra systems in calculus. Existing to the computer center. software of this type requires one to learn many fussy details and a powerful but subtle command language. The Impact So before we impose such software on our students, we The completeness and uniformity of MathLAN has need a better understanding of its potential benefits. encouraged the mathematics faculty to use computing By contrast, students quickly pick up MAX and more heavily yet. We want even better software, of MATLAB just by watching the instructor use them in course, and we want the system to be even easier to class. use, but the workshops we run for ourselves and the The computer lab has been a great convenience, tailoring we do on packages such as MA TLAB have but especially for the Statistics and Programming been helping us make good use of our system quickly. with Pascal classes, which had only marginal lab For example, our dependence on mathematical word facilities previously. Also, the superior programming processing software is complete. (All our classroom environment on the Suns have helped us raise the level handouts, exams, and preprints look beautiful!) We of our programming classes. The interactive debugger are also more likely than ever to use the computer and the powerful Unix utilities have been particularly spontaneously in class for graphing and numerical valuable. computations. And, for the first time, we have been Our MathLAN computer system has also given thinking seriously of getting large classes such as students and faculty in the department a stronger Calculus using the computer. sense that we are working together in a common However, the greatest impact on our courses contin­ environment toward common goals. We take pride in ues to be at the sophomore level. MAX has helped us having put together such an extraordinary resource, improve our Linear Algebra and Differential Equations but we are certainly not complacent; the job of course, as we could never do without the computer. We improving and making better use of computing goes now emphasize eigenvalues and eigenvectors, realistic on and on. applications, and the interplay of linear algebra with Professor Gene Herman differential equations. The software lets students eas­ Department of Mathematics ily get the results of otherwise tedious computations, Grinnell College so they can spend their time more productively on Email: Herman@grin l.bitnet

246 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

at a time. More than this number of workstations can be served, but only by chaining together more file servers. In contrast, ELS v2.0a restricts the network to linking only eight workstations and allows only four Reviews of Mathematical Software of them to be "on-line."

System Configuration Each of the classroom buildings at Augustana has a computer classroom with Compaq computers and NetWare by Novell a NetWare-controlled file server containing a 130 Mark Sand Mbyte hard disk. These are used for teaching in all disciplines, independent student work, departmental and some facu1ty research. Each file Introduction administration, drives two or three printers. NetWare by Novell, Inc. is a software package designed server also to allow IBM or IBM-compatible microcomputers to share common resources. NetWare has been widely Accessing The System used in business applications for several years, and is In order to access the system, I insert a floppy disk now breaking into the educational market. into the disk drive of a workstation and tum on the While a true network would allow information power (the file server is always powered-up). This disk on screen or in storage to move directly from one contains MS-DOS to boot the workstation and the computer to another, NetWare achieves an intercon­ programs which connect the workstation to the server. nection through a file server system. This means that A batch file executes these in the proper order, clears one computer, containing a hard disk drive with a the screen, and gives the prompt: Enter your login large storage capacity, is dedicated to serving as the name:. After typing marks and pressing "Enter" the storage medium for all connected machines. Then this system checks to see if my account is secured by a stored information can be accessed from the file server password. Finding that it is, it gives the prompt: Enter by anyone with the proper security clearance. your password:. Upon typing the password, which In the October, 1988 issue of Notices, R. Palais doesn't show on the screen, and pressing "Enter" detailed the advantages of networks, so I shall attempt again, I am connected to the file server and can access to describe the usage of, advantages of, and problems some of its files. with this particular networking system. I would like The system comes in a standard configuration in to thank Loren Koepsell, our Director of Academic which retrieving files or programs from the file server Computing, for his assistance in using NetWare and and manipulating them is done through commands in writing this article. given on a command line, similar to using DOS. In fact, NetWare acts as a "shell" around DOS, so that Hardware And Software Requirements it recognizes all DOS commands and some additional To use NetWare it is necessary to have an 80286 or network ones. 80386 computer with 2 Mbytes of memory and a large With hundreds of users, each having a subdirec­ hard disk to function as the file server. The computers tory in which to store information, and dozens of connected to this server, referred to as workstations or application programs stored on the disk, it is not nodes, can be any IBM-compatible computers, must surprising that the directory structure on the disk can have enough memory to run whatever applications are be very complicated. To make it a little easier to move desired, and must be fitted with an expansion card around this directory, a system of "drive pointers" called a NIC card. NetWare comes in many versions, is used. Suppose that I routinely need to use files in with widely varying capabilities. These start at the the \Package\Private\Lotus and \Package\ subdirec­ cheaper and less-complex end with ELS, for "Entry tories. Instead of having to type cd\Package\ \Pcfile Level System," go through the standard versions, and for example, to move from one to the other, these can end with the most-powerful versions, referred to as be assigned to letters. If I type map F: = \Package\ SFT NetWare for "System Fault Tolerance." In SFT Private\ and map G: = \Package\ Public\Pcfile, then NetWare v2.1, the version used at Augustana, there merely typing F: or G: will move me from one place can be up to 256 workstations physically connected to to another, similar to switching from drive A to drive the server, with up to 100 of them actually "on-line" B on a computer with two floppy disk drives.

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Another feature which makes the complicated But What Good Is It? structure easier to use is the "search drive." This is Our network has been used more for teaching than similar to the PATH command in DOS, but is necessi­ for any other purpose. Although features such as tated by the fact that PATH can only affect the drives sharing of data and electronic mail make research that are local to the workstation, not a network drive. and administration more efficient, I shall refer the For example, suppose that there is a file in my per­ reader to the article by R. Palais on these matters and sonal directory, \Faculty\ Marks, called novell.tex that describe how we are using the network for education. I want to edit with the word processor PC-Write, and PC-Write is located in the directory \Package\Public\ Pcwrite. If I type ed novell.tex then nothing happens because the program named ed (which invokes PC­ Teaching Write) is not in the currently active directory. So I After using the networked classroom the first time, it first type map sl:=\Package\ Public\Pcwrite to make was disappointing to not be able to use it every day. Of the files in the \Package\ Public\Pcwrite accessible course, in some classes, there probably isn't a reason from any other directory. This makes ed novell.tex the to use it every day. But having each computer used proper thing to type from the directory containing by only one or two students in class allows for much novell.tex. more investigation than a demonstration performed by the lecturer. What goes on is what I think of Menus as "guided individual instruction." What I mean is All of these details seem like a bother, and they that instead of leading the students through a fixed certainly can be just that. But the above description series of examples or problems, each student can ask is of the default setup, which can be substantially a different question or have different questions asked changed to exactly fit each individual user's needs. of them, and then use the resources at their fingertips Menus can be used to avoid the command-line input to find the answers. For example, when teaching the altogether. When I log onto the system, NetWare Trapezoidal rule or Simpson's rule for approximate looks for my "login script," which is a sequence of integration, each student is able to take an existing commands to be executed in order to automatically program in BASIC (or other language) and customize set up the drive pointers and search drives that will it to find the areas of those regions that they find help me. This script then invokes a menu of choices, interesting. similar to the one shown in figure 1. If the application program currently being used The top line of the menu is highlighted, and I use isn't the right one to help, they can immediately the cursor keys to move the highlight to the desired switch to another one which is better. There is no line. Pressing "Enter" causes execution of whatever conflict over a small number of machines that contain commands are stored for that line. Possible results the necessary hardware and software. Even an exam are: ( 1) If the line contains the name of an application can be customized so that each student receives a program, that program is invoked. (2) If the line different set of problems, which are then graded right contains a network operation, such as changing my on the computer. password, those network commands are executed. (3) Reducing paperwork can be another result of using If the line contains a general topic, a sub-menu is the network. A special subdirectory can be created shown where a further selection can be made. This for a specific course, where the instructor can store third outcome is shown in figure 2. files containing notes and assignments. In return, the After an operation is completed or an application students can "hand in" their homework by storing it program is exited, I am returned to the menus and can in this directory instead of submitting a paper copy. either select another application or log off the system. This is especially nice for computer programming Also, to access something not included in the menus, assignments, since they can then be individually test I use the "Escape" key to exit the menu structure and run-a much better method than checking over a stack return to the command-line interface. of program listings. A network of personal computers Any user can create his or her own menu structure has an advantage over a mainframe in this area, to be invoked upon login. However, this task involves since some of the students and faculty have similar some familiarity with the details of the NetWare computers at home and can all work simultaneously system, and is usually reserved for a very small subset with no competition for terminals or phone lines to of users that are referred-to as "supervisors." the mainframe.

248 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Laboratory Use "trustee assignments." It is also necessary to create a When the classroom is not occupied with a class, separate subdirectory under some proper category in it is available for use by any student or faculty which Johndoe will be able to store files, for example member on a walk-in basis. As the sample menus \ Student\ Johndoe. show, the system is used for many purposes. They For each directory in the trustee assignments list, can be put into four categories, each of which serves there are eight different rights which can be granted an important role: ( 1) The standard applications of or revoked for a user. These include such capabilities word processing, spreadsheet, and database software as Searching the directory, Opening a file, Creating a are available, of course. These are used both to file, Reading a file, Writing to a file, Deleting files, prepare assignments for the courses that teach these and others. So there is great flexibility in making applications, and to assist in projects in almost every the assignments. For example, the rights Read-Open­ discipline. (2) Programming, for Computer Science Search are commonly given for a directory in which course assignments and for problem-solving in other there is an application program which the user should science courses, is done in the available languages. be able to use but not alter in any way. In contrast to (3) A few special-purpose packages, such as a CADD that, Johndoe needs to have all rights to the directory program or MathCAD are available for advanced \ Student\ Johndoe. students. ( 4) Tutorials in many disciplines are loaded Only a minute or so is needed to create a new onto the network. Some of these were commercially account with the proper assignments. However, to produced and some were written by a faculty member create many accounts at one time by this method in that discipline. would take too long, so there are ways to make it much more efficient. A NetWare utility called MAKEUSER Help for the Novice can be used, or the users can be assigned to an existing For the true beginner, who has never used a computer, group of users, or both. The one-at-a-time method is the command-line interface of NetWare would seem best reserved for only a few special situations. truly frightening. But because of the menus described The NetWare security is present at several levels: above, a computer novice may be better off using First, there is an account name and preferably a a NetWare workstation than a stand-alone PC. Ev­ password required for access to the system (although erything that a beginner would need to do can be students being a friendly lot, these are often not accomplished by choosing the correct lines from the kept secret). Secondly, a user is given access to menu. I have found that when working with novices, only that information which the supervisor allows. it is only necessary to give them a five-minute in­ A third method of security is also available, that troduction to logging onto the system and what the coming on the file level. In any directory, the files menus can do, and they are then able to get to work can be "flagged" with certain attributes. They may on some application program or tutorial. In general, it be "sharable" or "non-sharable" (many simultaneous takes much longer to become familiar with a typical users or maximum of one user), and they may be application, such as a word processor, than to become "read-write" or "read-only" (files may or may not comfortable with accessing that application on the be altered). As necessary as all this security is, even network. The only areas in which most users need in an educational setting, it can have the effect of occasional reminders are in storing and printing files. discouraging some from using the network.

Supervisors and Security Documentation NetWare can be fairly accurately described by the one As you may suspect, NetWare comes with an entire word "security." When a new account is created, say fleet of manuals to describe all the aspects of the Johndoe, the user Johndoe has very few capabilities system. In fact, one of the manuals is entitled "Guide other than logging onto the system and changing his To Manuals." This includes a glossary of the terms password. So a list of "trustee rights" is assigned used in all the manuals, and some advice on where to to his account by someone who is designated as a look for various problems that might arise. It refers "supervisor" and has been given access to all accounts to eight installation manuals (not touched except by and files on the network. This means calling up the single installer), four manuals for supervisors, the account name Johndoe from a NetWare menu and four manuals for users. All are supplemented by utility named SYSCON (for SYStem CONfiguration) "Quick Reference Cards." I have found the manuals and entering the path to the desired directories and somewhat daunting just by their sheer volume, but application packages into a list under the heading those that I am familiar with (which is most of them)

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are very easy to understand. The writers must have packages are not sophisticated enough to be able to realized that a sloppy presentation can obscure the use the network in the most efficient way. many details being described, and were extra careful to not let that happen. Each section begins with a Legalities summary of the purpose and use of the command The capabilities of a LAN make it easy for unscrupu­ or utility being described. The available options are lous users to ignore software copyrights. Some steps then listed, followed by an example of the use of must be taken to insure that the copyrights are pro­ the command. The examples are truly detailed-in tected for all software that is not shareware. If users comparison, they are much more informative than at all workstations need to simultaneously access a the examples given in a standard DOS manual. Also, software package, then a registered copy of that pack­ those statements that would be typed by the user are age must be purchased for each workstation, even printed in red ink. Other products should have such a though only one gets loaded onto the file server. If clear presentation of what the user sees on the screen only one copy is purchased and stored on the server, and what is entered from the keyboard. then those files must be flagged as "non-sharable" so Actually, most users never need to refer to a that only one user at a time can access them. Also, the manual, since all of the software that they use can be executable program files have extensions of either .exe accessed through the menu system that is set up by or .com. These need to be given the "execute-only" the supervisor, and other capabilities of the network attribute by the supervisor, which prevents them from are needed infrequently. The more that the supervisor being copied off of the disk. This helps to assure is familiar with the network and can customize it to the software-writing companies that networks are not the users, the less that the users need to know about merely places for easy illegal copying. the manuals and the details they contain. Printing In our experience, the aspect of the system that has caused the most headaches is printing. Since most of Difficulties Encountered our software packages are the same ones used on stand­ alone computers, they have no special provisions for Network Configuration printing from a network. A newer "network version" Other than the frequency with which students forget of any software package will almost certainly make their account names or passwords, probably the most printing less painful. inconvenient aspect of our network is that a separate Printing is done by using one of two possible floppy disk is required to boot up the workstation methods. Some packages won't print on the network and establish its connection to the file server. An (only to a locally-connected printer), so the output is "auto-boot" card can be installed in each machine, stored on a newly-created file, and then the network at additional cost, to establish this connection upon directed to print the file. If the file is named test.tex, turning on the workstation. for example, the necessary command is nprint test.tex p=O. The p=O ending to the command sends the file Using Application Software to a printer queue numbered 0. There can be several To use any software package, it is merely loaded onto printers connected to the file server, each served by the file server in the same way that it would be loaded one or more queues operating under the expected first­ onto the hard disk of a separate microcomputer. in first-out order. The second method is for packages However, we have found that the directory tree on that will print on the network, the problem being that the file server, being more complex than the directory the output must be routed to the desired printer. This tree found on most hard disks, makes some packages requires that a command such as capture p=O be typed more difficult or impossible to use. One package we before the application program is invoked. Then any tried wouldn't run when placed deeper into the tree printer output is directed to printer queue 0. The than the root directory. Another package, a calculus menu system can take care of both of these methods tutorial program, will only run on the workstations automatically, of course. from a floppy disk (which is about one-tenth as fast as Various printing problems can occur, most of them using the file server). The problem is that the program difficult to explain but relatively harmless. The most always looks for its data files on disk drives A and serious problem that we have frequently seen can occur B, and there is no way to re-route the data searches when a user makes a mistake while programming in to the network drive. Thus we have found that some a language. For example, it is fairly common for a

250 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

student to unknowingly create an infinite loop in a file server connection card, and $1600 for the repeater BASIC program. If that loop contains an LPRINT box to extend the network beyond 600 feet. statement, then the output enters the printing queue A newer version, v2.12, has been released which and the printer "gets stuck" into printing that user's clears up a few bugs in the accounting capabilities output forever. Then the printer must be left off, and makes installation easier. Version 2.15, which the which blocks anyone else from printing until this company expects to release during the winter or spring, infinite loop can be removed from the print queue. will allow Macintosh computers to be connected to The quickest solution is to ask the user owning the the file server while still using the standard Mac offending program to delete that file from the print windows, and will store Macintosh files. However, it queue, by using the NetWare utility PCONSOLE. will not automatically convert them into DOS files. To However, the user may not realize the problem or may accomplish that will still require additional software. leave exactly because of the problem. In that case, any Mark Sand is Assistant Professor ofMathematics at supervisor or other user designated as a "print queue Augustana College in Sioux Falls, South Dakota. operator" can delete the unwanted file from the queue.

Summary

I do not have personal experience with other network­ ing software packages. However, I have contacted FITLIB - PC Scientific several people familiar with both NetWare and other Herbert L. Holden packages, and all agreed that NetWare has more power and flexibility than the software they have used. It is a very good system, and also very complex, which FITLIB provides the user with FORTRAN subroutine makes the job of system supervisor extremely im­ libraries in both source code and object code format portant. Working from the command line, NetWare for the purpose of fitting data with tension splines. is much less user-friendly than DOS. However, if a Both periodic and nonperiodic data may be processed user's login script is properly written, and the menus and the data may be interpolated or smoothed. While are detailed enough to contain all of the needed op­ there are no explicit provisions for variable tension tions, then the user is fairly well insulated from the splines, there are instructions for modifying source details of the system. Knowing the difference between code to accommodate them. There are subroutines the choices available on the menus is all that is needed for both curve and surface fitting and the fitting to use the network, and this can even be discovered function may be specified in a variety of formats with by experimentation. We have found that students and as many dependent and independent variables as is faculty members alike become quickly accustomed to mathematically reasonable. using the system, and are now competing for the avail­ In addition to the subroutine libraries, there are able access. The success of the network encourages us nine tutorial programs, fifteen example programs, and to look forward to the day when the entire campus 72 "skeleton" programs which contain variable dec­ will be linked with NetWare. larations, initialization, and error checks to facilitate the production of user programs. This is a most wel­ come feature. The source code is well written, well Product Availability commented, and carefully documented. FITLIB requires an IBM PC (or compatible) and NetWare is available from Novell, Inc. at 122 East a FORTRAN compiler. The following compilers are 1700 South, Provo, Utah 84601. Retail prices range supported: from $595 for ELS NetWare v2.0a to $4695 for SFT NetWare v2.1. Novell currently has an educational Microsoft FORTRAN Version 3.31 or Version 4.01 discount program in order to get into the education IBM FORTRAN Version 2.00 market, and many colleges and universities have re­ Ryan-McFarland FORTRAN Version 2.42 ceived the software free of charge. Other retail prices Lahey F77L FORTRAN Version 2.22 are: $395 for the workstation NIC card, $895 for the (requires coprocessor)

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The operating system requirements and minimal However, the documentation for FITLIB contains memory requirements are determined by the particular extensive, meticulous, ano well written discussions compiler used. of the tutorial programs which provide an excellent A math coprocessor is optional since two versions vehicle for learning about spline fitting given a modest of the subroutine libraries are provided: one for background in calculus. Users of glitzy, pop-up, pull­ computers with a math coprocessor and one for down, window-oriented packages designed in total computers without. Parameters to the subroutines are ignorance of the basic principles of communication single precision whether or not you use a coprocessor. arts and requiring the use of protective eyeware may The coprocessor can process single precision variables be disappointed but I found the tutorials effective and in its extended format much faster than the 8088 easy to use with information displayed in a clean, or 8086 can and there is also some advantage in uncluttered, simple format. computing intermediate results in a higher precision. FITLIB is a PC version of the mainframe software The documentation indicates that a hard disk is product FITPACK which was developed by A. K. recommended but not required. However, I would be Cline and distributed by NCAR (National Center most reluctant to compile and link without one since for Atmospheric Research). The package appeared in the multiple support libraries are quite large. There is embrionic form in 1972 and six program units from graphics output to the screen in the tutorial programs this package appear as Algorithm 476 in the issue of and some monochrome or color graphics capability is Comm. ACM cited above. A nice discussion of the desirable. techniques appears in There are no plotter drivers provided. It is up to Cline, A.K. - Curve Fitting Using Splines Under the user to write subroutines which can plot points Tension, Atmospheric Technology No 3 Sept 1973 and lines or save output on disk for later processing 60-65 to produce graphics. I have a strong preference for the By 1977 the package was rewritten and expanded to later technique since it accommodates minor plotting 25 subroutines and in 1985 it was converted to run on disasters (such as running out of ink) and makes the a IBM PC by PC Scientific with minor modifications results readily available for repeated processing in (respecifying constants, etc.) to the source code (which various formats. now consists of some 20,000 lines) and the addition of Most software vendors indicate that users should object libraries, tutorials, skeleton files, etc. to support be "experienced". In the world of personal computers the PC environment. we have at one end of the skill scale the "novice" who Thus, the software has a long history of successful has recently learned to operate a PC and chew gum at application. It is used in contour mapping programs the same time without crashing either system. At the at NCAR and is used in software packages marketed other extreme we have the "black belt power user," by other commercial vendors not all of whom extend whatever that is. All intermediate skill levels are called the courtesy of acknowledging its use. (Courtesy: Old "experienced". earth custom popular in the slower-paced societies Here is my opinion (Procrustean as it may be) of which existed before the computer revolution.) the necessary background for a user of this software. The product is available on 5 1 I 4 or 3 1 12 inch The user should have knowledge equivalent to a three disks (the software occupies ten 5 1 I 4 inch disks) credit semester course in FORTRAN, have written at and is accompanied by a Reference Manual ( 427 least 5000 lines of FORTRAN code, and performed pages) and a Users Guide and Tutorial (286 pages) the compile and link process on a PC at least 10 published by McGraw-Hill. (A note on the McGraw­ times. To take full advantage of this program, the Hill announcement of mathematical software available user should have been introduced to spline fitting via from PC Scientific appears in Academic Computing a numerical analysis course (or advanced engineering Jan 1989 p6.) The manuals (5 112 by 8 112 page mathematics) and not feel severe emotional distress size) come in three ring binders with ample sized D in reading source material such as: rings for easy page turning and the plain text is in Schweikert, D.G. - An interpolation curve using a 10 pt type. (Since I often read manuals in poor light spline in tension, J. Math. and Physics, 45 ( 1966) I would have preferred 12 pt type.) There is a good 312-317 bibliography and relatively few typos. Cline, A.,K.- Scalar- and Planar-Valued Curve Fit­ I had occasion to call PC Scientific with questions ting Using Splines Under Tension, Comm. ACM, regarding their product and the impression I received Apr 1974 218-223 was one of a congenial and knowledgeable staff.

252 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Current pricing for the FITLIB product (or the shared programs and other resources. Another virtue is technical support by phone which is available for an that it can reduce costs in various ways; maintenance additional fee) can be obtained from: agreements are usually cheaper in bulk, and it takes Alyce Grover, Sales Manager fewer people to become experts with such a system PC Scientific, Inc. involving one kind of machine than it does with 6 Pine Tree Drive, Suite 250 a system using several radically different machines. St. Paul, MN 55112 Also, dead machines can be cannibalized to repair Phone: (612) 490-0615 other machines. Other sources of information can found in ad­ These are all sound reasons for seriously consider­ vertisements which appear in the January issues of ing a homogeneous environment. At least I hope so, journals such as NASA Tech Briefs, Pers. Eng. and since they are the considerations that were behind our Inst. News, Sci. Comp. and Auto., SIAM News, and decision to opt for such a system in the early days of Tech Minnesota. CSLI. However, I discovered the hard way that there Herbert Holden authored a text on FORTRAN IV are serious problems with such a system, problems (Macmillan 1970). He has served as chief of applica­ that eventually doomed ours. tions programming at UC Davis, senior programmer at One problem is that in most academic settings SRI International and is currently associate professor there are widely divergent computational needs and of mathematics at Gonzaga University. abilities. A few users will use computers only for email. Many will use it only for mail and tex processing. But many others will use it in research. And some will even use it in teaching. So a fair number will be actually doing computations, either symbolic or numerical. The problem with a homogeneous environment in Three Issues for such a setting is that inevitably some users are going to be using machines that are inappropriate to their Computational Environments needs or abilities. What a waste of a workstation to in Academic Departments give it to someone who does nothing but read mail. And what a waste of a mathematician to force him to carry out memory intensive computations on a small personal microcomputer. A related problem stems from the fact that many The above article by Gene Herman, and the review mathematicians already have a stock of programs, by Mark Sand report the creation of computational en­ either purchased or created, that they use regularly. vironments in two college mathematics departments. It is unlikely that a newly created homogeneous In an effort to get a discussion going, I want to make environment is going to support them all. So either explicit three of the many issues that are implicit in people will not switch to the new environment, or these articles.* else there will be a tremendous waste of previous investment in hardware, software, and learn time. Shared vs. homogeneous environments Similarly, what is going to happen to the ho­ While there are a number of differences in the systems mogeneous environment in two or three years? The created at Grinnell and Augusta, there are a number of computers that make it up are no longer state of the similarities. One of the most striking is the decision to art, or start failing. As you replace them, do you start opt for what I would call a homogeneous environment, over again, or give up homogeneity and evolve into a one where isomorphic machines are hooked together heterogeneous system? by a LAN. There are a number of things to be said These pressures have led to the heterogeneous for such a system. Herman ends his article with an system now in place at CSLI: a hodge-podge of eloquent statement of the attitude such a system is terminals, Macintosh Pluses, SE's and II's, some IBM creating in his own department. A major advantage is PC's, and various high-end workstations, all connected that people can work together building up a stock of by ethernet to a large file server which doubles as a time-sharing host, as well as highpowered workstations ofvarious sorts (SUN, HP, Xerox), all linked together * I would like to thank Bill Croft of CSLI for helpful comments over a LAN to a pair of central mainframes which draft of this editorial. on a double as file servers. While there are some economic

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disadvantages of such a system, still it is cheaper First, just try giving a lecture in a room with 20 than if we were all using the most expensive sorts or 25 computers running. The noise (and heat) are of workstations, on which many of us were unhappy something to contend with, as are the various things anyway. And for the most part, people have gravitated the students can find to play with on the machines, to the kind of machine on which they are most and the line-of-sight problems mentioned in Herman's comfortable. We have not lost the sense of a shared article. environment, due to the extensive use of electronic Second, as far as I can tell, few teachers actually mail, common programs like lt-TEX, and the file servers take advantage of the student machines, especially which allow us to work collaboratively. in college level math courses. What they want is the So my experience makes me wonder whether or ability to illustrate their lectures on the computer. not a strictly homogeneous environment is the best But for this, all they need is one computer with an use of resources, and whether or not it is stable over overhead projector. At best, the students' computers time, especially in departments with widely divergent sit silent.* computer use. Technology becomes obsolete so quickly Third, when a Type II room doubles as a Type III and user demands vary so radically that that it is room, there is competition for space. True computer seldom wise to put all your eggs in one basket. I labs are busy night and day around here. It is very think it is more prudent to spread the risk around frustrating for a student in the middle of an assignment with a heterogeneous system, and not to spend too to have to leave, making room for a class, when they much money all at once. And if you want to hedge know perfectly well that the machines are not going a bit on the technology, invest in known standards, to be used by that class. such as ethernet, TCP /IP, common lisp, C, Pro log, Fourth, any Type II classroom is going to be based X windows, UNIX, TEX, etc. Then as the hardware on some particular type of computer. This means that changes you will be able to port your work to new at least half the available courseware will not run on platforms. the machines in your classroom. So instead of buying two computers that, between them, run 90% of all Computers in classrooms courseware, you have purchased 25, which run less First, a distinction. There are currently four ways to than 50%. Something seems wrong there. get computer technology into the mathematics class­ Fifth is loss of room space. At Stanford, we are room. Type 1: One method is to have individual very short of classrooms. Setting up a classroom with classrooms equipped with a single, permanent com­ individual computers cuts the classroom capacity in puter (or maybe two, of different kinds) and projection half, at least. equipment of some sort. Type II: Another method is Personally, I favor a combination of rooms of to have a classroom set up with a bevy of computers, Type I and Ill. This is the route Stanford is (slowly!) so that the instructor and students can all use them in following. I reserve a room for the term that has class. Type III: the computer lab, which is not really the kind of computer I need for my courseware. intended for class use, but for individual use. Type (In addition, I reserve one of the computer labs to IV: Finally, at the other extreme, we have rooms that hold a problem session once a week when needed.) have no permanent computer equipment, but where However, there should be a back-up system, in case the equipment is wheeled in on carts on an ad hoc the computer or projection system fails. Last term, the basis. projector in my classroom went out the week before Notice that while a room of Type II can be used school started, and was repaired just in time for the as one of Type III, and vice versa, the optimum final. In between, zilch, since there was no back-up arrangements for each type differ. For example, a system. I had to completely rethink the course, getting lab might have a variety of computers, for use with by with computer lab work on the student's part. different kinds of software. And it might have things For some schools, a Type IV system might prove set up without any regard to lines of sight, perhaps workable, at least for starters. You can get going having machines around the wall, or back to back. with fewer computers, and there are fewer installation Grinnell and Augusta have each set up a Type II costs. However, compared with a type I system, it classroom. I used to think this the way to go. However, my experience here at Stanford (not particularly at CSLI, where there is little teaching) has led me to * Of course, it could be argued that this represents a lack of training or imagination on the part of the faculty, but I am not question it, on several grounds. convinced.

254 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

does put one more obstacle between the instructor Mathematical Freeware and Shareware and using computers in the classroom, and every such obstacle looses people who might otherwise take the MathReader plunge. In January, Wolfram Research announced that they are distributing MathReader, a program for use in Costs viewing Notebooks prepared with Mathematica, free Cheap as they are becoming, relatively speaking, com­ of charge. Although actual calculations require the puters still cost a lot of money in absolute terms, full Mathematica system, MathReader allows a user especially by mathematics department standards. And to view notebooks prepared Mathematica. It supports common wisdom is that they last three to five years, on text outlining and graphics animation, but not editing the average. And they take good people to keep them or printing of documents. The Macintosh version is running. This makes the creation and maintenance available with a Mathematica demonstration disk that of an adequate computational environment an very runs on any Macintosh. To obtain, contact Christine expensive proposition. Especially given the kinds of Schankin at Wolfram Research, (217) 398-0700. money schools are used to spending on mathematics, compared with the other sciences. Is it worth it? Or should we just let those mathe­ cc The Calculus Calculator (CC) evaluates algebraic maticians that really use computers buy them on their and transcendental functions, computes integrals and own, or perhaps with grants? I suppose the answer derivatives, solves equations, and displays graphs in to this is still out. Herman's essay says that 40% of both cartesian and polar coordinates. It will also graph their students use the departments computers outside parametric equations. CC can perform these opera­ of class, and then for an average of one hour a week. tions on any single-variable function that you define, That does not seem like very much time. And yet including functions with derivatives and indefinite in­ Herman's essay makes clear that his department feels tegrals. It was designed to be used by calculus students, the payoff is more than worth the investment. My own and the distribution disk includes a 50 page manual experiences with the use of computers in logic classes showing how many different calculus problems can be bears this out. Part of what happens is that computer solved with CC. use is very uneven during the term. Parts of the course CC runs on any IBM-compatible PC with at least are computation intensive, others are not, very much 512K of memory and one of the standard video like a chemistry lab in a chemistry course. graphics systems (CGA, Hercules, EGA, or VGA). If we are going to justify the expense of these Printer output is supported. systems, we must learn to use them effectively. But we Copies may be obtained from: must also stop thinking of mathematics as the cheap science, the one that can be done only with a pencil, David Meredith paper, and waste basket. The computer is changing all Mathematics Applications Group that forever. We must learn how to make the case to Department of Mathematics the university or college administration, to government San Francisco State University agency, and to the public, that mathematics has the 1600 Holloway Avenue same need for computational support as any other San Francisco, CA 94132 science, including computer science. Only when we Requests should included a return envelope and a believe this ourselves will we be able to convince blank 5 1I 4" disk. others, and so get the resources that are necessary. Rubik Algebra Questions, not answers Rubik Algebra is primarily a tool for illustrating, As I said earlier, these remarks are by way of raising motivating and exploring a variety of ideas and basic questions. I am not pretending to know the answers. theorems from elementary group theory, using Rubik's My own experiences have led me to have strong cube. The program allows the user to see the results opinions, but I would be the first to admit that they are of applying arbitrary sequences of face rotations to not thoroughly tested. I am also aware that conditions Rubik's cube. More important, however, is the facility vary a great deal from institution to institution. I hope to decompose an arbitrary sequence of face rotations some of you with different or more informed views into disjoint cycles. One can use the visual image will express them here. of Rubik's cube along with cycle decompositions to

MARCH 1989, VOLUME 36, NUMBER 3 255 Computers and Mathematics

illustrate ideas such as (a) the order of an element in the ability to "undo" rotations already performed, a a finite group, (b) how to calculate the order of an random scrambler, an unscrambler, menus and help element from its cycle decomposition, (c) the effect of screens. conjugation on cycle structure and (d) even and odd The program runs on IBM PCs and compatibles permutations. with CGA graphics. It is being distributed as shareware Useful (for actually solving Rubik's cube) se­ with a price of $10. A copy may be obtained for quences of face rotations can be built using the evaluation by sending either a disk and self-addressed notions of commutators and conjugates. The impossi­ stamped disk mailer or $1.00 for a 5 1/4 inch disk bility of certain operations on Rubik's cube, such as a or $1.80 for a 3 1/2 inch disk to Charles G. Fleming single transposition, can be illustrated. or Judy D. Halchin, Department of Mathematics, Other features of the program are the ability to Eastern Illinois University, Charleston, IL 61920. store on disk sequences of face rotations for later use,

A Century of Mathematics in America - Part II

Peter L. Duren, Editor with the assistance of Richard A. Askey and Uta C. Merzbach (History of Mathematics, Volume 2) This volume is the second in the History of Mathematics glimpse into the mathematical world of 1946, the discussions series, initiated in 1988 to commemorate the Centennial are put into a contemporary context with commentary by of the Society. The inaugural volume, Part I of A Century current leaders in these areas. of Mathematics in America, presented a collection of In the last section, various aspects of America's mathematical autobiographically oriented historical articles by senior past are explored on the political, social, and scientific American mathematicians. Similar in perspective to Part I but levels. The influence of women in American mathematics, differing in organization and emphasis, the present volume the burgeoning of differential geometry in the last 50 years, focuses on some key elements in the making of mathematics and discussions of the work of von Karman and Wiener are in America. among the topics covered. The first section of the book deals with some of the influential Also included are the Joint AMS-MAA Invited Addresses mathematics departments in the United States. Functioning presented at the AMS Centennial Celebration. as centers of research and training, these departments played a major role in shaping the mathematical life in this Mathematicians, historians of science, and students alike will country. The section is organized around seven departments: find this book illuminating and rewarding, and it would make Harvard, Yale, Chicago, Princeton, Stanford, Berkeley, and an excellent addition to any library collection. That the lessons NYU. Several of the articles are primary accounts, and most of the past can guide the resolution of future problems makes of these are supplemented by other recent articles. this book important reading for all who are concerned with the development of mathematics. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's 1980 Mathematics Subject Classification: 00 bicentennial. The war had just ended, mathematicians had ISBN 0-8218-0130-9 returned to their university positions, and a large number ISSN 0899-2428 578 pages (hardcover), January 1989 of veterans were beginning or resuming graduate work. Individual member $42, List price $70, The conference brought together many of the leading Institutional member $56 mathematicians of that era to take stock of open problems To order, please specify HMATH/2NA and to try to chart the future course of research in nine broad Shipping/Handling: 1st book $2, each add'! $1, $25 areas. Reprinted here are written versions of the discussions max. By air, 1st book $5, each add'! $3, $100 max. in which von Neumann, Weyl, Whitehead, Hopf, Courant, Prepayment required. Order from AMS, P.O. Box 1571, Zariski, Godel, and many others pondered the present and Annex Station, Providence, Rl 02901- 1571, or call future of mathematical research. Providing a fascinating 800-556-7774 to use VISA or MasterCard.

256 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Elections (b) The term of office for nominating committee shall be three years. Three members shall be Robert M. Fossum elected each year, so that the total membership is The Committee on Election Scheduling reported to the 9. Council at its Phoenix meeting on 10 January 1989. (c) Phase-in. At the time this provision is enacted, The Committee consists of Jane P. Gilman, Irwin Kra, the President shall designate one member of the William P. Thurston, William A. Veech, and James first-year class of the nominating committee, and A. Voytuk. Below I present the recommendations of two members of the second-year class, to have the Committee. Preceding each recommendation, the their terms extended to the 31 August follow­ current practice regarding the item addressed is stated ing the previous expiration date of their term. in capsule form. Immediately following this article Afterward, the schedule will be in a steady state. by Allyn Jackson about the is another article written It should be noted that recommendations (b) and In Jackson's article, one can find Council meeting. (c) were passed by the April 1988 Council. The on this report that were made during and comments January 1989 Council approved (a). It is expected that after the Council meeting. this change will go into effect for the next election. The Nominating Committee. Vice-President. of the Nominating Committee in There is no mention The office of Vice-President is named in the Bylaws. the Bylaws of the Society. Currently the Nominating Currently there are three Vice-Presidents at any one Committee consists of eight members, each with a two­ time, each with a term of two years. In the years are elected by preferential year term. Four members that the Society elects a President-Elect, two Vice­ election held by the membership ballots in the annual Presidents are elected. In the other years, one Vice­ each fall. The newly elected members of the committee President is elected. Elections are contested, and take office on 1 January of the year following election. candidates can be nominated by petition. The report Six candidates for the election are named by the of the Committee on Election Scheduling concerning President. Nomination by petition is allowed, but if the Vice-Presidents is as follows: fewer than two candidates are nominated by petition, then the President names enough candidates so that a 2. Vice President. for election. slate of eight is presented (a) The term of office for Vice President shall be This method of electing the Nominating Commit­ increased to three years. tee was decided upon by the Council in August 197 5 (b) Alternative I. One Vice President shall be of the Committee of Commit­ upon recommendation elected each year. In the year that this provision tees, which had delivered an extensive report to that takes effect, the President shall designate one or Council. two of the current Vice Presidents, as necessary, The report of the Committee on Election Schedul­ to have their terms extended to three years so that ing concerning the Nominating Committee is as fol­ the term of office of one Vice President expires in lows: each of the current years, the following year, and 1. Nominating Committee. the year after the following year. (a) The term of members of nominating commit­ (b) Alternative II. In each year that a President is tee shall begin on 1 September of each year. elected, one Vice President shall be elected, while

MARCH 1989, VOLUME 36, NUMBER 3 257 Inside the AMS

in every other year, two Vice Presidents shall be Fine Adjustments to terms of office. elected. Vice Presidents holding office before the Currently, all terms of office (with very few exceptions) provision lengthening their term takes effect shall in the Society end on 31 December and new terms serve for two years, while Vice Presidents elected begin on 1 January. This includes most of the terms for after this provision takes effect shall serve for committee membership. The Committee on Election three years. Scheduling makes the following recommendation for terms of office: Treasurer and Associate Treasurer. 4. Fine adjustments to terms of office. Terms of Both the Treasurer and Associate Treasurer are named office for Council, Vice Presidents, and Presidents as officers in the Bylaws. Each has a term of two shall begin on 1 February following the election. years. Candidates have run in uncontested elections In the year that this provision takes effect, all in the past. The report of the Committee on Election terms which were to expire on 1 January are Scheduling concerning the Treasurer and Associate extended by one month, to expire on 1 February. Treasurer is as follows: Presentation of candidates to the membership. 3. Treasurer and Associate Treasurer. At present, candidates for election to the offices of (a) The term of office for Treasurer and Associate the Society are named in some appropriate issue Treasurer shall be five years. A Treasurer or of Notices. Biographical material and statements by Associate Treasurer may be re-elected for at most the candidates are included in the material that is one additional term. mailed, along with the ballots, to the membership. (b) Phase-in. At the time this provision takes The Committee on Election Scheduling recommends effect, the current term of the Associate Treasurer the following procedures for presenting the candidates will be extended by two years. A Treasurer or to the membership: Associate Treasurer, at the end of a term of less than five years, who has served a total of three 5. Presentation of candidates to the membership. or more years may be elected for at most one (a) The statements and biographical material on additional five-year term, and any Treasurer or candidates shall be published in Notices at least Associate Treasurer who has served two years or two weeks before ballots are mailed, and the less may be elected for two additional five-year material shall also be included with the ballots. terms. (b) The candidate material should be gathered (c) Treasurer-designate and Associate Treasurer­ and organized in accordance with the discussion designate. One year before the end of the last below, and discussion in Council. A committee term of a Treasurer or Associate Treasurer, as of the Council shall be established to help with determined either by a letter of intent to resign the gathering and reorganization of candidate or by the provisions above, a Treasurer-designate material, in cooperation with the Secretary and or Associate Treasurer-designate shall be elected. the AMS staff. The Treasurer-designate and Associate Treasurer­ [The "discussion below" to which the recommen­ designate will be a nonvoting member of all bodies dation alludes is not included here. Briefly it asks on which the corresponding officer is an ex officio that more complete biographical material be gath­ member. ered and that an "interview" with the candidates (d) Ex Officio membership. The Treasurer and for President-Elect be published.] Associate Treasurer shall be ex officio members of the Board of Trustees, but not the Council. This President. provision shall take effect at the beginning of the term following the first election after it is enacted. The office of President is named in the Bylaws. The (e) Number of Candidates. Two qualified can­ term of office is two years. In each odd calendar didates shall be sought for each election for a year a single candidate is presented for election by Treasurer-designate, a Treasurer when there is the membership to the position of President-Elect. In no Treasurer-designate, an Associate Treasurer­ the year following election the person elected serves designate, or an Associate Treasurer when there as President-Elect. The President-Elect takes over the is no Associate Treasurer-designate. office of President at the beginning of the next calendar

258 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

year. After serving two years as President, this person here only for reference, since it is the last formal then serves for one year as Ex-President. Thus, at recommendation of the Committee. any time, the Society has a President and either The Council would be happy to receive comments a President-Elect or an Ex-President. That a single from the membership on these recommendations. candidate is presented for election is based upon Comments may be directed to any member of the tradition. The Bylaws do not call for an uncontested Council, a list of which is found elsewhere in this election. The report of the Committee on Election issue of Notices, or they may be sent directly to the Scheduling concerning the President is as follows: Secretary, who will forward them to the Council. Discussion on these items will take place at the and the 6. President. The nominating committee April 1989 Council, which will be held in Worcester, shall put forward two candidates for Council Massachusetts on 15 April 1989, at 7:00 p.m. at the President. Howard Johnson's Motor Lodge adjacent to the Holy Cross campus. Executive Committee. Any final action that may require changes in Bylaws will take place during the August 1989 Council is named in The Executive Committee of the Council meeting, which will be held on 6 August 1989, in It consists of four elected members and the the Bylaws. Boulder, Colorado. President, the Secretary, the President-Elect (during even-numbered years), and the Ex-President (during odd-numbered years) as ex officio members. The Executive Committee of the Council is empowered Phoenix Council Meeting to act for the Council on matters which have been delegated by the Council. Any member of the Council Allyn Jackson who is not an ex officio member of the Executive A typical agenda for the AMS Council runs about is eligible for election to the Executive Committee half an inch thick, replete with proposals, ideas, and Committee. One person is elected each year for a term reports to be dicussed and considered. With about 35 of four years. The Committee on Election Scheduling of the 42 members present at the Council meeting makes the following recommendation concerning the in Phoenix in January, the discussion ranged from Executive Committee. If passed, it would require a animated to unfocused to acerbic to humorous. The change in the bylaws: meeting lasted 7 1/2 hours, so a portion of it was 7. Executive Committee. bound to be soporific, but for the most part the interest (a) The term of office for Council representatives and commitment of the members brought the meeting on the executive committee shall be increased to to life. five years, beginning with the first member chosen At the meeting, a host of issues were discussed, from Council after this provision is enacted. from ways to make the research announcements in (b) At the time that the fifth 5-year member is the Bulletin more accessible, to adoption of an en­ chosen, the Secretary shall become a nonvoting dorsement of school mathematics standards prepared member of the EC. by the National Council of Teachers of Mathematics, to selling TEX software to South Africa. Among those presenting reports were Kenneth M. Hoffman of the results. Election Joint Policy Board for Mathematics, who updated the The current practice regarding the results of the Council on the Washington scene; Marcia P. Sward election is to announce the numerical tallies to the of the Mathematical Sciences Education Board at the Council, but to announce only the winners in Notices. National Research Council, who described a plethora The report of the Committee on Election Schedul- of projects of that Board; and Ronald G. Douglas of ing concerning the Election results is as follows: the State University of New York, Stony Brook, who reported on the deliberations of the AMS Committee 8. Election results. The numerical tallies of elec­ on Science Policy. tions for officers shall be available to any Society member on request, and shall be distributed as an Focus on Election Procedures attachment to the regular Council agenda. Despite the various questions competing for the Coun­ It should be noted that this has already been cil's attention, there was one set of issues that formed adopted by the April 1988 Council. It is mentioned the focus of the meeting: election procedures for AMS

MARCH 1989, VOLUME 36, NUMBER 3 259 Inside the AMS

officers, and, specifically, the merits and disadvan­ scientific societies-among them the American Chem­ tages of contested elections. Though these topics have ical Society, the American Physical Society, the Asso­ surfaced repeatedly in recent years, the current dis­ ciation for Computing Machinery, the Mathematical cussion began last April, when the Council considered Association of America, and the Society for Industrial a number of proposals put forth by Council member and Applied Mathematics-and found that all had Irwin Kra of the State University of New York, Stony contested elections for president. In addition, most Brook, and AMS Vice President William P. Thurston had contested elections for vice president, but there of Princeton University. As a result, the Council ap­ was variability for the offices of secretary and trea­ pointed the Committee on Election Scheduling, the surer. During the meeting, Council member Lawrence charge of which went considerably beyond the ques­ Corwin of Rutgers University pointed out that most tion of scheduling to explore other election matters. learned societies in nonscientific areas such as his­ Besides Kra and Thurston, the Committee members tory and philosophy also choose their presidents in were Jane P. Gilman of Rutgers University, William contested elections. A. Veech of Rice University, and James A. Voytuk, However, AMS Vice President Barry Simon of then associate executive director of the AMS. the California Institute of Technology noted that the Given that only about 3700 out of 22,500 AMS practices of other organizations may provide little members voted in the last election, perhaps some insight into what is appropriate for the AMS. He background on election procedures is in order. Cur­ said that because the top researchers in other sci­ rently, the President, Treasurer, Associate Treasurer, entific areas are likely to run laboratories or other Secretary, and Associate Secretaries (there are four) research facilities, they are usually more accustomed are chosen in uncontested elections. to administrative work than are mathematicians. In These offices are filled by de facto appointments addition, their research can continue at the laboratory by the AMS Nominating Committee, for, although or facility even if they are not personally overseeing it. the candidates appear on AMS ballots, there is no "It's a different culture in other sciences," said Simon. minimum number or percentage of membership votes "Mathematicians' research is much more exclusive. If required to approve the Committee's choices. Write-in a mathematician doesn't do the research, it doesn't candidates are permitted for all positions, but fewer get done, so it's more difficult to make the time than 20 write-in votes are cast for uncontested offices commitment necessary to be President." In comments in a typical election. The Vice Presidents (there are presented in the report, Past-President G. D. Mostow three at any given time) and the Members-at-Large of of Yale University noted that "the principal responsi­ the Council are chosen in contested elections from a bility and time commitment [of the AMS President] pool of candidates twice as large as the number of remains to his (or her) mathematical research." Both positions to be filled. The names come either from the Mostow and the current President, William Brow­ Nominating Committee or from petitions submitted der of Princeton University, have indicated that they by members. would not have run in contested elections. Several for­ The Committee on Election Scheduling presented mer presidents have indicated that they would have to the Council a report which made several recom­ run had their elections been contested, but others said mendations on such matters as the length of terms they might have declined. of office, the number of vice presidents, and the number of members on the Nominating Committee. An Honorary Office In addition, the report presented views on election One of the main arguments for keeping the pres­ procedures solicited from a number of prominent idential elections uncontested is that the office has members of the mathematical sciences community. historically been an honorary, rather than a policy­ But perhaps the most controversial provision of their making, one, so asking candidates to compete for the report was the proposal to hold contested elections for position is inappropriate. Many have said that, given AMS president. Also controversial but drawing less the time commitment involved, few individuals of the debate was the proposal that contested elections be appropriate stature and distinction would run for the held for treasurer and associate treasurer. The report office unless it were seen as a singular honor. also recommended exploring in future years the idea Those favoring contested elections believe that of contested elections for the Board of Trustees and someone who really wants to be president should Secretary. run for the office. In comments presented in the In preparing the report, the Committee on Elec­ report, Council member Richard S. Palais of Brandeis tion Scheduling investigated the practices of 11 other University says that while being named as president

260 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

is an honor, "there is certainly much more honor in candidates. Two "unwritten rules"-that the president the vote of confidence one receives by being truly should be a member of the National Academy of Sci­ elected, rather than virtually appointed. And if one is ences and a former AMS vice president-reduce the going to transact the business and spend the money pool of names to draw from. Though many feel that of the Society, one will do it with more confidence the Academy rule provides added insurance that the and a better spirit if really chosen for that task by the president would be a respected member of the larger members." scientific community, others believe that the rule is At the Council meeting, Thurston said that while "elitist" and provides no insurance that a candidate the AMS has been fortunate to have had good, hard­ has the necessary qualifications to be president. working officers, institutional constraints are ham­ pering the Society's effectiveness. "There are many Issues External to the AMS issues facing the community-the declining number Is the entire debate about election procedures deflect­ of people entering the profession, the lack of women ing attention from more important issues? Council and minorities, tight funding for research, the poor member Michael C. Reed of Duke University said school curriculum," he said. "If we had contested at the meeting that he fears contested elections may elections, we would get officers with a more active increase infighting. "We mathematicians love to argue involvement in solving the problems of the mathemat­ and feel righteous," he said. "Will there be a pro-SDI ical community." Thurston is also a strong supporter and an anti-SDI candidate? A pro-South Africa and of one of the report's provisions recommending a an anti-South Africa candidate?" In addition, he be­ more in-depth presentation of presidential candidates, lieves that placing so much emphasis on internal AMS including statements and biographical material pre­ procedures may be counterproductive. "This debate sented in Notices. In addition, he favors the idea of can detract from the outward issues such as education, publishing informal interviews with the candidates. government funding, and relations with the public and Some are fearful that contested elections would in­ other areas of science. We may be setting ourselves up ject an unhealthy element of politics into the AMS. In for more bickering that will impair our ability to act in comments presented in the Committee's report, David concert on these important issues." Echoing this view, Sanchez of Lehigh University said that contested elec­ Associate Secretary Lance W. Small of the University tions were unnecessary and possibly detrimental. "I of California at San Diego said after the meeting, imagine that the vast number of loyal, hardworking "There are so many problems in the mathematical AMS members out there in the hinterlands would be community, and the Council is arguing about whether hard pressed to decide between two eminent academi­ to have 3 vice presidents or 4." cians, both of whom they have likely never heard, Nonetheless, the debate has generated some excite­ never met, and never understood," he wrote. "To cre­ ment and interest that demonstrates the commitment ate the possiblity of deals, campaigns, and propaganda of the Council members to their role in the Society. needed to enlist these loyal members is moving the At the Phoenix meeting, the Council adopted one AMS in a direction fraught with danger and may proposal of the report, which called for increasing cross the line from greater participation to greater the size of the Nominating Committee from 8 to politicization." 9 members and moving the start of their terms to Some also say that there are very few mathe­ September 1 to allow the Committee more time to maticians of appropriate stature and distinction to consider candidates for elections. The remaining pro­ represent the Society, so that if two names were put posals concerning contested elections will be settled at forth in each election, the AMS would run out of suit­ the Council meeting in August in Boulder, Colorado. able candidates in a few years. Some call this argument If the report's provisions are adopted, the first presi­ specious, saying that, with a membership of 22,500, dent to be chosen in a contested election would take the Society should have no problem finding suitable office in 1991.

MARCH 1989, VOLUME 36, NUMBER 3 261 ANNOUNCING...

Ill MathSci™on CD-ROM Ill

Now you can access Mathematical Reviews (MR) and Current Mathematical Publications (CMP) on CD-ROM (Compact Disc-Read Only Memory). The CD, called MathSci Disc, will combine the search­ ing features of online MathSci with the browsing ease of printed MR. For a fixed annual fee, MathSci Disc can be used at leisure without access charges or telephone connections.

Semi-Annual Issue MathSci Disc will be produced by SilverPlatter• and will be issued semi-annually. The first MathSci Disc, available in January 1989, will contain all the reviews and abstracts from MR 1985 through 1988 and over 68,000 entries from CMP. The July disc will have all the information on the January disc plus the January-June updates. Access to current information between successive CD issues is available online from MathSci, which is updated monthly on DIALOG, BRS, and ESA.

MathSci Disc will be available for both the ffiM PC and the Macintosh. SilverPlatter's user-friendly CD software with help screens and menus will make MathSci Disc easy to use. Words and phrases in the text of the reviews and abstracts will be searchable with an adjacency operator. Records can be downloaded from the CD to the hard disk for editing or for processing with £X software into typeset form with mathematics.

Fixed Cost

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The 1989 MathSci Disc will be available at a low annual lease fee, equal to that of the printed MR: Nonmembers: List price- $3,510* AMS members & MR subscribers: additional leases- $2,106* AMS Members: $2,808* MR subscribers: $2,106* AMS members with an MR or first MathSci Disc subscription: $1,685*

Individuals at institutions subscribing to MathSci Disc can order a copy for personal use at a 90% discount: $351 *. (*Plus shipping & handling for addresses outside the U.S. and Canada.)

For more information on MathSci Disc or to receive a copy of the lease agreement, please contact Taissa Kusma, Head, Database Services, American Mathematical Society, P. 0. Box 6248, Providence, RI 02940 or call (800) 556-7774 in the continental U.S. or (401) 272-9500. Internet: TTK®MATH.AMS.COM; Telex: 797192; FAX: 401-331-3842.

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Kenneth M. Hoffman

measurements of each others' shoulder widths and This month's column is written by Hans J. Oser, arm lengths. After entering the measurements for each who is a consultant to the Office of Governmental person (using a pocket calculator), they discussed the and Public Affairs of the Joint Policy Board for numbers with their teacher. They speculated on the Mathematics in Washington, D.C. proximity of the ratio to the golden mean which they had discussed previously in the context of art and Everybody Counts: Three-year Study architecture. Shirley Hill, Chair of the MSEB, stated of U.S. Math Education Released that the purpose of this classroom demonstration was to show that group learning and interaction can lead At a Washington press conference, held jointly by to better involvement by the students. The demon­ the National Academy of Sciences and the National stration also signals a departure from the traditional Academy of Engineering, the long-awaited report, doctrine of teaching "the way it was taught": in this Everybody Counts, A Report to the Nation on the exercise, the students developed an appreciation for Future of Mathematics Education, was released to the magnitude of numbers and a critical attitude to­ the public on January 26. Prepared jointly (under ward accepting measured results, and demonstrated the auspices of the National Research Council) by that learning mathematics is not necessarily restricted the Mathematical Sciences Education Board (MSEB), to the individual, but that it can be a collective effort the Board on Mathematical Sciences (BMS), and the by a group learning together. Committee on the Mathematical Sciences in the Year In separate statements, the Chair of the BMS, 2000, the report outlines a strategy for reforming math Phillip Griffiths, and Fred Bucy, Chair of the Com­ instruction in our schools and colleges over the next mittee on the Mathematical Sciences in the Year 2000 two decades. (usually referred to as MS 2000), offered their as­ In the foreword to the report, the President of the sessments for the need of substantial reform. They National Academy of Sciences, Frank Press, signals the conveyed a sense of urgency and a commitment among commitment of the two Academies and the Institute the teachers of mathematics, to begin the long process of Medicine to participate in the long-term work of changing the curriculum for the year 2000 and of rebuilding mathematics education in the United beyond. States. While admitting that the situation in the U.S. is The press conference was opened by Robert M. unique among nations with its highly decentralized White, President of the National Academy of Engi­ educational system, all speakers were confident that neering. He praised the panels' work and echoed the the proposed reforms would be adopted in due time message put forth by Frank Press. White had encour­ without massive infusion of new federal money. To aged the mathematics education community, during the contrary, Bucy said, there is now $330 billion an earlier gathering at the Academy, to be a pump, not being spent for education in the U.S. and spending it a filter, in the process of educating our young people more wisely will allow carrying out part of the reforms in the sciences and engineering. within the current system. (Of that amount, more than In a departure from the usual format, the press $25 billion is spent for math education nationwide.) conference began with a live class, consisting of eight Other members of the panel were Marcia Sward, sixth-graders and their teacher, Paula Duckett, from Executive Director of the MSEB, and Ronald Dou­ River Terrace Community School in Northeast Wash­ glas, State University of New York at Stony Brook. ington. During a 25-minute period, the students took Reporters from national and local news media raised

MARCH 1989, VOLUME 36, NUMBER 3 263 Washington Outlook

the (rather anticipated) question whether calculators student proficiency. He called the report a milestone in the classroom prevent students from learning the and praised the mathematics research community "basics." Behind this question looms the suspicion for its readiness to be influential in effecting the that our children must be trained exactly the same changes in math education that are imminent both at way we learned mathematics in school. What needs to the precollege and undergraduate levels. He warned be understood is that mathematics did not stand still the audience, however, that this report was just the and that exciting developments have taken place in beginning, and that continuous involvement by all the past few decades that need to be taught. Getting participants will be necessary. NSF, he said, expects the students to participate in discovery, rather than to be a part of this effort. drilling them mindlessly, will be the challenge for teachers in the 1990s and beyond. No longer can we accept the excuse "My child does not have any aptitude Academies Offer White Papers for math," or we shall find a majority of high school to the New President graduates entering the work force as "innumerates." Industry now has to retrain high school graduates in Late last year, the National Academy of Sciences order for them to develop the skills necessary to op­ (NAS), the National Academy of Engineering (NAE), erate complex machinery, to diagnose malfunctioning and the Institute of Medicine (I OM) issued four white components in measuring instruments, and to be able papers to the then President-Elect George Bush. The to decide when intervention is necessary in automated white papers deal with policy issues the three bodies manufacturing systems. urge the new president to consider because of the Asked by reporters what kind of math is not now urgency with regard to the health of science and the being taught, the panel suggested that students have nation in general. to get better at problem solving and to appreciate The 10M and NAS, in a joint white paper, recom­ mathematics for its significance for the understanding mend action with regard to HIV infection with AIDS, of real world problems in biology, the environment, issues that these two bodies have studied since 1985. economics, manufacturing, science, and engineering. Specific steps are suggested to the new administration Current attitudes must be changed, said Shirley Hill, ranging from the effective use of the National Com­ and the pressure has to be kept on the system at all mission on AIDS to patient care, education, research, levels and in all components, including the textbook and international health efforts. publishers, testing services, parents, teachers, and The NAS, NAE, and 10M, in another white paper, students. The momentum for reform is there; it is recommend that the new President's science adviser be important not to lose it. The future of our children given high-level status in the White House. Without the and the country depends on a successful reform in the status of Assistant-to-the-President, the paper states, way we teach and in what we teach. the science adviser could not effectively deal with As math instruction in the secondary schools im­ issues such as industrial competitiveness, weapons proves, less time will be needed for remedial teaching programs, setting of budget priorities in the $62 in the colleges, thus allowing teachers to spend more billion federal R&D program, AIDS, changes in the time with individual students. We cannot envision global environment, or establishing national goals for future math teachers without at least a bachelor's space exploration, to name the most pressing ones. degree in mathematics teaching our high school stu­ The NAS, NAE, and 10M, in a white paper on dents. A lack of appreciation of new developments in Global Environment Change, warn that global climate mathematics, science, and engineering on the part of warming, ozone depletion, tropical deforestation, and teachers is often cited as a reason why high school acid depletion are issues that need attention early science and math are being perceived as dull and in the new administration. The issue of global envi­ irrelevant. We must change that attitude. ronment change and the development of responsive It is appropriate to mention that there is still policies must figure more prominently in the sci­ another player in the league of science education who entific, political, and foreign policy agendas of the is equally committed to reform: the National Science United States. The three bodies recommend the estab­ Foundation. NSF Director Erich Bloch, in a dinner lishment of a central point for oversight of national speech the night before the release of the report, efforts toward the global environment in order to im­ endorsed its main objectives, the new standards of prove coordination and allocation of resources among instruction, upgrading of the teaching profession, and related activities in government and to foster linkages development of more effective procedures for assessing between scientific understanding and policy options.

264 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook

The academies also recommend that specific steps be Each special initiative would require an additional $3 taken in the near term (which is Academy-speak for billion to $4 billion in peak years. Examples are the saying action is urgent): space station and human exploration of Mars or the • Policies to foster energy efficiency and conservation Moon. • Deeper reductions in emissions of ozone-destroying International partnership with other space-faring chemicals, and the eventual phaseout of chloroflu­ nations such as the Soviet Union, Western Europe, orocarbons in accord with the Montreal Protocol Japan, and China, should yield cost savings and po­ • A plan for agriculture, water resources, forestry, litical, scientific, and technical benefits not otherwise coastal protection, and other climate-sensitive ac­ achievable. tivities Recommended Actions: In consultation with • National policies to reduce acid deposition Congress, the Administration should establish long­ • Increase of investment in research and monitoring term goals for space. Such goals might include au­ of the global environment tomated scientific exploration; human exploration of The NAS and NAE, in a fourth white paper, of­ the Moon or Mars in the next century, for which a fer recommendations for the Civil Space program. space station is a prerequisite; expanded monitoring The two academies call for a commitment of $30 of the Earth for environmental and scientific purposes. billion over the next decade to move ahead with a Configuration and deployment of the Space Station manned space station, without waiting for the final should follow from these goals. configuration to be determined now. Two structural The four white papers are available from the components must be assured for the future space pro­ National Academy Press. Telephone: (202) 334-3313 grams: the first, a base program that ensures the U.S. (or 3113). competence in all space activities. The recommended JPBM's Washington office now has email addresses. level of funding: about $1 0 billion annually. The The Office of Governmental and Public Affairs is second component consists of long-term special initia­ now connected to the ARPA and BITNET electronic tives that serve U.S. scientific, political, cultural, and mail systems. Ken Hoffman, Hans Oser, Kirsten foreign policy objectives. These, the two Academies Sampson, and Katherine Molloy can be reached at say, should be funded separately from the base pro­ [email protected] on the ARPANET or at gram to ensure that operational expediency does not JPBM@UMD2 on BITNET. Try it some time. We'd again erode the nation's basic capabilities in space. enjoy hearing from you!

CLASSICAL GROUPS AND RELATED TOPICS Alexander J. Hahn, Donald G. James, and Zhe-Xian Wan, Editors (Contemporary Mathematics, Volume 82)

During his lifetime, L. K. Hua played a leading role in To honor his memory, a joint China-U.S. conference on and exerted a great influence upon the development in Classical Groups and Related Topics was held at Tsinghua China of modern mathematics, both pure and applied. His University in Beijing in May 1987. This volume represents the mathematical career began in 1931 at Tsinghua University proceedings of that conference and contains both survey where he continued as a professor for many years. Hua articles and research papers focusing on classical groups and made many significant contributions to number theory, closely related topics. algebra, geometry, complex analysis, numerical analysis, and 1980 Mathematics Subject Classifications: 11E, 18F, 20C, 200, 20F, operations research. In particular, he initiated the study of 20G, 20H classical groups in China and developed new matrix methods ISBN 0-8218-5089-X, LC 88-31519 which, as applied by him as well as his followers, were ISSN 0271-4132 instrumental in the successful attack of many problems. 272 pages (softcover). January 1989 Individual member $17, List price $28, Institutional member $22 To order, please specify CONM/82NA

Shipping/Handling: 1st book $2, each additional $1, maximum $25; by air, 1st book $5, each additional $3, maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-1571, or call toll free SOD-556-7774 to charge with VIsa or MasterCard

MARCH 1989, VOLUME 36, NUMBER 3 265 News and Announcements

J. Frank Adams the theory of higher order cohomol­ 1957-1958 at the Institute for Ad­ 1930-1989 ogy operations and invented what is vanced Study, and he was for many now called the Adams spectral se­ years a regular spring visitor to the Frank Adams, one the world's most quence, which has become the most University of Chicago. - brilliant and influential algebraic to­ fundamental tool in stable homotopy J. Peter May pologists, died in an automobile ac­ theory. In the course of solving the University of Chicago cident on January 7, 1989. His work second of these problems, he intro­ was the dominant force in the cre­ duced what are now called the Adams Ronald J. DiPerna ation of the modern subject of stable operations in topological K-theory. 1947-1989 homotopy theory, and his ideas and In a fundamental series of papers, contributions pervade virtually every Adams posed what is now called the Ronald J. DiPerna, who at a young area of algebraic topology. Adams conjecture, a basic assertion age was already a major figure in Adams was educated at Bedford about the relationship between vector analysis and nonlinear partial dif­ School and Trinity College, Cam­ bundles and spherical fibrations, and ferential equations, died on January bridge. His first teaching position was developed its consequences. The later 8, 1989 at the age of 41. Ronald at Trinity Hall, Cambridge. He spent proofs of this remarkable insight led DiPerna was a professor of mathe­ the years 1962-1970 at the Univer­ to such major mathematical devel­ matics at the University of Califor­ sity of Manchester, first as Reader opments as Sullivan's construction nia at Berkeley and was a member and later as the Fielden Professor of localizations and completions of of the Institute for Advanced Study of Pure Mathematics. He returned topological spaces and Quillen's in­ in Princeton, N.J. at the time of his to Trinity College and Cambridge vention of higher algebraic K-theory. death. His wife, Maria Schonbek, is a University as the Lowndean Profes­ Adams was intensely interested in professor of mathematics at the Uni­ sor of Astronomy and Geometry in all developments in algebraic topol­ versity of California at Santa Cruz. 1970. He was elected to the Royal ogy, and his expository lecture notes DiPerna was born in Sommerville, Society in 1964 and was awarded and monographs on a variety of top­ Massachusetts in 1947 and received its Sylvester Medal in 1982. He was ics in the subject are a vital part of his Ph.D. in 1972 from the Courant elected a foreign associate of the Na­ the current literature. He took great Institute of Mathematical Sciences tional Academy of Sciences in 1985. pains to ensure that his own work of New York University. He held Adams regarded himself primar­ met the highest standards of rigor, faculty positions at Brown Univer­ ily as a problem solver, and he first elegance, and clarity of exposition, sity, the University of Michigan, the became famous for his solutions to and he expected others to at least at­ University of Wisconsin and Duke the Hopf invariant one problem and tempt to measure up to the same high University. to the vector fields problem. One standards. His influence was exerted DiPerna was best known for his version of the former problem asks not only through his publications, but development of the method of com­ which dimensions are possible for a also through the refereeing of papers, pensated compactness. This is a very division algebra over the real num­ which he took very seriously, and an powerful method for controlling os­ bers (answer: 1, 2, 4, or 8). The latter enormous volume of mathematical cillation and thereby proving exis­ problem asks how many linearly in­ correspondence. tence theorems. DiPerna proved ex­ dependent vector fields there are on Adams was a long time member istence of weak solutions in the large the n-sphere for each n. of the American Mathematical So­ for equations of compressible gas In the course of solving the first ciety and a frequent visitor to the dynamics and he obtained impor­ of these problems, Adams developed United States. He spent the year tant results concerning uniqueness

266 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements of solutions, their large time behav­ operators and their application to of contemporary mathematics. The ior and their local regularity as ele­ important problems in partial differ­ current state of the classification of ments of BY spaces. His recent work ential equations." His work has had topological, piecewise linear, and dif­ concerned the Boltzmann equation a lasting impact on the shape of con­ ferentiable manifolds rests in large (jointly with P. L. Lions) and the two temporary Fourier analysis and on its measure on his research in topology dimensional Euler equation Uointly connections with real variables, com­ and algebra. Professor Milnor's work with A. Majda). plex analysis, and partial differential on "exotic" differentiable structures DiPerna liked hard problems and equations. In particular, his contribu­ (i.e., those different from the stan­ he perservered to conquer them. His tions to the theory of singular integral dard structures) launched the subject courage and mathematical vision will operators have been decisive, both by of differential topology. His research stand as an inspiration to all who bringing to the theory the sharpest in algebraic geometry on singular were privileged to know him and to technical tools and by applying the points of complex hypersurfaces re­ those who will learn from his works. theory in imaginative ways to impor­ lates exotic spheres to links around James Glimm tant problems in partial differential singularities. In combinatorics, he SUNY, Stony Brook equations. He received the Bacher of disproved the longstanding conjec­ theAMS in 1978 for a paper on the ture of algebraic topology known as 1989 Wolf Prizes Cauchy integral on Lipschitz curves. the Hauptvermutung. Professor Mil­ A student of Antoni Zygmund, Pro­ nor received his Ph.D. from Prince­ The Wolf Foundation has announced fessor Calderon received his Ph.D. ton University in 1954. the 1989 prize winners in mathemat­ from the University of Chicago in The awards will be presented by ics. The $100,000 prize in math­ 1950. the President of Israel, Chaim Her­ ematics will be shared by Alberto zog, in May during ceremonies at the P. Calderon of the University of Parliament in Jerusalem. The Wolf Chicago and John W. Milnor of the Foundation, an Israel-based, interna­ Institute for Advanced Study, Prince­ tional organization, presents annual ton. prizes for achievements in chemistry, agriculture, medicine, physics, math­ ematics, and the Arts. Established in 197 5 by the late Dr. Ricardo Wolf to "promote sci­ ence and art for the benefit of man­ kind," the Wolf Foundation also grants stipends each year to hundreds of students and researchers in Israel. Dr. Wolf, a German-born chemist, philanthropist, and diplomat, emi­ grated to Cuba before World War I and became Cuban Ambassador to Israel in 1961. He died in Israel in 1981.

1989 MAA Awards

The Mathematical Association of John W. Milnor America (MAA) presented its Award for Distinguished Service to Mathe­ JOHN W. MILNOR, born in Or­ matics and the Chauvenet Prize at ange, New Jersey in 1931, was rec­ its 72nd annual meeting in Phoenix ognized for "his ingenious and highly on January 13. Alberto P. Calderon original discoveries in geometry which IVAN NIVEN, Professor of Mathe­ have opened important new vistas in matics at the University of Oregon, Born in Mendoza, Argentina in topology from the algebraic, com­ Eugene, Oregon, received the Distin­ 1920, ALBERTO P. CALDERON has binatorial, and differentiable view­ guished Service Award in recognition been selected for his "groundbreak­ point[s]." His work has exerted a of service that has had significant na­ ing work on singular integral major influence on the development tionwide influence on mathematics

MARCH 1989, VOLUME 36, NUMBER 3 267 News and Announcements and mathematics education. In addi­ of the Netherlands Academy of Sci­ 1971, recognizes young individuals tion to serving as President of the ences. who have made outstanding tech­ (1983-1984), Professor Niven nical contributions to the computer MAA ACM Awards has been a member of the Asso­ industry by age 30. Steele has pub­ ciation's Board of Governors since Three mathematical scientists re­ lished more than two dozen technical 1982 and has served on at least 30 ceived awards from the Association papers on the subject of LISP, in ad­ MAA committees. As President, Pro­ for dition to three books on LISP and fessor Niven was influential in the Computing Machinery at the ACM other computer science topics. At creation of the American Mathemat­ Computer Science Conference in Thinking Machines, he works with ics Project, which seeks new ways Louisville, Kentucky on February 22, parallel programming languages and to improve the teaching of mathe­ 1989. other systems software for the Con­ matics at the secondary and primary IVAN SUTHERLAND has received nection Machine. He received his levels. He has also served as chair the 1988 ACM Turing Award for A.B. in applied mathematics from and governor of the Pacific North­ his pioneering and visionary contri­ Harvard University ( 1975) and his west Section of the MAA and on butions to computer graphics. This S.M. ( 1977) and Ph.D. ( 1980) de­ numerous sectional committees. The award, the highest honor in com­ grees in computer science and ar­ author of seven books and some 70 puter science research and applica­ tificial intelligence from the Mas­ papers, Professor Niven received his tions given by the ACM, has been sachusetts Institute of Technology. B.A. from the University of British presented annually since 1966 for CHARLES L. BRADSHAW, Chair­ Columbia in 1934 and his Ph.D. contributions of lasting and major man of the Computer Science De­ from the University of Chicago in technical importance to the comput­ partment at Mississippi State Uni­ 1938. ing field. The prize is named for the versity, received the 1988 ACM Dis­ JACOB KoREY AAR, Professor of British mathematician A. M. Tur­ tinguished Service Award for "over Mathematics at the University of ing, whose pioneering work was in­ thirty-five years of valuable and last­ Amsterdam, received the Chauvenet strumental in the development of ing contributions and service to the Prize for his paper, "Ludwig Bieber­ computer science and applications. government, academic, and profes­ bach's conjecture and its proof by Sutherland, Vice President and Tech­ sional computing community as a Louis de Branges," which appeared in nical Director of Sutherland, Sproull, computer scientist, educator, admin­ The American Mathematical Monthly and Associates, Incorporated, is the istrator, and ACM leader." With ser­ in 1986. The prize is given yearly inventor and developer of the interac­ vice to ACM spanning more than 25 to the author of a noteworthy ex­ tive graphics program called Sketch­ years, Bradshaw's career in scientific pository survey paper. Upon mak­ pad. The ACM Awards Committee computing has centered primarily on ing its selection, the Committee on cited Dr. Sutherland for the many in­ various space flight projects. From the Chauvenet Prize said of Kore­ novations in Sketchpad, including "a 1971 until 1988 he was Director of vaar's paper, " ...we are reminded display file for screen refresh, a recur­ Computing at Vanderbilt University. that the beauty and power of a few sively traversed hierarchical structure Bradshaw received his B.S. degree in simple ideas can sometimes lead to for modeling graphical objects, recur­ mathematics from Tennessee Tech­ very deep results that can even be sive methods for geometric transfor­ nological University in 1947 and his understood by students just starting mations and an object-oriented pro­ M.A., also in mathematics, from the to seriously study mathematics. El­ gramming style. Later innovations in­ University of Tennessee in 1950. like those included clude a 'Lorgnette' for viewing stereo egant arguments Fulkerson Prizes Awarded in this paper are one of the best ways or colored images and elegant algo­ of attracting students to mathemat­ rithms for registering digitized views, The Fulkerson Prize for outstanding ics." Professor Korevaar's research clipping polygons, and representing papers in the area of discrete math­ areas are complex analysis and ap­ surfaces with hidden lines." ematics is sponsored jointly by the proximation theory, with a focus on GuY L. STEELE, Senior Scientist Mathematical Programming Society Tauberian theorems and Muntz-type at the Thinking Machines Corpora­ and the American Mathematical So­ approximation. Born and educated tion, received the 1988 ACM Grace ciety. The prize was established to in the Netherlands, he spent 25 years Murray Hopper Award for "his gen­ encourage mathematical excellence in the U.S., mostly at the University eral contributions to the development in the fields of research exempli­ of Wisconsin at Madison and the of Higher Order Symbolic Program­ fied by the works of Delbert Ray University of California, San Diego. ming, principally for his advance­ Fulkerson and is awarded for papers Since 1974 he has been at the Univer­ ment of lexical scoping in LISP." that have been published in a rec­ sity of Amsterdam. He is a member The Hopper Award, established in ognized journal during the preceding

268 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements six years. Beginning in 1979, up to University of California, Santa Bar­ of this issue of Notices for the an­ three awards are presented at each bara. no\.n1cement inviting proposals from (triennial) International Symposium prospective institutions for next of the Mathematical Programming Honors for Soviet Women year's Regional Conference. Society. Mathematicians The regional conferences for this The 1988 Fulkerson Prizes were coming year are: awarded to EvA T ARDOS of Eotvos Olga Oleinik, Head of the Depart­ Discrete Groups, Expanding Lorand University, Budapest, Hun­ ment of Differential Equations at Graphs and Invariant Measures, at gary, and to NARENDRA KARMARKAR Moscow State University, was awarded the University of Oklahoma, with of AT&T Bell Laboratories, Murray the U.S.S.R. State Prize for her Alexander Lubotsky as lecturer. Andy Hill, New Jersey. Professor Tardos achievements in mathematical re­ Magid is the Principal Investigator received the award for her paper "A search. (405-325-2052). May 1989. strongly polynomial minimum cost In addition, Oleinik and Olga La­ Function Estimation in the Con­ circulation algorithm", Combinator­ dyzhenskaia of the Leningrad Branch text of Independent and Dependent ica, Volume 5 ( 1985) pages 247- of the Mathematics Institute were Observations, at the University of 256; and Dr. Karmarkar received elected to the Academy of the Lin­ California, Davis, with Murray the award for his paper "A new cei, a scientific academy in Rome, Rosenblatt as lecturer. George Rous­ polynomial-time algorithm for linear Italy. Both participated in the cere­ sas is the Principal Investigator (916- programming", Combinatorica, Vol­ monies in Rome on November 26, 752-8142). June 1989. ume 4 ( 1984) pages 373-395. The when the President of the Republic Harmonic Analysis, Real Function prizes were awarded on the recom­ of Italy presented them with the in­ Spaces and Related Areas, at Auburn mendation of a committee consist­ signia and documents of membership University, with Guido Weiss as lec­ ing of M. Padberg (chairman), M. in the Academy. turer. Geraldo DeSouza is the Princi­ Grotschel, and G.-C. Rota. pal Investigator (205-826-4290). June NSF-CBMS Regional Conferences 12-16, 1989. U.S.S.R. Academy of Sciences in the Mathematical Sciences Projection Pursuit and Related Elects 16 Americans Computationally Intensive Techniques To stimulate interest in mathemat­ for Analyzing Multivariate Data, at The U.S.S.R. Academy of Sciences ical research, the National Science George Washington University, with recently announced the election of Foundation (NSF) is sponsoring I 0 Jerome Friedman as lecturer. Robert 44 foreign members. Sixteen of the regional conferences between May Smythe is the Principal Investigator newly elected foreign members are 1989 and January 1990. A panel (202-994-6356). June 12-16, 1989. from the U.S. Prior to this election, chosen by the Conference Board of Circuit Complexity, at the Univer­ there were only 13 U.S. members the Mathematical Sciences, under a sity of Chicago, with Michael Sipser (out of a total of 93 foreign mem­ contract with the NSF, made the se­ as lecturer. Janos Simon is the Princi­ bers). The Soviet academy said the lections from among submitted pro­ pal Investigator (312-702-3488). June honor had been bestowed upon them posals. 25-30, 1989. for outstanding achievements in the Each five-day conference typically Scientific Computation, at Butler natural sciences and humanities and has about 25 participants, and fea­ University, with RichardS. Varga as also for the promotion of interna­ tures 10 lectures presented by a single lecturer. Amos Carpenter is the Prin­ tional cooperation. The election is guest lecturer. The lecturer subse­ cipal Investigator (317-283-9436). generally regarded as another sign quently prepares and submits to the June 26-30, 1989. of the continuing improvement in Conference Board a paper based on Algebraic Ideas in Ergodic The­ relations between the U.S. and the these lectures, which normally is pub­ ory, at the University of Washington, U.S.S.R. lished as a monograph as part of a re­ with Klaus Schmidt as lecturer. Dou­ The Americans elected to the gional conference series. Depending glas Lind is the Principal Investigator U.S.S.R. Academy of Sciences who on the Conference topic, publication (206-543-1723). July 17-21, 1989. are of particular interest to read­ is sponsored by the American Math­ Heat Equations in Geometry, at ers of Notices are: LARS V. ALFORS, ematical Society or the Society for the University of Hawaii, Honolulu, Harvard University; PETER D. LAX, Industrial and Applied Mathematics, with RichardS. Hamilton as lecturer. Courant Institute of Mathematical or jointly by the American Statisti­ Joel Weiner is the Principal Inves­ Sciences; Eow ARD N. LORENZ, Mas­ cal Association and the Institute of tigator (808-948-8595). July 24-29, sachusetts Institute of Technology; Mathematical Statistics. 1989. FRANK PRESS, National Academy of See the Funding Information for Singular Integral Operators, at Sciences; and J. RoBERT ScHRIEFFER the Mathematical Sciences section the University of Montana, with

MARCH 1989, VOLUME 36, NUMBER 3 269 News and Announcements

F. Michael Christ as lecturer. William Equations" (June 26-30) organized questions, vector bundles, fundamen­ Derrick is the Principal Investigator by: R. Caviness and M. Singer. tal groups, etc. (406-243-5569). August 24-Septem­ About 25 Soviet algebraic geome­ ber 1, 1989. ters and 35 American algebraic ge­ The tenth Conference was ap­ U.S.-U.S.S.R. ometers have been invited to par­ proved for January 1990 at the Uni­ Algebraic Geometry Symposium ticipate (not including the expected versity of Miami. The lecturer was Chicago area participants). to be Ronald DiPerna, who died on The Mathematical Disciplines Cen­ The organizers are S. Bloch, W. January 8, 1989. Further informa­ ter and the Department of Mathe­ Fulton, R. Swan, and J. P. May. tion regarding this conference will be matics of the University of Chicago Mathematicians wishing to partici­ announced at a future date. will hold a joint Soviet and Amer­ pate should write the organizers at ican symposium on algebraic geom­ the Department of Mathematics, the etry from June 19 through July 14, University of Chicago, Chicago, Illi­ News from the 1989. The National Academy of Sci­ nois 60637 or call 312-702-7100. Institute for Mathematics ences and the Academy of Sciences and Its Applications of the U.S.S.R. gave their joint en­ Society for Mathematical Biology University of Minnesota dorsement of the symposium at their annual interacademy meeting in De­ The Society for Mathematical Biol­ The Board of Governors of IMA cember 1989. Partial funding has ogy, in conjunction with the Insti­ in its last meeting in October 1988, been requested from the NSF. tute for Mathematics and its Ap­ has approved a proposal for Applied The main purpose of the Sym­ plications, is sponsoring a meeting Linear Algebra as the annual program posium is to assemble as strong a entitled "Classics of Theoretical Biol­ for 1991-1992. The organizers are: group of algebraic geometers as pos­ ogy," in Oxford, England during July Richard A. Brualdi, George Cybenko, sible from each of the two countries 3-8, 1989. The speakers and topics Alan George, Gene Golub, Paul van and to do all that is possible to allow include John Rinzel and Jack Cowan, Dooren, and Mitchell Luskin. them to work together for a sub­ Neurophysiology; James Murray, De­ The board also approved Time stantial amount of time. Although velopment; William Reed, Bioeco­ Series and Radar and Sonar as topics some of the invited participants will nomics; Robert May, Ecology; Roy for the summer of 1990. The Radar give talks, most of the time will Anderson, Epidemiology; and William and Sonar program is being orga­ be devoted to discussions, informal Provine, Population Genetics. The nized by: Alberto Grunbaum, Mar­ and formal, especially about open proceedings will be published as a vin Bernfeld, Richard Blahut, and problems and directions for future special issue of the Bulletin of Math­ Richard Tolimieri (June 18-29). The work. There will be plenty of time ematical Biology and as a separate Time Series program is being or­ for small groups to work on joint volume by Pergamon. ganized by: Emanuel Parzen, David projects. Thus the emphasis will be Funding for partial travel support Brillinger, R. Gnanadesikan, Murray more on participation in research for graduate students is available Rosenblatt, Murad Taqqu, and John than on transmittal of information. from the Society for Mathematical Geweke (July 2-31). Different broad areas of algebraic Biology (see the Funding Informa­ The annual program for 1989- geometry will be emphasized dur­ tion for the Mathematical Sciences 1990 is Dynamical Systems and Their ing different phases of the Sympo­ section of this issue of Notices for Applications and for 1990-1991 is sium. The main emphasis of the further information). Phase Transitions and Free Bound­ first week will be arithmetic alge­ For more information, contact ary Problems. The Institute is open braic geometry. Tentatively, the sec­ Marc Mangel, Department of Zo­ to suggestions of new proposals, for ond week will emphasize applica­ ology, University of California at both annual and short term pro­ tions to physics, K-theory, and rep­ Davis, Davis, CA 95616, 916-752- grams. People interested in writing resentation theory. Other topics of 8830 (email msmangel@ucdavis). up a proposal should contact the Di­ discussion will include motivic co­ rector, Avner Friedman. homology, Hodge theory, intersec­ Joint Meeting with It was recently decided to have tion homology, perverse sheaves, D­ LMS in 1992 two additional workshops in the spring modules, three-folds and higher di­ of 1989: "Microlocal Analysis and· mensional varieties, and recent prog­ For the first time, the AMS and the Nonlinear Waves" (May 15-19) or­ ress in such classical geometric topics London Mathematical Society (LMS) ganized by: M. Beals, R. Melrose as curves, surfaces, rationality and will collaborate on a joint conference and J. Rauch, and "Symbolic Com­ birationality questions, Abelian va­ to be held in the summer of 1992 putation Methods and Differential rieties, projective geometry, moduli in Cambridge, England. The meeting

270 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements will feature five, one-hour invited off with a reception on August 7, and sponsoring the conference as part addresses by mathematicians from there will also be the PME banquet of the National Initiative for Sci­ the United States and Great Britain, and other activities. "We hope it ence and Technology Education. The in addition to Contributed Papers will be a mathematically enriching conference will serve as the initia­ and Special Sessions. There will also and festive time," says Eileen Poiani, tive's genesis for formulating a na­ be a festive banquet. President of PME. tional agenda and specific strategies This auspicious event indicates In addition to the events at the for raising the science literacy of the the spirit of cooperation between the Boulder meeting, PME plans to is­ general public. Covering the mathe­ AMS and the LMS and the impor­ sue a special commemorative issue matical sciences on the program will tance of strengthening ties in the of the np.E Journal as part of the Di­ be Lynn Arthur Steen of St. Olaf international community of mathe­ amond Jubilee. PME has published College. matical scientists. The friendly rela­ the semiannual journal since 1952. The registration fee for the con­ tionship between the the two soci­ PME was founded in 1914 at ference is $225. For more informa­ eties has a long history, for it was Syracuse University with the goal tion, call 800-621-8335. In Illinois, the LMS that inspired the founder of promoting scholarship in mathe­ call collect, 312-645-4987. of the AMS to establish in 1888 a matics. Through its more than 260 mathematical society in the United chapters nationwide, PME seeks to States. encourage more students to persist Database Connects The meeting will be held June 29- in mathematics and to pursue ca­ Jobseekers and Employers July 2, 1992. Mark your calendars reers in mathematics research and now, and watch for more informa­ related areas. Members are generally The AMS recently signed an agree­ tion on this historic meeting. inducted into PME as undergradu­ ment with an organization that man­ ate students and remain members ages a resume data bank used pri­ Pi Mu Epsilon Diamond for life. However, individuals need marily by non-academic employers Jubilee Celebration not be students to join, and they interested in hiring professional per­ need not be affiliated with academic sonnel with training in mathematics, In celebration of its 75th anniversary, institutions. science, and engineering. AMS mem­ Pi Mu Epsilon (PME), Incorporated, PME encourages colleges and uni­ bers may now use this service free of the international honorary mathe­ versities to send undergraduate stu­ charge. matical society, will hold a Diamond dent speakers and delegates to the Di­ The service, called Scientists and Jubilee celebration, which will take amond Jubilee. There will be travel Professional Engineering Employment place at the Joint Mathematics Meet­ grants available for delegates and for Registry (SPEER), includes a com­ ings in Boulder, Colorado, August students selected to present papers at puterized database of resumes from 7-10, 1989. As part of the celebra­ the meeting. Information about the a cross section of professionals in­ tion, PME is planning a number of travel grants will be sent this month terested in career opportunities. Em­ special scientific and social events. to colleges and universities across the ployers specify their requirements for To mark this special event, the nation. a particular job, and SPEER selects AMS has provided funds for a new For more information, contact the individuals having the skills, ex­ Diamond Jubilee commemorative Eileen Poiani, President of PME, perience, education, salary require­ prize. The $1 000 prize will be ad­ Saint Peter's College, 2641 Kennedy ments, geographic preferences, and ministered and awarded annually by Boulevard, Jersey City, NJ 07306; or other characteristics matching the job PME, beginning this year. Robert Woodside, Secretary-Treasurer requirements. In Boulder, the celebration will of PME, Department of Mathemat­ To indicate their interest in a include an expanded scientific pro­ ics, East Carolina University, Green­ particular individual meeting their gram, featuring the J. Sutherland ville, NC 27858, telephone 919-757- job requirements, employers send to Frame Lecture by Jane Cronin Scan­ 6414. SPEER a "contact request." SPEER lon of Rutgers University. In addi­ mails the request to the jobseeker, tion, Joseph A. Gallian ofthe Univer­ Science Literacy Conference who is then free to respond directly sity of Minnesota-Duluth will present to the company to arrange an inter­ a special AMS-MAA-PME address. A "Strategies for Change," a conference view. If the individual is not inter­ series of contributed paper sessions on improving science literacy, will be ested in the position, SPEER notifies will give undergraduate students an held March 13-15, 1989, in Wash­ the employer of the decision, and the opportunity to present papers. ington, DC. The American Medical individual remains anonymous. In Several social events are planned Association and several other groups addition, the resumes are specially for Boulder. The celebration kicks concerned with science literacy are coded so that a jobseeker's current

MARCH 1989, VOLUME 36, NUMBER 3 271 News and Announcements employer will not view the individ­ on neural networks, and programs "Women in Physics-Why So Few?" ual's resume. focusing on statistical methods. included a presentation by Mary Beth Employers pay a flat-rate sub­ Michael H. Freedman of the Uni­ Ruskai of the Courant Insitute of scription fee to use SPEER, but there versity of California, San Diego pre­ Mathematical Sciences. Though fo­ is no cost or obligation to the job­ sented one of the "Frontiers of the cusing on physics, the session pro­ seeker. Individuals may update their Physical Sciences" lectures. His talk vided insight into the particular chal­ resumes on file at SPEER and may on an application of topology to lenges faced by women in all areas have their names removed at any incompressible fluids balanced geo­ of science and mathematics. time. metric intuition and technical details Overall, the meeting offered much For more information about to make the content accessible to of interest to the mathematical sci­ SPEER, AMS members should write mathematicians and nonmathemati­ ences community. In addition, with to AMS-SPEER, cjo Career Tech­ cians alike. Wang Yuan, professor at over 600 reporters in attendance, the nologies Corporation, 138 Old River the Institute of Mathematics at the meeting provided an excellent oppor­ Road, Andover, Massachusetts 01810 Chinese Academy of Sciences and tunity to develop public awareness of or call (508)683-0098. President of the Chinese Mathemat­ science and mathematics. ical Society, was one of the members Section A, the mathematics sec­ of the Chinese delegation attending tion of AAAS, is interested in pro­ Mathematics Makes a Showing the meeting. He spoke on advances moting and increasing the partici­ at AAAS Meeting in number theory in China and their pation of the mathematical sciences applications to numerical analysis. community in future AAAS meet­ Ten thousand people turned out for AAAS meetings also provide a ings. Warren Page, Secretary of Sec­ the largest meeting in two decades forum for discussion and analysis tion A, says that he has found the of the American Association for the of broad issues of science policy. AAAS program committee to be gen­ Advancement of Science (AAAS). One session entitled "Federal Fund­ uinely interested in having more sym­ Holding the meeting in San Fran­ ing of the Academic Physical Sci­ posia on mathematical topics of cur­ cisco probably boosted attendance, ences" featured six panelists, among rent interest. He noted that the suc­ but even those who came only for them William P. Thurston of Prince­ cess of the mathematics programs at some mild California weather in the ton University and Richard M. Karp the San Francisco meeting showed middle of January found much of of the University of California at that top mathematical researchers interest on the extensive scientific Berkeley; Barbara L. Simons of the can communicate effectively to a program. Unlike most scientific con­ IBM Almaden Research Center in broad audience of scientists. "I need ferences, AAAS meetings cover a San Jose, California was the mod­ and welcome suggestions from the broad range of disciplines and there­ erator. The lively discussion ranged mathematics community on possible fore provide a way for researchers to over such topics as setting priori­ topics and individuals to serve as learn of developments in areas other ties among federally funded science organizers," he said. than their own. projects, the increasing proportion of Plans are now being formulated The several sessions in the math­ academic research funded through for mathematics sessions to be held ematical sciences were well-attended military agencies, and the changing at the next meeting in New Orleans and attracted many nonmathemati­ role of universities in the science on February 15-20, 1990. Those who cians. One program, entitled "Logic research endeavor of the nation. have ideas for possible topics are Today" and organized by Harvey Several interesting sessions on ed­ urged to contact Warren Page, Sec­ Friedman of Ohio State University, ucation and pipeline issues indicated retary (Section A), New York City focused on a number of current top­ the broad attention such matters Technical College, CUNY, Depart­ ics in mathematical logic and the are receiving in the general scien­ ment of Mathematics, 300 Jay Street, implications for computer program­ tific community. One session on mi­ Brooklyn, NY 11201; telephone 914- ming. "Mathematics and Molecular norities in science and engineering 476-6446. Biology" was organized by Michael featured Los Angeles mathematics S. Waterman of the University of teacher Jaime Escalante, whose story Southern California, featured topics was told in the movie Stand and De­ Math Awareness Week 1989 ranging from how knot theory has liver. Arnold Ross of Ohio State Uni­ elucidated DNA recombination to versity assembled a panel of promi­ This year Mathematics Awareness the use of statistical methods in an­ nent mathematicians and scientists Week will be held April 23-29, 1989. alyzing heredity. In addition, there who described the early experiences An effort to improve public under­ was a 3-day session on chaos and that had stimulated their interest in standing of mathematics, this na­ dynamical systems, a host of talks their disciplines. A session entitled tional event gives the mathematical

272 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements sciences community an opportunity • Inviting the general public to a Voytuk succeeds Bernard L. Madi­ to celebrate mathematics and to com­ computer demonstration. son, who served as the first director municate to the public the impor­ • Hanging a banner proclaiming of MS2000 and who has now re­ tance, relevance, and beauty of the "Mathematics Awareness Week" out­ turned to the University of Arkansas. discipline. The theme for 1989 is side mathematics department offices. Over the next few years, the project "Mathematics: Discovering Patterns." • Initiating an effort to secure will develop a national plan for en­ Last year's Mathematics Aware­ a local, city, or state proclamation hancing the flow of mathematical ness Week proved very successful declaring April 23-29 Mathematics talent, renewing faculty, reinvigorat­ and brought high-level exposure to Awareness Week. ing teaching and scholarship, and mathematics. For example, the Na­ • Asking local public television making fundamental changes in the tional Academy of Sciences exhibited stations to run (or rerun) the series, curriculum at the college and univer­ a number of mathematical works of "For All Practical Purposes: Intro­ sity level. art, including the AMS Centennial duction to Contemporary Mathemat­ One of the major events in which poster and colorful fractal images. ics." This series of 26, half-hour pro­ MS2000 was involved was the na­ Fifty-seven radio stations in Penn­ grams are free to PBS stations. For tional colloquium, "Calculus for a sylvania carried a spot prepared and information, contact the Consortium New Century," held in October 1987. distributed by the public informa­ for Mathematics and Its Applications In addition, MS2000 cosponsored, tion office at Pennsylvania State Uni­ at 617-641-2600. along with the two NRC boards, the versity. The spot featured George These are just a few possibilites recently-released "Everybody Counts: Andrews commenting on the impact for ways of celebrating during Mathe­ A Report to the Nation on the Future of mathematics in everyday life. A matics Awareness Week. For more in­ of Mathematics Education." MS2000 news story on Mathematics Aware­ formation, contact Kirsten Sampson, is currently working on a report, due ness Week was fed to outlets of Mathematics Awareness Week Coor­ out this spring, on talent flow in the United Press International nation­ dinator, Office of Governmental and mathematical sciences. wide. Many colleges and universities Public Affairs, Joint Policy Board for across the nation sponsored special Mathematics, 818 Connecticut Av­ events for high school students and enue, N.W., Suite 515, Washington, Richard Nicholson teachers. DC 20006; telephone 202-659-6444. Named Director of AAAS The Joint Policy Board for Math­ For those who do sponsor activities ematics is promoting the participa­ for Mathematics Awareness Week, Richard S. Nicholson has been se­ tion of the mathematical sciences the Board would appreciate receiving lected as Executive Officer of the community in Mathematics Aware­ written descriptions of the activities American Association for the Ad­ ness Week by supplying ideas for and their success. vancement of Science(AAAS).Nichol­ various activities that mathematics son succeeds Alvin W. Trivelpiece, faculty can undertake during this Voytuk New Head of MS2000 who left the AAAS position late last week. Some of these ideas are: year to become director of the Oak • Sponsoring a mathematics con­ James A. Voytuk, former Associate Ridge National Laboratory. test for a local high school or school Executive Director of the AMS, has Nicholson will assume the AAAS district. been named as Project Director of office on or before April 15. He is cur­ Sciences in the Year rently Assistant Director for Mathe­ • Distributing a radio spot about Mathematical 2000: Assessment for Renewal in matical and Physical Sciences at the mathematics education to the local U.S. Colleges and Universities. Known National Science Foundation (NSF), media via public information offices. as MS2000, this project is jointly a position that oversees the larger • Hosting a film and reception for sponsored by the Board on Mathe­ organizational structure housing the mathematics majors in your depart­ matical Sciences and the Mathemat­ NSF's Division of Mathematical Sci­ ment. ical Sciences Education Board of the ences. • Arranging an exhibit of art, National Research Council (NRC). Nicholson began at the NSF in tools, photos, etc., which describe Voytuk, who joined the AMS staff 1970 as director of the chemical mathematics generally or specific in 1985, also served as Managing Ed­ analysis program in the chemistry mathematical events at your insti­ itor of Notices. Before taking his division. He became deputy direc­ tution. position at the Society, Voytuk was tor of the chemistry division in 1975 • Sponsoring a special symposium Executive Officer and Associate Pro­ and director of the division two years on a mathematically-related topic fessor in the Mathematical Sciences later. He held a number of other po­ of community interest and inviting Department at Rensselaer Polytech­ sitions at the Foundation before he community leaders. nic Institute. was named assistant director.

MARCH 1989, VOLUME 36, NUMBER 3 273 News and Announcements

Prior to joining the NSF, Nichol­ to Physics was held at the Univer­ granted to mark the 25,000th award son was in the chemistry department sity of Pennsylvania December 9-10, in the Foundation's Graduate Re­ of Michigan State University. He 1988. The speakers were Raoul H. search Fellowship Program, which received his B.S. in chemistry in 1960 Bott, Ljudvig D. Faddeev, Charles L. began in 1952. The two designated form Iowa State University and his Fefferman, Izrail' M. Gel'fand, Elliott lecturers are former NSF Graduate Ph.D., also in chemistry, in 1964 H. Lieb, Yurii I. Manin and Sergei Fellows who have gone on to dis­ from the University of Wisconsin at P. Novikov, Over 180 mathemati­ tinguished careers in mathematical Madison. cians and physicists participated. The research. They are David S. Fried Symposium was sponsored by the of Boston University (Fellow, 1971- New Head of NSA Math Program Department of Mathematics and the 1973) and Peter S. Landweber of Natural Science Association of the Rutgers University (Fellow, 1960- Marvin C. Wunderlich, former Depu­ University of Pennsylvania with par­ 1962). ty Director of the Mathematical Sci­ tial support from several National ences Program at the National Secu­ Science Foundation grants. Errata rity Agency, is now the director of that program. He succeeds S. Brent NSF Graduate Fellow In the February 1989 issue of Notices, Morris, now the executive secretary Commemorative Lectures page 165, the Colloquium Lecturer at of the agency's scientific advisory the August 1989 meeting in Boulder board. At the Joint Mathematics Meetings was incorrectly identified. The Col­ in January, two of the AMS In­ loquium Lecturer will be William P. U.S.-U.S.S.R. Symposium Held vited Addresses were designated as Thurston. National Science Foundation (NSF) A joint U.S.-U.S.S.R. Symposium Graduate Fellowship Commemora­ on Mathematics and its Applications tive Lectures. The distinction was

REPRESENTATION THEORY AND NUMBER This volume contains the proceedings of the conference THEORY IN CONNECTION WITH THE LOCAL "Representation Theory and Number Theory in Connection with the Local Langlands Conjecture," held in December LANGLANDS CONJECTURE 1985 at the University of Augsburg. The program of the J. Ritter, Editor conference was divided into two parts: (i) the representation (Contemporary Mathematics, Volume 86) theory of local division algebras and local Galois groups, The Langlands Program summarizes those parts of and the Langlands conjecture in the tame case; and (ii) new mathematical research belonging to the representation theory results, such as the case n = p, the matching theorem, of reductive groups and to class field theory. These two principal orders, tame Deligne representations, classification topics are connected by the vision that, roughly speaking, the of representations of GL(n), and the numerical Langlands irreducible representations of the general linear group may conjecture. The collection of papers in this volume provides an well serve as parameters for the description of all number excellent account of the current state of the local Langlands fields. In the local case, the base field is a given p-adic field Program. K and the extension theory of K is seen as determined by the irreducible representations of the absolute Galois group 1980 Mathematics Subject Classifications: 11 S37, 11 S40, 11 S45, GK of K. Great progress has been made in establishing 20G25, 22E50 correspondence between the supercuspidal representations ISBN 0-8218-5093-8, LC 88-39030 of GL(n, K) and those irreducible representations of GK ISSN 0271-4132 280 pages (softcover), January 1989 whose degrees divide n. Despite these advances, no book Individual member $17, List price $28, or paper has presented the different methods used or even Institutional member $22 collected known results. To order, please specify CONM/86NA

Shipping/Handling: 1st book $2, each additional $1, maximum S25; by air, 1st book S5, each additional S3, maximum S100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with VIsa or MasterCard

274 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information for the Mathematical Sciences

Travel Support for your status and financial situation, Program officers may be con­ Foreign Graduate Students and the name of the AMS confer­ tacted via electronic mail. To form ence you plan to attend. an individual's address, take the first The Society is pleased to announce initial and last name, and append that travel support for foreign grad­ Proposals for the NSF's @note.nsf.gov for Internet, @nsf.arpa uate students attending 1989 con­ Division of Mathematical Sciences for CSNET, or @nsf for BITNET. ferences is expected to be available For example, to contact Jonathan again this year through a grant from Proposals submitted to the National Lubin by Internet, use the address the STEP program of the Institute Science Foundation (NSF) for sup­ [email protected]. of International Education. An ap­ port of research in the mathematical plication has been filed by the Soci­ sciences should be submitted six to Mittag-Leffler Institute ety for foreign students attending the nine months prior to the expected 1989-1990 Grants AMS Summer Research Institute, the start date to ensure timely notifica­ AMS-SIAM Summer Seminar, and tion of outcome. The Division of The Mittag-Leffler Institute announces the AMS-IMS-SIAM Joint Summer Mathematical Sciences (DMS) will a number of grants for the year 1989- Research Conferences. Full informa­ accept such proposals at any time of 1990. The program of the institute tion on these conferences may be the year. The program officers in the starts on September 1 and ends on found in the November issue of DMS are listed below: May 31. The grants are intended Notices, pages 1374-1380, and sub­ for recent Ph.D.'s or advanced grad­ sequent issues. Algebra and Number Theory uate students and amount to 8.500 To be eligible for these grants, Jonathan Lubin 202-357-3695 Swedish crowns per month, or 85.000 the foreign student must be enrolled Ann Boyle for those who attend for the dura­ in full-time graduate studies at a Applied Mathematics tion of the program. Housing on the U.S. institution of higher education. Peter Bates 202-357-3686 premises of the institute can be of­ Students are ineligible if they are Bart Ng fered to some of the participants. receiving any U.S. government funds Classical Analysis The subject for 1989-1990 is Hy­ for academic support or if they are John Ryff 202-357-3455 perbolic geometry and quasiconfor­ on refugee, immigrant, or tourist visa Computational Mathematics mal mappings. status. Previous recipients of STEP Raymond Chin 202-357-3691 Several aspects of the field will be awards are ineligible for a second treated, such as Geometric Analysis grant. • Riemann surfaces Russell Walker 202-357-3451 To apply for a STEP grant: First, • Kleinian groups follow the application procedure for Modern Analysis • Teichmiiller spaces 202-357-3697 the conference you wish to attend William Paschke • Hyperbolic manifolds outlined in the announcements in Special Projects • Quasiconformal groups this issue. Second, enclose with your Deborah Lockhart 202-357-3453 • Quasiregular mappings application to the conference coor­ Elbert Walker The following experts in the field dinator a letter stating your name, Statistics and Probability have already agreed to take part in home country, student status, the Mary Ellen Bock 202-357-3693 the program for an extended period: name of the institution at which you Peter Arzberger Lars V. Ahlfors, Boris Apanasov, are enrolled, the name of an offi­ Topology and Foundations Lipman Bers, Adrien Douady, Clif­ cial at the institution who can verify Ralph Krause 202-357-3457 ford J. Earle, David B. A. Epstein,

MARCH 1989, VOLUME 36, NUMBER 3 275 Funding Information

Jose Fernandez, Michael H. Freed­ defense. Since its inception in 1986, Research Triangle Park, NC 27709- man, Frederick W. Gehring, Jane the URI has made almost $300 mil­ 2211. P. Gilman, Mikhael Gromov, John lion available to U.S. universities. • Office of Naval Research, phys­ Harer, Tadeusz Iwaniec, Troels Jor­ For fiscal year 1989, the program is ical and structural acoustics. Logan gensen, Linda Keen, Steven Kerck­ budgeted for $5 million. Hargrove, Physics Division, ONR, hoff, Irwin Kra, Ravi Kulkarni, Al­ The awards will range from 800 North Quincy St., Arlington, VA bert Marden, Gaven Martin, Bernard $50,000 to $250,000 per year. The 22217-5000. Maskit, Curt McMullen, Bruce Palka, new program will place special em­ • Defense Advanced Research Pierre Pansu, Ulrick Pinkall, Martin phasis on education and human re­ Projects Agency, transport processes Reimann, Uri Srebro, Kurt Strebel, sources and will provide substantial related to the synthesis of advanced Dennis P. Sullivan, Nicholas funds for equipment. In addition, the materials. Ben Wilcox, Defense Sci­ Varopoulos, Scott Wolpert, Michel new URI is directed at institutions ences Office, DARPA, 1400 Wilson Zinsmeister. that have the capability to perform Blvd., Arlington, VA 22209-2308. The following Scandinavians also defense research, but may lack re­ plan to stay at the institute during sources to assemble multidisciplinary Society for Mathematical Biology some period: teams. The competition is open to Travel Awards Kari Astala, Kari Hag, Juha Hei­ historically black colleges and uni­ nonen, Tero KilpeHiinen, Tapani Ku­ versities, other minority institutions, The Society for Mathematical Biol­ usalo, Peter Lindqvist, Jouni Luukai­ and any academic institution that re­ ogy has funds to partially support nen, Olli Martio, Raimo Nakki, Mar­ ceived less than $4 million from tlfe-,\ the travel of graduate students to jatta Naatanen, Mika Seppala, Tuo­ DOD for research and developmetn meetings co-sponsored by the Soci­ mas Sorvali, Matti Vuorinen. in either 1986 or 1987. ety including the Institute for Math­ Application forms can be ob­ The deadline for proposals is ematics and its Applications meeting tained from the institute and should March 30, 1989. The four main DOD in Oxford, England (July 3-8, 1989), be returned to: The Board of the agencies that fund basic research the Fortieth Annual Meeting of the Mittag-Leffler Institute, Auravagen will handle the URI program. Each American Institute of Biological Sci­ 17, S-182 62 Djursholm, Sweden, agency has specified certain research ences in Toronto, Canada (August before March 31, 1989. Telephone areas in which mathematical scien­ 6-10, 1989), and the Second An­ (46) 80-755 1809. tists might have an interest. These nual Meeting of the International are listed below with the appropriate Neural Network Society (September DOD Announces contact person in each agency. 5-9, 1989). Graduate students who New URI Competition • Air Force Office of Scientific Re­ wish support may apply to: Michael search, nonlinear mathematical mod­ C. Reed, Department of Mathemat­ The Department of Defense (DOD) eling. Contact Arje Nachman, Mathe­ ics, Duke University, Durham, NC has announced a new competition matical and Information Sciences Di­ 27706. for 1989 in its University Research rectorate, AFOSR, Bolling Air Force The application, which should be Initiative (URI) program. The URI Base, DC 20332-6448. received by May 1, 1989, should is intended to strengthen the capa­ • Army Research Office, smart include a one page research summary bility of universities and colleges to materials and structures. Contact An­ and one letter from a faculty sponsor. perform basic multidisciplinary re­ drew Crowson, Materials Science search in areas important to national Division, ARO, P.O. Box 12211,

276 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 AMS Elections

Nominations by Petition

Vice-President or Member-at-Large Joan S. Birman Victor Klee Weinstein Two positions of vice-president and member of the Council James E. Humphreys Alan 0. Two members to be named by the President. ex officio for a term of two years are to be filled in the election of 1989. The Council intends to nominate four candidates, The new members will be elected in a preferential bal­ whose names may be expected to appear in the June issue of lot. The President will name five candidates for these three Notices, which is scheduled to be mailed by the printer on places. The names may be expected to appear in the June 25 May. Nominations by petition as described in the rules issue of Notices. Nominations by petition, in the manner de­ and procedures are acceptable. scribed in the rules and procedures, will be accepted. Should Five positions of member-at-large of the Council for a the final number of candidates be less than six, the President term of three years are to be filled in the same election. The will bring it up to six. Council intends to nominate seven candidates, whose names The name of a candidate for member of the Nominat­ may be expected to appear in the June Notices. Nominations ing Committee may be placed on the ballot by petition. The by petition in the manner described in the rules and pro­ candidate's assent and petitions bearing at least 100 valid sig­ cedures are acceptable. The Council has stated its intent to natures are required for a name to be placed on the ballot. In have at least ten candidates and will bring the number up to addition, several other rules and operational considerations, ten if the nominations by petition do not do so. described below, should be followed. Petitions are presented to the Council, which, according Rules and Procedures to Section 2 of Article VII of the bylaws, makes the nomi­ Use separate copies of the form for each candidate for vice­ nations. The Council of 23 January 1979 stated the intent president, member-at-large, or member of the Nominating and of the Council of nominating all persons on whose behalf Editorial Boards Committees. there were valid petitions. The Council of 20 January 1987 1. To be considered, petitions must be addressed to Robert established a policy that, beginning with the interval 1987- M. Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island 1996, the Council intends to approve no more than two nom­ 02940, and must arrive by 6 July 1989. of the candidate must be given as it appears in inations by petition of the same individual in any ten year 2. The name the Combined Membership List. If the name does not appear in period. the list, as in the case of a new member or by error, it must aid of a Prior to presentation to the Council, petitions in be as it appears in the mailing lists, for example on the mailing candidate for the position of vice-president or of member­ label of the Notices. If the name does not identify the candidate at-large of the Council must have at least 50 valid signatures uniquely, append the member code, which may be obtained from and must conform to several rules and operational consider­ the candidate's mailing label or the Providence office. ations, which are described below. 3. The petition for a single candidate may consist of several sheets each bearing the statement of the petition, including the Editorial Boards Committee name of the position, and signatures. The name of the candidate Two places on the Editorial Boards Committee will be filled must be exactly the same on all sheets. by election. The new members will be elected in a prefer­ 4. On the next page is a sample form for petitions. Copies may petitioners may make ential ballot. The President will name three candidates for be obtained from the Secretary; however, use photocopies or reasonable facsimiles. these two places. The names may be expected to appear in and 5. A signature is valid when it is clearly that of the member Nominations by petition, in the the June issue of Notices. whose name and address is given in the left-hand column. manner described in the rules and procedures, will be ac­ 6. The signature may be in the style chosen by the signer. cepted. Should the final number of candidates be less than However, the printed name and address will be checked against four, the President will bring it up to four. the Combined Membership List and the mailing lists. No attempt The name of a candidate for member of the Editorial will be made to match variants of names with the form of name Boards Committee may be placed on the ballot by petition. in the CML. A name neither in the CML nor on the mailing lists is The candidate's assent and petitions bearing at least 100 not that of a member. (Example: The name Robert M. Fossum is valid signatures are required for a name to be placed on that of a member. The name R. Fossum appears not to be. Note can be peeled off and affixed the ballot. In addition, several other rules and operational that the mailing label of the Notices the petition as a convenient way of presenting the printed name considerations, described below, should be followed. to correctly.) The Nominating Committee for 1990 7. When a petition meeting these various requirements appears, the Secretary will ask the candidate whether he is willing to have be filled Three places on the Nominating Committee will his name on the ballot. Petitioners can facilitate the procedure by election. There will be six continuing members of the by accompanying the petitions with a signed statement from the Nominating Committee, namely: candidate giving his consent.

MARCH 1989, VOLUME 36, NUMBER 3 277 NOMINATION PETITION FOR 1989 ELECTION

The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one): D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 January, 1990; or 1 September, 1990, in the case of member of the Nominating Committee.

Name and Address (printed or typed, or Notices mailing label)

Signature

Signature

Signature

Signature

Signature

Signature

278 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences of the AMS

FUTURE MEETINGS

Worcester, Massachusetts April15-16 281

Chicago, Illinois May 19-20 291

Invited Speakers and Special Sessions 294

FUTURE CONFERENCES

Pure Mathematics Symposium Sundance Resort, Sundance, Utah, May 26-30 297

Summer Research Institute University of California, Santa Cruz, July 10-30 299

MARCH 1989, VOLUME 36, NUMBER 3 279 Coming Events

With a scientific program of superior quality and a setting of breath­ taking natural beauty, the August meetings in Boulder promise to be among the best. Especially exciting will be the debut of the new AMS lecture series Progress in Mathematics, featuring DusA McDuFF of the Institute for Advanced Study, who will speak on recent developments in symplectic geometry, and HAIM BREZIS of the University of Paris, who will speak on liquid crystals. (More information on this lecture series appears on page 149 of the February issue of Notices.)

The popular series of AMS-MAA Invited Addresses on the history and development of mathematics will continue with four excellent speak­ ers covering a broad range of topics. Speakers include JoHN CoN­ WAY, SERGE LANG, and JEAN TAYLOR. PERSI DIACONIS will present the MAA's Hedrick Lectures, and WILLIAM P. THURSTON will be the AMS Colloquium Lecturer.

Such an outstanding program makes the Boulder meetings a must! Mark your calendars now and be sure not to miss the June 1 deadline for preregistration and housing. A full announcement of the Boulder meetings, including the Preregistration/Housing Form, will appear in the next issue of Notices.

280 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Worcester, Massachusetts College of the Holy Cross April15-16

Program

The eight-hundred-and-forty-eighth meeting of the Amer­ Contributed Papers Mathematical Society will be held at the College of ican There will also be sessions for contributed ten-minute the Holy Cross in Worcester, Massachusetts, on Saturday, papers. Late papers will not be accommodated. April 15, and Sunday, April 16, 1989.

Council Invited Addresses The Council of the Society will meet at 7:00 p.m. on By invitation of the Committee to Select Hour Speakers Saturday, April 15, 1989, in Sturbridge Rooms A and for Northeast Sectional Meetings, there will be four in­ B at the Howard Johnson's Motor Lodge, located at vited one-hour addresses. The speakers, their affiliations, 800 Southbridge Street, Worcester, MA 01610, which is the titles of their talks, and the scheduled times of adjacent to the College of the Holy Cross campus. presentation are: IGOR FRENKEL, Yale University, Vertex operator al­ Other Events of Interest gebras and quantum groups, 11:00 a.m. Sunday. ADRIAN 0CNEANU, Pennsylvania State University, From 9:00 a.m. to 3:00 p.m. on Saturday, April 15 and The structure ofsymmetries of quantum space, 11:00 a.m. 9:00 a.m. to noon of Sunday, April 16, there will be Saturday. several tables set up in the atrium in Swords Hall with THOMAS H. PARKER, Michigan State University, The a selection of AMS publications and information about geometry of the Yang-Mills moduli space, 1:30 p.m. member services. Several electronic and optical retrieval Saturday. systems for accessing MathSci will also be demonstrated, KARL RuBIN, Columbia University, The arithmetic of including the online and the new CD-ROM systems elliptic curves, 1:30 p.m. Sunday. for browsing and searching Mathemati.caLReviews' and Current Mathematical Publications. Information on TeX software will also be available. All participants are invited to visit the display. Special Sessions of the same committee, there will be five By invitation Registration special sessions of selected twenty-minute papers. The topics, names and affiliations of the organizers are as The registration desk will be located in Swords Hall and follows: signs will be posted directing participants to the meeting Operator algebras, Galois theory and representations, registration area. The meeting registration desk will be RICHARD HERMAN and ADRIAN 0CNEANU, Pennsylvania open from 8:00 a.m. to 3:00 p.m. on Saturday, April State University. 15, and on Sunday, April 16, from 8:00 a.m. to 11:00 Infinite-dimensional symmetries in mathematics and a.m. The registration fees are $30 for members of the physics, JAMES LEPOWSKY, Rutgers University. AMS, $45 for nonmembers, and $10 for students or Gauge theory and differential geometry, THOMAS H. unemployed mathematicians. PARKER. L-functions and arithmetic, KARL RuBIN, and GLENN Social Event STEVENs, Boston University. Knot theory and algebraic geometry in the large, LEE The Department of Mathematics will be hosting a Beer, RUDOLPH, Clark University. Soft Drink and Pizza party which will take place on

MARCH 1989, VOLUME 36, NUMBER 3 281 Meetings

Saturday evening, April 15, in the Atrium which is Telephone: (508) 835-4456 located in Haberlin and Swords Halls. The department will be providing the pizza for the guests of the meeting Single $59.50 Double $71.50 but it should be noted that beer and soft drinks will be Sheraton-Lincoln Inn available for purchase on a cash basis during the party. 500 Lincoln Street To insure that an ample amount of pizza is ordered, it Worcester, MA 01610 is requested that members intending to attend the social Telephone: (508) 852-4000 please so indicate when registering on Saturday. Single $85 or $95 poolside Double $95 or $105 poolside Petition Table Worcester Marriott A petition table will be set up in the registration area. 10 Lincoln Square Additional information about petition tables can be Worcester, MA 01610 found in a box in the Phoenix meeting announcement Telephone: (508) 791-1600 on page 1502 of the December 1988 issue of Notices. Single $115 Double $127 Accommodations Yankee Budget Motor Lodge 531 Lincoln Street There are no accommodations available for housing on Worcester, MA 01610 campus during the meeting. Telephone: (508) 852-5800 Rooms have been blocked at the Howard Johnson's Motor Lodge adjacent to the campus. Participants should Single $33.73 Double $38.29 make their own reservations directly with the motel of Yankee Drummer Inn their choice and identify themselves as attending the 624 Southbridge Street meeting of the American Mathematical Society at the Auburn, MA 0 150 I College of the Holy Cross. The deadline for reservations Telephone: ( 508) 832-3221 at these locations was February 28. The rates below are subject to change and do not include applicable taxes. Single $74.90 Double $79.90 Howard Johnson's Motor Lodge 800 Southbridge Street Worcester, MA 01610 Food Service Telephone: (508) 791-5501 A variety of options are available for luncheon in Hogan Center on Saturday and Sunday. A special section will be Single $49 Double $53 designated as the dining area for meeting participants, The following motels are located between two and where meal service is cafeteria-style. The most efficient five miles from campus. Although rooms have not been avenue for getting a suitable lunch is a large Burger blocked at any of these locations, they are included here King adjacent to the Howard Johnson's across from for information purposes. the campus. Information on other campus food service options and restaurants in the Worcester area will be Best Western Centrum Inn available at the meeting registration desk. 110 Summer Street Worcester, MA 01610 Telephone: (508) 757-0400 Travel Single $52 Double $58 The Worcester airport is located about five miles from Days Lodge of Worcester the campus. Airline service to Worcester is provided 50 Oriol Drive by Northwest Airlines, Piedmont, Continental Express, Worcester, MA 01610 and United Express, with direct flights from Baltimore, Telephone: (508) 852-2800 Washington, Pittsburgh, Newark and New York City. There is an extensive array of connecting airlines directly Single $56.88 Double $61.88 into the Worcester Airport. Since travel time from Logan Howard Johnson's Motor Lodge International Airport in Boston can involve more than West Boylston Street two hours, flying directly into Worcester is recommended West Boylston, MA 01583 if possible.

282 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY CAMPUS OF HOLY CROSS COLLEGE

Enter here, gate 7, for field house, Campus Center, llart Center, Visitors' Parking Area.

s:: > {):D :I: ~ "'CD -"' < ~ 0 t'll r t'll c ;· s:: IJQ- m ~ c.> 51' z c s:: Ol m :D c.>

Enter here, gate 2, for Administrative and Admissions offices, Vi,itors' Parking Area

G) SWORDS HALL 0 HABERLIN HALL 0 VISITORS' PARKING AREA

,1, ,1, J,

1\) Gilw Meetings

Those participants electing Logan International should Special Needs make use of the Worcester Limousine Service, which will Participants attending the meeting who may have special transport passengers directly to the campus or elsewhere needs with regard to their talks in terms of audio­ in Worcester. Reservations are necessary and may be visual aids, etc., should contact Leonard Sulski in the obtained by calling (508) 756-4834; at the same time in­ Department of Mathematics at College of the Holy Cross formation will be provided concerning passenger pickup either by mail or telephone and be quite specific. Every at Logan. attempt will be made to meet such requests. Worcester is also served by Peter Pan Bus Lines and AMTRAK rail service. The bus station is about one mile from the campus. Taxi service is available from the bus Parking station to the campus for approximately $5.00 Free parking is available at several lots located on the Participants driving to the meeting should use Auburn College of the Holy Cross Campus. Hogan Lot is the best Exit No. 10 from the Massachusetts Turnpike, then take option. Route 290 East to Worcester. The College Square Exit from Route 290 is a block from the campus.

JOINT MATHEMATICS MEETINGS

August 7-10, 1989 • University of Colorado • Boulder, Colorado

284 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

The time limit for each contributed paper in the sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in the sessions at this meeting will be found in the March 1989 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting.

Saturday, April15 AMS Special Session on Infinite-dimensional Symmetries in Mathematics and Physics, I

AMS Session on Graphs, Trees and Groups 9:00 a.m.-10:50 a.m. Room 236, Haberlin Hall 9:00 a.m. Multiplicities in the discrete series of the Virasoro 8:55 a.m.-10:50 a.m. Room 19, Haberlin Hall (9) algebra. Alvany Rocha, Bernard M. Baruch College, City 8:55 a.m. On the structure of the strong orientations of a graph. University of New York (848-17-63) (1} John Donald and John Elwin*, San Diego State University (848-05-31} (Sponsored by Edgar J. 9:30 a.m. The KP deformations of vector bundles over an elliptic Howard} (10} curve. Preliminary report. Emma Previato*, Boston University, and George 9:10 a.m. Construction of self-dual graphs. Wilson, Imperial College, London (848-14-38) (2) Peter R. Christopher* and BrigiHe Servatius, Worcester Polytechnic Institute (848-05-73) 1 0:00 a.m. A correspondence between an infinite Grassmannian (11) and arbitrary vector bundles on algebraic curves. 9:25 a.m. Three and four-dimensional Catalan numbers. Motohico Mulase, Temple University and Institute for (3) Stephen Snover* and Stephanie Troyer, University of Advanced Study (848-58-10) Hartford (848-05-95) 10:30 a.m. Catastrophes, conformal theories and Calabi-Yau 9:40a.m. m-Dimensional Catalan numbers. (12} manifolds. (4) Stephen Snover and Stephanie Troyer*, University of Cumrun Vafa, Harvard University (848-81-84) Hartford (848-05-94) (Sponsored by James I. Lepowsky} 9:55 a.m. Rigidity trees. (5) BrigiHe Servatius, Worcester Polytechnic Institute (848-05-46) AMS Special Session on Gauge Theory 10:10 a.m. Completely norma/lattices. Preliminary report. and Differential Geometry, I (6) Constantine Tsinakis, Vanderbilt University (848-06-75) 10:25 a.m. The Tits conjecture and the five-string braid group. 9:00 a.m.-10:50 a.m. Room 328, Swords Hall (7) Carl Droms*, James Madison University, Jacques 9:00 a.m. Constructing the Floer cycles. Lewin, Syracuse University, and Hermann Servatius, (13} Cliff Taubes, Harvard University (848-53-67) College of the Holy Cross (848-20-32) (Sponsored by Thomas H. Parker) 10:40 a.m. Surface subgroups of infinite Coxeter groups. 9:30 a.m. Vortices on Kahler manifolds. (8) Preliminary report. (14} Steven Bradlow, Stanford University (848-53-17) Carl Droms, James Madison University, BrigiHe 10:00 a.m. lnstantons and the geometry of the nilpotent variety. Servatius, Worcester Polytechnic Institute, and (15) Peter Kronheimer, Institute for Advanced Study Hermann Servatius*, College of the Holy Cross (848-53-20) (848-20-52) 1 0:30 a.m. Converging Ricci flow for metrics with indefinite ( 16) curvature in arbitrary dimensions. James Isenberg, University of California at San Diego, La Jolla, and University of Oregon (848-53-15)

MARCH 1989, VOLUME 36, NUMBER 3 285 Program of the Sessions

Saturday, April 15 (cont'd) AMS Invited Address

11:00 a.m.-12:00 noon Room 103, Haberl in Hall

AMS Special Session on (26) The structures of symmetries of quantum space. L-functions and Arithmetic, I Adrian Ocneanu, Pennsylvania State University, University Park (848-99-92) 9:00 a.m.-10:50 a.m. Room 414, Haberlin Hall 9:00a.m. A formal Mellin transformation in the arithmetic of AMS Invited Address (17) function fields. David Goss, University of Maryland, Baltimore County (848-14-23) 1:30 p.m.-2:30p.m. Room 103, Haberlin Hall 9:30 a.m. Representations of the Wei/ group. (27) The Yang-Mills moduli space. (18) George Zettler*, Columbia University, and Don M. Thomas H. Parker, Michigan State University Blasius, University of California, Los Angeles (848-53-91) (848-11-96) (Sponsored by Karl Rubin) 10:00 a.m. Arithmetic ampleness. (19) Christophe Soule, Centre National de Ia Recherche AMS Special Session on Infinite-dimensional Scientifique and Harvard University (848-11-65) Symmetries in Mathematics and Physics, II (Sponsored by Glenn Howard Stevens) 10:30 a.m. Modular caps, totally real fields, and periods of 2:45 p.m.-5:05 p.m. Room 236, Haberlin Hall (20) Eisenstein series on GL(n). Preliminary report. Glenn Stevens, Boston University (848-11-66) 2:45 p.m. Representation theory and the Schubert calculus. (28) Dale H. Peterson, University of British Columbia (848-22-88) (Sponsored by James I. Lepowsky) AMS Special Session on Operator Algebras, 3:15 p.m. Vertex operators and integral bases of affine Lie Galois Theory and Representations, I (29) algebras. Shari Prevost, Rutgers University, New Brunswick (848-17 -62) 9:30 a.m.-10:50 a.m. Room 238, Haberlin Hall 3:45p.m. Constructions of vertex operator superalgebras and 9:30a.m. Noncommutative toroidal orbifolds. (30) para-algebras. (21) Ola Bratteli, University of Trondheim, Norway, Alex J. Feingold*, John F. X. Ries, State University George A. Elliott*, University of Toronto, David E. of New York, Binghamton, and Igor B. Frenkel, Yale Evans, University College of Swansea, Wales, and University (848-17 -39) Akitaka Kishimoto, Tohoku University, Japan 4:15p.m. Level two standard representations of affine special (848-46-49) (31) linear Lie algebras. 10:00 a.m. Representations of projections. Preliminary report. Kailash C. Misra, North Carolina State University (22) Man-Duen Choi, University of Toronto (848-47-50) (848-17-82) 10:30 a.m. Symmetries of the CAR algebra. 4:45 p.m. Vertex operator relations for affine Lie algebras. (23) Bruce Blackadar, University of Nevada, Reno (32) Preliminary report. (848-46-87) Stefano Capparelli, Yale University (848-17 -57)

AMS Special Session on Knot Theory and AMS Special Session on Gauge Theory Algebraic Geometry in the Large, I and Differential Geometry, II

10:00 a.m.-10:50 a.m. Room 359, Swords Hall 2:45 p.m.-5:05 p.m. Room 328, Swords Hall

10:00 a.m. The equisymmetric stratification of the moduli space. 2:45 p.m. On the existence of hyperbolic monopoles. (24) Preliminary report. (33) L. M. Sibner*, Polytechnic Institute of New York, R. J. S. Allen Broughton, Cleveland State University Sibner, Brooklyn College, City University of New (848-14-54) York, and Karen Uhlenbeck, University of Texas, 10:30 a.m. Homology of Abelian covers. Preliminary report. Austin (848-53-79) (25) A. Libgober, University of Illinois, Chicago 3:15p.m. The geometry of magnetic monopoles. (848-99-98) (34) Peter J. Braam, University of Utah and Merton College, England (848-53-22) 3:45 p.m. Torsion constraints in supergeometry. (35) John Lott, University of Michigan, Ann Arbor ( 848-53-19)

286 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

4:15 p.m. Classifying connections by holonomy. (36) R. J. Sibner*, Brooklyn College, City University of AMS Session on Geometry, Topology New York, and L. M. Sibner, Polytechnic Institute of and Applied Mathematics New York (848-53-80) 4:45 p.m. Fixed points of finite group actions on 3-manifolds. 2:45 p.m.-5:10 p.m. Room 19, Haberlin Hall (37) Preliminary report. Nicholas Buchdahl*, Slawomir Kwasik, Tulane 2:45 p.m. A note on K.-uniform rotundity. University, and Reinhard Schultz, Purdue University, (47) Srinivasa Swaminathan, Dalhousie University West Lafayette (848-53-21) (848-46-43) 3:00p.m. Interior hull inequalities for lattice polygons. (48) Stanley Rabinowitz, Westford, Massachusetts AMS Special Session on (848-52-74) L-functions and Arithmetic, II 3:15 p.m. Invariant affine connections on symmetric spaces. (49) H. Turner Laquer, Case Western Reserve University (848-53-53) 2:45 p.m.-5:05 p.m. Room 414, Haberlin Hall 3:30p.m. Complete stable minimal surfaces in R3. 2:45p.m. L-functions of universal elliptic curves over lgusa (50) Marty Ross, Stanford University (848-53-09) (38) curves. 3:45 p.m. Comparison of the handle and tunnel numbers of Douglas L. Ulmer, Massachusetts Institute of (51) classical knots. Preliminary report. Technology (848-11-24) John Erbland, University of Hartford (848-57-45) 3:15p.m. Trilinear forms and local f-factors for GL2. 4:00 p.m. The interbubble medium: Inflationary IBM. Preliminary (39) Dipendra Prasad, Harvard University (848-11-42) (52) report. 3:45p.m. Averages of L-functions and their derivatives. Stephen L. Weinberg, Berkeley Academy of (40) V. Kumar Murty*, University of Toronto, and Ram Artscience, Berkeley, California (848-85-06) Murty, McGill University (848-11-72) (Sponsored by 4:15p.m. The force field holor. Glenn Howard Stevens) (53) Shama Y. Uma, Bridgewater State College, and 4:15 p.m. The formal group of the Jacobian of an algebraic Domina Eberle Spencer*, University of Connecticut, (41) curve. Storrs (848-78-13) Margaret N. Freije, College of the Holy Cross 4:30 p.m. Electromagnetic field holors. (848-11-70) (54) Shama Y. Uma*, Bridgewater State College, and 4:45 p.m. Modular quaternionic L-value congruences. Domina Eberle Spencer, University of Connecticut, (42) Preliminary report. Storrs (848-78-12) Ted Chinburg, Columbia University (848-11-08) 4:45 p.m. A theory of duality in mathematical programming. (55) Andrzej Wieczorek, Polish Academy of Sciences, Warsaw (848-90-07) AMS Special Session on Knot Theory and 5:00p.m. Computing characteristic classes of continuous lattice Algebraic Geometry in the Large, II (56) gauge fields. A. V. Phillips, State University of New York, Stony 2:45 p.m.-5:05 p.m. Room 359, Swords Hall Brook, and David A. Stone*, City College, City University of New York (848-81-44) 2:45 p.m. Higher codimensional algebraic knots. Preliminary (43) report. Alan H. Durfee, Mount Holyoke College (848-57-26) AMS Special Session on Operator Algebras, 3:15p.m. Complex algebraic plane curves via their links at Galois Theory and Representations, II ( 44) infinity. Walter D. Neumann, Ohio State University, Columbus (848-57-34) 3:15 p.m.-4:35p.m. Room 238, Haberlin Hall 3:45 p.m. A congruence between link polynomials. 3:15p.m. Continuous semigroups of •-endomorphisms of B(H). (45) Lee Rudolph, Clark University (848-57-30) (57) Robert Powers, University of Pennsylvania 4:15 p.m. The fundamental group of the complement of an (848-46-28) (46) algebraic curve. 3:45p.m. The CO-algebras generated by pairs of semigroups of Stepan Yu Orevkov, Moscow, USSR (848-14-51) (58) isometries satisfying certain commutation relations. (Sponsored by Lee N. Rudolph) Geoffrey Price, United States Naval Academy 4:45 p.m. Discussion ( 848-46-81 ) 4:15p.m. Index theory for pairs of factors of infinite index. (59) Richard Herman* and Adrian Ocneanu, Pennsylvania State University, University Park (848-46-85)

MARCH 1989, VOLUME 36, NUMBER 3 287 Program of the Sessions

10:30 a.m. Duality, crossing and Mac Lane's coherence. Saturday, April 15 (cont'd) (69) Ram Brustein, Yuval Neeman, Tel Aviv University, Israel, and Shlomo Sternberg*, Tel Aviv University, Israel and Harvard University (848-18-64) (Sponsored by James I. Lepowsky) AMS Council

7:00 p.m.-10:00 p.m. Sturbridge A & B, Howard AMS Special Session on Johnson's Motor Lodge L-functions and Arithmetic, Ill

8:30 a.m.-10:50 a.m. Room 414, Haberlin Hall Sunday, April 16 8:30a.m. Cohomology of GL(n, Z). Preliminary report. (70) Avner Ash, Ohio State University, Columbus (848-11-05) AMS Special Session on Operator Algebras, 9:00a.m. Relations among L-functions attached to algebraic (71) varieties. Preliminary report. Galois Theory and Representations, Ill Michael Rosen, Brown University (848-11-71) 9:30a.m. The Markov equation X 2 + Y2 + z2 = 3XY Z over 8:30 a.m.-10:50 a.m. Room 238, Haberlin Hall (72) quadratic imaginary fields. Preliminary report. University (848-11-04) 8:30a.m. Applications of equivariant Kasparov theory. Joseph H. Silverman, Brown (60) Preliminary report. 10:00 a.m. Vanishing and nonvanishing of certain L-functions. Peter Haskell, Virginia Polytechnic Institute and State (73) Preliminary report. University (848-46-41) David Rohrlich, Rutgers University, New Brunswick 9:00 a.m. de Rham cohomology for discrete groups. (848-11-55) (61) Paul Baum*, Pennsylvania State University, University 10:30 a.m. Mock Heegner points and congruent numbers. Park, and Alain Connes, College of France, Paris (74) Paul Monsky, Brandeis University (848-11-25) (848-46-89) 9:30a.m. Comparison of (negative) algebraic and topological (62) K-theory for C*-algebras. AMS Session on Analysis Jonathan Rosenberg, University of Maryland, College Park (848-55-29) 8:40 a.m.-10:50 a.m. Room 19, Haberlin Hall 10:00 a.m. Transverse cyclic cocycles via elliptic renormalization. (63) Preliminary report. 8:40a.m. On 8 4-sequences. Ronald G. Douglas, State University of New York, (75) John C. M. Nash, Marshall University (848-11-68) Stony Brook (848-58-56) 8:55a.m. L-functions and differential equations. Preliminary 10:30 a.m. Operator algebraic invariants for elliptic operators. (76) report. (64) Jerry Kaminker, Indiana University-Purdue University, Peter F. Stiller, Institute for Advanced Study Indianapolis (848-46-86) (848-14-33) 9:10a.m. Compact subgroups and compactly generated (77) subgroups of topological groups. AMS Special Session on Infinite-dimensional R. W. Bagley*, T. S. Wu and J. S. Yang, University of Symmetries in Mathematics and Physics, Ill Miami (848-22-02) 9:25a.m. Properties of power-series coefficients of H2(I1+) (78) functions. 8:30 a.m.-10:50 a.m. Room 236, Haberlin Hall Charles Slavin, University of Maine, Orono 8:30 a.m. Higher-order Sugawara operators for affine Lie ( 848-30-11 ) (65) algebras. 9:40 a.m. Positive almost periodic solutions of some delay Roe Goodman* and Nolan R. Wallach, Rutgers (79) integral equations. University, New Brunswick (848-22-48) A. M. Fink* and J. A. Gatica, University of Iowa 9:00a.m. Bernstein-Gelfand-Gelfand resolution for arbitrary (848-34-03) (66) Kac-Moody algebras. 9:55 a.m. On some inequalities for polynomials. Shrawan Kumar, Institute for Advanced Study (80) Narendra K. Govil, Auburn University, Auburn (848-22-61) (Sponsored by James I. Lepowsky) (848-41-36) 9:30 a.m. Vertex operators, symmetric polynomials and 10:10 a.m. On equations in Banach spaces involving composition (67) symmetric groups. (81) products of set-valued mappings. Naihuan Jing, Yale University (848-17-37) Frank U. Williamson, Jr., Vitry sur Seine, France (848-93-01) 10:00 a.m. Z2-orblfold theory. (68) Yi-Zhi Huang, Rutgers University, New Brunswick (848-17-59)

288 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

10:25 a.m. Unique base-normed predual Banach spaces and (82) quantum logics. Preliminary report. AMS Invited Address Yewande Olubummo, University of Massachusetts, Amherst (848-46-16) 1:30 p.m.-2:30p.m. Room 103, Haberlin Hall 10:40 a.m. On merging of probabilities. Preliminary report. (92) The arithmetic of elliptic curves. (83) Anthony D'Aristotle*, State University of New York, Karl Rubin, Columbia University (848-11-90) College at Plattsburgh, Persi Diaconis, Stanford University, and David Freedman, University of California, Berkeley (848-54-14) AMS Special Session on Infinite-dimensional Symmetries in Mathematics and Physics, IV AMS Special Session on Gauge Theory and Differential Geometry, Ill 2:45 p.m.-4:35 p.m. Room 236, Haberlin Hall 2:45p.m. Einstein's equations and representation theory. 9:00 a.m.-10:50 a.m. Room 328, Swords Hall (93) Bertram Kostant, Massachusetts Institute of Technology (848-22-83) 9:00 a.m. Non-unitary anomalies in semiclassical Yang-Mills (84) theory. 3:15p.m. A Jacobi identity for relative twisted vertex operators. Steven Rosenberg, Boston University (848-58-76) (94) Chongying Dong• and James Lepowsky, Rutgers University, New Brunswick (848-17-58) 9:30 a.m. Applications of Donaldson theory to the topology of (85) algebraic surfaces. 3:45p.m. Relative Z2-twisted vertex operators and standard John Morgan, Columbia University (848-53-69) (95) s1(2)--modules. Cristiano Husu, Rutgers University, New Brunswick 10:00 a.m. The L 2 superior metric on Yang-Mills moduli spaces. (848-17-60) (86) David Groisser, University of Florida (848-53-77) 4:15p.m. String path integral realization of vertex operator 10:30 a.m. Higher-order singularities in gauge fields. (96) algebras. (87) Thomas Otway, University of Texas, Austin Haruo Tsukada, University of California at San Diego, (848-35-18) La Jolla (848-22-97)

on Knot Theory and AMS Special Session AMS Special Session on Gauge Theory and the Large, Ill Algebraic Geometry in Differential Geometry, IV 9:30 a.m.-10:50 a.m. Room 359, Swords Hall 2:45 p.m.-4:05 p.m. Room 328, Swords Hall 9:30a.m. Cohopficity of 3-manifold groups. 2:45p.m. Smooth 2-spheres in indefinite 4-manifolds. (88) F. Gonzillez-Acuna, University Nac Autonoma de (97) Daniel Ruberman, Brandeis University (848-57-78) Mexico, and Wilbur Whitten•, University of Southwestern Louisiana (848-57-40) 3:10 p.m. Applications of fixed point varieties of unipotent (98) transformations to the space of SU(n)-instantons on 10:00 a.m. Spherical 3-orbifo/ds which do not fiber over the four-sphere. Preliminary report. (89) 2-orbifolds. Martin A. Guest, University of Rochester (848-81-35) William Dunbar, Pennsylvania State University, Erie (848-57-27) 3:45 p.m. Discussion 10:30 a.m. Skein modules of an interval bundle over a surface. (90) Jim Hoste, Pomona College, and Jozef H. Przytycki*, University of British Columbia and AMS Special Session on Warsaw University, Poland (848-57-47) L-functions and Arithmetic, IV

2:45 p.m.-4:05 p.m. Room 414, Haberlin Hall AMS Invited Address 2:45 p.m. Discussion

11:00 a.m.-12:00 noon Room 103, Haberlin Hall W. Wistar Comfort Associate Secretary (91) Vertex operator algebras and quantum groups. Middletown, Connecticut Igor B. Frenkel, Yale University (848-99-93)

MARCH 1989, VOLUME 36, NUMBER 3 289 Presenters of Papers

Numbers following the names indicate the speakers' positions on the program. • AMS Invited Lecturer * AMS Special Session Speaker

*Ash, A., 70 *Goodman, R., 65 • Ocneanu, A., 26 * Sibner, R. J., 36 Bagley, R. W., 77 * Goss, D., 17 Olubummo, Y., 82 *Silverman, J. H., 72 * Baum, P., 61 Govil, N. K., 80 * Orevkov, S. Y ., 46 Slavin, C., 78 * Blackadar, B., 23 * Groisser, D., 86 *Otway, T., 87 Snover, S., 3 * Braam, P. J., 34 *Guest, M. A., 98 • Parker, T. H., 27 * Soule, C., 19 *Bradlow, S., 14 *Haskell, P., 60 *Peterson, D. H., 28 Spencer, D. E., 53 *Broughton, S. A., 24 *Herman, R., 59 *Powers, R., 57 *Sternberg, S., 69 * Buchdahl, N., 37 *Huang, Y.-Z., 68 * Prasad, D., 39 *Stevens, G., 20 *Capparelli, S., 32 * Husu, C., 95 * Previa to, E., I 0 Stiller, P. F., 76 *Chinburg, T., 42 *Isenberg, J., 16 *Prevost, S., 29 Stone, D. A., 56 * Choi, M.-D., 22 * Jing, N., 67 *Price, G., 58 Swaminathan, S., 47 Christopher, P.R., 2 * Kaminker, J., 64 * Przytycki, J. H., 90 * Taubes, C., 13 D'Aristotle, A., 83 * Kostant, B., 93 Rabinowitz, S., 48 Troyer, S., 4 *Dong, C., 94 * Kronheimer, P., 15 *Rocha, A., 9 Tsinakis, C., 6 *Douglas, R. G., 63 *Kumar, S., 66 * Rohrlich, D., 73 * Tsukada, H., 96 Droms, C., 7 Laquer, H. T., 49 * Rosen, M., 71 *Ulmer, D. L., 38 *Dunbar, W., 89 * Libgober, A., 25 *Rosenberg, J., 62 Uma, S. Y., 54 *Durfee, A. H., 43 * Lott, J., 35 *Rosenberg, S., 84 * Vafa, C., 12 *Elliott, G. A., 21 *Misra, K. C., 31 Ross, M., 50 Weinberg, S. L., 52 Elwin, J., I * Monsky, P., 74 * Ruberman, D., 97 *Whitten, W., 88 Erbland, J ., 51 *Morgan, J., 85 • Rubin, K., 92 Wieczorek, A., 55 *Feingold, A. J., 30 * Mulase, M., II * Rudolph, L., 45 Williamson, F. U., Jr., 81 Fink, A. M., 79 *Murty, V. K., 40 Servatius, B., 5 *Zettler, G., 18 *Freije, M. N., 41 Nash, J. C., 75 Servatius, H., 8 • Frenkel, I. B., 91 *Neumann, W. D., 44 * Sibner, L. M., 33

290 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Chicago, Illinois Loyola University of Chicago May 19-20

Second Announcement

The eight-hundred-and-forty-ninth meeting of the Amer­ Arithmetic geometry and intersection theory, HENRI ican Mathematical Society will be held on the Lake Shore GILLET Campus of Loyola University of Chicago on Friday, May Recursion theory, CHRISTINE HAUGHT, University of 19, and Saturday, May 20, 1989. All special sessions and Chicago sessions for contributed papers will be held in Damen Codes and designs, NEAL BRAND, North Texas State Hall and all invited addresses in the auditorium of University, and CARY HuFFMAN, Loyola University of Flanner Hall. Chicago Algebraic topology and varieties, RONNIE LEE, Yale University, and STEVEN WEINTRAUB, Louisiana State Invited Addresses University By invitation of the Committee to Select Hour Speakers Partial differential equations, NICHOLAS LERNER for Central Sectional Meetings, there will be four invited Quadratic forms and real algebraic geometry, CoLM one-hour addresses. The speakers, their affiliations, and MuLCAHY, Spelman College, VICTORIA PowERS, Emory the titles of their talks are: University HENRI GILLET, University of Illinois at Chicago, Nonlinear analysis and its applications, S. P. SINGH, Analogies between number fields and function fields Memorial University of Newfoundland NICHOLAS LERNER, Purdue University, Microlocal analysis and applications Contributed Papers RICHARD RocHBERG, Washington University, Esti­ mates for singular numbers of integral operators There will also be sessions for contributed ten-minute SHMUEL WEINBERGER, University of Chicago, Flexi­ papers. Late papers will not be accommodated. bility and rigidity of stratified spaces Registration Special Sessions The meeting registration desk will be located in room By invitation of the same committee, there will be thir­ 14 7 of Damen Hall and will be open from 8:00 a.m. to teen special sessions of selected twenty-minute papers. 5:00 p.m. on Friday, May 19, and 8:00 a.m. to noon The topics, names and affiliations of the organizers, are on Saturday, May, 20. The registration fees are $30 for as follows: members of the AMS, $45 for nonmembers, and $10 for Noncommutative ring theory, JEFFREY BERGEN, De­ students or unemployed mathematicians. Paul University Sequence spaces and summability, MARTIN BuNTI­ Petition Table NAS, Loyola University and BILLY RHOADES, Indiana University A petition table will be set up in the registration area. Geometric topology, TIM D. CocHRAN, Northwestern Additional information about petition tables can be University found in a box in the Phoenix meeting announcement Numerical methods in harmonic analysis, JONATHAN on page 1502 of the December 1988 issue of Notices. CoHEN, DePaul University Kazhadan-Lusztig theory and related topics, VINAY Accommodations DEODHAR, Indiana University. Algebraic groups and related topics, STEPHEN DoTY, Blocks of rooms are being held in Mertz Hall on the Lake Loyola University of Chicago Shore Campus. This air conditioned facility is adjacent

MARCH 1989, VOLUME 36, NUMBER 3 291 Meetings to a campus parking lot, cafeteria, and athletic facilities. Travel It is a three-minute walk to Damen and Flanders Halls. Participants should make reservations by calling 312- To reach Loyola University's Lake Shore Campus at 508-3300, and should indicate that they are attending 6525 North Sheridan Road, corner of Sheridan Road on the AMS meeting. After May 1, 1989, reservations will Loyola Avenue: be accepted on a space available basis. Families are FROM MIDWAY AIRPORT: Take the Continental welcome in Mertz Hall, and arrangements can be made Airport bus to the Park Hyatt Hotel on Chicago Avenue. to stay longer than the time of the conference. The rates Walk two blocks west on Chicago Avenue to the State are $32 for single occupancy and $22 per person double Street subway and take the Howard line north to Loyola occupancy. Avenue. Or, take the Outer Drive Express bus (CTA For participants staying on campus, housing registra­ #147), or the Sheridan Howard Terminal bus (CTA tion and check-in will be in the Front Desk Lobby on the #151 ), north to Sheridan and Devon (catch this bus on second floor of Mertz Hall. The Front Desk is open daily the north-east corner of Water Tower Place). By taxi it from 7:00 a.m. until midnight. If the Front Desk is not is fifty-six blocks north. open, please refer to the Conference Staff Duty Roster FROM O'HARE FIELD: Take the Continental Air­ that is posted at the Front Desk for the extension of the port bus to the Park Hyatt Hotel on Chicago Avenue. staff member on duty. Dial the four digit extension on Walk two blocks west on Chicago Avenue to the State the beige house phone located around the corner from Street subway and take the Howard line north to Loyola the Front Desk and the person on duty will come to the Avenue. Or, take the Outer Drive Express bus (CTA Front Desk. #147), or the Sheridan Howard Terminal bus (CTA Although rooms have not been blocked at either of the # 151 ), north to Sheridan and Devon (catch this bus on following locations, they are included for information. the north-east corner of Water Tower Place). By taxi it Rates are subject to change. Both are approximately 20 is fifty-six blocks north. minutes by car and 30 minutes by public transportation Alternately, take the airport bus to the Holiday Inn in from Loyola. Evanston and a taxi to Loyola. This would be a shorter ride. Or, take the O'HarejCongress or O'HarejDouglas Holiday Inn, Evanston subway (located under the O'Hare Hilton) downtown to 1501 Sherman Ave. Washington Street. Get off at Washington and take the Evanston, IL 60201 stairs down to the tunnel and walk across to the State Telephone: (312) 491-6400 Street subway and take the Howard Line north (A or B Single $70 Double $78 train) to Loyola Avenue. FROM THE GREYHOUND OR TRAILWAYS BUS Orrington Hotel STATION: From the Greyhound Station walk east on 1710 Orrington Ave. Randolph to State Street (two blocks) and take the Evanston, IL 60202 Howard Line subway north to Loyola Avenue Station. Telephone: (312) 866-8700 From the Trailways Station walk west on Randolph Single $90 Double $100 to State Street and take the Howard Line subway north to Loyola Avenue Station. FROM UNION STATION (AMTRAK): Take the Food Service Sheridan/Devon (CT A # 151) to State Street, then take The campus food service is located on the second floor the Howard Line subway north to Loyola Avenue Station. of Centennial Forum, across the patio from Mertz Hall. FROM THE ILLINOIS CENTRAL STATION A daily meal pass costing $10 can be purchased at (SOUTH SHORE): Take the Outer Drive Express bus the housing registration desk (second floor, Mertz Hall). (CTA #147) at Michigan Avenue north to Loyola Av­ Present this pass or pay the appropriate price to gain enue, or walk west to State Street and take the Howard entry into any meal. Among the features offered by the Line subway north to Loyola Avenue Station. food service are a variety of cereals, a salad bar with a BY AUTOMOBILE: If arriving from the south, east, multitude of fresh fixings, a daily soup bar, menu variety or west by Interstates 55, 57, 90, or 94, take an exit for both meat eaters and vegetarians, a selection of ice to Lake Shore Drive north to its limit. Turn north on cream, a large array of beverages, and unlimited seconds. Sheridan Road and take it to Loyola. There are several restaurants and fast food establish­ If arriving on Interstate 94 from the north, take ments within walking distance or a short drive. A list of Touhy Avenue eastbound to its limit at Sheridan Road these will be available at the meeting registration desk in South. Take a right on to Sheridan Road. Loyola is on Damen Hall 14 7. the left approximately 8 or 9 blocks south.

292 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

. If arriving on Interstate 194 or 294 from the north swimming pool, six racketball/handball courts, weight or northwest, take Foster Avenue east to Broadway or rooms with free-weight and Nautilus equipment, two Sheridan, then north to Loyola. aerobic dance rooms, three full length basketball courts, and an indoor track (an outdoor track is also available). Parking Weather Parking is available in the parking lot south of Mertz Hall. The fee is 50 cents. To park in the lot overnight, The average high temperature in Chicago in May is 70° please obtain a parking sticker at the housing desk. F and the average low is 48° F. Because the university is located on the shore of Lake Michigan, it may be slightly cooler during the daytime. The average rainfall for the Athletic Facilities month is 3.15 inches. All meeeting participants will be given complimentary Andy Roy Magid access to the new George Halas Jr., Sports Center Associate Secretary on Loyola's campus. This facility has an olympic-size Norman, Oklahoma

A Century of Mathematics in America - Part I

Peter L. Duren, Editor book presents the personal recollections Mathematicians, historians of science, with the assistance of Richard A. of a number of mathematicians who and students alike will find this book have influenced the development of illuminating and rewarding. That Askey and Uta C. Merzbach mathematics in this country. the lessons of the past can guide the resolution of present problems makes One of the highlights of the volume In the 100 years since the founding this book important reading for all who is Lipman Bers's paper which was of the AMS, the American mathematical are concerned with the development of presented as an AMS-MAA Joint Invited community has grown from a small mathematics. It will also make a fine Address in Atlanta in January 1988 and group heavily dependent on European addition to any library collection. which gives a moving account of the mathematicians to a large and influen­ reception that he and other European 1980 Mathematics Subject Classification: 01 tial group that in many areas sets the ISBN 0-8218-0124-4, LC 88-22155 standard for the rest of the world. By refugee mathematicians received in this ISSN 0899-2428 the 1930s, there was a flourishing math­ country. Described here are some of 486 pages {hardcover), August 1988 ematical community to welcome the the success stories of this century-such List price $57, Institutional member $46, as classification of finite simple groups, Individual member $34 influx of mathematicians fleeing Europe. To order, please specify HMATH/1NA These refugees supplied additional delineated by Daniel Gorenstein-as strength and new vigor to a field that well as some of the problems-such as increased dramatically as a re- the McCarthy period, chronicled by sult of World War II and the postwar Chandler Davis. Paul R. Halmos, one recognition of mathematics. of the most influential textbook writers, tells of the textbooks he used when he This volume, the first in the new History was a student and young professor and of Mathematics series, brings together a how they influenced him. Among the Shipping/Handling: 1st book $2, each add1 $1, variety of perspectives on the political, papers reprinted here are some that have $25 max. By air, 1st book $5, each add1 $3, social, and mathematical forces that appeared in journals not ordinarily read $100 max. Prepayment required. Order from have shaped the American mathematical by mathematicians, such as the article by AMS, P. 0. Box 1571, Annex Station, Provi­ community in the past century. science historian Nathan Reingold, which dence, RI 02901-1571, or call 800-556-7774 to Humorous, edifying, and poignant, this appeared in The Annals of Science. use VISA or MasterCard.

MARCH 1989, VOLUME 36, NUMBER 3 293 Invited Speakers and Special Sessions

Invited Speakers at the time this issue of Notices went to the printer. at AMS Meetings The section below entitled Information for Organizers describes the timetable for announcing the existence The individuals listed below have accepted invitations of Special Sessions. to address the Society at the times and places in­ dicated. For some meetings, the list of speakers is May 1989 Meeting in Chicago incomplete. Central Section Associate Secretary: Andy Roy Magid Deadline for organizers: Expired Chicago, May 1989 Deadline for consideration: Expired Henri Gillet Richard Rochberg Jeffrey Bergen, Noncommutative ring theory Nicholas Lerner Shmuel Weinberger Martin Buntinas and Billy Rhoades, Sequence spaces Boulder, August 1989 and summability Geometric topology Maury D. Bramson Serge Lang (AMS-MAA) Tim D. Cochran, Numerical methods in harmonic Haim Brezis Howard A. Masur Jonathan Cohen, (Progress in Dusa McDuff analysis Kazhdan-Lusztig theory and related Mathematics Lecture) (Progress in Vinay Deodhar, John Conway (AMS-MAA) Mathematics Lecture) topics Algebraic groups and related topics Persi Diaconis Jean Taylor (AMS-MAA) Stephen Doty, Arithmetic geometry and intersection (Hedrick Lecture) William Thurston Henri Gillett, Joseph A. Gallian (Colloquium Lecture) theory theory (AMS-MAA-PME) Christine Haught, Recursion Brand, Codes and designs Shizuo Kakutani Cary Huffman and Neal Weintraub, Algebraic topology (AMS-MAA) Ronnie Lee and Steven of varieties Hoboken, October 1989 Nicholas Lerner, Partial differential equations Russel Caflisch Bruce Kitchens Colm Mulcahy and Victoria Powers, Quadratic forms Fang Hua Lin Sheldon E. Newhouse and real algebraic geometry Nonlinear analysis and its applications Muncie, October 1989 S. P. Singh, Paul S. Muhly Laszlo Lempert August 1989 Meeting in Boulder Kenneth Meyer Steven Sperber Associate Secretary: Andy Roy Magid Louisville, January 1990 Deadline for organizers: Expired Deadline for consideration: April 25, 1989 Sun-Yung Alice Chang Shlomo Sternberg Richard A. Askey, History of orthogonal polynomials George B. Dantzig (Colloquium Lecture) Maury D. Bramson and David S. Griffeath, Complex (Gibbs Lecture) random phenomena and Topics George J. Fix and Rangabhary Kannan, Mathematical Organizers questions in computational geometry of Special Sessions Kirk E. Lancaster and Edward W. Stredulinsky, Free The list below contains all the information about boundary problems and partial differential equa­ Special Sessions at meetings of the Society available tions

294 NOTICES OF THE AMERIC'~N MATHEMATICAL SOCIETY Invited Speakers and Special Sessions

Howard A. Masur and John Smillie, Dynamics and According to the "Rules for Special Sessions" of the moduli space Society, Special Sessions are selected by the Program Kevin S. McCurley, Computational number theory and Committee from a list of proposed Special Sessions in applications essentially the same manner as Invited Speakers are selected. The number of Special Sessions at a Summer October 1989 Meeting in Hoboken or Annual Meeting is limited. The algorithm that Eastern Section determines the number of Special Sessions allowed at Associate Secretary: W. Wistar Comfort a given meeting, while simple, is not repeated here, Deadline for organizers: Expired but may be found in "Rules for Special Sessions" Deadline for consideration: July 26, 1989 which can be found on page 614 in the April 1988 Prabir Bhattacharya and Robert A. Melter, Geometry issue of Notices. related to computer vision Each Invited Speaker is invited to generate a Stephen Bloom, Algebraic semantics Special Session, either by personally organizing one Mark Feighn, Lee Mosher and Ulrich Oertel, Low- or by having a Special Session organized by others. dimensional topology Proposals to organize a Special Session are sometimes Bruce P. Kitchens and Sheldon Newhouse, TBA requested either by the Program Committee or by Richard Lyons and Richard O'Nan, Finite groups the Associate Secretary. Other proposals to organize Charles Sims, Computational algebra a Special Session may be submitted to the Associate Marvin D. Tretkoff, Algebraic geometry, p-adic aspects Secretary in charge of that meeting (who is an ex­ officio member of the committee and whose address October 1989 Meeting in Muncie be in the Central Section may be found below). These proposals must Associate Secretary: Andy Roy Magid hands of the Program Committee well in advance of Deadline for organizers: Expired the meeting and, in any case, at least nine (9) months Deadline for consideration: July 26, 1989 prior to the meeting at which the Special Session is Alan Adolphoson and Steven Sperber, Number theory to be held in order that the committee may consider and algebraic geometry all the proposals for Special Sessions simultaneously. David Bennett and Laszlo Lempert, Complex analysis Proposals that are sent to the Providence office of the Ananda Gubbi, Extremally disconnected spaces and Society, to Notices, or directed to anyone other than their applications the Associate Secretary will have to be forwarded and David Larson, Triangular operator algebras may not be received in time to be considered for Kathryn Porter, Functions spaces and topology acceptance. T. K. Puttaswamy, Differential equations It should be noticed that Special Sessions must be announced in Notices in such a timely fashion November 1989 Meeting in Los Angeles that any member of the Society who so wishes may Far Western Section submit an abstract for consideration for presentation Associate Secretary: Lance W. Small in the Special Session before the deadline for such Deadline for organizers: Expired consideration. This deadline is usually three ( 3) weeks Deadline for consideration: July 26, 1989 before the Deadline for Abstracts for the meeting in question. January 1990 Meeting in Louisville Special Sessions are very effective at Sectional Associate Secretary: Joseph A. Cima Meetings and can usually be accommodated. They Deadline for organizers: March 22, 1989 Deadline for consideration: September 28, 1989 are selected by the Committee to Select Hour Speak­ ers for the Section. The processing of proposals for Special Sessions for Sectional Meetings is handled Information for Organizers by the Associate Secretary for the Section, who then Special Sessions at Annual and Summer Meetings are forwards the proposals to the Committee to Select held under the supervision of the Program Committee which makes the final selection of the proposals. Each for National Meetings. They are administered by Invited Speaker at a Sectional Meeting is invited to the Associate Secretary in charge of that meeting organize a Special Session. Just as for national meet­ with staff assistance from the Meetings and Editorial ings, no Special Session at a Sectional Meeting may Departments in the Society office in Providence. be approved so late that its announcement appears past the deadline after which members can no longer

MARCH 1989, VOLUME 36, NUMBER 3 295 Invited Speakers and Special Sessions

send abstracts for consideration for presentation in Information for Speakers that Special Session. A great many of the papers presented in Special Ses­ The Society reserves the right of first refusal for sions at meetings of the Society are invited papers, but the publication of proceedings of any Special Ses­ any member of the Society who wishes to do so may sion. These proceedings appear in the book series submit an abstract for consideration for presentation Contemporary Mathematics. in a Special Session, provided it is received in Prov­ More precise details concerning proposals for and idence prior to the special early deadline announced organizing of Special Sessions may be found in the above and in the announcements of the meeting at "Rules for Special Sessions" or may be obtained from which the Special Session has been scheduled. Con­ any Associate Secretary. tributors should know that there is a limitation in size of a single special session, so that it is sometimes Send Proposals for Special Sessions to the true that all places are filled by invitation. Papers Associate Secretaries The programs of sectional meetings are arranged by the Associate not accepted for a Special Session are considered as Secretary for the section in question: ten-minute contributed papers. Far Western Section (Pacific and Mountain) Abstracts of papers submitted for consideration for Lance W. Small, Associate Secretary presentation at a Special Session must be received by Department of Mathematics the Providence office (Editorial Department, American University of California, San Diego Mathematical Society, P. 0. Box 6248, Providence, La Jolla, CA 92093 RI 02940) by the special deadline for Special Sessions, (Telephone 619- 534- 3590) which is usually three weeks earlier than the deadline Central Section for contributed papers for the same meeting. The Andy Roy Magid, Associate Secretary has decreed that no paper, whether invited or Department of Mathematics Council University of Oklahoma contributed, may be listed in the program of a meeting 601 Elm PHSC 423 of the Society unless an abstract of the paper has been Norman, OK 73019 received in Providence prior to the deadline. (Telephone 405-325- 2052) Eastern Section W. Wistar Comfort, Associate Secretary Department of Mathematics Number of Papers Presented Wesleyan University Joint Authorship Middletown, CT 06457 an individual may present only one ten­ (Telephone 203- 34 7-9411) Although minute contributed paper at a meeting, any combina­ Southeastern Section of joint authorship may be accepted, provided Joseph A. Cima, Associate Secretary tion Department of Mathematics no individual speaks more than once. An author can University of North Carolina, Chapel Hill speak by invitation in more than one Special Session Chapel Hill, NC 27599-3902 at the same meeting. (Telephone 919-962- 1050) An individual may contribute only one abstract by As a general rule, members who anticipate organizing Special title in any one issue of Abstracts, but joint authors Sessions at AMS meetings are advised to seek approval at least are treated as a separate category. Thus, in addition nine months prior to the scheduled date of the meeting. No Special Sessions can be approved too late to provide adequate advance to abstracts from two individual authors, one joint notice to members who wish to participate. abstract by them may also be accepted for an issue.

296 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Symposium on Complex Geometry and Lie Theory Sundance, Utah May 26-May 29, 1989

With the support from the National Science Founda­ Registration tion, Duke University, and the University of Utah, The symposium registration desk will be located in a symposium on Complex Geometry and Lie Theory the Cottage Reception Center. The desk will be staffed will take place Friday through Monday, May 26-29, from 2:00 p.m. until 7:00 p.m. on Thursday, from 1989 at the Sundance Center, Sundance, Utah. 7:00 a.m. until 4:30 p.m. Friday through Sunday, The topic was selected by the AMS Committee and from 7:00 a.m until 11:00 a.m. on Monday. on Summer Institutes and Special Symposia whose Participants opting for the meal plan should check in members at the time of selection were: Eric M. at the symposium desk in order to obtain a meal card. Friedlander, Steven L. Kleiman, Paul H. Rabinowitz, There is a restaurant to serve participants not on the Thomas C. Spencer, Robert B. Warfield, Jr., and John meal plan. Wermer. Proceedings will be published by the American Mathematical Society. Registration Fees The Organizing Committee for the symposium includes JAMES A. CARLSON, University of Utah (co­ All participants including speakers and committee chair); C. HERBERT CLEMENS University of Utah (co­ members are required to pay a $25 social fee and chair); and DAVID MORRISON, Duke University. a $15 registration fee. The social fee will cover the This symposium will review the interaction of the cost of refreshments served at breaks and evening two fields of complex geometry and Lie theory, with refreshments. These fees cannot be prorated for those concentration on the interaction related to Hodge participants choosing not to attend the full period theory. Speakers will also present current work and of the symposium. Cash, travelers' checks, and per­ discuss possible future directions. sonal checks will be accepted; credit cards cannot be The list of invited speakers includes ENRICO AR­ accepted. BARELLO, University of Rome, Italy; ROBERT BRYANT, Duke University; JAMES CARLSON, University of Utah; Accommodations EDUARDO CATTANI, University of Massachusetts, Amherst; C. HERBERT CLEMENS, University of Utah; The accomodations are a collection of privately owned MAURIZIO CORNALBA, University di Pavia, Italy; homes scattered among the aspen and pine. They range ROBERT FRIEDMAN, Columbia University; PHILLIP from the rustic charm of log homes to contemporary GRIFFITHS, Duke University; MARK GREEN, Uni­ architecture. Individual needs can be met with single versity of California, Los Angeles; RICHARD HAIN, accomodations to large Inns holding up to twelve peo­ University of Washington; JosEPH HARRis, Harvard ple. All units are equipped with kitchen and bathroom University; AROLDO KAPLAN, University of Mas­ units. Many units also have fireplaces and jacuzzi spas. sachusetts, Amherst; JANOS KoLLAR, University of Two types of accommodations are available. The Utah; ROBERT MACPHERSON, Massachusetts Institute first, referred to as cottages, are units consisting of of Technology; JoHN MoRGAN, Columbia University; two-bedroom and three-bedroom complexes, all with DAVID MoRRISON, Duke University; CHRIS PETERS, kitchenettes, living rooms, and private bathrooms. University of Leiden, The Netherlands; MoRIHIKO The bedding configuration varies greatly from one SAITO, RIMS Kyoto; WILFRIED ScHMID, Harvard twin bed to two queen-sized beds per room. University; CARLOS SIMPSON, Princeton University; The second type of accommodations are private ANDREW SOMMESE, Notre Dame University; JOSEPH homes, referred to as cabins, along the mountainside STEENBRINK, University of Nijmeigen, The Nether­ of Mt. Timpanagos. These cabins range in size from lands; STEPHEN ZUCKER, Johns Hopkins University. two-bedroom to seven-bedroom homes. All cabins

MARCH 1989, VOLUME 36, NUMBER 3 297 Meetings

have at least two full baths, several parlors, full Travel kitchens, and many have at least one jacuzzi spa. The bedding configuration in these cabins is more varied The Salt Lake City International Airport has service than the cottages, with one king or queen-sized bed to from all parts of the country, and the major carrier is four assorted sized beds per room. Delta Airlines. The distance to the Sundance Resort is Participants with special dietary needs are encour­ 50 miles and approximately a one-hour drive by car. aged to bring any special foods required and are Limousine service directly to the resort is provided free to make use of the kitchen facilities in any of by Key Limo Transportation at a cost of approxi­ the accommodations. Utensils are supplied in kitchen mately $40 round trip. A shuttle service will also be areas. available to participants for travel to and from the Participants desiring accomodations at the resort Salt Lake City area and the resort. A schedule for this cannot be guaranteed the preferred type of housing service will appear in the April issue of Notices. due to the unique configurations of the bedroom areas offered. Final housing assignments are responsiblity of Social Event the Organizing Committee. A housing form for participants to use to reserve A professionally organized two day river trip on the accommodations can be found at the back of this Colorado River is planned following the symposium. issue. Deadline for receipt of this form is April 7, 1989. The trip does not require river skills, and the total cost including all food, and transportation to and from Sundance and the Salt Lake City airport is $235. Check-In Locations and Times Individuals who do not have the necessary camping The residence check-in desk will be located at the gear such as sleeping bags and parkas will be charged Cottage Reception Center. The desk is open on a an additional $30 rental fee. 24-hour basis. Participants opting for the meal plan The bus taking participants to the embarkation should refer to the schedule listed in the Registration point on the Colorado River will leave Sundance at section of this announcement. 6:00 a.m. on Tuesday morning, May 30, arriving at the starting point by 2:00 p.m that afternoon. Return Room and Board Rates service is on Wednesday afternoon at approximately Due to the limited nature of dining facilities and the 2:00 p.m., at which time participants will be bussed isolated location of the Sundance Resort a complete back to Salt Lake City by early evening. At present meal plan is being offered to participants beginning there are only 35 openings and reservations can with dinner on Thursday evening, May 25 from 7:00- be made by contacting Herb Clemens, Mathematics 9:00 p.m, and ending with a continental breakfast on Department, University of Utah, Salt Lake City, Tuesday morning, May 30. The cost for the meal plan UT 84112. The telephone number is 801-581-5275. is $225.00. Reservations can also be made by contacting Barbara Single occupancy $60.00 Smoot at 801-581-7710. The deadline for making Double occupancy $30.00 reservations is April 7, 1989.

298 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 Summer Research Institute Several Complex Variables and Complex Geometry University of California, Santa Cruz, July 10-30

The thirty-seventh Summer Research Institute spon­ tial equations and algebraic geometry-especially the sored by the American Mathematical Society will be intersection of theory of complex varieties. devoted to Several complex variables and complex A second partial differential equation arising in sev­ geometry and will take place at the University of eral complex variables is the complex Monge-Ampere California, Santa Cruz. Members of the Organizing equation. This equation is a nonlinear generaliza­ Committee are: ERIC BEDFORD, Indiana University tion of the Laplacian. This equation is important in at Bloomington; JoHN D'ANGELO, University of Illi­ plurisubharmonic function theory, the construction of nois at Urbana-Champaign, ROBERT E. GREENE, Uni­ Kahler metrics, and in the potential theory of several versity of California, Los Angeles; and STEVEN G. complex variables. The existence and regularity theory KRANTZ, Washington University (chair). It is antici­ for this equation does not fit any standard mold and pated that the institute will be partially supported by has brought many surprises. a grant from the National Science Foundation. Pro­ Biholomorphic and proper maps have been in­ ceedings of the institute will be published in the AMS tensely studied in recent years. In 1974, C. Fefferman series Proceedings of Symposia in Pure Mathematics. proved that biholomorphic mappings of strongly pseu­ This topic was selected by the 1987 Committee on doconvex domains continue smoothly to the boundary. Summer Institutes and Special Symposia whose mem­ More recently, new methods have been found which bers were ERIC FRIEDLANDER, STEVEN L. KLEIMAN, apply to broader classes of domains and to proper PAUL H. RABINOWITZ, THOMAS c. SPENCER, ROBERT mappings and correspondences as well. At the same B. WARFIELD, JR., and JOHN WERMER (chair). time, proper mappings of domains in different di­ In 1975, a summer institute was held on several mensions are revealing surprising pathologies. These complex variables; prior to that an institute was held pathologies, and the methods used to construct them, in 1953 (to celebrate the solution of the Levi problem). are related to the inner functions of Aleksandrov and The institute for 1989 marks a substantial lapse of L0w. Inner functions have aided in the resolution of a time and at least as great an increment of growth in number of problems in constructive function theory. the subject. There follows a discussion of some of the Yet another method in holomorphic mapping the­ new developments which will be treated during this ory is complex analytic dynamics. Fifty years ago H. institute. Cartan used this method to study automorphisms of The partial differential equations that define holo­ domains in en. More recently, these methods have morphic functions are called the Cauchy-Riemann been used to obtain new constructions of Fatou­ equations (or the a equation). Theorems about these Bieberbach mappings (entire mappings with "small equations go hand in hand with the solution of range") and to prove new characterizations of auto­ function-theoretic problems, because one can perform morphisms. real variable constructions with smooth functions and The intersection theory of complex analytic va­ correct them with the a equation. In these con­ rieties has been used by D'Angelo to describe the structions, regularity at the boundary is of crucial geometry of real hypersurfaces in en. When the importance. However the a-Neumann problem is not hypersurface bounds a domain, then the boundary elliptic at the boundary and new techniques had to geometry influences the function theory on the inte­ be developed by Kohn to obtain so-called subelliptic rior. The invariant metrics of Bergman, Caratheodory, estimates on strongly pseudoconvex domains; local Kobayashi/Royden are a useful device for mediat­ boundary regularity follows. More recently, Catlin has ing between boundary geometry and interior function found necesesary and sufficient conditions for subel­ theory. The theories of Hardy spaces, Bloch func­ lipticity. The conditions are in terms of order of tions, the Lindeloff Principle, and so forth, are being contact of complex varieties with the boundary and increasingly treated with this metric language. In reveal surprising connections between partial differen- addition, the work of Lempert on extremal discs for

MARCH 1989, VOLUME 36, NUMBER 3 299 Summer Research Institute

the Kobayashi/Royden metric has tied invariant met­ PREISS ROTHSCHILD, University of California, San rics to the Monge-Ampere equation and to mapping Diego; ELIAS M. STEIN, Princeton University; FRAN­ problems. COIS TREVES, Rutgers University; SIDNEY WEBSTER, The function theory of complex manifolds is also University of Minnesota, Minneapolis. predominantly geometric. Even for topologically triv­ A tentative list of the topics to be addressed ial complex manifolds, many different function theo­ follows. Please note, however, that the program is ries can arise: the curvatures of complex geometries subject to change. specify the possibilities. If one specializes to Hermi­ Week One: Complex Function Theory tian symmetric spaces, Kahler manifolds, parabolic manifolds, inbedded CR manifolds, or other con­ Biholomorphic and proper maps, complex poten­ texts with structure, then a subject rich in texture tial theory, plurisubharmonic functions, approxima­ emerges. In the last decade powerful machines such as tion theory, complex analytic dynamics, convolution nonlinear partial differential equations, positive and equations, analytic multifunctions, inner functions. negative vector bundles, Hodge theories and vanishing Week Two: Complex Manifolds and Complex theorems have been exploited to further the subject. Geometry Complex analysis in several variables has grown considerably since 1975. A significant component Hermitian and Kahler geometry, curvature, holo­ of this growth has stemmed from the interaction morphic mappings, invariant metrics, deformations, with other parts of mathematics. The 1989 institute parabolic manifolds, finite type conditions, positive will make explicit many of these connections and and negative vector bundles, vanishing theorems, review several of the major achievements stemming Hodge theory. from them. One principal purpose of the institute Week Three: Analysis and Partial Differential is to foster and encourage further interaction among Equations complex analysts with diverse interests. Cauchy-Riemann equations, CR geometry of hy­ The list of principal speakers for week one includes persurfaces, CR functions, complex Monge-Ampere DAVID BARRETT, University of Michigan; STEVEN equation, integral kernels and asymptotics, pseudo­ BELL, Purdue University; Bo BERNDTSSON, Chalmers convexity, hyperfunctions. Institute of Technology, Sweden; FRANC FORSTNERIC, Accommodations will be available in the campus University of Ljubljiana; LASZLO LEMPERT, Purdue residence halls for participants; cafeteria style meals University; JEAN MARTINET, University de Stras­ will be available. All facilities will be accessible to the bourg, France; SERGEI PINCHUK, Ufa State University, handicapped. USSR; JEAN PIERRE RosAY, University of Wisconsin, Information on housing, dining, travel and the Madison; NESSIM SIBONY, University de Paris-Sud, local area will be sent to invited participants in the France; BERIT STENSONES, Rutgers University; A. G. spring. Each participant will pay a registration fee VITUSHKIN, Steklov Mathematical Institute, USSR. and a social fee to cover the costs of social events The list of principal speakers for week two in­ scheduled during the institute. cludes EDWARD BIERSTONE, University of Toronto, Those interested in receiving an invitation to par­ Canada; JAMES CARLSON, University of Utah; PIERRE ticipate in the institute should send the following DEMAILLY, Universite de Grenoble, France; AKITO information to Wayne S. Drady, Summer Institute FUTAKI, Chiba University, Japan; NGAIMING MOK, Conference Coordinator, American Mathematical So­ Columbia University; TAKEO 0HSAWA, Kyoto Uni­ ciety, Post Office Box 6248, Providence, RI 02940, versity, Japan; YuM ToNG Sm, Harvard University; prior to April 1, 1989, or through electronic mail GANG TIAN, Princeton University; SHING TUNG YAU, [email protected]. Harvard University. Please type or print the following: The list of principal speakers for week three 1. Full name; includes M. SALAH BAOUENDI, University of Cali­ 2. Mailing address; fornia, San Diego; DAVID CATLIN, Purdue Univer­ 3. Telephone number and area code for office and sity; MICHAEL CHRIST, University of California, Los home; Angeles; YAKOV ELIASHBERG, University of Califor­ 4. Which week or weeks you wish to attend; nia, Berkeley; JoHN FoRNAEss, Princeton University; 5. Your scientific background relevant to the institute GENNADI M. HENKIN, Mathematical Institute AN, topic; USSR; JosEPH T. KoHN, Princeton University; LINDA 6. Financial assistance requested;

300 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Summer Research Institute

7. Indicate if support is not required, and if interested will be considered after April 1, 1989, and applicants in attending even if support is not offered. selected will receive formal invitations and notification Requests for invitations will be forwarded to the of financial assistance beginning in mid-May. Organizing Committee for consideration. Requests

reviews in GLOBAL ANALYSIS Introduction by 1980-86 Anthony J. Tromba

The term "global analysis" refers to the These five volumes contain the more 1980 Mathematics Subject Classification: 58 general area of analysis on manifolds, in than 18,000 reviews that appeared ISBN 0-8218-0104-X, LC 88-10565 which the methods of modern algebra, in Mathematical Reviews from 1980 5 volumes, 4060 pages (softcover), August 1988 analysis, geometry, and topology are through 1986 and have a primary or List price $295, Institutional member $236, blended. Although the beginnings of a secondary classification in Global Individual member $177, Reviewer $148 these ideas can be traced to the 17th Analysis (classification number 58). To order, please specify REVGL0/86PNA century, major contributions in this Relevant cross-references are provided direction were made by Lie, Riemann, with each review. The fifth volume and Poincare toward the end of the of this set contains author and key Combination offer. Reviews in Partial last century, followed by the work indexes, making it very easy to locate Differential Equations, 1980-86, and of G. D. Birkhoff, E. Cartan, and items written by a specific author or Reviews in Global Analysis, 1980-86 Morse in the early part of this century. to get information about collections or (REVPDE/86 and REVGL0/86). However, it is only in recent years that conference proceedings dealing with List $472, Institutional member $378, the subject has attained its present global analysis. Individual member $283, Reviewer $236. central position in mathematics. The To order, Please specify subject has many rich applications to Contents: REVPGL/86PNA fields outside mathematics--such as Volume 1: Global analysis, analysis on mechanics, quantum physics, and general manifolds; General theory of differentiable relativity--as well as within mathematics manifolds; Infinite-dimensional manifolds; itself. Calculus on manifolds; nonlinear operators; Spaces and manifolds of mappings; Variational problems in infinite­ Today, this vital and active field is Volume 2: Prepayment required. Order from AMS. undergoing a virtual explosion of new dimensional spaces; Ordinary differential P.O. Box 1571. Annex Station. Providence. and important results. Reviews in equations on manifolds; dynamical systems; Rl 02901-1571. or call 800-556-7774 to use Global Analysis makes information about Volume 3: Ordinary differential equations VISA or MasterCard. the most recent contributions to this on manifolds; dynamical systems; Volume 4: rapidly growing field accessible both to Partial differential equations on manifolds; specialists working in global analysis, differential operators; Pseudogroups and and to those in other areas of pure and general structures on manifolds; Volume 5: applied mathematics. Series contents; Author index; Key index.

MARCH 1989, VOLUME 36, NUMBER 3 301 A New Way to View Mathematics

AMS-MAA Invited Addresses and ICM-86 Plenary Addresses now on videotape!======~ Today's eminent mathematicians ... The AMS is now offering a selection of important mathematics lectures on videotape: Joint AMS-MAA Invited Addresses, presented at the January Joint Mathematics meetings, and Plenary Addresses presented at the International Congress of Mathematicians in August, 1986. The lecturers in these two series are among the world's most distinguished mathematicians . ... bring the subject to life Because these lectures are intended to be expository and to appeal to a wide audience, the videotapes make excellent teaching tools. This medium communicates the excitement and enthusiasm for mathematics in a way that written material cannot. Students, teachers, and researchers will all appreciate these videotapes not only for their important mathematical content, but also for the historical perspective and personal touches the speakers bring to them.

Joint AMS-MAA Invited Addresses D Soft and hard symplectic geometry by Mikhael VHS Format, approx. one hour, Gromov, Code VIDGROMOV /NA Price $59 each D Efficient algorithms in number theory, by D The European Mathematicians' Migration to Hendrik W. Lenstra, Code VIDLENSTRAJNA America, by Lipman Bers, Code VIDBERS/NA D New developments in the theory of geometric D Zoll Surfaces, by Victor Guillemin, partial differential equations, by Richard M. Code VIDGUILLEMIN/NA Schoen, Code VIDSCHOEN/NA

D Matrices I Have Met, by Paul R. Halmos, D Classifying general classes, by Saharon Shelah, Code VIDHALMOS/NA Code VIDSHELAH/NA

D Episodes in the Origins of the Representation D Complexity aspects of numerical analysis, by Theory of Lie Algebras, by Thomas Hawkins, Stephen Smale, Code VIDSMALE/NA Code VIDHA WKINS/NA D Problems in harmonic analysis related to D How Computers Have Changed the Way I oscillatory integrals and curvature, by Teach, by John G. Kemeny, Elias M. Stein, Code VIDSTEIN /NA Code VIDKEMENY /NA D Representations of reductive Lie groups, by D The Flowering ofApplied Mathematics David A. Vogan, Jr., Code VIDVOGAN/NA in America, by Peter D. Lax, D String theory and geometry, by Edward Code VIDLAXJNA Witten, Code VIDWITTEN/NA D Oscar Zariski and His Work, by David D Also available from ICM-86: Addresses on Mumford, Code VIDMUMFORD/NA the Work of the 1986 Fields Medalists and ICM-86 Plenary Addresses Nevanlinna Prize Winner (These four talks VHS Format, approx. one hour, are on one tape.) Code VIDMEDAL/NA Price $49 each On the work of Simon K. Donaldson, Fields D Geometry offour-manifolds, by Simon K. Medalist, by Michael F. Atiyah; On some of Donaldson, Code VIDDONALDSON/NA the mathematical contributions of Gerd Fait- ings, Fields Medalist, by Barry Mazur; On the D Underlying concepts in the proof of the work of Michael Freedman, Fields Medalist, Bieberbach conjecture, by Louis de Branges, by John W. Milnor; On the work of Leslie G. Code VIDDEBRANGES/NA Valiant, Nevanlinna Prize Winner, by Volker Strassen D Recent progress in arithmetic algebraic geome- try, by Gerd Faltings, Code VIDFALTINGS/NA

PREPAYMENT REQUIRED. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Provi­ dence, RI 02901-1571 USA or call (800) 556-7774 in the continental U.S. to charge on VISA or MasterCard. All prices are subject to change without notice. Please add shipping & handling: I st video $2, each add'l $1, max. $25; by air, I st video $5, each add'l $3, max. $100. I 9 88-1 9 89. Academic Year Devoted to Mathematical Sciences Operator Algebras, Mittag-Leffler Insti­ tute, Djursholm, Sweden. (February 1988, Meetings p. 307) and Conferences October 1988-August 1989. Symposium on Singularity Theory and Its Applica­ tions, University of Warwick, Coven­ try, United Kingdom. (May /June 1988, p. 724) 1989. 40th Anniversary of Kansas Gamma of Pi Mu Epsilon, Wichita State Uni­ versity, Wichita, Kansas. (January 1989, p. 63) 1989. Concentration Year on Fluid Dy­ namical Aspects of Combustion Theory, THIS SECTION contains announcements of meetings and conferences of interest to lnstituto Per Le Applicazioni Del Cal­ some segment of the mathematical public, including ad hoc, local, or regional meetings, and meetings or symposia devoted colo, Rome, Italy. (January 1989, p. 63) to specialized topics, as well as announcements of regularly scheduled meetings of national or international mathematical organizations. 1989-1990. Academic Year Devoted to (Information on meetings of the Society, and on meetings sponsored by the Society, will Hyperbolic Geometry and Quasiconfor­ be found inside the front cover.) mal Mappings, Mittag-Leffler Institute, AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, Djursholm, Sweden. (December 1988, and specifies the place, date, subject (when applicable), and the speakers; a second p. 1584) full announcement will be published only if there are changes or necessary additional information. January !-December 23, 1989. Math­ Once an announcement has appeared, the event will be briefly noted in each issue until it has been held and a reference will be given in parentheses to the month, ematisches Forschungsinstitut Oberwol­ year, and page of the issue in which the complete information appeared. Asterisks (*) fach (Weekly Conferences), Federal Re­ mark those announcements containing new or revised information. public of Germany. (April 1988, p. 629 IN GENERAL, announcements of meetings and conferences held in North America carry and November 1988, p. 1381) only date, title of meeting, place of meeting, names of speakers (or sometimes a general statement on the program), deadlines for abstracts or contributed papers, and source of further information. Meetings held outside the North American area may carry more March 1989 detailed information. In any case, if there is any application deadline with respect to participation in the meeting, this fact should * 19-23. Workshop on Novikov's Conjec­ be noted. All communications on meetings and conferences in the mathematical sciences should be sent to the Editor tures, University of of Notices, Chicago, Chicago, care of the American Mathematical Society in Providence. Illinois. DEADLINES for entries in this section are listed on the inside front cover of each issue. In PROGRAM: Survey talks on Novikov's order to allow participants to arrange their travel plans, organizers of meetings are urged conjectures will be given on March to submit information for these listings early enough to allow them to appear in more than one issue of Notices prior to the meeting in question. To achieve 19, coinciding with one of the regu­ this, listings should be received in Providence SIX MONTHS prior to the scheduled date of the meeting. lar quarterly Midwest Topology Sem­ inars. Technical talks and working sessions will be held on the following days. 28-31. Annual Scientific Conference 31-April I. Spring Conference on the INVITED SPEAKERS: M. Bokstedt; D. of the Society of Applied Mathematics First Two Years: Teaching the Mathemat­ Burghelea; S. Cappell; G. Carlsson; and Mechanics (GAMM), University of ical Core, University of Hartford, West R. Cohen; T. Goodwillie; T. Farrell; Karlsruhe, Federal Republic of Germany. Hartford, Connecticut. (January 1989, S. Ferry; W.-C. Hsiang; B. Hughes; (September 1988, p. I 058) p. 64) J. Jones; L. Jones; I. Madsen; H. 30-31. Workshop on Applied Computing '89, Stillwater, Oklahoma. (October 1988, Moscovici; A. Nicas; F. Quinn; A. April1989 Ranicki; J. Rosenberg; J. Shaneson. p. 1242) INFORMATION: M. Rothenberg (312- 30-April I. Conference Honoring Richard 2-6. Fifth Conference on the Scien­ 702-71 00), S. Weinberger (312-702- S. Varga, Kent, Ohio. (October 1988, tific Use of Statistical Software (Soft­ 7345), or B. Williams (312-702-7349), p. 1242) Stat '89), Heidelberg, Federal Republic Department of Mathematics, the Uni­ 31-April I. Sixth Southeast Mathemati­ of Germany. (October 1988, p. 1242) versity of Chicago, Chicago, Illinois cal Ecology Conference, Wakulla Springs, 2-8. Spektraltheorie Singuliirer Gewohn­ 60637. Florida. (December 1988, p. 1586) licher Differentialoperatoren, Oberwolfach, 31-April I. Fifth South-Eastern Analysis Federal Republic of Germany. (February 27-30. Twentieth Annual Iranian Mathe­ 1989, p. 175) matical Conference, University of Tehran, Meeting (SEAM 5), University of Geor­ Tehran, Iran. (October 1988, p. 1242) gia, Athens, Georgia. (November 1988, p. 1383)

MARCH 1989, VOLUME 36, NUMBER 3 303 Meetings and Conferences

3-5. Third SIAM Conference on Opti­ 7-9. Fifth Annual Geometry Festival, INFORMATION: W. Drady, American mization, Boston, Massachusetts. (Octo­ State University of New York at Stony Mathematical Society, Post Office Box ber 1988, p. 1242) Brook, Stony Brook, New York. (January 6248, Providence, Rhode Island 02940. Conference on 1989, p. 65) 3-6. IEEE International 16-20. NCGA '89, Philadelphia Civic Is­ 8. Algebra Day, University of Ottawa, Control and Applications, Jerusalem, * Center, Philadelphia, Pennsylvania. (Sep­ Canada. rael. (April 1988, p. 638) Ontario, tember 1988, p. 1058) on 3-7. Seventh International Conference SPONSORs: Carleton University and 17-21. Minisymposium on Computa­ Prob­ Finite Element Methods in Flow the University of Ottawa. tional Issues for Nonlinear Hyperbolic in Hunts­ lems, University of Alabama INVITED SPEAKERs: V. Deodhar, Indi­ Waves, Institute for Mathematics and its ville, Huntsville, Alabama. (January 1989, ana University; M. P. Malliavin, Uni­ Applications, Minneapolis, Minnesota. p. 65) versite de Paris; M. Schacher, Univer­ (September 1988, p. 1058) 3-7. Forty-first British Mathematical sity of California, Los Angeles. 17-21. Minisymposium on Front Track­ Colloquium, University of Nottingham, INFORMATION: M. Racine, Depart­ ing in a Supercomputer Environment, In­ Nottingham. (December 1988, p. 1586) ment of Mathematics, University of stitute for Mathematics and its Applica­ 3-14. Workshop on Multidimensional Ottawa, Ottawa, Ontario, Canada KIN tions, Minneapolis, Minnesota. (October Hyperbolic Problems and Computations, 6N5. 1988, p. 1243) Institute for Mathematics and its Appli­ Sem­ 17-28. Topical Meeting on Hyperbolic cations, Minneapolis, Minnesota. (Sep­ * 8-9. Twelfth Annual Texas PDE Houston, Geometry and Ergodic Theory, Trieste, tember 1988, p. 1058) inar, University of Houston, Texas. Italy. (October 1988, p. 1243) Techno­ 5-7. The Worker in Transition: * 21-22. Joint MAA-KS Meeting, Hutchin­ of CALL FOR PAPERs: The deadline for logical Change, Washington, District son Community College, Hutchinson, contributed papers is March 20. Columbia. (January 1989, p. 65) Kansas. * 7-8. Sixty-seventh Annual Meeting of INFORMATION: G. Auchmuty or B. the Southeastern Section of the MAA, Fitzgibbon, Department of Mathe­ INFORMATION: K. Dundas, Program University of Tennessee, Knoxville, Ten­ matics, University of Houston, Hous­ Chair 1989 Conference, Hutchinson nessee. ton, Texas 77204-3476. Community College, 1300 North Plum, Hutchinson, Kansas 67501. PROGRAM: A short course entitled 8-9. Midwest Partial Differential Equa­ "Microcomputer Use in the Mathe­ tions Seminar, University of Illinois at 21-22. Conference Honoring the 60th matics Curriculum" will be conducted Chicago, Chicago, Illinois. (February Birthday of Sir Michael Atiyah, Oxford, by L. Husch of the University of Ten­ 1989, p. 175) England. (December 1988, p. 1586) nessee, Knoxville. 9-13. Fourth Copper Mountain Con­ 23-29. International Conference on Com­ INVITED SPEAKERS: H. S. Wilf, Uni­ ference on Multigrid Methods, Copper puting and Information, Session I, Mc­ versity of Pennsylvania, The White­ Mountain, Colorado. (October 1988, Master University, Hamilton, Ontario, Screen Problem; C. Linder, Auburn p. 1242) Canada. (February 19~9, p. 176) University, Graph Decompositions 10-12. Conceptual and Numerical Analy­ 25-27. International Conference on An­ and Quasigroup Identities; H. Reit­ sis of Data, Universitat Augsburg, Federal alytic Number Theory, University of Illi­ ner, the University of North Carolina Republic of Germany. (October 1988, nois Conference Center at Allerton Park. at Charlotte, In Search of Mathemat­ p. 1242) (October 1988, p. 1243) - Some Successes and a ical Meaning 10-13. IEEE Artificial Neural Networks 27-29. Third Annual Conference on Failure. Conference, Sheraton International Con­ Undergraduate Research, Trinity Univer­ INFORMATION: J. G. Ware, Secre­ ference Center, Reston, Virginia. (Note sity, San Antonio, Texas. (October 1988, tary /Treasurer, Department of Math­ date change, March 1988, p. 465) p. 1243) ematics, University of Tennessee at As­ Chattanooga, Chattanooga, Tennessee 11-13. EUROCRYPT '89: Workshop on 28-29. 1989 Spring Meeting of the 37403. the Theory and Applications of Crypto­ sociation for Symbolic Logic, Chicago, graphic Techniques (IACR), Houthalen, Illinois. (November 1988, p. 1384) * 7-8. Spring Meeting of the Missouri Sec­ Belgium. (October 1988, p. 1243) * 29-30. Southern California Analysis and tion of the MAA, University of Missouri­ 13-15. Operators and Function Theory: Partial Differential Equations Conference, Columbia, Columbia, Missouri. The Role of de Branges's Spaces, Univer­ University of California, San Diego, La INFORMATION: S. K. Katti, Depart­ sity of Arkansas, Fayetteville, Arkansas. Jolla, California. (September 1988, p. 1058) ment of Statistics, 314 Mathemati­ INVITED SPEAKERs: A. Chang, Uni­ cal Sciences Building, University of 15. Conference on the Future of Cal­ versity of California, Berkeley, and Missouri-Columbia, Columbia, Mis­ culus, Ithaca College, Ithaca, New York. University of California, Los Angeles; souri 65211. (January 1989, p. 65) M. Crandall, University of Califor­ 15-16. Eastern Section Meeting of the nia, Santa Barbara; L. Lempert, Pur­ Sixth Annual Auburn Miniconfer­ 7-8. AMS, College of the Holy Cross, Worces­ due University; L. Nirenberg, New Auburn Univer­ ence on Real Analysis, ter, Massachusetts. (May/ June 1988, York University, Courant Institute sity, Alabama. (December 1988, p. 1586) p. 731)

304 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

of Mathematical Sciences; L. Simon, CoNFERENCE TOPics: Infinite-Dimen­ Washington, District of Columbia. (Feb­ Stanford University. sional Diffusions; Measure-Valued and ruary 1989, p. 176) INFORMATION: S. Baouendi or L. Roth­ Distribution-Valued Processes; Sto­ 22-26. Meeting on Rational Mechanics schild, Department of Mathematics, chastic Partial Differential Equations. and Analysis in Honor of Clifford Trues­ University of California, San Diego, INVITED SPEAKERs: D. Dawson; E. dell on His 70th Birthday, Pisa, Italy. La Jolla, California 92037. B. Dynkin; I. Gyongy; T. Kurtz; E. (December 1988, p. 1587) Perkins; T. Shiga; J. Walsh. 22-June 3. NATO Advanced Study Insti­ INFORMATION: Mathematical Sciences May 1989 tute on Orthogonal Polynomials and Their Institute, 20 I Caldwell Hall, Cornell Applications, The Ohio State Univer­ * NSF-CBMS Conference on Discrete University, Ithaca, New York 14853, sity, Columbus, Ohio. (September 1988, Groups, Expanding Graphs, and Invari­ 607-255-7740, 8005 or 7763. p. 1059) ant Measures, University of Oklahoma, 15-1 7. 1989 New Zealand Mathemat­ * 23-26. Association for Computing Ma­ Norman, Oklahoma. ics Colloquium, Palmerston North, New chinery Sigmetrics and Performance '89 LECTURER: A. Lubotsky. Zealand. (May 1June 1988, p. 731) Conference, Berkeley, California. INFORMATION: A. Magid, Department I 5-19. Moments de Geometrie Symplec­ INFORMATION: L. Cabrera, IBM Al­ of Mathematics, University of Ok­ tique, Marseille, France. (February 1989, maden Research Center, Mail Code lahoma, Norman, Oklahoma 73019, p. 176) K521803, San Jose, California 95120- 405-325-2052. 15-19. Workshop on Microlocal Analysis 6099. and Nonlinear Waves, Institute for Math­ 1-31. Geometry of Loop Spaces, Max­ 23-26. Third International Conference on Pianck-lnstitut fur Mathematik, Bonn, ematics and its Applications, Minneapo­ lis, Minnesota. (February 1989, p. 176) Numerical Combustion, Antibes, France. Federal Republic of Germany. (January (December 1988, p. 1587) 1989, p. 65) 17-19. Joint IMAISMAI-GAMNI Con­ 23-27. International Conference on Com­ 4-5. Twentieth Annual Pittsburgh Con­ ference on Computational Methods in Aeronautical Fluid Dynamics, Sophia An­ puting and Information, Toronto, On­ ference on Modeling and Simulation, Pitts­ tario, Canada. (April 1988, p. 638) burgh, Pennsylvania. (September 1988, tipolis, France. (October 1988, p. 1243) 25-26. Eleventh Symposium on Mathe­ p. 1058) 17-19. SIAM Conference on Control and matical Programming with Data Pertur­ 4-7. Mathematicians and Education Re­ Systems Theory, San Francisco, Califor­ nia. (December 1988, p. 1586) bations, The George Washington Univer­ form Network, University of California, sity, Washington, District of Columbia. 19-20. Central Section Meeting of the Berkeley, Berkeley, California. (January (January 1989, p. 66) 1989, p. 66) AMS, Loyola University, Chicago, Illi­ nois. 25-27. Fourth Annual Lehigh University * 5. Mathematical Modeling in Biology, Geometry and Topology Conference, Beth­ State University of New York, Stony INFORMATION: W. Drady, American lehem, Pennsylvania. (November 1988, Brook, New York. Mathematical Society, Post Office Box p. 1384) INVITED SPEAKERS: C. Peskin, Courant 6248, Providence, Rhode Island 02940. 26-30. AMS Pure Mathematics Sym­ Institute of Mathematical Sciences; 22-24. International Conference on Al­ posium on Complex Geometry and Lie C. DeLisi, Mount Sinai School of gebraic Methodology and Software Tech­ Theory, Sundance, Utah. Medicine. nology, AMAST, Iowa City, Iowa. (De­ INFORMATION: W. Drady, American INFORMATION: E. Beltrami, Depart­ cember 1988, p. 1587) Mathematical Society, Post Office Box ment of Applied Mathematics and 22-24. Sparse Matrix Meeting, Salisham 6248, Providence, Rhode Island 02940. Statistics, State University of New Resort, Oregon. (October 1988, p. 1243) York at Stony Brook, Stony Brook, 28-June I. Sixteenth International Sym­ on Vortex Methods, New York 11794, 516-632-8367. 22-24. Workshop posium on Computer Architecture, Jeru­ Mathematical Sciences Research Insti­ salem, Israel. (September 1988, p. I 059) 8-1 0. Forty-Third Annual Quality Con­ tute, Berkeley, California. (September gress, Toronto, Canada. (March 1988, 1988, p. I 059) 29-June I. Third International Confer­ ence in Mathematics: Fractional Calculus p. 465) 22-24. SIAM Conference on Sparse and Its Applications, Nihon University, 8-12. Algorithmique Et Programma­ Matrices, Portland, Oregon. (November Tokyo, Japan. (May 1June 1988, p. 731) lion Pascal, Marseille, France. (February 1988, p. 1384) 29-June 2. NSF-CBMS Regional Con­ 1989, p. 176) Dublin Differential Equa­ 22-25. Second ference on Discrete Groups, Expanding 8-12. Workshop on Arithmetic Groups tions Meeting, Dublin, Republic of Ire­ Graphs, and Invariant Measures, Univer­ and Buildings, Mathematical Sciences land. (November 1988, p. 1384) sity of Oklahoma, Norman, Oklahoma. Research Institute, Berkeley, California. 22-26. Cohomolgie des Groupes Arith­ (February 1989, p. 177) (March 1988, p. 465) metiques, Marseille, France. (February 29-June 2. AVIGNON '89: Ninth In­ 14-16. Workshop on Markov Processes * 1989, p. 176) ternational Workshop on Expert Systems in Functional Spaces, Cornell University, 22-26. Capital City Conference on Com­ and their Applications, Avignon, France. Ithaca, New York. binatorics and Theoretical Computer Sci­ (February 1989, p. 177) ence, George Washington University,

MARCH 1989. VOLUME 36. NUMBER 3 305 Meetings and Conferences

29-June 2. Ondelettes, Marseille, France. INFORMATION: C. Kohanski, Ameri­ (February 1989, p. 177) can Mathematical Society, Post Office June 1989 Rhode Island * 29-June 3. Conference on Wavelets and Box 6248, Providence, Some of Their Applications, Marseille­ * IMACS International School on Lyapunov 02940. Functions, Irkutsk, Union of Soviet So­ Luminy, France. IEEE International Conference cialist Republics. 4-8. 1989 PuRPOsE: This conference aims to on Computer Vision and Pattern Recog­ give a status report on wavelets by de­ INFORMATION: V. M. Matrosov, Di­ nition, San Diego, California. (October scribing specific examples where some rector of the Irkutsk Computing Cen­ 1988, p. 1243) important problems were solved using ter, Siberian Branch, Union of Soviet 4-9. Geometrical and Algebraical Aspects wavelet techniques. Socialist Republics Academy of Sci­ in Several Complex Variables, Cetraro INVITED SPEAKERs: A. Arneodo, Cen­ ences, Lermontov Str. 134, 664033 (CS), Italy. (November 1988, p. 1385) Union of Soviet Socialist Re­ tre de Recherche Paul Pascal; M. Irkutsk, 4-30. 1989 Complex Systems Summer Farge, ENS Paris; M. Holschneider, publics. School, Santa Fe, New Mexico. (January M. Basseville, IRISA, CPT Marseille; * NSF-CBMS Conference on Function Es­ 1989, p. 67) ICPI, Lyon; R. Rennes; P. Flandrin, timation in the Context of Independent 5-7. An International Symposium on M. Duval-Destin; S. Coifman, Yale; and Dependent Observations, University Asymptotic and Computational Analysis, Institute of Mathe­ Mallat, Courant of California, Davis, California. Winnipeg, Manitoba, Canada. (Septem­ matical Sciences; R. Kronland­ ber 1988, p. l 059) Martinet, LMA, Marseille. LECTURER: M. Rosenblatt. 5-8. International Colloquium on Com­ CONFERENCE TOPICS: Wavelets, Dy­ INFORMATION: G. Roussas, Depart­ plex Analysis and Sixth Romanian-Finnish namical Systems and Richardson Cas­ ment of Statistics, University of Cali­ Seminar, University of Bucharest, Roma­ cades in Turbulence; Wavelets and fornia, Davis, California 95616, 916- nia. (December 1988, p. 1588) Non-stationary Signal Processing; 752-8142. Wavelets and Numerical Analysis; 5-8. Fourth Annual Symposium on Logic Meeting of the Wavelets and Image Processing; * 1-3. Annual Summer in Computer Science (LICS), Asilomar, Society, Univer­ Wavelets and Acoustics. Canadian Mathematical California. (October 1988, p. 1244) Ontario. INFORMATION: Y. Meyer, Ceremade, sity of Windsor, Windsor, 5-9. International Symposium on Bayesian Universite Paris Dauphine, 75775- PROGRAM: The meeting will include Decision Theory, Sherbrooke, Canada. Paris Cedex 16, France. Telephone: four special sessions, each featuring (January 1989, p. 67) (33)-l-47277503. a plenary speaker. There will be a 5-9. Chaos and the Microcomputer, Sal­ session for 15-minute contributed pa­ isbury State University, Salisbury, Mary­ on Computer and 29-June 3. Meeting pers. land. (January 1989, p. 67) Commutative Algebra (COCOA II), Di­ INVITED SPEAKERS: F. Atkinson, Dif­ in Mathematical Anal­ partimento di Matematica, Universita, 5-9. Conference ferential Equations; D. Passman, in Honor of the Memory of Jose Genova, Italy. (February 1989, p. 177) ysis Group Algebras; B. Kostant, Lie and Luis Rubio de Francia, El Escorial, Spain. Summer 29-June 9. Joint AMS-SIAM Nonassociative Algebras; D. Friedan, (February 1989, p. 178) Seminar on the Mathematics of Random Mathematical Physics. Number Theory, Centre Media, Virginia Polytechnic Institute and 5-10. Analytic CALL FOR PAPERS: Two copies of Universite State University, Blacksburg, Virginia. de recherches mathematiques, each abstract should be submitted to (Please note date change (Please note date change from MayfJune de Montreal. the organizing committee by March from September 1988, p. I 059) 1988, p. 731) 15. 0. William H. Roever Lectures in INFORMATION: F. Lemire, Chairman, * 5-l INFORMATION: B. Verducci, Ameri­ Geometry, and Algebraic Geometry Con­ Organizing Committee, Department can Mathematical Society, Post Office ference, Washington University, Saint of Mathematics and Statistics, Uni­ Box 6248, Providence, Rhode Island Louis, Missouri. 02940. versity of Windsor, Windsor, Ontario, Canada N9B 3P4. SPONSORs: Washington University and 30-June 2. 1989 Annual Meeting of the the National Science Foundation. Statistical Society of Canada, Ottawa, On­ 1-l 0. Third Annual Meeting of the In­ PuRPOSE: The conference will bring tario, Canada. (November 1988, p. 1385) ternational Workshop In Analysis and together specialists in various branches Its Applications, Dubrovnik-Kupari, Yu­ 31-June 2. Workshop on Blow-up and of algebraic geometry to discuss recent goslavia. (October 1988, p. 1243) Extinction for Parabolic and Other Sys­ developments, results, and problems tems, Heriot-Watt University, Edinburgh. 2-5. Seminar on Fractional Calculus, Ni­ in their fields. (January 1989, p. 66) hon University, Koriyama, Japan. (Feb­ MAIN SPEAKER: W. Fulton, University ruary 1989, p. 177) 31-June 3. Seventh Biennial Confer­ of Chicago, will deliver five 90-minute ence of the Association of Christians in 3-August 5. Joint AMS-IMS-SIAM talks on Toric Varieties. the Mathematical Sciences, Messiah Col­ Summer Research Conferences in the OTHER INVITED SPEAKERs: H. Clemens, lege, Grantham, Pennsylvania. (Decem­ Mathematical Sciences, Humbolt State University of Utah; S. Bloch, Uni­ ber 1988, p. 1587) University, Arcata, California. versity of Chicago; R. Lazarsfeld,

306 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

University of California, Los Ange­ INFORMATION: R. Smythe, Depart­ geometry and rigidity of regular and les; L. Ein, University of Illinois at ment of Statistics, George Washing­ random packing of spheres, the nu­ Chicago; T.-t Moh, Purdue Univer­ ton University, Washington, District merical simulation of arrays of hard sity; D. Morrsion, Duke University; of Columbia 20052, 202-994-6356. or elastic spheres, and the modeling of Z. Ran, University of California at the mechanical behavior of idealized Riverside; D. Harbater, University of 12-16. Greco Calcul Forme!, Marseille, granular materials. Pennsylvania; M. P. Murthy, Univer­ France. (February 1989, p. 178) INVITED SPEAKERS: A. Bezdek; K. sity of Chicago; R. Donagi, University 12-16. Decision Making and the Micro­ Bezdek; C. S. Chang; R. Connelly; of Pennsylvania. computer, Salisbury State University, Sal­ H. Frost; Z. Gaspar; J. T. Jenkins; J. INFORMATION: D. Wright or D. Webb, isbury, Maryland. (January 1989, p. 67) Papadopoulos; E. Petrakis; T. Rosato; Department of Mathematics, Wash­ 12-16. Computers and Mathematics, M. Satake; T. Tarnai; W. Whiteley. ington University, Saint Louis, Mis­ Massachusetts Institute of Technology, INFORMATION: For further informa­ souri, 314-889-6781. Cambridge, Massachusetts. (July 1August tion on the scientific program, contact 1988, p. 894) J. Jenkins, Department of Theoreti­ 5-10. Theorie du Point Fixe et Applica­ 12-17. Conference on the Geometry of cal and Applied Mechanics, Cornell tions, Marseille, France. (February 1989, University, Ithaca, New York 14853, p. 178) Banach Spaces, Strobl on Wolfgangsee, Austria. (October 1988, p. 1244) 607-255-7185 or 5062. To attend the 5-16. Workshop on the Geometry of 12-July 8. Summer Conference on Com­ workshop, contact the Mathematical Hamiltonian Systems, Mathematical Sci­ Sciences Institute, 201 Caldwell Hall, ences Research Institute, Berkeley, Cali­ plex Analysis, Bordeaux, France. (Febru­ ary 1989, p. 178) Cornell University, Ithaca, New York fornia. (April 1988, p. 638) 14853, 607-255-7740, 8005 or 7763. 13-15. Third Chico State Western States 6-8. Fourth International Conference (Note: Limited funding is available Topology Conference, on Boundary Element Technology, Wind­ California State for partial support of predoctoral and University, sor, Ontario, Canada. (September 1988, Chico, Chico, California. (Feb­ young postdoctoral attendees.) p. 1059) ruary 1989, p. 178) 15-23. CIME Course on Methods of 7-9. Canadian Applied Mathematics So­ * 13-17. Mathematical Modeling, North- Nonconvex Analysis, Villa Monastero, ciety Tenth Annual Meeting, Winnipeg, ern Illinois University, DeKalb, Illinois. Varenna Lake (Lake of Como), Italy. Canada. (September 1988, p. I 059) SPONSOR: Illinois Section of the Math­ (January 1989, p. 67) 7-10. International Conference on Dif­ ematical Association of America. 18-24. Reelle Analysis, Oberwolfach, ferential Equations: Theory and Applica­ PuRPOSE: This conference is designed Federal Republic of Germany. (February tions in Stability and Control, University to give teachers insight and techniques 1989, p. 178) of Colorado at Colorado Springs and useful for a course in modeling. The Colorado College, Colorado Springs, PRINCIPAL SPEAKERS: F. R. Giordano, 18-24. Conference on Nonlinear Analy­ Colorado. (November 1988, p. 1385) United States Military Academy; M. sis, Academia Sinica, Taiwan, Re­ public of China. (February 1989, p. 179) 8-16. Singapore Probability Conference, D. Weir, Naval Postgraduate School. National University of Singapore, Re­ INFORMATION: R. F. Wheeler, De­ * 19-20. IFAC/IMACS Workshop on public of Singapore. (November 1988, partment of Mathematical Sciences, Computer-Aided Control Systems Design, p. 1385) Northern Illinois University, Dekalb, Alma-Ata, Union of Soviet Socialist Re­ Illinois 60115, 815-753-6738. publics. 11-14. SRCOS-ASA Summer Research Conference, Unicoi State Park, Georgia. 14-1 7. International Conference on Dy­ INFORMATION: V. I. Venets, Union (January 1989, p. 67) namical Systems, Control Theory, and Ap­ of Soviet Socialist Republics Nat. * 12-16. NSF-CBMS Conference on Har­ plications, Wright State University, Day­ Comm. on Automatic Control, 65 monic Analysis, Real Function Spaces ton, Ohio. (October 1988, p. 1244) Profsoyuznaya Street, 117806 Moscow and Related Areas, Auburn University­ 15-1 7. Northeast Conference on General GSP-7, Union of Soviet Socialist Re­ Auburn, Auburn University, Alabama. Topology and Applications, The College publics. LECTURER: G. Weiss. of Staten Island, City University of New 19-21. Bar-IIan Symposium on the Foun­ INFORMATION: G. DeSouza, Depart­ York, Staten Island, New York. (January dations of Artificial Intelligence, Bar-Ilan ment of Mathematics, Auburn Uni­ 1989, p. 67) University, Ramat Gan, Israel. (February versity-Auburn, Auburn University, 15-18. Third Boston Workshop for 1989, p. 179) Alabama 36849, 205-826-4290. Mathematics Faculty, Wellesley College, 19-22. Fourth Annual Conference on Wellesley, Massachusetts. (February 1989, Structure in Complexity Theory, Univer­ * 12-16. NSF-CBMS Conference on Pro­ p. 178) sity of Oregon, Eugene, Oregon. (Decem­ jection Pursuit and Related Computation­ * 15-1 9. Workshop on the Packing and ber 1988, p. 1588) ally Intensive Techniques for Analyzing Mechanics of Aggregates of Spheres, Cor­ 19-23. 1989 International Symposium on Mulitivariate Data, George Washington nell University, Ithaca, New York. University, Washington, District of Co­ the Mathematical Theory of Networks and lumbia. PURPOSE: This workshop will bring Systems (MTNS-89), Amsterdam, The together researchers working in the Netherlands. (October 1988, p. 1244) LECTURER: J. Friedman.

MARCH 1989, VOLUME 36, NUMBER 3 307 Meetings and Conferences

19-24. Harmonizable Fields and Re­ disciplines to discuss the state of the * 26-30. Short Course on the Mathematics lated Topics, Marseille, France. (February art in this area. of Computer Graphics, Carleton College, 1989, p. 179) CONFERENCE TOPICS: Possible top­ Northfield, Minnesota. include polynomial-time logics, * 19-Ju1y 14. US-USSR Algebraic Ge­ ics SPONSOR: North Central Section of of arithmetic and ometry Symposium, The University of bounded versions the Mathematical Association of theory of fea­ Chicago, Chicago, Illinois. lambda calculus, proof America. systems, feasible polymorphic sible PRINCIPAL LECTURER: J. Goldfeather. PuRPOSE: The main purpose of the and polynomial time ver­ languages, PROGRAM: There will be a short symposium is to assemble as strong a analysis. sions of algebra and course on computer graphics together group of algebraic geometers as pos­ M. Ajtai; L. Blum; INVITED SPEAKERs: with several invited lectures and con­ sible from each of the two countries Crossley; S. Cook; S. Buss; P. Clote; J. tributed papers. and to do all that is possible to allow Gurevich; K-I. Ko; J-Y, Girard, Y. INFORMATION: S. Galovich, Depart­ them to work together for a substan­ J. Remmel; D. Leivant; A. Nerode; ment of Mathematics and Computer tial amount of time. A. Scedrov; P. Scott; G. Takeuti; A. CONFERENCE TOPICS: Different broad Science, Carleton College, Northfield, Urquhart. Minnesota 55057. areas of algebraic geometry will be INFORMATION: For more information emphasized during different phases of on the scientific program, contact S. * 26-30. AAECC-7 International Confer- the symposium. The main emphasis Buss, Department of Mathematics, ence, P. Sabatier University, Toulouse. of the first week will be arithmetic University of California at San Diego, algebraic geometry. The second week La Jolla, California 92093, 619-534- CONFERENCE TOPICS: Error Correct­ is tentatively scheduled to emphasize 6455 or P. Scott, Department of ing Codes (theory and applications) applications to physics, K-theory, and Mathematics, University of Ottawa, and Computational Algebra and Ge­ representation theory. Ontario, Canada KIN 6N5, 613-564- ometry. INFORMATION: J. P. May, The Uni­ 5884. To attend the workshop, contact INFORMATION: A. Poli, Lab. AAECC/ versity of Chicago Mathematical Dis­ the Mathematical Sciences Research LSI, P. Sabatier University, 118 route ciplines Center, 5734 University Av­ Institute, 201 Caldwell Hall, Cornell de Narbonne, 31062 Toulouse cedex enue, Chicago, Illinois 60637. University, Ithaca, New York 14853, (F). 8005, or 7763. (Note: 20-22. 1989 National Educational Com­ 607-255-7740, 26-30. Centenaire Halpen, Marseille, funding is available for par­ puting Conference (NECC '89), Boston, Limited France. (February 1989, p. 179) tial support of predoctoral and young Massachusetts. (October 1988, p. 1244) 26-30. Workshop on Symbol Manipula­ postdoctoral attendees.) 21-23. Thirty-second Meeting of the So­ tion, Institute for Mathematics and its ciety for Natural Philosophy on Geomet­ 26-28. Qualitative Theory of Vector Applications, Minneapolis, Minnesota. rical and Toplogical Methods in Mechan­ Fields, Centre de Recherches Mathe­ (February 1989, p. 179) ics, Calgary, Canada. (December 1988, matiques (CRM) Universite de Montreal. 27-30. Second Conference of the Inter­ p. 1588) (January 1989, p. 68) national Federation of Classification So­ 25-28. Western Regional Meeting of the * 26-29. IFAC/IMACS/IFIP Symposium cieties (IFCS), Charlottesville, Virginia. Biometric Society (WNAR) and the In­ on Control of Distributed Parameter Sys­ (October 1988, p. 1244) stitute of Mathematical Statistics, Davis, tems, Perpignan, France. California. (January 1989, p. 68) INFORMATION: A. El Jai, Lab. d'Auto­ July 1989 * 25-30. NSF-CBMS Conference on Cir­ matique IMP du CNRS, Universite de * Logic at Botik '89: A Seminar on Log­ cuit Complexity, University of Chicago, Perpignan, 50 Avenue de Villeneuve, ical Foundations of Computer Science, Chicago, Illinois. F-66000 Perpignan, France. Pereslavl-Zalessky, Union of Soviet So­ LECTURER: M. Sipser. ICOSAHOM '89: International cialist Republics. INFORMATION: J. Simon, Department 26-29. on Spectral and High Order of Computer Science, University of Conference INFORMATION: Logic at Botik '89, Differential Equa­ Chicago, Chicago, Illinois 6063 7, 312- Methods for Partial Post Office Box 11, Program Sys­ Italy. (February 1989, p. 179) 702-3488. tions, Como, tems Institute of the Union of So­ * 26-30. NSF-CBMS Conference on Sci­ viet Socialist Republics Academy of 25-July 1. 18th Conference on Stochastic entific Computation, Butler University, Sciences, 152140 Pereslavl-Zalessky, Processes and Their Applications, Uni­ Indianapolis, Indiana. Union of Soviet Socialist Republics. versity of Wisconsin-Madison, Madison, R. S. Varga. Wisconsin. (January 1989, p. 68) LECTURER: 2-7. Fourth Gregynog Symposium on INFORMATION: A. Carpenter, Depart­ Differential Equations, Gregynog Confer­ * 26-28. Workshop on Feasible Mathe­ ment of Mathematics, Butler Uni­ matics, Cornell University, Ithaca, New ence Center, University of Wales, United versity, Indianapolis, Indiana 46208, Kingdom. (December 1988, p. 1588) York. 317-283-9436. 2-8. Twelfth International Conference on gather PuRPOSE: This workshop will General Relativity and Gravitation, Boul­ various together researchers from der, Colorado. (February 1989, p. 179)

308 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

2-16. Fifth Workshop on Nonlinear Evo­ 3-21. SMS-NATO ASI: Fractal Geome­ (M/C 249), Box 4348, Chicago, lution Equations and Dynamical Systems, try and Analysis, Universite de Montreal, Illinois 60680, 312-996-2439. Kolymbari near Chania, Crete. (Novem­ Montreal, Canada. (January 1989, p. 68) 10. Tutorial Short Courses, Trinity Col­ ber 1988, p. 1386) *5-7. Workshop on Hardware Specifica­ lege, Dublin, Ireland. (November 1988, International tion, Verification and Synthesis: Mathe­ * 3-7. IFAC/IMACS/IFORS p. 1386) Symposium on Advanced Information Pro­ matical Aspects, Cornell University, cessing in Automatic Control, CRAN, Ithaca, New York. 10-14. Fifteenth Australasian Confer­ Nancy, France. ence on Combinatorial Mathematics and PuRPOSE: This workshop will present Computing, University of Queensland, INFORMATION: CRAN-IFAC Congress current research into formal methods Brisbane, Australia. (November 1988, Secretary, Faculte des Sciences- B.P. for hardware design. The goal of re­ p. 1386) 239, 54506 Vandoeuvre Cedex, France. search into formal methods for hard­ 10-21. NATO Advanced Study Insti­ ware design is to develop methods for tute: Computation of Curves and Surfaces, 3-7. NSF-CBMS Regional Research improving the design process and the Conference in the Mathematical Sciences: Puerto de Ia Cruz, Canary Islands, Spain. quality of the resulting designs. (February 1989, p. 180) Harmonic Analysis and Real Function INVITED SPEAKERs: D. Basin; G. Birst­ 10-21. Microprogram on Noncommu­ Spaces, Auburn University, Auburn Uni­ wistle; R. Bryant; R. Campesano; S-K. tative Rings, Mathematical Sciences Re­ versity, Alabama. (February 1989, p. 179) Chin, E. Clarke; W. Hunt; S. Johnson; search Institute, Berkeley, California. 3-7. Annual General Meeting of the Aus­ J. Joyce; C. Lengauer; P. Lowenstein; (May fJune 1988, p. 731) tralian Mathematical Society, Macquarie A. Martin; G. Milne; M. Sheeran; M. University, Sydney, New South Wales, K. Srivas; P. A. Subramanyam; D. 10-30. AMS Summer Research Insti­ Australia. (December 1988, p. 1589) Weise. tute on Several Complex Variables and 3-7. The Third Hungarian Colloquium INFORMATION: For more information Complex Geometry, University of Cali­ on Limit Theorems in Probability and on the scientific program, contact G. fornia, Santa Cruz, California. Statistics, Sopron, Hungary. (November Brown, 406 Phillips Hall, Cornell INFORMATION: W. Drady, American 1988, p. 1386) University, Ithaca, New York 14853, Mathematical Society, Post Office Box 3-7. Computational Ordinary Differen­ 607-255-8804. To attend the work­ 6248, Providence, Rhode Island 02940. tial Equations, London, England. (April shop, contact the Mathematical Sci­ 1988, p. 638) ences Institute, 201 Caldwell Hall, 10-September 1. IMA Summer Program Ithaca, New York in Robustness, Diagnostics, Computing 3-7. Fourteenth IFIP Conference on Cornell University, 8005, or 7763. and Graphics in Statistics, Institute for System Modelling and Optimization, 14853, 607-255-7740, is available Mathematics and its Applications, Min­ Leipzig, German Democratic Republic. (Note: Limited funding neapolis, Minnnesota. (December 1988, (November 1988, p. 1386) for partial support of predoctoral and young postdoctoral attendees.) p. 1589) 3-7. International Category Theory Meet­ 11-14. The Sixth International Con­ ing 1989, Bangor, Wales, United King­ 5-19. Microprogram on Noncommuta­ ference on Numerical Analysis of Semi­ dom. (November 1988, p. 1386) tive Rings, Berkeley, California. (Febru­ conductor Devices and Integrated Cir­ 3-7. Fourth International Conference on ary 1989, p. 180) cuits, Trinity College, Dublin, Ireland. the Teaching of Mathematical Model­ * 6-9. Third Mathematicians and Educa­ (November 1988, p. 1387) ing and Applications, Roskilde Univer­ tion Reform Network Workshop, Univer­ 12-14. Robotics: Applied Mathematics sity Centre, Denmark. (November 1988, sity of Minnesota, Minneapolis. and Computational Aspects, Loughbor­ p. 1386) ORGANIZERS: The MER Network, sup­ ough, England. (February 1989, p. 180) 3-7. Twelfth British Combinatorial Con­ ported by a grant from the National 16-29. 1989 NATO Advanced Study ference, Norwich, England. (November Science Foundation, is directed by Institute: Fourier Analysis and its Appli­ 1988, p. 1386) P. Wagreich, University of Illinois at cations, Tuscany, Italy. (February 1989, 3-7. International Symposium on Ap­ Chicago, and H. B. Keynes, Univer­ p. 180) proximation, Optimization, and Comput­ sity of Minnesota. * 17-21. NSF-CBMS Conference on Alge­ ing, Dalian University of Technology, PuRPOSE: The aim of the network braic Ideas in Ergodic Theory, University Dalian, China. (November 1988, p. 1386) is to strengthen ties among mathe­ of Washington, Seattle, Washington. 3-11. CIME Course on Microlocal Anal­ maticians involved in precollege ed­ ysis and Applications, Villa "La Querc­ ucational activities and to encourage LECTURER: K. Schmidt. eta," Montecatini Terme (Pistoia), Italy. more mathematicians to become ac­ INFORMATION: D. Lind, Department (January 1989, p. 68) tive in educational projects at the of Mathematics, University of Wash­ * 3-13. Surfaces Minimales, Marseille, precollege level. ington, Seattle, Washington 98195, France. INFORMATION: N. Fisher, Associate 206-543-1723. University Director, MER Network, 17-21. SIAM Annual Meeting, San CHAIRMAN: A. Rosenberg, Paris. Office of Mathe­ of Illinois at Chicago, Diego, California. (November 1988, INFORMATION: A. Zeller-Meier, CIRM, matics and Computer Education Luminy, Case 916, F-13288 Marseille p. 1387) Cedex 9.

MARCH 1989, VOLUME 36, NUMBER 3 309 Meetings and Conferences

* 17-22. Journees Arithmetiques, Mar- CALL FOR PAPERS: The deadline for l-5; Munich, 6-9, Federal Republic of seille, France. submission of one-page abstracts of Germany. (April 1988, p. 639) contributed papers is April l, 1989. CHAIRMAN: G. Lachaud, Marseille. * 2-5. Seventh International Congress on INFORMATION: R. T. Oehrle, Depart­ and Computer Modeling, INFORMATION: A. Zeller-Meier, CIRM, Mathematical ment of Linguistics, Douglass 200E, Marseille Chicago, Illinois. Luminy, Case 916, F-13288 University of Arizona, Tucson, Ari­ Cedex 9. zona 85721. CALL FOR PAPERS: Send two copies of abstracts (300 words for full-length 17-August 4. Conference on Matrix 24-27. Gauss Symposium on Mathemat­ papers, 100 words for short reports) Theory for Applications, University of ics and Theoretical Physics, Guaruja, SP, to the address given below. Wyoming, Laramie, Wyoming. (Decem­ Brazil. (November 1988, p. 1387) INFORMATION: Xavier J. R. Avula, ber 1988, p. 1589) * 24-29. NSF-CBMS Conference on Heat Department of Mechanical and Aero­ 19-22. Workshop on Mathematical The­ * Equations in Geometry, University of space Engineering, University of ory of Modern Financial Markets, Cornell Hawaii, Honolulu, Hawaii. Missouri-Rolla, Rolla, Missouri 6540 l, University, Ithaca, New York. 314-341-4661. LECTURER: R. S. Hamilton. PURPOSE: This workshop will focus INFORMATION: J. Weiner, Department 6-7. AMS Short Course on Cryptol­ on how mathematical research has of Mathematics, University of Hawaii, ogy and Computational Number Theory, contributed to the understanding of Honolulu, Hawaii 96822, 808-948- Boulder, Colorado. financial markets. The approach will 8595. be theoretical and, therefore, of inter­ INFORMATION: M. Foulkes, Ameri­ est primarily to researchers involved * 24-August 5. 1989 European Summer can Mathematical Society, Post Office in probability and financial theory. Meeting of the Association for Symbolic Box 6248, Providence, Rhode Island TOPics: Optimal consumption; port­ Logic, West Berlin. (Please note date 02940. folio management; mathematical mod­ change from November 1988, p. 1387) 6-l 0. 1989 Joint Statistical Meetings, els of financial markets, including ar­ 27-29. International Symposium on bitrage and martingale measures. Washington, District of Columbia. (March Cauchy and the French Mathematical 1988, p. 466) INVITED SPEAKERS: P. Artzner; K. World, Paris, France. (November 1988, * 6-12. Kommutative Algebra Und Alge­ Back; T. Cover; F. Delbaen; D. Duffie; p. 1387) P. Dybvig; H. Follmer; T. Ho; C.­ braische Geometrie, Oberwolfach, Fed­ * 28-September l. Homologie des Groupes F. Huang; R. Jarrow; I. Karatzas; eral Republic of Germany. et K-Theorie: Applications Geometriques, T. Kurtz; J. Lehoczky; A. Morton; Marseille, France. CHAIRMEN: E. Kunz, Regensburg; S. Pliska; P. Protter; S. Richard; S. H.-J. Nastold, Munster; L. Szpiro, Shreve; C. Stricker; W. Willinger. CHAIRMEN: M. Cathelineau, Nice; P. Paris. INFORMATION: For more information Cartier, Palaiseau; J. Dupont, Aarhus; INFORMATION: Mathematisches For­ on the scientific program, contact D. M. Sah, Stony Brook. schungsinstitut Oberwolfach Geschaft­ Heath, 318 Upson, Cornell Univer­ INFORMATION: A. Zeller-Meier, CIRM, sstelle: Alberstrasse 24 D-7800 sity, Ithaca, New York 14853, 607- Luminy, Case 916, F-13288 Marseille Freiburg im Breisgau. 255-9125. To attend the workshop, Cedex 9. contact the Mathematical Sciences In­ 7. AMS-SIAM-SMB Symposium on stitute, 20 l Caldwell Hall, Cornell 29-August 12. Conference on Groups­ Some Mathematical Questions in Biol­ University, Ithaca, New York 14853, Saint Andrews 1989, Saint Andrews, Scot­ ogy: Sex Allocation and Sex Change, 607-255-7740, 8005, or 7763. (Note: land. (December 1988, p. 1589) Experiments and Models, University of Limited funding is available for par­ 30-August 12. Harmonic Analysis on Re­ Toronto, Toronto, Ontario, Canada. tial support of predoctoral and young ductive Groups, Bowdoin College, Bruns­ (February 1989, p. 181) postdoctoral attendees.) wick, Maine. (January 1988, p. 160) * 7-ll. Thirteenth Johns Hopkins Math­ 31-August 4. Sixteenth Annual Confer­ ematical Sciences Summer Lecture Se­ on Logic and Lin­ * 23-24. Conference ence on Computer Graphics and Interac­ ries, Johns Hopkins University, Balti­ guistics, University of Arizona, Tucson, tive Techniques, Boston, Massachusetts. more, Maryland. Arizona. (December 1988, p. 1590) PRINCIPAL SPEAKER: A. F. Veinott, PuRPOSE: The conference, held in Re­ 31-August 4. Thirty-ninth Gordon Jr., Lattice Programming. with the LSA/MLA Lin­ conjunction search Conference on Statistics in Chem­ INFORMATION: J. Pang, Department guistic Institute, will focus on theo­ New istry and Chemical Engineering, of Mathematical Sciences, Maryland of linguistics and retical interactions Hampton, New Hampshire. (October Hall, Johns Hopkins University, Bal­ logic. l988,p.l245) timore, Maryland 21218, 301-338- PROGRAM CoMMITTEE: D. T. Langen­ 7216. doen; V. McGee; R. T. Oehrle; J. L. Pollock. August1989 7-ll. Fourth International Seminar on l-9. Eighteenth International Congress Random Graphs and Probabilistic Meth­ of the History of Science, Hamburg, ods in Combinatorics and Computer

310 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

Science, Poznan, Poland. (November 1988, * 16-September 2. Nineteenth Summer * 24-26. Twenty-fourth Actuarial Research p. 1387) Session on Probability Theory, Saint- Conference, Concordia University, 7-17. Annual CMS Seminar: Lie The- Flour (Cantal), France. Montreal, Canada. ory, Differential Equations and Repre­ INVITED SPEAKERs: D. L. Burkholder, SPONSOR: The Society of Actuaries. sentation Theory, Centre de Recherches University of Illinois at Urbana­ PROGRAM: The intent is to include Mathematiques (CRM) Universite de Champaign; E. Pardoux, Universite preliminary reports on the research Montreal. (January 1989, p. 69) de Provence (Aix-Marseille I); A. S. projects recently funded by the Soci­ l 0-12. International Conference on Com­ Sznitman, Courant Institute of Math­ ety of Actuaries. putational Techniques and Applications, ematical Sciences. CALL FOR PAPERS: The deadline for Brisbane, Australia. (February 1989, CONFERENCE TOPICS: Explorations in abstracts of contributed papers is July p. 181) martingale theory and its applica­ l, 1989. * 13-18. Fifth International Conference on tions; nonlinear filtering and the as­ INFORMATION: J. Garrido, Twenty­ Stochastic Programming, University of sociated stochastic partial differential fourth Actuarial Research Conference, Michigan, Ann Arbor, Michigan. equations; propagation of chaos. Department of Mathematics and Sta­ INFORMATION: P. L. Hennequin, tistics, Concordia University, 1455 De PROGRAM: This conference will fo­ Mathematiques Appliquees F63177 Maisonneuve Boulevard W, Montreal, cus on stochastic programming theory Aubiere Cedex. Telephone: 73.26.41.1 0, Quebec, H3G l M8, Canada. Tele­ and applications with particular em­ Poste 34-07. phone: 514-848-3222. phasis on computation. A tutorial ses­ sion will introduce new investigators 20-24. Ninth Annual Crypto Conference, * 24-September l. NSF-CBMS Confer­ and users to the field. University of California at Santa Bar­ ence on Singular Integral Operators, Uni­ CALL FOR PAPERS: Anyone wishing to bara, Santa Barbara, California. (Febru­ versity of Montana, Missoula, Montana. submit a paper should send a title ary 1989, p. 181) and abstract by March 31, 1989, to LECTURER: F. Michael Christ. 20-25. Second Conference of the Cana­ INFORMATION: W. Derrick, Depart­ the address below. dian Number Theory Association, Uni­ INFORMATION: J. R. Birge, Depart­ ment of Mathematics, University of versity of British Columbia, Vancouver, Montana, Missoula, Montana 59812, ment of Industrial and Operations Canada. (December 1988, p. 1590) Engineering, 1205 Beal, the Univer­ 406-243-5569. 20-26. Eleventh International Joint Con­ sity of Michigan, Ann Arbor, Michi­ ference on Artificial Intelligence, Detroit, * 28-31. IFAC/IFORS/IMACS Sympo­ gan 48109-2117, 313-764-9422. Michigan. (October 1988, p. 1245) sium on Large Scale Systems: Theory and * 13-19. Kombinatorische Und Reell Al­ 20-September 6. Nineteenth Ecole d'ete Application, Berlin, German Democratic gebraische Geometrie, Oberwolfach, Fed­ de Calcul des Probabilities, Saint-Flour, Republic. eral Republic of Germany. Cantal. (March 1988, p. 466) INFORMATION: H. Fuchs, Academy CHAIRMEN: E. Becker, Dortmund; A. 21-24. International Conference on Re­ of Sciences of the German Demo­ Dress, Bielefeld; J. Wills, Siegen. cent Developments in Statistical Data cratic Republic, Kurstrasse 33, D- INFORMATION: Mathematisches For­ Analysis and Inference In Honor of C. 1086 Berlin, German Democratic Re­ schungsinstitut Oberwolfach Geschiift­ R. Rao, Neuchatel, Switzerland. (Novem­ public. ber 1988, p. 1387) sstelle: Alberstrasse 24 D-7800 * 28-September 1. Homologie des Groupes on Al­ Freiburg im Breisgau. * 21-25. International Conference et K-Theorie: Applications Geometriques, I. Mal'tsev, gebra in Memory of A. Marseille, France. * 13-l 9. Combinatorical Convexity and Al­ Novosibirsk, Union of Soviet Socialist gebraic Geometry, Oberwolfach, Federal Republics. CHAIRMEN: M. Cathelineau, Nice; P. Republic of Germany. Cartier, Palaiseau; J. Dupont, Aarhus; Mathemat­ ORGANIZERS: Institute of M. Sah, Stony Brook. CHAIRMEN: G. Ewald, Bochum; P. of the ics of the Siberian Branch INFORMATION: A. Zeller-Meier, CIRM, McMullen, London; R. Stanley, Cam­ Academy of Sciences of the USSR bridge. Luminy, Case 916, F-13288 Marseille and Novosibirsk State University. Cedex 9. INFORMATION: Mathematisches For­ INFORMATION: Novosibirsk State Uni­ schungsinstitut Oberwolfach Geschiift­ versity, 90, VI. Pirogov, 2, 630090, 28-September 1. International Confer­ sstelle: Alberstrasse 24 D-7800 Novosibirsk, Union of Soviet Social­ ence on Symplectic Geometry and Compu­ Freiburg im Breisgau. ist Republics. Telephone: 65-62-44. tational Hamiltonian Dynamics, Beijing, China. (January 1989, p. 69) 13-19. Colloquium on Universal Alge­ 21-25. EQUADIFF 7, Prague, Czechoslo­ bra, Szeged, Hungary. (November 1988, vakia. (February 1989, p. 181) 28-September 1. IFIP 89: Eleventh p. 1387) World Computer Conference, San Fran­ 21-25. First Canadian Conference on cisco, California. (April 1988, p. 639) 13-19. Fourth Conference on Differen­ Computational Geometry, McGill Univer­ tial Equations and Applications, Rousse, sity, Montreal, Quebec, Canada. (Febru­ 28-September 2. Second International Bulgaria. (May /June 1988, p. 731) ary 1989, p. 181) Conference on Function Spaces, Poznan, Poland. (November 1988, p. 1387)

MARCH 1989, VOLUME 36, NUMBER 3 311 Meetings and Conferences

28-September 8. Topical Meeting on * 11-13. Supercomputers: Emerging Appli­ Poincare et E. Cartan: Epistemologie et Variational Problems in Analysis, Trieste, cations in Manufacturing, Minneapolis, Histoire, Paris, France. Italy. (October 1988, p. 1245) Minnesota. CHAIRMEN: A. Chenciner, Paris; C. 29-September 6. Forty-seventh Session INFORMATION: Program Review Com­ Houze!, Paris; J. Petitot, Paris; B. of the International Statistical Institute, mittee, Minnesota Supercomputer Cen­ Teissier, Paris. Paris, France. (April 1988, p. 639) ter, Inc., 1200 Washington Avenue INFORMATION: L. Boi, Centre d' Analyse South, Minneapolis, Minnesota 55415, et de Mathematiques Sociales, Ecole 612-626-1888. des Hautes Etudes en Sciences So­ September 1989 ciales, 54 Boulevard Raspail, F-75270 Antibes, 1-1 0. Summer School of Algebra and * 11-14. Analyse des Donnes, Paris, Cedex 06. Ordered Sets, The Jeseniky Mountains, France. 21-22. Mathematics in the Car Indus­ Czechoslovakia. (January 1989, p. 69) National de INFORMATION: Institut try, Warwick, England. (November 1988, Con­ et en Au­ * 4-8. Twelfth CNMAC Brazilian Recherche en Informatique p. 1388) gress on Computational and Applied Math­ tomatique, Domaine de Voluceau, Roc­ * 24-30. Kryptographie, Oberwolfach, Fed- ematics, Sao Jose Do Rio Preto, Sao quencourt, F-78153 Le Chesnay cedex. eral Republic of Germany. Paulo State, Brazil. Mar- * 11-15. Journees de Probabilites, CHAIRMEN: A. M. Odlyzko, Murray PROGRAM: The meeting will consist seille, France. Hill; C. P. Schnorr, Frankfurt; A. of minicourses, plenary lectures and Shamir, Rehovot. minisymposia (still to be scheduled) CHAIRMAN: J. Azema, Paris. CIRM, INFORMATION: Mathematisches For­ and contributed papers. All papers INFORMATION: A. Zeller-Meier, schungsinstitut Oberwolfach Geschaft­ must be mailed to the address given Luminy, Case 916, F-13288 Marseille sstelle: Alberstrasse 24 D-7 800 below by the end of May 1989. Cedex 9. im Breisgau. In­ Freiburg INFORMATION: Twelfth CNMAC, Il-l 5. Fifth International Conference Bento stituto De Matematica, 9500 on Numerical Methods in Engineering, * 24-0ctober 6. Extrapolation et Approxi- RS Goncalves, 91500 Porto Alegre Lausanne, Switzerland. (November 1988, mation Rationelle, Marseille, France. Brazil. p. 1388) CHAIRMAN: C. Brezinski, Lille. 4-8. Centenary Workshop of Heun's 11-16. Trends in Functional Analysis and INFORMATION: A. Zeller-Meier, CIRM, Equation: Theory and Applications, Approximation Theory, Acqua Fredda Luminy, Case 916, F-13288 Marseille Rottach-Egern, Federal Republic of Ger­ di Maratea (Potenza), Italy. (February Cedex 9. many. (November 1988, p. 1388) 1989, p. 182) * 25-27. SSA-IMACS 1989 Biennial Con­ 4-8. Colloquium on Computational Num­ 16-0ctober 20. Sixth World Congress ference on Modelling and Simulation, ber Theory, Debrecen, Hungary. (Novem­ on Medical Information, Beijing, China. Canberra, Australia. ber 1988, p. 1388) (April 1988, p. 639) *5-8. Third European Simulation Con- 17-22. The ICME Conference on the CONFERENCE TOPICS: Air quality mod­ gress, Edinburgh, Scotland. Popularization of Mathematics, Leeds, elling; bushfire modelling; ecosystem England. (January 1989, p. 70) modelling; modelling for forestry and INFORMATION: United Kingdom Sim­ 18-21. Traffic Theories for New Telecom­ agriculture; catchment modelling; ulation Council, cjo D. J. Murray­ munications Services, Adelaide, Australia. groundwater modelling. Smith, Department of Electronics and (November 1988, p. 1388) INFORMATION: SSA-89 Secretariat, A. Electrical Engineering, University of Centre for Resource and 18-21. SIAM Conference on Mathe­ J. Jakeman, Glasgow, Glasgow G 12 800, Scotland, Australian Na­ matics of Geophysical Sciences, Houston, Environmental Studies, United Kingdom. GPO Box 4, Can­ Texas. (November 1988, p. 1388) tional University, berra ACT 260 I, Australia. Telephone: 5-15. Opening Workshop: An Intro­ 18-22. Bifurcations et Orbites Peri- * (062) 49 4277. duction to Dynamical Systems, Institute odiques des Champs de Vecteurs du Plan, for Mathematics and its Applications, Marseille, France. * 25-28. SIAM Conference on Mathemati­ Minneapolis, Minnesota. (December in Geophys­ CHAIRMEN: R. Roussarie, Dijon; J.P. cal and Computational Issues 1988, p. 1590) Mechanics, Houston, Francoise, Paris. ical Fluid and Solid 6-8. Fourteenth Symposium on Opera­ INFORMATION: A. Zeller-Meier, CIRM, Texas. tions Research, Universitat Ulm, Federal Luminy, Case 916, F-13288 Marseille of Con­ Republic of Germany. (January 1989, CoNFERENCE THEMEs: Systems Cedex 9. Flow; Fluid p. 70) servation Laws; Reactive and Solid Mechanics of Geological 8-14. COSMEX '89: International Con­ 18-23. Conference on Integral Equations Materials; Partial Differental Equa­ ference on Stochastic Methods in Exper­ Inverse Problems, Varna, Bulgaria. and tions of Geosciences; Wave Propaga­ imental Sciences, Technical University (November 1988, p. 1388) tion and Materials Response. of Wroclaw, Poland. (November 1988, * 19-23. 1830-1930 Un Siecle de Geome­ CALL FOR PAPERS: A brief description p. 1388) trie, De C. F. Gauss et B. Riemann A. H. of each talk, not exceeding I 00 words,

312 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

must be submitted on a SIAM abstract will be presented by each of the four CHAIRMEN: D. Braess, Bochum; P. form, which can obtained from the speakers on each of the three days. Ciarlet, Paris; E. Stein, Hannover. address given below. A contributed INFORMATION: H. Simpson, G. Baker, INFORMATION: Mathematisches For­ presentation consists of a 17-minute R. Svirsky, Department of Mathe­ schungsinstitut Oberwolfach Geschaft­ talk, followed by three minutes of matics, the University of Tennessee, sstelle: Alberstrasse 24 D-7800 questions. The deadline for abstracts Knoxville, Tennessee 3 7996-1300, Freiburg im Breisgau. is April 12, 1989. 615-974-4261, 974-2461, or 974-4350. 2. Workshop on Homotopy INFORMATION: SIAM Conference Co­ * 30-November Mathematical Sciences Research ordinator, II 7 S. 17th Street, 14th 12-14. Second Interdisciplinary Confer­ Theory, Berkeley, California. Floor, Philadelphia, Pennsylvania ence on Natural Resource Modeling and Institute, Florida State University, Talla­ 19103, 215-564-2929. Analysis, PROGRAM: This is the first of three Florida. (January 1989, p. 70) hassee, workshops planned as part of MSRI's 25-29. Third International Conference 15-18. Fourth International Workshop on yearlong 1989-1990 program on Alge­ on the Theory of Groups and Related High-Level Synthesis, Kennebunkport, braic Topology and its Applications. Topics, Australian National University, Maine. (December 1988, p. 1590) ORGANIZER: G. Carlsson. Canberra. (May/ June 1988, p. 732) 16-20. Sixth World Congress on Medi­ INFORMATION: I. Kaplansky, Direc­ 26-28. Third International Workshop cal Informatics, Beijing, China. (February tor, Mathematical Sciences Research on Distributed Algorithms, La Colle-sur­ 1989, p. 182) Institute, I 000 Centennial Drive, Loup, France. (February 1989, p. 182) 16-20. Workshop: Patterns and Dynam­ Berkeley, California 94720. * 29-0ctober I. Sixth IFAC/IFIP/IFORS ics in Reactive Media, Institute for Math­ 30-December 1. College on Differential /IMACS Symposium on Information Con­ ematics and its Applications, Minneapo­ * Trieste, Italy. trol Problems in Manufacturing Technol­ lis, Minnesota. (February 1989, p. 182) Geometry, ogy, Madrid, Spain. 20-24. Hamiltonian Systems, Trans­ CHAIRMEN: J.P. Bourgignon; B. Law­ CONFERENCE PURPOSE: The aim of formation Groups and Special Trans­ son; M. Do Carmo; R. Tribuzy. the symposium is to present, discuss, form Methods, Centre de Recherches INFORMATION: International Center and summarize research on new theo­ Mathematiques (CRM) Universite de for Theoretical Physics, Post Office ries, as well as advanced applications, Montreal. (January 1989, p. 70) Box 586, Miramare, Strada Costiera of automatic systems used in Com­ 21-22. Eastern Section Meeting of the II, 1-34100 Trieste. puter Integrated Manufacturing. AMS, Stevens Institute of Technology, INFORMATION: E. A. Puente, Head Hoboken, New Jersey. (May/June 1988, November 1989 of Systems Engineering Department, p. 732) UPM, Jose Gutierrez Abascal 2, E- * 2-4. Second Annual Conference on Tech­ INFORMATION: W. Drady, American 28006 Madrid, Spain. nology in Collegiate Mathematics, The Mathematical Society, Post Office Box Ohio State University, Columbus, Ohio. 6248, Providence, Rhode Island 02940. October 1989 PROGRAM: The conference will fea­ * 23-26. Beijing International Conference ture lectures by nationally recognized *2-6. IMACS-GAMM International Sym­ on System Simulation and Scientific Com­ technology innovators, papers describ­ posium on Computer Arithmetic and Self­ puting, Beijing, China. ing current work in colleges across the Validating Numerical Methods, Univer­ INFORMATION: BICSC Conference Sec­ United States, workshops, and mini­ sity of Basel, Basel, Switzerland. (Please retary Group, Automatic Control De­ courses. note date change from November 1988, partment, Beijing Institute of Aero­ CALL FOR PAPERS: Individuals wish­ p. 1388) nautics and Astronautics, Beijing ing to present a paper at the confer­ INFORMATION: C. Ullrich, Institut fur 100083, China. ence should send a one-page abstract Informatik, Universitat Basel, Mit­ and two self-addressed, stamped en­ tlere Strasse 142, CH-4056 Basel, 26-28. The Riccati Equation In Control, velopes to the address below by June Switzerland. Systems and Signals, Villa Gallia, Como, 1, 1989. Papers accepted for presen­ Italy. (January 1989, p. 70) tation will be included in the Con­ * 4-6. Geometry and Mathematical Physics: 27-28. Central Section Meeting of the ference Proceedings. Papers are re­ John H. Barrett Memorial Lectures, The AMS, Ball State University, Muncie, In­ stricted to at most four pages m University of Tennessee, Knoxville, Ten­ diana. (MayjJune 1988, p. 732) length. nessee. INFORMATION: F. Demana and B. INFORMATION: W. Drady, American Waits, 1989 Technology Conference, INVITED SPEAKERs: M. F. Atiyah; I. Mathematical Society, Post Office Box the Ohio State University Department M. Singer; C. Taubes; K. Uhlenbeck. 6248, Providence, Rhode Island 02940. of Mathematics, 231 W. 18th Avenue, PROGRAM: The lectures are aimed to Columbus, Ohio 43210. cover both a survey of developments * 29-November 4. Computational Meth­ in mathematical physics and geometry ods in Solid Mechanics, Oberwolfach, 6-10. SIAM Conference on Applied in recent years as well as material of Federal Republic of Germany. Geometry, Tempe, Arizona. (November current research. A one-hour lecture 1988, p. 1388)

MARCH 1989, VOLUME 36. NUMBER 3 313 Meetings and Conferences

* 6-l 0. SIAM Conference on Geometric algorithm development, and other re­ CHAIRMEN: M. J. Ablowitz, Pots­ Design, Tempe, Arizona. lated subjects. dam; B. Fuchssteiner, Paderborn; M. INVITED SPEAKERs: W. D. Hillis, The Kruskal, Princeton. R. E. Barnhill, Arizona ORGANIZER: Thinking Machines Corporation; J. INFORMATION: Mathematisches For­ State University. Sethian, University of California, schungsinstitut Oberwolfach Geschaft­ PAPERS: The deadline for CALL FOR Berkeley; A. Egolf, United Technolo­ sstelle: Alberstrasse 24 D-7800 June l, 1989. abstracts is gies Research Center; K. A. Winkler, Freiburg im Breisgau. TOPics: Teleological mod­ CoNFERENCE Los Alamos National Laboratory; A graphics; parametric Annual Meeting of the eling; computer van Dam, Brown University; W. God­ 17-20. 96th surfaces in CAGD; im­ Louisville, Kentucky. (April 1987, curves and dard, California Institute of Technol­ AMS, domain processing ages of matrices; ogy; D. B. Gannon, Indiana Univer­ p. 553) and manipulation; surface fitting and sity, Bloomington; K. Kennedy, Rice INFORMATION: H. Daly, American other related subjects. University; D. Gelernter, Yale Uni­ Mathematical Society, Meetings De­ INVITED SPEAKERs: A. Barr, Califor­ versity. partment, Post Office Box 6248, Prov­ nia Institute of Technology; P. J. ORGANIZER: J. J. Dongarra, Argonnne idence, Rhode Island 02940. Brown University; R. Farouki, Davis, National Laboratory. Massachusetts In­ IBM; D. Gossard, ABSTRACT DEADLINE: June l, 1989. * 21-27. Modelltheorie, Oberwolfach, Fed- Technology; J. Gregory, stitute of INFORMATION: SIAM Conference Co­ eral Republic of Germany. C. Moler, Ardent Brunei University; ordinator, 11 7 S. 17th Street, 14th Corporation; J. Rice, Pur­ CHAIRMEN: L. van den Dries, Urbana; Computer Floor, Philadelphia, Pennsylvania University; L. Schumaker, Van­ A. Prestel, Konstantz; P. Roquette, due 19103-5052, 215-564-2929. derbilt University; T. Sederberg, Heidelberg. INFORMATION: Mathematisches For­ Brigham Young University; P. Wil­ * 17-23. Theory and Numerical Meth­ Oberwolfach Geschiift­ son, General Electric; M. Wozny, ods for Initial-Boundary Value Problems, schungsinstitut sstelle: Alberstrasse 24 D-7800 Rensselaer Polytechnic Institute. Oberwolfach, Federal Republic of Ger­ Freiburg im Breisgau. INFORMATION: SIAM Conference Co­ many. ordinator, 117 S. 17th Street, 14th H. Kreiss, Los Angeles; * 28-February 3. Regelungstheorie, Ober- Floor, Philadelphia, Pennsylvania CHAIRMEN: 0. Pasadena. wolfach, Federal Republic of Germany. 19103-5052, 215-564-2929. J. Lorenz, INFORMATION: Mathematisches For­ CHAIRMEN: H. W. Knobloch, Wiirzburg; 13-17. Workshop: Dynamical Issues in schungsinstitut Oberwolfach Geschaft­ M. Thoma, Hannover. Combustion Theory, Institute for Mathe­ sstelle: Alberstrasse 24 D-7800 INFORMATION: Mathematisches For­ matics and its Applications, Minneapolis, Freiburg im Breisgau. schungsinstitut Oberwolfach Geschaft­ Minnesota. (December 1988, p. 1591) sstelle: Alberstrasse 24 D-7800 of 18-19. Far Western Section Meeting January 1990 Freiburg im Breisgau. the AMS, University of California, Los Angeles. * l-6. Zeitreihenanalyse, Oberwolfach, Federal Republic of Germany. February 1990 INFORMATION: W. Drady, American Mathematical Society, Post Office Box CHAIRMEN: P. L. Davies, Essen; J. * 4-l 0. Funktiontheoretische Methoden Integral­ 6248, Providence, Rhode Island 02940. Franke, Berlin; G. Neuhaus, Ham­ Bei Partiellen Differential Und burg. gleichungen, Oberwolfach, Federal Re­ INFORMATION: Mathematisches For­ public of Germany. December 1989 schungsinstitut Oberwolfach Geschaft­ CHAIRMEN: H. Begehr, Berlin; E. Meis­ * 10-16. Asymptotic Methods for Computer­ sstelle: Alberstrasse 24 D-7800 ter, Darmstadt. Intensive Procedures in Statistics, Ober­ Freiburg im Breisgau. INFORMATION: Mathematisches For­ Federal Republic of Germany. schungsinstitut Oberwolfach Geschiift­ wolfach, * 7-13. Mathematische Optimierung, Ober- sstelle: Alberstrasse 24 D-7800 CHAIRMEN: R. Beran, Berkeley; D. W. wolfach, Federal Republic of Germany. Freiburg im Breisgau. Heidelberg. Muller, CHAIRMEN: B. Korte, Bonn; K. Ritter, Mathematisches For­ INFORMATION: Munchen. * 4-10. Nukleare Frechet-Riume, Ober- Oberwolfach Geschiift­ schungsinstitut INFORMATION: Mathematisches For­ wolfach, Federal Republic of Germany. Alberstrasse 24 D-7800 sstelle: schungsinstitut Oberwolfach Geschiift­ Freiburg im Breisgau. CHAIRMEN: E. Dubinsky, Potsdam; R. sstelle: Alberstrasse 24 D-7800 Meise, Dusseldorf; D. Vogt, Wupper­ * 11-13. Fourth SIAM Conference on Par­ Freiburg im Breisgau. tal. Processing for Scientific Computing, INFORMATION: Mathematisches For­ allel * 14-20. Nonlinear Evolution Equations, Illinois. schungsinstitut Oberwolfach Geschaft­ Chicago, Solitons and the Inverse Scattering Trans­ sstelle: Alberstrasse 24 D-7800 CONFERENCE TOPICS: Massively par­ form, Oberwolfach, Federal Republic of Freiburg im Breisgau. allel computing; visualization of sci­ Germany. entific computation; tools for parallel

314 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

* 11-17. Funktiontheorie, Oberwolfach, 16-1 7. Central Section Meeting of the INFORMATION: T. J. Snodgrass, De­ Federal Republic of Germany. AMS, Kansas State University, Manhat­ partment of Engineering Professional tan, Kansas. Development, 80 I Extension Build­ CHAIRMEN: F. Gehring, Ann Arbor; E. ing, University of Wisconsin, Madi­ Mues, Hannover; Ch. Pommerenke, INFORMATION: W. Drady, American son, Wisconsin 53706, 608-263-3371. Berlin. Mathematical Society, Post Office Box INFORMATION: Mathematisches For­ 6248, Providence, Rhode Island 02940. * 18-20. Joint WNAR-IMS Regional Meet­ schungsinstitut Oberwolfach Geschaft­ ing, Montana State University, Bozeman, 18-24. Masstheorie, Oberwolfach, Fed­ sstelle: Alberstrasse 24 D-7800 * Montana. Freiburg im Breisgau. eral Republic of Germany. INFORMATION: WNAR information CHAIRMAN: D. Kolzow, Erlangen. * 18-24. Mathematische Modelle in Der from G. Morris Southward, Depart­ INFORMATION: Mathematisches For­ Biologie, Oberwolfach, Federal Republic ment of Experimental Statistics, New schungsinstitut Oberwolfach Geschaft­ of Germany. Mexico State University, Las Cruces, sstelle: Alberstrasse 24 D-7800 New Mexico 88003, 505-646-2936. CHAIRMEN: W. Alt, Bonn; K. P. Freiburg im Breisgau. IMS information from L. Billard, Hadeler, Tiibingen; U. an der Hei­ Department of Statistics and Com­ den, Witten. 18-24. Third Centenary Celebration of puter Science, University of Geor­ INFORMATION: Mathematisches For­ the Mathematische Gesellschaft in Ham­ gia, Athens, Georgia 30602, 404-542- schungsinstitut Oberwolfach Geschaft­ burg, BundesstraBe, Hamburg. (January 5232. sstelle: Alberstrasse 24 D-7800 1989,p. 71) Freiburg im Breisgau. * 25-31. Kontinuumsmechanik der Festen Korper, Oberwolfach, Federal Republic July 1990 * 25-March 3. Eigenwertaufgaben In Natur of Germany. Und Ingenieurwissensachaften Und Ihre * 1-18. Twentieth Summer Session on Numerische Behandlung, Oberwolfach, CHAIRMEN: G. Herrmann, Stanford; Probability Theory, Saint-Flour (Cantal), Federal Republic of Germany. H. Lippmann, Miinchen. France. INFORMATION: Mathematisches For­ CHAIRMEN: J. Albrecht, Clausthal; L. schungsinstitut Oberwolfach Geschaft­ INVITED SPEAKERS: D. Donoho, Uni­ Collatz, Hamburg; P. Hagedorn, Darm­ sstelle: Alberstrasse 24 D-7800 versity of California, Berkeley; M. stadt; W. Velte, Wiirzburg. Freiburg im Breisgau. Friedlin, University of Maryland; J. INFORMATION: Mathematisches For­ F. Legal!, Universite de Paris VI. schungsinstitut Oberwolfach Geschaft­ CONFERENCE TOPICS: Open problems sstelle: Alberstrasse 24 D-7800 May 1990 related to statistical applications; large deviations and nonlinear differential Freiburg im Breisgau. 21-25. Eleventh United States National equations; fine analysis of Brownian Congress of Applied Mechanics, Tucson, motion. Arizona. (November 1988, p. 1389) March 1990 INFORMATION: P. L. Hennequin, 25-31. Tenth International Conference Mathematiques Appliquees, F63177 * 4-10. Interval Methods for Numerical on Pattern Recognition, Resorts Hotel, Computation, Oberwolfach, Federal Re­ Aubiere Cedex. Telephone: 73.26.41.1 0, Atlantic City, New Jersey. (March 1988, Poste 34-07. public of Germany. p. 466) CHAIRMEN: 0. E. Lanford, Zurich; A. 16-20. SIAM Annual Meeting, Chicago, Neumaier, Freiburg. Illinois. (November 1988, p. 1389) June 1990 INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschaft­ 6-12. 1990 Barcelona Conference on August 1990 sstelle: Alberstrasse 24 D-7800 Algebraic Topology, Centre de Recerca Freiburg im Breisgau. Matematica, Barcelona, Spain. (Septem­ 6-9. 1990 Joint Statistical Meetings, ber 1988, p. 1060) Anaheim, California. (March 1988, p. 466) 5-7. SIAM Conference on Applied Prob­ 11-14. World Organization of Systems 8-11. 93rd Summer Meeting of the AMS, ability in Science and Engineering, New * and Cybernetics Eighth International Con­ Ohio State University, Columbus, Ohio. Orleans, Louisiana. (November 1988, gress, New York, New York. p. 1389) INFORMATION: H. Daly, American * 11-1 7. Mathematische Stochastik, Ober- INFORMATION: C. V. Negoita, Con­ Mathematical Society, Post Office Box wolfach, Federal Republic of Germany. gress Chairman, Department of Com­ 6248, Providence, Rhode Island 02940. puter Science, Hunter College, City CHAIRMAN: H. Follmer, Bonn. University of New York, 695 Park 12-18. Pre-Congress Topology Confer­ INFORMATION: Mathematisches For­ Avenue, New York, New York 10021. ence, University of Hawaii, Honolulu, schungsinstitut Oberwolfach Geschaft­ Hawaii. (February 1989, p. 183) sstelle: Alberstrasse 24 D-7800 * 13-15. Seventh Annual Quality and Pro­ 21-29. The International Congress of Freiburg im Breisgau. ductivity Research Conference, Madison, Mathematicians 1990, Kyoto, Japan. Wisconsin. (November 1988, p. 1389)

MARCH 1989, VOLUME 36, NUMBER 3 315 Meetings and Conferences

* 28-30. IMACS European Simulation 19-22. 1991 Joint Statistical Meetings, Solving by Simula­ Atlanta, Georgia. (March 1988, p. 466) Meeting on Problem November 1990 tion, Esztergom, Hungary. 2-3. Central Section Meeting of the A. Javor, Central Re­ INFORMATION: AMS, University of North Texas, Den­ January 1992 search Institute for Physics of the ton, Texas. 8-11. 98th Annual Meeting of the AMS, Hungarian Academy of Sciences, H- Baltimore, Maryland. 1525 Budapest 114, Post Office Box INFORMATION: W. Drady, American 49, Hungary. Mathematical Society, Post Office Box INFORMATION: H. Daly, American 6248, Providence, Rhode Island 02940. Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940. September 1990 December 1990 Neuronet-90: IMACS International Sym­ * June 1992 posium on Neural Nets and Neural Com­ 3-7. 1990 Australasian Conference on puters, Prague, Czechoslovakia. Combinatorics, Palmerstown North, New * 29-July I. Joint Meeting with the Lon­ Zealand. (February 1989, p. 183) don Mathematical Society, Cambridge, INFORMATION: V. Hamata, General England. Computing Center, Czechoslovak Academy of Sciences, 182 07 Prague January 1991 INFORMATION: H. Daly, American 8, Post Office Box 5, Czechoslovakia. Mathematical Society, Post Office Box of the AMS, 16-19. 97th Annual Meeting 6248, Providence, Rhode Island 02940. * IMACS Symposium on Modelling and San Francisco, California. of Electrical Machines, EN­ Simulation INFORMATION: H. Daly, American Nancy, France. January 1993 SEM- Mathematical Society, Post Office Box INFORMATION: J. Robert, Institut Mon­ 6248, Providence, Rhode Island 02940. 13-16. 99th Annual Meeting of the AMS, teflore, B-28, Sart Tilman, B-4000 San Antonio, Texas. Liege, Belgium or R. LeDoeuff, EN­ July 1991 INFORMATION: W. Drady, American SEM 2, Rue de Ia Citadelle, BP850- Mathematical Society, Post Office Box 54100 Nancy, France. Conference 8-12. Second International 6248, Providence, Rhode Island 02940. on Industrial and Applied Mathemat­ Conference, * 3-6. Fourth Asian Logic ics, Washington, District of Columbia. Japan. Tokyo, (November 1988, p. 1389) January 1994 CALL FOR PAPERS: Submissions to Con­ * 22-26. Thirteenth IMACS World 5-8. tOOth Annual Meeting of the AMS, the conference are invited from ar­ and Applied Math­ gress on Computing Cincinnati, Ohio. eas relating to mathematical logic. ematics, Trinity College, Dublin Univer­ The deadline for submissions will be sity, Dublin, Ireland. INFORMATION: H. Daly, American March 1990. Mathematical Society, Post Office Box J. H. Miller, Univer­ INFORMATION: Send all correspon­ INFORMATION: 6248, Providence, Rhode Island 02940. School of Mathemat­ dence, including requests for further sity of Dublin, College, Dublin 2, Ire­ information, to K. Kakehi, Depart­ ics, 39 Trinity ment of Mathematics, Waseda Uni­ land. versity, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 160, Japan. August 1991 * 3-7. IMACS Symposium on Intelligent 8-11. 94th Summer Meeting of the AMS, Models in Systems Simulation, Brussels, University of Maine, Orono, Maine. Belgium. INFORMATION: H. Daly, American INFORMATION: S. Tzafestas, National Mathematical Society, Post Office Box Technical University of Athens, Di­ 6248, Providence, Rhode Island 02940. vision of Computer Science, Depart­ ment of Electrical Engineering, 157 73 Zographou, Athens, Greece.

316 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

R. Gobel and C. Sen gel hoff, Vector spaces with four ABELIAN GROUP THEORY distinguished subspaces and applications to modules U. Albrecht, Abelian groups A such that the category of Laszlo Fuchs, RUdiger Gobel, A-solvable groups is preabelian and Phillip Schultz, Editors 0. Mutzbauer, Type invariants of torsion-free abelian groups (Contemporary Mathematics, Volume 87) U. Albrecht and P. Hill, Separable vector groups C. Metelli, Bihomogeneous groups The traditional biennial international conference of abelian H. P. Goeters and J. D. Reid, On the p-rank of Hom(A, B) group theorists was held in August, 1987 at the University M. Dugas and J. Hausen, Torsion-free E-uniserial groups of of Western Australia in Perth. With some 40 participants infinite rank from five continents, the conference yielded a variety of M. Dugas and S. Shelah, E-transitive groups in L papers indicating the healthy state of the field and showing P. Hill and Ch. Megibben, The local equivalence theorem the significant advances made in many areas since the last R. S. Pierce, E-modules such conference in Oberwolfach in 1985. This volume brings L. Fuchs, Some applications of abelian group theory to together the papers presented at the Perth conference, modules together with a few others submitted by those unable to attend. L. Salce and P. Zanardo, Finitely generated modules over The first section of the book is concerned with the structure valuation domains of p-groups. It begins with a survey on H. Ulm's contributions T. H. Fay, Torsion divisible dimension to abelian group theory and related areas and also describes A. D. Sands, Some remarks on A-radicals the surprising interaction between set theory and the structure K. Eda, Cardinality restrictions on preradicals of abelian p-groups. Another group of papers focuses S. H. Mohamed and B. J. MUller, Continuous modules have on automorphism groups and the endomorphism rings of the exchange property abelian groups. The book also examines various aspects of 1980 Mathematics Subject Classifications: 20KXX, 06815, 13C05, torsion-free groups, including the theory of their structure 16A21, 16A65 and torsion-free groups with many automorphisms. After one ISBN 0-8218-5068-7, LC 89-163 paper on mixed groups, the volume closes with a group of ISSN 0271-4132 papers dealing with properties of modules which generalize 312 pages (softcover), Individual member $20, List price $33, corresponding properties of abelian groups. Institutional member $26 Contents To order, please specify CONM/87N R. Gobel, Helmut Ulm: His work and its impact on recent mathematics K. Benabdallah, D. Cutler, and A. Mader, Extensions of torsion-complete p-groups LARGE DERIVATIONS, FREE ENERGY K.-Y. Honda, Plain global bases of reduced abelian p-groups FUNCTIONAL AND QUASI-POTENTIAL FOR Patrick Keef, On set theory and the balanced-projective A MEAN FIELD MODEL OF INTERACTING dimension of Cn groups D. Cutler, A. Mader, and Ch. Megibben, Essentially DIFFUSIONS indecomposable abelian p-groups having a filtration of D. A. Dawson and J. Gartner prescribed type (Memoirs of the AMS, Number 398) W. Liebert, Isomorphic automorphism groups of primary abelian groups II Large exchangeable systems of reversible diffusions in W. May, Endomorphism rings of mixed abelian groups Rd with mean field interaction serve as useful models for P. Schultz, Endomorphism rings of finite valuated p-groups studying the dynamical aspects of the phenomena of phase D. Arnold and C. Vinsonhaler, Quasi-endomorphism rings for transitions, tunneling, and metastability in statistical physics. a class of butler groups The nonlinear McKean-VIasov equation describes the limiting D. M. Arnold, Representations of partially ordered sets and behavior of the empirical measure process in a fixed time abelian groups interval as the number of particles increases to infinity.

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MARCH 1989, VOLUME 36, NUMBER 3 317 New AMS Publications

The objective of this work is to study large deviations for operators. Recently, these methods have been combined with such systems in order to investigate such dynamical behavior geometric perturbation theory and the method of spectral as metastability in longer time scales. The main result deals deformation in order to study the spectral resonances of with the relationship between the quasipotential, which is certain Schri:idinger operators. These resonances describe related to the large deviation behavior of the nonequilibrium metastable states of a physical system: they behave as dynamics, and the free energy functional, which is related to localized bound states over short time periods, but are coupled the equilibrium distribution of the system. The quasipotential to the continuum and therefore eventually move off to infinity. of a measure with repect to a stable stationary state of the McKean-VIasov equation is obtained by minimizing the This work focuses on one example of resonances, that of action along all paths joining the stationary state to the shape resonances, which are formed by potentials that are measure. The authors show that this quasipotential coincides attractive inside a compact set and repulsive outside of it. with the domain of attraction of the stationary state with In this case, the coupling to the continuum is achieved by additive constant. Moreover, they establish that the time quantum mechanical tunneling through the potential barrier. In reversed trajectory of the McKean-VIasov dynamics attains the classical limit-which corresponds to the situation in which the minimum action. These results make precise the heuristic the height of the barrier becomes infinite-all tunneling is fact that the free energy functional serves as a potential suppressed, and the analogous quantum mechanical system, for the McKean-VIasov dynamics with respect to a weak described by a Hamiltonian H0 , has eigenvalues embedded in Riemannian structure on the space of probability measures its continuous spectrum. As soon as the coupling is restored by on Rd, viewed as an infinite-dimensional manifold. lowering the height of the barrier, these eigenvalues disappear.

Contents By comparing this approximate Hamiltonian H0 to the full The mean field model. Basic notation Hamiltonian H in the semiclassical regime of small Planck's Main results constant, the authors show that the embedded eigenvalues of into the lower half of the complex plane and become The equilibrium behavior Ho move Moreover, they prove that the imagi­ The dynamical behavior spectral resonances of H. of these resonances, which has the physical interpre­ Quasipotential and free energy functional nary part tation of the inverse of the lifetime of the state, is exponentially Large deviations for the invariant distributions small. The exponential factor has a geometric interpretation: it Quasipotential and free energy functional for non-interacting is the geodesic distance, in the Agmon metric associated with systems the potential, through which the particle must tunnel in order Transition operators, Doeblin's condition, and exponential to become free. This is the multidimensional generalization of result obtained by the WKB theory. F0-convergence to equilibrium the one-dimensional The quasipotential Contents Quasipotential and free energy functional for interacting systems The model and the approximate Hamiltonian Recurrence properties of the empirical process Preliminaries: The spectra of Ho(>-) and H(>.) Transition probability functions and Doeblin's condition The distorted Hamiltonians The quasipotential Harmonic approximation 1980 Mathematics Subject Classifications: 60K35, 60F1 0; 82A05 Existence of resonances ISBN 0-8218-2461-9, LC 89-164 ISSN 0065-9266 Exponential decay of eigenfunctions 100 pages ( softcover), March 1989 Width of the resonances Individual member $8, List price $13, Institutional member $10 Comments To order, please specify MEM0/398N 1980 Mathematics Subject Classifications: 81C12, 35J10; 81F99 ISBN 0-8218-2462-7, LC 89-182 ISSN 0065-9266 SEMICLASSICAL THEORY OF SHAPE 132 pages ( softcover), March 1989 RESONANCES IN QUANTUM MECHANICS Individual member $10, List price $16, Institutional member $13 P. D. Hislop and I. M. Sigal To order, please specify MEM0/399N (Memoirs of the AMS, Number 399) Semiclassical methods have helped greatly to expand understanding of the discrete spectrum of Schri:idinger

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318 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

SCATTERING OPERATOR, EISENSTEIN PROBABILISTIC PROBLEMS OF DISCRETE SERIES, INNER PRODUCT FORMULA AND MATHEMATICS "MAASS-SELBERG" RELATIONS FOR V. F. Kolchin, Editor KLEINIAN GROUPS (Proceedings of the Steklov Institute, Volume 177) Nikolaos Mandouvalos The papers in this collection are devoted to probabilistic (Memoirs of the AMS, Number 400) questions in discrete mathematics and focus mainly on three areas: random mappings of finite sets, problems connected with the polynomial distribution, and the theory of branching In this work, the author introduces and studies the Eisenstein processes. series and scattering operator for Kleinian groups. He Contents also formulates and proves the inner product formula and V. A. Vatutin and S. M. Sagitov, A decomposable critical the ''Maass-Selberg·· relations for Kleinian groups. Two branching process with two types of particles different points of view in the present theory are particularly 0. V. Viskov, A noncommutative approach to classical emphasized. The first considers the theory as part of problems of analysis the Selberg-Langlands program concerning the analytic A. M. Zubkov, Estimates for sums of finitely dependent continuation of Eisenstein series for nonarithmetic groups. indicators and for the instant of first occurrence of a rare event The second point of view is related to the spectral theory of V. A. Ivanov, Randomized decomposable statistics certain hyperbolic manifolds. This spectral theory becomes, G. 1. lvchenko, Yu. I. Medvedev, and A. F. Ronzhin, in light of Thurston's work, especially significant in the case Decomposable statistics and goodness-of-fit tests for of 3-dimensional manifolds. The techniques the author has polynomial samples developed also form the main ingredients for producing a 1. B. Kalugin, A class of random mappings trace formula and a zeta function for such groups. V. G. Mikhailov, On the asymptotic normality of U-statistics with nonnegative kernels Contents A. 1. Pavlov, On an equation in a symmetric semigroup Yu. L. Pavlov, On random mappings with constraints on the Scattering operator and Eisenstein series number of cycles Analytical and geometrical considerations V. E. Tarakanov, Linear transformations and (0, 1 )-matrices The scattering operator and Eisenstein integral A. N. Trunov, Limit theorems in the problem of distributing ·-oesingularizations·· of the scattering operator and identical particles in different cells construction of a smooth parametrix A. V. Chistyakov and N. V. Chistyakova, On asymptotically The inner product formula efficient estimators of system parameters from complex testing Integration over a horosphere designs The constant term theorem A. L. Yakymiv, Asymptotics of the survival probability of critical Formulation and proof of the inner product formula Bellman-Harris branching processes ··Maass-Selberg·· relations and functional equation 1980 Mathematics Subject Classifications: 05, 15, 20, 40, 41, 60, 62; 26, 43, 82 2 12, 13, Two modified L -versions of the Eisenstein integral ISBN 0-8218-3123-2, LC 88-36875 The first ··Maass-Selberg·· relation ISSN 0081-5438 The second ''Maass-Selberg·· relation and the functional 224 pages (softcover), March 1989 equation Individual member $59, List price $98, Institutional member $78 Epilogue To order, please specify STEKL0/177N Extension to discrete groups on H"+1

SPACE MAPPINGS WITH BOUNDED 1980 Mathematics Subject Classifications: 10020, 11 F72, 58G25, 35P25;30F40, 22E40,53C20 DISTORTION ISBN 0-8218-2463-5, LC 89-180 Yu. G. Reshetnyak ISSN 0065-9266 (Translations of Mathematical Monographs, Volume 73) 96 pages (softcover), March 1989 Individual member $8, List price $13, Institutional member $1 0 This book is intended for researchers and students concerned To order, please specify MEM0/400N with questions in analysis and function theory. The author

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MARCH 1989, VOLUME 36, NUMBER 3 319 New AMS Publications

provides an exposition of the main results obtained in recent years by Soviet and other mathematicians in the theory of mappings with bounded distortion, an active direction in SOME MAJOR RESEARCH DEPARTMENTS contemporary mathematics. The mathematical tools presented OF MATHEMATICS can be applied to a broad spectrum of problems that go Saunders Mac Lane beyond the context of the main topic of investigation. For a number of questions in the theory of partial differential With a biting wit and an engaging manner, Saunders Mac Lane, equations and the theory of functions with generalized elder statesman of the American mathematical community, derivatives, this is the first time they have appeared in an provides a historical perspective on the development of internationally distributed monograph. mathematics research departments in this country in this videotaped presentation. Starting with Berlin at the turn of Contents the century and Gottingen in the 1930s, Mac Lane chronicles Introduction the influence of these departments on the development of Some facts from the theory of functions of a real variable mathematics in this country. He describes the strengths Functions with generalized derivatives of some of the most influential American departments and Mobius transformations evaluates the theory of ··mathematical inheritance·· as a Definition of a mapping with bounded distortion method of building an excellent research department. He also Mappings with bounded distortion on Riemannian spaces provides interesting commentary on such issues as ""objective rankings·· of departments, some science policy issues, Main facts in the theory of mappings with bounded distortion and the ills of calculus textbooks. In addition, Mac Lane's Estimates of the moduli of continuity and differentiability well-known affinity for verse comes into play as he enlivens almost everywhere of mappings with bounded distortion the lecture with a number of humorous poems illustrating Some facts about continuous mappings on R" various themes in his talk. Conformal capacity The concept of the generalized differential of an exterior 1980 Mathematics Subject Classification: 01 VHS format, approx. one hour, March 1989 form Price $59 Mappings with bounded distortion and elliptic differential To order, please specify VIDMACLANE/N equations Topological properties of mappings with bounded distortion Local structure of mappings with bounded distortion Characterization of mappings with bounded distortion by the property of quasiconformity Sequences of mappings with bounded distortion The set of branch points of a mapping with bounded GEORG CANTOR: THE BATTLE FOR distortion and locally homeomorphic mappings TRANSFINITE SET THEORY Extremal properties of mappings with bounded distortion Joseph W. Dauben Some further results Some results in the theory of functions of a real variable and In this lively and engaging videotaped lecture, Dauben the theory of partial differential equations presents a fascinating look at Georg Cantor and the theory. Dauben traces the Functions with bounded mean oscillation development of transfinite set Harnack's inequality for quasilinear elliptic equations evolution of Cantorian set theory with an emphasis on contemporaries. This Theorems on semicontinuity and convergence with a the opposition it met from Cantor's functional for functionals of the calculus of variations meticulously researched lecture covers the mathematical, Some properties of functions with generalized derivatives technical, philosophical, theological, and even psychological Dauben describes Cantor's On the degree of a mapping aspects of Cantor's struggle. mental illness, the personal and mathematical attacks he endured, and his single-minded approach to his work. The 1980 Mathematics Subject Classifications: 30-02, 30C60; 30C20, use of photographs and other illustrations bring the subject 30C35,30C85,46E35, 53820,31815,35J99,53A30 to life as Dauben paints a gripping portrait of the brilliant but ISBN 0-8218-4526-8, LC 89-72 tormented life of Georg Cantor. ISSN 0065-9282 380 pages (hardcover), March 1989 1980 Mathematics Subject Classifications: 01, 00 Individual member $77, List price $129, VHS format, approx. one hour, March 1989 Institutional member $1 03 Price $59 To order, please specify MMON0/73N To order, please specify VIDDAUBEN/N

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320 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Recent Appointments Browder (ex officio) and Robert complex analysis, introduced by M. Fossum (ex officio). CHARLES HIMMELBERG. Hugh L. Montgomery (AMS), P. Roselle (MAA), Mary Committee members' terms of David Special Sessions Ellen Rudin (MAA), and Peter office on standing committees By invitation of the same com­ 31 of the Sarnak (AMS) have been appointed expire on December mittee, there were twelve special fol­ by Presidents William Browder year given in parentheses sessions of selected twenty-minute oth­ (AMS) and Lida K. Barrett (MAA) lowing their names, unless papers. The topics, organizers, and erwise specified. to the Joint Program Committee for the Louisville Meeting. Profes­ speakers follow: Partial differential sor Sarnak will serve as chairman. equations- Geometric theory, AN­ DREW ACKER, Wichita State Uni­ Richard W. Beals ( 1991 ), Sylvain Reports of Past Meetings versity. Speakers included Andrew E. Cappell (1991), and Michael E. Acker, Alan Elcrat, Victor Isakov, Taylor ( 1991) were appointed by The October Meeting Kirk E. Lancaster, Gary Lieber­ Past President G. D. Mostow to in Lawrence man, Kenneth Miller, Harold R. the Editorial Board for Contem­ The eight-hundred-and-forty-fifth Parks, George Paulik, Edward W. porary Mathematics. Daniel M. meeting of the American Math­ Stredulinski, Gerhart Stromer, C. Wente Burns, Jr. ( 1989) was appointed ematical Society was held at the Thomas Vogel, and Henry chairman. Continuing members of University of Kansas in Lawrence, Geometry and mathematical Univer­ the committee are David Eisen­ Kansas on Friday, October 28, and physics, JoHN K. BEEM, E. bud ( 1989), Jonathan Goodman Saturday, October 29, 1988. There sity of Missouri and PHILLIP Univer­ (1990), Gerald J. Janusz (1989), were 333 registrants, including 289 PARKER, Wichita State Ian M. and Jan Mycielski ( 1990). members of the Society. sity. Speakers included Boris Schein has been appointed Anderson, Tevian Dray, G. G. by President William Browder to Invited Addresses Emch, Paul Ehrlich, Francis J. Fla­ the Advisory Committee for the By invitation of the Committee herty, Gregory J. Galloway, Justin Russian-English Dictionary. Con­ to Select Hour Speakers for Cen­ C. Huang, David Lerner, Corrine tinuing members of the committee tral Sectional Meetings, there were A. Manogue, Bahram Mashhoon, are Joseph N. Bernstein, Ralph P. four invited one-hour addresses as Adrian Melott, F. R. Miller, David Boas, chairman, James R. Bunch, follows: BJ0RN DAHLBERG, Wash­ G. Retzloff, John R. Urani, S. Wal­ Courtney S. Coleman, Joseph L. ington University, Elliptic bound­ ter Wei, and Steve Wilkinson. Doob, Bogdan Dudzik, Eugene ary value problems in nonsmooth Numerical linear algebra, Dynkin, Mark I. Freidlin, Paul domains, introduced by JILL PI­ RALPH BYERS, University of Kan­ R. Halmos, Edwin Hewitt, John PHER, STEVEN E. HURDER, Uni­ sas. Speakers included Gregory S. R. Isbell, John McCarthy, Boris versity of Illinois at Chicago, Ge­ Ammar, Jessie L. Barlow, Chris Mityagin, Eric John Fyfe Prim­ ometry and the index theory offo­ Beattie, Michael Berry, Christian rose, Lawrence A. Shepp, and Ben liations, introduced by NoRBERTO H. Bischof, G. A. Geist, William Silver (ex officio). SALINAS, PETER ScoTT, Univer­ B. Gragg, Nicholas J. Higham, President William Browder has sity of Michigan, Ann Arbor, Least E. R. Jessup, Stephen G. Nash, appointed Morris W. Hirsch ( 1990), area surfaces in 3-manifolds, intro­ Alex Pothen, N. H. Rhee, D. C. Rhonda J. Hughes ( 1990), and Ir­ duced by DARRYL McCuLLOUGH, Sorensen, Daniel B. Szyld, and win Kra ( 1990) to the Committee and SIDNEY M. WEBSTER, Uni­ Robert van de Geijn. on Committees. Continuing mem­ versity of Minnesota, Minneapo­ Algebraic geometry, BRUCE bers of the committee are William lis, The integrability problems of CRAUDER and SHELDON KATz,

MARCH 1989, VOLUME 36, NUMBER 3 321 AMS Reports and Communications

Oklahoma State University. Speak­ Young Choi, Yves Carriere, Daniel Reid, Martin Scharlemann, Abi­ ers included Donu Arapura, James Gallo, William Goldman, Richard gail Thompson, and Wilbur Whit­ A. Carlson, Susan Jane Colley, Hain, Yoshinobu Kamishima, Ravi ten. Brucer Crauder, Anthony V. Gera­ S. Kulkarni, Karl Luttinger, and Contributed Papers mita, Brent B. Gordon, Brian Har­ Larry Lok. bourne, Sheldon Katz, Gary Ken­ Operator theory and applica­ There were 3 sessions for con­ nedy, William E. Lang, Gennady tions to geometry, STEVEN E. HuR­ trubuted papers. The session times, Lyubeznik, Juan C. Migliore, A. DER, and NORDER TO SALINAS, Uni­ numbers of papers, and names of P. Rao, Roy Smith, and Robert versity of Kansas. Speakers in­ presiders follow: Friday afternoon, Varley. cluded Kevin F. Clancey, Jeffrey 1 paper, Sherry Gale of the Uni­ Control theory, TYRONE DUN­ Fox, James L. Heitsch, Gary R. versity of Kansas. Saturday morn­ CAN, University of Kansas. Speak­ Jensen, Palle Jorgensen, Franz W. ing, 4 papers, Al Jenab of the ers include: Thomasz Bielecki, Kamber, Jerome Kaminker, University of Kansas. Saturday af­ of William M. Boothby, Richard Michael Lamoureaux, Paul S. ternoon, 5 papers, Dave Nelson Datko, Tyrone Duncan, Kurt Muhly, Andrew Rich, Richard the University of Kansas. Helmes, P. R. Kumar, Irena Rochberg, Walter Rudin, Philippe Local Arrangements Lasiecka, Lawrence Markus, Clyde Tondeaur, Albert J. L. Sheu, Keren Local arrangements wer handled F. Martin, Bozenna Pasik-Duncan, Yan, and Kehe Zhu. by Philip Montgomery of the Uni­ Raymond Rishel, Roberto Trig­ Commutative algebra, DANIEL versity of Kansas. giani, and F. S. Van Vleck. KATz and JEFFREY LANG, Univer­ Applications of set theory, sity of Kansas. Speakers included Andy Roy Magid WILLIAM FLEISSNER, University of S. S. Abhyankar, D. D. Anderson, Associate Secretary Kansas. Speakers included Zoltan Hara Charalambous, Sangki Choi, Norman, Oklahoma Balogh, Paul Bankston, Dennis Shankar Dutta, John A. Eagon, Burke, Paul Corazza, Peg Daniels, William Heinzer, Craig Huneke, S. W. Davis, Alan Dow, Gary Melvin Rochester, Bernard John­ Gruenhage, Winifred Just, John ston, David Lantz, Gennady Lyu­ The Council Meeting Kulesza, Witold Marciszewski, beznik, Stephen McAdam, Mat­ in Phoenix Arnold W. Miller, Peter J. Nyikos, thew Miller, T. T. Noh, Chris­ The Council met at 5:00 p.m. on Jack R. Porter, Karel Prikry, Judy tel Rotthaus, Sunsook Troh, Bernd 10 January 1989 in the Phoenix Roitman, Mary Ellen Rudin, Ulrich, Roger Wiegand, and Sylvia Ballroom of the Hyatt Regency Charles Schlindwein, and Franklin Wiegand. Hotel. President William Browder D. Tall. Potential theory and partial dif­ was in the chair. Real analysis, JAMEs FoRAN, ferential equations in nonsmooth The Council approved the Min­ University of Missouri at Kansas. domains, JILL PIPHER, University utes of Business by mail of 21 De­ Speakers included Ali Alikani, Ed­ of Chicago and GREGORY VER­ cember 1988 in which it approved ward M. Arnold, Jack B. Brown, CHOTA, University of Illinois at Michael Crandall, D. J. Lewis, and P. S. Bullen, Krzysztof Ciesielski, Chicago. Speakers included Chris­ Robert E. L. Turner for member­ Geraldo De Souza, Chris Freil­ topher J. Bishop, Russell M. Brown, ship on the Editorial Committee ing, Henry Fast, James Foran, Jonathan Cohen, Eugene Fabes, of Notices. Richard Gibson, B. Garrett, Lee Robert Fefferman, Carlos E. Kenig, The Council received the re­ Hart, Hans P. Heinig, Paul D. John L. Lewis, Charles Moore, A. port of the Tellers for the 1988 Humke, Kenneth R. Kellum, Lee M. Murray, Jill Pipher, Zhang­ Election. (The results are noted Larson, Sandra Meinershagen, Wei Shen, Gregory Verchota, and elsewhere in this issue of Notices.) Krzysztof Ostaszewski, Gyuri Jang-Mei Wu. It received the report of the Teller Petruska, Zbigniew Piotrowski, 3-manifolds, PETER ScoTT, Uni­ for the Election to the Nominating Brian S. Thomson, and Daniel versity of Michigan. Speakers in­ Committee. The new members of Waterman. cluded Colin Adams, Mark D. the Nominating Committee are Flat bundles and geometric Baker, Dave Gabai, Cameron Gor­ structures, WILLIAM MARK GoLD­ don, Joel Hass, John Hempel, John Joan S. Birman MAN, University of Maryland. Kalliongis, Ravi Kulkarni, D. D. James E. Humphreys Speakers included Daniel M. Long, Darryl McCullough, Robert Victor Klee Burns, Jr., James A. Carlson, Suh Meyers, Ulrich Oertrel, Alan W. Alan D. Weinstein

322 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

The Council received reports that the President immediately ap­ issue of Notices.) It approved the from several committees, among point six members of the EBC, two report's recommendation on the them the Committee on Science with terms through 1989, two with term and number of members of Policy, the Committee on Hu­ terms through 1990, and two with the Nominating Committee. The man Rights of Mathematicians, terms through 1991. term of office for the Nominating the Committee on Fellowship Pol­ The Council supported and en­ Committee will be three years, the icy, the AMS-MAA Committee on dorsed the vision of school math­ term will begin on September 1 Employment and Educational Pol­ ematics contained in the National the year after election, and three icy, the AMS-AAAS-MAA Com­ Council of Teachers of Mathe­ members will be elected each year. mittee on Opportunities in Math­ matics "Curriculum and Evalua­ The Council tabled a motion ematics for Underrepresented Mi­ tion Standards for School Mathe­ that would increase the term of of­ norities, the Committee on Elec­ matics" by passing the following fice of the Vice-President to three tion Scheduling (see below), and resolution: years. The Council agreed to con­ the Committee to Review Proce­ The AMS recognizes and ap­ sider further the recommendations dures of the Council in Consider­ preciates the quality and quantity in the report at its meeting in April ing Issues. of effort of the Working Groups 1989. The Council, on recommenda­ of the Commission on Standards The Council heard a report tion of the Chairman of the Bul­ for School Mathematics of the from Kenneth Hoffman, the Head letin Editorial Committee, Roger National Council of Teachers of of the Office of Governmental and Howe, authorized the Bulletin Edi­ Mathematics. The Society wel­ Public Affairs of the Joint Pol­ torial Committee to treat Research comes the proposal of these Stan­ icy Board for Mathematics. Also, Announcements for the Bulletin in dards as a model set of valued Marcia Sward, the Executive Di­ a manner in which it feels appro­ outcomes for school mathematics rector of the Mathematical Sci­ priate, for a period of two years. (K-12) and supports and endorses ences Education Board, reported The Committee proposed a "shift the vision of school mathematics on Mathematics Education in the in focus, to more heavily weighted contained in the Standards. National Spotlight. expository values" and this shift The Society joins in calling for: The Council and the Board of has been approved by the Council Trustees have agreed on one new for a trial period. i. considerable strengthening publishing venture and a modifica­ In the 1988 Election, the mem­ of programs to train teachers tion of an already existing series. bership approved an amendment of school mathematics; The Council agreed to establish a to the bylaws that removed the ii. efforts to promote suffi­ series entitled Proceedings of Re­ selection of editors from the elec­ cient funding and support by gional Conferences of the USSR tion ballot to the membership. local, state, federal and pri­ that the Board of Trustees had The selection of editors is now vate sources to ensure that provisionally approved. It agreed lodged with the Council accord­ the Standards can be effec­ to co-publish, with the London ing to Council action of 5 Jan­ tively implemented; Mathematical Society, the series uary 1988. The Council has estab­ iii. active involvement by AMS History of Mathematics, again fol­ lished an Editorial Boards Com­ members in joining with lo­ lowing the Board of Trustees' pro­ mittee (EBC) that will be elected cal groups to work for the visional approval. by the membership in a manner betterment of school mathe­ The Council approved the fol­ similar to that in which the Nom­ matics. lowing resolution (at the request inating Committee is elected. In The Council approved partici­ of ArborText, Inc.): the steady state, two members of pation of the Society for Industrial the EBC are elected by the mem­ and Applied Mathematics (SIAM) The Council agrees that or­ bership by 10 November of each in the AMS-MAA joint publica­ ders from South Africa for Ar­ year. Since the bylaw affecting this tion UME TRENDS, a newsletter borText, Inc. products sold by change was not in place for the for collegiate mathematics. the Society be returned to the 1988 Election, but is in place now, The Council considered sev­ sender along with a statement the manner in which an Edito­ eral items from the report of the that ArborText, Inc. does not rial Boards Committee should be Committee on Election Schedul­ allow sales in South Africa. named was referred to the Coun­ ing. (A detailed account of this Finally, the Council agreed with cil. The Council recommended report appears elsewhere in this the Board of Trustees to establish

MARCH 1989, VOLUME 36, NUMBER 3 323 AMS Reports and Communications

an annual prize to be adminis­ week (see the article in the front The two proposed amendments tered by Pi Mu Epsilon, the na­ of this issue of Notices) and that to the bylaws, the one concerning tional honorary mathematics soci­ Dr. Gordon Walker, Executive Di­ sexist language and the other con­ ety, with the stipulation that the rector of the Society from 1959 cerning the Editorial Boards Com­ name of the Society be associated to 1977, had died in December mittee, were approved. with the prize. 1988 (see page 139 of the Febru­ The composition of the Coun­ The Council had recessed for ary 1989 issue of Notices). After cil for 1989 follows. dinner from 7:00 p.m. to 8:00 p.m. brief mention that the Society is and adjourned at 12:50 a.m. the embarking on its second century, COUNCIL FOR 1989 following day. the Secretary reported on the ac­ tions of the Council as detailed Ex-President Robert M. Fossum above. George Daniel Mostow Secretary The meeting then dissolved it­ Urbana, Illinois President selfinto a Committee of the Whole, William Browder with Andrew Gleason in the chair, The Business Meeting to discuss the report to the Council Vice Presidents in Phoenix of the Society by the ad hoc Elec­ Sun-Yung Alice Chang tion Scheduling Committee. (This Barry Simon The Business Meeting was held on report is discussed elsewhere in William P. Thurston 12 January 1989 in the Ballroom this issue of Notices.) of the Civic Plaza immediately fol­ Former Secretary After rising from the Commit­ Everett Pitcher lowing the session for the award of tee of the Whole (with no report) the Bocher Prize. President Brow­ and with President Browder in the Secretary der was in the chair. chair, the Meeting thanked the Lo­ Robert M. Fossum The President announced that cal Arrangements Committee for Associate Secretaries Herbert Freedman of the Cana­ it efforts in arranging the 95th An­ Joseph A. Cima dian Mathematical Society had nual Meeting and then adjourned. presented the Society with a copy W. Wistar Comfort Andy Roy Magid of the Fields Medal struck from Robert M. Fossum Lance W. Small the original molds as a gift from Secretary the Canadian Mathemtical Society Urbana, Illinois Treasurer in honor of the Centennial of the Franklin P. Peterson Society. Election Results of 1988 The President then gave the Associate Treasurer floor to Ronald L. Graham who in The Tellers for the 1988 Elec­ Steve Armentrout turn introduced Dr. Boris Stechkin, tion reported counting 3741 and Members-at-Large member of the Steklov Institute 2/3 ballots. The newly elected Jonathan L. Alperin and Secretary of the Soviet Com­ Vice-President is Sun-Yung Alice Fan R. K. Chung mittee of the Bernoulli Society for Chang. The newly elected Mem­ Lawrence J. Corwin Mathematical Statistics and the bers-at-Large of the Council are Richard K. Guy Theory of Probability. In com­ Jonathan L. Alperin, Fan R. K. Rhonda J. Hughes memoration of the Society's Cen­ Chung, Lawrence J. Corwin, Robion C. Kirby tennial, Dr. Stechkin presented it Michael C. Reed, and Hugo Rossi. Irwin Kra with a bronze medal struck in The newly elected Trustee is Paul H. Blaine Lawson, Jr. the Soviet Union on the occa­ J. Sally, Jr. Albert Marden sion of the First General World All candidates in uncontested Yiannis N. Moschovakis Congress on Mathematical Statis­ elections were elected to their re­ Linda A. Ness tics and the Theory of Probability spective offices. Michael C. Reed held in Tashkent, Soviet Union, in The candidates elected to the Marc A. Rieffel 1986. Nominating Committee of 1989- Hugo Rossi The Secretary reported that Pro­ 1990 are Joan S. Birman, James Harold M. Stark fessor Marshall Stone, President E. Humphreys, Victor L. Klee, Jr., William A. Veech 1943-1944, had died earlier that and Alan D. Weinstein. CarolS. Wood

324 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Representatives of Committees Mathematical Reviews Science Policy Committee Committee to Monitor Problems Editorial Committee Ronald G. Douglas, Chairman in Communication Melvin Hochster, Chairman Richard S. Palais, Chairman Mathematical Surveys TRUSTEES FOR 1989 AMS Representative, Board of Editorial Committee M. Susan Montgomery, Chairman Editors of American Journal M. Susan Montgomery, Chairman Ronald L. Graham, Secretary of Mathematics Mathematics of Computation Franklin P. Peterson, ex officio M. Salah Baouendi Editorial Committee Steve Armentrout, ex officio Bulletin Editorial Committee Walter Gautschi, Chairman William Browder, ex officio Roger E. Howe, Chairman Proceedings Editorial Committee Ramesh A. Gangolli Frederick W. Gehring Colloquium Editorial Committee William J. Davis, Chairman Paul J. Sally, Jr. Raoul H. Bott, Chairman Andrew Odlyzko Journal of the AMS Transactions and Memoirs Editorial Committee Editorial Committee Michael Artin, Chairman Ronald L. Graham, Chairman

ALGEBRAIZABLE LOGICS W. J. Blok and Don Pigozzi (Memoirs of the AMS, Number 396)

Although most of the familiar logical systems are known to 1980 Mathematics Subject Classifications: 03G99; 03B45, 03B55, have an algebraic counterpart, no general and precise notion 03B60, 03C05,08C15 of an algebraizable logic exists upon which a systematic ISBN 0-8218-2459-7, LC 88-8130 ISSN 0065-9266 investigation of the process of algebraization can be based. 88 pages ( softcover), January 1989 In this work, the authors propose and begin such an Individual member $8, List price $13, investigation. Their main result is an intrinsic characterization Institutional member $1 0 of algebraizability in terms of the Leibniz operator n, which To order, please specify MEM0/396NA associates to each theory T of a given deductive system S a congruence relation nr on the formula algebra. nT identifies all formulas that cannot be distinguished from one another, on the basis of T, by any property expressible in the language of S. The characterization theorem states that a deductive system S is algebraizable if and only if n is one-to-one Shipping/Handling: 1st book S2. each add'l $1. S25 and order-preserving on the lattice of 5-theories and also max. By air. 1st book $5. each add'l S3. S100 max. preserves directed unions. The authors illustrate these results Prepayment required. Order from AMS. P.O. Box 1571. with a large number of examples from modal and intuitionistic Annex Station. Providence. Rl 02901-1571. or c.all logic, relevance logic, and classical predicate logic. 800-55&-7774 to use VISA or MasterCard.

MARCH 1989, VOLUME 36, NUMBER 3 325 Miscellaneous

Personal Items Ellen Torrance, formerly of 41. He was a member of the Soci­ M & R Services, Inc., is now an ety for 18 years. (See the News and Zhao Yi Chun, of the People's Associate Actuary at First Colony Announcements section of this is­ of China, will be a visit­ Republic Life Insurance Company in Lynch­ sue of Notices.) professor at Appalachian State ing burg, Virginia. Manfred Kochen, of Ann Ar­ the spring semes­ University during bor, died on January 7, 1989, at ter of 1989. His area of research the age of 60. He was a member theory. interest is operator Deaths of the Society for 35 years. Lawrence H. Cox Director Kenneth P. McDowell, formerly Sciences' Elliot T. Adams, of Newtonville Board on Mathematic~! of Wilfred Laurier University, died Massachusetts, died on January 3: National Academy of Sciences, ha~ on September 26, 1988, at the age in the 1989, at the age of 89. He was been elected to membership of 41. He was a member of the a member of the Society for 11 International Statistical Institute. Society for 14 years. of years. Otomar Hajek, Professor Marshall H. Stone, Professor Re­ J. Frank Adams, Lowndean Mathematics at Case Western Emeritus of the University of Mas­ has received a Professor of Astronomy and Ge­ serve University, sachusetts, Amherst, died on Jan­ of ometry at the University of Cam­ joint appointment as Professor uary 9, 1989, at the age of 85. He bridge, died on January 7, 1989, at Systems Engineering at this same was a member of the Society for the age of 58. He was a member of institution. 62 years. A memorial service will was one of the Society for 31 years. (See the Benoit Mandelbrot be held for him on Sunday, April of the newly News and Announcements section the joint recipients 8, 1989 at the University of Mas­ of this issue of Notices.) created /M.oeL, Hennessy-Louis sachusetts, Amherst. For details, Luther Thomas Conner, Jr., As­ Vuitton (~VMH) Science for Art please contact T. A. Cook, 413- work sociate Professor Emeritus of the prize. He was honored for his 545-0874, or M. K. Bennett, 413- College of William and Mary, died in fractal geometry. 549-0545, at the Department of on November 4, 1988, at the age Patrick L. Reilly, of Alcatel Mathematics and Statistics. (See of 56. He was a member of the Network Systems, was appointed the item at the beginning of this Society for 23 years. a reviewer for IEEE Transactions issue of Notices.) on Communications and listed in Ronald J. DiPerna, of the Uni­ Who's Who in the South and versity of California, Berkeley, died Southwest, 1989. on January 8, 1989, at the age of

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

ORDINARY MEMBERS Victor V Cifarelli Kris L Holderness University of California, San Diego Grand Junction, Colorado La Jolla, California Bruce D Holenstein Alexander B Abacus Joseph N Closs Compucon Service La Jolla, California Philadelphia, Pennsylvania West Chester, Pennsylvania Lara L Aist Stephane Blaise Collart Askol'd Georgievic Hovanskii Catonsville, Maryland Zurich, Switzerland VNIISI Alton L Amidon Moscow, USSR J Kevin Colligan Havelock, North Carolina Silver Spring, Maryland Everett W Howe E Ya Arnaudova San Leandro, California Manuel De Leon Higher Institute of Architecture and Consejo Superior de Investigaciones Paul M Hunt Construction Cientificas Williamston, Michigan Sofia, Bulgaria Madrid, Spain Cheryl L Ingram Czeslaw Baginski Matthew J Dempsey Joplin, Missouri University of Warsaw St Louis, Missouri Bialystok, Poland Antal Ivanyi Tong Ren Ding Eotvos Lorand University Randall K Bahr Peking University Budapest, Hungary Tucson, Arizona Beijing, People's Republic of China Piotr Jaworski Lucas M Bernard Do Van Luu University of Warsaw New York, New York Hanoi, Socialist Republic of Vietnam Warsaw, Poland David P Blecher Michael A Eckhoff Nitin S Joshi University of Houston Bay St Louis, Mississippi Flushing, New York Houston, Texas Alexandre Ern V M Kharlamov Dona V Boccio Ecole Polytechnique Leningrad, U S S R Bayside, New York Palaiseau, France John F Kinkel Jerald S Brodkey Marian Fabian Irvine, California Beachwood, Ohio Prague, Czechoslovakia I A Klipker Alton R Brown Jin Xuan Fang Tbilisi, U S S R Mitre Nanjing, People's Republic of China McLean, Virginia Kenneth A Koblun S S Goncharov San Ramon, California Michael J Bryan Novosibirsk, U S S R Terre Haute, Indiana Ulle Kotta Carol Harris Estonian SSR Academy of Sciences Elmer J Bryson Lexington, Kentucky Tallinn, U S S R National City, California John C Hedreen Dimitry A Leites !-Liang Chern Baltimore, Maryland University of Stockholm New York University, Courant Stockholm, Sweden Institute of Mathematical Sciences Robert E Heyman New York, New York University of Maryland S Z Levendorskii College Park, Maryland Rostov-on-Don, U S S R Zhong Wu Chu Harbin Institute of Technology Robert N Hightower Florence J Lin Harbin, People's Republic of China Ann Arbor, Michigan Upton, New York

MARCH 1989, VOLUME 36, NUMBER 3 327 New Members of the AMS

Long Wei Lin Cornel Pasnicu Jun Yong Shin Zhongshan University IN CREST Arlington, Texas Guangzhou, People's Republic of Bucharest, Romania James S Sochacki China Luca F Pavarino James Madison University Paul R Lowe New York University, Courant Harrisonburg, Virginia Sciences Monterey, California Institute of Mathematical Carol J Stafney New York, New York Adam Lozowicki Platteville, Wisconsin Szczecin, Poland Wieslaw Pawlucki Elizabeth K Stage Jagiellonian University University of California, Berkeley Rodney Neal Lynch Krakow, Poland Crawfordsville, Indiana Berkeley, California Pham Huy Dien Satyagopol Mandai William W Symes Institute of Mathematics Rice University University of Kansas Hanoi, Socialist Republic of Vietnam Lawrence, Kansas Houston, Texas Glenn A Pico David Alan Taff Dragan Marusic Sacramento, California Koper, Yugoslavia Golden, Colorado Robert M Purcell S V Talalov Deborah Gibson McAtee King of Prussia, Pennsylvania Montana State University Kuibyshev, U S S R Bozeman, Montana Charles C Quillen Maged S Tawfik Gate City, Virginia Phillip E McNeil 3D/Eye Incorporated Norfolk State University Fuyao Ren Ithaca, New York Norfolk, Virginia Fudan University Lawrence J Teitelman Shanghai, People's Republic of China Albert J Milani New York, New York University of Wisconsin-Milwaukee Diane Resek Mark Renwick Temple-Raston Milwaukee, Wisconsin Berkeley, California University of Arizona Ralph J Money Jr Nenad Rijavec Tucson, Arizona Bridgeport, Connecticut Fort Collins, Colorado Andrey V Tetenov Michael S Moore Roger A Roberts Novosibirsk, USSR Pomona, California Littleton, Colorado Bertrand C Theuveny Richard P Morris Michael H Ruge Schlumberger Centreville, Virginia Louisiana State University Rio de Janeiro, Brazil Baton Rouge, Louisiana Rajeev Motwani John M Thomason Stanford University William Joseph Ryan Beeville, Texas Stanford, California Willingboro, New Jersey Annabelle Lee Treacy Toshikazu Natsume Ronald D Sandstrom La Canada, California State University of New York at Fort Hays State University Mary Ann Tyl Buffalo Hays, Kansas Broadview, Illinois Buffalo, New York Leland Sapiro S K Vodop'yanov Mary Louise Nigro Paul Quinn College Novosibirsk, U S S R Newton Square, Pennsylvania Waco, Texas Jeffrey K Woodhead David M Obrzut Stanislaw Sedziwy Davis, California Laurel, Maryland Jagiellonian University Krakow, Poland I I Yurik Anatol Odzijewicz Kiev, USSR Warsaw University Michael Joseph Segal Biatystok, Poland Williamsville, New York Nai Ying Zhang Chalmers University of Technology Haluk Ogmen Douglas A Sharp Goteborg, Sweden University of Houston St John's School Houston, Texas Houston, Texas Yishao Zhou Royal Institute of Technology John Pais Diana Frost Shelstad Stockholm, Sweden Webster University Tarrytown, New York St Louis, Missouri Ken C Ziejewski Meir Shillor Chicago, Illinois Tim F Parrott Oakland University Easley, South Carolina Rochester, Michigan

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

Jorge Passamani Zubelli Michele Rene Norton Institute for Defense Analyses University of California, Berkeley Gail E Nowicki I>avid L desJardins Berkeley, California Troy E O'Brien Loyola Marymount University Linda K Smoke Connie J Weeks Andrew Jay Tierman Mankato State University RECIPROCITY MEMBERS Clark University Tim Braam Jun Chang Allahabad Mathematical Society Shu-Ling Chang M S Mittal College of the Holy Cross Chien-Chow Chen Balasubramanian Natarajan Michele Intermont Charles J Felber Deutsche Mathematiker- Vereinigung e. V. Tamara S Trombetta Chien-Chuan Tang Shu-Chin W Weng Wilhelm Plesken Colorado College Horst R Thieme Mary K Gessley McMaster University Anita Bhardwaj Gesellschaft fiir Angewandte Mathematics Cornell University Xiangdong Chen und Mechanik Chung-Kwan Choi Yannis Papageorgiou Herbert Niessner I>arroch Faught Peter Teichner Boris Goldfarb Iranian Mathematical Society Qiang Zhu Ali A Alikhani Vee Ming Lew Jiaqi Luo Miami University, Oxford Sociedade Portuguesa de Matemdtica Scott Alan Mitchell Jeremy S Case Olga Azenhas Claudia M Neuhauser Joan Elizabeth Hart Svenska Matematikersamfundet Poorvi L Vora I>avid L Stuckey Patrick A Worfolk Henrik O,Egnell Michigan State University Dartmouth College Faouzi Azzouz I>avid N Bray Richard Weston Beverly NOMINEE MEMBERS Alisa A I>eStefano Brian K Bury Beloit College Michael J Glenn Benjamin E Caldwell Tames Lengyel Margaret Hagopian I>ouglas Olaf Carlson Thalia I> J effres Halil I Celik Bowdoin College Peter J Kostelec Tsyr-Min Chang Susan M L Anderson Larry Joseph Langley Jing-Fen Chen Bowling Green State University Thomas E Leathram I>awn Alisha Crumpler Alphonse K A Arney Stephen R Peeples Patrick M Garrity Cynthia Gwilym Gregory A Bastian Duke University MingJin Stephen P Bean Shandelle M Henson Stanley S Johnson Kaddour Boukaabar Christopher Scott Peterson Jack A Jordan John H Carson Charles M Vuono I>exin Chen Mirjana S Jovovic Elise C Goldie Duquesne University Jeffrey W Koch Sunil M Koswatta Vivien C Wang Timothy M Koponen Timothy F LaVan I>ianne I Mesker Florida Atlantic University Samir I Lababidi Supriya Mohanty Manny B I>eCastro Meng-Shiun Lai Piotr J Wojciechowski Arumugam Muhundan Jungho Lee John E Zimmerman Xuegong Wu BoLing Xuan Xu Brock University Sanjay Sadanand Mundkur Peggy Ann Rosehart Franklin f3 Marshall College Ecaterina Nagy Bucknell University Marjolein de Wit Fouad S Nakhli Edgar A Ramos Carmen 0 Acuna Harvard University Richard A Reynolds Eric I>avid Belsley Carnegie Mellon University Hassen Sadri Srdjan I>ivac Nenad Antonic Radhouane Sellami Kefeng Liu Edgar 0 Baules Wenxian Shen Michael Liam McQuillan Chih-Wen Cheng Kejian Shi Luca Migliorini Enrico Tronci Stephen P Smith Wei-I>ong Ruan Kostas Vassilakis Todd M Swanson Jeffrey Silver Yoshihiko Tazawa Central Michigan University I>onald C Weitzman Paul M Carolin William A Wallace Patti L Freet Haverford College Heungsu Yi William M Higdon Marc J Melitz Xiangfei Zeng Patrick Lo Jennings Zhonggang Zeng

MARCH 1989, VOLUME 36, NUMBER 3 329 New Members ofthe AMS

New York University, Courant Institute of Kathryn M Sibert University of Chicago Mathematical Sciences Kimberly M Storz Hare! Barzilai Vincenzo Nesi Jan Cheah Simon Fraser University Youngsoo Choi Northeast Missouri State University S Bhatia Najmuddin A Fakhruddin David L Bergevin Salil K Das Young-Rock Kim William J Sehnert Carlos A Wong Holger Philipp Kley Siming Zhar Northern Illinois University Byung Ho Song Wei-Han Chang Southern Oregon State College Troy R Zerr Samar Chaudhary Reider S Peterson University of Florida Ran Baik Lee Stanford University Thomasenia Lott Adams Frank J Marzano Victoria E Bourne James Timothy Bock Janet M Norbrothen David B Cruz Mohammad Habibi Sheryl L Wills John Whitaker Havlicek Tohien Thi Hoang Oklahoma State University, Stillwater Bryna R Kra Jun H Li Brian W Box Jianan Lu Michael Alan Marks Dorothy A Jones Christopher D Overton Melissa Landers McCool Renming Song John D Lorch Texas A f1 M University Charles A Matthews T J Wangerman Gregory Lindstrom Yongzhi Yang Deborah Ann Moore Michael Lee Wade Kimberly A Overstreet Huixia Zhu Martha Ellen Waggoner Trinity College University of Georgia Stanislaus Whittlesey Princeton University Francis Levi Barnes Nikolaos Bournaveas Tufts University Peiqing Jiang Galia D Dafni Babette M Benken University of Idaho Charles R Farenbaugh Martha A Sunderhauf Peter Joel Bloomsburg Chien-Hao Liu Zhenhua Zhang Tae Sug Do Robert F Sherry Yiying Zhou Burma L Hutchinson Jaroslaw Wroblewski University of California, Irvine Chao-Hui Lan Providence College Ramakrishna Kakarala Mark C Lotspeich Jeffrey T Hoag Michael J Shearer Charles H Newberg Robert R Park Purdue University University of California, Los Angeles John J Thurber Geon Cho David S Blackwell Stewart M Tung Darrel F Czubala Eric Neil Boe Kimberly M Vincent Donatella Delfino Douglas C Bowman Kai Deng Roger E Hagen University of Illinois at Urbana- Steve Fan Brian Joseph Hagerty Champaign Mark R Johnson Erik J Hanson Maitreyee Bera Shanzhong Lai Guanghan Liu Donna J Berg Moohyun Lee Erding Luo QYBu Hua-Lun Li Maria M Morril Bruce F Carpenter Xianjin Li Bradley Moskowitz Catherine E Cavagnaro Nianzheng Liu Mark N Olson Felix T K Cheng Radha Mohan Roberto Paoletti Rick G Faber Eun Jae Park Jie Qing Kevin F Fitzgerlad Maria Tjani Eliaho Regwan M Fritz Bert G Wachsmuth Carlos Sanchez-Fuentes Steven Robert Gale Li-Ming Yeh Larry Lucian Scott TomS Harke Ikkwon Yie William R Sherman Karin Luisa Johnsgard Seongan Yie Rodney F Sinclair Seongtag Kim Bo Zhang Martin G St Pierre Joseph Gerard Leichter Minda Zhang Mark M Sussman Soren Kaj Lundsgaard Zhuoyuan Zhang Brian Scott Taber Christopher L Miller Hai H Vu Kenneth R Neff Rice University Brad Lee Wilson Oki Neswan Ning Lu Yunwei Zhao David T Ose Chi Cheung Poon Lisette G de Pillis-Lindheim Gareth Scott Rohde John W Zweck Randal K Sharpe University of California, San Diego Mark G Thomas Shippensburg University of Pennsylvania Mark S Foskey Sandra Gorka Ming-Hwa Torng Donald A Morton Marilea B Widick

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

Harlili Wono Yong Liu Arthur R Perleberg Setya Budhi Wono Jim Ma Douglas Jay Peters John Conrad Merkel III University of Lethbridge University of North Florida Birte M Mesoy Glenda D Slingerland Heather J Goodling Mojtaba Moniri Xiaolin Wu Hyun A Moon University of Notre Dame University of Louisville Miguel A Moreles-Vazquez Guangzhong Chen Michael C Ackerman Richard E Morrell Mary G Neyer Glenna Lea Grider Preston Nichols Julann O'Shea Ruth A Hendrix Tod A Olson Christopher C Puin Teri Rene Herzog David H Olwell University of Oregon Roy Q Yu William L Oostendorp Mark C Henderson Houyao Pan University of Lowell Martin A Jackson Yong Pan Sharon L Grasso Daniel E Kotlar Pablo Pedregal Nathaniel A Meyers University of Maryland, College Park Daniel Eduardo Penazzi Sin-Chnuah Cheah Paul A Pries University of Pittsburgh, Pittsburgh David Goldberg Erik E Rantapaa Yolande N Au Weimin Han Jaiok Roh Ronald E Barnhart William H Heller James J Romanowski Anthony D Capriotti James Ernst Helmreich Roberto A Scotto Paula J Friedrich Dan-Run Huang Joel A Setterholm Jaecheul Kim Max A Karlovitz Zhoude Shao Chun Kong Law Joseph D Lakey Joel C Shepherd Hugh W McNiece Claudia Troster Leme Chia-Chen Soong Sze-man Ngai Christopher J Mark M Patricia Souza Ada Dawn Owens Christoph Schwab Heidi A Staebler Patricia Jo Saliga James F Troendle Thomas S Sundquist Cun-Qi Wang Zhimin Zhang Eduardo D Tabacman Jianrong Wang Fangcheng Tien Richard T Wenzel University of Massachusetts, Amherst Leonard Volovets Eric R Williams Eileen Marie Adams Jianhua Zhang Xiu Ye Maria Elsa Correal Honghui Zou Jinqiao Duan University of Richmond William T Dugan Jr University of Missouri, Kansas City James A Davis Bo Guan Paula G Johnson Michael George Kerchove Pamela T Hardiman University of Missouri, St Louis University of Toledo Jean Karl Jian Qin Kim Kuan Chan Gordon D Kieffer Vijaya L Gompa Patrick D Miller University of Montana Karuna Jayathilake George 0 Omamo John E Caratti Showwu Li Lincoln S Robertson Renate R Elder Jagath Kapila Silva John A Valente Pankaj Garg Prem Kumar Nyayapati Swami CD Yang Debbre S Hawkins Yu Wang Eva Kwok Yin Lee University of Minnesota, Minneapolis Jui-Lan Andy Li University of Utah David Carlos Adams Kyung H Nam Tim S Barclay Jon R Anderson Joe Nevin James P Brandt Carl P Bostrom Young H Park Melanie Breaker Bill Christ Robert Lynn Turnquist Alessio Corti Jonathan M Hanen Ninghui Zhong Paul F Cox Gary Hatfield Xinghe Zhoul Kathy Anne Dopp Dug Hun Hong Joseph E Dvorak Qing Kang University of North Dakota, Grand Forks Mary Ellen Furner Annette M Kavanaugh Scott C Binde Jill E Gebelt Meejoung Kim Patricia A Brown Dale S Graebner Pekka J Koskela Daryl M Delzer Nan C J Haymet Hyukjin Kwean Karen M Hagler Jennifer Hooper Stephan K Lapic Cheryl L Hakrow Laurel Fearuley Langford Seongwoo Lee Shari G Hensrud Heidi M Latvala Sungyoung Lee Myra Koch Tina Seaon Ma Changchun Li DeVon David Larson JeffS McGough Lii-Pemg Liou Jeff A Morel Tina Cavell Moore Wenxiong Liu Tom A Murphy

MARCH 1989, VOLUME 36, NUMBER 3 331 New Members of the AMS

Karen L Myers Gregory A Langkamp Virginia Polytechnic Institute and State Mary Ellen Oman Mark G Lawrence University Melinda J Schlafman Adam B Levy Ravi S Krishnamurthy Robert D Shalla William Whipple Neely Peng Lei Paula D White Janet E Perdue Arun N Shastri John Charles Roth Ruben Daniel Spies of Vermont University Vimaladevi Sivakumaran R Bergeron Washington University Diane Joanna M Staniszkis-Czapska Christopher James Compton Zhen Qing Chen Steve M Dosland University of Western Ontario Richard Ian Laugesen Eric Heller Zaiqing Li Daniela Stalteri Robert M Maxham Chuanyi Zhang Jiye Yu Timothy J Molsberry University of Wisconsin-Milwaukee Wayne State University A Murray Carol George A Avirappattu Xisuo Liu Tebogo Nyezi Xenia H Kramer Wichita State University Allan L Wilson M Pattanaik Lalit Mehdi Pousti University of Washington Seog-Hoon Rim Pavel L Buzyisky Jianping Yang Williams College John A Carruthers Mark A Conger University of the West Indies Frederick D Colwell Roland R Lloyd Youngstown State University Deng Sien Priscilla W Sidrak Stephen G Gomori Thad A Fugua David L Kweder John Gossman Daniel T Stephan Thanh D Hoang

PARTITION PROBLEMS IN TOPOLOGY Stevo Todorcevic (Contemporary Mathematics, Volume 84)

This book presents results on the case of the Ramsey problem 1980 Mathematics Subject Classifications: 04-02, 03E05, 03E50; 50-02, for the uncountable: When does a partition of a square of 54A25 an uncountable set have an uncountable homogeneous set? ISBN 0-8218-5091-1, LC 88-39032 ISSN 0271-4132 This problem most frequently appears in areas of general 130 pages (softcover), January 1989 topology, measure theory, and functional analysis. Building on Individual member $13, List price $22, his solution of one of the two most basic partition probll3ms Institutional member $18 in general topology, the ··s-space problem;· the author To order, please specify CONM/84 NA has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set Shipping/Handling: 1st book $2, each add'l $1, theory at the level of a first year graduate or advanced $25 max. By air, 1st book $5, each add'l $3, undergraduate student. The book may also be of interest $100 max. Prepayment required. Order from to the exclusively set-theoretic reader, for it provides an AMS. P.O. Box 1571, Annex Station, excellent introduction to the subject of forcing axioms of set Providence. Rl 02901-1571. or call theory, such as Martin's axiom and the Proper forcing axiom. 800-556-7774 to use VISA or MasterCard.

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SUGGESTED USES for classified advertising are positions available, books or lecture notes VIRGINIA TECH for sale, books being sought, exchange or rental of houses, and typing services. THE 1989 RATE IS $42.50 per inch on a single column (one-inch minimum), calculated The Department of Mathematics is ac­ from the top of the type; $18 for each additional 1/2 inch or fraction thereof. No discounts tively seeking applications in the area for multiple ads or the same ad in consecutive issues. For an additional $10 charge, of discrete mathematics and combina­ announcements can be placed anonymously. Correspondence will be forwarded. torics. We anticipate making several Advertisements in the ''Positions Available·· classified section will be set with a minimum one-line headline, consisting of the institution name above body copy, unless additional tenure-track appointments at the assis­ headline copy is specified by the advertiser. 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SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and speak to Paula Montella for further information. SEND AD AND CHECK TO: Advertising Department, Attn: Paula Montella, AMS, P. 0. Box 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 UNIVERSITY OF SOUTH CAROLINA Charles Street, Providence, Rhode Island 02904. Individuals are requested to pay in advance, Department of Mathematics institutions are not required to do so. AMS FAX 401-331-3842. Applications are invited for anticipated tenure-track faculty positions at all ranks. POSITIONS AVAILABLE Applications in all areas of mathemat­ UNIVERSITY OF NORTH ics will be considered. The Department CAROLINA AT CHARLOTTE seeks to build on existing research Department of Mathematics strengths and to increase the scope UNIVERSITY OF NEBRASKA-LINCOLN Charlotte, NC 28223 Department of Mathematics of its programs, particularly in applied and Statistics At least two tenure-track positions at and computational mathematics. Faculty Lincoln, NE 68588-0323 Asst./Assoc./Full Prof. level in Mathe­ research is supported by excellent in­ matics and Statistics. Rank and salary house library and computing facilities. Tenure-track position at the Assistant depend on qualifications. A Ph.D. and The Department's computer center sup­ Professor level (Associate Professor a serious commitment to teaching and ports network access to the University's level considered for exceptionally strong research are required. Preferred spe­ FPS array processor and 1.024 node hy­ cases) available Fall 1989. Ph.D. re­ cialties are: Analysis, Algebraic Topol­ percube supercomputer. The Ph.D. de­ quired with strong potential for research ogy, Control Theory, Numerical Analy­ gree or its equivalent is required, and all and quality teaching. Subject to the sis, Smooth Dynamical Systems, Sta­ appointments will be consistent with the requirement that the candidates be out­ tistics, but strong candidates in other Department's commitment to excellence standing, preference will be given to areas are encouraged to apply. Also in research and teaching at the under­ candidates in commutative algebra or possible are visiting and lecturer (one graduate and graduate levels. A detailed algebraic geometry, then to candidates or two year renewable; M.A./M.S. re­ resume, containing a summary of re­ in areas related to those already in the quired) positions. Send vitae, list of search accomplishments and goals, and department. Send vita and three letters four references, and abstracts of cur­ four letters of recommendation should of recommendation to Professor Roger rent research to Prof. Ram Tiwari for be sent to: Wiegand, Hiring Committee Chair, De­ Statistics position and to Prof. Hae-Soo Dr. Colin Bennett, Chairman partment of Mathematics and Statistics, Oh for all other positions at the above Department of Mathematics University of Nebraska-Lincoln, Lincoln, address. Closing date: Feb 3, 1989, but University of South Carolina NE 68588-0323. AA/EOE. Application applications will be considered until the Columbia, South Carolina 29208 deadline March 3, or until position is positions are filled. UNCC IS AN EQUAL The University of South Carolina is an Af­ filled. Women and minorities are espe­ OPPORTUNITY/ AFFIRMATIVE ACTION firmative Action/Equal Opportunity Em­ cially encouraged to apply. 402-472-3731 EMPLOYER. ployer.

MARCH 1989, VOLUME 36, NUMBER 3 333 Classified Advertisements

POSITIONS AVAILABLE UNIVERSITY OF ROCHESTER CANISIUS COLLEGE Department of Mathematics Department of Mathematics

UNIV. OF N.C. AT CHAPEL HILL Several tenure-track positions at all lev­ A second tenure track position (As­ Dept. of Mathematics els will be available beginning September sistant Professor) in mathematics is Chapel Hill, NC 27599 1989. Applicants showing significant re­ available in late August 1989. Applicants search accomplishments or exceptional must have a Ph.D. in mathematics and a research promise, as well as evidence strong commitment to quality teaching. Applications are invited for a senior level of a commitment to excellent teaching, Salary and fringe benefits are competi­ tenured appointment in the general area are invited to apply. Initial tenure-track tive commensurate with credentials and of applied and computational mathe­ appointment is for four years. There is experiences. matics, effective Fall 1989. Rank and no restriction as to field. In addition to Applicants should send resume, tran­ salary depend on qualifications. A Ph.D. a curriculum vitae, candidates should scripts and three letters of recommenda­ and demonstrated excellence in research send a summary of research plans, tion to Dr. Richard Escobales, Chairman, and teaching are required. Applications available preprints or reprints, and have Dept. of Mathematics, Canisius College, will be accepted until the position is at least three reference letters sent to: Buffalo NY 14208. filled. Contact Jon Toile, Mathematics Samuel Gitler, Chairman The Department is looking to expand Department, Box 3250 Phillips Hall, UNC Mathematics Department its offerings and options while at the at Chapel Hill, Chapel Hill, NC 27599. University of Rochester same time maintaining its sound prepa­ EO/AA Employer. Women and minorities Rochester, New York 14627 ration for students with mathematical are encouraged to identity themselves An equal opportunity I affirmative action potential. EOE/ AA. voluntarily. employer.

...... •...... ••...... •. -!\~~\IEM~l'il;f ALGEBRAIC K-THEORY AND ALGEBRAIC $~-::_·~\9. BANACH SPACE THEORY NUMBER THEORY ; ;~~,...... ; .. ~ Bor-Luh Lin, Editor ~\ ! !1,. "-.;! Michael R. Stein and R. Keith Dennis, Editors '\ - ···- . (Contemporary Mathematics, Volume 85) "'t:.\.;;i~:> ,'$' (Contemporary Mathematics, Volume 83) • This volume contains the proceedings from a Research This volume contains the proceedings of a seminar on Workshop on Banach Space Theory held at the University Algebraic K-theory and Algebraic Number Theory, held at the of Iowa in Iowa City in July 1987. The workshop provided East-West Center in Honolulu in January 1987. The seminar, participants with a collaborative working atmosphere in which which hosted nearly 40 experts from the U.S. and Japan, ideas could be exchanged informally. Several papers were was motivated by the wide range of connections between the initiated during the workshop and are presented here in two topics, as exemplified in the work of Merkurjev, Suslin, their final form. Also included are contributions from several Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, experts who were unable to attend the workshop. None of Thomason, and lhara. As is evident from the diversity of topics the papers will be published elsewhere. During the workshop, represented in these proceedings, the seminar provided an two hours each day were devoted to seminars on current opportunity for mathematicians from both areas to initiate problems in such areas as weak Hilbert spaces, zonoids, further interactions between these two areas. analytic martingales, and operator theory, and these topics are reflected in some of the papers in the collection. 1980 Mathematics Subject Classifications: 20G35, 20E07 ISBN 0-8218-5090-3, LC 88-38151 1980 Mathematics Subject Classifications: 46-06, 46B10, 46B20, ISSN 0271-4132 46B22, 46B25 450 pages ( softcover), January 1989 ISBN 0-8218-5092-X, LC 88-38106 Individual member $28, List price $46, ISSN 0271-4132 Institutional member $37 536 pages ( softcover), January 1989 To order, please specify CONM/83NA Individual member $29, List price $48, Institutional member $38 Shipping/Handling: 1st book $2, each add'l Sl, $25 max. By To order, please specify CONM/85 NA air, 1st book $5, each add'l $3, $100 max. Prepayment Shipping/Handling: 1st book $2, each add'! $1, $25 required. Order from AMS, P.O. Box 1571, Annex Station, max. By air, 1st book $5, each add'l $3, $100 max. Providence, Rl 02901-1571, or call 800-556-7774 to use VISA Prepayment required. Order from AMS, P.O. Box or MasterCard. 1571, Annex Station, Providence, Rl 02901-1571, or call 800-556-7774 to use VISA or MasterCard . ••••••••••••••••••••••••••••••••••••••••••••••••••••

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POSITIONS AVAILABLE THE COLLEGE OF INSURANCE ST. MARY'S COLLEGE OF MARYLAND POSITION AVAILABLE ST. MARY'S CITY, MARYLAND 20686 CASE WESTERN RESERVE UNIVERSITY The Actuarial Science Department of The St. Mary's College of Maryland invites Department of Mathematics College of Insurance invites applications applications tor a one-year sabbatical and Statistics for a full time, tenure track position at the replacement in mathematics beginning rank of Assistant Professor, beginning in August 1989. The position may lead Tenure-track, possibly senior, positions September 1 , 1989. to a permanent appointment pending anticipated to begin August 15, 1989. A Ph.D. in Mathematics or a related approval of an additional line tor mathe­ Outstanding research record and/or discipline is required as is a demon­ matics/computer science. proven research potential and teach­ strated commitment to teaching excel­ St. Mary's is a four-year state­ ing excellence required. Preferred ar­ lence. Candidates in Statistics, Proba­ supported liberal arts college of about eas: statistics and probability (including bility or a field of Applied Mathematics 1400 students located 68 miles south­ applications in physics, chemistry and related to Actuarial Science are particu­ east of Washington, DC. The mathe­ computer science) but candidates in larly encouraged as are those interested matics faculty consists of five full-time areas of global analysis, dynamical sys­ in developing and pursuing a career in teachers. The program provides a gen­ tems, functional analysis, partial differ­ Actuarial Science. eral studies mathematics course tor all ential equations, and numerical analysis The College of Insurance is a pri­ students and many mathematics and will also be considered. Women and mi­ vate, selective institution located in New computer science courses tor science nority groups candidates are especially York City's Financial District. The salary and mathematics majors. We would like encouraged to apply. Visiting positions in is competitive and the fringe benefits to employ a person with a Ph.D. in math­ the above areas also possible. Send vita excellent. ematics who is interested in teaching plus three letters of recommendation to Applications will be accepted until undergraduates and willing to teach a Professor W. A. Woyczynski, Chairman, the position is filled. Send letter of wide variety of courses ranging from col­ Department of Mathematics and Statis­ application, curriculum vitae and letters lege algebra to upper-division courses tics. Case Western Reserve University, of recommendation to: S. Ramanujam, tor mathematics majors. Teaching in Cleveland, OH 44106. An affirmative ac­ Chairman, Actuarial Science Division, computer science is also possible. The tion equal opportunity employer. The College of Insurance, 101 Murray teaching load is three courses (twelve Street, New York, New York 10007. credits) per semester, and the State of Maryland provides a good package of UNIVERSITY OF OKLAHOMA EOE/AA fringe benefits. St. Mary's College is an Applications are invited for one or more AA/EOE employer. anticipated tenure or tenure-track po­ Rank and salary are open. Applica­ sitions in Mathematics beginning Fall tions will be considered until the position FLORIDA INTERNATIONAL is filled. Send letter and resume to Dr. 1989. Candidates must have a Ph.D. UNIVERSITY Paul Blanchette, Head, Division of Natu­ degree, demonstrated excellence in re­ The State University of Florida at Miami search, and potential for high-quality ral Science and Mathematics, St. Mary's teaching. Strong candidates in all ar­ The Department of Mathematics an­ College of Maryland, St. Mary's City, eas will be considered with preference nounces tenure track positions at the Maryland 20686. (301-862-0362) given to research interests compatible assistant professor level beginning Au­ with those of our current faculty. Duties gust 1989. Candidates must have a include research, normally teaching six Ph.D. in Mathematics and a commit­ GEORGIAN COURT COLLEGE hours per semester, and Departmental ment to research and quality teaching. and University service appropriate to Preferred areas of specialization include Applications are invited for position at rank. Salary and rank will be commensu­ harmonic analysis, logic, representation the assistant professor level starting rate with qualifications and experience. theory, several complex variables, and Fall 1989. Ph.D. in mathematics, alge­ There may also be visiting positions. functional analysis. Qualified candidates bra preferred, other areas considered. Applicants should send their vita and in other areas will be considered. Publications and record of successful have at least three letters of reference Teaching load consists of 15 semester college teaching essential. Applicant will sent to Dr. Darryl McCullough, Search hours per academic year. Send resume teach both graduate and undergraduate Committee Chair, Department of Math­ and 3 letters of recommendation to courses. Tenure-track; salary and fringe ematics, University of Oklahoma, 601 Recruitment Committee, Department of benefits competitive. Send letter of ap­ Elm Avenue, Norman, Oklahoma 73019. Mathematics, Florida International Uni­ plication, resume, transcripts, names, Closing dates are December 15, 1988 versity, Miami, FL 33199. addresses and telephone numbers of and every two weeks thereafter, until Florida International University is the three references to Chair, Mathemat­ the final closing on April 20, 1989. The State University of Florida at Miami. ics Department, Georgian Court College, University of Oklahoma is an Affirmative The University is an equal opportu­ Lakewood, NJ 08701. Georgian Court Action/Equal Opportunity Employer. nity /affirmative action employer. College is an EO/AA employer.

MARCH 1989, VOLUME 36, NUMBER 3 335 Classified Advertisements

POSITIONS AVAILABLE AMERICAN UNIVERSITY OF BEIRUT UNIVERSITY OF CALIFORNIA AT BERKELEY UNIVERSITY OF ALBERTA TEACHING OVERSEAS: The Depart­ Department of Mathematics Department of Mathematics ment of Mathematics at the American Berkeley, CA 94720 University of Beirut, Beirut, Lebanon TEMPORARY POSTDOCTORAL Applications are invited for a tenure-track {AUB) invites applications for faculty POSITIONS position, in Approximation Theory (File positions at the level of Assistant Pro­ Several temporary positions beginning or Associate Pro­ AP-2) at the Assistant fessor, available October 1, 1989, in in Fall 1989 are anticipated for new July 1, 1989. Re­ fessor level, beginning the following fields: Analysis, Mathemat­ and recent Ph.D.s of any age, in the a Ph.D. and proven ability quirements are ical Statistics (Probability Theory), and areas of algebra, analysis, applied math­ demonstrated potential for research or Topology. ematics, foundations, or geometry and salary range is and teaching. Current Applicants should hold the Ph.D. de­ topology. The terms of these appoint­ per annum de­ from $33,144 (Canadian) gree in mathematics and will be ex­ ments may range from one to three qualifications. Send vitae pending upon pected to engage in undergraduate and years. Applicants for NSF or other three letters of refer­ and arrange for graduate teaching, as well as research. postdoctoral fellowships are encouraged ence to be sent to: Professor L. H. Postdoctoral experience is preferred. to apply for these positions; combined Department of Mathe­ Erbe, Chairman, Appointments are normally made for teaching/research appointments may be matics, University of Alberta, Edmonton, a three-year period. Interested persons made for up to three years. Mathemati­ 2G1. In accordance with Canada, T6G should send a curriculum vitae and three cians whose research interests are close requirements, pri­ Canadian Immigration letters of recommendation by March to those of regular department members to Canadian citizens ority will be given 31, 1989 to: Dean, Faculty of Arts & will be given some preference. Send by residents of Canada. and permanent Sciences, American University of Beirut, April 1, 1989, a resume, and reprints, is April 30, Closing date for applications cjo New York Office of AUB, 850 Third preprints, and/or a dissertation abstract. quote file number when 1989. Please Avenue, 18th Floor, New York, New York Ask three people to send letters of rec­ responding to this advertisement. The 10022, USA. ommendation to Marc A. Rieffel, Vice of Alberta is committed to the University AUB is an EO/AA employer. Chair for Faculty Affairs, at the above in employment. principle of equity U.S. passports are presently invalid address. (Applications received for our for travel to, in or through Lebanon, earlier January 15, 1989, deadline will au­ and for residence in Lebanon, by order tomatically be considered for this dead­ THE CITADEL of the Department of State, and there­ line also.) The University of California is fore applications from individuals who an Equal Opportunity 1Affirmative Action Applications are invited for a tenure track would travel to reside in Lebanon on Employer. position at the assistant or associate a U.S. passport cannot at this time be level. Qualifications include a Ph.D. in considered. a mathematical science with a strong AUGUSTANA COLLEGE dedication to undergraduate teaching MATHEMATICS: Augustana College and a continuing interest in research. (South Dakota) invites applications for Preference will be given to individuals VIRGINIA TECH an Assistant Professor of Mathemat­ in applied or computational areas of ics. Two year appointment with possible The Department of Mathematics is ac­ mathematics. Salary negotiable. conversion to tenure track. Teach under­ tively seeking applications in the area The Citadel is a state-supported lib­ graduate mathematics courses, lower of computational mathematics and nu­ eral arts, military college offering under­ and upper division courses and involve­ merical analysis. We anticipate making graduate degrees in the Arts, Sciences, ment in student research projects. Exact several tenure-track appointments at the Engineering, Education, and Business assignment will depend on qualifications. assistant professor level or above be­ Administration. The Department of Math­ Ph.D. in Mathematics, or ABD preferred. ginning in the fall of 1989. A Ph.D. is ematics and Computer Science offer the Masters degree required. A commitment required. Applications will be reviewed B.S. and B.A. degrees in mathematics to the mission of a church-related lib­ as they are received and will be accepted and a B.S. degree in computer science. eral arts college expected. Preference until the positions are filled. A formal let­ Please send resume and three letters of given to applications received prior to ter of application expressing interest, a reference to Charles E. Cleaver, Head April 1 , 1989. Send letter of application, resume, and the names, addresses, and Department of Mathematics/Computer vita, complete graduate transcripts (di­ telephone numbers of three references Science, The Citadel, Charleston, S.C. rect from registrar's office), names, tele­ should be sent to Chairman, Numerical 29409. Review of applications will begin phone numbers, an identities of at least Analysis Search Committee, Department April 15 and continue until position is three current references, and a state­ of Mathematics, Virginia Tech, Blacks­ filled. ment of personal and professional goals burg, VA 24061-0123. Virginia Tech is Minorities and women are encour­ to: Jeanne Kruse, Administrative Assis­ an Equal Opportunity1 Affirmative Action aged to apply. The Citadel is an equal tant, Augustana College, Sioux Falls, SD Employer. opportunity I affirmative action employer. 57197. EOE/AA employer.

336 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE Jean B. Schaake, Chair; TAMS Search THE UNIVERSITY OF TOLEDO Committee, College of Arts and Sci­ DEAN UNIVERSITY OF NORTH TEXAS ences, University of North Texas, P.O. College of Arts and Sciences DIRECTOR Box 5187, Denton, Texas 76203. TEXAS ACADEMY OF The College of Arts and Sciences at The Review of applications will begin April MATHEMATICS AND SCIENCE University of Toledo seeks a new dean. the position 1 , 1989, and continue until The college enrolls 5,224 students in 19 The University of North Texas invites is filled. departments and offers seven doctoral nominations and applications for the po­ The University of North Texas is programs. The University of Toledo is Opportunity sition of director of the Texas Academy an Affirmative Action/Equal the fourth largest public university in of Mathematics and Science to begin Employer. Ohio with a total enrollment of 22,086 August 1, 1989. in 8 colleges with 21 doctoral programs, The Texas Legislature established including the J.D. and Pharm.D. It is the Texas Academy of Mathematics and a member of the National Association Science in 1988 within the University of of State Universities and Land Grant North Texas in Denton. The Academy is a Colleges. two-year, public, coeducational, tuition­ Candidates should have an earned free institution which functions as an Ph.D. in one of the disciplines in the col­ early admission program for Texas high UNIVERSITY OF OKLAHOMA lege, substantial teaching and research school students who are particularly CHAIRPERSON experience. They should be prepared to talented in science and mathematics. DEPARTMENT OF MATHEMATICS lead the college to continued growth in A maximum of 200 students who the quality of instruction and the volume Nominations and applications are in­ have completed the tenth grade can be of research. vited for the position of Chairperson in accepted on a competitive basis each Salary is negotiable. The position is the Department of Mathematics effective year. The curriculum consists of fresh­ available on July 1, 1989. Nominations Fall, 1989. Candidates must possess an man and sophomore university courses and applications should be sent to: earned doctorate, a substantial record taught by full-time University of North Dr. William N. Free of research achievement, a commitment Texas faculty and provides the students Vice President for Academic to excellence in teaching, and leadership with a rigorous program in science and Affairs and administrative abilities appropriate mathematics and innovative study in the THE UNIVERSITY OF TOLEDO to a growing department that is dedi­ humanities. Graduates receive a high Toledo, OH 43606 cated to a balanced program of quality school diploma as well as two years The University of Toledo is an Equal Op­ research and teaching. The Mathemat­ of university credits. The Academy stu­ portunity I Affirmative Action Employer. dents are in residence at the University ics Department has over thirty faculty of North Texas campus. The University members, most of whom are actively in­ of North Texas is an emerging na­ volved in research, and offers programs UNIVERSITY OF CALIFORNIA tional research institution in the vibrant for the bachelors, masters, and Ph.D. DEPARTMENT OF MATHEMATICS and rapidly expanding Dallas-Fort Worth degrees. There is also an extensive pro­ RIVERSIDE, CALIFORNIA metropolitan area with over 700 regular gram of scientific activity supplemented Applications are invited for temporary faculty and over 24,000 students. by a substantial endowment for discre­ faculty positions beginning in Septem­ Applicants should hold a Ph.D. prefer­ tionary funds. Candidates should send a ber 1989. These positions are funded ably in science or mathematics, have cover letter, vita, selected reprints, and at the Assistant Professor level, but earned tenure at the University level, arrange to have four letters of reference there is some slight flexibility in salary. and be willing to give long-term com­ (including at least one concerning ad­ They are open to applicants from all mitment to working with talented young ministrative abilities) sent to: Dr. Kevin research areas within Mathematics and freshmen. The duties of the director will Grasse, Chair Search Committee, De­ Computer Science with significant ac­ include student recruitment, resource de­ partment of Mathematics, 602 Elm-Phsc complishments or high potential in both velopment and fund raising, working with 423, Norman, Oklahoma 73019. Phone research and teaching. constituents external to the university­ 405-325-2903. Candidates should send a vita and local, state and national, overall curricu­ Closing dates for applications are arrange for at least three letters of rec­ lum development and the general di­ March 15, 1989, and every two weeks ommendation to be sent to: John de rection and leadership of the Academy. thereafter until either the position is Pillis, Chair, Search Committee, Depart­ Salary will be on a 12-month basis and filled or the final closing date of June ment of Mathematics and Computer Sci­ will be commensurate with qualifications 1, 1989. The University of Oklahoma is ence, University of California, Riverside, and experience. Applications should in­ an Affirmative Action/Equal Opportunity CA 92521. The University of California is clude a letter of interest, resume, and the Employer. an Equal Opportunity 1Affirmative Action names, addresses and phone numbers Employer. of three to five references to:

MARCH 1989, VOLUME 36, NUMBER 3 337 Classified Advertisements

POSITIONS AVAILABLE UNIVERSITY OF POSTE EN MATHEMATIQUES WISCONSIN-MADISON APPLIQUES THE CATHOLIC UNIVERSITY OF Department of Mathematics AMERICA Position in Mathematics Le Department de mathematiques et Mathematics Department Extension and Outreach de statistique sollicite des candida­ Washington, DC 20064 tures pour un poste de professeur en Applications are solicited for a tenure­ mathematiques appliquees. Les taches Several Assistant Professor positions are track position directing and teaching in principales sont: subject to final budgetary ap­ expected the extension and outreach program -Professeur au Departement de mathe­ All are tenure track with salary proval. in mathematics at the University of matiques et de statistique; to $30,000 for 8.5 month to $27,000 Wisconsin-Madison beginning July 1, -Enseignement aux trois cycles et en­ teach undergrad. and grad. courses in 1989. The appointment will be as an cadrement d'etudiants; 3 courses per semester Mathematics assistant professor in the Department -Recherche et direction d'etudiants des starting 9-1-89. Requirements: Ph.D. in of Mathematics unless qualifications and 2e et 3e cycles; with good research poten­ Mathematics experience require appointment at a -Participation au fonctionnement gemeral and dedication to teaching. All areas tial higher rank. The responsibilities of the du Departement. of mathematics are of interest. Send re­ position include administration and de­ Critere de selection: graduate transcripts, and letters of sume, velopment of and teaching in programs -Le candid at devra posseder un doctorat to: Dr. P. Saworotnow, recommendation of the Division of University Outreach en mathematiques ou dans une discipline Committee Chairman, Mathemat­ Search and a limited amount of teaching in connexe, avec une orientation marquee ics Department, CUA, tel. 202-635-5222. the Department of Mathematics. The en mathematiques appliquees. April 7, 1989, or until positions Dealine: outreach programs include correspon­ -L'aptitude du candidat a developper are filled. dence study and noncredit continuing­ de nouveaux axes de recherche ou a is an AA/EO employer. Applica­ CUA education courses which have a large s'integrer aux secteurs forts deja ex­ women and minority group tions from audience throughout the state at both istants (analyse numerique, mecanique members are encouraged. the high school and university levels. The des milieux continus, optimisation) sera new faculty member will have the chal­ consideree comme un atout majeur lenge of developing continuing and pro­ tout comme un interet marque pour THE WITCHITA STATE UNIVERSITY fessional education programs designed le recherche pluridisciplinaire. Wichita, KS 67208 to introduce new developments in the -Le candidat devra etre apte a dis­ pub­ Professor Stephen W. Brady, Search mathematical sciences to the broad penser, en langue fran<;:aise, des cours Committee Chairman Department of lic at all career levels. s'adressant a une clientele variee com­ Mathematics and Statistics To assure full consideration all materi­ posse, non seulement d'etudiants en 1, 1989. Assistant Professor tenure eligible po­ als should be received by March mathematiques mais aussi d'etudiants from sition starting August 1989. Specializa­ Application forms are available d'autres secteurs des sciences et du tion in Complex Analysis and Several Mathematics Extension Search Commit­ genie. Complex Variables will be given spe­ tee, Mathematics Department, 223 Van Conformement aux exigences rela­ cial consideration. All areas of Applied Vleck Hall, 480 Lincoln Drive, Madison, tives a !'immigration au Canada, cet avis Mathematics will be considered. A Ph.D. WI 53706. de concours s'adresse en premier lieu in Mathematics is required. Candidate The University of Wisconsin-Madison aux citoyen(ne)s canadien(ne)s et aux is expected to be active in research, is an Equal Opportunity I Affirmative Ac­ resident(e)s permanent(e)s du Canada. participate in the doctoral program, and tion Employer. Un curriculum vitae doit parvenir avant have a strong interest in teaching. Salary Note: The Immigration Reform and Con­ le ler mai a l'adresse suivante: competitive. Send application letter, de­ trol Act of 1986 requires the University to Robert Cote, Directeur tailed resume, and arrange to have three verify the identity and work authorization Department de mathematiques reference letters sent. Deadline March of the successful applicant. Offer of em­ et de statistique 15, 1989, then monthly until position is ployment is contingent upon verification. Faculte des sciences et de genie filled. The Wichita State University is Pavilion Alexandre Vachon an Equal Opportunity I Affirmative Action Universite Laval, Quebec Employer. G1K 7P4

338 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE cations representing the candidates re­ UNIVERSITY OF BRISTOL search expertise) to the Dean of the England JOHANNES KEPLER UNIVERSITY School of Technical Sciences, Prof. Dr. Full Professor Underthe New Academic Appointments Tenured Position of a Peter WeiB, Johannes Kepler Univer­ for Symbolic Computation Scheme the University expects to ap­ sity, A4040 Linz (Austria). (Telephone at the Johannes Kepler point a Professor of Pure Mathematics Austria (732) 2468-312), by March 31, University in Linz (Austria) in the Department of Mathematics from 1989. Futher information can also be ob­ (Research Institute for 1 August 1989 or as soon as possible tained from the Chairman of RISC-LINZ, Symbolic Computation) thereafter. Suitable candidates will be Prof. Dr. Bruno Buchberger, Johannes considered from any area of pure math­ Applications are invited for a newly cre­ Kepler University, A4040 Linz. (Tel: Aus­ ematics. The successful candidate will ated tenured position of a full professor tria (732) 2468-9219. Electronic mail: be expected to provide academic lead­ at the School of Technical Sciences, [email protected].) Johannes Kepler University in Linz, Aus­ ership in both teaching and research. tria. Candidates should have an out­ It is intended that further expansion in standing research record in at least one the general research area of the new of the main areas of symbolic com­ professor will take place after the ap­ putation (computer algebra, computer pointment. NATIONAL ACADEMY OF SCIENCES Applications, including a curriculum analysis, computational geometry, com­ BOARD ON vitae and the names and addresses of putational logic, automatic programming MATHEMATICAL SCIENCES referees, should be sent, to arrive etc.), a commitment to excellence in Senior Program Officer three graduate teaching, and the ability and not later than 24 March 1989 to the Reg­ willingness to combine, in their field The BOARD ON MATHEMATICAL SCI­ istrar (for the attention of Nesta Babb), of expertise, mathematical/algorithmic ENCES is preparing a project to up­ Senate House, University of Bristol, Bris­ foundations with potential industrial ap­ date the 1984 David Report, ··Reviewing tol BS8 HH, UK, quoting Ref 0188/ A. plications (for example, expert systems, U.S. Mathematics: Critical Resource for Further particulars can be obtained by geometrical modeling, robot program­ the Future:· for the National Science Tel: 010-44-272 303030 or FAX: (0272) ming, scientific software). Teaching and Foundation. The update will analyze the 251424. For informal enquires, telephone supervising of students may also be in current state of support for research in Prof D V Evans on 01 0-44-272-303532. English. Candidates from foreign coun­ the mathematical sciences and assess tries are explicitly encouraged. progress against the recommendations The School of Technical Sciences of the original David Report. It will go THE UNIVERSITY OF ALABAMA has installed an independent institute further to briefly scientifically assess the SENIOR POSITION for symbolic computation (RISC-LINZ, field and identify promising opportunities The department anticipates filling a se­ Research Institute for Symbolic Compu­ for interdisciplinary research. nior level position (Full Professor or, tation) with an 8 member faculty under Incumbent will be responsible for or­ possibly, senior Associate Professor), the direction of Prof. Bruno Buchberger. ganizing and supporting the work of the to begin August 16, 1989. Applications RISC-LINZ operates in close interac­ committee, chaired by Dr. Edward E. are invited from mathematicians whose tion with the Department of Computer David, Jr., former presidential science credentials demonstrate excellence in Science (a twenty-six member faculty) advisor. Requires excellent organiza­ both teaching and research and an abil­ and the Department of Mathematics (a tional, writing, and interpersonal skills ity to provide programmatic leadership. twenty-two member faculty). and familiarity with mathematical sci­ Areas of special interest are: algebra, At Johannes Kepler University, the ences research and issues. A Ph.D. or analysis, continuum mechanics, compu­ symbolic computation effort is a part of equivalent experience in a mathemat­ tational mathematics, differential equa­ and a major driving force for a planned ical science is required. The National tions, differential geometry, optimization, expansion (by 10 full professorships) of Research Council is an Equal Opportu­ stochastic modeling, and toplogy. In the the School of Technical Science in the nity I Affirmative Action Employer. event that a permanent appointment is direction of ··mechatronics·· (intelligent The closing date is March 15, but not made, we also invite applications control of technical production) in close applications will be accepted until a from visitors. Women and minorities are cooperation with Austrian industry. suitable candidate is identified. Please particularly encouraged to apply. Send The new site of RISC-LINZ, a med­ submit a resume or cv with salary history a curriculum vitae, a sample of re­ ieval castle 15 minutes from Linz, equip­ and the names of three references to: cent reprints and/or preprints, and the ped with excellent computing facilities, NATIONAL RESEARCH COUNCIL names of at least three references to: combines the advantages of city life with Board on Math Sciences Professor Alan Hopenwasser, Depart­ the pleasures of a rural environment in NAS 312 (LC) ment of Mathematics, The University of one of the most beautiful landscapes 2101 Constitution Ave., N.W. Alabama, Box 870350, Tuscaloosa, AL and in the cultural heart of Austria and Washington, DC 20418 35487-0350. The University of Alabama Europe. EOE is an Equal Opportunity Employer. Applicants should send a resume (together with a few important publi-

MARCH 1989, VOLUME 36, NUMBER 3 339 Classified Advertisements

AVAILABLE POSITIONS FAIRFIELD UNIVERSITY The Foundations of Mathematics Based Upon a Cosmological Constant UNIVERSITY OF The Department invites applications for New to Natural Science WISCONSIN-SUPERIOR a tenure track position at the Assistant By John Lawrence Waters Mathematical Sciences Professorship level beginning in Sept. Superior, WI 54880 1989. The normal teaching load is 3 ABSTRACT process yields courses a semester with some research Analysis of the counting One tenure track position in Mathemat­ formula for the natural expected. A Ph.D. in Mathematics is re­ the equilibration ics beginning September 1989. A Ph.D. author introduces a two di­ quired with teaching competence in Nu­ unity. The in a Mathematical Science is required. model for unity which merical analysis or Statistics desirable. mensional dynamic Excellence in teaching and continuing static segment of Fairfield is a Jesuit University located replaces the traditional scholarly activity is expected. All areas The author constructs on the Connecticut coast 60 minutes the number line. considered but preference given to ar­ model for nat­ from New York City. For full consid­ the correct mathematical eas of analysis or operations research. eration, send curriculum vitae and 3 ural space. A Computer Science Option is offered analysis of verbaliza­ letters of reference to Joseph B. Den­ Mathematical within the department. Computer expe­ spontaneous activity nin, Chair, Department of Mathematics tion, counting and rience is desirable. Rank and salary are human sub­ and Computer Science, Fairfield Univer­ in autistic and non-autistic negotiable/competitive. Applications will product of two radius sity, Fairfield, CT 06430-7524. Fairfield is jects leads to the be accepted until March 15, 1989, or ite directions an Equal Opportunity1 Affirmative Action vectors spinning in oppos until a successful candidate is found. a vibrational energy Employer. by the power of Submit a formal letter of application ex­ "'omega·· of constant frequency. Re­ pressing interest, a resume, and arrange peated testing suggests this model is for three letters of recommendation to valid. be sent to Dr. Ronald Roubal, Division of For a copy of this paper, send eight Sciences and Mathematics, University of U.S. dollar;s~to: John Waters POB 706, Wisconsin-Superior, Superior, WI 54880. Trinidad, CA 95570-0706 U.S.A. No per­ AA/EO Employer. sonal checks. Foreign currency OK.

PUBLICATIONS

NEW PUBLICATION

The Red Book: 100 Practice Prob­ lems for Undergraduate Mathematics UNIVERSITY OF IOWA and IOWA CITY, IOWA 52242 Competitions, compiled with hints solutions by Kenneth S. Williams and Mathematics of the The Department of Kenneth Hardy. Gerhard Renner, Bookseller University of Iowa invites applications Copies of The Red Book and its ear­ PO Box 1648 for at least one tenure-track position, lier companion The Green Book available D-7470 ALBSTADT-2 FRGermany beginning August, 1989. All levels will at $20 per copy from: be considered. Priority will be given to Integer Press, P.O. Box 6613, Station J, As a bookseller of old and new books candidates whose presence would com­ Ottawa, Ontario, Canada. K2A 3Y7 specializing in MATHEMATICS I shall be plement or strengthen existing research delighted to send catalogues on request groups or who specialize in harmonic free: or stochastic analysis. Applicants should Catalogue 66: Livres de Mathemati­ send a vita and have three letters of ques Frangais du 189 au 209 siecle 2085 recommendation sent to: William A. Kirk, items includ. Libri Matematici ltaliani Chair, Department of Mathematics, Uni­ Catalogue 67: MATHEMATICS includ. versity of Iowa, Iowa City, Iowa 52242. Philosophy and History of Science, By making this appointment the de­ Physics, Astronomy, Computer Science. partment hopes to attain diversity on MATH SCI PRESS, 53 Jordan Rd., About 3000 books and journals from the the faculty. Minority and women can­ Brookline, MA 02146, 617-738-0307. 16th to 20th cent. in German, English didates are especially urged to apply. TOPICS IN PHYSICAL GEOMETRY, by and other languages. The University of Iowa is an Affirmative R. Hermann. $80. Sale on selected back I am always purchasing mathematical Action/Equal Opportunity Employer. list titles. books and collections.

340 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

FOR SALE SITUATIONS WANTED

WYSIWYG for Macintosh. DISTINGUISHED RESEARCH AND Mathematical TEACHING MATHEMATICIAN With SCIPAGE, type, reposition, re­ Research wide experience in pure shape: complex fractions, roots, inte­ Exceptionally Combine a self-directed grals, matrices, frames and grids,. .. and applied mathematics (algebraic program of mathematical Anywhere on a page! Ideal for lecture topology, algebra, differential geometry, research with participation notes, exams, ... $40 postpaid. Write for analysis, POE's, mathematical physics, in team-oriented, interdis­ samples. METAMATH, Box 26, Chris­ dynamic meteorology), over 90 publica­ ciplinary R&D projects by tiana, PA 17509. tions, seeks teaching/research position, joining MITRE's Signal preferably involving Ph.D. supe.~Wsion. Processing and Mathemat­ Details upon request. Write to:( "~pli­ ical Research Group. cant Code 123, Advertising Department, CLIFFORD ALGEBRA MICRO-COMPU­ AMS. P.O. Box 6248, Providence, Rl Members of the group TER PACKAGE for IBM PC. CLICAL, 02940. have diverse research in algebra, analy­ Clifford algebra calculator program can interests sis, combinatorics, com­ for teaching or research in be used puting theory, and geome­ complex number, vector and Clifford try. Ongoing R&D projects Mathematics seek­ algebra calculations. CLICAL for single Doctorate in Applied involve signal processing, personal use $20; 13 copies for local ing assistant professorship, one publi­ communications, radar, department use $95. Order from: cation in Computer and Mathematics, concurrent processing, Pertti Lounesto 5 years teaching assistant experience, neural networks, and Institute of Mathematics won a teaching award, available now, VLSI design. Helsinki University of Technology resume upon request phone: (412) 361- SF-02150 Espoo, Finland 5338 Mathematicians in all areas of specialization are invited to apply. Qualifica­ tions include a Ph.D. or equivalent in mathematics, superior research ability in a chosen field, and a broad MEMOIRS background in many fields of the of mathematics. Practical American Mathematical Society knowledge of Fourier anal­ ysis, probability, numerical No. 388 analysis, or statistics would be helpful but is not TOPOLOGICAL INVARIANTS necessary. U.S. citizen­ ship is required. OF QUASI-ORDINARY To apply submit a curric­ SINGULARITIES ulum vitae to: Signal by Joseph Lipman Processing and Mathe­ matical Research Group, E025, The MITRE Corpo­ EMBEDDED TOPOLOGICAL ration, Burlington Rd., Bedford, MA 01730. CLASSIFICATION OF QUASI­ To apply for positions in ORDINARY SINGULARITIES the Washington DC area, by Yih-Nan Gau write to M.X. Mason, The MITRE Corporation, 7525 Colshire Drive, is dedicated to the memory of PETER SCHERK. Mclean, VA 22102. We regret that this dedication was inadvertently An Equal Opportunity Employer omitted from the book. American Mathematical Society MITRE

MARCH 1989, VOLUME 36, NUMBER 3 341 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 over 9600 pages, it is an important addition to any mathematics library and is now available at further discount to individual AMS members and reviewers of MR.

With this set of indexes at hand, readers can:

• access fully, by both author and subject area, the mathematical literature of five years, 1980 through 1984

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

• obtain information about approximately 8000 additional items that were not reviewed individually, but which are fully classified and cross-referenced in these indexes

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

• access, via a key index, all those publications that do not have named authors or editors

•locate, under each subject index heading, all items having this classification as either a primary or a secondary classification

ISBN 0-8218-0105-08, LC 42-4221 12 volumes, 9653 pages; 1986 List $1875, Inst. mem. $1500, Indiv. mem. $1125, Rev. $938 To order, please specify MREVINI80I84NA

Combination offer. A special price is offered when the Author and Subject Indexes ofMathe­ matical Reviews, 1980-84 (MREVIN I 80I 84) is purchased together with the Author and Subject Indexes ofMathematical Reviews, 1973-79 (MREVINI73I79). List $2950, Inst. mem. $2360, Indiv. mem. $1770, Rev. $1475 To order, please specify MRCINI73I84NA

Prepayment required. Order from the American Mathematical Society, Annex Station, P. 0. Box 1571, Providence, RI 02901-1571 or cal1401-272-9500 (800-556-7774 from within the continental U. S.) to use VISA or MasterCard. a conference on Computers& Mathematics

June 13-17, 1989, MIT, Cambridge, Mass

A conference focusing on the relationship of computers to research and education in the mathematical sciences SPECIAL EVENTS The conference will serve as a forum for the Scientific Visualization: Lecture and Video Program interaction between developers of computer-related Maxine Brown (Illinois) tools for mathematics and those interested in their use. Computer Art, Music, and Video Show Carol Chiani (NYC/SIGGRAPH), Producer Wine and Demo Buffet (The Computer Museum) KEYNOTE ADDRESS Demos of mathematical software Sir Peter Swinnerton-Dyer (Cambridge) Boston Schools Computer Contest Awards

INVITED TALKS TUTORIAL MINICOURSES Computers & Mathematical Education Comp. Graphics & Diff. Geometry in 2-, 3-. & 4-Space Judah Schwartz (Harvard). Dennis Stanton (Minnesota) Thomas Banchoff (Brown) Computers & Physics Groebner Bases: Foundation for Constructive Algebra Rodney J. Baxter (Aust. Nat. Univ), Alan H. Guth (MIT), Lorenzo Robbiano (Genoa) Michael J. Creutz (Brookhaven), Richard H. Miller (Chicago) The Regrettable Failure of Automated Error Analysis Mathematics & Supercomputing William M. Kahan (Berkeley) David V. & Gregory V. Chudnovsky (Columbia), Monty M. Computers in Undergraduate Mathematics Denneau (IBM Research), Joseph W. Goodman (Stanford) Stanley Devitt (Saskatchewan), Michael Henle (Oberlin) Computers & New Directions in Mathematics Symbolic Integration is Algorithmic! George Andrews (Penn State). Peter Borwein (Dalhousie). Manuel Bronstein (IBM Research), James H. Davenport Alexandre Chorin (Berkeley), R. William Gosper (Bath), Barry M. Trager (IBM Research) Mathematics & Computer Graphics An Introduction to Computational Group Theory George K. Francis (Illinois). Michael F. Barnsley (Georgia John Cannon (Sydney), Gregory Butler (Sydney) Tech), Donna Cox (Illinois), Alvey Ray Smith (Pixar, Inc) The HP-28S: A Bridge Between Theory & Applications Computers & Combinatorics Yves Nievergelt (E. Washington) J. H. Conway (Princeton), N.J. A. Sloane (AT&T The Science of Fractal Images Bell Labs), Andrew Odlyzko (AT&T Bell Labs), Heinz-Otto Peitgen (Bremen), Richard F. Voss (IBM) Herbert S. Wilt (Pennsylvania)

DEMONSTRATIONS EXHIBITS CAYLEY (Sydney), DELIA (Acad. Sciences, USSR) Products relating to Research and Education Derive (Soft WareHouse), MACSYMA (Symbolics) Institution-based Research Projects Macaulay (Columbia), Maple (Waterloo), Computer Mathematics Classrooms Mathematica (Wolfram Research). Milo (Paracomp), Boston Schools Computer Competition Winners REDUCE (RAND Corp.), Scratchpad (IBM Research) Publishers

For registration and campus housing forms, contact: Heather A. Schmidt, Conference Secretary Computers & Mathematics 1989 62 Eastview, Pleasantville, New York 10570 CSNET: cm89 at ibm.com; BITNET: cm89 at yktvmz Telephone: (914) 769-2725 Editor Games and Ehud Kalai Northwestern University, Evanston, Illinois

Economic Games and Economic Behavior publishes original and survey papers dealing with game-theoretic model­ Behavior ing in the social, biological, and mathematical sciences. Papers published are mathematically rigorous as well as accessible to readers in related fields. The purpose of the journal is to facilitate cross-fertilization between the theory and application of game-theoretic reasoning.

Managing Editor IMPACT of Peter Deuflhard computing in Konrad Zuse Center, Berlin, Federal Republic of Germany IMPACT of Computing in Science and Engineering focuses on articles from the areas of mathematical and Science and scientific modeling, scientific computing, computer science, and scientific and engineering applications. The journal is interdisciplinary. Its papers will touch Engineering upon a combination of at least two of the four main areas-with the exception of the combination of model­ ing and applications, for which other journals may be more appropriate. Articles typically will describe real­ life problems attacked by a new or specifically adapted algorithm or by any other new computing technique.

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NUMBER THEORY, TRACE INITIAL-BOUNDARY VERTEX OPERATOR FORMULAS AND VALUE PROBLEMS ALGEBRAS AND THE DISCRETE GROUPS Heinz-Otto Kreiss and MONSTER Symposium in Honor of Atle Jens Lorenz Igor B. Frenkel, James Lepowsky, Selberg, Oslo, Norway, July This book provides a systematic and Arne Meurman 14-21, 1987 treatment of time dependent partial This book is motivated by and de­ edited by differential equations of parabolic, velops connections between several Karl Egil Aubert, Enrico Bombieri, hyperbolic or mixed type. Written for branches of mathematics and phys­ and Dorian Goldfeld graduate students and researchers ics-the theories of Lie algebras, fi­ in mathematics and engineering, the nite groups and modular functions One of the most powerful mathe­ book covers the theory of an impor­ maticians of this century, Atle in mathematics, and string theory in tant class of evolutionary systems physics. The first part of the book Selberg has almost single handedly and provides background material changed the course of modem ana­ presents a new mathematical theory for their numerical treatment. The of vertex operator algebras, the alge­ lytic number theory. This volume Navier-Stokes equations of fluid dy­ contains the proceedings of an inter­ braic counterpart of two-dimen­ namics-compressible and incom­ sional holomorphic conformal quan­ national conference that was held in pressible-serve as an important ex­ honor of his 70th birthday in Oslo, tum field theory. The remaining part ample to illustrate the results. Con­ constructs the Monster finite simple July 14-21. 1987. The aim of the structive methods (difference conference was to survey Selberg's group as the automorphism group of schemes, iterations) are used a very special vertex operator alge­ principle contributions to mathe­ throughout the text to show the ex­ bra, called the "moonshine module" matics in the areas of prime number istence of solutions. theory and zeta functions, sieve because of its relevance to "mon­ strous moonshine." methods, trace formulas and dis­ March 1989, c. 400 pages crete groups, and also to focus on $49.50 (tentative) March 1989, 512 pages, $69.95 their most recent development. The ISBN: 0- 12-426125-6 ISBN: 0-12-267065-5 nine survey papers can serve as a graduate-level introduction to the field. ALGEBRAIC ANALYSIS REPRESENTATIONS OF Papers Dedicated to February 1989, c. 536 pages FINITE GROUPS Professor Mikio Sato on the $69.95 (tentative) Hirosi Nagao and Yukio Tsushima ISBN: 0-12-067570-6 Occasion of His Sixtieth Birthday This book is a self-contained expo­ Volumes I and II sition of the general theory of ordi­ edited by nary and modular representations of INFINITE CROSSED Masaki Kashiwara and finite groups, including some recent Takahiro Kawai results. It provides sufficient prepa­ PRODUCTS ration for reading recent research Donald Passman This is a collection of very high articles on this subject. The authors level research papers in the area of have kept their explanations as Crossed products are another analysis and mathematical physics comprehensive as possible by only meeting place for group theory and edited by two outstanding Japanese assuming familiarity with the basic ring theory. Historically, they first mathematicians on the occasion and undergraduate algebra and some occurred in the study of finite di­ in honor of Professor Mikio Sato's Galois theory. mensional division algebras and 60th birthday. central simple algebras. More re­ April 1989, c. 448 pages cently, they have become closely re­ Volume I $59.50 (tentative) lated to the study of infinite group February 1989, 494 pages, $59.95 ISBN: 0-12-513660-9 algebras, group-graded rings, and ISBN: 0-12-400465-2 the Galois theory of noncommuta­ Volume II tive rings. This book is mainly con­ March 1989. 504 pages, $59.95 cerned with these newer develop­ ISBN: 0-12-400466-0 ments. January 1989, c. 483 pages $54.50/ISBN: 0-12-546390-1

ACADEMIC PRESS L ______Harcourt Brace •Jovanovich, Publisher·s..______...... Book Marketing Department #35039, 1250 Sixth Avenue, San Diego, CA 92101 © 1989 by Academic Press, Inc. All Rights Reserved. CALL TOLL FREE X•80G-~:ZX•SO.. Prices subject to change without notice. CB/ES #35039. Michel Herve Analyticity in Infinite Dimensional Spaces 1989. VIII, 206 pages. 17 x 24 em. Cloth US $64.95 ISBN 0-89925-205-2 (de Gruyter Studies in Mathematics, Volume 10)

In recent years, infinite dimensional holomorphy has been the object of intensive research, both in its own right and because of the often unexpected, nontrivial applications to other areas such as, for instance, potential theory and quantum field theory. Much of the impetus for the study of holomorphic functions in infinite dimensions has been provided by the investigation of topological properties of spaces of such mappings. The aim ofth!s book is to pre­ sent the analytic aspects of the theory in its setting of complex analysis in locally convex spaces. The exposition is en­ tirely self-contained and links together the beautiful results obtained in the last twenty years mainly by Creure, Dineen, Lelong, Vigue, but also by Kiselman, Nguyen, Noverraz, Siciak, Vesentini, and others.

Group Theory Proceedings of the Singapore Group Theory Conference held at the National University of Singapore, June 8-19, 1987 Edited by K. N. CHENG andY. K. LEONG 1989. XVIII, 586 pages. 17 x 24 em. Cloth US $94.00 ISBN 0-89925-406-3 This volume contains thirty-nine selected articles based on short lecture courses and talks presented at the conference by leading experts in the field. Both survey and original research articles cover a wide spectrum of modern group theory and related areas, ranging from finite simple groups, Galois realizations for certain finite groups, Burnside­ type problems, locally finite groups, cohomological methods in infinite groups to combinatorial and computational aspects of the theory.

Contents: Workshop Lectures. 0. H. Kegel: Four lectures on Sylow theory in locally finite groups· D. J. S. Robinson: Cohomology in infinite group theory. Invited Lectures. S. L Adian, A. A. Razborov, N. N. Rep in: Upper and lower bounds for nil potency classes ofLie algebras with Engel conditions · R. D. Blyth, D. J. S. Robinson: Recent progress on rewritability in groups· W. Feit: Some finite groups with nontrivial centers which are Galois groups· B. Hartley: Actions on lower central factors of free groups· G. Higman: Some countably free groups· N. Ito: Automorphism groups ofDRADs ·A. L Kostrikin: Invariant lattices in Lie algebras and their automorphism groups · B. H. Neumann: Yet more on finite groups wit.h few defining relations· M. Suzuki: Elementary proof of the simplicity of sporadic groups · J. G. Thompson: Fricke, free groups and SL2 • J. G. Thompson: Heeke operators and noncongruence subgroups. Contributed Papers. B. Amberg, S. Franciosi, F. de Giovanni: Soluble groups which are the product of a nilpotent and a polycyclic subgroup · S. Bachmuth, H. Y. Mochizuki: The tame range of automorphism groups and GLn ·A. J. Berrick: Universal groups, binate groups and acyclicity ·A. K. Bhandari, LB. S. Passi: Residual solvability of the unit groups of group algebras · C. J. B. Brookes: Stabilisers of injective modules over nilpotent groups · R. A. Bryce, J. Cossey, E. A. Ormerod: Fitting classes after Dark · C. M. Campbell, E. F. Robertson, R. M. Thomas: On groups related to Fibonacci groups· H. Cardenas, E. Lluis: On the Chern classes of representations of the symmetric groups· L. P. Comerford, Jr., C. C. Edmunds: Solutions of equations in free groups· Y. Fan: Block covers and module covers of finite groups· A.M. Gaglione, H. V. Waldinger: A theorem in the commutator calculus · etc. Appendices. List of participants · List of lectures.

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PROGRESS IN MATHEMATICS MONOGRAPHS IN MATHEMATICS Riemannian Foliations Singularities of Differentiable Maps, Vol. I Pierre MoliHo The Classification of critical points, caustics and wave fronts This book presents the first elementary exposition of basic V.I. Arnold, A.N. VarcheHko, S.M. GuseiH-Zade results in Riemannian foliations obtained in the last ten years. 19841372 pages I 0-8176-3187-91$44.951 MMA. Vol. 82 Jan. 88 1360 pages I 0-8176-3370-71$44.00 I PM, Vol. 73 Singularities of Differentiable Maps, Vol. II Andreotti-Grauert Theory by Integral Formulas Monodromy and Asymptotic Integrals GeHHadi HeHkiH aHd ]urgeH Leiterer V.I. Arnold, S.M. GuseiH-Zade, A.N. VarcheHko In the last twenty years, integral representation formulas for Nov. 88I400pagesl 0-8176-3185-21$95.001 MMA. Vol. 83 solutions of the Cauchy-Riemann equation have had an important influence on the theory of functions of several complex variables. This monograph develops the Andreotti­ OTHER NEW TITLES IN MATHEMATICS Grauert theory, i.e. the theory of the Dolbeault cohomology of q-convex and q-concave manifolds, from this standpoint A History of Algebraic and Differential Topology: Oct. 88 1272 pages I o-8176-3413-41 $44.90 I PM, Vol. 74 1900-1960 Seminaire de Theorie des Nombres, Paris 1986-87 ]eaH DieudoHHe CatheriHe GoldsteiH, ed. Written by a world-renowned mathematician, this book traces the history of algebraic topology beginning with its Nov. 88 1480 pages I 0-8176-3414-21 $49.00 I PM, Vol. 75 creation by Henri Poincare in 1900, and describing in detail Enriques Surfaces I the important ideas introduced in the theory before 1960. FraHcoise Cossec aHd Igor Dolgachev Feb. 891 approx. 672 pages I 0-8176-3388-x I $79.00 Enriques surfaces are key examples of the classification theory Textual Studies in Ancient and Medieval Geometry of complex alfebraic surfaces. Using the arithmetic and Wilbur KHorr combinatoria structures on the Picard group, this book An important new study of the problems of documentation explores the geometry of these surfaces by purely geometric in ancient technical texts. Coverage includes: the primary methods, involving delicate combinatorial analysis, Greek valid evidence on cube in arbitrary characteristics. duplication; selected medieval Arabic texts on cube duplication and angle trisection; an in-depth look at Jan. 891400 pages I 0-8176-3417-7 I $42.50 I PM, Vol. 76 Archimedes Dimension of the Circle. June 891 approx. 640 pages I 0-8176-3387-11$89.00 CONTEMPORARY MATHEMATICIANS Graded Orders Collected Works of Arne Beurling L. le Brn}'H. M. VaH deH Bergh, aHd E VaH OystaeyeH L. CarlesoH, P. MalliaviH, ]. Neuberger,]. Wermer, eds. In a clear, well-developed presentation, this book provides the first systematic treatment of structure results for algebras Arne Beurling's contributions to mathematics include the which are graded by a group. areas of complex analysis, functional analysis, operator theory; Aug. 88 I approx. 200 pages 0-8176-3360-x potential I I theory, harmonic analysis and semi-groups of $25.00 (Paper) operators. These volumes make available for the first time his extensive body of published work. Complex Analysis April 8912 volume set I 0-8176-3412-61 $120.00 (tent.) Articles dedicated to Albert Pfluger on the occasion of his Volume 11 approx. 450pages I 0-8176-3415-ol $60.00 (tent.) 80th birthday Volume 21 approx. 450pagesl 0-8176-3416-91$60.00 (tent.) Joseph Hersch aHd Alfred Huber. eds. Julio Rey-Pastor: Selected Papers This volume contains articles pertaining to a wide variety of Eduardo Ortiz, ed. subjects such as conformal and quasiconformal mappings and related extremal problems, Riemann surfaces, meromorphic A careful selection of the most important papers of the functions, subharmonic functions, approximation and Argentinean mathematician Julio Rey-Pastor, especially noted interpolation, and other questions of complex analysis. for his work on classical projective geometry, conformal Nov. 88 1246 pages I 0-8176-1958-51$72.50 representation, the theory of functional analysis and the theory of series. Introduction in English. Papers in Spanish Numerical Methods for Grid Equations and French. A.A. Samarskii aHd E.S. Nikolaev May 891 approx. 3 50 pages I 0-8176-3447-7 I $39.00 (tent.) These volumes are devoted to the construction and analysis of numerical methods of solving systems of algebraic Available at your local scientific bookstore or order directly equations that arise in the application of the network method from the publisher: to problems of mathematical physics. Direct Methods-Vol. 11242 pages I 0-8176-2276-41 Birkhauser Boston, Inc. $99.50 c/o Springer-Verlag Distribution Center Iterative Methods-Vol. 21 502 pages I 0-8176-2277-21 IJ P.O. Box 2485 $190.00 Secaucus, NJ 07096-2491 Nov. 8 8 12 volume set I 0-817~-2278..0 I $260.00 Useful, High Quality Books for Researchers and Students

Revised Edition! New! DIFFERENTIAL AND DIFFERENCE EQUATIONS CRITICAL POINT THEORY AND HAMILTONIAN THROUGH COMPUTER EXPERIMENTS SYSTEMS With a Supplementary Diskette Containing PHASER: An By Jean Mawhin and Michel Willem Animator/Simulator for Dynamical Systems for IBM The aim of this book is to initiate the reader to the funda­ Personal Computers mental techniques of critical point theory and apply them to SECOND EDITION periodic solutions problems for Hamiltonian systems. The By Hiiseyin Ko~ak presentation of the text should be appealing to people trained An illustrated guide to the wonderful world of experimental and interested in ordinary differential equations as well as by and theoretical dynamics in which the subject of ordinary specialists in differential topology, partial differential equa­ differential and difference equations comes alive! tions, and optimization. PHASER, a sophisticated program for IBM Personal Comput­ Contents Include: The Direct Method of the Calculus of Varia­ ers,* which enables users to experiment with differential and tions. The Fenchel Transform and Duality. Minimization of the difference equations and dynamical systems in an interactive Dual Action. Minimax Theorems for Indefinite Functionals. A environment using graphics, now has the capacity to take Borsuk-Ulam Theorem and Index Theories. Morse-Ekeland advantage of the higher resolution EGA or VGA graphics.** Index and Multiple Periodic Solutions with Fixed Period. Morse Theory. Applications of Morse Theory to Second Order From reviews ofthe first edition: Systems. Nondegenerate Critical Manifolds. "Both the book and its accompanying software are of the Bibliography (with extensive references). highest quality in terms of mathematical taste, pedagogical 1989. 277 pp., 1 illus. Hardcover $54.00 usefulness, and professional programming technique:' -Byte ISBN 96908-X "The program worked so well that not only students, but also Applied Mathematical Sciences, Volume 74 researchers, are interested in using it:' -Mathematical Reviews ELEMENTS OF MATHEMATICS 1989. 224 pp., 108 illus. Softcover $49.95 By Nicolas Bourbaki ISBN 96918-7 (including diskettes Version 1.1, 5 Y4 in. , and Version 1.1, two 3 Y2 in. diskettes). COMMUTATIVE ALGEBRA Diskettes Available Separately: 2ND PRINTING (1989) Version 1.1 (5 Y4 in. diskette): $29.95 ISBN 96920-9 The thorough coverage of this book enables the reader to Version 1.1 (two 3 Y2 in. diskettes): $34.95 ISBN 14202-9 go further and study algebraic or arithmetical geometry. *XT, AT, or PS/2 with an IBM Color Graphics Board. Includes useful exercises at the end of each chapter. • *For those who have only CGA graphics, the original version of Contents: Flat modules. Localization. Graduations, filtrations , and PHASER is also included. This low resolution version has now topologies. Associated prime ideals and primary decomposition. In­ been modified to run on EGA/VGA boards as well, primarily for use tegers. Valuations. Divisors. with inexpensive LCD projectors. 1972 (1st ed.). 656 pp. Hardcover $69.00 ISBN 19371-5 Go •. PORT PUASE ...... -·~ ; . Cleal' X Min X ...ax LIE GROUPS AND LIE ALGEBRAS DiMension -1.1ala 1. liMiMit Part 1: Chapters 1-3 Algol'i th10 y Min y ..ax 2ND PRINTING (1989) Step size -1.1ala 1 1.1iMiMit TiMe 0~33··- . ,~..tf!: This is one of the best references on this subject! . .-,, __ ,.( -' X tend Contents: Lie algebras. Free Lie algebras. Lie groups. Coxeter groups Equation and Tits systems. Groups generated by reflections. Root systems. Pa:ra...ete:r c:roeMona 2 D Difference Ini tConds a=l..32 1975 (1st ed.). 468 pp. Hardcover $59.00 ISBN 50218-1 Sta.. t:la.lalalitlala End:2lalala.lala WindoSize t e p :1 • laliKHJiala Ju.. ps/Plt:l Ju.. ps/Plt s GENERAL TOPOLOGY )( ·axis: xl. y .a.Kis:xa z -..xis: UTILITIES Plane:Ax + By + Cz + D = Ia p Chapters 5-10 VISUALAID IC:fil.~Siala Ia. 91iKHJ 2ND PRINTING (1989) Quit a.sqea la.7181a I A continuation of Chapters 1-4 of General Topology. Both !Hake a cho1ce : _ volumes include a historical note and numerous exercises. Contents: Topological structures. Uniform structures. Topological Illustration from Differential and Difference Equations Through groups. Real numbers. One-parameter groups. Real number spaces, Computer Experiments by H. Krn;ak. affine and projective spaces. The additive groups R n Complex num­ bers. Use of real numbers in general topology Function spaces. Order Infonnation: 1966 (1st ed.). 363 pp. Hardcover $59.00 ISBN 19372-3 Call Toll-Free 1-800-SPRINGER. For mail orders, send payment plus $2.50 for postage to: Springer-Verlag New York, Inc., Attn. : S. Klamkin, 175 Fifth Avenue, New York, NY 10010. Or, use our new FAX # (201) 348-4505. We accept Visa, MasterCard, American Ex­ press, personal checks and money orders. (Please include exp. date .~ Springer-Verlag and signature for all charges and add applicable sales tax if you re­ ~ New York Berlin Heidelberg Vienna London Paris Tokyo Hong Kong side in NY, NJ or CA).