OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

Boulder Meeting {August 7-10) page 701

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 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 subjeet 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 850 • August 7-10, 1989 Boulder, Colorado Expired July I 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 t (96th Annual Meeting) • March 16-17, 1990 Manhattan, Kansas December 12 February March 23-24, 1990 Fayetteville, Arkansas December 12 February •• April 7-8, 1990 University Park, Pennsylvania January 25 March 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 752 for listing of special sessions. •• Please note a change in this date making it earlier than previously published. t Preregistration/Housing deadline is November 17 I Conferences

June 3-August 5, 1989: Joint Summer Research August 7, 1989: AMS-SIAM-SMB Symposium on Some Conferences in the Mathematical Sciences, Humboldt Mathematical Questions in Biology, Sex Allocations and State University, Arcata, California Sex Change: Experiments and Models, University of August 6-7. 1989: AMS Short Course on Cryptology and Toronto. Computational Number Theory, Boulder, Colorado June/July 1990: AMS-Siam Summer Seminar on Vortex Dynamics and Vortex Methods, location to be announced. Deadlines

October Issue November Issue December Issue January Issue Classified Ads* Aug 28, 1989 Oct 3, 1989 Oct 27, 1989 Nov 27, 1989 News Items Aug 29, 1989 Oct 5, 1989 Nov 2, 1989 Nov 27, 198~ Meeting Announcements•• • Aug 22, 1989 Sept 26, 1989 Oct 26, 1989 Nov 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

669 Feminist Critiques of Science 667 Letters to the Editor Are certain radical feminist critiques discouraging women from entering 684 News and Announcements mathematics and science? In this article, Allyn Jackson surveys recent literature that has drawn fire from some women mathematicians. 695 Funding Information for the Mathematical Sciences 699 Meetings and Conferences of the AMS (Listing) 758 1989 AMS Elections FEATURE COLUMNS 759 Mathematical Sciences Meetings and Conferences

674 Computers and Mathematics Jon Barwise 770 New AMS Publications Four programs for use with matrices, calculus, typesetting, and 2 - D 781 Miscellaneous cellular automata are reviewed in this column. Also included is one letter Personal Items, 781 from a reader who discusses why mathematics departments routinely Deaths, 781 to comments about favor the PC environment, and another responding 782 Visiting Mathematicians a proof of Godel's Incompleteness Theorem. (Supplement)

682 Washington Outlook Kenneth M. Hoffman 784 Reciprocity Agreements This month's column, written by Hans J. Oser, questions the slowness 792 New Members of the AMS of key Bush administration appointments and provides an inside look at 796 AMS Policy on Recruitment recent Capitol Hill hearings on the state of mathematics and science education. Advertising 797 Classified Advertising 817 Forms

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 665 International Cooperation in Mathematics

Mathematics often is referred to as an "international language," allowing commu­ AMERICAN MATHEMATICAl. SOCIETY nication and understanding beyond limitations that might otherwise be imposed by language and cultural barriers. Where the free flow of information has been possible, we see collaborative development in mathematics, irrespective of national differences. Recent developments in electronic communication are having a dramatic effect on the EDITORIAL COMMITTEE flow of information. It is now commonplace to carry on an interactive exchange with Robert J. Blattner, Michael G. Crandall colleagues located in various parts of the world via electronic mail andfor facsimile. Robert M. Fossum (Chairman) While these mechanisms are not always readily available for communication with the Lucy J. Garnett, D. J. Lewis Soviet Union, "glasnost" has inaugurated an exciting era of information exchange and Nancy K. Stanton, Robert E. L. Turner collaboration with our Soviet colleagues. INTERIM MANAGING EDITOR James W. Maxwell A principal goal of the Society is facilitating exchange of mathematical information, primarily through its publication and meetings programs. Both activities have long ASSOCIATE EDITORS promoted international cooperation, but we are now seeing them take on an even Ronald L. Graham, Special Articles broader scope. Jeffrey C. Lagarias, Special Articles

SUBSCRIPTION INFORMATION The Society has been a leading supplier of mathematical literature translated from Subscription prices for Volume 36 (1989) are Russian and other Slavic languages and has begun a translation program from Chinese $1081ist; $86 institutional member; $65 individual and Japanese. Two new series of publications in the Russian Translation Program member. (The subscription price for members is will appear during the next year, Proceedings of Regional Conferences and Advances included in the annual dues.) A late charge of 10% of the subscription price will be imposed in Soviet Mathematics. The AMS will also translate a new Soviet journal, Algebra upon orders received from nonmembers after and Analysis, which will be published as The Leningrad Mathematical Journal. The January 1 of the subscription year. Add for post­ London Mathematical Society, a long-term partner with the AMS in the publication age: Surface delivery outside the United States of the English translation of the Soviet journal, Trudy Moscow, has now joined the and lndia-$10; to lndia-$20; expedited deliv­ AMS in publishing a new series devoted to the history of mathematics. The Society ery to destinations in North America-$15; else­ is also supporting the efforts of the Third World Academy of Sciences, the American where-$38. Subscriptions and orders for AMS Association for the Advancement of Science, and others in providing mathematical publications should be addressed to the Amer­ literature to our colleagues around the world. ican Mathematical Society, P.O. Box 1571, An­ nex Station, Providence, Rl 02901-9930. All or­ ders must be prepaid. Meetings involving Society sponsorship are also incorporating greater international co­ operation. The AMS is jointly sponsoring a meeting with the London Mathematical ADVERTISING Society, which is to be held in Cambridge, England, in the summer of 1992, and is Notices publishes situations wanted and classi­ exploring the possibility of joint meetings with representatives of other mathematical fied advertising, and display advertising for pub­ lishers and academic or scientific organizations. organizations around the world. New international agreements and programs are be­ Copyright@ 1989 by the American Mathemat­ ing developed for collaborative meeting activity; examples include the new agreement ical Society. All rights reserved. Printed in the established between the National Science Foundation and the Soviet Academy of Sci­ United States of America. ences reported in this issue of Notices and an increase in support for mathematicians The paper used in this journal is acid-free and travelling between North and South America. falls within the guidelines established to ensure permanence and durability. €9 Most of this pub­ The Society has maintained an international perspective on the flow of mathematical lication was typeset using AMS -TE)<, the Amer­ information and the support of mathematics and mathematicians. In an attempt to ican Mathematical Society's TeX macro system. provide our colleagues outside the United States with access to the benefits of the So­ [Notices of the American Mathematical Society is ciety, we have an active reciprocity membership program, which allows members of published ten times a year (January, February, participating mathematical societies to join the AMS at a reduced membership rate, March, April, MayfJune, July/August, Septem­ as well as allowing similar arrangements for AMS members to join the reciprocity ber, October, November, December) by the Amer­ societies. A full list of reciprocating societies appears in this issue of Notices. New ican Mathematical Society at 201 Charles Street, Providence, Rl 02904. Second class postage paid possibilities for improvement in the exchange of information and in cooperative ar­ at Providence, Rl and additional mailing offices. rangements with our international colleagues are presently under consideration. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, It is an exciting time with many possibilities for improving the collaboration and coop­ Membership and Sales Department, American eration within the international mathematical community. The Society and American Mathematical Society, P. 0. Box 6248, Provi­ mathematics has greatly benefited from the support of our international colleagues, dence, Rl 02940.] Publication here of the Soci­ and we look forward to the new and exciting possibilities that are being explored. ety's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. All correspondence should William H. Jaco be mailed to the Post Office Box, NOT the street Executive Director address.

666 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY doubtedly convenient line of de­ vent advocates of this model do not markation unfortunate because it deny that major advances have re­ Letters means that there is one way of sulted from the adoption of suitable handling students, with which the notations, of which the Indo-arabic to the Editor conference will not be concerned­ numeral system is an example, but although, as the paper itself remarks, they have not been able to acco­ it is responsible for producing "fear", modate a theory of notation within "hatred", and other "negative re­ their model. Not surprisingly, there­ many works J. F. Adams actions" towards mathematics-and fore, what characterizes another way of handling adult popu­ of popularization is the absence of all The obituary notice of J. F. Adams, lations capable of providing financial symbolic notation, however easy to in the March issue of Notices, con­ support to the mathematical commu­ learn and handle, and the presence tains an inaccuracy. Adams' first nity. of simplified but seldom very con­ teaching post was a Junior Lecture­ Now, it is the same basic con­ vincing proofs. The question whe­ ship at Oxford, in 1955-1956. This cept, Motivation, that underlies both ther such "proofs" are not a disaster was an important step in his devel­ improved classroom instruction in from the educational point of view opment since it brought him directly mathematics and more effective pop­ deserves to be explicitly raised at the under the influence of J.H.C. White­ ularization of mathematics, and I conference. head. The appointment at Trinity think ICMI will take a big step if Indeed, if "most people ... would Hall, Cambridge, was in 1958, fol­ it arrives at a comprehensive, official not even consider mathematics to lowing his first visit to the United definition of this term. In fact it may be a living science", is this belief States. even be possible to do better and, by Perhaps I could take the oppor­ slightly extending the conventional tunity to mention that I have been language of mathematics (a little in Policy on Letters to the Editor appointed by the Royal Society to the way in which symbolic logic and Letters submitted for publication in Notices write the Bibliographical Memoir of are reviewed by the Editorial Committee, computer languages do so), formal­ whose task is to determine which ones are Adams and would be grateful for per­ ize an intuitively acceptable , even suitable for publication. The publication sonal reminiscences from those who if necessarily rather narrow, notion schedule normally requires from two to knew him, especially during his visits of motivation. I intend to submit a four months between receipt of the letter in to the United States. These can be short paper on this topic. Providence and publication of the earliest sent to me at the Mathematical In­ issue of Notices in which it could appear. Mathematics is one among several Publication decisions are ultimately stitute, 24-29 St. Giles, Oxford OX 1 intellectual disciplines, and compar­ made by majority vote of the Editorial 3LB. isons can be very enlightening. A sim­ Committee, with ample provision for prior ple question, more significant than discussion by committee members, by mail I. M. James might first appear, is this: why is mo­ or at meetings. Because of this discussion University of Oxford tivation required for the reading of period, some letters may require as much (Received April 24, 1989) as seven months before a final decision is a mathematical text, but not for that made. Letters which have been, or may be, of a novel or a poem? Does it have considered, but 1989 ICMI Conference published elsewhere will be nothing to do with the fact that win­ the Managing Editor of Notices should be The Howson-Kahane-Pollak back­ ners of the Nobel Prize for literature informed of this fact when the letter is sub­ ground paper in January 1989 No­ mitted. are seldom, and winners of the Fields The committee reserves the right to tices lays down several themes for the Prize for mathematics are almost al­ edit letters. September 1989 ICMI Leeds Confer­ ways, professors? Is this lack of a Notices does not ordinarily publish ence on the Popularization of Mathe­ clear distinction between the creative complaints about reviews of books or arti­ matics. I wish to suggest some further and the critical roles not one of the cles, although rebuttals and correspondence themes and a somewhat different ap­ concerning reviews in Bulletin of the Amer­ major handicaps of mathematics and ican Mathematical Society will be consid­ proach. the main hurdle in communication ered for publication. All published letters The background paper defines pop­ with the public? must include the name of the author. ularization as " ... efforts ... to bridge Despite the rise of the computer, Letters should be typed and in legible the gap between scientific advances the essentially occidental axiom - def­ form or they will be returned to the sender, and public knowledge and informa­ theorem - proof model of the possibly resulting in a delay of publication. inition - Letters should be mailed to the Editor tion, apart from those which take Greeks, brought up to date by Hilbert of Notices, American Mathematical Soci­ place within school systems and in and Bourbaki, still dominates mathe­ ety, P.O. Box 6248, Providence, RI 02940, higher education". I think this un- matics. Of course even the most fer- and will be acknowledged on receipt.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 667 Letters to the Editor unrelated to the mathematician's pre­ A model that is not open to this not yet ready to abandon the time­ occupation with "proof'? Today, if criticism is the one proposed by Imre honoured Hilbert-Bourbaki model in one person were to discover and Lakatos, a disciple of Karl Popper, their own professional work, the publish a new computer verifiable in his book Proofs and RefUtations forthcoming ICMI conference could formula in, let us say, combinatorics (CUP). Based on conjecture/refuta­ at least broach the question of whe­ or number theory, and another were tion by counterexample/improved ther the Lakatos model is not the one then to formally prove it, the lion's conjecture, this model treats formal best suited to the needs of popular­ share of the credit would certainly go justification as no more than a stage izers of mathematics. The precedence thus ac­ in mathematical investigation, always to the latter. Jasmer Singh to the critical over the creative liable to be superseded by a fresh dis­ corded Boulogne, France function naturally strikes laymen and covery. Even if mathematicians are (Received April 4, 1989) experimental scientists alike as a re­ versal of priorities.

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, RI 02901- 1571, or call future of mathematical research. Providing a fascinating BO!J-556-7774 to use VISA or MasterCard.

668 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Feminist Critiques of Science

controversy over this literature reflects not an attack on Mathematics is among those fields of science with the low­ feminism but rather an attempt to combat misconcep­ est participation of women. The issue of encouraging more tions about the nature of science that much of the general women in mathematics is of concern to the entire mathemat­ public, not just feminists, continues to hold. The term ical community, especially given the changing demographics "feminist" is used here for convenience to identify the indicating that, in the future, women and minorities must fill po­ authors of this literature, but such opinions by no means sitions in science and mathematics traditionally filled by white represent the thinking of all feminists. males. This article surveys some recent radical feminist liter­ ature that may have the effect of discouraging women from entering mathematics and science. In addition, because some Science: Permeated With Male Bias? of this literature perpetuates stereotypes and misconceptions about mathematics and science, it is related to the larger is­ Many of the feminist critiques of science came in sue of public perceptions about mathematics and science, an response to flawed biological theories about women and issue with which the AMS has become increasingly concerned hormones [2] and studies purporting to show that men in recent years. have more innate talent for mathematics and science than do women. Attempts to link mathematical and spatial ability with such things as testosterone levels in utero or left-handedness have been exposed as scientifically "Small wonder that women . . . working in natural flawed or greatly overstated. The well-known Benbow­ science and engineering are rarities. It is difficult Stanley study, which used the Scholastic Aptitude Test enough to suppress halfof oneself to pursue knowledge to allege that boys are biologically superior to girls in of the natural world as a woman. " mathematics, has been debunked by many critics, but continues to be cited in the media as authoritative [3]. A No, this wasn't written by a 19th century misogynist great deal of convincing evidence challenges such views; trying to tell women they are biologically unfit to study recent examples include an international study of boys' science. Ironically, it was written in 1983 by Hilary Rose, and girls' mathematical performance [4] and a long-term professor of social policy and director of a research center study of performance on standardized tests [5]. Still, on women at the University of Bradford in England [I]. reports claiming the biological superiority of males in Recently, a controversy has been brewing over some mathematics and science continue to make the headlines. radical feminist critiques which take the view that Everyone agrees on the importance of revealing flaws in the nature of science itself alienates women. Some this kind of research. women academics-including several mathematicians­ But some radical feminist scholars claim that science have challenged the critiques, saying that this literature itself is so permeated with male bias as to be inimical to contains a strong "anti-science" bias based on miscon­ women. For example, Kathy Overfield, an independent ceptions regarding the nature of science. They claim scholar in Wales, asserts that it is pointless to encourage these views may perpetuate damaging stereotypes and girls and women in science, for "science is now the discourage women from entering science and mathemat­ embodiment of values currently esteemed as male and ics. Because the feminist critics are quoted in the media, masculine. It is not feminine or female; nor are women their views on science reach beyond the journals in which or female values wanted." [6]. Patrocinio Schweickart, they write. a University of New Hampshire English professor with Women scientists do not object to feminism per se. background in chemical engineering and mathematics, Indeed, many who strongly disagree with this literature writes that "the masculinist psychology of the men who nonetheless consider themselves to be feminists. The control science also informs its logic. The scientific

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 669 Feminist Critiques of Science

method itself-not just its applications-is implicated "genetic fallacy," in which a thing is confused with in the domination of women in a patriarchal society." its origins and rejected on that basis. Even if Bacon's [7]. According to Leanna Standish, "[science] embodies repugnant imagery had been crucial in the development the quintessential values of a patriarchal culture. The of modern science, she points out that "that would very word science implies masculinity." [8]. Such themes have been completely irrelevant to the verifiability and appear frequently in this literature. accuracy of the scientific theories inspired by those The idea that science is inextricably intertwined with metaphors." As for Newton's "rape manual," Levin capitalism, domination, and oppression is another promi­ states that mechanistic metaphors were important in the nent theme, and some writers in fact deny that science development of science because they provided a way has any redeeming qualities. Says Overfield, "[Scientific] of understanding complex phenomena by viewing them values are those of exploitation and dominance: the as systems of simpler mechanisms. "Harding would not abuse of nature and destruction of the environment if want to maintain, presumably, that rape metaphors have not directly of populations ... Male science furthers the led to any comparable increase in knowledge." capitalist, imperialist tradition in which it was begotten: it exploits, rapes, destroys." Critique of Mathematics In a sardonic rebuttal to these critiques [9], Margarita Levin, a mathematically trained philosopher at Yeshiva It is not always clear to what extent such critiques University, maintains that these scholars "identify 'male' are intended to apply to mathematics, and few address science with weapons and strip mining, all intended for it directly, but Harding's book does contain a section use, as [Sandra Harding, professor of philosophy and di­ on mathematics. "I will not argue that mathematics is, rector of women's studies at the University of Delaware] in fact, male-biased," she writes, but she explains why writes, 'in the service of sexist, racist, homophobic, and one may "regard as mythical the possibility of pure classist projects'." What these scholars fail to take seri­ mathematics." She says one reason is that justification ously, Levin and others say, is "the fact that so-called for any conceptual system must come from outside the masculine science works ... [They] seem unaware that system. "Leading mathematical theorists point out that science is anything more than MX missiles conceived the ultimate test of the adequacy of a mathematical as embodiments of male aggression. What they overlook concept or proof always has been pragmatic: Does it is that those missiles would not present a danger to 'work' to explain the regularities in the world for which humanity if scientific theories about atomic fission and it was intended to provide an explanation?" A second ballistics were not literally and absolutely true." reason is that "mathematical statements regarded as true at one time in history are occasionally regarded as false "plausibility or usefulness" in Science at a later time," so that the Misogynist Metaphors of some mathematical concepts is "socially negotiated." Several writers have focused on metaphors of domi­ Levin points out how Harding's attempts to specif­ nation and rape that have appeared in early scientific ically show "social fingerprints" in mathematics are writings, especially those of Francis Bacon. For example, betrayed by Harding's lack of mathematical expertise. In Bacon wrote, "I am come in very truth leading you to addition, Levin asserts that Harding's approach "run[s] Nature with all her children to bind her to your service together the true and not very controversial statement and make her your slave," and spoke of "torturing" Na­ that mathematical concepts began in attempts by 'so­ ture's secrets out of her. Such metaphors do speak to the cial' beings to solve practical problems, with the more male-dominated social environment in which science de­ dramatic but utterly unsubstantiated claim that mathe­ veloped, but some feminist scholars believe this imagery matical truth somehow depends upon or is relative to has influenced the very fabric of science. Harding, in a social concepts." particularly radical interpretation, writes, "[If] we are to As for physics, Harding maintains that its subject believe that mechanistic metaphors were a fundamen­ matter "is so much less complex than the subject matters tal component of the explanations [science] provided, of biology and the social sciences. Physics looks at why should we believe that the gender metaphors were either simple systems or simple aspects of complex not? ... [Why] is it not as illuminating and honest to systems." Questioning the foundational role physics plays refer to Newton's laws as 'Newton's rape manual' as to in science, she writes, "perhaps, in the science of the call them 'Newton's mechanics'?" [10]. future, physics will be relegated to the backwaters of Noting Bacon's "quite marginal stance in the ac­ knowledge-seeking and thought to be concerned only tual development in science," Levin responds by saying with esoteric problems that have little impact on the way that Harding and others commit what logicians call the we live."

670 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Feminist Critiques of Science

Male vs. Female Science than men," Ruskai writes. "Thus both group research and individual research have been alleged to be inimical If current science is inherently masculine, what would a to women." Carol S. Wood, a mathematician at Wesleyan more feminine science be like? Rose writes that "because University, points to another contradictory picture. She of the significance of science and technology as major says some claim, on the one hand, that women are more instruments of both ideological and material oppression, creative than men, but their creativity is denigrated. On the need for a feminist science is increasingly acute." The the other hand, they sometimes maintain that science difference, she says, would be that, "Unlike the alienated puts a premium on genius, and male scientists devalue abstract knowledge of science, feminist methodology the importance of the "plodding, consistent women seeks to bring together subjective and objective ways scientists," Wood says. "Obviously it's impossible to of knowing the world." She sees the need to bring hold both views at the same time. They seem to use the "caring, intimate, emotionally demanding labor" of either view, depending upon what conclusions they want women to bear on science. "Transcendence of [the] to reach." Part of the problem is the stereotyping in division of labor set up among hand, brain, and heart some of the feminist critiques which, as Ruskai puts it, make possible a new scientific knowledge and technology "seek to impose a black and white view upon science." that will enable humanity to live in harmony rather than Ruskai also objects to the critics' view that women antagonism with nature." scientists have little to contribute to feminism. "Some Levin rejects such claims as vacuous. "These promis­ feminist theorists appear to disregard the opinions of sory notes address only the more morally elevated atti­ women scientists because they feel that we have been tudes that feminist scientists would, presumably, have" corrupted by our contact with the male scientific estab­ without explaining how existing scientific theories would lishment," she writes. Ruskai also notes that some of be revised when viewed from a feminist perspective. these critics perpetuate the myth that there are no women Janet Sayers, who teaches women's studies, social work, scientists. For example, Harding writes, "The inevitable and social psychology at the University of Kent in examples of Marie Curie and now Barbara McClintock England, objects to the way some scholars "uncritically notwithstanding . . . there are few women worthies to [accept] the ideology of sexual difference that equates restore to science's halls of fame." women essentially with mothering . . . They reiterate rather than question our society's belief that women are closer to nature, that they are more instinctive, intuitive, The Effects of the Literature expressive, and emotional, that they embody softness These critiques of science usually appear in women's and things of the heart, whereas men embody hardness studies journals, but their effect reaches beyond this and things of the brain-reason, instrumentality, and sphere. The news media often quote these scholars on science." [ 11 ]. issues concerning women and science, so that these critics appear to represent women scientists. For example, Woman Scientist: A Contradiction? an article in the Boston Globe [ 13] described some research showing that men and women have equal Some theorists seem to believe that being a woman aptitude for working with computers, but women have and a scientist is a contradiction in terms. "A woman far less interest. One of the researchers, Mary Poplin, a scientist is cut in two," writes Rose. "Her involvement faculty member at the graduate school of education at with the abstraction of scientific practice as it has Claremont College, said that few women go into science developed under capitalism and patriarchy, on one hand, partly because science "doesn't deal with subtleties" and is in painful contradiction with her caring labor, on the because women do not like fields "that use number other." Rose sees the lack of women in science as related as their whole means of discovery ... [Women] trust to motherhood. "The dialectical relationship between .. . numbers less." "Because women can deal with ambiguity the production of things and the production of people .. . better [than men]," she said, "they feel less driven to holds the explanation ... of why there are so few women make decisions based on numbers or quantification." In in science." a letter to the newsletter of the Association for Women in Women scientists are often portrayed in contradictory Mathematics [14], Ruskai criticized this kind of thinking ways. In a recent article [ 12], Mary Beth Ruskai, a as "suspiciously like a rewording of the old bigoted male mathematical physicist at the University of Lowell, accusation that women can't think logically." notes that while some of these scholars say science is Some believe these critiques may have the effect of unappealing to women because scientists are essentially discouraging women from going into science and math­ "factory workers" in the impersonal world of modern, ematics. Science historian Ann Hibner Koblitz believes industrialized science, others claim that "working alone that much in this literature is useful and valid, but is unfeminine because women are more people-oriented objects to what she sees as "an incredible oversimplifica-

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 671 Feminist Critiques of Science tion." She has learned of college and university faculty appearance in a formal, conventional abstract formula­ who, influenced by these writings, warn their women tion from which all evidence of false trails, inadequate students away from science majors. In a recent paper reasoning or misunderstandings have been eliminated. [15], she points out that, ironically, the proliferation of Unfortunately for our pupils, the majority are given studies claiming the biological superiority of males in access only to the public world." mathematics and science is reinforced by radical femi­ To some extent, then, the fault rests with scientists nist literature. "When the media are blaring out the news and mathematicians themselves. In a recent paper [ 17], that 'radical' feminists have come to the same conclusion Ruskai says that, "scientists bear a heavy responsibility about women's unsuitability for science (or science's un­ for many of the misconceptions about science. In the past, suitability for women) as have the cognitive specialists, scientists have often emphasized the differences between the combination has some rather ominous implications science and other fields in ways which emphasized for little girls hoping to become scientists." the objective and analytic aspects, while obscuring the The feminist critiques "have an impact on people role of creativity and intuition . . . Only by presenting who give advice to young women," says Judith Roit­ a more balanced view can scientists hope to counter man, a mathematician at the University of Kansas. "I the mythical division between the supposed masculine worry about their indirect affect on high school teachers scientific perspective and a traditional feminine one." and guidance counselors. Also, many elementary school teachers are untrained in mathematics and science, so they may uncritically accept what the mass media re­ [1] Sex and Scientific Inquiry, edited by Sandra Harding and ports. I doubt that most teachers and counselors have Jean F. O'Barr, 1987. even heard of these critiques, but the critiques contribute [2] Women Look at Biology Looking at Women, edited by R. to an atmosphere in which these kinds of views are more Hubbard, M.S. Henifin, and B. Fried, 1979. [3] .. Girls and Math: Is Biology Really Destiny?"", New York acceptable than they otherwise would be." Times, Education Section, August 2, 1987. Despite their severe criticisms of the radical femi­ [4] .. Mathematics Achievement of Girls and Boys in Grade nist views of science, many women scientists consider Eight: Results from Twenty Countries;· Gila Hanna, Educational themselves to be feminists and are concerned with Studies in Mathematics, May, 1989. the kinds of issues feminism has traditionally focused [5) .. Sex Differences in Reasoning Skills is on the Decline, on-educational and professional opportunities, working Research Finds, .. Los Angeles Times, January 16, 1989. conditions, salaries, the influence of the "old boys' net­ [6] Men's Studies Modified, edited by Dale Spender, 1981. work," and so on. Koblitz notes that the problems women [7] Machina Ex Dea: Feminist Perspectives on Technology, scientists now face "are concerned less with any abstract edited by Joan Rothschild, 1983. concept of gender than with overt and covert sexual dis­ [8] ·women, work, and the scientific enterprise;· Leanna crimination, social expectations and the socio-political Standish, Science for the People, vol. 14, no. 5, 1982. [9] ··caring New World: Feminism and Science,.. by Mar­ atmosphere." Ruskai echoes this view: "Some women garita Levin, The American Scholar, Winter 1988. scientists are concerned that the feminist theorists, in [10] The Science Question in Feminism, by Sandra Harding, making critiques based on stereotypes, may detract from 1986. the existing, serious problems that still confront women [11) Analyzing Gender: A Handbook of Social Science Re­ scientists." search, edited by Beth B. Hess and Myra Marx Ferree, 1987. [12] AWM Panel on Gender and Science, Joint Mathemat­ Stereotypes about Science ics Meetings, Salt Lake City, August 5, 1987; printed in AWM Persistent Newsletter, November-December, 1987, vol. 17, no. 6. One of the main objections to the critiques is their view [13] ·women and computers, .. Boston Globe, July 7, 1985. of science and mathematics as inherently masculine. This [14] AWM Newsletter, May-June 1988, vol. 16, no. 3. view is based on stereotypes of science and mathematics; [15) ··A historian looks at gender and science, .. Ann Hibner the problem is that some of these scholars have taken Koblitz, International Journal of Science Education, 1987, vol. 9, the stereotypes literally. Why has this view of science no. 3. [16] .. Femmes et Mathematiques: Y-a-til une Intersection?'' persisted? Leone Burton of the School of Social and by Leone Burton, AWM Newsletter, November-December, 1988, Environmental Education at Thames Polytechnic Uni­ vol. 18, no.6. versity in England addressed this question in the area [17] .. How Stereotypes about Science Affect the Participa­ of mathematics [ 16]. She writes: "It would appear that tion of Women, .. by Mary Beth Ruskai, meeting of the American there is a private and public world of mathematics. The Association for the Advancement of Science, January 1989. private world is where struggle, failure, incomprehension, intuition, and creativity dominate ... The public world Allyn Jackson is where the results of the private struggle make their Staff Writer

672 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The Joint Policy Board for Mathematics (JPBM), representing the American Mathematical Society, Mathematical Association of America, and the Society for Industrial and Applied Mathematics, seeks candidates for the post of Head of the Office of Governmental and Public Affairs (OGPA).

OGPA was created in 1985 as the action arm of the three mathematical societies in Washington. Under the leadership of Professor Kenneth M. Hoffman, OGPA has been involved in a number of activities supporting the mathematical sciences such as the implementation of the David report, the establishment of MSEB, and the promotion of the public image of mathematics through the media including the development of Mathematics Awareness Week.

Specific goals for the activites of OGPA include

1. Maintaining interaction with all branches of government, including granting agencies, on matters of importance to the mathematical community.

2. Increasing the participation of mathematicians in Washington activities and also keeping the community informed of the developments on the Washington scene.

3. Promoting the national dialog on mathematics education and research.

The terms of appointment are flexible. We envisage either a full-time or a part-time position beginning as soon as possible after 1 January 1990. We expect that the initial appointment will be for at least two years with possible renewal. Salary will be commensurate with background and experience.

Applications or nominations should be sent to

Dean Hugo Rossi Chairman of the Search Committee for OGPA College of Science University of Utah Salt Lake City, Utah 84112

Names of suitable references should be provided. The selection process will begin 1 August 1989.

The JPBM organizations are affirmative action - equal opportunity employers.

For further information contact one of the following I. E. Block, Managing Director, SIAM W. H. Jaco, Executive Director, AMS A. B. Willcox, Executive Director, MAA Computers and Mathematics

Edited by Jon Barwise

Editorial notes the portfolio of patterns investigated by mathe­ matical scientists. As this portfolio grows, so do Computers and the nature of mathematics the applications of mathematics and the cross­ Over the past months, various aspects of the impact of linkages among subdisciplines of mathematics. computers on mathematics have been discussed in this column. In a recent article in Science, Lynn Arthur Because of computers, we see more than ever be­ Steen suggests an additional dimension. Namely, he fore that mathematical discovery is like scientific argues that computers can help us see more clearly just discovery. It begins with the search for pattern in what the genuine subject matter of mathematics is. I data-perhaps in numbers, but often in geomet­ will quote most of the conclusion. The entire article ric or algebraic structures. Generalization leads is excellent reading, and provides the justification for to abstraction, to patterns in the mind. Theories the conclusions quoted below. emerge as patterns of patterns, and significance is measured by the degree to which patterns in one Mathematics is often defined as the science of area link to patterns in other areas. Subtle patterns space and number, as the discipline rooted in with the greatest explanatory power become the geometry and arithmetic. Although the diversity deepest results, forming the foundation for entire of modern mathematics has always exceeded this subdisciplines. definition, it was not until the recent resonance of computers and mathematics that a more apt Texas physicist Steven Weinberg, echoing Harvard definition became fully evident. mathematician Andrew Gleason, suggests that the reason why mathematics has the uncanny ability Mathematics is the science of patterns. The math­ to provide just the right patterns for scientific ematician seeks patterns in number, in space, in investigation may be because the patterns inves­ science, in computers, and in imagination. Math­ tigated by mathematicians are all the patterns ematical theories explain the relations among there are. If patterns are what mathematics is all patterns; functions and maps, operators and mor­ about, then the "unreasonable effectiveness" of phisms bind one type of pattern to another to yield mathematics may not be so unreasonable after lasting mathematical structures. Applications of all.* mathematics use these patterns to "explain" and predict natural phenomena that fit the patterns. This says more eloquently than I have been able to Patterns suggest other patterns, often yielding pat­ much of what I have come to believe, both about the terns of patterns. In this way mathematics follows nature of mathematics, and about the importance of its own logic, beginning with patterns from sci­ the computer in mathematical research. ence and completing the portrait by adding all patterns that derive from the initial ones. This month's column To the extent that mathematics is the science of This month's column contains three software reviews, patterns, computers change not so much the na­ and one contribution to the ongoing discussion of ture of the discipline as its scale: computers are to mathematics what telescopes and microscopes are *L. A. Steen, "The science of patterns," Science 616 (April 29, to science. They have increased by a millionfold 1988).

674 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

computer environments. The latter is in the form of a order to do the job at hand. The poorer entities can letter from Alex Feldman, of Boise State University. barely afford one PC, and so do not have any other There is also a letter from George Boolos of MIT, alternatives open to them. The result is a campus responding to comments he has received on his article full of PC's, and a Data Center which spends a good in a previous column. portion of its budget maintaining and training people on these machines, and everyone else spending their money upgrading what they have, afraid to move to another hardware platform because of their investment in current software and training. So we see networked Correspondence and (some day) multitasking PC's which are doing a bad job of replicating what has been available for several years on slightly more sophisticated machines. This last argument, that investment in current hardware and software precludes moving to a new A Letter from Alex Feldman computational environment, I find particularly re­ In several of your recent editorials you have encour­ markable coming from the mathematical community. aged us to use the computer, and not for the "tradi­ Good heavens, Ladies and Gentlemen, if not us, who? tional" uses of number crunching but rather for things In fact it may be that the PC environment is the like email, text preparation, and courseware. There most appropriate for many math departments around have also been several reviews of what various depart­ the country (I would be surprised), and it is not my ments are doing and some reviews of various tools intention to argue from a position of ignorance that it that we might use to help us do these things. Some of is not. I do feel, however, that many of the decisions these, particularly the review of Novell Net Ware, have made by colleges and universities on how to acquire reawakened an old concern of mine, namely the PC computers are made out of ignorance, and that we revolution and the mindset that equates "computer" are a fertile field for aggressive salespeople. I know with "IBM compatible microcomputer, and maybe, this is true, because I have spoken with colleagues in possibly, a Mac". I think this is very harmful, and I mathematics and other disciplines who have no idea think it is an easy trap to fall into, and one that should what it is they are doing with their machines, and be avoided at all costs. for whom a computer IS the WordPerfect manual. I I will be sloppy and refer to anything from an IBM realize that most people have less reason to know what PC to a PS/2, and all the various and sundry com­ a computer really is than they have to learn arithmetic patibles as a "PC". I specifically want to distinguish - and we know what has happened to the learning of these from microprocessor based computers such as arithmetic ... but the process by which many comput­ the HP, DEC or Sun workstations. ers are purchased for higher education does not do Before one can use a computer, one must either credit to many of these institutions. Decisions should acquire it or acquire access to it. Given the choice, be made from a position of knowledge rather than many humans choose the former condition, so that ignorance, and too often this knowledge encompasses no one else can take the machine away when money a very narrow band of the spectrum of computing. tightens up later. If the acquisition involves money, I have excoriated PC's without offering any alter­ then one must either spend one's own money, invari­ natives, and of course every department is different ably a meager hoard, or convince someone else to and has its own peculiar needs. My point is not that make the purchase. In the latter case, the adage that a PC is necessarily the wrong choice, but just that it "no one ever got fired for buying IBM" applies. It is may be the right choice, and in my opinion, probably easy (these days) to justify a PC simply because they is. However, I will offer as an alternative a Unix based are ubiquitous. environment, with workstations if you can afford them These arguments favoring the purchase of PC's and terminals if you cannot. Such a system can be apply to the rich and the poor alike. Boise State is put in place for the same cost as a collection of PC's, not a wealthy university by any means, but some with some added headaches such as wiring (which one entities here (like everywhere else) have larger budgets must do if one wants to network the PC's anyway). than others. The offices containing these entities are This is not the place to list alternatives - I trust that distinguished by more and fancier PC's, most of will be done in the coming months as more reviews of which are far more powerful than they need to be in installed facilities are published in this column.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 675 Computers and Mathematics

The world of computing has moved very quickly, essentially the one given by GOdel himself in the and it is hard for anyone to keep up. I think that if introduction to his famous "On Formally Undecidable people get a feel for what is possible they will find all Propositions ... "; sorts of uses for computers, and there are some very Say that m applies to n if F([n]) is in the output dramatic changes in our profession, and I hope people of M, where F(x) is the formula with GOdel will look beyond the PC for these new applications. number m. Let A(x,y) express "applies to", and Alex Feldman let n be the Godel number of -A(x,x). If n Department of Mathematics applies to n, the false statement -A([n], [n]) is Boise State University in the output of M, impossible; thus n does not apply to n and -A([n], [n]) is a truth not in the Editor's reply output of M. I agree with the main thrust of this letter, that wise What is concealed in this argument is the large decisions about building computer environments can amount of work needed to construct a suitable formula only be made by an informed community. That is why A(x,y); proving the existence of the key formula I have solicited articles on different types of computer C(x, z) in the "New Proof' via Berry's paradox environments that are being put in place around the requires at least as much effort. What strikes the country. author as of interest in the proof via Berry's paradox As has been pointed out repeatedly in this column is not its brevity but that it provides a different sort of over the past months, there are many different uses reason for the incompleteness of algorithms. for computers. The spectrum of possible uses in George Boolos mathematics departments and research centers is even Massachusetts Institute of Technology larger than in most settings, since it involves teaching and doing mathematical research, in addition to the more typical uses involving text processing, electronic communication, bookkeeping, and other forms of information processing. My personal opinion is that lower priced worksta­ Reviews of Mathematical Software tions like the Apple Mac II, with maybe a few Mac SE's thrown in for the more casual users, networked together by Appletalk, provide a pretty good com­ promise between what Feldman sees evolving around him and the sort of environment he seems to favor. /(z) (And the word is still out on the NeXT machine.) But given the current state of mathematical software and Reviewed by Marvin S. Margolis* courseware development, it seems hard to imagine an adequate computational environment for a mathemat­ Introduction ics department which did not have both the Apple and f(z) is an interactive microcomputer graphics program the IBM worlds represented to some extent. designed to aid in the study of functions of a complex I hope other mathematicians around the country variable. A typical use of f(z) is to draw a region of will add their own opinion to this dialogue. the complex plane on one part of the screen and the image of that region under some specified function on another part of the screen. f(z) is intended for professors teaching or students taking a course in A letter from George Boolos complex variables. Several readers of my "New Proof of the Godel Hardware Requirements Incompleteness Theorem," (Notices, April 1989, pages f(z) requires an IBM PC, XT, AT, PS2 or compatible 388-390) have commented on its shortness, apparently equipped with at least 384K bytes of available memory supposing that the use it makes of Berry's paradox is responsible for that brevity. It would thus seem appropriate to remark that once syntax is arithmetized, *Marvin S. Margolis is an Assistant Professor of Economics at an even briefer proof of incompleteness is at hand, Millersville University.

676 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

and a CGA or EGA adaptor. It will run on PS2 a quadratic function, f(z) then mapped lines in the systems equipped with the VGA. f(z) supports CGA domain grid into curves in the image plane one at with two levels of graphics: medium (320 x 200 a time. f(z) also mapped orthogonal families in the pixels) and high (640 x 200 pixels) resolution. In domain into orthogonal families in the image plane. CGA medium resolution four colors are available In certain cases the simultaneous graphing happened while CGA high resolution allows only black and so quickly that I wanted to slow the execution speed white. EGA mode supports 640 x 350 pixels in 16 of the computer in order to see better the one-to-one colors. f(z) produces 640 x 350 printouts even if mappings. you cannot achieve that resolution on a CGA screen I liked the design of the menus and the many with an IBM dot matrix graphics printer, Epson options. The options for the domain plane include cir­ graphics printer, or compatible. The program supports cles, lines, hyperbolic geodesics, or individual points. the Hewlett-Packard line of pen plotters. Besides the Each of these options has a separate menu of choices. regular version, f(z) includes an 8087/80287 version Parameters for the domain plane can be stored in a for faster speed. separate file and retrieved later for another problem. f(z) worked perfectly the first time I tried it on an Once one selects a standard function, a function editor IBM PS2 with a VGA adaptor and an IBM dot matrix helps one to select the function's parameters. One can printer. However, when I tried the same program on also save a function in a file for later recall for a an AT compatible it failed after the opening screen. different problem once one selects all the function's I received a version of f(z) that worked on the parameters. compatible soon after I telephoned Marty Lapidus of Specific domain and image graphs on a screen can Lascaux Graphics, the company that produces and be saved in a file for later use. In the language of f(z), sells the program, and explained my problem. An f(z) a saved file of one or more graphs on one screen is demonstration disk is available to test how well it called a page. A page can be divided into as many works on non-standard compatibles. as ten figures. Pages of graphs that are saved as files can be bound together in a notebook. When the user Main Features of the Program loads a notebook, the user only needs to press the f( z) can graph rational functions, e=, log( z) and the page down key to step through each page (screen) of Riemann zeta function. Besides these primitive func­ figures. tions, it can compose, add, substract, multiply, divide, f(z) comes with a demonstration notebook of differentiate, and integrate complex functions and also seventeen pages. Each page of the notebook illustrates display vector fields. It can draw on either the complex a different aspect of the program. In one page, six plane or the Riemann sphere. The f( z) package con­ figures are used to show the limit of an exponential tains a separate program called f(z)-Mandelbrot that function. The first figure shows the domain of the can be used to explore graphically the Mandelbrot set. independent variable. As the independent variable f(z) requires no user programming skills since it is converges through five values to a particular limit, menu driven. It is easy to learn to use even for students the remaining five figures show how the exponential who are either unfamiliar with the theory of complex function changes. The labels of the numerical values variables or with microcomputers. At the opening for the coordinate axes are not shown on the figures "command level" menu one presses keyboard function themselves. To ascertain the coordinate values one keys to invoke the domain, function, operator, and must return to the appropriate menu item. other menus. After selecting the domain, function, Other software programs can possibly substitute and many other options for a particular problem and for f(z). Matlab, Gauss, Math CAD, and other math­ returning to command level each time, one selects ematical microcomputer software that are similar to the draw command. If the resulting lines and curves them all have some capability for complex analy­ on the domain and image planes for the problem do sis and sophisticated graphics. As Barry Simon and not appear on the screen as desired, one reselects the Richard M. Wilson stated in their September, 1988, appropriate function keys, changes the options, and review, "Supercalculators on the PC," in this journal, then draws again. no one program is superior to all the others on every On a computer with an 80287 chip, I did each application. If all one wants are numerical solutions step rapidly and never with the feeling that the menus of complex calculations reported without graphs, then were impeding my progress. f( z) draws points in both I do not recommend choosing f(z). domain and image planes simultaneously. When I Even if graphs of the complex functions are my selected a grid of lines in the domain plane and chose first priority, I still may choose one of the other

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 677 Computers and Mathematics

programs. In the January, 1989, issue of Academic The procedure normally gives the potential as Computing, S. H. Davis of Rice University in an a complicated function of the position in the article, "Owlnet: The Rice University Engineering original plane. Reversing the process with com­ Educational Network," describes how he uses Matlab puting facilitates the students' ability to directly for complex analysis in a complex analysis course. find isopotential lines in the plane for the same problems that are amenable to solution by the of complex variables analysis is Applications direct method. greatly enhanced by graphical presentation of results. A student needs only a reliable base set The mapping programs can generate flow stream­ of complex functions and simple graphics pack­ lines for fluid flow around different objects. ages for plotting both complex and real functions. Matlab software offers both features. Davis then describes how he developed approxi­ mately 50 complex function programs with the help When students first encounter functions of a of several graduate students. The programs simplified complex variable, they have trouble developing the use of Matlab graphics and complex analysis in a mental picture of the relations between the producing two-dimensional mappings and by giving independent and dependent variables. A graphical three-dimensional views of functions. representation of the relation usually depends on If one needs a general purpose mathematical pro­ mappings of points from one plane to the other, gram with additional capabilities beyond or before described by: complex analysis, then f(z) is not the most appropri­ ate computer program. As Dr. Davis explains above, f(z) = u(x,y) + iv(x,y) for z = x + iy. Matlab, with some programming effort, can be made to Matlab's mesh function enables the student to emulate some of the features of f(z). In addition, both view directly the functions u(x,y) and v(x,y) as Matlab's many matrix commands and programming functions of x and y. Although Matlab simplifies features give it significant advantages and flexibility this representation, it is still tedious for the over f(z). student to perform. Therefore, additional Matlab However, if complex algebra graphics, for example, programs were written to make the process seem for conformal mapping, are a major priority and the straightforward and friendly to the user. program must be easy to use without major prior preparation, then f(z) is an excellent program for In one version of the program, all the student learning about complex variables. needs to do is: f(z) is available from Lascaux Graphics, 3220 1) type the program name, cmeshi; Stuben Ave., Bronx, NY 10467, for $59.95 plus shipping and handling. Phone 212-654-7429. 2) answer prompts about the ranges for x,y, and the mesh size; 3) give the complex function of z; and MATCALC - A Matrix Analysis Package 4) give any one-to-four scaler properties of the Reviewed by V. S. Ramamurthi* function to display. MATCALC is a matrix calculation package designed algebra concepts as Complex mappings are extensively used to solve for use in teaching basic linear methods in linear and potential problems in two dimensions. Courses well as modern computational matrix algebra. The public domain linear algebra pro­ that do not use computing usually give students are designed for fast the following instructions: grams UNPACK and EISPACK computation on non-singular systems. But, for teach­ purposes, fast computation is not very relevant 1) given a region inside of which you want a ing it is necessary to treat singular systems. Further, solution to Laplace's equation, find a mapping and Jordan form which arises out of repeated eigenval­ that takes that region to one in which the solution the is not treated in these may be more readily found, ues is an important idea which 2) find the solution in the simpler region, *V. S. Ramamurthi is Professor of Mathematics at the Univer­ 3) insert the mapping function into the solution sity of North Florida, Jacksonville, FL 32216. His email address is to find the solution in the original region. [email protected].

678 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

packages. MA TCALC aims to fill these gaps. The pro­ with statements in between. FUNCTION definitions gram has 101 built-in procedures and functions to deal are like procedure definitions without output argument with various aspects of matrix computations. But it is list. small in size and further flexible in the sense that it The statements in procedures can involve the IF can be tailored to meet specific requirements. Subsets and LOOP constructs as well as the various predefined of MATCALC can be created by including only the MATCALC procedures and functions. desired routines. This will help in designing teaching On-line help is available. Typing HELP PROCS lists modules which will restrict students' access to high available procedures and typing HELP procedure_name end routines. On the other hand, the user can write displays an explanation of the particular procedure. procedures using the already available MATCALC Each command must provide an output location-the routines and the MATCALC programming language screen or variable(s). The SHOW command sends output to solve any specific problem he has. It is also pos­ to the screen. A record of screen activity can be sent sible to write routines in C and compile them into to a disk by using the command WRITE "filename". MATCALC. However this requires a C compiler. Recording can be stopped by the command WRITE OFF. MATCALC has predefined facilities for doing the User written procedures or data can be read from a following: disk by the command READ "filename". If one wants 1. selecting rows or columns of a matrix to record only the variables and procedures defined 2. permuting rows or columns during a session, one can use the SAVE "filename" 3. extracting entries above, below or on the diagonal command. The "zero threshold" viz., the smallest 4. computing row (column) sums, the euclidean, L1 number recognized by the program as being non-zero, and L00 norms, the determinant, rank and trace, can be set by the TINY command. The number of the adjoint and the inverse significant digits displayed can be specified by the 5. immediate input of various standard matrices like SCREEN # command. Of course, the effect of these identity matrices, zero matrices, matrices with all commands is dependent on the machine environment. entries equal to 1, matrices with random number The program occupies only 216K of memory and entries etc., runs from a single floppy disk (I am speaking here 6. scaling rows or columns with respect to an MS DOS system). There is no 7. obtaining LU and QR factorizations graphics facility, since the program is meant to be a 8. Gram-Schmidt orthogonalization purely matrix analysis package. There is no built-in 9. finding the independent and dependent columns in editor for writing procedures, test them and edit them a row echelon matrix in case of errors. However the ! character can be used 10. finding the kernel and range of a matrix to exit to the operating system level and use any of 11. calculating eigenvalues and eigenvectors and im- the operating system commands, as the memory will proving their accuracy allow. For instance, I use a small (3072 bytes) text 12. constructing the Jordan form editor called TED.COM (this is a PC Magazine free 13. finding the singular value decomposition utility) which I call by typing !ted filename from a 14. finding a least square solution of AX = B MATCALC prompt. After I finish with the editing, 15. polynomial arithmetic and root finding the file is saved and control is returned to MATCALC 16. various standard mathematical functions and I read the file into MATCALC by typing READ MATCALC supports two programming constructs: "FILENAME". 1. IF condition THEN statements ELSEIF statements The user manual is thin for a change (about ... ENDIF for conditional execution and 80 pages) but very well written. It contains clear 2. LOOP variable FROM start TO end statements instructions on how to use the program, an index ENDLOOP for repetitions. with descriptions of the predefined procedures, an PROCEDURE definitions start with instructive collection of MATCALC programs, and short tutorial on writing C language routines to be DEF(input argument list > added to MATCALC. MATCALC is available for MS output argument list) DOS, UNIX and VAX systems and costs 9 5Australian dollars. The user manual costs 15 Australian dollars and end with if bought separately. The address of the publisher is: Unisearch Limited, P.O.Box 1, Kensington, NSW ENDDEF 2033, Australia.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 679 Computers and Mathematics

MicroCalc 4.0 The modules are quite uneven in quality; some, like the one on second degree curves, come quite close to Reviewed by Gustaf Gripenberg* what anyone could need for a calculus course whereas, e.g., when solving differen- in others ' the restrictions, . MicroCalc is a program for learning and teaching tial equations or linear equations, are all too obv1ous. calculus. It requires a PC-compatible computer, at But this is to a very large extent a matter of taste. least 320K main memory, two 360K disks, one 720K There are some printing errors of no consequence in disk or a hard disk, and a CGA, EGA, VGA, or the manual, but the most serious problem I found Hercules graphics card. One version needs a math was when solving a linear system Ax = b because the coprocessor, but there is also a version available that solution given seems to be the last component of x, does not need it. not the whole vector x. * Technically there are no problems with using Mi­ The main weakness (which in other respects is a croCalc; it is very easy to set up and use the program strength) of MicroCalc is perhaps that it is a program, since it is completely menu driven. It is probably not not a programming environment. This means that quite as simple to utilize it effectively in teaching a it is not possible to modify the program in any calculus course, but I have no experience on this part significant way. There are choices that must be made of its use. There is a printable manual included on about how different aspects of calculus are presented, the disks, but one hardly needs this at all since the and, irrespective of how good the choices one person documentation appearing on the screen is so good. makes, they are unlikely to satisfy everyone. . After one starts the program, the main menu MicroCalc is licensed to school, college, and um­ appears organized in five columns with ten items versity departments, allowing unlimited copies to be in each. The topics include "Graph of y = F(x)", made for faculty and student use. The only copy pro­ "Secants and tangents", "Step functions", "Parametric tection is that the licensee's name is embedded in the plane curves", "Iterated integrals" etc. Once one topic disk and appears on menu screens. The price is $425 is chosen a screen with explanations appears that with discounts for upgrades from earlier versions and shows how to use this module and how it works. Then it is available from MathCalcEduc, 1449 Covington one must give the functions and numerical constants. Drive, Ann Arbor, MI 48103. In this task a large number of preprogrammed function keys is of great help, but it takes some training to use them effectively and they do not always work quite as intelligently as one would like. One difficulty is that it does not seem to be possible to get the help screen back in view once one starts to give the data, that is, Mathematical Freeware at the point when one really needs to know what is and Shareware required. MicroCalc does symbolic differentiation and is not especially choosy about how formulas are entered, one can write "Sin x", or "sin(x)" etc. to get the same result. It is reasonable, but not very fast, and some of the otherwise very nice graphical routines are infuriatingly slow, mainly due to the complicated OzTFX and LifeLab algorithms used. MicroCalc can be of great use when teaching Andrew Trevorrow calculus, but it does not seem to be the definite Kathleen Lumley College program for this, probably because no single program North Adelaide, SA, 5006, Australia can really do it. The strongest parts are the ones Telephone: (08) 267 1060 where graphics are used. In fact, I think graphical Email: [email protected] (ACSnet) presentations could have been used on more topics.

* Editor's Note: Harley Flanders tells me that this bug has been *Gustaf Gripenberg is currently at the Department of Mathe­ fixed in more recent releases. matics of the University of Helsinki.

680 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

OzTEX and LifeLab are public domain programs for • The dimensions of the 2-D grid can be almost the Macintosh Plus and newer models. Here is a brief any rectangular size (limited only by available description of each: memory). • The various generating commands can detect when a pattern dies out, becomes stable or reaches the Oz'JFX edge of the grid. The Auto command also: OzTEX is a public domain Macintosh implementation - Increases the size of the grid as a pattern expands. of Donald Knuth's TEX typesetting system. It aims - Removes isolated gliders moving away from the to provide a standard TEX environment that can be rest of the pattern. easily extended or customized and should run on any - Detects horizontal symmetry and speeds up ac­ Mac with at least 1 Meg of memory. Some further cordingly. details: - Stops if a pattern starts oscillating (with • The complete distribution requires ten 800K disks. period~ 8). Five of these are full of PK files (for a 300dpi write­ • A rectangular region of the grid can be selected and black laser printer like the LaserWriter). Another then cut, copied, pasted, cleared, rotated, randomly two disks contain the entire source code. OzTEX filled, etc. is written in TML Modula-2 which requires MPW • Different transition rules can be selected, not just (the Macintosh Programmer's Workshop). the original Life rules chosen by John Conway. • The OzTEX application includes TEX (actually • Patterns and their transition rules can be saved in INITEX so users can create their own format files), files for later recall. A large library of interesting a DVI page previewer and a PostScript driver that patterns is supplied. can send output to the current printer or to a text • The Search menu allows you to systematically file. search for a number of interesting species (Space­ • There is no integrated text editor. OzTEX is dis­ ships, Oscillators, Still Lifes or Methuselahs). tributed with I:Edit, a public domain DA editor The following people have volunteered to help written by Leonard Rosenthal. distribute OzTEX (LifeLab is stored on one of the • The three most popular formats are supplied: Plain, OzTEX disks): IHFX and A.MS-TE)(. • OzTFX reads standard TFM and PK files and In Australia and New Zealand: creates standard DVI files. The previewer can read Ron Addie, Melbourne [email protected] a DVI file generated by any standard TEX system. Grant Keady, Perth [email protected] • OzTEX has a Help menu which you can easily Russell Standish, Canberra rks [email protected] extend or modify. Russell Fulton, Auckland [email protected] • A configuration file is read when starting up. This In the UK and Europe: simple text file can be edited to suit your particular requirements. Some of the parameters you can Peter Abbott, UK [email protected] specify include the printer resolution, the paper Martti Nikunen, Helsinki [email protected] dimensions, a list of the formats that appear in the In the USA: TEX menu, and a list of all TFM file names for printer-resident PostScript fonts. Walter Carlip, Chicago [email protected] Ted Nieland, Dayton [email protected] • \special handling is fairly unsophisticated. OzTEX Stephen Spencer, Columbus [email protected] allows the inclusion of a PostScript file along with the file. optional code prefixed to Please get in touch with the person nearest you. By is supplied, including its • A 22-page user guide the time you read this article it is likely that OzTEX ~TEX source. will also be available electronically from various Mac archive sites. People without access to email should Life Lab try their local Mac user group. LifeLab is a public domain Macintosh program for experimenting with 2-D cellular automata. It has a number of interesting features:

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 681 Washington Outlook

Kenneth M. Hoffman

education in the U.S. on May 23 and 24. Witnesses This month's column is written by Hans J. Oser, included administrators from the states of Texas who is a consultant to the Office of Governmental and New York, and Frank Newman, president of and Public Affairs of the Joint Policy Board for The Education Commission of the States. Newman Mathematics in Washington, D.C. alluded to the intensifying international competition, the pressure for a better educated workforce and the The President's Science Adviser impact of technology in our lives in the workforce our lives as citizens and voters. Math and D. Allan Bromley, physics professor at Yale Univer­ and in he said, serve as a bellwether for American sity, was nominated in mid-April by the White House science, But the nature of the material that has to to be science adviser and assistant to the President. education. has changed, especially in math and science. After a two month delay, this nomination was finally be taught the committee that the answer was not to forwarded to the Senate on June 6, 1989. He warned force more rote learning upon the students, but rather Slow Pace for Getting Appointments Processed to facilitate a fundamental shift in how we teach in Congressional committees are frustrated over the pace order to insure mastery of reasoning. To accomplish at which the administration is moving into policy this, Newman said, it is necessary to examine not setting. Four months in the office and still almost only what we teach, but how we teach. The student 80 percent of the political appointments are vacant. has to become an active participant in the process of But even those already in office appear to be moving learning how to think and to reason. But, in contrast without any particular haste. Secretary Sullivan of to the National Research Council's report, Everybody Health & Human Services lost his battle with the Counts, Newman's summary offered no plan as to how White House over the choice of his administrator for his objectives might be reached: the Family Support Administration, Robert Fulton, • Strengthen math and science requirements for all who had his name withdrawn in the face of con­ students servative opposition. Secretary of Education Lauro • Develop new modes of testing Cavazos refuses to appear before the House hearings • Change textbooks on science and math education (see below). Astonish­ • Retrain existing math and science teachers ment and dismay about his absence echoed through • Revitalize teacher education the hearing room, beginning with chairman Robert A. • Provide alternate forms of certification Roe and other members of both parties, including the Because we are far behind, a crash effort is needed, Ranking Republican, Bob Walker, one of the more but a thoughtful one because the issues are complex. conservative House members. Commerce Secretary Most important, Newman said, we will not get more Mosbacher engages in Japan bashing but fails to ap­ unless we expect more. point an Undersecretary for Technology, a director for Energy Department Leads the Way the National Institute of Standards and Technology (formerly NBS), or a director for the Census Bureau. The second day of the hearings brought government witnesses before the committee. Most impressive was Hearings on the State of the lead-off witness, Admiral James D. Watkins, Sec­ Mathematics and Science Education retary of Energy. On the job just a couple months, The House Science, Space and Technology Committee he has already articulated for his department a com­ held hearings on the state of science and mathematics mitment to math and science education that leaves

682 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook

little doubt that DOE will be a major player in the • Increase participation of women, minorities, and upcoming reforms of math and science education. The the disabled in science education programs Energy Department employs over 135,000 people in • Forge stronger public/private sector partnerships more than 50 contractor-operated research laborato­ in education ries. The nine multi-program National Laboratories • Encourage greater volunteerism in teaching and thirty specialized laboratories carry out most of the department's fundamental scientific research and And Watkins told the committee that: energy technology R&D (plus all the defense-related • We must take advantage of what we already know These laboratories employ over 60,000 people, R&D). works- and run with it more than half of them scientists, engineers and tech­ • We must think of mathematics as the fundamental is shared by DOD and nicians. DOE's concern, which language of the future of new talent to replace NASA as well, is the supply • We in government must increasingly use our activities an­ the aging workforce. In defense-related world-class scientists, engineers, and facilities to factor comes into play: the increasing number of other help motivate and educate America's young - and foreign graduate students in science and engineering, America's teachers who cannot expect to be eligible for sensitive work. Watkins is concerned our teaching of science is Watkins has already challenged the directors of the generally directed at the top ten percent of our DOE national laboratories to come back to him with students - and even those are not doing too well in innovative programs that reach the inner cities. He international comparisons. By 1994 the pipeline of asked all program directors to name two employees youngsters coming into the workforce will be at a low with a record of outstanding volunteer efforts. The and even those few will be less prepared to handle the department has active programs at the precollege increasingly sophisticated work environments than at level, undergraduate and graduate programs, and a any time in our history. The 1990s will also see a wave faculty program that reaches over 800 people each of retirements, both in the federal workforce and in year. scientific and engineering the universities. This hits the Secretary Cavazos would have benefited from hear­ Unless we train our young disciplines especially hard. ing what Watkins is doing for education in the Energy environment they are about people for the technical Department. Cavazos had an opportunity to give numbers of less skilled to enter, we wiil have growing meaning to the President's $441 million proposal and work around technology people forced to live for improving education, but he chose not to use and that they may never that they do not understand it. (George Will notes in a recent column that this be able to effectively master in order to better their amount is over $100 million less than what Michael lives. They will be locked into the hopelessness of Milken made in 1987.) an educationally disadvantaged and non-competitive position in the workforce, Watkins prophesied. The committee also heard from NSF Deputy Di­ Turning this around, he is optimistic that it can rector John H. Moore, NIH Director James B. Wyn­ be done. He astonished the committee by suggesting gaarden (who will resign by July 1), Assistant Secretary that it would not even take a lot of new money. of Agriculture for Science and Education Charles E. The investment has already been made, he said. Hess, the Director of Personnel Management in DOD, We have the technology, we have the teachers, and Frank P. Cipolla, and Robert W. Brown, Director of we have the variety of community-based and other Educational Affairs at NASA. organizations in partnership out there who know what works. Two things must be done: first, to weld a More Hearings to Come strong consensus that we need to solve this national problem together; and second, to redirect our thinking House hearings continue on June 7 when scientists toward new initiatives, targeting different populations and teachers, together with some of their students, and different goals that will provide the desired skills, will be telling the Science, Space and Technology health, and motivation for the workforce by the turn Committee about specific programs and curriculum of the century. Watkins' summary recommends that developments with encouraging results. A demonstra­ the following steps be taken: tion of computer-based teaching aids developed in • Increase our emphasis on the middle school years the Apple Classroom of Tomorrow will conclude the • Focus more attention on "average" students hearing.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 683 News and Announcements

Edward J. McShane member at large of the AMS Coun­ methods he developed in the general 1904-1989 cil (1939-1941), AMS vice presi­ theory of manifolds, the study of dif­ dent ( 19 50-19 51), AMS representa­ ferentiable functions on closed sets, Edward J. McShane, Alumni Emeri­ tive to the National Research Council geometric integration theory, the ge­ tus Professor of Mathematics of the ( 1952-1955), and AMS representa­ ometry of the tangents to a singular University of Virginia, died on June tive on the Council of the American analytic space, as well as many oth­ 1, 1989, at the age of 85. McShane Association for the Advancement of ers, have become a part of the very was born in New Orleans, Louisiana, Science (1954-1955). He was the So­ fabric of these subjects and have had on May 10, 1904. He received B.E. ciety's Colloquium Lecturer at the tremendous influence on subsequent and B.S. degrees from Tulane Uni­ summer meeting in New Brunswick work. When he received the presti­ versity in 1925 and the M.S. in 1927. in 1943. He also served on numer­ gious Wolf Prize, the citation stated, He received his Ph.D. from the Uni­ ous AMS committees, including the "His work inaugurated the style of versity of Chicago in 1930; his thesis Committee for Mathematical Sur­ geometric and combinatorial reason­ advisors were G. A. Bliss and L. M. veys ( 1941 ), the Transactions Edi­ ing that has become the standard Graves. In 1949, Tulane University torial Committee ( 1944-1946) and for the second half of the twentieth awarded him an honorary degree. the Nominating Committee for the century." Professor McShane received aNa­ 1962 election. The celebrated Whitney Embed­ tional Research Council Fellowship A tribute to Professor McShane is ding Theorem was an important con­ (1930-1932) and held a postdoctoral being prepared and the editors expect ceptual advance in the understand­ appointment at Goetingen Univer­ it will be ready in time to appear in ing of manifolds, for it ties together sity (1932-1933). He was an assistant the September issue of Notices. the intrinsic and extrinsic definitions professor at Princeton University be­ of a manifold. The theorem states fore joining the faculty of the Uni­ that any n-dimensional manifold can versity of Virginia in 1935. At the Hassler Whitney be embedded in m-dimensional Eu­ University of Virginia he held the 1907-1989 clidean space, for m sufficiently large; position of professor of mathemat­ later he showed that m = 2n was suf­ ics from 1935 until his retirement in Hassler Whitney, Professor Emeritus ficient. The trick he introduced in 1974 when he became emeritus pro­ at the Institute for Advanced Study the proof is still a standard tool of fessor of mathematics. During the in Princeton, died on May 10, 1989 topologists. period 1942-1945, he served as a in Princeton, New Jersey. A leading Professor Whitney was also one mathematician at the Ballistics Re­ world figure in mathematics in this of the founders and early propo­ search Laboratory, Aberdeen Proving century, Professor Whitney's ideas nents of the theory of cohomolgy. Grounds. have had a pervasive and profound He, along with E. Cech, invented Professor McShane was elected influence in many areas of mathe­ the first clear and correct definitions to the National Academy of Sci­ matics. In addition, during the last of the cup product in cohomology. ences in 1948. He served as president two decades of his life, he devoted Whitney also pioneered the use of of the Mathematical Association of substantial time and energy to math­ vector and sphere bundles as a tool America in 1953-1954 and presi­ ematics education. in the solution of topological prob­ dent of the American Mathematical A pioneer in topology, Profes­ lems. Stiefe1-Whitney classes, which Society in 1959-1960. In 1964 he sor Whitney combined unusual but are important invariants of vector received the MAA's Distinguished very fruitful perspectives with great bundles, were discovered by Whit­ Service Award. In addition, he was a technical prowess. The ideas and ney and E. Stiefel around 1935.

684 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Through most of his career, Pro­ a part of the student's world, without Emil Grosswald fessor Whitney was interested in connections with anything outside or 1912-1989 properties of differentiable functions. with the student's experience," he His ideas were instrumental in the stated. "It removes all the pleasure development of the field of differen­ of discovery and denigrates human The distinguished number theorist, tial topology, which in turn led to powers." Emil Grosswald, passed away on his work on the theory of analytic Hassler Whitney was born on April 11, 1989. Despite long failing varieties. With Rene Thorn, Whitney March 23, 1907, in New York City. health, Professor Grosswald main­ launched the theory of singularities His grandfather was Simon New­ tained an active mathematical life, and established that the generic sin­ comb, a noted astronomer and the including his extensive international gularities of maps from the plane to fourth President of the AMS ( 1897- correspondence, until he entered the the plane are folds and cusps. 1898). Professor Whitney received hospital a few days before his death. Like most mathematicians, Pro­ bachelor's degrees in physics ( 1928) Grosswald wrote some hundred fessor Whitney had a keen artistic and music ( 1929) from Yale Univer­ articles in number theory, classi­ sensibility for his subject. In his sity and his doctorate in mathematics cal analysis and related subjects, statement upon receiving the AMS from Harvard University (1932). In and he is the author of the well­ Steele Prize in 1985, he said, "I do 1931, he received a fellowship from known books, Topics from the the­ feel that the essence of fine mathe­ the National Research Council to go ory of numbers ( 1966, 2nd edition matics is its pure limpid simplicity, to Princeton for two years. He re­ 1984), Dedekind sums (with Hans branching out into a myriad of pat­ turned to Harvard in 1933, where he Rademacher, 1972), Bessel polyno­ terns and interconnections that defy advanced to the rank of professor. mials ( 1978) and Representations of imagination." He also said that his In 1952, he moved to the Institute integers as sums of squares ( 1985). career consisted of "searching out for Advanced Study in Princeton as In addition, he was the editor of interesting problems of a simple va­ a professor of mathematics and was Hans Rademacher's collected works riety" and establishing some results. named professor emeritus in 1977, a and co-editor (along with J. Lehner When the field would get "too big position he held until his death. and M. Newman) of Rademacher's and complex, I would move out and Topics in analytic number theory. look for new things," he said. His honors and awards include Born in Rumania in December, Professor Whitney was intensely election to the National Academy of 1912, Grosswald, like many Jews, concerned with what he saw as the Sciences in 1945, the Wolf Foun­ fled to Paris in the late 1930's to failure of the U.S. educational sys­ dation Prize in 1982 (shared with escape the Nazi terror. With the Ger­ tem in mathematics, and during the Mark Grigorevich Krein), and the man occupation of that city immi­ past 20 years he pursued this concern AMS Leroy P. Steele Career Award nent, in June, 1940 he travelled on with great energy, particularly on the in 1985. In 1976, President Carter foot to Orleans, eventually making elementary school level. He pointed conferred the National Medal of Sci­ his way to the safety of Cuba, by way out that young children's intuitive ence on Professor Whitney. He deliv­ of Spain. He remained in Havana ways of thinking are similar to that ered the AMS Colloquium Lectures until 1946, and then spent two years of mathematicians. However, school in August, 1945, and served as AMS in Puerto Rico. mathematics is presented in terms Vice President, 1948-1949. In addi­ In 1948 Grosswald came to the of narrow objectives and in language tion, he served on the editorial com­ United States to attend the Uni­ that has little meaning to the chil­ mittees of Transactions of the AMS versity of Pennsylvania, where he dren. By the end of their schooling, (1942-1949) and of Mathematical studied number theory with Hans most students have learned not to Reviews (1949-1952). Rademacher, earning the Ph.D. in think when they see a mathematics Among Professor Whitney's non­ 1950. After teaching for two years at problem; they either hit a mental mathematical pursuits were avid in­ the University of Saskatchewan, he block or respond with a formula or terests in music and mountain climb­ returned to the University of Penn­ preset strategy. He saw standardized ing. He played the violin, viola, and sylvania as a member of the faculty, testing as one of the main culprits. piano and was concertmaster of the remaining there for sixteen years. In Professor Whitney believed that Princeton Community Orchestra. He 1968 Grosswald accepted a profes­ it was important not to simply teach was fond of mountaineering trips, sorship in the department of math­ the final results of a mathematical and particularly enjoyed the Swiss ematics at Temple University and concept, but to show where the con­ Alps. With his cousin, he established he taught there until his retirement cept comes from. "Teaching the final the Whitney-Gilman Route on Can­ in 1980. Twice he was a member results only leaves a lifeless jewel, not non Mountain in New Hampshire. of the school of mathematics at the

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 685 News and Announcements

Institute for Advanced Study; on sev­ Kothe died on April 30, 1989 at sity of Goettingen in 1932, worked eral occasions he was a visiting pro­ Frankfurt. with Julius Wolff in Utrecht during fessor at the Technion, in Haifa. M. S. Ramanujan 1933, and came to Columbia Univer­ Professor Grosswald was survived University of Michigan sity in 1934. Warschawski founded by his wife of many years, Elizabeth two mathematics departments dur­ (nee Rosenthal, deceased May 11, Stefan E. Warschawski ing his career; one at the Institute 1989) and his daughters, Blanche, 1904-1989 of Technology of the University of of Berkeley, California, and Vivian Minnesota in 1952, the other in 1963 Steve Warschawski, one of the lead­ Murphy, of Pittsburgh, Pennsylvania. at the University of California, San ing authorities on the boundary be­ He was buried in Mount Sharon Diego. Prior to going to the Uni­ havior of conformal mapping, died Cemetery, Springfield, Pennsylvania, versity of Minnesota he held posi­ on May 5, 1989. In a speech he gave onApril14, 1989. tions at the University of Rochester at the celebration of his 85th birth­ Marvin I. Knopp and Washington University. In 1944 day a month earlier, he discussed his Bryn Mawr College he joined the Applied Mathematics exception to the effort to become an Group at Brown University to work is a young saying that mathematics on problems related to the war ef­ Gottfried Kothe person's game. He loved mathemat­ 1905-1989 fort. After his retirement from the was active in it ics his enitre life and University of California, San Diego Graz, until he became ill the day after this Gottfried Kothe was born in in 1971, Warschawski continued to he celebration speech. Austria on December 25, 1905; teach occasional courses there and mathematics, physics, chem­ Warschawski's early research led studied also at San Diego State University. grad­ conditions which istry and philosophy and was to sharp geometric His research flourished during his re­ insure that the Riemann mapping uated from Graz in 1927. He wrote tirement years. Indeed, one third of a disk to a region will his habilitation at MUnster, in 1931. function from his papers were published after his he have a derivative at a point or along In his early mathematical career retirement. with Emmy Noether in an arc of the boundary circle. These collaborated Warschawski directed the research Bonn results led him to the first complex Gottingen, Otto Toeplitz in of nineteen Ph.D. students. He was Kellogg's theorem. and Heinrich Behnke in MUnster; his analysis proof of generous with help and advice to all to show that the work with Toeplitz was a forerun­ He was the first who approached him. Even through satisfies and ner in the area of functional analysis mapping function f' his retirement years, lines formed at now referred to as Kothe sequence 1/!' E Hp for all p > 0 if the region his door near qualifying exam time II has a continuously turning tangent. spaces. In the post World War as graduate students would come to notions of "linear era he was a leading force in the He introduced the him for help. Students who never "regulaer unbewallt" area of topological vector spaces and unbewallt" and had a class with him knew by his related to the mod­ the author of a two-volume trea­ which are closely reputation that he would be a good quasiconformal and tise on topological vector spaces. His ern notions of person to talk to. curves. He close association with the French asymptotically conformal He is survived by his wife, lise to make system­ school of Dieudonne, Grothendieck was one of the first Kayser Warschawski, who was the measure-he and Schwartz and his leadership in atic use of harmonic center of his life during their 43 measure" follow­ Germany produced a leading group called it "conformal years of marriage. As a couple they in he obtained his of functional analysts, particularly ing Ostrowski. Later helped to make the departments at of now classical results on the existence Germany. Kothe was a person Minnesota and San Diego into warm higher derivatives broad mathematical interests and a and continuity of and friendly places. Their gracious to at the boundary. In addition to his source of affection and inspiration hospitality is remembered by every­ behavior he made many students and colleagues. work on boundary one who was fortunate enough to of important contributions to approxi­ Kothe taught at the universities know them. MUnster, Giessen, Marburg, Mainz, mation theory, minimal surfaces, and Burt Rodin mappings Heidelberg and finally at Frankfurt other aspects of conformal University of California, San Diego from which he retired; he was also such as integral equation methods Rector at Mainz and at Heidel­ for effectively computing the map­ Newly Elected Members berg. His honors included honorary ping function. of the NAS doctorates from Mainz, Montpellier, Warschawski was born April 8, MUnster and Saarbriicken, as well 1904 in Lida, now part of the Soviet The National Academy of Sciences as the Gauss medal from the Brun­ Union. He received his Ph.D. under (NAS) is a private organization of schweig Academy of Science. Alexander Ostrowski at the Univer- scientists and engineers dedicated to

686 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements the furtherance of science and its of a free, independent, and virtuous view with the Chronicle of Higher use for the general welfare. The NAS people." Education, Gomory said it was too was established in 1863 by a congres­ Among the 83 individuals re­ early to say what changes he might sional act of incorporation, signed by cently honored by election to the make at Sloan, but noted that he Abraham Lincoln, that calls upon the AAAS were three prominent mathe­ would like to address "the problems Academy to act as an official advi­ maticians: PERSI DIACONIS, Harvard of industrial competitiveness." sor to the federal government, upon University, FREDERICK W. GEHRING, request, in any matter of science or University of Michigan, and Wu­ Willcox Moves to the Office of technology. CHUNG HsiANG, Princeton Univer­ Governmental and Public Affairs At their 126th annual meeting sity. In addition, ALAIN CONNES of in April, the NAS elected 60 new the College de France, Paris, and Alfred B. Willcox will assume the po­ members and 14 foreign associates MIKHAEL GROMOV of the Institute sition of Interim Head of the Office from eight countries in recognition des Hautes Etudes Scientifiques, Bures­ of Governmental and Public Affairs of their distinguished and continu­ sur-Yvette, were elected as Foreign of the Joint Policy Board for Mathe­ ing achievements in original research. Honorary Members. matics (JPBM), beginning September This election brings the total num­ 1. Willcox, well-known as the Exec­ ber of current members to 1,573; the Gomory Heads utive Director of the Mathematical total number of foreign associates to Sloan Foundation Association of America (MAA), is 262. retiring from that position after 21 The following mathematical sci­ Ralph E. Gomory, formerly senior years. entists were elected to the NAS: PAUL vice-president for science and tech­ In his new position, Willcox re­ C.-W. CHu, University of Houston; nology at IBM, was named president places Kenneth M. Hoffman, who ROBERT C. DYNES, AT&T Bell Lab­ of the Sloan Foundation. Gomory, will head the Mathematical Sciences oratories; HILLEL FURSTENBERG, He­ known for his research in the math­ Education Board (MSEB) of the Na­ brew University; FREDERICK W. ematics of discrete optimization, be­ tional Research Council. The current GEHRING, University of Michigan; gan in the new position in June. head of MSEB, Marcia P. Sward, is JoHN McCARTHY, Stanford Univer­ The Sloan Foundation is one of leaving to replace Willcox in the top sity; LAWRENCE A. SHEPP, AT&T Bell the nation's 25 largest private funds, position at the MAA (see Notices, Laboratories; and GEN SHIRANE, with assets of more than $550 mil­ May/June 1989, page 573). Brookhaven National Laboratories, lion. A major supporter of higher An advertisement for the nation­ Upton, NY. MIKHAEL GROMOV of education, the Foundation made $20 wide search for a permanent head the Institute des Hautes Etudes Sci­ million in grants last year and has of the JPBM Office of Governmen­ entifiques, Bures-sur-Yvette, was programs in liberal arts; economics; tal and Public Affairs appears in this elected as a foreign associate. and science, technology, and mathe­ issue of Notices. The JPBM is the matics. The Sloan Research Fellow­ public policy arm of the AMS, the Newly Elected Members ship Program awards each year some MAA, and the Society for Industrial of the AAAS 90 fellowships to young scholars in and Applied Mathematics. the sciences. The American Academy of Arts and Gomory received his Ph.D. in Department Chairs' Colloquium Sciences (AAAS) was founded in mathematics from Princeton Univer­ Set for October 1780 by John Adams and other lead­ sity in 1954. He served in the Navy ers of the American Revolution and and was a Higgins Lecturer in Math­ Each year, the Board on Mathe­ is an international honorary society. ematics at Princeton before joining matical Sciences of the National For over two centuries, the AAAS has IBM's Research Division in 1959. A Research Council sponsors a two­ been a leading force in American in­ member of the National Academy day Department Chairs' Colloquium. tellectual life and, among its current of Sciences, the National Academy These meetings provide an opportu­ membership of over 3300 scientists, of Engineering, and the American nity for mathematical sciences de­ artists, business and public figures, Academy of Arts and Sciences, Go­ partment chairs, federal agency rep­ it counts 148 Nobel Laureates and mory received last year the nation's resentatives, and other interested par­ 58 Pulitzer Prize Winners. The pur­ top honor in science, the National ties to meet and discuss issues of pose of the Academy, as set forth Medal of Science. mutual concern in a relaxed yet stim­ in its original 18th-century charter, In taking the new position, Go­ ulating environment. is to "cultivate every art and science mory replaces Albert Rees, who will This year's colloquium will be which may tend to advance the in­ become a senior research economist held October 27-28 at the Holiday terest, honor, dignity, and happiness at Princeton University. In an inter- Inn Crowne Plaza in Crystal City,

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 687 News and Announcements

Virginia, just outside Washington, • Fostering Undergraduate Pro­ The report covers the budgets of DC. The theme for the colloquium is grams in Statistics: Panel of statis­ all federal agencies supporting re­ "Chairing the Mathematical Sciences tics administrators, organized by J. search in the mathematical sciences. Department of the 1990s." The pro­ Sethuraman, Florida State Univer­ Copies of the report (publication # gram is designed to highlight the role sity. NSF89-306) are available from: Mar­ of the department chair as the man­ Space is limited for the collo­ garet Meredith, Government Studies ager of a unit of a college or univer­ quium, and advance registration is Group, Division of Science Resource sity, with responsibility for adminis­ required; the deadline is October Studies, Room L-602, 1800 G Street tration, research, and education. 9. A nonrefundable registration fee NW, Washington, DC 20550; tele­ Of particular interest will be the of $150 will be charged. For fur­ phone 202-634-4636. panel of deans and provosts, who ther information, contact the Board will discuss how mathematical sci­ on Mathematical Sciences, telephone Report Reviews ences departments compete for re­ 202-334-2421. NSF Calculus Program sources with other academic depart­ ments and how mathematical sci­ The National Science Foundation ences chairs can use the competition NSF Issues (NSF) has received a report evalu­ to their best advantage. The program Federal Budget Study ating the Foundation's year-old pro­ also includes panels on examining gram in calculus curriculum reform. curricular issues, expanding opportu­ The federal government's fiscal year The study was conducted by William nities for funding mathematical sci­ 1990 budget proposes an increase of Browder of Princeton University, ences research and program develop­ nearly 10% in funding for research President of the AMS, and Lida ment, and broadening the participa­ and development (R&D), with de­ Barrett of Mississippi State Uni­ tion of mathematical scientists in all fense programs as the major share, versity, President of the Mathemat­ of scientific research. according to a recent report by the ical Association of America. Robert The sessions, together with their National Science Foundation (NSF). F. Watson, Director of the Divi­ organizers, are: Federal funding for civilian R&D sion of Undergraduate Science, Engi­ • The View from Above: Panel programs is slated to increase by 11% neering and Mathematics Education of deans and provosts, organized by in fiscal 1990 to $23.5 billion. De­ (USEME), the larger organizational Ronald Douglas, State University of fense funding for R&D is proposed structure housing the calculus pro­ New York at Stony Brook. to rise by only 9%, but would still gram, requested the report. • Curricular Issues: Initiating stud­ comprise 65% of the total R&D bud­ Reviewing the first year of the ies and stimulating change, organized get. NSF Calculus initiative, the report by FrankL. Gilfeather, University of The general science budget func­ states that the breadth of activity New Mexico. tion, 95% of which supports basic proposed and the involvement of • Funding Opportunities: Overview research, is to receive an 11% in­ major state institutions, liberal arts of funding sources and modes, orga­ crease. The report says that most of colleges, and premier private institu­ nized by James Glimm, State Uni­ the increase would go to the NSF tions indicated the pervasive nature versity of New York at Stony Brook. to support Science and Technology of the concern about the content and • Federal Agencies Forum: Rep­ Centers, Engineering Research Cen­ teaching of calculus. resentatives from funding agencies, ters, and Supercomputer Centers, as The reviewers also made the fol­ organized by Charles Holland, Air well as to support basic research at lowing recommendations for future Force Office of Scientific Research. the Department of Energy. Of all years: • MS2000 Update: Status report the R&D budget functions, the space • Institutions must have the op­ on the MS2000 project, organized R&D budget function is to receive portunity to continue projects lead­ by James Voytuk, National Research the largest increase, 34%. Much of ing to further innovation. A future Council. this increase is attributable to the direction for the calculus curriculum • David Report Update: Progress Space Station Freedom. has not been clearly established, and to date and discussion of uses for the Other civilian programs to re­ a premature end to exploration could report, organized by Lawrence Cox, ceive increases are the National Hu­ be counterproductive. A parallel can National Research Council. man Immunodeficiency Virus Pro­ be seen with "new math" of the 1960s • Statistics and Operations Re­ gram, the Human Genome Project, and 1970s, which may have failed search in the 1990s: Discussion of and the Superconducting Supercol­ in part because the implications of trends and challenges, organized by lider. The NSF increase is part of the the innovations were not worked out J. Sethuraman, Florida State Univer­ Administration's plan to double the in detail before new curricula were sity. NSF budget by 1993. adopted for classroom use.

688 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

• The NSF should support one or ence Foundation, 1800 G. Street The NSF plans to include in the more large scale projects that would NW, Washington, DC 20550. new awards the last year of the cen­ pull together and focus the current ters' current contracts and the fol­ efforts in order to guide future direc­ NSF Makes Four lowing 5 years, so that the centers tions. EPSCoR Awards will be fully supported through 1995. • The diversity of institutions in­ The average yearly funding for each volved in the projects should con­ The National Science Foundation center will be increased from the tinue. Calculus is taught everywhere: (NSF) has awarded four new grants present level of about $1 0 million high schools, community colleges, to the states of Idaho, Louisiana, to $14 million, allowing for upgrad­ small and large schools, and schools Mississippi, and South Dakota ing of facilities and expansion for with varying quality of faculty and through its Experimental Program education and training activities at students. Changes must be designed to Stimulate Competitive Research the centers. The increase is part of for implementation in many different (EPSCoR). Part of the programs in the NSF's fiscal year 1990 budget settings and for meeting the needs of Louisiana and Mississippi will sup­ request, which is still subject to Con­ the diversity of student populations. port research in the mathematical gressional approval. • Issues related to the delivery of sciences. The center whose funding was not the calculus course-teaching meth­ Begun in 1978, EPSCoR now in­ renewed is the John von Neumann ods, the nature and preparation of volves 16 states and Puerto Rico in Center in Princeton, which is run by students, the size of the institution, a program designed to improve the a consortium of 13 universities. The the objectives of the student and the quality of science and engineering re­ center's supercomputer was built by curriculum for the utilization of the search, to increase the number of sci­ Control Data Corporation, which has calculus, the quality and educational entists and engineers able to compete closed ETA Systems, Inc., its super­ level of the faculty-are all as im­ successfully for federal grants, and computer division. Control Data will portant to the development of a new to foster long-term improvements in continue to maintain the machine calculus course as the factual content. research and education in participat­ and its software for 7 years. Care should be taken so that, in fu­ ing states and their academic institu­ The other four centers are already ture multi-year grants, these delivery tions. considering which new machines to issues are not neglected. The four states awarded the new buy. The Pittsburgh Supercomputing • Calculus is probably the key grants will receive $1.8 million each Center has ordered a Cray III, which course, at the collegiate level, for all over a three-year period. The funds is still under development. The cen­ scientists. Because of this unique role will be used to strengthen academic ter at the University of Illinois in in the curriculum, it is crucial that departments and to support the re­ Urbana-Champaign is considering a the experimentation of the calculus search of individual scientists and "massively parallel" machine to sup­ program continues and, at the same engineers. The states receiving the plement its two Crays. And several time, a future focus and direction or grants will also contribute a total of centers are said to be interested in a set of directions be found. nearly $32 million to this effort. The new supercomputer being developed The report concluded by stating specific activities to be supported in by International Business Machines that curriculum development is a this program have been selected by Corporation. long term and continuous process, the states and merit reviewed by the The five supercomputing centers and that it is crucial that the NSF NSF. were established in 1984 as cooper­ program be continued and expanded. ative projects funded by the NSF, Finally, the presidents stated their Four NSF Supercomputer states, universities, computer ven­ hope that the NSF would provide Centers Renewed dors, and other industrial partici­ support to address the improvement pants. The NSF supercomputer re­ of courses in the advanced part of the Four of the five supercomputer cen­ sources are used primarily for non­ mathematics curriculum beyond cal­ ters sponsored by the National Sci­ proprietary work by academic, gov­ culus. At the suggestion of the NSF, ence Foundation (NSF) received 5- ernment, individual, and industrial the full report will be published in the year renewal awards in May. The researchers. The centers also have October issue of the UME TRENDS fifth center was asked to submit are­ programs in education, training, and newsletter. vised proposal, which will be consid­ software development and frequently Copies of the report may be ob­ ered in August, because its primary act as test sites for new computing tained by writing to: JohnS. Bradley, supercomputer vendor dropped pro­ hardward and software. A wide va­ Program Director for Calculus, duction of the line of machine used riety of research disciplines are sup­ USEME, Room 639, National Sci- at the center. ported at the centers.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 689 News and Announcements

News from the Mathematical Everybody Counts. This report, rials and suggestions for stimulating Sciences Education Board which presents an overview and anal­ and sustaining interest in mathemat­ ysis of U.S. mathematics education, ics. The MSEB is seeking funding for was released in January. The atten­ an additional 20,000 kits. In 1985, the National Research Coun­ tion and debate the report attracted Making Mathematics Work for cil (NRC) established the Mathe­ indicate the nation's intense interest Minorities. Workshops in six cities matical Sciences Education Board in issues of mathematics education across the nation will be held during (MSEB), to provide national leader­ in the schools. Over 25,000 compli­ the fall, culminating in a national ship in mathematical sciences educa­ mentary copies of the report and half convocation in Washington, DC, in tion from kindergarten through col­ as many of the summary were sent spring 1990. The goal is to focus lege. The MSEB is designed to pro­ to leaders in scientific, engineering, national attention on helping more vide sustained attention over many and educational organizations and to minority students succeed in mathe­ years to the major issues affecting the key public officials. A reprint run of matics by utilizing the opportunities quality of learning and instruction in 15,000 copies was completed in May created by the current reform move­ the mathematical sciences. Since its to fill 8000 standing orders and to ments in mathematics education. In inception, the Board has grown into a meet the continued demand. addition, the project will identify powerful advocate for improvement Curriculum Philosophy and Frame­ successful programs for minority stu­ and innovation in mathematical sci­ work. Perspectives on School Mathe­ dents and devise ways of linking with ence education. matics: A Philosophy and Framework minority advocacy groups. The 34-member Board, carefully for the Curriculum will be published Wellspring meeting. Last Decem­ chosen to represent the various groups this fall. This document will serve as ber, representatives of some 40 cor­ having an interest in excellence in a bridge between Everybody Counts porations attended an MSEB sympo­ mathematical sciences education, is and Curriculum and Evaluation Stan­ sium on mathematics in the work­ comprised of mathematics teachers dards, published in March by the Na­ place. With the success of the sym­ and supervisors, college and univer­ tional Council of Teachers of Math­ posium, the MSEB now proposes to sity mathematicians, educational ad­ ematics (NCTM) and will emphasize establish a Corporate Council for ministrators, and representatives of computer technology and changing Mathematics Education. government, business, and industry. perspectives on mathematics. Pilot State Mathematics Coali­ The MSEB is chaired by Shirley A. Strands of the K-12 Curriculum. tions. During May and June, the Hill, professor of mathematics and This project examines fundamental MSEB held exploratory meetings in education at the University of Mis­ ideas of mathematics around which four cities to gather information souri at Kansas City. When her term new curricula could be built. The about forming state-level groups to expires in January, 1990, the new MSEB has commissioned 5 mathe­ improve the quality of mathematics chair will be Alvin W. Trivelpiece, maticians to lay out his or her ideas education. This fall, the MSEB will director of the Oak Ridge National about the various "strands": Change, make a number of grants to fledgling Laboratory. Ian Stewart; Dimension, Thomas Ban­ state coalitions. Since the Board's formation, Mar­ choff; Quantity, James Fey; Shape, Standards for Mathematics Teach­ cia P. Sward has served as Exec­ Marjorie Senechal; and Uncertainty, ers. The MSEB is working with the utive Director. In September, she David Moore. The publication target NCTM and the MAA on a 2-3 year will move to the top position at the date is December 1989. project to involve the entire math­ Mathematical Association of Amer­ A Year of National Dialogue. The ematical sciences community in de­ ica (MAA). Taking her place at Carnegie Corporation of New York veloping plans for a set of standards MSEB will be Kenneth M. Hoffman, has provided funds for various activ­ for excellence in mathematics teach­ Head of the Office of Governmental ities during 1990, which the MSEB ing. It is hoped that these standards and Public Affairs for the Joint Pol­ has designated as the year of national will eventually be used in the vol­ icy Board for Mathematics. Hoffman dialogue on educational issues in the untary certification program being will oversee the MSEB staff of thir­ mathematical sciences. developed by the National Board for teen and budget totaling about $1.8 PTA Kits. The MSEB has dis­ Professional Teaching Standards. million, which comes from govern­ tributed mathematics kits to 32,000 NCTM Standards Review. The ment agencies and private founda­ Parent-Teacher Associations. The MSEB is just completing a coordi­ tions. kits, designed to involve parents in nated project with the NCTM to pro­ The MSEB's coordinated efforts their children's mathematics educa­ vide an analysis of the NCTM's Cur­ encompass a wide range of pro­ tion, contain ideas for parent/child riculum and Evaluation Standards. grams. Some of this year's highlights activities, a motivational videotape, The analysis will assist the MSEB include: posters, a calculator, and other mate- and the NCTM in identifying

690 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements stumbling blocks to implementation accommodations, call the Statler Ho­ and applications (physical and chem­ of the Standards. tel, 607-255-2500. ical) of recent advances in theory of MS2000. This is a joint project Hamiltonian systems (lobes and turn­ of the MSEB and the NRC's Board stiles, cantori); extensions to many Fall Workshops on Mathematical Sciences. The goal degrees of freedom, incorporation of of the project is to develop a plan for The MSI, Cornell University, is kick­ quantum effects, adiabatic invariance the revitalization and renewal of col­ ing off 1989-1990 with four fall and adiabatic switching. legiate mathematics. This summer, workshops, three of which make up A fourth workshop on Large-Scale MS2000 will publish a background a major series in Applied Analysis, Numerical Optimization will be held report on the mathematics pipeline. one of the five major program areas on October 19-20. Organized by T. A paper on resources for collegiate of the Institute. Coleman and Y. Li, Cornell Univer­ mathematics is in preparation, and Under the general direction of sity, the workshop will discuss re­ work has begun on a paper on cur­ Jerrold E. Marsden, Cornell Uni­ cent algorithmic and software devel­ ricula. versity, the three associated work­ opments in numerical optimization The MSEB is located at 818 Con­ shops include: Geometric Phases in with a special focus on large-scale necticut Avenue, NW, Suite 500, Mechanics, October 9-13, organized problems. Particular emphasis will Washington, DC; telephone 202-334- by T. Ratiu, University of Califor­ be on practical methods, specific ap­ 3294. Visitors are always welcome. nia at Santa Cruz and R. Mont­ plications, and parallel computation. gomery, Mathematical Science Re­ In addition, recent advances in paral­ search Institute, Berkeley; Geomet­ lel methods for sparse linear systems News from the ric and Algebraic Integration Algo­ will be considered and discussed with Mathematical Sciences Institute rithms, November 4-8, organized respect to their relevance for large­ Cornell University by R. Grossman, University of Illi­ scale optimization. nois at Chicago, and C. Scovel, Los Those interested in attending any Symposium Alamos National Laboratory; and MSI workshop or event should con­ The Mathematical Sciences Institute Classical and Quantum Transport tact the MSI administrative offices (MSI) will hold a special symposium in Hamiltonian Systems, November at 201 Caldwell Hall, Cornell Uni­ titled, "Mathematics as Art, Mathe­ 17-20, organized by G. S. Ezra, Cor­ versity, Ithaca, NY 14853-2602, 607- matics as a Consumer Good," March nell University, and S. R. Wiggins, 255-8005. 29-31, 1990, at Cornell University. California Institute of Technology. This symposium will be devoted Geometric Phases in Mechanics AMS Awards Prizes to developing fruitful mechanisms will address holonomy via recon­ at International Science for education and research to best struction of dynamics, adiabatic pro­ & Engineering Fair encourage the interplay of mathe­ cesses, averaging, rotating and cou­ matics and its applications in busi­ pled structures, and nonlinear stabil­ The AMS awarded seven prizes total­ ness, industry, and government. The ity and control. Both quantum and ing $3000 to seven outstanding high symposium will bring together math­ classical phases will be discussed. A. school students for exhibits at the ematicians, scientists, engineers, and Pines, University of California at 40th International Science and Engi­ those responsible for mathematics Berkeley, and F. Wilczek, Institute neering Fair held in Pittsburgh, PA, applications from business, industry, for Advanced Study, Princeton, are on May 7-13. There were a total of and government. One outcome of the among the principal invited speakers. 746 exhibits at the fair, of whom symposium will be recommendations Topics to be covered at the work­ SO were in the mathematics classi­ for developing exciting environments shop on Geometric and Algebraic fication. The exhibitors qualified for which will attract young people into Integration include Hamilton Jacobi this fair by winning prizes at regional the mathematical sciences. theory and numerical integrators, fairs held in the U.S. and abroad. A A reception on Thursday, March chaotic systems, Symplectic and Lie­ panel of nine judges representing the 29, from 7 to 9:30 p.m., at Cornell Poisson integrators, integration in AMS examined all of the mathemat­ University's Statler Hotel will be the closed form, symbolic integration ics entries and several in other clas­ opening event of the symposium. of differential equations, mixed nu­ sifications which had obvious math­ Details about the symposium pro­ meric/symbolic integration algo­ ematical content (one prize-winning gram will be announced as they be­ rithms, and trees and integration al­ entry was in the chemistry section), come available. For general informa­ gorithms. and interviewed the exhibitors. All tion, contact MSI at Cornell Uni­ The workshop on Classical and of the judges interviewed each of the versity, 201 Caldwell Hall, Ithaca, Quantum Transport in Hamiltonian twelve students whose exhibits were NY 14853-2602, 607-255-8005. For Systems will address development found to be the most interesting, and

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 691 News and Announcements

finally selected one first prize winner n-tuples of Integers"; VLADIMIR TE­ At the same time, he was an active to receive $1000, two second prize ICHBERG, 17, Bronx High School of member of the Vienna Circle, which winners to receive $500 each, and Science, New York, for "Solution in the 1920s was Europe's premiere four third prize winners to receive Set of the Inequality phi(x) > B"; cross disciplinary intellectual group, $250 each. Each prize was accompa­ and NICOLE STEINBERG, 17, Mid­ and he organized and lead the Vienna nied by a certificate from the Society. wood High School at Brooklyn Col­ Mathematical Colloquium. After im­ The interviewing process was the lege, Brooklyn, New York, for "The migrating to the United States in most significant part of the judg­ Octagon Anomaly". Skinner and 1936, he continued mathematical re­ ing, offering the judges opportunity Mootha were repeat winners from search in his previous fields of inter­ to meet with very talented and en­ the 1988 fair. est and extended his work to studies thusiastic students and offering the The judges representing the AMS in the foundations of non-Euclidean students a chance to have substan­ were Professors Michael H. Albert, geometry, probabilistic geometry and tive discussions with working math­ Jerry L. Bona, Rami Grossberg, Stu­ the algebra of functions. Perceiving ematicians, and to obtain, in some art Hastings, Ignace I. Kolodner, that mathematics was a branch, albeit cases, pointed criticism from them. Walter Noll, Daniel Sleator, William an especially powerful one, of human It seemed a worthwhile experience to Williams, and Carol Wood. thought, Menger also explored the re­ both groups. William 0. Williams lationship between ordinary and in­ Carnegie Mellon University tuitionistic logic. Throughout his life Menger was a great and dedicated Karl Menger Fund teacher. He loved his students and he loved teaching them. He sought to A fund has been established in the develop new and clearer means for memory of Karl Menger, a mathema­ articulation of the underlying con­ tician who was very devoted to both cepts of mathematics, especially of research and education. The ma­ calculus. He strove to make young jor contributors to the Karl Menger people comfortable with the study of Fund were his family and the fund mathematics so that he might share currently totals $40,000. with them his love for the beauty Clockwise from top left: Vladimir Teich­ Income from this fund will be and power of mathematics. It is to berg, Jordan Ellenberg, W. Williams (AMS used to support the AMS's participa­ help perpetuate that effort that the judge), Andrew Lines, Vamsi K. Mootha, tion in the International Science and award in his name has been estab­ Michael Stern, Nicole Steinberg, and Engineering Fair (see the preceding lished. Individuals interested in mak­ Christopher Skinner. news item.) Effective in 1990, the ing a donation to this fund may send (Photograph courtesy of FocusOne.) AMS awards at the Science Fair will their contributions, payable to Karl The first prize was awarded to be named the Karl Menger Awards. Menger Fund/American Mathemati­ CHRISTOPHER SKINNER, 16, of Hall Karl Menger ~as particularly con­ cal Society, to P.O. Box 1571, Annex High School, Little Rock, Ark., for cerned with encouraging young peo­ Station, Providence, RI 02901-1571. "On the Diophantine Equation apx + ple who showed an interest in math­ bqY = C + DP2 Qw". Second prize ematics. In establishing the fund, his Winners of the awards went to VAMSI K. MooTHA, daughter Professor Eve L. Menger U.S. Math Olympiad 18, Monsignor Kelly High School, felt that the Science Fair awards Beaumont, Texas, for "New Findings would be a fitting memorial to her Eight mathematically talented stu­ Related to P1-Sets"; and MICHAEL father because they recognized merit dents have won Olympiad Medals in STERN, 18, Armand Hammer United and creativity in young people in the 18th annual USA Mathematical World College, Montezuma, New mathematics. Olympiad (USAMO). The winners Mexico, for "Chemical Chaos: Com­ Professor Karl Menger had wide were honored on June 13 at the US­ puter Modelling of the Belousov­ interests which included, but ranged AMO Awards Ceremony, held at the Zhabotinskii Reaction". Third prize far beyond, pure mathematics. His National Academy of Sciences and awards were made to ANDREW LINES, mathematical research while a mem­ the State Department in Washington, 16, Yorktown High School, Arling­ ber of the faculty at the University DC. The three-stage competition in­ ton, Virginia, for "Computer Mod­ of Vienna included contributions to volved more than 400,000 students eling of Minimal Surfaces"; JoRDAN the theory of dimensions, metric and nationwide. ELLENBERG, 17, Winston Churchill distance geometry and curve theory; The eight USAMO winners, in High School, Potomac, Maryland, his work in the latter field produced order of their scores, are: JoRDAN S. for "An Investigation of k-ary Menger's Theorem in Graph Theory. ELLENBERG, Winston Churchill High

692 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

School, Potomac, MD; ANDREW H. Putnam Exam Winners The five highest scoring individ­ KRESCH, Haverford Township Se­ Announced uals are designated as Putnam Fel­ nior High School, Havertown, PA; lows and each receive a $500 award. JoNATHAN T. HIGA, Ialani School, The forty-ninth annual William Low­ Their names are: DAVID J. GRA­ Honolulu, HI; RICHARD S. RusczYK, ell Putnam Mathematical Competi­ BINER, Princeton University; JEREMY Austin High School, Decatur, AL; tion was held on December 3, 1988. A. KAHN, DAviD J. MoEws, BJORN JEFFREY M. VANDERKAM, North Ca­ Administered by the Mathematical M. PooNEN, Harvard University; rolina School of Science and Mathe­ Association of America (MAA), the RAVI D. VAKIL, University of matics, Durham, NC; DAVID B. CARL­ prestigious competition drew 2096 Toronto. TON, Oberlin Senior High School, contestants from 360 colleges and The next six highest ranking indi­ Oberlin, OH; SAMUEL K. VANDER­ universities from across the U.S. and viduals receive $250 each. They are: VELD£, Amherst County High School, Canada. WILLIAM P. CROSS, California Insti­ Amherst, VA; DEMETRIO D. MUNOZ, The competition consists of an ex­ tute of Technology; SERGE ELNIT­ Thomas Jefferson High School for amination, given in two, three-hour SKY, Carleton University; KARL M. Science and Technology, McLean, sessions. Designed to test original­ WESTERBERG, Carnegie-Mellon Uni­ VA; (David Carlton and Samuel Van­ ity as well as technical competence, versity; GLEN T. WHITNEY, Harvard dervelde tied for sixth place). the examination covers undergradu­ University; SIHAO Wu, Yale Univer­ One hundred forty-six selected ate mathematics through differential sity; JosHUA R. ZucKER, Stanford students took the rigorous exami­ equations. It also may include ques­ University. nation designed to test problem solv­ tions that cut across various disci­ William Lowell Putnam, a mem­ ing ingenuity as well as knowledge plines, as well as self-contained ques­ ber of the Harvard class of 1882, of mathematics. The USAMO com­ tions that do not fit into the usual began the competition that bears his petitors were the top performers in categories. name in 1938. The idea grew out two earlier competitions, the Amer­ An institution with at least three of Putnam's profound belief in the ican High School Mathematics Ex­ registered participants obtains a team value of organized team competition amination and the American Invi­ rank based on the rank of three des­ in college studies. In 1927, Putnam's tational Mathematics Examination, ignated individual contestants. How­ wife created a trust fund to support held in schools throughout the U.S. ever, each contestant works indepen­ such activities. The first competition and Canada in February and March. dently on the examination, even if was in the field of English, and, a Following the awards ceremony, designated as a team member. few years later, a second competition the winners and 16 other students The five winning teams are listed was held in mathematics. who did well on the USAMO par­ below, in order of their ranking. (In Distribution Policy for ticipated in an intensive, four-week all of the lists that follow, con­ New Assistantships & Graduate training session at the U.S. military testants' names are in alphabetical Fellowships academy at West Point. The pur­ order.) Harvard University: DAVID pose of the training session is to J. MOEWS, BJORN M. POONEN, CoN­ When the decision was made to re­ prepare a U.S. team of 6 students STANTIN S. TELEMAN; Princeton Uni­ move the assistantship and graduate for the 1989 International Mathe­ versity: DANIEL J. BERNSTEIN, DAVID fellowship information from the De­ matical Olympiad (IMO), to be held J. GRABINER, MATTHEW D. MULLIN; cember issue of Notices and include in Brunswick, West Germany, July Rice University: HUBERT L. BRAY, it in an independent publication, 13-24. The training session also pre­ THOMAS M. HYER, JOHN W. MciN­ a first-year distribution policy was pares students for IMOs in subse­ TOSH; University of Waterloo: FRANK established. This distribution policy quent years. M. D'IPPOLITO, COLIN M. SPRINGER, did not effectively get the informa­ Romania initiated the IMO in MINH-TUE Vo; California Institute tion into the hands of those to whom 1959, and the U.S. has participated of Technology: WILLIAM P. CROSS, it is most useful. Consequently, be­ in the contest since 1974. Typically, ROBERT G. SOUTHWORTH, GLENN P. ginning with the 1990-1991 edition, 30-35 nations send teams to the com­ TESLER. the distribution of Assistantships and petition. The U.S. team has usually The first place team receives an Graduate Fellowships in the Mathe­ placed among the top three nations award of$5000, and each team mem­ matical Sciences has been expanded. in this prestigious competition, and ber receives $250. The awards for In addition to the institutional in 1977, 1981, and 1986, the U.S. second place are $2500 and $200; distribution, individual AMS mem­ earned first place. Last year, the So­ for third place, $1500 and $150; for bers will be able to request one viet Union received the top honor, fourth place, $1000 and $1 00; and free copy. A special form to re­ while the U.S. placed sixth. for fifth place, $500 and $50. quest this copy was included with the

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 693 News and Announcements individual member dues notices that agreements with two additional for­ first revision, they must be received were mailed in June. AMS members eign mathematical societies, the Janos not later than October 1, 1989. should complete and return this form Bolyai Mathematical Society (Hun­ Please send suggestions to: by the deadline of October 1, 1989 to gary) and the Ramanujan Mathemat­ ensure receipt of their copies when ical Society (India). Under the terms American Mathematical Society the issue is published. of these agreements, AMS members Attention: REDMS The institutional distribution will may join these societies and mem­ P.O. Box 6248 consist of two complimentary copies bers of these societies may join the Providence, RI 02940 to each institutional member and AMS at reduced dues rates. The most useful suggestions are one complimentary copy to the other Further information about these those accompanied by citations of mathematical sciences departments societies and other societies with their Russian sources-preferably jour­ that grant at least a bachelor's degree which the AMS has reciprocity agree­ nal or book title, volume and page and are listed in the Mathematical ments may be found in the complete numbers, and author's name. Please Sciences Professional Directory. list of reciprocity agreements else­ include your own best guesses at the AMS members (individual and where in this issue of Notices. translation of any words or phrases institutional) may also purchase ad­ that you suggest. ditional copies of Assistantships and Revision of Graduate Fellowships in the Math­ Russian-English Dictionary ematical Sciences at a special pre­ Electronic Submission publication price. Information about of Abstracts Deadline for this prepublication offer, which is Receipt of Suggestions only available until October 1, 1989, The MayfJune 1989 issue of No­ is included on the special form in the It is expected that the first revision of tices contained a news item on the dues notice mailing or may be ob­ the AMS Russian-English Dictionary electronic submission of abstracts for tained by contacting the AMS Cus­ of the Mathematical Sciences will be talks given at Society meetings (pages tomer Service Department at P.O. published in 1990. (See the April 574-575.) Because of an unfortunate Box 6248, Providence, RI 02940 or 1988 issue of Notices, page 54 7.) line break, the electronic address by calling 800-556-7774. Suggestions of Russian words and given in that item was ambiguous. phrases to be added to the dictionary Requests to obtain the package of AMS Reciprocity Agreements will be welcome at any time, since files for use in submitting abstracts the dictionary will be updated from electronically should be sent to the The American Mathematical Society time to time. However, in order for Internet address below. has recently established reciprocity suggestions to be considered for this [email protected]

ASYMPTOTIC BEHAVIOR OF DISSIPATIVE Hausdorff dimension, and the stability of the flow on the SYSTEMS global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications Jack K. Hale and especially emphasizes delay equations, reaction-diffusion (Mathematical Surveys and Monographs, Volume 25) equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the This book is directed at researchers in nonlinear ordinary existence of a global attractor, and, for several examples, he and partial differential equations and at those who apply discusses some properties of the flow on the global attractor. these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on 1980 Mathematics Subject Classifications: 34, 35, 58 the global attractor for a discrete or continuous dynamical ISBN 0-8218-1527-X, LC 87-33495 system. The author presents a detailed discussion of abstract ISSN 0076-5376 March 1988 smooth maps and 200 pages (hardcover), properties and examples of asymptotically Individual member $32, List price $54, semigroups. He also covers some of the continuity properties Institutional member $43 of the global attractor under perturbation, its capacity and To order, please specify SURV /25 NA

Shipping/Handling: 1st book $2, each additional Sl, maximum S25; by air, 1st book $5, each additional S3. maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-9930, or call toll free 800-556-7774 to charge with VIsa or MasterCard

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

AMS Centennial program. The Trustees have arranged 1990; 2. will have earned, by the be­ Research Fellowships a matching program from general ginning of their fellowship tenure, a Invitation for Applications, funds in such fashion that funds for doctoral degree in one of the mathe­ 1990-1991 at least one fellowship are guaran­ matical sciences; 3. will have held the Deadline December 1, 1989 teed. Because of the generosity of the doctorate for no more than five years AMS membership it was possible to as of January 1, 1990; and 4. will not These fellowships are intended to award two fellowships for 1987-88, previously have held any other NSF provide enhanced opportunities for three fellowships for 1988-89, and postdoctoral fellowship. The evalu­ research to talented mathematicians three fellowships for 1989-90; how­ ation of applicants will be based, who have had relatively few such ever, in the several preceding years, it in part, on ability as evidenced by opportunities in the past. These fel­ was not financially possible to award past research work and letters of rec­ lowships are open to any individual more than one fellowship. ommendation, likely impact on the who is seven to twelve years past the The deadline for receipt of appli­ future scientific development of the Ph.D.; i.e., has received the Ph.D. cations is December 1, 1989. Awards applicant, and scientific quality of degree between January 1, 1978, and will be announced in February 1990, the research likely to emerge. Appli­ December 31, 1983. It is expected or earlier if possible. cants' qualifications will be evaluated that applicants will have had a min­ For application forms, write to by a panel of mathematical scientists. imum of three years of full-time the Executive Director, American For copies of the application bro­ teaching or comparable industrial ex­ Mathematical Society, P.O. Box 6248, chure or further information, contact perience. In addition, the selection Providence, RI 02940. (It should be the Special Projects Program, Divi­ committee will give preference to ap­ noted that completed application and sion of Mathematical Sciences, Na­ plicants who have not had extensive reference forms should NOT be sent tional Science Foundation, 1800 G postdoctoral research support. to this address, but to the address Street, NW, Washington, DC 20550; The stipend for fellowships award­ given on the forms.) tel. 202-357-3453; or the American ed in 1990-91 has been set by the Mathematical Society at tel. 401-272- Trustees of the Society at $36,000 for Mathematical Sciences 9500. nine months. In addition, there will Postdoctoral Research Fellowships The deadline for applications is be an expense allowance of $1,000. November 15, 1989. Applicants must be citizens or per­ The NSF Mathematical Sciences Post­ manent residents of a country in doctoral Research Fellowship pro­ U.S.-U.S.S.R. Cooperative North America. The fellowship may gram is designed to permit recipients Agreement at NSF be combined with other stipends to choose research environments that and/or part-time teaching; this op­ will have maximal impact on their fu­ The U.S. and the U.S.S.R. have tion can be used to extend the award ture scientific development. Awards signed agreements creating new op­ to cover a period of up to two years. will be made for appropriate research portunities for joint scientific re­ For further information about the in pure mathematics, applied mathe­ search programs. One part of the acceptability of such arrangements, matics and operations research, and agreements involves cooperative individuals should contact the Secre­ statistics at an appropriate nonprofit projects between the National Sci­ tary of the Society. United States institution. ence Foundation (NSF) and the The number of fellowships to be The fellowships will be offered U.S.S.R. Academy of Sciences. awarded is small and depends on the only to persons who 1. are U.S. cit­ The agreements address cooper­ amount of money contributed to the izens or nationals as of January 1, ative efforts in basic rather than

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 695 Funding Information applied science. The Memorandum summer or early in the fall. For Undergraduate Research of Understanding signed by the NSF more information, contact Bernard Program at NSF and the U.S.S.R. Academy of Sci­ McDonald, Deputy Director, Divi­ ences will enable scientific exchange sion of Mathematical Sciences, 202- The National Science Foundation activities in the areas of mathemat­ 357-9669. The contact in the Di­ (NSF) has for the past two years ics, theoretical physics, chemistry, vision of International Programs is sponsored the Research Experiences life sciences, basic engineering re­ Gerson Sher, 202-357-7494. The ad­ for Undergraduates (REU), a pro­ search, arctic and cold region re­ dress is National Science Founda­ gram providing talented undergrad­ search, and science policy. Several tion, 1800 G Street NW, Washington, uate students with hands-on experi­ mathematical topics have been se­ DC 20550. ence doing research in science, math­ lected for support: complex analy­ ematics, and engineering. The idea is sis, geometry (differential, algebraic, to expose students to the excitement and topology), string theory, differ­ Deadlines for of research while they are still in the ential equations, algebraic structures, International Programs process of making career choices. representation theory, control the­ The REU program makes two ory, dynamical systems, algebra, and The National Science Foundation kinds of awards: Sites and Sup­ mathematical physics. has several programs supporting in­ plements. REU Sites bring together Three kinds of activities will be ternational collaborative research in groups of students during the sum­ supported through this program: co­ science and engineering. These pro­ mer for an organized program of re­ operative research projects, limited­ grams provide support for various search activities. The programs vary size seminars and workshops, and kinds of projects, including coopera­ in size from 6 to 12 students and last individual scientific visits. The pur­ tive research between individual in­ at least 7 weeks. REU Supplements poses of the seminars and workshops vestigators, long- and medium-term are less extensive: they permit an will be to identify joint scientific for young researchers, and research­ NSF principal investigator to add an priorities and to develop proposals oriented seminars or workshops. undergraduate to his or her research for joint research projects. The indi­ Two of these international pro­ grant. vidual scientific visits will be for the grams have upcoming deadlines. The The REU Sites program in the same purposes and will be confined to first supports cooperative research, Division of Mathematical Sciences exceptional circumstances; the proce­ seminars or workshops, and long­ (DMS) received the same number dures for these visits were not deter­ term visits (4-12 months) in Aus­ of proposals in 1988 as in the first mined at the time of this writing. tria, Germany, the Netherlands, Den­ year of the program, despite far more Proposals for support of travel to in­ mark, Finland, Norway, Sweden, the advance notice and publicity in the ternational meetings in the U.S.S.R. United Kingdom, and Switzerland. second year. Out of 27 proposals are specifically excluded. For more information, contact Chris­ received in 1988, there were 9 new Proposals for these activities will tine French or Christine Glenday, awards and 7 continuing awards, for go to the Division of International Division of International Programs, a total of about $0.5 million. Programs at the NSF. Cooperative 202-357-9700. The deadline is For 1989, the NSF has asked research projects in mathematics will September 15. Congress for a 75% increase for be forwarded to the NSF's Divi­ The second program supports sev­ the REU program. However, this sion of Mathematical Sciences for eral science activities in developing increase has not yet been appropri­ handling and funding. Seminars and countries: short-term planning visits, ated by Congress. In addition, the workshops in mathematics will be collaborative research, seminars, and increase would apply to the REU handled primarily by the interna­ dissertation improvement of grad­ programs across all disciplines in the tional division, with the cooperation uate students in developing coun­ NSF, so the amount by which the of the mathematics division. tries. For more information con­ DMS/REU budget might increase is There are no formal deadlines tact Ed Field (North Africa and unknown at this point. Nonetheless, for the program. However, because Turkey), 202-357-9402; Osman Shi­ there is likely to be an increase in proposals for international collabora­ naishin (South and West Asia), 202- the program's budget, and the DMS tions often require negotiation with 357-9402; Gerald Edwards (East is hoping for a greater number of the other country, in addition to the Asia), 202-357-9537; Harold Stolberg quality proposals for this important NSF's regular merit review, proposal or David Kelland (Latin America program. processing time will likely be longer and the Caribbean) 202-357-7421. John V. Ryff, Program Director than the usual 6 months. Though proposals may be submitted for the REU program in the DMS, An announcement about these at any time, the next target date is notes several aspects of the REU pro­ programs will be issued late this September 1. gram that proposals should cover in

696 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information order to improve chances of obtain­ Ryff emphasizes that a research (May/ June 1988, page 686), and the ing funding. experience does not necessarily mean 1989 awards were listed in Notices, • The program is intended to give simply proving theorems. There may (April 1989, page 413). In addition, students experience in research. This be educational and experimental com­ the UME TRENDS newsletter re­ must be the central goal of the ponents to the project as well as op­ cently carried an article on the REU project. portunities for writing and presenting program (May 1989, page 5). • Housing, meals, and social activity results. Deadline Change for Submission The 1989 deadline for REU Sites are the responsibility of the principal of NSA Research Proposals investigator. Proposals must provide proposals to the DMS is October details of how such day-to-day needs 10. For more information, contact The National Security Agency (NSA) will be met. John V. Ryff, Program Director, Re­ Mathematical Sciences Program • Daily scheduling of meetings, class­ search Experiences for Undergradu­ awards research grants to universities es, laboratory work, and any other ates, Division of Mathematical Sci­ in the areas of algebra, number the­ elements of the project must be de­ ences, Room 339, National Science ory, discrete mathematics, probabil­ scribed so that reviewers can assess Foundation, 1800 G Street, NW, ity and statistics. The next deadline the reasonableness of the plan and Washington, DC 20550; telephone for submitting proposals to the pro­ its potential for success. 202-357-3455; electronic mail: gram has been changed from Novem­ • The space allocated for student [email protected] (Internet) or ber 1, 1989, to October 15, 1989. work and meetings should be de­ jryff@note (Bitnet). Grants which are awarded in this scribed. REU Supplements may be re­ funding cycle can begin to incur ex­ • Sharing of resources by the host quested at any time, through a letter penses by June 1, 1990 and awards institution should be included in the sent to the program director han­ are made for a period of one, two proposal or in the budget. dling the research grant of the indi­ or three years. For further informa­ • Detailed recruitment procedures vidual requesting the supplement. It tion about the program, please call and provisions for allowing full ac­ is advisable to discuss the REU Sup­ 301-859-6438 or write to Marvin C. cess to all eligible students should be plements with the program director Wunderlich, Director, Mathematical included. before submitting first-time requests. Sciences Program, National Security • Proposals should consider means An article about the REU pro­ Agency, Attn. RMA, Fort George G. for evaluation and follow-up. gram in the DMS appeared in Notices Meade, MD 20755-6000.

NOMINATIONS FOR THE 1990 WIENER PRIZE

This prize of $4000, in honor of Norbert Wiener, is normally awarded every five years by the American Mathematical Society and the Society for Industrial and Applied Mathematics for an outstanding contribution to applied mathematics in the highest and broadest sense. The recipient must be a member of one of these societies and a resident of the U.S., Canada, or Mexico.

Nominations and suggestions by members of the mathematics community are eagerly sought. Please send them (hopefully with supporting documentation) to each of the following three people: I. M. Singer, Mathematics Department, Massachusetts Institute of Technology; E. H. Lieb, Mathematics Department, Princeton University; S. Smale, Mathematics Department, University of California, Berkeley. The letters should arrive by August 15, 1989.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 697 Look what's new in Mathematical Surveys and Monographs The Mathematical Smveys and Monographs sertes 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. Tarnarkin was pub­ lished. The sertes 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 give a swvey of the subject and a brtef introduction to its recent developments and unsolved problems. 71Je editorial committee. •• Victor W. Guillernin M. Susan Montgomery (Chairnlan) 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 hlgh 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 perfect reference books or possible textbooks for graduate level wurses.

0 Amenability by Alan L. T. Paterson, 1988, 416 pp. 0 Introduction to various aspects of degree theory in nsBN o-8218-1529-6]. Ust $90, Inst mem. $72, Banach spiCe& by E. H. Rothe, 1985, 254 pp. (LC 85- hxliv. mem. $54, Code SURV/29NA 8038; ISBN 0-8218-1522-9]. Ust $62, lnst mem. $50, hxliv. mem. $37, Code SURV/23NA 0 Direct and inverse scattering on tbe 6ne l:y Richard Beals, Percy Deift, and Carlos Torn:i, 1988, 0 Nonrommutative harmonic analysis by Mlchael E. Thyhr, 209 pp. (LC 88-14487; ISBN 0-8218-1530-X). Ust 1985, 344 pp. (LC 85-10924; ISBN 0-8218-1523-7). Ust $53, lnst mem. $42, Indiv. mem. $32, Code SURV/28NA $70, lnst mem. $56, Indiv. mem. $42, Code SURV/22NA

0 Basic bypergeometric aeries and applications by 0 1be meberbach coqJecture: Proceecliogll of the Nathan J. Fine, 1988, 144 pp. (LC 88-6235; ISBN 0-8218- symposium on the occasion of tbe proof, edited by 1524-5]. Ust $39, Inst mem. $31, Indiv. mem. $23, Albert Baemstcin, David Dmsin, Peter Duren, and Code SURV/27NA Albert Marden, 1985; reprinted 1987, 260 pp. (LC 85-10843; ISBN 0-8218-1521-0]. Ust $46, lnst mem. $37, Indiv 0 Operator theory and arithmetic in H by Hari Beroovici, mem. $28. Code SURV/21NA 1988, 275 pp. (LC 88-10344; ISBN 0-8218-1528-8]. Ust $67, lnst mem. $54, Indiv. mem. $40, Code SURV/26NA 0 Partially ordered abelian groups with int.erpo]ation by Kenneth R Goodearl, 1986, 358 pp. (LC 00-7876; 0 Asymptotic bebavior of dissipative systems l:y ISBN 0-8218-1520-2]. Ust $70, lnst mem. $56, Indiv. Jack K Hale, 1988, 198 pp. (LC 87-33495; ISBN 0-8218- mem. $42, Code SURV/20NA 1527-X). Ust $54, lnst mem. $43, Indiv. rrem $32, Code SURV/25NA

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

Standing orders are acreptcd for this and any other series published by the Society. Proronna invoices are sent to standing order custorrers prior to the publication of each new volurre. Shiprrent is made upon receipt of payment and publication To begin a standing order, please contact the Mernbershlp and Sales Department of the AMS.

PREPAYMENT REQUIRED. Order fium the American Mathematical Society, P. 0. Box 1571, Armex: Station, Providence, RI 02901-1571, or call 800-556-7774 fium within the wntinental U S. (401-272-9500, elsewhere] to use VISA or Maste!Card. Prices subject to change. Please add fOr SHIPPING AND HANDUNG: first book $2, each additional $1, $25 maximum By air, first book $5, each additional $3, $100 maximum Meetings and Conferences of the AMS

FUTURE MEETINGS

Boulder, Colorado August 7-10 701

Hoboken, New Jersey October 21-22 747

Muncie, Indiana October 27-28 749

Invited Speakers and Special Sessions 752

FUTURE CONFERENCES

Symposium on Some Mathematical Questions in Biology University of Toronto, August 7 755

Call for Topics 756

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 699 Coming Events

The January 17-20, 1990 Joint Mathematics Meetings will be held in Louisville, Kentucky. Full details on these meetings will appear in the October issue of Notices. Preliminary information on contributed paper sessions of the Mathematical Association of America can be found on page 588 of the May/June issue of Notices.

Louisville, Kentucky's largest city, is perhaps best known as the home of the famed Kentucky Derby. But this unique city offers much more: as the g~tewa,y to A_!llerica's westward expansion, a busy and energetic business center, and a focal point for innovative research in medical technology, Louisville is a rich blend of the past, present and future.

From the Louisville Falls Fountain, the world's largest floating fountain, anchored in the Ohio River, to the gracious Southern home of Farmington, designed by Thomas Jefferson, Louisville offers a range of attractions, new and old. The city boasts the largest collection of 19th century cast iron storefronts in the country outside of New York's SoHo district. Combining past and future, Louisville's Main Street shows off the striking, modernistic architecture of the international hospital chain Humana, Inc., and the Kentucky Center for the Performing Arts. Gracing the city is a system of 137 parks, 16 of which were designed by Frederick Law Olmstead, creator of New York's Central Park. The Museum of History and Science's IMAX Theater provides the ultimate motion picture experience with four-story screens and six-track sound, while the J. B. Speed Art Museum offers the more stately diversions of Rembrandt, Rubens, Monet, and Picasso, among others. Nine all-new trolleys, charming replicas of 18th century streetcars, provide free transportation between Louisville's central business district and the Ohio River waterfront area. Shopping takes on a distinctive flair, with many galleries selling handmade quilts, baskets, furniture, and pottery. Whether relaxing with one of the trademark mint juleps or strolling through the park-like setting of the Louisville Zoo, visitors will appreciate the variety of offerings in this remarkable city.

700 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Boulder Meetings August 7-10, 1989

Program

The August 1989 Joint Mathematics Meetings, including the 92nd The members of the Local Arrangements Committee are Larry W. Summer Meeting of the AMS, the 68th Summer Meeting of the Baggett, William L. Briggs, Frieda K. Holley, Richard A. Holley, Mathematical Association of America, and the 1989 summer meetings William H. Jaco (ex-officio), Andy Roy Magid (ex-officio), Arlan of the Association for Women in Mathematics and Pi Mu Epsilon will Ramsay (Chairman), William N. Reinhardt, Kenneth A. Ross (ex­ be held August 7-10 (Monday-Thursday), 1989, at the University officio), and Richard L. Roth. of Colorado, Boulder. Sessions will take place on the campus of the university. AMS-MAA-ITME Invited Address Pi Mu Epsilon, Inc., the national honorary mathematical society founded in 1914 at Syracuse University, will WHERE TO FIND IT PAGE celebrate its 75th anniveiSary at the Boulder meetings. HOW TO OBTAIN ACCOMMODATIONS 709 In honor of the occasion, AMS and MAA will cospon­ sor with Pi Mu Epsilon an invited address on The math­ AMS-MAA-llME INVITED ADDRESS 701 ematics of identification numbers by JosEPH A. GALLIAN, AMS-MAA INVITED ADDRESSES 701 University of Minnesota, Duluth. This talk is scheduled SUMMER MEETING OF THE AMS 702 for Wednesday, August 9, at 2:30 p.m. Progress in Mathematics Lectures, Colloquium Lectures, Prizes, Invited Addresses, Special Sessions, Contr~buted Papers, Council, Business Meeting AMS-MAA Invited Addresses OTHER JOINT AMS-MAA SESSIONS 703 By invitation of the AMS-MAA Joint Program Commit­ AMS SHORT COURSE 746 tee (Sheldon Axler, Chairman; Alexandra Bellow; Hugh SUMMER MEETING OF THE MAA 703 Montgomery; and Mary Ellen Rudin), four speakers will Hedrick Lectures, Invited Addresses, Minicourses, Contributed address the AMS and MAA on the history and devel­ Papers, Student Papers, Other Sessions, Business Meeting, Board opment of mathematics. The names of the speakers, of Governors, Section Officers, Banquet for 25-Year Members OTHER ORGANIZATIONS 708 AWM, JPBM, llME IMPORTANT DEADLINES TIMETABLE 721 AMS Abstracts OTHER EVENTS OF INTEREST 708 For consideration for special sessions Expired Of contributed papers Expired Book Sales, AMS Information Booth, Exhibits, Handout Table, Petition Table, Summer List of Applicants MAA Abstracts Of contributed papers Expired 715 REGISTRATION AT THE MEETINGS Summer List of Applicants Expired Fees, Dates, Times, Services Preregistration and Housing Expired MISCELLANEOUS INFORMATION 717 MAA Minicourse Preregistration Expired Athletic Facilities, Camping and RV Facilities, Car Rental, Child Motions for AMS Business Meeting Expired Care, Handicapped, Libraries, Local Information, Medical MAA Banquet (50% refund) Expired Services, Parking, Smoking, Social Events, Tour, Travel, Weather Western Hoe Down (50% refund) Expired MAPS 710,711, 714 llME Banquet (50% refund) Expired Rocky Mountain National Park Tour (50% refund) Expired PRESENTERS OF PAPERS 745 Hotel Changes and Cancellations July 17 PROGRAM OF THE SESSIONS 733 Residence Hall Package Cancellation (90% refund) July 17 Preregistration Cancellations (50% refund) July 31

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 701 Meetings their affiliations, the titles, dates, and times of their talks HAIM BREZIS, Rutgers University and Universite de follow: Paris VI, Liquid crystals, 1:15 p.m. Thursday. JOHN H. CoNWAY, Princeton University, ax2 +hxy+ DusA McDuFF, SUNY at Stony Brook, Applications cy2 = n, 10:10 a.m. Thursday. of PDE methods by Gromov, Floer, and others to sym­ SHIZUO KAKUTANI, Yale University, The principle of plectic geometry of manifolds, 2:30 p.m. Tuesday. duality in functional analysis, 10:10 a.m. Wednesday. SERGE LANG, Yale University, Case studies ofpolitical Colloquium Lectures opinions passed off as science and mathematics, 10: 10 a.m. Tuesday. A series of four Colloquium Lectures will be given by JEAN E. TAYLOR, Rutgers University, New Brunswick, WILLIAM P. THURSTON of Princeton University. The title Crystals, in equilibrium and otherwise, 11 :00 a.m. Mon­ of this lecture series is Geometry, groups, and self-similar day. ti/ings. The lectures will be given at 1: 15 p.m. daily, Monday through Wednesday, August 7-9, and at 3:00 p.m. on Thursday, August 10. 92nd Summer Meeting of the AMS August 7-10, 1989 Prizes Progress in Mathematics Lectures The 1989 Leroy P. Steele Prizes will be awarded at 4:35 Beginning with the Boulder meetings, the Society will p.m. on Tuesday, August 8. inaugurate a new kind of lecture series titled Progress in Mathematics. This series will provide a forum for Invited Addresses the exposition of mathematical topics that have come into prominence in the past five years. The members of By invitation of the Program Committee, there will be the Selection Committee for these lectures are Armand two fifty-minute invited addresses. The names of the Borel, Paul H. Rabinowitz, Hugo Rossi, John T. Tate, speakers, their affiliations, the dates, times and titles of and Alan Weinstein. their talks follow: The names and affiliations of the speakers, their titles, MAURY D. BRAMSON, University of Wisconsin, Madi­ and the days and times they will talk are as follows: son, Limiting behavior of densities for annihilating sys­ tems of particles, 9:35 a.m. Monday. HowARD A. MASUR, University of Illinois at Chicago, The dynamics of billiards in polygons, 8:30a.m. Monday.

Special Sessions By invitation of the same committee, there will be five special sessions of selected twenty-minute papers. The topics of these special sessions, the names and affilia­ tions of the mathematicians arranging them, the dates and times they will meet, and the names of speakers are as follows: History of orthogonal polynomials, RICHARD A. AsKEY, University of Wisconsin, Madison, Thursday 8:00 a.m. and 3:00 p.m. W. A. Al-Salam, Richard A. Askey, Walter Gautschi, Mourad E. H. Ismail, Martin E. Muldoon and Ranjan Roy. Mathematical questions in computational geometry, GEORGE J. FIX and RANGABHARY I

702 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Thursday 8:00 a.m. Andrew Acker, Fred Almgren, Council Meeting Jr., Thomas K. DeLillo, Robert Finn, Ronald B. Guen­ The Council of the Society will meet at 2:00 p.m. on ther, Nicholas Korevaar, Kirk Lancaster, Peter Laurence, Sunday, August 6. Dening Li, Harold Parks, David Siegel, Ed Stredulinsky, Jean Taylor, David E. Tepper, and Thomas I. Vogel. Business Meeting Dynamics and moduli space, HowARD A. MASUR and The Business Meeting of the Society will take place JoHN SMILLIE, Cornell University, Monday 4:00 p.m., immediately following the award of the Steele Prizes at Tuesday 8:00 a.m., and Wednesday 8:30 a.m. Michael 4:35 p.m. on Tuesday, August 8. The secretary notes the D. Boshernitzan, Todd A. Drumm, Albert Fathi, Lisa R. following resolution of the Council: Each person who Goldberg, William M. Goldman, Andrew Haas, Linda attends a Business Meeting of the Society shall be willing Keen, Steven Kerckhoff, Howard A. Masur, William A. and able to identify himself as a member of the Society. Veech, and Michael Wolf. In further explanation, it is noted that each person who is Computational number theory and applications, to vote at a meeting is thereby identifying himself as and KEVIN S. McCURLEY, I.B.M. Almaden, Tuesday 8:00 claiming to be a member of the American Mathematical a.m., Wednesday 8:00 a.m. and 2:25 p.m., Thursday Society. For additional information on the Business 8:00 a.m. and 4:00 p.m. Eric Bach, Joan Boyar, Jo­ Meeting, please refer to the box titled Committee on the hannes Buchmann, Paul D. Domich, Gove Effinger, Dan Agenda for Business Meetings. Gordon, Kireeti Kompella, Jeffrey C. Lagarias, Susan Landau, Arjen K. Lenstra, Peter L. Montgomery, Gary Other AMS- MAA Joint Sessions L. Mullen, A.M. Odlyzko, Carl Pomerance, Jeffrey Shal­ lit, Daniel Shanks, Victor Shoup, Samuel S. Wagstaff, Everybody Counts Panel Discussion Jr., H. C. Williams, and Marvin Wunderlich. The AMS and MAA are cosponsoring a panel discus­ Contributed Papers sion of the recent report Everybody Counts. This report, which was prepared by the Mathematical Sciences Edu­ There will be sessions for contributed papers Monday cation Board of the National Research Council, describes afternoon, Tuesday morning, Wednesday morning and weaknesses in our mathematics education enterprise and afternoon, and Thursday morning and afternoon. issues a call for action. The panel will outline the find­ Late papers will not be accepted. ings of the report and discuss how the mathematical community can help. JoHN A. THORPE, SUNY at Buffalo Committee on the Agenda and Chair of the MAA Science Policy Committee, is the for Business Meetings organizer and moderator. Panelists include DAVID W. The Society bas a Committee on the Agenda for Business Meetings. BALLEW, Western Illinois University; RONALD G. Dou­ The purpose is to make Business Meetings orderly and effective. GLAS, SUNY at Stony Brook; WADE ELLIS, JR., West The committee does not have legal or administrative power. It is intended that the committee consider what may be called "quasi­ Valley College; MARCIA P. SwARD, MSEB; and LYNN A. political" motions. The committee has several possible courses of STEEN, St. Olaf College. This session is scheduled from action on a proposed motion, including but not restricted to 2:30p.m. to 4:00p.m. on Monday, August 7. (a) doing nothing; (b) conferring with supporters and opponents to arrive at a mutually accepted amended version to be circulated in advance of the meeting; 68th Summer Meeting of the MAA (c) recommending and planning a format for debate to suggest August 7-10, 1989 to a Business Meeting; (d) recommending referral to a committee; Hedrick Lectures (e) recommending debate followed by referral to a committee. There is no mechanism that requires automatic submission of The 37th Earle Raymond Hedrick Lectures will be given a motion to the committee. However, if a motion has not been by PERSI DIACONIS of Harvard University. These lectures submitted through the committee, it may be thought reasonable by a Business Meeting to refer it rather than to act on it without benefit are scheduled at II: I5 a.m. on Tuesday, Wednesday and of the advice of the committee. Thursday, August 8- IO. The titles of the lectures are The committee consists of M. Salah Baouendi, Robert M. as follows: Lecture I- The mathematics of mixing things Fossum (chairman), and Carol L. Walker. In order that a motion for the Business Meeting of August 8, up: From card shuffling to counting and back; Lecture 1989, receive the service offered by the committee in the most II- The mathematics of mixing things up: Reversible effective manner, it should have been in the hands of the secretary chains and eigenvalues of the Laplacian; Lecture III- The by July 7, 1989. Robert M. Fossum, Secretary mathematics of mixing things up: Modern Markov chain theory.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 703 Meetings

Invited Addresses August 7, and Part B from 4:00 p.m. to 6:00 p.m. on Monday, August 7. Enrollment is limited to 80. fifty-minute addresses. The There will be five invited The effective use of personal computers in an un­ their affiliations, the dates, times, names of the speakers, dergraduate linear algebra course is the focus of this and titles follow: course. In Part A, goals and strategies for their imple­ ADDISON, JR., University of California, JoHN W. mentation are established through the use of the less a unifying theme in math­ Berkeley, Se/fdual quantifiers: sophisticated software. This is followed by a review of a.m., Tuesday; ematics and logic, 8:40 the mathematical literacy required for a student to be College, CUNY, It­ ~INDA KEEN, Herbert H. Lehman proficient with the software. By removing the constraints automorphisms ofthe Bernoulli eratmg rational maps and imposed by computation, attention is directed toward Monday; shift, 2:30 p.m., the design of problem sets that reenforce the fundamen­ University of Wisconsin, Madi­ MARY ELLEN RUDIN, tals in the underlying theory. Among the areas in an 3:35 p.m., Monday; son, Metrizability in manifolds, introductory course in which challenging exercises are University of Colorado, WOLFGANG M. SCHMIDT, needed are the sum and intersection of vector spaces, the of Diophantine equa­ ~oulder, The number of solutions LU-decomposition, least squares, projections, quadratic Thursday; and tzons, 8:40 a.m., forms, and orthogonal transformations. In Part B, a University of Notre Dame The NANCY K. STANTON, format will be suggested through examples for each area. 3:35p.m., Wednesday. Riemann mapping non-theorem, Participant involvement will be encouraged. Experience in teaching undergraduate linear algebra is the only Minicourses prerequisite. Computer anxiety is permitted. Minicourse #2: Combinatorics via functional equations being offered by the MAA. The Nine Minicourses are is being organized by DoNALD R. SNow, Brigham Young of the organizers, the topics, the names and affiliations University. Part A is scheduled from 8:45a.m. to 10:45 meetings, and the enrollment dates and times of their a.m. on Monday, August 7, and Part B from 4:00p.m. each are as follows: limitations of to 6:00p.m. on Monday, August 7. Enrollment is limited of personal computers in an Minicourse #1: The use to 80. course is being organized by introductory linear algebra Many combinatorial functions can be described stud­ of New Hampshire. Part HOMER BECHTELL, University ied, and unified by using a simple functional equ~tions to 10:45 a.m. on Monday, A is scheduled from 8:45a.m. approach. These functions include combinations and permutations with various allowable repetitions or no repetitions, sums of the powers of the integers formulas, and many generalizations of these. This gives a method of describing the functions based on its combinato­ rial interpretation, studying its properties, obtaining its generating function in a direct manner, showing how all these functions are related, and giving several new results. Some of these combinatorial functions yield gen­ eralizations of Pascal's Triangle and their proprieties yield generalizations of the Pascal triangle properties of binomial coefficients. Some of these more interesting properties will be illustrated using computer printouts. The needed background in functional equations will be developed in the Minicourse so only a knowledge of calculus will be assumed. M~nicourse #3: Chaotic dynamical systems is being orgamzed by RoBERT L. DEVANEY, Boston University. Part A is scheduled from 4:00 p.m. to 6:00 p.m. on Monday, August 7, Part B from 8:00a.m. to 10:00 a.m. on Tuesday, August 8, and Part C from 2:25 p.m. to 4:25 p.m. on Tuesday, August 8. Enrollment is limited to 80. The goal of this Minicourse is to introduce some of the main ideas of dynamical systems theory in as simple a setting as possible, namely, iteration of functions of a single real or complex variable. Lectures Persi Diaconis, Hedrick Lecturer will be devoted to such topics as chaos, Julia sets, the

704 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Mandelbrot set, and bifurcations. Computer graphics proposals for such funding. A representative (current or experiments which yield the fascinating images from recent past) of the National Science Foundation will be dynamics will be described. Most of the lectures will available to give first-hand information about funding be aimed at describing the mathematics behind the possibilities there. concept of "chaos," but some time will be devoted Minicourse #6: Group theory through art is being to ways to incorporate ideas from dynamics into the organized by THOMAS BRYLAWSKI, University of North undergraduate curriculum, ranging from precalculus and Carolina, Chapel Hill. Part A is scheduled from 8:00 calculus courses to advanced student research projects. a.m. to 10:00 a.m. on Wednesday, August 9, and Part B Minicourse #4: Faculty-managed programs that pro­ from 2:30 p.m. to 4:30 p.m. on Wednesday, August 9. duce minority mathematics majors is being organized by Enrollment is limited to 80. RAY SHIFLETT, California State Polytechnic University, This Minicourse will explore how most of the the­ Pomona, and URI TREISMAN, University of California, ory introduced in a first course in group theory can Berkeley. Part A is scheduled from 8:00 a.m. to 10:00 be illustrated (and better understood) using discrete a.m. on Tuesday, August 8, and Part B from 2:25 p.m. groups of isometries (frieze and wallpaper patterns). to 4:25 p.m. on Tuesday, August 8. Enrollment is limited Using only synthetic plane geometry as a basis, the to 40. two-dimensional groups will be classified. In classifica­ Freshman Calculus and Pre-calculus have been burial tion concepts such a isomorphism (of both groups and grounds for the aspirations of the great majority of Black short exact sequences), examples of subgroup, index, cen­ and Hispanic students who enter college to prepare for tralizer, conjugate, quotient group, free abelian groups, careers in mathematics- or science-based professions. homomorphism, commutator, etc. occur naturally and These courses have been insuperable barriers, even for are illustrated by patterns from many cultures (e.g., many minority students who are well prepared mathematically colored patterns each give examples of non-isomorphic and who want to become mathematics majors. This groups, each isomorphic to a subgroup of the other). Minicourse is an exploration of a faculty-managed and Hand-in-hand with this analytic theory, going from the departmentally-based approach to helping students excel pattern to its symmetry group, goes the synthetic theory of creating patterns from the group and a fundamen­ in first-year college mathematics. It is an alternative to remedial or developmental programs-the standard re­ tal region. Here, kaleidoscopes illustrate generators and sponses to minority student failure. The approach has relations, word problems, and Dirichlet tessellations. led to dramatic improvements in Black and Hispanic stu­ Minicourse #7: HP-28S short course for nearly inex­ dents' performance at Berkeley, where it was developed perienced users is being organized by JEROLD MATHEWs, in the mid-1970's. It has now been adapted successfully Iowa State University. Part A is scheduled from 8:00 at Cal Poly Pomona and at more than 30 other colleges a.m. to 10:00 a.m. on Wednesday, August 9, and Part B and universites nationwide. from 8:00 a.m. to 10:00 a.m. on Thursday, August 10. Enrollment is limited to 80. Minicourse #5: Starting, funding and sustaining math­ This Minicourse will provide a jump-start for nearly ematics laboratories is being organized by STAVROS N. inexperienced users toward using the power of the HP- BusENBERG, Harvey Mudd College. Part A is scheduled 28S. Each participant is expected to bring along an HP- from 8:00a.m. to 10:00 a.m. on Tuesday, August 8, and 28S (those with an HP-28C will be able to participate Part B from 2:25 p.m. to 4:25 p.m. on Tuesday, August fully, excepting one or two topics). The course will 8. Enrollment is limited to 75. include an introduction to reverse Polish and algebraic This course will familiarize participants with suc­ entry modes, use of some of the built-in functions, cessful examples of the use of computer laboratories in and writing, entering, editing, and running user-written the undergraduate mathematics curriculum. The course functions and programs. A handout will be distributed, will feature descriptions of ongoing examples of such including course notes, programs, and a bibliography of laboratories by three or four faculty who have been HP-28S literature and program sources. Participants will involved in them at a variety of settings: a small col­ work through (i.e., discuss, enter, edit, and run) built­ lege, a private university, a large state university, and ins including (as time permits) SOLV, DRAW, CROSS, a two-year college. The presentations will describe the DOT, MOD, FACT, LR, IFTE, and dfdx., as well as curricular innovations that have been made possible by several programs. These may include a program for the the availability of a mathematics computer laboratory, game in which the player chooses a positive integer n, the software that has been found to be useful, and the replaces it by n/2 or 3n+1, depending on whether n means by which the laboratories obtained their initial is even or odd, and then repeats until 1 is obtained fund and continuing support. (if ever), a Pythagorean triples generator, recursive and Part of the Minicourse will outline sources of funding a non-recursive Fibonacci sequence programs, a polar and methods for increasing the probability of success for plotting program, and a Newtons method program. We

JULY /AUGUST 1989, VOLUME 36, NUMBER 6 705 Meetings will try to arrange a program exchange for those who are mode of teaching. Readings and a syllabus will be sent interested. to participants prior to the meeting. Minicourse #8: Applications of the HP-28S for experi­ Participants interested in attending any of the MAA enced users is being organized by THOMAS W. TucKER, Minicourses should have completed the MAA Minicourse Colgate University. Part A is scheduled from 2:30p.m. to Preregistration Form and sent it directly to the MAA 4:30p.m. on Wednesday, August 9, and Part B from 1:15 office at the address given on the form so as to arrive p.m. to 3:15 p.m. on Thursday, August 10. Enrollment is prior to the June 1 deadline. Please note that these MAA limited to 80. Minicourses are NOT the AMS Short Course. After the This Minicourse will illustrate uses of the HP-28S deadline, potential participants are encouraged to call supercalculator in various undergraduate mathematics the MAA headquarters at 800-331-1622. courses. Particular emphasis will be given to the cre­ The MAA Minicourses are open only to persons who ation of environments customized for experimenting register for the Joint Mathematics Meetings and pay the or problem-solving in a given part of a course: curve Joint Meetings registration fee. If the only reason for sketching for calculus with various features (automatic registering for the Joint Meetings is to gain admission range finding, single-button computation of extrema and to a MAA Minicourse, this should have been indicated inflection points), comparison of numerical integration by checking the appropriate box on the MAA Minicourse techniques also for calculus, numerical solution of dif­ Preregistration Form. Then, if the Minicourse is fully ferential equations and trajectory plotting, pivoting and subscribed, full refund can be made of the Joint Meetings matrix editing, and viewing for linear algebra, curve preregistration fee. Otherwise, the Joint Meetings prereg­ fitting for data analysis, routines for number theory istration will be processed, and then be subject to the 50% (factoring, prime testing, linear congruence solving, pow­ refund rule. Participants should take care when cancelling ering). Although there will be some playing around with Minicourse preregistration to make clear their intention fractals or music, attention will generally be restricted to as to their Joint Meetings preregistration, since if no in­ things the HP-28S can do quickly and easily; things best struction is given, the Joint Meetings registration will also left to a computer (e.g. 3-dimensional graphics) are left be cancelled. PREREGISTRATION FORMS FOR THE to a computer. JOINT MEETINGS SHOULD HAVE BEEN MAILED Participants will be expected to bring their own TO PROVIDENCE PRIOR TO THE DEADLINE OF HP-28S calculators and be comfortable with the main JUNE 1. features of the HP-28S. In particular, it is assumed The registration fee for each MAA Minicourse is $30. that participants have done some programming on the calculator. Contributed Papers Minicourse #9: A seminar on women in mathematics is being organized by MIRIAM P. CooNEY esc, Saint Mary's Contributed papers were accepted on three topics in College, Notre Dame, Indiana. Part A is scheduled from collegiate mathematics. The topics, the names and af­ 8:00 a.m. to 10:00 a.m. on Thursday, August 10, and filiations of the organizers, and days they will meet Part B from 1:15 p.m. to 3:15 p.m. on Thursday, August are: 10. Enrollment is limited to 30. • Pedagogical uses of symbolic computer systems, The goal of this Minicourse is to prepare participants ARNOLD M. OsTEBEE, St. Olaf College, Monday af­ to conduct a seminar that identifies women mathemati­ ternoon, Tuesday morning and afternoon. cians (past and present), studies their lives and the Symbolic computer systems (also known as computer mathematical times as a context for their work, and algebra systems) make machine-based graphical, nu­ reveals mathematics as a human pursuit. Applying the merical, and symbolic computing accessible to stu­ assumption that social-emotional aspects of learning are dents. Examples of such systems are muMATH, De­ important. to students of mathematics, the Minicourse rive, Macsyma, Maple, Mathematica, Reduce, SMP, will provide strategies for creating a seminar that pro­ and the HP-28S calculator. Papers are invited that de­ vides a support group to encourage potential mathematics scribe experiences using symbolic computer systems majors, both women and men. in instructional settings at all levels, from pre-calculus The content of the Minicourse, like the seminar, will to graduate-level courses. include history and stories of women mathematicians, gender bias and its historic causes, research on gender • Calculus revision, THOMAS W. TUCKER, Colgate Uni­ differences, alternate teaching/learning styles, and re­ versity, for the CUPM Subcommittee on Calculus search on "women's ways of knowing." The format will Reform and the First Two Years, Tuesday afternoon follow seminar-style discussions, including consideration and Wednesday morning. of the difficulties in learning the discussion process as a

706 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

The session will feature papers describing recent DAviD A. SMITH, Duke University and Chair of CCIME; developments in revising the content and pedagogy and PAUL ZoRN, St. Olaf College. This session is sched­ of calculus. This is a continuation of the session uled from 8:00 a.m. to 9:55 a.m. on Thursday, August What is happening with calculus revision presented at 10. Phoenix, January 1989. Individuals wishing to submit papers for any of these Video sessions should have sent information to MAA by May On Tuesday, August 8, at 2:30 p.m. a 30-minute video­ 17. tape by LORRAINE L. FOSTER, California State Univer­ sity, Northridge, will be shown. The video is titled Finite Undergraduate Student Paper Session symmetry groups in three dimensions. MAA is, for the second time, cosponsoring an Under­ graduate Student Paper Session with Pi Mu Epsilon, Audio-Visual Equipment the undergraduate mathematics honorary society, and Rooms where MAA sessions will be held are equipped the MAA Student Sections. The talks are scheduled for with one overhead projector and screen. (Invited 50- Tuesday afternoon, August 8. minute speakers are automatically provided with two overhead projectors.) Blackboards will be available in some rooms only. Other MAA Sessions Persons having other equipment needs should have Public Hearing on Accreditation contacted the secretary (Kenneth A. Ross, Department of The ad hoc Committee on Accreditation (John D. Ful­ Mathematics, University of Oregon, Eugene, OR 97403) ton, Chair) is sponsoring a "public hearing" while in the prior to June 1. process of drafting an accreditation document for under­ graduate mathematics. It will propose accreditation for Prize Session and Business Meeting mathematics among U.S. colleges (including two-year) The MAA Prize Session and Business Meeting is sched­ and universities and will include guidelines for accredi­ uled from 4:40 p.m. to 5:40 p.m. on Wednesday, August tation. Alternatively, the completed document could be 9. The 1989 Beckenbach Book Prize and Merten M. used as a model to delineate guidelines for undergrad­ Hasse Prize will be awarded. In addition, the 1989 uate programs in the mathematical sciences. JOHN D. Carl B. Allendoerfer, Lester R. Ford, and George P6lya FuLTON, University of West Florida, will moderate the Awards will be presented. A bylaw change that would add panel. Participants are CALVIN T. LoNG, Washington the chair of the Committee on Sections to the Executive State University and LYNN A. STEEN, St. Olaf College. Committee will be voted on by the membership. This This session is scheduled from 8:30 a.m. to 9:55 a.m. on meeting is open to all members of the Association. Tuesday, August 8.

A Fomm on Mathematics Majors Board of Governors A forum on Are we teaching majors the right mathemat­ The MAA Board of Governors will meet at 8:30a.m. on ics? Are we teaching it the right way? is scheduled from Sunday, August 6. This meeting is open to all members 8:30 a.m. to 9:55 a.m. on Wednesday, August 9. The of the Association. participants include BETTYE ANNE CASE, Florida State University, who is Chair of the CUPM Subcommittee on the Major in the Mathematical Sciences; JAMES R.C. Section Officers LEITZEL, Ohio State University, who is Chair of the There will be a Section Officers' meeting at 4:40 p.m. on Committee on the Mathematical Education of Teachers Monday, August 7. (COMET); and LYNN A. STEEN, St. Olaf College, who is Chair of the Committee on the Undergraduate Program MAA Banquet for 25-year Members in Mathematics (CUPM). The fourteenth annual banquet for individuals who have Computers in Calculus Reform been members of the Association for twenty-five years The Committee on Computers in Mathematics Educa­ or more will be held on Wednesday, August 9, in the tion (CCIME) is sponsoring a panel discussion on The University Club dining room. A reception with cash bar role of the computer in calculus reform. The moderator will take place from 5:45 p.m. to 6:30 p.m. Dinner will for this panel is EuGENE A. HERMAN, Grinnell Col­ be served at 6:30 p.m. lege. Participants include ROBERT L. DEVANEY, Boston University; KENNETH R. HOFFMAN, Hampshire College;

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 707 Meetings

Activities of Other Organizations Other Events of Interest Book Sales The Association for Women in Mathematics (AWM) is sponsoring a panel discussion on Women in operations re­ Books published by the AMS and MAA will be sold at search: Their work and experiences, on Tuesday, August 8, discounted prices somewhat below the cost for the same at 9:00a.m. The moderator is JILL P. MESIROV, Thinking books purchased by mail. These discounts are available Machines Corporation. Panelists are MARGARET BRAN­ only to registered participants wearing the official meeting DEAU, Stanford University; JANICE HAMMOND, Harvard badge. Visa and MasterCard credit cards will be accepted Business School; and MARGARET WRIGHT, AT&T Bell for book sale purchases at the meeting. The book sales Laboratories. are open the same days and hours as the exhibits. The AWM Membership Meeting will be held at 8:30 a.m. on Tuesday, August 8. AMS Information Booth An open reception is planned for Tuesday evening, August 8, at 9:30 p.m. Please visit the AMS information booth in the exhibit area during the meeting. Complimentary coffee and tea The Joint Policy Board for Mathematics (JPBM) Com­ will be served for participants. Carol-Ann Blackwood, mittee for Mathematics Department Heads has organized Member Services Manager of the Society, will be at the a National Meeting of Department Heads on Evaluat­ information booth to meet members personally. Bring ing teaching in mathematics at 7:00 p.m. on Monday, Mrs. Blackwood your comments and compliments about August 7. Speakers include DONALD W. BUSHAW, Wash­ member services. ington State University, DAVID J. LUTZER, College of William and Mary (moderator), ToM TROTTER, Arizona Exhibits State University (organizer), and THOMAS W. TucKER, Colgate University. The book and educational media exhibits are open Monday through Thursday, August 7- 10. The hours As previously mentioned, Pi Mu Epsilon is celebrating they are open are 1:00 p.m. to 5:00 p.m. on Monday, its 75th anniversary in Boulder. 9:00 a.m. to 5:00 p.m. Tuesday and Wednesday, and The llME Reception will be held on Monday, August 9:00 a.m. to noon on Thursday. All participants are 7, at 7:00 p.m. and all participants are welcome to attend. encouraged to visit the exhibits during the meeting. There will be sessions for contributed papers Tuesday morning and afternoon and Wednesday morning. The Summer List of Applicants llME Council will meet from noon to 1:00 p.m. on Tuesday, August 8. At the direction of the AMS-MAA-SIAM Committee llME invites all participants to help celebrate its on Employment Opportunities, which is charged with 75th anniversary at the Western Hoe Down on Tuesday operation of the Employment Register and with the pub­ evening, August 8, at 6:30 p.m. A special program of lication of Employment Information in the Mathematical entertainment will be presented by llME members. Sciences, the Society will publish a Summer List of math­ The llME Dutch Treat Breakfast will take place on ematical scientists seeking employment for distribution Wednesday, August 9, at 8:00 a.m. at the Boulder meeting. The llME Banquet will take place on Wednesday, Copies of the 1989 summer list of applicants will be August 9, at 6:30 p.m. followed by the Frame Lecture. available at the Transparencies section of the registra­ The banquet will be held in the East Dining Room tion desk for $5. Following the meeting, they may be located in the University Memorial Center on campus. purchased from the AMS office in Providence for $7. The J. Sutherland Frame Lecture will be delivered This list should prove useful to employers who have on Wednesday, August 9, at 8:30 p.m. by JANE CRONIN last-minute openings in the latter part of the summer or ScANLON, Rutgers University, New Brunswick, on En­ in the fall. trainment offrequency: a recurring theme. The deadline for receipt of applicant forms to appear llME will cosponsor undergraduate student paper in this summer list was June 1. sessions with MAA. Further information can be found Instead of an Employment Register at the Summer in the MAA section of this announcement. Meeting in Boulder, there will be an opportunity for There will be an exhibit of llME memorabilia on posting of both applicant resume forms and employers' campus at a location to be announced. Materials for announcements of open positions in or near the main this exhibit are on loan from Syracuse University where meeting registration area. There will be no special room llME was founded in 1914. set aside for interviews. No provisions will be made by the Society for interviews; arrangements will be the

708 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings responsibility of each employer and applicant. Messages penalty. Therefore, it is requested that proper caution may be left in the message box located in the registration be exercised to avoid this charge. At checkout, all keys area. must be returned to the check-in desk. Should the clerk Special applicant and employer forms will be available not be present, please ensure that your name is left at at the Transparencies section of the registration desk both the check-in desk with the key. Participants can park for applicants to post resumes and for employers to post temporarily in the Visitor's Parking Lot, located just forms announcing positions. outside of the Commons Office, while checking in. There Applicants who submit an applicant form, but do not will be students available to help carry bags. plan to attend the meeting, will appear on the printed list only. There is no provision made for posting resumes Room and Board Rates for participants who do not attend the meeting. No printed lists of employers or applicants who register at The following rates apply for residence hall accommo­ the meeting will be available after the meeting. dations at the University of Colorado. The rate on the board portion is 6.43% and on the room portion 9.4%. How to Obtain Residence Hall The university allows a maximum of two adults and Accommodations one child in each room. Should a family with two children request accommodations, two rooms would be required The use of the services offered by the Mathematics and the double rate (with appropriate adjustments for Meetings Housing Bureau requires preregistration for the children six to 13 years of age) applies in each case. Joint Mathematics Meetings. All reservation requests for Room and board rates can be found in a box in this university accommodations must be received in writing announcement. Meals for children under six years of age and be processed through the Housing Bureau. Telephone are free. requests cannot be accepted. Please do not contact the university directly, since they will only refer callers back Please note that a minimum room-and-board package to the Housing Bureau. Preregistrants will receive an would be one night's lodging, one dinner and one acknowledgement of their room requests. However, the breakfast. The university will accept changes in packages university is responsible for making room assignments in reserved up until two weeks prior to check-in. After that, the residence halls. no changes may be made. Any requested exceptions to this Participants desiring confirmed reservations in the policy should be addressed to the Kittredge Conference University of Colorado, Boulder, residence halls should Manager, (303) 492-6777. With the exception of August read carefully the section on University Housing and 4 and August 8, all daily room and board packages then choose preferred accommodations. include dinner on the night of arrival and breakfast the next day. The last meal of a package will be breakfast. There will not be any refunds issued for meals missed. On University Housing August 4, there are no meals included in the package and Those participants wishing to be assigned a dormitory on August 8, there is no dinner included in the package. room onsite must go to the Kittredge Commons Office, Any participant not attending the social event on August located in the Commons Building on the upper level 8 but planning to dine on campus should indicate this on of the North Wing. The office is open Sunday through the preregistration form AND purchase a meal card at Friday from 7:00 a.m. to 11:00 p.m. and Saturday from the Meetings Registration Desk for that meal. The cost 7:00a.m. to 9:00p.m. Should assistance be needed when for this meal card is $7.75 per person. Meal tickets are the office is closed, a Conference Aide will be on duty, nonrefundable. whose name and telephone extension will be posted in Food Services front of the desk of the Commons Office. Those participants being assigned a room onsite by Residence hall guests may dine either in the East or West the check-in desk will be required to fill out a housing dining rooms of the Commons Building, which may be form and pay for their room, thus enabling them to approached from both sides of the serving area using receive a room key. Payments can be made with cash, either of the stone stairways from the ground floor of traveler's checks, personal checks, Visa and MasterCard. the Commons. There are no ramps for handicapped; Spouses desiring a room key must follow this procedure however, service elevators can be used if sufficient no­ also. Please note that, although there is no deposit tice is given ahead of time to the Kittredge Conference required for keys, a penalty of $10 will be imposed for Manager, (303) 492-6777. Serving hours for breakfast each key lost or not returned. It is the responsibility of are 6:30 a.m. to 8:00 a.m. Serving hours for dinner are the Mathematics Meetings Housing Bureau to collect this

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 709 Meetings

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710 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

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JULY/AUGUST 1989, VOLUME 36, NUMBER 6 711 Meetings

5:00 p.m. to 6:30 p.m. (As long as someone is inside the The Tabor Inn. Lunch is served there from 11:00 a.m. to dining hall by 6:30 p.m., he/she will be served.) Meal 1:00 p.m. tickets must be presented at each meal for admission There are also several restaurants within the imme­ by to the dining area. Children must be accompanied diate vicinity of the university, on Arapahoe Avenue. area. A typical breakfast is eggs, parents in the dining They range from fast food (burgers, pizza, tacos, etc.) to ham, bacon, sausage, cereal, toast, muffins, assorted ethnic. fresh fruit, juices, etc. A typical dinner offers one or two entrees, vegetables, rolls, salad bar, desserts, fresh fruit, ice cream, and beverages. Servings are generous; Hotel Accommodations unlimited seconds are allowed. There are no Kosher meals available. As an alternative to university housing, the Housing A very limited number of meals is available on a cash Bureau lists the following hotels/motels with group rates. basis for guests in the dining rooms. All are located within walking distance of the university. Rates are subject to a 9.4% state room tax and are firm. Within the University Memorial Center on campus Participants should make their own reservations di­ in the there are several eating establishments located rectly with the hotels/motels, and should identify them­ 7:00 Grill, which is a food court. Serving hours are from selves as participants in the Joint Mathematics Meetings. area, a.m. to 5:00 p.m. There is also a sit-down dining Participants making reservations should be prepared to

University of Colorado, Boulder Room/Board Rates (per person)

Children Children 6-13 6-13 years Children Adults years in bed in rollaway under 6 years *

8/4 $29 single $14 single $3 $3 (no meals) $19 double $9 double

8/5 $41 single $23 single $12 $3 $31 double $18 double

8/6 $41 single $23 single $12 $3 $31 double $18 double

8/7 $41 single $23 single $12 $3 $31 double $18 double

8/8 $34 single $18 single $6 $3 $23 double $12 double

8/9 $41 single $23 single $12 $3 $31 double $18 double

8/10 $41 single $23 single $12 $3 $31 double $18 double

* There will be a $3 rollaway or crib charge for all children under 6 years of age, for whom meals are free. Smoking and nonsmoking rooms are available upon request.

712 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings remit a one night's deposit to the hotel or motel or give available. Participants were strongly advised to make their a major credit card number in order to guarantee their reservations with this hotel VERY EARLY. room reservation. Holiday Inn, across the street from the East side of In all cases "single" refers to one person in one bed; campus (near Events Center) "double" refers to two persons in one bed; and "twin 800 28th Street double" refers to two persons in two beds. A rollaway cot Boulder, CO 80303 for an extra person can be added to a room; however, Telephone: 303-443-3322 not all hotels are able to do so and for those that do, Single $52 the number of cots available is limited and given on a Double $52 first-come, first-served basis. Triple $52 $60 Participants should be aware that it is general hotel Triple wjcot* $52 practice in most cities to hold a nonguaranteed reser­ Quadruple vation until 6:00 p.m. only. When one guarantees a Quadruple wjcot $60 Upon request reservation by paying a deposit or submitting a credit Suites limited, based on availability. card number as guarantee in advance, however, the hotel * Cots are very hotel. Restaurant, lounge, indoor recre­ usually will honor this reservation up until checkout Full service that includes indoor swimming pool, jacuzzi, time the following day. If the individual holding the ation center room, and exercise room. Free parking. reservation has not checked in by that time, the room is sauna, game years and younger are free in same room then released for sale, and the hotel retains the deposit Children 18 Visa, MasterCard, American Express, and or applies one night's room charge to the credit card as parents. checks are number submitted. Diner's Club credit cards accepted. Personal accepted only with a major credit card and drivers' If you hold a guaranteed reservation at a hotel, but license. are informed upon arrival that there is no room for you, Boulder Inn, across the street from the there are certain things you can request the hotel do. Best Western of campus First, they should provide for a room at another hotel in Southeast corner town for that evening, at no charge. (You have already 770 28th Street 80303 paid for the first night when you made your deposit.) Boulder, CO They should pay for taxi fares to the other hotel that Telephone: 303-449-3800 evening, and back to the meetings the following morning. Single $48 They should also pay for one telephone toll call so that Double ( 1bed) $48 you can let people know you are not at the hotel you Double (2 beds) $54 expected. They should make every effort to find a room Triple $58 for you in their hotel the following day, and if successful, Triple wjcot $64 pay your taxi fares to and from the second hotel so that Quadruple $58 you can pick up your baggage and bring it to the first Quadruple wjcot $64 hotel. Not all hotels in all cities follow this practice, so Suites Upon request your request for these services may bring mixed results, *Room-Car package$69.95 or none at all. Cots are very limited and based on availability. Clarion Harvest House (Headquarters), across the street Full service hotel. Outdoor swimming pool, free park­ from the Northeast end of the campus ing, restaurant, fitness club, free continental breakfast, 1345 28th Street and lounge. Children 16 years and younger are free in Boulder, CO 80302 same room as parents. Visa, MasterCard, American Ex­ Telephone: 303-443-3850 press, and Diner's Club credit cards accepted. Personal Single $60 checks are accepted with one form of identification and Double $60 a major credit card. Upon check-in, all guests will be Suites Upon request asked to fill out a registration card and must have some Full service hotel, restaurant, lounge, free parking, in­ official form of identification. door/ outdoor pools, tennis courts, volleyball courts, *The Best Western Boulder Inn offers a Room and workout room, jacuzzi, and jogging trail. Children 12 Car package that includes sleeping room ( 1 or 2 beds), years and younger are free in same room as parents. rental car with free unlimited mileage, complimentary Visa, MasterCard, American Express, and Diner's Club continental breakfast, car pickup and return at Denver credit cards accepted. The Clarion is the headquarters Stapleton Airport or hotel lobby, complimentary nearby hotel, and so there is a very LIMITED number of rooms

JULY /AUGUST 1989, VOLUME 36, NUMBER 6 713 Meetings

CLEMATIS OR 7 GAI.LAROIA RO 3 MORNING Gl DRY 4 PIIMROSE RO > ASTER 6 l~INE

scale

1 mile DOWNTOWN BOULDER

1 BOULDER INN 2 BROKER INN 3 HOLIDAY INN 4 UNIVERSITY OF COLORADO 5 THE CLARION HARVEST HOUSE 6 HIGHLANDER INN 7 MARRIOTT RESIDENCE INN

714 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings health club privileges, free morning newspapers, and free Studio suites accommodate up to three people; penthouse local telephone calls. ROOM AND CAR ARE SUBJECT suites accommodate up to four people. There is no TO AVAILABILITY and 48 hour advance reservation was restaurant on the property. The nearest restaurant is requested. For further information and reservations, call the Boulder Court, on 28th Street. The Residence Inn 303-449-3800 or 1-800-233-8469. offers many other amenities including fully-equipped kitchens, grocery shopping service, private entrances, Broker Inn, two blocks from the Southeast corner of private patios or balconies, living rooms with fireplaces, campus free continentia} breakfast, free parking, outdoor pool, 555 30th Street and jacuzzi and sport court. Visa, MasterCard, American Boulder, CO 80303 Express, and Diner's Club credit cards accepted. Telephone: 303-444-3330 Participants should be aware that when major con­ Single $49 (on weekends only) ventions occur in any city, additional safety problems are Single ( 1 bed) $53 (on weekdays) created, especially at night. Those who are attending the Double (1 bed) $49 (on weekends only) meetings alone, or who are concerned about walking to and Double (1 bed) $63 (on weekdays) from the meetings after dark, are encouraged to choose Double (2 beds) $49 (on weekends only) a hotel in close proximity to the campus. Participants Double (2 beds) $63 (on weekdays) are also urged to read the "Words to the Wise" in the Triple (2 beds) $63 local information insert in the program they receive at the King size beds are $10 additional meetings. Full service hotel. Outdoor swimming pool, jacuzzi, free parking, restaurant, lounge, and aerobic & fitness club. Children 18 years and younger are free in same Registration at the Meetings room as parents. Visa, MasterCard, American Express, Meeting registration fees only partially cover expenses and Diner's Club credit cards accepted. of holding meetings. All mathematicians who wish to Highlander Inn, across the street from the East corner of attend sessions are expected to register, and should be campus (near Events Center) prepared to show their meeting badge, if so requested. 970 28th Street Badges are required to obtain discounts at the AMS Boulder, CO 80303 and MAA Book Sales and to cash a check with the Telephone: 303-443-7800 meeting cashier. If a preregistrant should arrive too late Single $46.95 in the day to pick up his/her badge, he/she may show Double ( 1 bed) $48.95 the acknowledgement received from the Mathematics Double (2 beds) $48.95 Meetings Housing Bureau as proof of registration. Triple $50.95 The fees for Joint Meetings registration at the meeting Quadruple $52.95 listed below are 30% more than the preregistration fees. King Suites and Apartment Suites Upon request Joint Mathematics Meetings Single rooms have queen size beds, while double rooms Member of AMS, Canadian Mathematical contain one queen size bed and one double bed. King Society, MAA, liME $ 82 size beds and waterbeds (very limited) are available Emeritus Member of AMS, MAA $ 23 upon request and at a higher rate. There are no rollaways Nonmember $127 available. There is also no restaurant on the property. The Student/Unemployed $ 23 nearest restaurant, Perkins, is one-and-one-half blocks AMS Short Course away. Outdoor solar-heated swimming pool, free parking. Student/Unemployed $ 20 Marriott Residence Inn, two miles Northeast of campus All Other Participants $ 50 All suites hotel MAA Minicourses 3030 Center Green Drive (if openings available) Boulder, CO 80301 Minicourses # 1 - 9 $ 30 Telephone: 303-449-5545 or 800-331-3131 Studio ( 1 Bedroom - 1 to 6 nights) $ 99 Modes of payment which are acceptable, provided they Studio ( 1 Bedroom - 7 to 29 nights) $ 89 are payable in U.S. dollars to the order of the American Penthouse (2 Bedroom- 1 to 6 nights) $119 Mathematical Society, are U.S. Postal Money Orders, Penthouse (2 Bedroom- 7 to 29 nights) $109 certified U.S. Bank checks, U.S. bank money orders, Rollaways are $1 0 extra. personal checks drawn on a U.S. bank, or credit card (Visa or MasterCard only).

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 715 Meetings

There is no extra charge for members of the families Audio-Visual Assistance of registered participants, except that all professional A member of the AMS/MAA staff will be available to mathematicians who wish to attend sessions must register advise or consult with speakers on audio-visual usage. independently. Rooms where special sessions and contributed paper All full-time students currently working toward a sessions will be held are equipped with an overhead degree or diploma qualify for the student registration projector and screen. Blackboards will be available in fees, regardless of income. some rooms only. The unemployed status refers to any person currently unemployed, actively seeking employment, and who is Baggage and Coat Check not a student. It is not intended to include any person Baggage and coats may be left in the Joint Meetings who has voluntarily resigned or retired from his or her registration area only during the hours that registration latest position. is open. The staff cannot, however, take responsibility Persons who qualify for emeritus membership in for lost or stolen articles. either the Society or the Association may register at the emeritus member rate. The emeritus status refers to any Check Cashing person who has been a member of the AMS or MAA for The Joint Meetings cashier will cash personal or traveler's twenty years or more, and is retired on account of age or checks up to $50, upon presentation of the official on account of long term disability from his or her latest meeting registration badge, provided there is enough position. cash on hand. Canadian checks must be marked for Nonmembers who preregister or register at the meet­ payment in U.S. funds. It is advisable that participants ing and pay the nonmember fee will receive mailings bring traveler's checks with them. When funds are low from AMS and MAA, after the meeting is over, contain­ the cashier will not be able to cash checks, and traveler's ing information about a special membership offer. checks can be easily cashed at local banks, restaurants, or hotels. Registration Dates and Times Local Information by members of AMS Short Course This section of the desk will be staffed volunteers Outside Room C250, Ramaley Biology the Local Arrangements Committee and other from the Boulder mathematical community. Sunday, August 6 8:30 a.m. to 2:30 p.m. Joint Mathematics Meetings [and MAA Minicourses (until filled)] Petition Table Glenn Miller Ballroom, University Memorial Center At the request of the AMS Committee on Human Rights Sunday, August 6 3:00 p.m. to 7:00 p.m. of Mathematicians, a table will be made available in the Monday, August 7 meeting registration area at which petitions on behalf of through 7:30 a.m. to 4:00 p.m. named individual mathematicians suffering from human Wednesday, August 9 rights violations may be displayed and signed by meeting Thursday, August 10 7:30a.m. to 1:00 p.m. participants acting in their individual capacities. Signs of moderate size may be displayed at the table, but must not represent that the case of the individual in Registration Desk Services question is backed by the Committee on Human Rights unless it has, in fact, so voted. Volunteers may be present Assistance, Comments, and Complaints at the table to provide information on individual cases, A log for registering participants' comments or com­ but notice must be sent at least seven (7) days in advance of the meeting to the Director of Meetings in Providence plaints about the meeting is kept at the Transparencies (telephone 401-272-9500). Since space is limited, it may section of the registration desk. All participants are also be necessary to limit the number of volunteers present encouraged to use this method of helping to improve at the table at any one time. The Committee on Human future meetings. Comments on all phases of the meeting Rights may delegate a person to be present at the table at are welcome. If a written reply is desired, participants any or all times, taking precedence over other volunteers. should furnish their name and address. Any material which is not a petition (e.g., advertisements, Participants with problems of an immediate nature resumes) will be removed by the staff. When registration requiring action at the meeting should see the Director closes, any material on the table will be discarded, so of Meetings, who will try to assist them. individuals placing petitions on the table should be sure to remove them prior to the close of registration.

716 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Lost and Found A telephone message center is located in the regis­ See the Joint Meetings cashier. Also, parttctpants can tration area to receive incoming calls for participants. the check at the Administrative Wing in the Engineering The center is open from August 6 through 10, during Center. hours that the Joint Mathematics Meetings registration desk is open. Messages will be taken and the name of Mail any individual for whom a message has been received All mail and telegrams for persons attending the meet­ will be posted until the message has been picked up ings should be addressed as follows: Name of Participant, at the message center. Once the registration desk has Joint Mathematics Meetings, cjo Office of Conference closed for the day there is no mechanism for contacting Services, 500 30th Street, University of Colorado Cam­ participants other than calling them directly at their pus Box 454, Boulder, Colorado 80309-0454. Mail and hotel. The telephone number of the message center is telegrams so addressed may be picked up at the mailbox 303-492-4186. in the registration area during the hours the registration Transparencies desk is open. U.S. mail not picked up will be forwarded after the meeting to the mailing address given on the Speakers wishing to prepare transparencies in advance of participant's registration record. their talk will find the necessary materials and copying machines at this section of the registration desk. A Personal and Telephone Messages member of the staff will assist and advise speakers on Participants wishing to exchange messages during the the best procedures and methods for preparation of their meeting should use the mailbox mentioned above. Mes­ material. There is a modest charge for these materials. and pencils are provided. It is regretted that sage pads Visual Index such messages left in the box cannot be forwarded to participants after the meeting is over. An alphabetical list of registered parttctpants, includ­ ing local addresses and arrival and departure dates, is maintained in the registration area. Handout Table The handout table at Joint Meetings of the AMS and MAA Miscellaneous Information is set up in the registration area for the dissemination of information of a nonmathematical nature of possible Athletic Facilities interest to the members. The administration of the table is Indoor facilities are in the Recreation Center, located AMS-MAA Joint Meetings Committee, as in the hands of the near the north edge of the campus, just west of the all arrangements for joint meetings. The following rules are building contains a swimming pool, a and procedures apply. stadium. This systems I. Announcements submitted by participants should diving pool, an ice rink, a weight room, a fitness bicycles and other equipment, ordinarily be limited to a single sheet no more than 8-!"x 1411 • room with stationary 2. A copy of any announcement proposed for the table courts for handball, racquetball and squash, and a room is to be sent to the Director of Meetings, American Math­ for volleyball and basketball. Tickets for use of this ematical Society, Post Office Box 6248, Providence, Rhode facility can be purchased on a daily basis for $2.50, or Island 02940 to arrive at least one week before the first day on a weekly basis for $7, at the main entrance to the of the scientific sessions. building. Additional family members under the age of 3. The judgment on the suitability of an announcement five are free. Over age five the cost is the same as for for display rests with the Joint Meetings Committee. It will the first member, up to a maximum cost for a family of make its judgments on a case by case basis to establish $21 for a week. Participants should bring their meeting precedents. badges when purchasing the tickets. The building is 4. Announcements of events competing in time or place Monday and Wednesday 7:30 a.m. to with the scheduled scientific program will not be accepted. open as follows: 5. Copies of an accepted announcement for the table are midnight, Tuesday and Thursday 6:30 a.m. to midnight, to be provided by the proponent. Announcements are not to Friday 7:30 a.m. to 11:00 p.m., Saturday 9:00 a.m. to be distributed in any other way at the meeting (for example, 11 :00 p.m., and Sunday from 10:00 a.m. to 10:00 p.m. not by posting or personal distribution of handbills). Tennis courts can be found just south of the Kittredge 6. It may be necessary to limit the number of events or Complex of dormitories. Sign-up sheets are available the quantity of announcements distributed at a meeting. for reserving courts of all kinds, one day in advance. 7. At the close of registration, the table will be swept Reservations can be made by calling 303-492-6561. clean. A proponent who wishes the return of extra copies should remove them. Camping and RV Facilities August is the highest month of the season, as possibly everyone knows.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 717 Meetings

Several campgrounds are managed by the National Jack and Jill Preschool and Kindergarten, 303-442- Forest Service in Roosevelt National Forest, west of 1571, 1301 North Street, Boulder, CO 80302. Director: Boulder. Most are not more than an hour's drive from Ruth Jones. Ages: 2 1/2 to 8. Hours: 6:30 a.m. to 6:00 town. All but one will have a water supply and trash p.m. Rates: $17/day, $72/week, $2/hour. pickup, and those will cost $6 per night. Olive Ridge, Kinder Learning Center, 303-440-0749, 3600 Hazel­ 1.5 miles north of Allenspark, may be on a reservation wood Court, Boulder, CO 80302. Director: Amy L. basis in August; call 303-444-6001 for information. The Austin. Ages: 12 months to 12 years. Hours: 6:30a.m. to others are on a first-come-first-camper basis. 6:00p.m. Rates: $22/day, $73/week for over 2 1/2. Boulder Mountain Lodge, on Four Mile Canyon Sacred Heart Childcare Program, 303-443-0684, 1317 Road, is a private camping facility, costing $14 per Mapleton Avenue, Boulder, CO 80302. Director: Louis night. Electricity and a hot tub are provided. They do Coenon. Ages: 3 to 12. Hours: 7:00 a.m. to 6:00 p.m. not take reservations, but are willing to tell how crowded Rates: $2/hour. it is one or two days ahead: 1-800-458-0882. Y.W.C.A., 303-449-1951, 1410 Mapleton, Boulder, Boulder County Fairgrounds Campground is at 9595 CO 80302. Director: Molly Cropp. Ages: 0 to 12. Hours: Nelson Road, Longmont. The nightly base rate is $10, 7:00a.m. to 6:00p.m. Rates: $1/hour to $3/hour. electricity is $2, and water is $1. Anyone staying seven In addition, a Parent-Child Lounge will be located nights pays for just six nights. Reservations can be made near the Joint Meetings registration area. It will be by calling 303-678-1525 starting in May. furnished with casual furniture, a crib, a changing area, some assorted toys and a televison set. Any child using Car Rental this lounge MUST be accompanied by a parent (not It has been arranged for participants to rent cars for simply an adult) who must be responsible for supervision the Boulder meetings from Thrifty Rent A Car. To book of the child. This lounge will be unattended and parents a reservation, participants should call 1-800-367-2277, assume all responsibility for their children. This lounge extension 314 between 8:00a.m. and 4:30p.m. Central will only be open during the hours of registration and all Time and tell the operator that they will be attending persons must leave the lounge at the close of registration the Joint Mathematics Meetings in Boulder, Colorado, each day. August 7- 10. Normal renter and credit requirements apply, including a valid driver's license, major credit Handicapped card, and minimum rental age. Taxes, refueling, and Most session rooms on campus are accessible by optional insurance (the property damage waiver is $8.95 wheelchair. The university will provide alternate accom­ per day) are not included in the rental costs. modations if necessary. Please contact Arlan Ramsay, [Note, as long as one has collision coverage on one's Department of Mathematics, Campus Box 426, Univer­ car at home, and it is not driven while one is on vacation, sity of Colorado, Boulder, CO 80309-0426, if there are most insurance companies will cover collision (PDW, any questions. formerly CDW) on the rental car; so there is no need to Participants with special needs should be sure to purchase it from the rental company. However, coverage indicate this on the Preregistration/Housing Form. will not extend if the rental car is for business purposes. Participants should check with their insurance agent for Libraries clarification of their specific policy.] The following rates Norlin Library is the main library on the campus. Most include unlimited mileage: mathematics books and journals are in the Math-Physics Day Week Library in the east end of Duane Physics Building on Sub-compact $24.99 $ 99.99 level one. Compact 26.99 109.99 The main branch of the Boulder Public Library is at Mid Size 27.99 129.99 1000 Canyon Boulevard. Full Size 29.99 149.99 Local Information (four doors) Luxury 34.95 244.65 For following directions, remember that the mountains ( 3 day notice) are to the west of Boulder. There are many things to do in the mountains near Boulder, including trails that start Child Care in the city. Please visit the Local Information section of Boulder has more than a few child care facilities that the Meetings Registration Desk to get more information accept drop-in clients. A booklet listing more will be about the hiking trails. Some start at the west end of available at the local information desk, but some are Baseline Road (Gregory Canyon, or Chautauqua Park), listed here. It is advisable to call a week or two in or at the National Center for Atmospheric Research advance to verify availability.

718 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

(NCAR) at the west end of Table Mesa Drive, or at the Social Events west end of Mapleton Avenue. ilME invites all participants to help celebrate its 75th Flagstaff Mountain is a city park. There is a bicycle anniversary at the Western Hoe Down on Tuesday and jogging/walking trail that runs along Boulder Creek evening, August 8, at 6:30 p.m. A special program of starting near the mouth of the canyon and going out to entertainment will be presented by ilME members, and 55th Street. a local square dance caller will show you how to swing NCAR and NIST (National Institute of Standards your partner and do-si-do. and Technology) are places to visit, as are museums The Hoe Down will take place in the Gardens at the on campus and in Denver. Central City, Leadville, and Clarion Harvest House. The hotel is located across the Georgetown are historical small cities. Rocky Mountain street from the Northeast corner of campus. The menu National Park is an hour's drive north of Boulder on includes barbecue chicken, ribs, and beef brisket, baked US36. Mesa Verde is in the Southwest Corner of the beans, creamed corn, tossed salad, Southern slaw, apple state, and all the roads that can be taken to arrive there cobbler, corn muffins, coffee, and tea. The children's go past beautiful scenery. Visit the Local Information menu includes soft drinks. For vegetarians, a vegetarian section for more hints on where to go after the meeting. lasagne will replace the three meats on the menu. Be aware that it is easier to sunburn at higher altitudes Tickets are $19 for adults' regular meal, $16 for and easier to get dehydrated. Sunblock and water bottles vegetarian meal, and $9 for children five through 12 years are essentials of hiking. of age. There is no charge for children under five years of age. Tickets may be purchased at the Transparencies Medical Services Section of the Meetings Registration Desk. Boulder Community Hospital is at Broadway and Bal­ sam; follow Broadway north from downtown, or go Travel west from 28th Street on Valmont (which connects to In August, Colorado is on Mountain Daylight Time. Balsam). Airline passengers will arrive at Stapleton International Boulder Memorial Hospital is at 311 Mapleton; go Airport in Denver. From there regular bus service to north on Broadway and turn left on Mapleton. Boulder via downtown Denver costs $2 and takes 1.25 Boulder Medical Center has an Urgent Care Center hours. The Boulder Airporter runs a shuttle service, for walk-in patients and is also located at Broadway and leaving every hour, costing $8 and taking about 40 Balsam. Hours are 8:00 a.m. to 7:00 p.m. minutes. Call 303-499-1559 for reservations. For all emergencies, on or off campus, dial 911. For some years now, the AMS-MAA Joint Meetings has engaged a travel agent for the January and Parking Committee August Joint Meetings in an effort to ensure that everyone Participants staying on campus can purchase permits for attending these meetings is able to obtain the best the Kittredge Permit Parking Lots for $1 per day at possible airfare. This service is presently being performed the check-in desk, located in the Kittredge Commons by Meetings, Incentives, Conventions of America, Inc. Office. These lots are only available for those residing at (MICA); their advertisement can be found elsewhere Kittredge. in this meeting announcement. Although any travel Participants driving in but not staying on campus can agent can obtain Supersaver or other such published purchase stickers at a cost of $3 per day for the Visitors' promotional fares, only MICA can obtain the special Parking Lot, located across the street from the University additional 5% discount over and above these fares, and Memorial Center. These stickers do not include in and the 40% off regular coach fare. The latter, of course, is out privileges. A new sticker will have to be presented to financially beneficial only when one does not qualify for the attendant every time one leaves the lot. These stickers one of the promotional fares. Participants should pay can be purchased at the Transparencies section of the particular attention to the cancellation policies stated in Meetings Registration Desk, located in the University the ad. Memorial Center. The Permit Parking Lot located next to the Engineer­ Weather ing building is free on weekends. Boulder is mainly on the plain, but next to (small) The humidity tends to be very low (20% Smoking mountains. to 30%). High temperatures at the time of the meeting Please note that smoking is not allowed in any of the average 84°F and the temperature drops rapidly in the buildings on the university campus, except for specially evening with overnight lows averaging 58°F. Of course, in designated areas. Smoking is not allowed in any of the the mountains it will be cooler. Afternoon and evening sessions. thundershowers are fairly common but usually brief. Keep an eye out for rainbows, if you like them.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 719 Meetings

(UJ UniTED AIRLinES

AIRLINE INFORMATION SPECIAL AIRFARES + 1-800-888-6422 MICA, Inc., the official travel management firm for the Joint Mathematics Meetings to be held in Boulder, Colorado, August 7-10, 1989, has arranged for special discounts aboard United Airlines!*

Save 5% off published promotional fares, meeting all restrictions, or 40% off regular roundtrip coach fares, with a 7 day advance purchase. The lowest fares require a Saturday night stay, are subject to an airline change/cancel­ lation penalty, and may be purchased at least 30 days prior to departure.

Every Joint Mathematics Meetings participant will also receive $100,000.00 flight insurance with each ticket purchased through MICA aboard any airline.

* United Airlines has been designated as the official airline for the Boulder meetings because it provides the best service for the majority of participants around the country. For some participants, United may not provide optimal service, but since the airlines permit only one carrier to be designated as the official airline, other airlines will not offer the discount convention airfares. However, if United does not provide convenient service to and from your location, MICA will inform you of the best available service and fare on another airline.

Call Today Toll-Free and Save: 1-800-888-6422 Monday- Friday, 8:30am-6:00pm EST

Meetings, Incentives, Conventions of America, Inc. (MICA, Inc.) Suite 303, 195 Farmington Avenue, Farmington, CT 06032

720 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Timetable (Mountain Daylight Time)

The final version of the Timetable and Program, including room assignments, will be distributed at the meeting.

UMC=University Memorial Center

Sunday, /,oan / •motioal August 6 /Ma~::atical Society / As~:~~ation of America

MORNING

SHORT COURSE SERIES CRYPTOLOGY AND COMPUTATIONAL NUMBER THEORY

8:30 a.m. - 2:30 p.m. SHORT COURSE REGISTRATION Outside Room C250, Ramaly Biology

8:30 a.m. - 4:00 p.m. BOARD OF GOVERNORS' MEETING

9:15 a.m. - 10:30 a.m. SHORT COURSE LECTURE #1 Introduction Carl Pomerance

10:45 a.m. - noon SHORT COURSE LECTURE #2 The search for provably secure cryptosystems Shafi Goldwasser

AFTERNOON

1 :30 p.m. - 2:45 p.m. SHORT COURSE LECTURE #3 Primality testing Arjen K. Lenstra

2:00 p.m. - 7:00 p.m. COUNCIL MEETING

3:00p.m.- 4:15p.m. SHORT COURSE LECTURE #4 Factoring Carl Pomerance

3:00 p.m. - 7:00 p.m. REGISTRATION FOR JOINT MATHEMATICS MEETINGS Glenn Miller Ballroom, UMC

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 721 TIMETABLE

Monday, /,icao /hematic.! August 7 /" /Ma~::atical Society / As~o:~~tion of America / Or~~~:zations

MORNING

7:30 a.m. - 4:00 p.m. REGISTRATION Glenn Miller Ballroom, UMC

8:00 a.m. - 9:15 a.m. SHORTCOURSELECTURE#5 The discrete logarithm problem Kevin S. McCurley

8:30 a.m. - 9:20 a.m. INVITED ADDRESS The dynamics of billiards in polygons Howard A. Masur

8:45a.m. - 10:45 a.m. MINICOURSE #1 (Part A) The use of personal computers in an introductory linear algebra course Homer Bechtel!

8:45 a.m. - 10:45 a.m. MINICOURSE #2 (Part A) Combinatorics via functional equations Donald A. Snow

9:30 a.m. - 10:45 a.m. SHORT COURSE LECTURE #6 The rise and fall of knapsack cryptosystems Andrew M. Odlyzko

9:35 a.m. - 10:25 a.m. INVITED ADDRESS Limiting behavior of densities for annihilating systems of particles Maury D. Bramson

11 :00 a.m. - 11 :50 a.m. AMS-MAA INVITED ADDRESS Crystals, in equilibrium and otherwise Jean E. Taylor

AFTERNOON

1:00 p.m. - 5:00 p.m. EXHIBIT AND BOOK SALE BOOK SALE Glenn Miller Ballroom, UMC Glenn Miller Ballroom, UMC

1:00 p.m. - 5:00p.m. EXHIBITS Glenn Miller Ballroom, UMC

722 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE

Monday, /hematioal /., August 7 (cont'd) /Ma~::atical/""" Society / As::~:tion of America / Or~~~:zations

AFTERNOON (cont'd)

1 :15 p.m. - 2:15 p.m. COLLOQUIUM LECTURE I Geometry, groups, and self-similar filings William P. Thurston

2:30 p.m. - 3:20 p.m. INVITED ADDRESS Iterating rational maps and automorphisms of the Bernoulli shift Linda Keen

2:30 p.m. - 3:45 p.m. SHORT COURSE LECTURE #7 Pseudorandom number generators in cryptography and number theory Jeffrey C. Lagarias

SESSIONS FOR CONTRIBUTED PAPERS 2:30 p.m. - 4:20 p.m. Applications

2:30 p.m. - 4:20 p.m. Algebra and combinatorics

2:30 p.m. - 5:10 p.m. CONTRIBUTED PAPER SESSION Pedagogical uses of symbolic computer systems, Part A Arnold M. Ostebee

2:30 p.m. - 4:00 p.m. AMS-MAA PANEL DISCUSSION Everybody Counts David W. Ballew Ronald G. Douglas Wade Ellis, Jr. Lynn A. Steen Marcia P. Sward John A. Thorpe (moderator)

3:35 p.m. - 4:25 p.m. INVITED ADDRESS Metrizability in manifolds Mary Ellen Rudin

SPECIAL SESSIONS 4:00 p.m. - 5:50 p.m. Dynamics and moduli space I

4:00 p.m. - 6:00 p.m. MINICOURSE #1 (Part B) The use of personal computers in an introductory linear algebra course Homer Bechtel!

JULVi AUGUST 1989, VOLUME 36, NUMBER 6 723 TIMETABLE

Monday /rioao /homotioal / .. August 7 (cont'd) /Ma~::atical Society / As~:~~tion of America / Or~~~:zations

AFTERNOON (cont'd)

4:00 p.m. - 6:00 p.m. MINICOURSE #2 (Part B) Combinatorics via functional equations Donald R. Snow

4:00 p.m. - 6:00 p.m. MINICOURSE #3 (Part A) Chaotic dynamical systems Robert L. Devaney

SESSIONS FOR CONTRIBUTED PAPERS 4:30 p.m. - 5:40 p.m. General Session

4:30 p.m. - 6:00 p.m. Algebra and Combinatorics

4:40 p.m. - 6:40 p.m. SECTION OFFICERS' MEETING

EVENING

7:00 p.m. - 9:00 p.m. NATIONAL MEETING OF DEPARTMENT HEADS Evaluating teaching in mathematics Donald W. Bushaw David J. Lutzer (moderator) Tom Trotter (organizer) Thomas W. Tucker

7:00 p.m. - 9:00 p.m. PI MU EPSILON RECEPTION

Tuesday, ~rican ~hematical ~er August 8 / Ma~::atical Society / As::~ation of America / Or~~~izations

MORNING 7:30a.m. - 4:00p.m. REGISTRATION Glenn Miller Ballroom, UMC

SPECIAL SESSIONS 8:00 a.m. - 9:50 a.m. Free boundary problems and partial differential equations I

724 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE

Tuesday, /,,., /hom";'" /, August 8 (cont'd) /Ma~::atical Society / As::~:tion of America / Or~~~:zations

MORNING (cont'd)

SPECIAL SESSIONS 8:00 a.m. - 9:50 a.m. Dynamics and moduli space II

Computational number theory and applications I

SESSIONS FOR CONTRIBUTED PAPERS 8:00 a.m. - 9:30 a.m. Topology

8:00 a.m. - 9:50 a.m. Analysis

8:00 a.m. - 9:55 a.m. CONTRIBUTED PAPER SESSION Pedagogical uses of symbolic computer systems, Part B Arnold M. Ostebee

8:00 a.m. - 9:55 a.m. PME CONTRIBUTED PAPER SESSIONS

8:00 a.m. - 10:00 a.m. MINICOURSE #3 (Part B) Chaotic dynamical systems Robert L. Devaney

8:00 a.m. - 1 0:00 a.m. MINICOURSE #4 (Part A) Faculty-managed programs that produce minority mathematics majors Ray Shiflett Uri Treisman

8:00 a.m. - 1 0:00 a.m. MINICOURSE #5 (Part A) Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg

8:30 a.m. - 9:55 a.m. PUBLIC HEARING ON ACCREDITATION John D. Fulton (moderator) Calvin T. Long Lynn A. Steen

8:30 a.m. - 9:00 a.m. ASSOCIATION FOR WOMEN IN MATHEMATICS MEMBERSHIP MEETING

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 725 TIMETABLE

Tuesday, /,;oan /hematical /., August 8 (cont'd) /Ma~::atical Society / As~:~~tion of America / Or~~~:zations

MORNING (cont'dl

8:40 a.m. - 9:30 a.m. INVITED ADDRESS Selfdual quantifiers: a unifying theme in mathematics and logic John W. Addison, Jr.

9:00 a.m. - 10:00 a.m. AWM PANEL DISCUSSION Women in operations research: Their work and experiences Margaret Brandeau Janice Hammond Jill P. Mesirov (moderator) Margaret Wright

9:00 a.m. - 5:00 p.m. EXHIBIT AND BOOK SALE BOOK SALE Glenn Miller Ballroom, UMC Glenn Miller Ballroom, UMC

9:00 a.m. - 5:00 p.m. EXHIBITS Glenn Miller Ballroom, UMC

10:10 a.m. - 11 :00 a.m. AMS-MAA INVITED ADDRESS Case studies of political opinions passed off as science and mathematics Serge Lang

11:15a.m.- 12:15p.m. EARLE RAYMOND HEDRICK LECTURE I The mathematics of mixing things up: From card shuffling to counting and back Persi Diaconis

AFTERNOON

noon - 1 :00 p.m. PME COUNCIL MEETING

1:15p.m.- 2:15p.m. COLLOQUIUM LECTURE II Geometry, groups, and self-similar tilings William P. Thurston

2:25 p.m. - 4:25 p.m. MINICOURSE #3 (Part C) Chaotic dynamical systems Robertl. Devaney

726 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE

Tuesday, /homatloaJ /,. August 8 (cont'd) /Ma~::atical/''"'" Society / As::~:tion of America / Or~~~:zations

AFTERNOON (cont'd)

2:25 p.m. - 4:25 p.m. MINICOURSE #4 (Part B) Faculty-managed programs that produce minority mathematics majors Ray Shiflett Uri Treisman

2:25 p.m. - 4:25 p.m. MINICOURSE #5 (Part B) Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg

2:30 p.m. - 4:00 p.m. PROGRESS IN MATHEMATICS LECTURE Applications of POE methods by Gromov, Floer, and others to symplectic geometry of manifolds Dusa McDuff

2:30 p.m. - 4:10 p.m. CONTRIBUTED PAPER SESSION Pedagogical uses of symbolic computer systems, Part C Arnold M. Ostebee

2:30 p.m. - 4:25 p.m. CONTRIBUTED PAPER SESSION Calculus revision, Part A Thomas W. Tucker

2:30 p.m. - 4:20 p.m. PME CONTRIBUTED PAPER SESSIONS

2:30 p.m. - 4:20 p.m. MAA-PME UNDERGRADUATE STUDENT PAPER SESSION

2:30 p.m. - 3:00 p.m. VIDEO PRESENTATION Finite symmetry groups in three dimensions Lorraine L. Foster

4:35 p.m. - 6:00 p.m. STEELE PRIZE SESSION AND BUSINESS MEETING

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 727 TIMETABLE

Tuesday, /Ooac / hematloal /., August 8 (cont'd) /Ma~::atical Society / As::~:tion of America / Or~~~:zations

EVENING

6:30 p.m. - 9:30 p.m. WESTERN HOE DOWN

9:30 p.m. - 11 :00 p.m. AWM RECEPTION

Wednesday, /rican /hematloal /er August 9 / Ma~::atical Society / As::~ation of America / Or~~~izations

MORNING

7:30 a.m. - 4:00 p.m. REGISTRATION Glenn Miller Ballroom, UMC

8:00 a.m. - 9:50 a.m. SPECIAL SESSIONS Mathematical questions in computational geometry I

Free boundary problems and partial differential equations II

Computational number theory and applications II

8:00 a.m. - 9:30 a.m. SESSIONS FOR CONTRIBUTED PAPERS Analysis II

8:00 a.m. - 9:55 a.m. CONTRIBUTED PAPER SESSION Calculus revision, Part B Thomas W. Tucker

8:00 a.m. - 9:55 a.m. PME CONTRIBUTED PAPER SESSIONS

8:00 a.m. - 10:00 a.m. MINICOURSE #6 (Part A) Group theory through art Thomas Brylawski

8:00 a.m. - 10:00 a.m. MINICOURSE #7 (Part A) HP-288 short course for nearly inexperienced users Jerold Mathews

728 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE

Wednesday, /rioao /homatioal /., August 9 (cont'd) / Ma~::atical Society / As::~:tion of America / Or~~~:zations

MORNING (cont'd)

8:00 a.m. - 9:00 a.m. PME DUTCH-TREAT BREAKFAST

SPECIAL SESSIONS 8:30 a.m. - 9:50 a.m. Dynamics and moduli space Ill

8:30 a.m. - 9:55 a.m. FORUM ON MATHEMATICS MAJORS Are we teaching majors the right mathematics? Are we teaching it the right way? BeHye Anne Case James R.C. Leitzel Lynn A. Steen

9:00 a.m. - 5:00 p.m. EXHIBIT AND BOOK SALE BOOK SALE Glenn Miller Ballroom, UMC Glenn Miller Ballroom, UMC

9:00 a.m. - 5:00 p.m. EXHIBITS Glenn Miller Ballroom, UMC

10:10 a.m.- 11:00 a.m. AMS-MAA INVITED ADDRESS The principle of duality in functional analysis Shizuo Kakutani

11:15a.m.- 12:15p.m. EARLE RAYMOND HEDRICK LECTURE II The mathematics of mixing things up: Reversible chains and eigenvalues of the Laplacian Persi Diaconis

AFTERNOON

1 :15 p.m. - 2:15 p.m. COLLOQUIUM LECTURE Ill Geometry, groups, and self-similar filings William P. Thurston

SPECIAL SESSIONS 1 :15 p.m. - 3:05 p.m. Free boundary problems and partial differential equations Ill

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 729 TIMETABLE

Wednesday, August 9 (cont'd) ~rio~ ation of America zations matical Society ~7matioal ~:' AFTERNOON (cont'dl

2:20p.m.- 3:30p.m. SESSIONS FOR CONTRIBUTED PAPERS Analysis and geometry

2:25p.m.- 4:15p.m. SPECIAL SESSIONS Mathematical questions in computational geometry II

Computational number theory and applications Ill

2:30p.m.- 3:20p.m. AMS-MAA-PME INVITED ADDRESS The mathematics of identification numbers Joseph A. Gallian

2:30p.m.- 4:30p.m. MINICOURSE #6 (Part B) Group theory through art Thomas Brylawski

2:30p.m.- 4:30p.m. MINICOURSE #8 (Part A) Applications of the HP-285 for experienced users Thomas W. Tucker

3:35p.m.- 4:25p.m. INVITED ADDRESS The Riemann mapping non-theorem Nancy K. Stanton

4:40p.m.- 5:40p.m. PRIZE SESSION AND BUSINESS MEETING

5:45p.m.- 10:00 p.m. BANQUET FOR 25-YEAR MEMBERS

EVENING

6:30p.m.- 8:15p.m. PME BANQUET

8:30p.m.- 9:30p.m. PME J. SUTHERLAND FRAME LECTURE Entrainment of frequency: A recurring theme Jane Cronin Scanlon

730 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE

Thursday, /hematloal /., August 10 /Ma~::atical/""" Society ~ As~:C~ation of America / Or~~~:zations

MORNING 7:30 a.m. - 1 :00 p.m. REGISTRATION Glenn Miller Ballroom, UMC

SPECIAL SESSIONS 8:00 a.m. - 9:50 a.m. History of orthogonal polynomials I

Mathematical questions in computational geometry Ill

Free boundary problems and partial differential equations IV

Computational number theory and applications IV

8:00 a.m. - 9:50 a.m. SESSIONS FOR CONTRIBUTED PAPERS Analysis and probability

8:00 a.m. - 9:55a.m. COMMITTEE ON COMPUTERS IN MATHEMATICS EDUCATION (CCIME) PANEL DISCUSSION The role of the computer in calculus reform Robert L. Devaney Eugene A. Herman (moderator) Kenneth R. Hoffman David A. Smith Paul Zorn

8:00a.m.- 10:00 a.m. MINICOURSE #7 (Part B) HP-28S short course for nearly inexperienced users Jerold Mathews

8:00a.m.- 10:00 a.m. MINICOURSE #9 (Part A) A seminar on women in mathematics Miriam P. Cooney esc

8:40 a.m. - 9:30 a.m. INVITED ADDRESS The number of solutions of Diophantine equations Wolfgang M. Schmidt

9:00 a.m. - noon EXHIBIT AND BOOK SALE BOOK SALE Glenn Miller Ballroom, UMC Glenn Miller Ballroom, UMC

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 731 TIMETABLE

Thursday, /,;,., /, August 10 (cont'd) /h•m•tio• /Ma~:~atical Society / As::~~tion of America / Or~~~:zations

MORNING (cont'd)

9:00 a.m. - noon EXHIBITS Glenn Miller Ballroom, UMC

10:10a.m.- 11:00a.m. AMS-MAA INVITED ADDRESS ax 2 +hxy+cy2 =n John H. Conway

11:15 a.m. -12:15 p.m. EARLE RAYMOND HEDRICK LECTURE Ill The mathematics of mixing things up: Modern Markov chain theory Persi Diaconis

AFTERNOON

1:15 p.m.- 2:45p.m. PROGRESS IN MATHEMATICS LECTURE Liquid crystals Haim Brezis

1 :15 p.m. - 3:15 p.m. MINICOURSE #8 (Part B) Applications of the HP-288 for experienced users Thomas W. Tucker

1 :15 p.m. - 3:15 p.m. MINICOURSE #9 (Part B) A seminar on women in mathematics Miriam P. Cooney esc

3:00 p.m. - 4:00 p.m. COLLOQUIUM LECTURE IV Geometry, groups, and self-similar filings William P. Thurston

SPECIAL SESSIONS 3:00p.m.- 5:10p.m. History of orthogonal polynomials II

4:00 p.m. - 5:50 p.m. Mathematical questions in computational geometry IV

4:00 p.m. - 5:50 p.m. Computational number theory and applications V

4:00 p.m. - 5:30 p.m. SESSIONS FOR CONTRIBUTED PAPERS Analysis Ill

732 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

If available, abstracts of papers presented by the AMS-MAA-llME Lecturer, AMS-MAA Lecturers, AMS Progress in Mathematics Lecturers, AMS Colloquium Lecturer, AMS invited 50-minute speakers, MAA Hedrick Lecturer, MAA invited 50-minute speakers, MAA contributed paper session speakers, and the OME Frame Lecturer will be found in a colored insert in the program given to registrants. Abstracts of papers presented in AMS Special Sessions and AMS Sessions for Contributed Papers will be found in the August issue of Abstracts of papers presented to the American Mathematical Society, which will also be provided to registrants at the meeting. Abstracts of talks other than AMS and MAA and the OME Frame Lecturer are not available. To maintain the schedule, beginning and ending times of presentations will be strictly enforced. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. Where a presenter is visiting another institution, the permanent affiliation is given first, followed by the name of the institution being visited.

Sunday, August& AMS Invited Address 9:35 a.m.-10:25 a.m. MAA Board of Governors (2) Limiting behavior of densities for annihilating systems of particles. 8:30 a.m.-4:00 p.m. Maury D. Bramson, University of Wisconsin, Madison (850-60-38)

AMS Council AMS-MAA Invited Address 2:00 p.m.-7:00 p.m. 11:00 a.m.-11:50 a.m. (3) Crystals, in equilibrium and otherwise. Jean E. Taylor, Rutgers University, New Monday, August 7 Brunswick

AMS Invited Address AMS Colloquium Lectures: Lecture I

8:30 a.m.-9:20 a.m. 1:15 p.m.-2:15p.m.

(1) The dynamics of billiards in polygons. (4) Geometry, groups, and self-similar tilings. Howard A. Masur, University of Illinois, Chicago William P. Thurston, Princeton University (850-58-39) MAA Invited Address MAA Minicourse #1 (Part A) 2:30 p.m.-3:20 p.m. 8:45 a.m.-10:45 a.m. (5) Iterating rational maps and automorphisms of The use of personal computers in an introductory linear the Bernoulli shift. algebra course. Homer Bechtel!, University of New Linda Keen, Herbert H. Lehman College, City Hampshire University of New York

MAA Minicourse #2 (Part A) AMS Session on Applications

8:45 a.m.-10:45 a.m. 2:30 p.m.-4:20 p.m.

Combinatorics via functional equations. Donald R. Snow, 2:30 p.m. Perturbation solution to a non-uniform shell Brigham Young University (6) subjected to a moving load. Preliminary report. Leonard J. Putnick, Siena College (850-73-26) (Sponsored by Thomas H. Rousseau)

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 733 Program of the Sessions

Monday, August 7 (cont'd) MAA Session on Pedagogical Uses of Symbolic Computer Systems, Part A

2:30 p.m.-5:1 0 p.m. 2:50 p.m. Forced oscillations near a Hopf bifurcation in a With CAS, engineers can do more than set (7) biological model. 2:30 p.m. (18) derivatives equal to zero. Alfonso Casal, Polyte::hnic University of Graves, Rose-Hulman Institute of Madrid, Spain, and Alfredo Somolinos*, Mercy G. Elton College (850-92-80) Technology 2:45 p.m. Educational research and suggestions in using 3:10p.m. The axisymmetric Cauchy-Poisson problem in a Maple and MACSYMA in the first year of college (8) stratified liquid. (19) calculus. Lokenath Debnath* and Uma B. Guha, R. Palmiter, Kenyon College University of Central Florida (850-76-83) JeaneHe p.m. Calculus I with computer algebra. 3:30 p.m. ARIMA models in commodities markets. 3:00 (20) Phoebe T. Judson, Trinity College (9) Albert E. Parish Jr., College of Charleston (850-90-29) (Sponsored by William L. 3:15p.m. Revitalizing undergraduate mathematics with Golightly) (21) symbol manipulating graphics calculators. John W. Kenelly* and Donald R. LaTorre, 3:50 p.m. The moduli space of generalized state space Clemson University (1 0) systems. Preliminary report. Joyce O'Halloran*, Portland State University, 3:45 p.m. Calculus, the HP-28S, and problem solving. and Diederich Hinrichsen, University of (22) John Selden* and Annie Selden, Tennessee Bremen, Federal Republic of Germany Technological University (850-93-11) 4:00 p.m. The power and the limitations of the HP-28S in 4:10p.m. Concerning random number generation. (23) the teaching and the learning of mathematics. (11) Preliminary report. J. A. Eidswick, University of Nebraska, Lincoln Nancy Boynton and Joseph Straight*, State 4:15p.m. Using symbolic computation in teaching University of New York, College at Fredonia (24) inventory models. (850-65-97) MarieHa J. TreHer* and Benito Flores, Texas A & M University, College Station 4:30 p.m. Using symbol manipulating calculators in AMS Session on Algebra and Combinatorics (25) pre-calculus. Paul R. PaHen, North Georgia College 2:30 p.m.-4:20 p.m. 4:45 p.m. Using REDUCE in undergraduate instruction. (26) V. S. Ramamurthi, University of North Florida 2:30 p.m. Finite semilattices whose monoids of 5:00 p.m. Enhancing sophomore engineering calculus (12) endomorphisms are regular. (27) with computer symbolic algebra. M. E. Adams, State University of New York, John H. Mathews, California State University, College at New Paltz, and MaHhew Gould*, Fullerton Vanderbilt University (850-06-17) 2:50 p.m. Rigidity matroids. (13) Jack Graver, Syracuse University (850-05-23) AMS-MAA Joint Panel Discussion 3:10p.m. Edge-graceful labeling of generalized Petersen (14) graphs. Sin-Min Lee*, San Jose State University, and 2:30 p.m.-4:00 p.m. Eric Seah, University of Manitoba (850-05-1 0) Everybody Counts. 3:30 p.m. Directed 3-colored (3c) triangulation (T.) Part. (15) II. Compositions and congruences. Conjecture W = A•. Preliminary report. MAA Invited Address Dov Tamari, New York, New York (850-05-84) 3:50 p.m. Magic squares of order 4-A classification 3:35 p.m.-4:25 p.m. (16) scheme using permutations. William A. Sammons, University of North (28) Metrizability in manifolds. Florida (850-05-86) (Sponsored by V. S. Mary Ellen Rudin, University of Wisconsin, Ramamurthi) Madison 4:10 p.m. On the arithmetic of quadratic function fields. (17) T. Kambayashi* andY. Takano, Tokyo Denki University, Japan (850-12-95)

734 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

5:10p.m. On irreducible representations of semidirect AMS Special Session on (35) products. Dynamics and Moduli Space, I Grzegorz Cieciura, Warsaw University, Poland, and Igor Szczyrba*, University of Northern 4:00 p.m.-5:50 p.m. Colorado (850-20-96) 5:30 p.m. On the surface classification theorem. 4:00 p.m. The growth function in billiards. (36) Gregory F. Martin, University of North Florida (29) William A. Veech, Rice University (850-58-21) ( 850-55-1 05) 4:30p.m. Billiards and rational periodic directions in (30) polygons. Michael D. Boshernitzan, Rice University AMS Session on Algebra and Combinatorics (850-58-1 07) 5:00 p.m. Upper bounds for the Hausdorff dimension of 4:30 p.m.-6:00 p.m. (31) the space of nonuniquely ergodic measured foliations. Preliminary report. 4:30p.m. Dihedral crossed product algebras. Howard A. Masur, University of Illinois, (37) Susan Williamson, Newton Centre, Chicago (850-32-43) Massachusetts (850-16-89) 5:30 p.m. Harmonic maps and Thurston's metric. 4:50 p.m. Exact and coexact matrices. (32) Preliminary report. (38) Edwin Connell*, University of Miami, and John Steven Kerckhoff, Stanford University Zweibel, Florida International University (850-53-68) (850-13-15) 5:10p.m. Polynomial automorphisms. (39) Edwin Connell, University of Miami, and John MAA Minicourse #1 (Part B) Zweibel*, Florida International University (850-13-16) 4:00 p.m.-6:00 p.m. 5:30 p.m. Representation with a prescribed initial ( 40) numerator and consecutive integer numerators. The use of personal computers in an introductory linear B. M. Stewart, Okemos, Michigan (850-11-03) algebra course. Homer Bechtel!, University of New 5:50 p.m. The density of a class of fractions. Hampshire (41) Don Redmond, Southern Illinois University, Carbondale (850-11-42) MAA Minicourse #2 (Part B) MAA Section Officers 4:00 p.m.-6:00 p.m.

Combinatorics via functional equations. Donald R. Snow, 4:40 p.m.-6:40 p.m. Brigham Young University JPBM National Meeting of Department Heads MAA Minicourse #3 (Part A) 7:00 p.m.-9:00 p.m. 4:00 p.m.-6:00 p.m. Evaluating teaching in mathematics. Chaotic dynamical systems. Robert L. Devaney, Boston University Tuesday, August 8 AMS General Session

4:30 p.m.-5:40 p.m. AMS Special Session on Free Boundary 4:30 p.m. Who was A. Miguel? Preliminary report. Problems and Partial Differential Equations, I (33) James R. Smart, San Jose State University (850-01-13) 8:00 a.m.-9:50 a.m. 4:50 p.m. When is a Markovian semigroup a group? 8:00 a.m. Convexity of level sets for solutions to elliptic (34) W. M. Priestley, University of the South (42) ring problems. Preliminary report. (850-46-88) Nicholas Korevaar, University of Utah (850-35-28) 8:30 a.m. Informal Discussion

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 735 Program of the Sessions

Tuesday, August 8 (cont'd) AMS Session on Topology 8:00 a.m.-9:30 a.m.

8:00a.m. Automorphisms of foliations defined by complex Nonuniqueness and uniqueness of capillary 9:00a.m. (53) linear vectorfields. (43) surfaces. S. Shahshahani, ICTP-Mathematics Group, California, Paul Concus, University of Trieste, Italy and University of Technology, Stanford Berkeley, and Robert Finn*, Tehran, Iran (850-58-82) University (850-49-49) 8:20a.m. A new proof that 1-ULC implies tameness. Damped shallow water waves. 9:30 a.m. (54) Preliminary report. Oregon State University (44) Ronald B. Guenther, Davis Finley, University of Texas, Austin Kirk E. Lancaster) (850-76-53) (Sponsored by (850-57-46) 8:40a.m. Heegaard genus 2 representations of two (55) 3-manifolds with the same finite fundamental AMS Special Session on group. Preliminary report. . Dynamics and Moduli Space, II Francis D. Lonergan, Webster, Massachusetts (850-55-33) 8:00 a.m.-9:50 a.m. 9:00a.m. Split compactifications. (56) Charles Aull, Virginia Polytechnic Institute and energy harmonic maps and 8:00 a.m. Infinite State University (850-54-64) ( 45) degeneration of hyperbolic surfaces in moduli 9:20 a.m. On semi-invariant sub-manifolds. Preliminary space. (57) report. Michael Wolf, Rice University (850-32-27) K. D. Singh, Lucknow University, India spectrum and Teichmiiller space. 8:30 a.m. Length (850-53-74) (Sponsored by Sankatha P. Singh) (46) Albert Fathi, University of Florida (850-53-22) 9:00a.m. Critical point surgery for rational maps of (47) degree 2. AMS Session on Analysis, I Lisa R. Goldberg, Brooklyn College, City University of New York, and Linda Keen*, Herbert H. Lehman College, City University of 8:00 a.m.-9:50 a.m. York (850-30-45) New 8:00a.m. Greatest common divisor matrices. II. 9:30 a.m. Rotation cycles on the unit circle (58) Keith Bourque, Steve Ligh*, University of (48) Lisa R. Goldberg, Brooklyn College, City Southwestern Louisiana, and Scott Beslin, University of New York (850-58-87) Nicholls State University (850-15-92) 8:20a.m. Least squares with constraints and generalized (59) eigenvalue problems. Preliminary report. AMS Special Session on Computational Geza Schay, University of Massachusetts, Number Theory and Applications, I Boston (850-15-76) 8:40a.m. A class of examples of D-sequences. 8:00 a.m.-9:50 a.m. (60) T. A. Bick, Union College, and John Coffey*, Purdue University, Calumet Campus 8:00a.m. The self-initializing quadratic sieve. Preliminary (850-28-40) report. (49) 9:00a.m. Fix-points of composite entire and meromorphic Carl Pomerance, University of Georgia (61) functions. (850-11-58) Walter Bergweiler, Cornell University and 8:30a.m. Design of an FFT continuation to the ECM RWTH Aachen, Federal Republic of Germany (50) method of factorization. Preliminary report. (850-30-19) Peter L. Montgomery, University of California, 9:20a.m. The boundary behaviour of harmonic univalent Los Angeles (850-11-25) (62) maps. 9:00 a.m. Factorization of integers. Preliminary report. Yusuf Abu-Muhanna, Kuwait University, (51) SamuelS. Wagstaff, Jr., Purdue University, Kuwait (850-30-02) (Sponsored by Waleed M. West Lafayette (850-11-71) Dee b) 9:30 a.m. Factoring by electronic mail. 9:40a.m. Quasilinearity and the first eigenvalue. (52) Arjen K. Lenstra, University of Chicago (63) Victor L. Shapiro, University of California, (850-11-56) Riverside (850-35-36)

736 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

MAA Session on Pedagogical Uses of PME Contributed Paper Sessions Symbolic Computer Systems, Part B 8:00 a.m.-9:55a.m. 8:00 a.m.-9:55 a.m. 8:00a.m. Calculus and computing: An exploratory study MAA Public Hearing on Accreditation (64) to examine the effectiveness of using a computer algebra system to develop increased conceptual understanding in a first semester 8:30 a.m.-9:55 a.m. calculus course. Connie S. Schrock, Emporia State University 8:15a.m. Symbolic computing in Calculus I. AWM Membership Meeting (65) Charlene Beckmann, Grand Valley State University 8:30 a.m.-9:00 a.m. 8:30a.m. Oracular failures of computer algebra systems. (66) Yves Nievergelt, Eastern Washington University MAA Invited Address 8:45a.m. Using a symbolic computer system in a calculus (67) laboratory. 8:40 a.m.-9:30 a.m. L. Carl Leinbach, Gettysburg College 9:00a.m. Calculus and mathematica. (72) Selfdual quantifiers: A unifying theme in (68) H. Porta* and J. J. Uhl, University of Illinois, mathematics and logics. Urbana-Champaign John W. Addison, Jr., University of California, 9:15a.m. Using CAS to explore calculus concepts. Berkeley (69) Zaven Karian, Denison University 9:30a.m. Calculus for engineers via Maple. (70) Robert J. Lopez, Rose-Hulman Institute of AWM Panel Discussion Technology 9:45a.m. Weak students, symbolic computing, and 9:00 a.m.-10:00 a.m. (71) calculus. Women in operations research: Their work and experiences. J. Douglas Child, Rollins College

AMS-MAA Invited Address MAA Minicourse #3 (Part B) 10:10 a.m.-11:00 a.m. 8:00 a.m.-10:00 a.m. (73) Case studies of political opinions passed off as Chaotic dynamical systems. Robert L. Devaney, Boston science and mathematics. University Serge Lang, Yale University

MAA Minicourse #4 (Part A) MAA Earle Raymond Hedrick Lectures: Lecture I

8:00 a.m.-10:00 a.m. 11:15 a.m.-12:15 p.m. Faculty-managed programs that produce minority (74) The mathematics of mixing things up: From mathematics majors. Ray Shiflett, California State card shuffling to counting and back. Polytechnic University, Pomona, and Uri Treisman, Persi W. Diaconis, Harvard University University of California, Berkeley

PME Council MAA Minicourse #5 (Part A) 12:05 p.m.-1:00 p.m. 8:00 a.m.-10:00 a.m.

Starting, funding and sustaining mathematics laboratories. Stavros N. Busenberg, Harvey Mudd College

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 737 Program of the Sessions

3:00p.m. Challenges for intelligent computer-based Tuesday, August 8 (cont'd) (79) calculus tutoring. Tryg A. Ager, Stanford University 3:15p.m. User friendly front ends and freshman calculus. AMS Colloquium Lectures: Lecture II (80) Edwin Rogers, Siena College 3:30 p.m. Using high level Maple packages on the (81) mainframe for calculus. 1:15 p.m.-2:15p.m. Neil E. Berger, University of Illinois, Chicago (75) Geometry, groups, and self-similar ti/ings. 3:45 p.m. Exploratory data analysis. William P. Thurston, Princeton University (82) Richard N. Barshinger, Pennsylvania State University, Worthington Scranton Campus 4:00 p.m. Symbolic computing in precalculus, calculas, MAA Minicourse #3 (Part C) (83) and beyond. Farley Mawyer, York College, City University of 2:25 p.m.-4:25 p.m. New York

Chaotic dynamical systems. Robert L. Devaney, Boston University MAA Session on Calculus Revision, Part A

2:30 p.m.-4:25 p.m. MAA Minicourse #4 (Part B) 2:30 p.m. The calculus program at NSF. 2:25 p.m.-4:25 p.m. (84) JohnS. Bradley, National Science Foundation 2:50 p.m. The calculus reform project at Rollins. Faculty-managed programs that produce minority (85) J. Douglas Child, Rollins College mathematics majors. Ray Shifflet, California State 3:10p.m. Some introductory problems on the geometry of Polytechnic University, Pomona, and Uri Treisman, (86) function graphs. University of California, Berkeley Peter D. Taylor, Queen's University 3:30 p.m. A humanistic calculus. (87) William E. Rosenthal, Ursinus College MAA Minicourse #5 (Part B) 3:50 p.m. A place for writing in a revised calculus (88) curriculum. 2:25 p.m.-4:25 p.m. Emelie Kenney, Wilkes College Starting, funding and sustaining mathematics laboratories. 4:10p.m. A four year plan to install a calculus lab. Stavros N. Busenberg, Harvey Mudd College (89) John Williams, University of Hartford 4:30p.m. Appropriate exam questions for Calculus I. (90) Charlene Beckmann and Ted Sundstrom*, AMS Progress in Mathematics Lecture Grand Valley State University

2:30 p.m.-4:00 p.m. PME Contributed Paper Sessions (76) Applications of PDE methods by Gromov, Floer, and others to symplectic geometry of 2:30 p.m.-4:20 p.m. manifolds. Dusa McDuff, State University of New York, Stony Brook MAA-PME Contributed Paper Session

MAA Session on Pedagogical Uses of 2:30 p.m.-4:20 p.m. Symbolic Computer Systems, Part C MAA Video 2:30 p.m.-4:10p.m. 2:30 p.m. MACSYMA in the advanced undergraduate 2:30 p.m.-3:00 p.m. (77) curriculum. Lester Senechal, Mount Holyoke College Finite symmetry groups in three dimensions. 2:45 p.m. Using computers to explore mathematics. (78) Emily H. Moore, Grinnell College

738 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

AMS Prize Session and Business Meeting AMS Special Session on Computational Number Theory and Applications, II 4:35 p.m.-6:00 p.m. 8:00 a.m.-9:50 a.m. 8:00 a.m. Some new computational results on Warings (99) problem. VVednesday,August9 Marvin Wunderlich* and Jeffrey Kabina, National Security Agency, Fort George G. Meade, Maryland (850-11-81) AMS Special Session on Mathematical 8:30a.m. Residual methods for computing the Hermite Questions in Computational Geometry, I (100) normal form. Paul D. Domich, National Institute of 8:00 a.m.-9:50 a.m. Standards & Technology, Boulder, Colorado (850-11-57) (Sponsored by Kevin S. McCurley) 8:00 a.m. Convex hull boundaries, trisupports, and stalls 9:00 a.m. Construction of special points for the Riemann (91) for space polygons. Preliminary report. (1 01) zeta function. Thomas F. Banchoff, Brown University A.M. Odlyzko, AT&T Bell Laboratories, Murray (850-52-63) Hill, New Jersey (850-11-60) 8:30 a.m. Supercomputing and minimal surfaces. 9:30a.m. Computing the Mordeii-Weil rank of curves of (92) Preliminary report. (102) genus 2. Preliminary report. Fred Almgren, Princeton University Dan Gordon*, University of Georgia, and David (850-49-66) Grant, University of Colorado, Boulder 9:00 a.m. Algorithms for developable surfaces. (850-11-48) (93) George Fix, University of Texas, Arlington (850-53-94) 9:30a.m. Surfacejsurface intersections in geometric AMS Session on Analysis, II (94) modeling. Wayne Tiller, Structural Dynamics Research 8:00 a.m.-9:30 a.m. Corporation, Milford, Ohio (850-68-1 03) (Sponsored by Rangabhary Kannan) 8:00 a.m. Oscillatory behavior of bounded solutions of a (103) higher order equation. Witold Kosmala, Appalachian State University AMS Special Session on Free Boundary ( 850-34-41 ) Problems and Partial Differential Equations, II 8:20a.m. Proper scoring rules for probability forecasters. (104) Pl. Kannappan, University of Waterloo, and P. K. Sahoo*, University of Louisville (850-39-91) 8:00 a.m.-9:50 a.m. 8:40 a.m. Norm inequalities and characterizations of inner 8:00a.m. Convexity of /eve/lines for semi-linear (105) product spaces. (95) equations. A.M. AI-Rashed, King Saud University, Saudi Peter Laurence*, Universita Degli Studii, Arabia (850-46-12) Milano, Italy, and Ed Stredulinsky, Lawrence 9:00a.m. Geometric traces and nuclear operators on Lp University (850-35-61) (106) spaces. Preliminary report. 8:30 a.m. Asymptotic behavior of minimal and capillary Chris Brislawn, University of Colorado, (96) surfaces over a semi-infinite strip. Boulder (850-47-90) David Siegel, University of Waterloo 9:20a.m. Strong convergence theorems for (850-35-47) (Sponsored by Kirk E. Lancaster) (107) pseudo-contractive mappings in Banach 9:00 a.m. More about crystal surfaces in equilibrium. spaces. (97) Preliminary report. Claudio Morales, University of Alabama, Jean Taylor, Rutgers University, New Huntsville (850-47-85) Brunswick (850-49-72) 9:30a.m. A one-phase hyperbolic Stefan problem in (98) multi-dimensional space. MAA Session on Calculus Revision, Part B Dening Li, West Virginia University (850-35-69) (Sponsored by Edward W. Stredulinsky) 8:00 a.m.-9:55 a.m. 8:00a.m. Why integrate calculus and physics? (1 08) Richard Yeatts, Colorado School of Mines

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 739 Program of the Sessions

9:30 a.m. Continued fractions with respect to Heeke Wednesday, August 9 (cont'd) (116) groups. Preliminary report. Andrew Haas, University of Connecticut, Storrs (850-11-93)

8:20a.m. Calculus and physics: Promoting the synergism. (109) Joan Rohrer Hundhausen, Colorado School of MAA Forum Mines 8:40a.m. Calculus revisited: Building an 'Introductory' 8:30 a.m.-9:55 a.m. (11 0) college course around the high school calculus experience. Are we teaching majors the right mathematics? Are we Alice P. Miller, Babson College teaching it the right way?. 9:00a.m. Writing to learn the calculus. (111) John Donnellan• and Ernest Manfred, United States Coast Guard Academy AMS-MAA Invited Address 9:20 a.m. One variable calculus from a modeling point of (112) view: Content. 10:10 a.m.-11:00 a.m. Dan Slaughter, Furman University (117) The principle of duality in functional analysis. 9:40a.m. HyperCalculus: A hypertext system for calculus Shizuo Kakutani, Yale University (113) instruction. Loren Argabright, Drexel University MAA Earle Raymond PME Contributed Paper Sessions Hedrick Lectures: Lecture II 11:15 a.m.-12:15 p.m. 8:00 a.m.-9:55 a.m. (118) The mathematics of mixing things up: Reversible chains and eigenvlues of the MAA Minicourse #6 (Part A) Laplacian. Persi W. Diaconis, Harvard University 8:00 a.m.-10:00 a.m. Group theory through art. Thomas Brylawski, University of AMS Colloquium Lectures: Lecture Ill North Carolina, Chapel Hill 1:15 p.m.-2:15p.m. MAA Minicourse #7 (Part A) (119) Geometry, groups, and self-similar filings. ·;•liam P. Thurston, Princeton University 8:00 a.m.-10:00 a.m. HP-28S short course for nearly inexperienced users. Jerold AMS Speciai Session on Free Boundary Mathews, Iowa State University Problems and Partial Differential Equations, Ill

AMS Special Session on 1:15 p.m.-3:05 p.m. Dynamics and Moduli Space, Ill 1:15 p.m. Convexity properties of solutions in an n-phase (120) fluid problem. Preliminary report. 8:30 a.m.-9:50 a.m. Andrew Acker, Wichita State University (850-35-54) 8:30 a.m. Fundamental polyhedra for 'Margulis 1:45 p.m. Crystal growth by Voronoi methods. Preliminary (114) space-times.· Preliminary report. (121) report. Todd A. Drumm, University of Maryland, Fred Almgren, Jr.•, Princeton University, and College Park (850-53-20) Jean Taylor, Rutgers University, New 9:00 a.m. Equidistant hypersurfaces in complex Brunswick (850-49-31) (115) hyperbolic space. Preliminary report. 2:15p.m. Stability of open channel sediment transport William M. Goldman, University of Maryland, (122) equations. Preliminary report. College Park (850-53-18) William McDougal and Harold Parks•, Oregon State University (850-35-77)

740 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

2:45 p.m. A constant vorticity Riabouchinsky flow based 2:55 p.m. Geodesic multidimensional continued fractions. (123) on a variational principle. Preliminary report. (131) Jeffrey C. Lagarias, AT&T Bell Laboratories, Thomas K. Delillo*, Alan R. Elcrat and Murray Hill, New Jersey (850-11-09) Kenneth G. Miller, Wichita State University (Sponsored by Kevin S. McCurley) (850-76-52) 3:25 p.m. On the worst-case complexity of three (132) algorithms for computing the Jacobi symbol. Preliminary report. AMS Session on Analysis and Geometry Jeffrey Shallit, Dartmouth College (850-11-59) 3:55p.m. Dihedral cubic approximations and series for 1r 2:20 p.m.-3:30 p.m. (133) and Cohen-Lenstra heuristics for class groups. Daniel Shanks, University of Maryland, College 2:20 p.m. Lemniscates and osculatory interpolation. Park (850-11-44) (124) Donald Teets*, South Dakota School of Mines and Technology, and Patrick Lang, Idaho State University (850-41-30) AMS-MAA-PME Invited Address 2:40p.m. Inclusions of H 1 in L2. (125) G. Muraz, lnstitut Fourier de Mathematics, Cedex, France, and Pawel Szeptycki*, 2:30 p.m.-3:20 p.m. University of Kansas (850-46-32) (134) The mathematics of identification numbers. 3:00 p.m. Duality results in multi-objective optimization. Joseph A. Gallian, University of Minnesota, (126) Preliminary report. Duluth R.N. Mukherjee, Banaras Hindu University, India (850-49-04) (Sponsored by Andy R. Magid) MAA Minicourse #6 (Part B) 3:20 p.m. The Coxeter group and the group of units of a (127) checkered matrix ring. 2:30 p.m.-4:30 p.m. Chul Kim, North Carolina State University (850-99-112) Group theory through art. Thomas Brylawski, University of North Carolina, Chapel Hill

AMS Special Session on Mathematical Questions in Computational Geometry, II MAA Minicourse #8 (Part A)

2:25 p.m.-4:15p.m. 2:30 p.m.-4:30 p.m.

2:25p.m. Stability analysis of curve and surface Applications of the HP-28S for experienced users. Thomas (128) transformations. W. Tucker, Colgate University R. T. Farouki, IBM T. J. Watson Research Center, Yorktown Heights, New York (850-99-11 0) MAA Invited Address 2:55 p.m. Spiral arcs: An interpolation problem. (129) Preliminary report. 3:35 p.m.-4:25 p.m. Harry Mclaughlin* and Bruce Piper, Rensselaer Polytechnic Institute (850-99-1 09) (135) The Riemann mapping non-theorem. Nancy K. Stanton, University of Notre Dame 3:25 p.m. Informal Discussion

AMS Special Session on Computational MAA Prize Session and Business Meeting Number Theory and Applications, Ill 4:40 p.m.-5:40 p.m. 2:25 p.m.-4:15p.m. 2:25 p.m. Figures of merit for digital multistep PME J. Sutherland Frame Lecture (130) pseudorandom numbers. Debra A. Andre, Gary L. Mullen*, 8:30 p.m.-9:30 p.m. Pennsylvania State University, University Park, and Harald Niederreiter, Austrian Academy of (136) Entrainment of frequency: A recurring theme. Sciences, Austria (850-11-37) Jane Cronin Scanlon, Rutgers University, New Brunswick

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 741 Program of the Sessions

Thursday,August10 AMS Special Session on Computational Number Theory and Applications, IV

AMS Special Session on History of 8:00 a.m.-9:50 a.m. Orthogonal Polynomials, I 8:00a.m. Subexponential class number algorithms. (143) Johannes Buchmann, Universitat des 8:00 a.m.-9:50 a.m. Saarlandes, Federal Republic of Germany (850-11-78) 8:00 a.m. Introduction 8:30a.m. An open architecture number sieve. theorems of orthogonal 8:20a.m. Characterization (144) H. C. Williams, University of Manitoba (137) polynomials. (850-11-07) w. A. AI-Salam, University of Alberta 9:00a.m. Program checkers for modular exponentiation. (850-01-35) (145) Preliminary report. 9:10a.m. Differential equations and zeros of orthogonal Kireeti Kompella, University of Southern (138) polynomials. California (850-11-79) (Sponsored by Kevin S. Martin E. Muldoon, York University McCurley) (850-33-102) 9:30a.m. Practical zero-knowledge proofs: Giving hints (146) and using deficiencies. Joan Boyar•, Katalin Friedl and Carsten Lund, AMS Special Session on Mathematical University of Chicago (850-68-08) (Sponsored Questions in Computational Geometry, Ill by Kevin S. McCurley)

8:00 a.m.-9:50 a.m. AMS Session on Analysis and Probability 8:00 a.m. Informal Discussion 8:00 a.m.-9:50 a.m. AMS Special Session on Free Boundary 8:00a.m. Waiting times for runs of rare events. Problems and Partial Differential Equations, IV (147) Preliminary report. Anant Godbole, Michigan Technological 8:00 a.m.-9:50 a.m. University (850-60-75) 8:20 a.m. Maximum and minimum sets for some 8:00a.m. Existence and geometry of solutions of a free (148) geometric mean values. (139) boundary problem for the heat equation. Richard E. Pfiefer, San Jose State University Andrew Acker and Kirk Lancaster*, Wichita (850-60-24) State University (850-35-51) 8:40a.m. Statistical tests for diagonality of a covariance 8:30 a.m. The onset of instability in the trapped drop (149) matrix. (140) problem. Jack Tomsky, Lockheed Missiles and Space Thomas I. Vogel, Texas A & M University, Company, Palo Alto, California (850-62-01) College Station (850-49-50) 9:00a.m. Computation of gradients in Banach spaces. 9:00a.m. Uniqueness of the solution to some free (150) Preliminary report. (141) boundary problems for the Laplace equation. lvie Stein, Jr., University of Toledo (850-65-65) David E. Tepper, Bernard M. Baruch College, 9:20a.m. Factorization without arithmetic. City University of New York (850-35-34) (151) Robert J. Valenza, Claremont McKenna 9:30 a.m. Regularity theory for grad differential equations. College (850-68-62) (142) Preliminary report. 9:40 a.m. Supermartingales and superadditive games: An Ed Stredulinsky*, Lawrence University, and (152) additivization alternative to Gilboa's. Peter Laurence, University Degli Studii, Thomas E. Armstrong, University of Maryland, Milano, Italy (850-35-73) Baltimore County (850-99-111)

MAA Panel Discussion

8:00 a.m.-9:55 a.m.

The role of the computer in calculus reform.

742 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions

MAA Minicourse #7 (Part B) MAA Minicourse #9 (Part B)

8:00 a.m.-10:00 a.m. 1:15 p.m.-3:15p.m. HP-288 short course for nearly inexperienced users. Jerold A seminar on women in mathematics. Miriam P. Cooney esc, Mathews, Iowa State University Saint Mary's College, Notre Dame, Indiana

MAA Minicourse #9 (Part A) AMS Colloquium Lectures: Lecture IV

8:00 a.m.-10:00 a.m. 3:00 p.m.-4:00 p.m. A seminar on women in mathematics. Miriam P. Cooney esc, (157) Geometry, groups, and self-similar filings. Saint Mary's College, Notre Dame, Indiana William P. Thurston, Princeton University

MAA Invited Address AMS Special Session on History of Orthogonal Polynomials, II 8:40 a.m.-9:30 a.m. 3:00 p.m.-5:1 0 p.m. (153) The number of solutions of Diophantine equations. 3:00 p.m. Orthogonal polynomials and numerical Wolfgang M. Schmidt, University of Colorado, ( 158) quadrature. Boulder Walter Gautschi, Purdue University, West Lafayette (850-01-99) 3:30 p.m. History of asymptotics of orthogonal AMS-MAA Invited Address (159) polynomials. Mourad E. H. Ismail, University of South 10:10 a.m.-11:00 a.m. Florida (850-01-14) 4:00 p.m. Chebyshev's work. Preliminary report. 2 (154) ax2 + hxy + cy = n. (160) Ranjan Roy, Beloit College (850-33-67) John H. Conway, Princeton University 4:30 p.m. Classical orthogonal polynomials. ( 161) Richard A. Askey, University of Wisconsin, Madison (850-01-98) MAA Earle Raymond Hedrick Lectures: Lecture Ill AMS Special Session on Mathematical 11:15 a.m.-12:15 p.m. Questions in Computational Geometry, IV (155) The mathematics of mixing things up: Modern Markov chain theory. 4:00 p.m.-5:50 p.m. Persi W. Diaconis, Harvard University 4:00 p.m. Informal Discussion

Mathematics Lecture AMS Progress in AMS Special Session on Computational Number Theory and Applications, V 1:15 p.m.-2:45p.m. (156) Liquid crystals. 4:00 p.m.-5:50 p.m. Haim Brezis, Rutgers University and Universite de Paris VI, France 4:00 p.m. Simplification of nested radicals. (162) Susan Landau, Wesleyan University (850-12-06) MAA Minicourse #8 (Part B) 4:30 p.m. Deterministic factorization of polynomials over (163) special finite fields. Preliminary report. Eric Bach, University of Wisconsin, Madison 1:15 p.m.-3:15p.m. (850-12-70) Applications of the HP-288 for experienced users. Thomas W. Tucker, Colgate University

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 743 Program of the Sessions

5:00 p.m. On the deterministic complexity of factoring 4:40 p.m. Open-restriction decomposition property. ( 164) polynomials over finite fields. (168) Ridgley Lange, Weidman, Michigan Victor Shoup, University of Wisconsin, (850-47-106) Madison (850-12-55) (Sponsored by Kevin S. 5:00 p.m. Quasi-compact operators. McCurley) (169) Amir Maleki, University of the Virgin Islands 5:30 p.m. Some alternate strategies for generating (850-99-1 08) ( 165) irreducible polynomials over finite fields. 5:20 p.m. Sampling expansions in discrete Walsh-Fourier Preliminary report. (170) analysis. Gove Effinger, Skidmore College (850-12-05) Nasser Dastrange, Buena Vista College (850-94-1 00) AMS Session on Analysis, Ill Andy Roy Magid AMS Associate Secretary Norman, Oklahoma 4:00 p.m.-5:30 p.m. Kenneth A. Ross 4:00 p.m. On the dimension of fractal functions defined on MAA Secretary (166) subsets of R", n > 1. Eugene, Oregon Peter R. Massopust, West Georgia College (850-26-1 01) 4:20 p.m. Best twin-value regions for continued fractions (167) K(an/1). Walter M. Reid, University of Wisconsin, Eau Claire (850-30-104)

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: 11 E, 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 $11, List price $28, Institutional member $22 ~~-~~~~ To order, please specify CONM/82NA ~~Ho~~{ fi ~jfffi~)~ 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 ""'ouiVDED\?fr Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with VIsa or MasterCard

744 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Presenters of Papers

Numbers following the names indicate the speakers' positions on the program. <> AMS-MAA Invited Lecturer • AMS Invited Lecturer +AMS-MAA-PME Invited Lecturer o MAA Invited Lecturer rr PME J. Sutherland Frame Lecturer * AMS Special Session Speaker

Abu-Muhanna, Y., 62 *Fix, G., 93 Massopust, P. R., 166 *Shall it, J ., 132 *Acker, A., 120 • Gallian, J. A., 134 *Masur, H. A., 31 *Shanks, D., 133 oAddison, J. W., Jr., 72 * Gautschi, W., 158 • Masur, H. A., I Shapiro, V. L., 63 Ager, T. A., 79 God bole, A., 14 7 Mathews, J. H., 27 *Shoup, V., 164 AI-Rashed, A. M., I 05 * Goldberg, L. R., 48 Mawyer, F., 83 *Siegel, D., 96 * AI-Salam, W. A., 137 *Goldman, W. M., 115 • McDuff, D., 76 Singh, K. D., 57 *Almgren, F., Jr., 121 *Gordon, D., I 02 *Mclaughlin, H., 129 Slaughter, D., 112 *Almgren, F., 92 Gould, M., 12 Miller, A. P., 110 Smart, J. R., 33 Argabright, L., 113 Graver, J ., 13 *Montgomery, P. L., 50 Somolinos, A., 7 Armstrong, T. E., 152 Graves, G. E., 18 Moore, E. H., 78 o Stanton, N. K., 135 *Askey, R. A., 161 *Guenther, R. B., 44 Morales, C., I 07 Stein, 1., Jr., 150 Aull, C., 56 *Haas, A., 116 Mukherjee, R.N., 126 Stewart, B. M., 40 * Bach, E., 163 Hundhausen, J. R., 109 *Muldoon, M. E., 138 Straight, J ., II * Banchoff, T. F., 91 *Ismail, M. E., 159 *Mullen, G. L., 130 *Stredulinsky, E., 142 Barshinger, R.N., 82 Judson, P. T., 20 Nievergelt, Y., 66 Sundstrom, T., 90 Beckmann, C., 65 <> Kakutani, S., I I 7 O'Halloran, J., 10 Szczyrba, 1., 35 Berger, N. E., 81 Kambayashi, T., 17 *Odlyzko, A.M., 101 Szeptycki, P., 125 Bergweiler, W., 61 Karian, Z., 69 Palmiter, J. R., 19 Tamari, D., 15 * Boshernitzan, M. D., 30 * Keen, L., 4 7 Parish Jr., A. E., 9 <>Taylor, J. E., 3 * Boyar, J ., 146 o Keen, L., 5 *Parks, H., 122 *Taylor, J., 97 Bradley, J. S., 84 Kenelly, J. W., 21 Patten, P. R., 25 Taylor, P. D., 86 • Bramson, M. D., 2 Kenney, E., 88 Pfiefer, R. E., 148 Teets, D., 124 • Brezis, H., 156 * Kerckhoff, S., 32 * Pomerance, C., 49 *Tepper, D. E., 141 Brislawn, C., 106 Kim, C., 127 Porta, H., 68 • Thurston, W. P., 4, 75, 119, *Buchmann, J., 143 * Kompella, K., 145 Priestley, W. M., 34 !57 Child, J.D., 71, 85 * Korevaar, N., 42 Putnick, L. J., 6 *Tiller, W., 94 Coffey, J., 60 Kosmala, W., 103 Ramamurthi, V. S., 26 Tomsky, J., 149 Connell, E., 38 * Lagarias, J. C., 131 Redmond, D., 41 Tretter, M. J., 24 <>Conway, J. H., 154 * Lancaster, K., 139 Reid, W. M., 167 Valenza, R. J., 151 Dastrange, N., 170 * Landau, S., 162 Rogers, E., 80 * Veech, W. A., 29 *Delillo, T. K., 123 <>Lang, S., 73 Rosenthal, W. E., 87 *Vogel, T. 1., 140 Debnath, L., 8 Lange, R., 168 *Roy, R., 160 *Wagstaff, S. S., Jr., 51 o Diaconis, P. W., 74, 118, 155 *Laurence, P., 95 o Rudin, M. E., 28 *Williams, H. C., 144 * Domich, P. D., 100 Lee, S.-M., 14 Sahoo, P. K., 104 Williams, J., 89 Donnellan, J., Ill Leinbach, L. C., 67 Sammons, W. A., 16 Williamson, S., 37 * Drumm, T. A., 114 * Lenstra, A. K., 52 rr Scanlon, J. C., 136 *Wolf, M., 45 *Effinger, G., 165 * Li, D., 98 Schay, G., 59 *Wunderlich, M., 99 Eidswick, J. A., 23 Ligh, S., 58 o Schmidt, W. M., 153 Yeatts, R., 108 * Farouki, R. T., 128 Lonergan, F. D., 55 Schrock, C. S., 64 Zweibel, J ., 39 * Fathi, A., 46 Lopez, R. J., 70 Selden, J., 22 Finley, D., 54 Maleki, A., 169 Senechal, L., 77 *Finn, R., 43 Martin, G. F., 36 Shahshahani, S., 53

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 745 American Mathematical Society Short Course Series Introductory Survey Lectures on Cryptology and Computational Number Theory Boulder, Colorado, August 6-7, 19 8 9

The American Mathematical Society, in conjunction with revolutionary changes in each, but has brought them closer its ninety-second Summer Meeting, will present a two day together. The catalyst for this development was the intro­ Short Course entitled "Cryptology and Computational Num­ duction of the RSA public-key cryptosystem in 1978. This ber Theory" on Sunday and Monday, August 6-7, 1989, at system is based on the relative ease of some number-theoretic the University of Colorado, Boulder. The program is un­ computations, such as primality testing and exponentiation der the direction of Carl Pomerance, University of Georgia. in modular arithmetic, versus the great difficulty in factoring Seven lectures are planned, and it is anticipated that proceed­ a large number composed of two roughly equal primes. Since ings will be published in the series Proceedings of Symposia then, the web of ties between cryptology and computational in Applied Mathematics. number theory has drawn more complex with the introduc­ Both cryptology and computational number theory have tion of schemes based on the supposed intractability of other been with us for centuries as independent branches of math­ number-theoretic problems, such as the computation of dis­ ematical thought. In the past decade, however, we have wit­ crete logarithms and the subset-sum problem. nessed an explosion in both fields that has not only brought

Sunday, August 6: 9:15 a.m.-I 0:30 a.m., CARL PoMERANCE, University of Georgia, Introduction. A few of the basic cryptographic systems based on number theory and the underlying number-theoretic themes. 10:45 a.m.-12:00 noon, SHAFI GoLDWASSER, Massachusetts Institute of Technology, The Search for Provably Secure Cryptosys­ tems. More advanced issues in cryptology, including zero knowledge proofs. 1:30 p.m.-2:45 p.m., ARJEN K. LENSTRA, University of Chicago, Primality Testing. How to distinguish between primes and composites - theoretically and practicaJiy. 3:00 p.m.-4:15p.m., CARL PoMERANCE, University of Georgia, Factoring. How to factor 100 digit numbers- emphasis on the quadratic sieve and the elliptic curve method. Monday, August 7: 8:00 a.m.-9: 15 a.m., KEVIN McCuRLEY, IBM Research and Sandia National Laboratories, The Discrete Logarithm Problem. Some algorithms with emphasis on the multiplicative group of a finite field. 9:30 a.m.-1 0:45 a.m., ANDREW M. 0DLYZKO, AT&T Bell Laboratories, The Rise and Fall ofKnapsack Cryptosystems. The use of lattice reduction algorithms in geometric number theory to break cryptosystems based on the subset-sum problem. 2:30 p.m.-3:45p.m., JEFFREY C. LAGARIAs, AT&T Bell Laboratories, Pseudorandom Number Generators in Cryptography and Number Theory. The relation of pseudorandom numbers to cryptology.

Synopses of the talks and accompanying reading lists ap­ Those who also plan to attend the Summer Meeting should peared in the April issue of Notices. Complete lecture notes take note of a Special Session entitled "Computational Num­ will be mailed to those who preregister for the course and ber Theory and Applications," organized by Kevin S. Mc­ will be available at the Short Course registration desk for Curley, of IBM Research and Sandia National Laboratories. those registering on site. For more information, see the Special Session section of the The lectures will require no advanced background in num­ Boulder meeting announcement in this issue of Notices. ber theory or cryptology and should be accessible to partic­ The Short Course was recommended by the AMS-MAA ipants with conventional graduate training in mathematics. Committee on Employment and Educational Policy (CEEP), However, some familiarity with elementary number theory whose members are Morton Brown, Stefan A. Burr, Edward would be desirable. In addition to specific reference mate­ A. Connors (chair), Philip C. Curtis, Jr., David J. Lutzer, rials suggested by the speakers, the foJiowing book contains and James J. Tattersall. The Short Course series is under the much of the spirit of the course: N. Koblitz, A Course in direction of the Short Course Subcommittee, whose mem­ Number Theory and Cryptography, Springer-Verlag, 1987. bers are Stefan A. Burr (chair), R. Peter DeLong, Lis! Novak Onsite registration fee: $50 ($20 student/unemployed). Gaal, Robert P. Kurshan, Barbara L. Osofsky, Marjorie L. 8:30 a.m.-2:30 p.m. Sunday, August 6. Stein, and James J. Tattersall.

746 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Hoboken, New Jersey Stevens Institute of Technology October 21-22 First Announcement

The eight-hundred-and-fifty-first meeting of the Ameri­ Finite groups, RICHARD N. LYONS AND RICHARD can Mathematical Society will be held at Stevens Institute TRETKOFF, Stevens Institute of Technology. of Technology in Hoboken, New Jersey on Saturday, Oc­ Computational algebra, CHARLES C. SIMS, Rutgers tober 21, and Sunday, October 22, 1989. University, New Brunswick. Algebraic geometry, p-adic aspects, MARVIN D. O'NAN, Invited Addresses Rutgers University, New Brunswick. Most of the papers to be presented at these special By invitation of the Committee to Select Hour Speakers sessions will be by invitation. However, anyone submit­ for Eastern Sectional Meetings, there will be four in­ ting an abstract for the meeting who feels that his or vited one-hour addresses. The speakers, their affiliations, her paper would be particularly appropriate for one of the titles of their talks, and the scheduled times of these special sessions should indicate this clearly on the presentation are: abstract form and submit it by by July 26, 1989, three RussEL CAFLISCH, Courant Institute and the Univer­ weeks bofore the deadline for contributed papers, in sity of California, Los Angeles, Mathematical analysis of order that it may be considered for inclusion. Partici­ vortex sheets, 1:30 p.m. Sunday. pants are reminded that a charge of $16 is imposed for BRUCE KITCHENS, IBM Thomas J. Watson Research retyping abstracts that are not in camera-ready form. Center, Yorktown Heights, Symbolic dynamics, 11:00 a.m. Sunday. Contributed Papers FANG HuA LIN, Institute for Advanced Study and University of Chicago, Level sets of solutions of elliptic There will also be sessions for contributed ten-minute and parabolic equations, 11:00 a.m. Saturday. papers. Abstracts should be prepared on the standard SHELDON E. NEWHOUSE, University of North Car­ AMS form available from the AMS office in Providence olina, Chapel Hill, The dynamics of two-dimensional or in Departments of Mathematics. Abstracts should be diffeomorphisms, 1:30 p.m. Saturday. sent to the Editorial Department, American Mathemat­ ical Society, Post Office Box 6248, Providence, Rhode Island 02940, so as to arrive before the August 16, Special Sessions 1989 abstract deadline. Participants are reminded that By invitation of the same committee, there will be eight a charge of $16 is imposed for retyping abstracts that special sessions of selected twenty-minute papers. The are not in camera-ready form. Late papers will not be topics, and the names and affiliations of the organizers, accommodated. are as follows: Geometry related to computer vision, PRABIR BHAT­ Electronic Submission of Abstracts TACHARYA, University of Nebraska, Lincoln, and RoBERT This service is now available to those who use the TEX A. MELTER, Long Island University. typesetting system and can be used with abstracts of Algebraic semantics, STEPHEN L. BLOOM, Stevens In­ papers to be presented at the autumn sectional meet­ stitute of Technology. ings of the AMS. Requests to obtain the package of Mathematical fluid dynamics, RussEL CAFLiscH. files may be sent electronically on Internet to abs­ Low-dimensional topology, MARK E. FEIGHN, LEE [email protected]. Requesting the files electroni­ D. MosHER, AND ULRICH OERTEL, Rutgers University, cally will likely be the fastest and most convenient way, Newark. but users may also obtain the package on IBM or Mac­ Smooth dynamical systems, BRUCE P. KITCHENS AND intosh diskettes, available free of charge by writing to: SHELDON E. NEWHOUSE.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 747 Meetings

Rosanne Granatiero, American Mathematical Society, Food Service Box 6248, Providence, RI Publications Division, P.O. Information regarding food service will appear m the When requesting the Abstracts package, 02940, USA. September issue of Notices. users should be sure to specify whether they want the plain TEX or the A.MS-TEX. Travel Registration From Newark Airport The meeting registration desk will be located in the lobby The Newark Airport is located about ten miles from of the Stevens Center and will be open from 8:00 a.m. to both the Stevens campus and the Holiday Inn Harmon 5:00p.m. on Saturday, October 21, and from 8:00a.m. Meadow. Taxi service is available to both the Stevens to I 2:00 noon on Sunday, October 22. campus and the Holiday Inn for approximately $25- The registration fees are $30 for members of the $30. By bus, participants should take the #300 New AMS, $45 for nonmembers, and $10 for students or Jersey Transit Airport Express to the Port Authority Bus unemployed mathematicians. Terminal in Manhattan at a cost of $7. This service runs every ten to fifteen minutes and takes approximately thirty minutes depending on the traffic. From the Port Event Social Authority Bus Terminal take the #126 New Jersey Transit A special reception and dinner is planned for Saturday bus to Hoboken ($1. 70), or the #320 New Jersey Transit evening, October 21, in the Bissinger room of Stevens bus to Harmon Meadow ($2.15). Center. Details will be announced in the September issue of Notices. From Penn Station Manhattan Go to the Port Authority Bus Terminal at 8th Avenue and 42nd Street and proceed as above, or take a PATH Petition Table train from 6th Avenue and 33rd Street to Hoboken ($1 required). From the Hoboken A petition table will be set up in the registration area. exact fare in bill or coins approximately one-half mile to Additional information about petition tables can be terminal it is a walk of taxi fare to Stevens Center is found in a box in the Boulder meeting announcement on the Stevens Center. The page 457 of the April I 989 issue of Notices. $2.75. By Car Accommodations Hoboken is located on the Hudson river across from Manhattan between the Lincoln and Holland Tunnels. A block of rooms has been reserved at the Holiday Inn The Holiday Inn Harmon Meadow is located off Route Harmon Meadow for Friday, October 20, and Saturday, #3 approximately three miles west of the Lincoln Tunnel. October 21, at a special rate of $69 per night for a The Stevens campus and the Holiday Inn are both easily single or double. The special rate may be available for accessible by car. Detailed directions will appear in the Sunday, October 22, but this is not guaranteed. The September issue of the Notices. rooms will be held until October 7, I 989. To reserve a room at this special rate, individuals must call the Holiday Inn Harmon Meadow at 201-348-2000, ask for Parking the sales office, and identify themselves as participants of the AMS meeting at Stevens Institute of Technology. Free parking is available on the Stevens campus. The Holiday Inn provides free return transportation to Newark Airport or Penn Station in Newark. Par­ ticipants must ask for this service when making room Weather reservations. October weather is usually pleasant in the Hoboken area. The Holiday Inn is located in a pleasant outdoor mall Meteorological averages for the month are 57P and 3.1 with several stores and restaurants and 14 movie theaters. inches of rain. It is approximately four miles from the Stevens campus to the mall and the Holiday Inn provides free shuttle service. The Holiday Inn has an exercise room and a car W. Wistar Comfort rental agency which offers cars for approximately $30 Associate Secretary per day. Middletown, Connecticut

748 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Muncie, Indiana Ball State University October 27-28

First Announcement

The eight-hundred-and-fifty-second meeting of the Amer­ Function spaces and topology, KATHRYN FROST ican Mathematical Society will be held at Ball State PORTER, Ball State University. University in Muncie, Indiana on Friday, October 27, Differential equations, JoHN F. PoRTER, Ball State and Saturday, October 28, 1989. University, and T. K. PuTTASWAMY, Ball State Univer­ sity. Most of the papers to be presented at these special Invited Addresses sessions will be by invitation. However, anyone submit­ By invitation of the Committee to Select Hour Speakers ting an abstract for the meeting who feels that his or for Central Sectional Meetings, there will be four invited her paper would be particularly appropriate for one of one-hour addresses. The speakers, their affiliations, and these special sessions should indicate this clearly on the some of the titles of their talks are: abstract form and submit it by by July 26, 1989, three LASZLO LEMPERT, Purdue University, Imbedding pseu­ weeks before the deadline for contributed papers, in doconvex domains into a ball, scheduled time to be order that it may be considered for inclusion. Partici­ announced. pants are reminded that a charge of $16 is imposed for KENNETH R. MEYER, University of Cincinnati, title retyping abstracts that are not in camera-ready form. of talk and scheduled time to be announced. PAULS. MuHLY, University of Iowa, title of talk and Contributed Papers scheduled time to be announced. STEVEN SPERBER, University of Minnesota, Min­ There will also be sessions for contributed ten-minute neapolis, title of talk and scheduled time to be an­ papers. Abstracts should be prepared on the standard nounced. AMS form available from the AMS office in Providence or in Departments of Mathematics. Abstracts should be sent to the Editorial Department, American Mathemat­ Special Sessions ical Society, Post Office Box 6248, Providence, Rhode By invitation of the same committee, there will be eight Island 02940, so as to arrive before the August 16, special sessions of selected twenty-minute papers. The 1989 abstract deadline. Participants are reminded that topics, and the names and affiliations of the organizers, a charge of $16 is imposed for retyping abstracts that are as follows: are not in camera-ready form. Late papers will not be Number theory and algebraic geometry, ALAN accommodated. ADOLPHOSON, Oklahoma State University, and STEVEN SPERBER. Electronic Submission of Abstracts Statistics and probability, M. MAsooM ALI, Ball State This service is now available to those who use the TEX University. typesetting system and can be used with abstracts of Complex analysis, DAVID E. BARRETT, University of papers to be presented at the autumn sectional meet­ Michigan, Ann Arbor, and LASZLO LEMPERT. ings of the AMS. Requests to obtain the package of Extremally disconnected spaces and their applications, files may be sent electronically on Internet to abs­ ANANDA GuBBI, Southwest Missouri State University. [email protected]. Requesting the files electroni­ Noncommutative algebra in geometry and arithmetic, cally will likely be the fastest and most convenient way, DARRELL E. HAILE, Indiana University. but users may also obtain the package on IBM or Mac­ Triangular operator algebras, DAVID R. LARSON, Texas intosh diskettes, available free of charge by writing to: A&M University. Rosanne Granatiero, American Mathematical Society,

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 749 Meetings

Publications Division, P.O. Box 6248, Providence, RI Muncie Inn (one-and-one-half miles) 02940, USA. When requesting the Abstracts package, 414 North Madison Street, Muncie, IN 47305 users should be sure to specify whether they want the Telephone: 317-282-5981 plain TEX or the A.MS-TEX. Single $25 Double $34 Waterbed $35 Includes morning coffee. Registration Radisson Hotel (one-and-one-half miles) The meeting registration desk will be located in the east 420 South High Street, Muncie, IN 47305 end of the second floor corridor of the Pittenger Student Telephone: 317-741-7777 Toll Free: 1-800-333-3333 Center on the Ball State University campus. The campus 1-2 persons $42 3-4 persons $48 is located at the corner of University Avenue and Kinley Includes buffet breakfast and two cocktails per Avenue. All sessions will be held in the Student Center. occupant per evening. The meeting registration desk will be open from 8:00 a.m. to 5:00p.m. on Friday, October 27, and from 8:00 Signature Inn (two-and-one-half miles) a.m. to noon on Saturday, October 28. 3400 Chadam Lane, Muncie, IN 47305 The registration fees are $30 for members of the Telephone: 317-284-4200 Toll Free: 1-800-822-5252 AMS, $45 for nonmembers, and $10 for students and unemployed mathematicians. Single $43 Each additional occupant $6 Includes continental breakfast. Petition Table Student Center Pittenger Hotel Ball State University, Muncie, IN 47306 A petition table will be set up in the registration area. Telephone: 317-285-1555 Use SUVON from Indiana Additional information about petition tables can be campuses. found in a box in the Boulder meeting announcement on page 457 of the April 1989 issue of Notices. Single $33 Double $38 Each additional occupant $4 Accommodations Super 8 Motel (two-and-one-half miles) 3601 West Foxridge Lane, Muncie, IN 47304 Blocks of rooms have been set aside in several area Telephone: 317-286-4333 Toll Free: 1-800-843-1991 motels and hotels. Participants should make their own reservations directly with the hotel or motel of their One person/one bed $30.88 choice, and identify themselves as AMS members in Two personsjone bed $34.88 order to obtain the special rates given below. Reservations Two persons/two beds $37.88 should be made no later than September 27, 1989. After Each additional occupant: $3 that date reservations will be accepted on a space­ Located on the Ball State University campus. available basis. The rates are subject to a ten percent tax. Distances given below are driving distances measured from the Student Center. Food Service the Days Inn (three miles) There are a number of restaurants on campus and listings will be available 2000 North Broadway, Muncie, IN 47303 surrounding areas. Complete desk. There will be several Telephone: 317-288-9953 Toll Free: 1-800-325-2525 at the meeting registration hundred visitors on campus on Friday, October 27, and Single $30 Double $37 it is anticipated that campus area dining facilities will be used to their capacities during the noon hour only. Lees Inn (two-and-one-half miles) A buffet lunch will be served for participants and their 3302 North Everbrook Lane, Muncie, IN 47304 guests in the Student Center at noon on Friday, October Telephone: 317-282-7557 Toll Free: 1-800-733-5337 27, and Saturday, October 28. It is recommended that Single $43 Each additional occupant: $6 participants have lunch at these buffets due to the tight Includes continental breakfast. schedule. There are no formal evening meals planned.

750 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Travel Weather Muncie is located approximately 60 miles northeast of Autumn weather in Muncie is likely to be clear, with downtown Indianapolis, and 7 5 miles from Indianapolis cool days and crisp nights. The average daily maximum International Airport. A number of major airlines and temperature at this time is 60°F, and the average daily several regional airlines serve Indianapolis. The Ameri­ minimum temperature is 38°F. The average rainfall for can Eagle Commuter Airline flies twice daily each way the month of October is 2.56 inches. between Chicago and the Muncie Airport, which is ap­ Andy Roy Magid proximately four miles from campus. Interstate 1-69 is Associate Secretary approximately eight miles west of the campus and runs Norman, Oklahoma north from Indianapolis into Michigan. The shortest route from 1-69 to the campus is from the exit at State Road #332.

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/86NA 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; this vital and active field is Volume 2: Variational problems in infinite­ Today, 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.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 751 Invited Speakers and Special Sessions

Invited Speakers October 1989 Meeting in Hoboken, New Jersey at AMS Meetings Eastern Section Associate Secretary: W. Wistar Comfort The individuals listed below have accepted invitations Deadline for organizers: Expired to address the Society at the times and places in­ Deadline for consideration: Expired dicated. For some meetings, the list of speakers is Prabir Bhattacharya and Robert A. Melter, Geometry incomplete. related to computer vision Stephen L. Bloom, Algebraic semantics Russel Caflisch, Mathematical fluid dynamics Hoboken, October 1989 Mark E. Feighn, Lee D. Mosher and Ulrich Oertel, Russel Caflisch Bruce P. Kitchens Low-dimensional topology Fang Hua Lin Sheldon E. Newhouse Bruce P. Kitchens and Sheldon E. Newhouse, Smooth Muncie, October 1989 dynamical systems Laszlo Lempert Paul S. Muhly Richard N. Lyons and Richard O'Nan, Finite groups Kenneth R. Meyer Steven Sperber Charles C. Sims, Computational algebra Marvin D. Tretkoff, Algebraic geometry, p-adic aspects Los Angeles, November 1989 Burton I. Fein Stephen M. Gersten Nicolas Spaltenstein Thomas H. Wolff October 1989 Meeting in Muncie, Indiana Central Section Louisville, January 1990 Associate Secretary: Andy Roy Magid Sun-Yung Alice Chang Henryk Iwaniec Deadline for organizers: Expired George B. Dantzig Janos Kollar Deadline for consideration: Expired (Gibbs Lecture) Israel M. Sigal Alan Adolphoson and Steven Sperber, Number theory Israel C. Gohberg Shlomo Sternberg and algebraic geometry Mike Hopkins (Colloquium Lectures) M. Masoom Ali, Statistics and probability David E. Barrett and Laszlo Lempert, Complex anal­ Manhattan, March 1990 ysis J. Brian Conrey Jang-Mei Wu Ananda Gubbi, Extremally disconnected spaces and Stewart B. Priddy their applications Columbus, August 1990 Darrell E. Haile, Noncommutative algebra in geometry and arithmetic Michael G. Crandall David R. Larson, Triangular operator algebras (Progress in Mathematics Lecture) Kathryn Frost Porter, Function spaces and topology Organizers and Topics John F. Porter and T. K. Puttaswamy, Differential of Special Sessions equations The list below contains all the information about Special Sessions at meetings of the Society available November 1989 Meeting in Los Angeles, California at the time this issue of Notices went to the printer. Far Western Section The section below entitled Information for Organizers Associate Secretary: Lance W. Small describes the timetable for announcing the existence Deadline for organizers: Expired of Special Sessions. Deadline for consideration: Expired

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

Roger C. Alperin and Karen Vogtmann, Geometric March 1990 Meeting in Manhattan, Kansas methods in combinatorial group theory Central Section James P. Lin, Algebraic topology Associate Secretary: Andy Roy Magid Quadratic Deadline for organizers: Expired David J. Saltman and Murray M. Schacher, Deadline for consideration: November 21, 1989 forms and simple algebras Andrew G. Bennett, Harmonic analysis and probability Thomas H. Wolff, Harmonic analysis theory David J. Foulis and Richard J. Greechie, Orthostruc- January 1990 Meeting in Louisville, Kentucky tures Associate Secretary: Joseph A. Cima Li, Partial differential equations Deadline for organizers: Expired Lige Deadline for consideration: September 21, 1989 Satyagopol Mandai, Commutative algebra Joseph A. Ball and Israel C. Gohberg, Linear operators, Alexander G. Ramm, Inverse problems and scattering matrix functions and control theory Joseph G. Conlon, The Schrodinger equation Joseph M. Rosenblatt, Ergodic theory Raul E. Curto and Paul S. Muhly, Multivariable Richard H. Schelp, Graph theory operator theory George E. Strecker, Applications of category theory Ethan S. Devinatz and Mike Hopkins, Homotopy theory April 1990 Meeting in University Park, Pennsylvania Robert S. Doran, Group representations and operator Eastern Section · Associate Secretary: W. Wistar Comfort algebras Deadline for organizers: Expired Bruce R. Ebanks, Functional equations and their ap­ Deadline for consideration: January 4, 1990 plications Florence D. Fasanelli and Victor J. Katz, History of August 1990 Meeting in Columbus, Ohio mathematics Associate Secretary: W. Wistar Comfort Robert E. Fennell and Suzanne Marie Lenhart, Control Deadline for organizers: November 15, 1989 of infinite dimensional systems Deadline for consideration: April 27, 1990 Naomi Fisher, Harvey B. Keynes and Philip D. Wagreich, Mathematics and education reform November 1990 Meeting in Denton, Texas Carl H. FitzGerald and Ted J. Suffridge, Geometric Central Section Associate Secretary: Andy Roy Magid function theory in one and several complex variables Deadline for organizers: February 15, 1990 Gary D. Jones, Oscillation theory in ordinary differen­ Deadline for consideration: July 16, 1990 tial equations Janos Kollar, Algebraic geometry Efim D. Khalimsky, Yung Kong ancl Ralph D. Information for Organizers Kopperman, Topology in computer graphics and Special Sessions at Annual and Summer Meetings are image processing held under the supervision of the Program Committee lnessa Levi and W. Wiley Williams, Semigroup theory for National Meetings. They are administered by Peter A. McCoy, Function theoretic methods in differ­ the Associate Secretary in charge of that meeting ential equations with staff assistance from the Meetings and Editorial Lynn McLinden and Jay S. Treiman, Optimization Departments in the Society office in Providence. and nonlinear analysis According to the "Rules for Special Sessions" of the Hugh L. Montgomery, Analytic number theory Society, Special Sessions are selected by the Program Peter A. Perry, Geometric spectral and inverse spectral Committee from a list of proposed Special Sessions in problems essentially the same manner as Invited Speakers are Philip E. Protter, Markov processes and stochastic selected. The number of Special Sessions at a Summer analysis or Annual Meeting is limited. The algorithm that determines the number of Special Sessions allowed at March 1990 Meeting in Fayetteville, Arkansas a given meeting, while simple, is not repeated here, Southeast Section but can be found in "Rules for Special Sessions" on Associate Secretary: Joseph A. Cima page 614 in the April 1988 issue of Notices. Deadline for organizers: Expired Each Invited Speaker is invited to generate a Deadline for consideration: November 21, 1989 Special Session, either by personally organizing one or by having a Special Session organized by others.

JULY/ AUGUST 1989, VOLUME 36, NUMBER 6 753 Invited Speakers and Special Sessions

Proposals to organize a Special Session are sometimes Send Proposals for Special Sessions to the requested either by the Program Committee or by Associate Secretaries the Associate Secretary. Other proposals to organize The programs of sectional meetings are arranged by the Associate a Special Session may be submitted to the Associate Secretary for the section in question: Secretary in charge of that meeting (who is an ex­ Far Western Section (Pacific and Mountain) officio member of the committee and whose address Lance W. Small, Associate Secretary Department of Mathematics may be found below). These proposals must be in the University of California, San Diego hands of the Program Committee well in advance of La Jolla, CA 92093 the meeting and, in any case, at least nine (9) months (Telephone 619-534- 3590) prior to the meeting at which the Special Session is Central Section to be held in order that the committee may consider Andy Roy Magid, Associate Secretary all the proposals for Special Sessions simultaneously. Department of Mathematics Proposals that are sent to the Providence office of the University of Oklahoma 60 I Elm PHSC 423 Society, to Notices, or directed to anyone other than Norman, OK 73019 the Associate Secretary will have to be forwarded and {Telephone 405- 325- 2052) may not be received in time to be considered for Eastern Section acceptance. W. Wistar Comfort, Associate Secretary It should be noted that Special Sessions must Department of Mathematics be announced in Notices in such a timely fashion Wesleyan University that any member of the Society who so wishes may Middletown, CT 06457 submit an abstract for consideration for presentation (Telephone 203-347 -9411) in the Special Session before the deadline for such Southeastern Section Joseph A. Cima, Associate Secretary consideration. This deadline is usually three (3) weeks Department of Mathematics before the Deadline for Abstracts for the meeting in University of North Carolina, Chapel Hill question. Chapel Hill, NC 27599- 3902 Special Sessions are very effective at Sectional (Telephone 919- 962- I 050) Meetings and can usually be accommodated. They As a general rule, members who anticipate organizing Special are selected by the Committee to Select Hour Speak­ Sessions at AMS meetings are advised to seek approval at least nine months prior to the scheduled date of the meeting. No Special ers for the Section. The processing of proposals for Sessions can be approved too late to provide adequate advance Special Sessions for Sectional Meetings is handled notice to members who wish to participate. by the Associate Secretary for the Section, who then forwards the proposals to the Committee to Select, which makes the final selection of the proposals. Each Information for Speakers Invited Speaker at a Sectional Meeting is invited to A great many of the papers presented in Special Ses­ organize a Special Session. Just as for national meet­ sions at meetings of the Society are invited papers, but ings, no Special Session at a Sectional Meeting may any member of the Society who wishes to do so may be approved so late that its announcement appears submit an abstract for consideration for presentation past the deadline, after which members can no longer in a Special Session, provided it is received in Prov­ send abstracts for consideration for presentation in idence prior to the special early deadline announced that Special Session. above and in the announcements of the meeting at The Society reserves the right of first refusal for which the Special Session has been scheduled. Con­ the publication of proceedings of any Special Ses­ tributors should know that there is a limitation in sion. These proceedings appear in the book series size of a single special session, so that it is sometimes Contemporary Mathematics. true that all places are filled by invitation. Papers More precise details concerning proposals for and not accepted for a Special Session are considered as organizing of Special Sessions may be found in the ten-minute contributed papers. "Rules for Special Sessions" or may be obtained from Abstracts of papers submitted for consideration for any Associate Secretary. presentation at a Special Session must be received by the Providence office (Editorial Department, American Mathematical Society, P. 0. Box 6248, Providence, RI 02940) by the special deadline for Special Sessions, which is usually three weeks earlier than the deadline

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

for contributed papers for the same meeting. The whether they want the plain TFX or the A.MS-TFX Council has decreed that no paper, whether invited or package. contributed, may be listed in the program of a meeting of the Society unless an abstract of the paper has been Number of Papers Presented received in Providence prior to the deadline. Joint Authorship Electronic submission of abstracts is now available Although an individual may present only one ten­ to those who use the TEX typesetting system. Requests minute contributed paper at a meeting, any combina­ to obtain the package of files may be sent electronically tion of joint authorship may be accepted, provided on Internet to [email protected]. Request­ no individual speaks more than once. An author can ing the files electronically will likely be the fastest and speak by invitation in more than one Special Session most convenient way, but users may also obtain the at the same meeting. package on IBM or Macintosh diskettes, available free An individual may contribute only one abstract by of charge by writing to: Rosanne Granatiero, American title in any one issue of Abstracts, but joint authors Mathematical Society, Publications Division, P.O. Box are treated as a separate category. Thus, in addition 6248, Providence, RI 02940, USA. When requesting to abstracts from two individual authors, one joint the Abstracts package, users should be sure to specify abstract by them may also be accepted for an issue.

Symposium on Some Mathematical Questions in Biology Toronto, Ontario, Canada August 7, 1989

The twenty-third annual Symposium on Some Mathemati­ Program cal Questions in Biology on Sex allocation and sex change: Experiments and models will be held on August 7, 1989, dur­ 9:00 a.m.- Presiding: MARC MANGEL, University of Califor­ ing the annual meeting of the American Institute of Biolog­ nia, Davis ical Sciences (AIBS), August 6- 10, 1989, at the University The adaptive advantage of sexual reproduction in plants. of Toronto. The symposium is sponsored by the American PAULETTE BIERZYCHUDEK, Pomona College Mathematical Society, the Society for Industrial and Applied Natural selection and allocation to sexual reproduction in Mathematics, and the Society for Mathematical Biology. flowering plants. MAUREEN STANTON, University of Califor­ The AMS-SIAM Committee on Mathematics in the Life nia, Davis Sciences serves as the Organizing Committee for the sympo­ sium. The committee consisted of Kenneth L. Lange, Michael Population genetics ofsex allocation. SABIN LESSARD, Uni­ C. Mackey, Marc Mangel (Organizer), Hans G. Othmer, Alan versity of Montreal S. Perelson, Richard E. Plant (Chairman), and John Rinzel. 2:00 p.m.- Presiding: MARC MANGEL The theme of the symposium is Sex allocation and sex change: Experiments and models. There will be two half-day Sex change in terrestrial slugs: Social and ecological fac­ sessions, each including one-hour lectures. tors. DoNNA M. FERNANDES, University of Liverpool For further information, contact Betty Verducci, Con­ Dynamics of sex change in Capite/lid polychaete. PETER ference Coordinator, AMS, P.O. Box 6248, Providence, RI S. PETRAITIS, University of Pennsylvania 02940, E-mail: [email protected]. Sex allocation in simultaneous hermaphrodites: testing lo­ cal mate competition theory. CHRISTOPHER W. PETERSEN, Friday Harbor Laboratories and University of Toronto Male allocation and the cost ofsex under local family com­ petition. CURT M. LIVELY, Rutgers University

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 755 Call For Topics For 1991 Conferences

Suggestions are invited from mathematicians, either Research Conferences in the Mathematical Sciences, a singly or in groups, for topics of the various confer­ one-, two-, or three-week conference may be proposed. ences that will be organized by the Society in 1991. The deadlines for receipt of these suggestions, as well as some relevant information about each of the conferences, are given below. An application form to 1991 AMS Summer Institute be used when submitting suggested topic(s) for any of these conferences (except the Short Course Series) Summer institutes are intended to provide an un­ may be obtained by writing to the Meetings Depart­ derstandable presentation of the state of the art in ment, American Mathematical Society, P.O. Box 6248, an active field of research in pure mathematics and Providence, RI 02940, or telephoning 401-272-9500, usually extend over a three-week period. Dates for or sending E-mail to [email protected]. a summer institute must not overlap those of the Individuals willing to serve as organizers should Society's summer meeting, which at the time of this be aware that the professional meeting staff in the printing have not yet been determined. There should Society's Providence office will provide full support be a period of at least one week between them. Pro­ and assistance before, during, and after each of these ceedings are published by the Society as volumes in the conferences. Organizers should also note that for all series Proceedings of Symposia in Pure Mathematics. conferences, except Summer Research Conferences, it Current and recent topics: is required that the proceedings be published by the 1987- Theta functions, organized by LEON EHREN­ Society, and that proceedings of Summer Research PREIS of Temple University and ROBERT GUNNING of Conferences are frequently published. A member of Princeton University. the Organizing Committee must be willing to serve as 1988- Operator theory /Operator algebras and applica­ editor of the proceedings. tions, organized by WILLIAM B. ARVESON of University All suggestions must include ( l) the names and of California, Berkeley, and RONALD G. DOUGLAS of affiliations of proposed members and the chairman State University of New York at Stony Brook. of the Organizing Committee; (2) a one- to two­ 1989-Several complex variables and geometry, orga­ page description addressing the focus of the topic nized by STEVEN G. KRANTZ of Washington Univer­ including the importance and timeliness of the topic, sity. and estimated attendance; (3) a list of the recent 1990-Differential geometry, organized by RoBERT E. conferences in the same or closely related areas; (4) a GREENE of University of California, Los Angeles, and tentative list of names and affiliations of the proposed SHING-TUNG YAu of Harvard University. principal speakers; and (5) a list of likely candidates Deadline For Suggestions: September 1, 1989 who would be invited to participate and their current affiliations. Any suggestions as to sites and dates should be made as early as possible in order to allow adequate time for planning. However, proposers of 1991 AMS-SIAM-SMB Symposium conferences should know that by action of the AMS Some Mathematical Questions in Biology Board of Trustees, the Meetings Department of the Society is responsible for the final selection of the site This one-day symposium, now under joint sponsorship for each conference and for all negotiations with the with the Society for Mathematical Biology, is usually host institution. Individuals submitting suggestions held in conjunction with the annual meeting of a for the conferences listed below are requested to biological society closely associated with the topic. recommend sites or geographic areas which would Papers from the symposia are published by the Society assist the Meetings Department in their search for as volumes in the series Lectures on Mathematics in an appropriate site. In the case of Joint Summer the Life Sciences.

756 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Call for Topics

Current and recent topics: mathematical activity, with emphasis on areas cur­ 1987-Models in population biology, organized by rently especially active. Careful attention is paid to ALAN HASTINGS of the University of California, Davis. subjects in which there is important interdisciplinary 1988- Dynamics of excitable media, organized by activity at present. Topics for the seventh series of HANS G. OTHMER of the University of Utah. one-week conferences, being held in 1989, are Proba­ 1989-Sex allocation and sex change: Experiments and bilistic and analytic methods in discrete mathematics; models, organized by MARC MANGEL of the University Statistical analysis of measurement error models and of California, Davis. applications; Relationships between continuum theory 1990-Neural Nets, organized by JAcK D. CowAN of and the theory of dynamical systems; Statistical multi­ the University of Chicago. ple integration; Integral geometry; Finite and algebraic groups: Modular representations and cohomology; The September 1, 1989 Deadline For Suggestions: geometry of Riemann surfaces and discrete groups; and Inverse problems in partial differential equations. If proceedings are published by the Society, they 1991 AMS-SIAM Summer Seminar will appear as volumes in the series Contemporary The goal of the summer seminar is to provide an Mathematics. environment and program in applied mathematics Deadline For Suggestions: February 1, 1990 in which experts can exchange the latest ideas and newcomers can learn about the field. Proceedings are published by the Society as volumes in the series Call for Topics for Lectures in Applied Mathematics. 1991 AMS Short Course Series Current and recent topics: The AMS Short Courses consist of a series of in­ 1987- Computational Aspects of VLSI Design with troductory survey lectures and discussions ordinarily an Emphasis on Semiconductor Device Simulation, extending over a period of one-and-one-half days of organized by RANDOLPH BANK of the University starting immediately prior to the Joint Mathematics California, San Diego. Meetings held in January and August each year. Each 1988- Computational solution of nonlinear systems theme is a specific area of applied mathematics or of of equations, organized by EuGENE ALLGOWER mathematics used in the study of a specific subject Colorado State University. or collection of problems in one of the physical, 1989- The mathematics of random media, organized biological, or social sciences, technology, or business. by WERNER KOHLER of Virginia Polytechnic Institute Current and recent topics: and BENJAMIN WHITE of Exxon Research & Engineer­ Cryptology and computational number theory (Au­ ing Company. gust 1989), Matrix theory and applications (January 1990- Vortex dynamics and vortex methods, orga­ 1989), Chaos and fractals (August 1988), Computa­ nized by CLAUDE GREENGARD of IBM T. J. Watson tional Complexity Theory (January 1988). Proceedings Research Center and CHRISTOPHER R. ANDERSON of are published by the Society as volumes in the series University of California, Los Angeles. Proceedings of Symposia in Applied Mathematics, with Deadline For Suggestions: September I, 1989 the approval of the Editorial Committee. Deadline for Suggestions: Suggestions for the January by July 1, 1989; Summer 1991 course should be submitted 1991 AMS-IMS-SIAM Joint suggestions for the August 1991 course should be Research Conferences in the submitted by December 1, 1989. Mathematical Sciences Submit suggestions to: Stefan A. Burr, Chairman, These conferences are similar in structure to those Short Course Subcommittee, Department of Computer NY 10031. held at Oberwolfach and represent diverse areas of Science, CUNY, City College, New York,

JULY/ AUGUST 1989, VOLUME 36, NUMBER 6 757 1989 AMS Elections

Council Nominations Continuing members are: Vice-Presidents and Members-at-Large Joan S. Birman Victor Klee Two vice-presidents and five members-at-large of the James E. Humphreys Alan D. Weinstein Council will be elected by the Society in a contested Two members to be named by the President. election in the fall of 1989. William Browder has named five of the Vice-presidents will serve for a term of two years President candidates for the other three places. They are: effective January 1, 1990. The Council has nominated six four candidates for the two positions, namely: Sylvain E. Cappell Ray A. Kunze M. Hardt Paul C. Roberts James G. Arthur James B. Serrin Robert Barbara Lee Keyfitz Phillip A. Griffiths Dennis P. Sullivan If nominations by petition have not appeared The"five members-at-large will serve for a term of the total number of candidates to at least six, three years. The Council nominated seven candidates. bringing be brought up to six by the President. They are: it will Joan S. Birman Amassa G. Fauntleroy Editorial Boards Committee Frank H. Clarke Edwin E. Floyd Two members of the Editorial Boards Committee are Charles Herbert Carl Pomerance to be elected in the fall of 1989 to serve for a term of Clemens Shing-Tung Yau three years. Continuing members are: The Council plans to name additional candidates Haynes R. Miller Daniel Zelinsky for member-at-large to bring their number to at least Richard M. Schoen ten. President William Browder has named two of the The deadline for petitions proposing additional four candidates for the other two places. They are: nominations is July 6. Such proposals will not reach Andrew M. Odlyzko Barry Simon after that the Council for action by mail ballot until If nominations by petition have not appeared date. bringing the total number of candidates to at least President's Candidates four, it will be brought up to four by the President. Nominating Committee Robert M. Fossum Committee are to Three members of the Nominating Secretary of 1989 to serve for a term of be elected in the fall Urbana, Illinois three years.

758 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1988-1989. Academic Year Devoted to Mathematical Sciences Operator Algebras, Mittag-Leffler Insti­ tute, Djursholm, Sweden. (Feb. 1988, Meetings and Conferences p. 307) 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 Univer­ sity, Wichita, KS. (Jan. 1989, p. 63) 1989. Concentration Year on Fluid Dy­ namical Aspects of Combustion Theory, announcements of meetings and conferences of interest to Instituto Per Le Applicazioni Del Cal­ THIS SECTION contains some segment of the mathematical public, including ad hoc, local, or regional meetings, Rome, Italy. (Jan. 1989, p. 63) colo, and meetings or symposia devoted to specialized topics, as well as announcements 1989-1990. Academic Year Devoted to of regularly scheduled meetings of national or international mathematical organizations. Hyperbolic Geometry and Quasiconformal (Information on meetings of the Society, and on meetings sponsored by the Society, will Mappings, Mittag-Leffler Institute, Djur­ be found inside the front cover.) sholm, Sweden. (Dec. 1988, p. 1584) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, the place, date, subject (when applicable), and the speakers; a second January !-December 23, 1989. Math­ and specifies will be published only if there are changes or necessary additional Oberwol­ full announcement ematisches Forschungsinstitut information. Once an announcement has appeared, the event will be briefly noted in each fach (Weekly Conferences), Federal Re­ issue until it has been held and a reference will be given in parentheses to the month, public of Germany. (Apr. 1988, p. 629 year, and page of the issue in which the complete information appeared. Asterisks (*) and Nov. 1988, p. 1381) mark those announcements containing new or revised information. IN GENERAL, announcements of meetings and conferences held in North America carry 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 June 1989 of further information. Meetings held outside the North American area may carry more detailed information. In any case, if there is any application deadline with respect to 3-August 5. Joint AMS-IMS-SIAM participation in the meeting, this fact should be noted. All communications on meetings Summer Research Conferences in the and conferences in the mathematical sciences should be sent to the Editor of Notices, Mathematical Sciences, Humbolt State care of the American Mathematical Society in Providence. for entries in this section are listed on the inside front cover of each issue. In University, Arcata, CA. DEADLINES order to allow participants to arrange their travel plans, organizers of meetings are urged INFORMATION: C. Kohanski, AMS, to submit information for these listings early enough to allow them to appear in more than P.O. Box 6248, Providence, RI 02940. one issue of Notices prior to the meeting in question. To achieve this, listings should be received in Providence SIX MONTHS prior to the scheduled date of the meeting.

July 1989 Logic at Botik '89: A Seminar on Log­ Wyoming, Laramie, WY. (Dec. 1988, 27-29. Sixth Annual Western Geomet­ Young ical Foundations of Computer Science, p. 1589) ric Topology Workshop, Brigham 1989, p. 492) Pereslavl-Zalessky, USSR. (May/Jun. 24-August 4. Cornell National Super­ University, Provo, UT. (Apr. 1989, p. 595) computer Facility Advanced Summer In­ 27-29. International Symposium on l 0-30. AMS Summer Research Insti­ stitute in Supercomputing, Ithaca, NY. Cauchy and the French Mathematical tute on Several Complex Variables and (May I Jun. 1989, p. 596) World, Paris, France. (Nov. 1988, p. 1387) Complex Geometry, University of Cali­ 24-August 5. 1989 European Summer 28-September I. Homologie des Groupes fornia, Santa Cruz, CA. Meeting of the Association for Sym­ et K-Theorie: Applications Geometriques, bolic Logic, West Berlin, Germany. (Mar. Marseille, France. (Mar. 1989, p. 31 0) INFORMATION: W. Drady, AMS, P.O. 1989, p. 310) 29-August 12. Conference on Groups­ Box 6248, Providence, RI 02940. 25-August 6. International Summer Saint Andrews 1989, Saint Andrews, Scot­ l 0-September I. IMA Summer Program School on Logic, Algebra, and Compu­ land. (Dec. 1988, p. 1589) in Robustness, Diagnostics, Computing tation, Marktoberdorf, Germany. (Apr. * 30-August 5. Konstruktive Approxima­ and Graphics in Statistics, Institute for 1989, p. 492) tionstheorie, Oberwolfach, Federal Re­ Mathematics and its Applications, Min­ 26-28. MAA Ohio Section Summer public of Germany. neapolis, MN. (Dec. 1988, p. 1589) Additive Num­ Short Course on Topics in CHAIRMEN: C. de Boor, Madison; College, Findlay, 17-August 4. Conference on Matrix ber Theory, Findlay R.A. DeVore, Columbia. Theory for Applications, University of OH. (MayfJun. 1989, p. 596)

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 759 Meetings and Conferences

INFORMATION: Mathematisches For­ INFORMATION: V. Shvyrkov, IS-SSE, 13-19. Fourth Conference on Differen­ schungsinstitut Oberwolfach Geschaft­ 536 Oasis Dr., Santa Rosa, CA; (707) tial Equations and Applications, Rousse, sstelle: Albertstr. 24 D-7800 Freiburg. 575-3529. Bulgaria. (May/Jun. 1988, p. 731) * 14-18. International Workshop on Multi­ 30-August 12. Harmonic Analysis on Re­ 6-12. Kommutative Algebra Und Alge­ variate Approximation and Interpolation, ductive Groups, Bowdoin College, Bruns­ braische Geometrie, Oberwolfach, Fed­ Duisburg, Federal Republic of Germany. wick, ME. (Apr. 1989, p. 492) eral Republic of Germany. (Mar. 1989, 31-August 4. Sixteenth Annual Confer­ p. 310) ORGANIZERs: C. K. Chui, College Sta­ ence on Computer Graphics and Interac­ 7. AMS-SIAM-SMB Symposium on tion; W. HauBmann, K. Jetter, Duis­ tive Techniques, Boston, MA. (Dec. 1988, Some Mathematical Questions in Biol­ burg; L. L. Schumaker, Nashville; F. p. 1590) ogy: Sex Allocation and Sex Change, I. Uteras, Santiago de Chile. 31-August 4. Thirty-ninth Gordon Re­ Experiments and Models, University of INFORMATION: K. Jetter, FB search Conference on Statistics in Chem­ Toronto, Toronto, Ontario, Canada. Mathematik der Univ. Duisburg, istry and Chemical Engineering, New (Feb. 1989, p. 181) D-41 00 Duisburg; Email: Hampton, NH. (Oct. 1988, p. 1245) 7-10. Joint Mathematics Meetings, Boul­ unido.uucp!unidui!hn277je. der, CO. (including the summer meetings * 14-20. Third International Conference of the AMS, AWM, MAA and PME.) on Recent Developments in Statistical Sci­ This is the Diamond Jubilee of PME. August 1989 ences, Neuchatel, Switzerland. INFORMATION: H. Daly, AMS, P.O. INFORMATION: Y. Dodge, Univ. de 1-5. Harbin Symposium on Univalent Box 6248, Providence, RI 02940. Neuchatel, Group d'Informatique et Functions and its Applications, Heilong­ * 7-1 0. Recent Developments and Prospects Statistique, Pierre-a-Maze! 7, CH-2000 jiang University, Harbin, People's Re­ in Complex Geometry, Research Institute Neuchatel. public of China. (May I Jun. 1989, p. 596) for Mathematical Sciences, Kyoto Uni­ * 14-24. Twenty-seventh International Sym­ 1-9. Eighteenth International Congress versity, Japan. posium on Functional Equations, Bielsko­ of the History of Science, Hamburg, Biala, Katowice and Krakow, Poland. 1-5; Munich, 6-9, Federal Republic of INFORMATION: T. Ohsawa, Research Germany. (Apr. 1988, p. 639) Institute for Mathematical Sciences, INFORMATION: R. Ger, Math. Inst., Kyoto Univ., Sakyo, Kyoto 606, Japan. 1-11. Annual CMS Seminar: Lie The­ Silesian Univ., PL-40-007 Katowice, ory, Differential Equations and Repre­ 7-11. Symposium on Combinatorics and B. Choczewski, Math. Inst., Univ. sentation Theory, Centre de Recherches Geometry, Royal Institute of Technology, Mining and Metallurgy, PL-30-059 Mathematiques (CRM) Universite de Stockholm, Sweden. (Apr. 1989, p. 492) Krakow, Poland, or J. Aczel, Dept. of Pure Mathematics, Univ. of Wa­ Montreal, Montreal, Quebec, Canada. 7-11. Thirteenth Johns Hopkins Math­ terloo, Ont. N2L 3G 1, Canada. (Please note date change from Jan. 1989, ematical Sciences Summer Lecture Se­ p. 69) ries, Johns Hopkins University, Balti­ 14-September 2. Third Workshop on 2-5. Seventh International Congress on more, MD. (Mar. 1989, p. 310) Representation Theory of Lie Groups and Mathematical and Computer Modeling, 7-11. Fourth International Seminar on Their Applications, Cordoba, Argentina. Chicago, IL. (Mar. 1989, p. 31 0) Random Graphs and Probabilistic Meth­ (May/ Jun. 1989, p. 597) 4-14. Workshop on New Trends and Ap­ ods in Combinatorics and Computer 15-18. Fourth Korea Institute of Technol­ plications of Distributed Parameter Con­ Science, Poznan, Poland. (Nov. 1988, ogy Workshop, Korea Institute of Tech­ trol Systems, Institute for Mathemat­ p. 1387) nology, Taejon, Korea. (May/Jun. 1989, ics and its Applications, University of I 0-12. International Conference on Com­ p. 597) Minnesota, Minneapolis, MN. (May/Jun. putational Techniques and Applications, 16-September 2. Nineteenth Summer 1989, p. 597) Brisbane, Australia. (Feb. 1989, p. 181) Session on Probability Theory, Saint­ 6-7. AMS Short Course on Cryptol­ 13-18. Fifth International Conference on Flour (Cantal), France. (Mar. 1989, p. 311) ogy and Computational Number Theory, Stochastic Programming, University of 18-20. Workshop for College Faculty on Boulder, CO. Michigan, Ann Arbor, MI. (Mar. 1989, Using Technology in Precalculus Mathe­ INFORMATION: M. Foulkes, AMS, P.O. p. 311) matics, Ohio State University, Columbus, Box 6248, Providence, RI 02940. 13-19. Kombinatorische Und Reell AI­ OH. (May/Jun. 1989, p. 597) gebraische Geometrie, Oberwolfach, Fed­ * 18-20. Wabash Extramural Functional 6-10. 1989 Joint Statistical Meetings, eral Republic of Germany. (Mar. 1989, Analysis Mini-Conference, University of Washington, DC. (Mar. 1988, p. 466) p. 311) Michigan, Ann Arbor, MI. * 6-1 0. Sixth International Conference on 13-19. Combinatorical Convexity and INVITED SPEAKERs: A. L. Shields, the New Quality Philosophy in Statisti­ Algebraic Geometry, Oberwolfach, Fed­ Univ. of Michigan; S. Axler, Michi­ cal Research and Statistical Education, eral Republic of Germany. (Mar. 1989, gan State; R. D. Lyons, Stanford; D. Washington, D.C. p. 311) E. Sarason, Univ. of California at SPONSORS: International Society of 13-1 9. Colloquium on Universal Algebra, Berkeley; H. S. Shapiro, Royal Insti- Statistical Science in Economics. Szeged, Hungary. (Nov. 1988, p. 1387)

760 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

tute of Technology, Stockholm; J. H. INVITED SPEAKERS: J. Christy; 28-September I. Homologie des Groupes Shapiro, Michigan State. S. DiMichalis; S. Fenley; R. Fintushel; et K-Theorie: Applications Geometriques, INFORMATION: C. Cowen, Dept. of C. Frohman; D. Gabai; K. Johans­ Marseille, France. (Mar. 1989, p. 311) Mathematics, Purdue Univ., West son; J. Luecke; G. Matic; Y. Minsky; 28-September I. International Confer­ Lafayette, IN 4 7907; 317-494-1943; P. Shalen; R. Stern; K. Walker; D. ence on Symplectic Geometry and Compu­ Email: [email protected]. Cooper. tational Hamiltonian Dynamics, Beijing, INFORMATION: N. Habegger, Univer­ China. (Jan. 1989, p. 69) 18-23. The Arthur Prior Memorial Con­ sity of Georgia, Department of Math­ 28-September I. NSF-CBMS Regional ference, University of Canterbury, New ematics, Athens, GA 30602, 404-542- Research Conference in the Mathemati­ Zealand. (May/ Jun. 1989, p. 597) 2545. Bitnet: HABEGGER@UGA. cal Sciences: Singular Integral Operators, 20-24. Ninth Annual Crypto Confer­ University of Montana, Missoula, MT at Santa 24-26. Twenty-fourth Actuarial Research ence, University of California (April 1989, p. 490). Barbara, Santa Barbara, CA. (Feb. 1989, Conference, Concordia University, I. IFIP 89: Eleventh p. 181) Montreal, Canada. (Mar. 1989, p. 311) 28-September San Fran­ 24-September I. NSF-CBMS Confer­ World Computer Conference, 20-25. Second Conference of the Cana­ cisco, CA. (Apr. 1988, p. 639) dian Number Theory Association, Uni­ ence on Singular Integral Operators, Uni­ 28-September 2. Second International versity of British Columbia, Vancouver, versity of Montana, Missoula, MT. (Mar. on Function Spaces, Poznan, Canada. (Dec. 1988, p. 1590) 1989, p. 311) Conference Poland. (Nov. 1988, p. 1387) 20-26. Eleventh International Joint Con­ * 24-September 2. Fifth Ecole d'ete de 8. Topical Meeting on ference on Artificial Intelligence, Detroit, Didactique Mathematiques, Pelestin Les 28-September Variational Problems in Analysis, Trieste, MI. (Oct. 1988, p. 1245) Greves, France. Italy. (Oct. 1988, p. 1245) * 20-26. Differentialgeometrie im Grossen, ORGANIZERS: G. Arsac, Lyon; 29-September 6. Forty-seventh Session Oberwolfach, Federal Republic of Ger­ Y. Chevallard, Marseille; R. Gras, of the International Statistical Institute, many. Nantes; S. Maury, Montpellier. Paris, France. (Apr. 1988, p. 639) CHAIRMEN: W. Ballmann, ZUrich; J.­ INFORMATION: R. Gras, Department Campus de * 30-September 2. Nonlinear Partial Dif­ P. Bourguignon, Palaiseau; W. Klin­ de Mathematiques, Beaulieu, F-35042 Rennes. ferential Equations and Their Applica­ genberg, Bonn. tions, Research Institute for Mathemati­ INFORMATION: Mathematisches For­ * 27-September 2. Special Complex Vari­ cal Sciences, Kyoto University, Japan. schungsinstitut Oberwolfach Gcschaft­ eties, Oberwolfach, Federal Republic of INFORMATION: M. Mimura, Fac. of sstelle: Albertstr. 24,D-7800 Freiberg. Germany. Science, Hiroshima Univ., Naka-ku, 21-24. International Conference on Re­ CHAIRMEN: W. Barth, Erlangen; A. Hiroshima 730, Japan. cent Developments in Statistical Data Van de Yen, Leiden. Analysis and Inference In Honor of C. INFORMATION: Mathematisches For­ R. Rao, Neuchiitel, Switzerland. (Nov. schungsinstitut Oberwolfach Geschaft­ September 1989 1988, p. 1387) sstelle: Albertstr. 24, D-7800 Freiburg. 1-10. Summer School of Algebra and 21-25. Workshop on Advances in Scien­ Ordered Sets, The Jeseniky Mountains, 28-29. Second Annual Meeting of SIAM tific Computing (With Emphasis on Lin­ Czechoslovakia. (Jan. 1989, p. 69) (May Jun. ear Problems), Espoo, Finland. (May 1Jun. Nordic Section, Espoo, Finland. 1 1989, p. 598) * 3-9. Topologie, Oberwolfach, Federal 1989, p. 597) Republic of Germany. of Neural Networks 21-25. EQUADIFF 7, Prague, Czechos­ * 28-30. Applications La CHAIRMEN: M. Kreck, Mainz; A. Ran­ lovakia. (Feb. 1989, p. 181) Focus of UCSD Extension Seminar, Jolla, CA. icki, Edinburgh; L. Siebenmann, Paris. 21-25. First Canadian Conference on INFORMATION: Mathematischcs For­ seminar will consist Computational Geometry, McGill Uni­ PROGRAM: This schungsinstitut Oberwolfach Geschaft­ of analyzing various neural network versity, Montreal, Quebec, Canada. (Feb. sstelle: Albertstr. 24, D-7800 Freiburg. 1989, p. 181) models in terms of their underlying 21-26. International Conference on Alge­ principles and behaviors as well as 4-8. Twelfth CNMAC Brazilian Con­ bra in Memory of A. I. Mal'tsev, Novosi­ address design and implementation gress on Computational and Applied Math­ birsk, USSR. (May I Jun. 1989, p. 598) issues from VLSI, optics, and hybrid ematics, Sao Jose Do Rio Preto, Sao approaches. * 23-27. Annual Georgia Topology Con­ Paulo State, Brazil. (Mar. 1989, p. 312) INFORMATION: UCSD Extensionlx- ference, University of Georgia, Athens, 4-8. Centenary Workshop of Heun's 00 I /La Jolla, CA 92093 or call GA. (Please note changes from May I June Equation: Theory and Applications, 1989) 6191534-3400. Rottach-Egern, Federal Republic of Ger­ many. (Nov. 1988, p. 1388) CoNFERENCE THEME: The focus of 28-31. IFAC/IFORSIIMACS Sympo­ 4-8. Colloquium on Computational Num­ the conference will be three and four sium on Large Scale Systems: Theory and ber Theory, Debrecen, Hungary. (Nov. dimensional topology. Application, Berlin, German Democratic Republic. (Mar. 1989, p. 311) 1988, p. 1388)

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 761 Meetings and Conferences

* 4-8. Recent Advances in Nonlinear Fi­ 11-13. Supercomputers: Emerging Appli­ INFORMATION: W. Kuich, Techn. Univ. nite Element Analysis, Lausanne, Switzer­ cations in Manufacturing, Minneapolis, Wien, Wiedner HauptstraBe 8-10, land. MN. (Mar. 1989, p. 312) A-1 040 Wien. Donnes, Antibes, CHAIRMEN: T.J.R. Hughes, Stanford 11-14. Analyse des * 17-23. Effiziente Algorithmen, Oberwol- 1989, p. 312) Univ.; T. Belytschko, Northwestern France. (Mar. fach, Federal Republic of Germany. Univ. * 11-14. Calculus of Variations and Re­ CHAIRMEN: K. Mehlhorn, Saarbriicken; INFORMATION: M. T. Howe, ZACE lated Topics, Research Institute for Math­ W. Paul, Saarbriicken; H.G. Walter, Services Ltd., I.C.E. Division, P.O.Box ematical Sciences, Kyoto University, Darmstadt. 2, CH-1015 Lausanne. Japan. INFORMATION: Mathematisches For­ N. Kikuchi, Fac. of * 5-7. International Conference on Appli­ INFORMATION: schungsinstitut Oberwolfach Geschiift­ & Technology, Keio Univ., cations of Supercomputers in Engineering, Science sstelle: Albertstr. 24, D-7800 Freiburg. 223, Japan. Southampton, Great Britain. Minato-ku, Yokohama 18-21. Traffic Theories for New Telecom­ INFORMATION: L. Newma, Confer­ 11-15. Journees de Probabilites, Mar­ munications Services, Adelaide, Australia. ence Secretary, Computational Me­ seille, France. (Mar. 1989, p. 312) (Nov. 1988, p. 1388) chanics Institute, Ashurst Lodge, 11-15. Fifth International Conference on 18-21. SIAM Conference on Mathe­ Ashurst, GB-Southampton S04 2AA. Numerical Methods in Engineering, Lau­ matics of Geophysical Sciences, Houston, sanne, Switzerland. (Nov. 1988, p. 1388) TX. (Nov. 1988, p. 1388) 5-8. Third European Simulation Con­ 11-16. Trends in Functional Analysis and Scotland. (Mar. 1989, 18-22. Bifurcations et Orbites Peri­ gress, Edinburgh, Approximation Theory, Acqua Fredda di p. 312) odiques des Champs de Vecteurs du Plan, Maratea (Potenza), Italy. (Feb. 1989, Marseille, France. (Mar. 1989, p. 312) 5-15. Opening Workshop: An Intro­ p. 182) duction to Dynamical Systems, Institute 18-23. Conference on Integral Equations * 11-1 7. Conference on Foliations (in mem­ for Mathematics and its Applications, and Inverse Problems, Varna, Bulgaria. ory of Bruce L. Reinhart), University of MN. (Dec. 1988, p. 1590) (Nov. 1988, p. 1388) Minneapolis, Maryland, College Park, MD. 6-8. Fourteenth Symposium on Opera­ 19-23. 1830-1930: A Century of Geom­ tions Research, Universitiit Ulm, Federal SPONSORS: The University of Mary­ etry, from C. F. Gauss and B. Riemann Republic of Germany. (Jan. 1989, p. 70) land and the National Science Foun­ to H. Poincare and E. Cartan; Episte­ mology, History, and Mathematics, Insti­ * 7-8. Second September Meeting of the dation. L. Conlon, D. tut Henri Poincare, Paris, France. (Apr. Irish Mathematical Society, Maynooth INVITED SPEAKERs: A. Haefliger, S. Hurder, H.B. 1989, p. 494) College, Co. Kildare, Ireland. Gabai, Lawson, P. Tondeur. 21-22. Mathematics in the Car Industry, INVITED SPEAKERs: F. Almgren, Prince­ INFORMATION: J. Rosenberg, Dept. Warwick, England. (Nov. 1988, p. 1388) ton; S.K. Donaldson, Oxford; J. Lewis, of Mathematics, Univ. of Maryland, 24-30. Kryptographie, Oberwolfach, Fed­ DIAS. College Park, MD 20742, (301)454- eral Republic of Germany. (Mar. 1989, INFORMATION: A.G. O'Farrell, Dept. 7069, email: [email protected]. p. 312) of Mathematics, Maynooth College, 24-0ctober 6. Extrapolation et Approxi­ Co. Kildare, Ireland. 12-15. National Computer Graphics As­ sociation Conference on CAD/CAM/­ mation Rationelle, Marseille, France. * 7-9. Cohomological Dimension and Soft CAE/CIM Aerospace and Electronics, (Mar. 1989, p. 312) Mappings, Research Institute for Mathe­ Santa Clara, CA. (Apr. 1989, p. 494) 25-27. SSA-IMACS 1989 Biennial Con­ matical Sciences, Kyoto University, Japan. 15-20. Sino-French Colloquium on Prob­ ference on Modelling and Simulation, Canberra, Australia. (Mar. 1989, p. 312) INFORMATION: A. Koyama, Osaka Ky­ ability and Statistics, Centre sino-franr;:ais oiku Univ., Tennoji-ku, Osaka 543, de Mathematiques et d'Informatique, 25-28. SIAM Conference on Mathemati­ Japan. Universite de Wuhan, 430072 Wuhan, cal and Computational Issues in Geophys­ People's Republic of China. (MayjJun. ical Fluid and Solid Mechanics, Houston, 8-14. COSMEX '89: International Con­ 1989, p. 598) TX. (Mar. 1989, p. 312) ference on Stochastic Methods in Experi­ 16-0ctober 20. Sixth World Congress 25-29. Third International Conference mental Sciences, Technical University of on Medical Information, Beijing, China. on the Theory of Groups and Related Wroclaw, Poland. (Nov. 1988, p. 1388) (Apr. 1988, p. 639) Topics, Australian National University, * I 0-16. Transformationsgruppen, Ober- 17-22. The ICME Conference on the Canberra. (May/June 1988, p. 732) wolfach, Federal Republic of Germany. Popularization of Mathematics, Leeds, * 25-29. Extrapolation et Approximation CHAIRMEN: T. tom Dieck, Gottingen; England. (Jan. 1989, p. 70) Rationelle, Marseille, France. T. Petrie, New Brunswick. * 17-22. Twelfth Osterreichischer Mathe­ CHAIRMEN: C. Brezinski, Lille. INFORMATION: Mathematisches For­ matikerkongress, Wien, Austria. INFORMATION: A. Zeller-Meier, CIRM, schungsinstitut Oberwolfach Geschiift­ ORGANIZERS: W. Kuich, Wien. Luminy, Case 916, F-13288 Marseille sstelle: Albertstr. 24, D-7800 Freiburg. Cedex 9.

762 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

26-28. Third International Workshop 2-6. Symposium on Applied and Indus­ search Institute, Berkeley, CA. (May I Jun. on Distributed Algorithms, La Colle-sur­ trial Mathematics, Island of San Servolo, 1989, p. 599) Loup, France. (Feb. 1989, p. 182) Venice, Italy. (Apr. 1989, p. 494) 16-20. Sixth World Congress on Medical * 27-29. Eighth Gamm Conference on 4-6. Geometry and Mathematical Physics: Informatics, Beijing, China. (Feb. 1989, Numerical Methods of Fluid Mechanics, John H. Barrett Memorial Lectures, The p. 182) Delft, The Netherlands. University of Tennessee, Knoxville, TN. 16-20. Workshop: Patterns and Dynam­ (Mar. 1989, p. 313) INFORMATION: Mrs. Komen-Zimmer­ ics in Reactive Media, Institute for Math­ mann, Congressbureau TU Delft, Stev- * 4-6. First European Workshop on Hyper­ ematics and its Applications, Minneapo­ inweg 1, NL-2628 Delft. cube and Distributed Computers, Rennes, lis, MN. (Feb. 1989, p. 182) France. * 17-20. /ltyperfunctions and Differential 29-30. Midwest Noncommutative Ring * INFORMATION: INRIA, Domaine de Equati(n,. Research Institute for Mathe­ Theory, Ohio University, Athens, OH. Voluceau-Rocquencourt, F-78153 Le matical SCiences, Kyoto University, Japan. INFORMATION: Call Jain R. Lopez­ Chesnay Cedex. INFORMATION: K. Kataoka, Fac. of Permouth, 614-593-1258 or 614-593- Science, Univ. of Tokyo, Bunkyo-ku, 1278 or 614-593-1254. 6-7. Conference on Issues in the Teaching Tokyo 113, Japan. of Calculus, Miami University, Oxford, 29-0ctober 1. Sixth IFACjiFIP/IFORS OH. (Apr. 1989, p. 494) 19-20. Workshop on Large-Scale Numer­ /IMACS Symposium on Information Con­ ical Optimization, Mathematical Sciences trol Problems in Manufacturing Technol­ * 8-14. Arbeitsgemeinschaft Geyer-Harder, Institute, Cornell University, Ithaca, NY. ogy, Madrid, Spain. (Mar. 1989, p. 313) Oberwolfach, Federal Republic of Ger­ (May I Jun. 1989, p. 599) many. * 19-21. Journees Mathematiques/Informa- Mathematisches For­ October 1989 INFORMATION: tique, Marseille, France. schungsinstitut Oberwolfach Geschiift­ Marseille. * 1-7. Topologische Methoden in der Grup­ sstelle: Albertstr. 24, D-7800 Freiburg. CHAIRMEN: C. Mauduit, pentheorie, Oberwolfach, Federal Repub­ INFORMATION: A. Zeller-Meier, CIRM, lic of Germany. 9-13. Workshop on Geometric Phases in Luminy, Case 916, F-13288 Marseille Geometric Phases in Mechanics, Mathe­ Cedex 9. CHAIRMEN: R. Bieri, Frankfurt; K. matical Sciences Institute, Cornell Uni­ S. Brown, Ithaca; K. W. Gruenberg, versity, Ithaca, NY. (May/Jun. 1989, 20-26. Hamiltonian Systems, Trans­ London. p. 599) formation Groups and Special Trans­ form Methods, Centre de Recherches INFORMATION: Mathematisches For­ 12-14. Second Interdisciplinary Confer­ schungsinstitut Oberwolfach Geschiift­ Mathematiques (CRM) Universite de ence on Natural Resource Modeling and Montreal. (Please note date change from sstelle: Albertstr. 24, D-7800 Freiburg. University, Talla­ Analysis, Florida State Jan. 1989, p. 70) hassee, FL. (Apr. 1989, p. 494) * 2-4. Topics in Univalent Functions and 21-22. Eastern Section Meeting of the Its Applications, Research Institute for 13-14. Ninth Annual Southeastern­ AMS, Stevens Institute of Technology, on Differ­ Mathematical Sciences, Kyoto Univer­ Atlantic Regional Conference Hoboken, NJ. sity, Japan. ential Equations, University of North Carolina at Charlotte, Charlotte, NC. INFORMATION: W. Drady, AMS, P.O. INFORMATION: S. Owa, Dept. of Math., (MayjJun. 1989, p. 599) Box 6248, Providence, RI 02940. Fac. of Sci. & Tech., Kinki Univ., Hi­ 15-18. Fourth International Workshop on gashiosaka, Osaka 577, Japan. * 22-28. Linear Operators and Applica­ Kennebunkport, High-Level Synthesis, tions, Oberwolfach, Federal Republic of 2-6. IMACS-GAMM International Sym­ ME. (Dec. 1988, p. 1590) Germany. posium on Computer Arithmetic and Self­ * 15-21. Geometrie, Oberwolfach, Federal Validating Numerical Methods, Univer­ Republic of Germany. CHAIRMEN: I. Gohberg, Tel Aviv; B. sity of Basel, Basel, Switzerland. (Mar. Gramsch, Mainz; H. H. Schaefer, Bern; U. 1989, p. 313) CHAIRMEN: V. Bangert, Tiibingen. Pinkall, Berlin. INFORMATION: Mathematisches For­ * 2-6. Geometrie Algebrique Reelle, Mar- INFORMATION: Mathematisches For­ seille, France. schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ sstelle: Albertstr. 24, D-7800 Freiburg. CHAIRMEN: M. Silhol, Montpellier; M. sstelle: Albertstr. 24, D-7800 Freiburg. Trotman, Paris. * 22-28. Second Osterreichisches Sym­ 16-18. Second International Conference INFORMATION: A. Zeller-Meier, CIRM, posium Zur Geschichte der Mathematik, on Data and Knowledge Systems for Man­ Luminy, Case 916, F-13288 Marseille Neuhofen a.d. Ybbs, Austria. ufacturing and Engineering, National In­ Cedex 9. stitute of Standards and Technology, INFORMATION: C. Binder, Inst. f. Techn. 2-6. Third Workshop on Computer Sci­ Gaithersburg, MD. (Apr. 1989, p. 495) Math., Techn. Univ. Wien, Wiedner A-1040 Wien. ence Logic, Kaiserslautern, West Ger­ 16-20. Workshop on Set Theory and the Hauptstr. 8-10/1141, many. (Apr. 1989, p. 494) Continuum, Mathematical Sciences Re-

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 763 Meetings and Conferences

23-26. Beijing International Confer­ * 5-11. Fastringe und Fastkorper, Ober- 13-1 7. Workshop: Dynamical Issues in ence on System Simulation and Scientific wolfach, Federal Republic of Germany. Combustion Theory, Institute for Mathe­ Beijing, China. (Mar. 1989, matics and its Applications, Minneapolis, Computing, CHAIRMEN: G. Betsch, Ti.ibingen. MN. (Dec. 1988, p. 1591) p. 313) INFORMATION: Mathematisches For­ * 25-27. Evolution Equations and Appli­ schungsinstitut Oberwolfach Geschlift­ * 13-17. Supercomputing '89, Reno, NV. cations to Nonlinear Problems, Research sstelle: Albertstr. 24, D-7800 Freiburg. INFORMATION: F. Ron Bailey, M/S Institute for Mathematical Sciences, Ky­ 258-5, NASA Ames Research Ctr., On the Structure of Solutions to oto University, Japan. * 6-8. Moffett Field, CA 94035; (415) 694- Partial Differential Equations, Research N. Kenmochi, Fac. of 4500. INFORMATION: Institute for Mathematical Sciences, Ky­ Education, Chiba Univ., Chiba 260, oto University, Japan. 15-1 7. Geometry of Manifolds, Research Japan. * Ky­ INFORMATION: S. Matsuura, Research Institute for Mathematical Sciences, 25-28. Workshop on Numerical Meth­ Institute for Mathematical Sciences, oto University, Japan. ods for Elliptic Systems, Espoo, Finland. Kyoto Univ., Sakyo-ku, Kyoto 606, INFORMATION: K. Kawakubo, Fac. of (May jJun. 1989, p. 599) Japan. Science, Osaka Univ., Toyonaka, Os­ 26-28. The Riccati Equation In Control, aka 560, Japan. Systems and Signals, Villa Gallia, Como, 6-9. International Conference on Italy. (Jan. 1989, p. 70) Computer-Aided Design, Santa Clara, CA. 17-20. Workshop on Classical and Quan­ 1989, p. 495) 27-28. Central Section Meeting of the (Apr. tum Transport in Hamiltonian Systems, AMS, Ball State University, Muncie, IN. 6-10. SIAM Conference on Applied Ge­ Mathematical Sciences Institute, Cornell (May/ June 1988, p. 732) ometry, Tempe, AZ. (Nov. 1988, p. 1388) University, Ithaca, NY. (May/ Jun. 1989, 6-10. SIAM Conference on Geometric p. 600) INFORMATION: W. Drady, AMS, P.O. Design, Tempe, AZ. (Mar. 1989, p. 314) 18-19. Far Western Section Meeting of Box 6248, Providence, RI 02940. * 8-10. Conference for Mathematics in the AMS, University of California, Los 29-November 4. Computational Methods Chemistry, College Station, TX. Angeles, CA. in Solid Mechanics, Oberwolfach, Fed­ INFORMATION: C. Spiegelman, Dept. INFORMATION: W. Drady, AMS, P.O. Republic of Germany. (Mar. 1989, eral of Statistics, Texas A&M Univ., Col­ Box 6248, Providence, RI 02940. p. 313) lege Station, TX; (409) 845-3141. 30-November 2. Workshop on Ho­ * 19-25. Random Partial Differential Equa­ motopy Theory, Mathematical Sciences I 0-11. Eighteenth Midwest Differential tions, Oberwolfach, Federal Republic of Research Institute, Berkeley, CA. (Mar. Equations Conference, Southern Illinois Germany. 1989, p. 313) University, Carbondale, IL. (Apr. 1989, CHAIRMEN: U. Hornung, Mi.inchen; P. * 30-November 2. Differential Analysis p. 495) Kotelenez, Utrecht; G. Papanicolao, and Differential Topology, Research In­ * I 0-11. Conference on Women in Mathe­ New York. stitute for Mathematical Sciences, Kyoto matics and the Sciences, St. Cloud State INFORMATION: Mathematisches For­ University, Japan. University, St. Cloud, MN. schungsinstitut Oberwolfach Geschaft­ sstelle: Albertstr. 24, D-7800 Freiburg. INFORMATION: S. Izumi, Fac. of Tech. SPONSORS: The Ford Foundation, Hon­ & Science, Kinki Univ., Higashiosaka, eywell Foundation, and Cray Research. * 20-24. Seminaire Sud-Rhodanien de Ge- Osaka 577, Japan. PURPOSE: Two-day conference with ometrie Differentielle, Marseille, France. small workshop opportunities to study 30-December I. College on Differen­ issues for women in mathematics CHAIRMEN: P. Donato, Marseille. tial Geometry, Trieste, Italy. (Mar. 1989, and the sciences at the undergraduate INFORMATION: A. Zeller-Meier, CIRM, p. 313) level. Luminy, Case 916, F-13288 Marseille INFORMATION: S. Keith, Dept. of Cedex 9. Mathematics, St. Cloud State Univ., November 1989 * 26-December 2. Methoden und Ver­ (612) St. Cloud, MN 56301 or phone fahren der Mathematischen Physik, Ober­ 2-4. Second Annual Conference on Tech­ 255-2282. wolfach, Federal Republic of Germany. nology in Collegiate Mathematics, Ohio State University, Columbus, OH. (Mar. 12-15. National Computer Graphics As­ CHAIRMEN: R.E. Kleinman, Newark; 1989, p. 313) sociation Mapping and Geographic Infor­ R. KreB, Gottingen; E. Martensen, mation Systems, Los Angeles, CA. (Apr. 2-5. Third International Conference on Karlsruhe. 1989, p. 494) Expert Systems in Law, Florence, Italy. INFORMATION: Mathematisches For­ (May/ Jun. 1989, p. 599) 13-1 7. Workshop on Logic Related to schungsinstitut Oberwolfach Geschaft­ Computer Science and Programming Lan­ 24, D-7800 Freiburg. 4-8. Workshop on Geometric and Alge­ sstelle: Albertstr. guage Theory, Mathematical Sciences Re­ braic Integration Algorithms, Mathemati­ search Institute, Berkeley, CA. (MayjJun. * 27-29. Computer Algebra and Its Appli­ cal Sciences Institute, Cornell University, 1989, p. 600) cation to Investigations for Mathematics, Ithaca, NY. (May/Jun. 1989, p. 599)

764 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

Research Institute for Mathematical Sci­ * 6-9. Algebraic Number Theory, Research stitute, Berkeley, CA. (MayjJun. 1989, ences, Kyoto University, Japan. Institute for Mathematical Sciences, Ky­ p. 600) oto University, Japan. 28-February 3. Regelungstheorie, Ober­ INFORMATION: S. Watanabe, Mathe­ wolfach, Federal Republic of Germany. matics Dept., Tsuda College, Kodaira, INFORMATION: K. Kato, Fac. of Sci­ (Mar. 1989, p. 314) Tokyo 187, Japan. ence, Univ. of Tokyo, Bunkyo-ku, Tokyo 113, Japan. 29-February 16. Second College on Vari­ * 27-29. The Recent Developments of High ational Problems in Analysis, Interna­ Technology and Mathematical Science I 0-16. Asymptotic Methods for tional Centre for Theoretical Physics, (II), Research Institute for Mathemati­ Computer-Intensive Procedures in Statis­ Trieste, Italy. (May/Jun. 1989, p. 600) cal Sciences, Kyoto University, Japan. tics, Oberwolfach, Federal Republic of Germany. (Mar. 1989, p. 314) INFORMATION: H. Kawarada, Fac. of Conference on Par­ February 1990 Engineering, Chiba Univ., Chiba 260, 11-13. Fourth SIAM Computing, Japan. allel Processing for Scientific 4-1 0. Funktiontheoretische Methoden Chicago, IL. (Mar. 1989, p. 314) Bei Partiellen Differential Und Integral­ * 29-December I. Numerical Analysis and * 11-14. Number Theory - Studies Related gleichungen, Oberwolfach, Federal Re­ Scientific Computing, Research Institute to Automorphic Forms, Research Insti­ public of Germany. (Mar. 1989, p. 314) for Mathematical Sciences, Kyoto Uni­ tute for Mathematical Sciences, Kyoto 4-10. Nukleare Frechet-Riiume, Ober­ versity, Japan. University, Japan. wolfach, Federal Republic of Germany. INFORMATION: M. Natori, Inst. of In­ INFORMATION: T. Yamazaki, Dept. of (Mar. 1989, p. 314) formation Sci. & Electronics, Univ. Math., Fac. of Science, Kyushu Univ., * 5-10. Eighth International Seminar on of Tsukuba, Niihari-gun, Ibaragi 305, Higashi-ku, Fukuoka 812, Japan. Model Optimization in Exploration Geo­ Japan. physics, with a Workshop on Geophysical 17-23. Theory and Numerical Meth­ Data Inversion in Environmental Research ods for Initial-Boundary Value Problems, and Planning, Berlin-West, Free Univer­ December 1989 Oberwolfach, Federal Republic of Ger­ sity of Berlin, Federal Republic of Ger­ * 3-9. Wiener-Hopf-Probleme, Topelitz­ many. (Mar. 1989, p. 314) many. Operatoren und Anwendungen, Oberwol­ SPONSOR: Mathematical Geophysics fach, Federal Republic of Germany. January 1990 Group. INFORMATION: A. Vogel, Institut fiir CHAIRMEN: I. Gohberg, Tel Aviv; M. Oberwolfach, 1-6. Zeitreihenanalyse, Geophysikalische, Wissenschaften, Kaashoek, Amsterdam; E. Meister, (Mar. Federal Republic of Germany. Mathematische; Geophysik, Pod­ Darmstadt. 1989, p. 314) INFORMATION: Mathematisches For­ bielskiallee 60, D-1 000 Berlin 33. 7-13. Mathematische Optimierung, Ober­ schungsinstitut Oberwolfach Geschaft­ wolfach, Federal Republic of Germany. 11-17. Funktiontheorie, Oberwolfach, sstelle: Albertstr. 24, D-7800 Freiburg. (Mar. 1989, p. 314) Federal Republic of Germany. (Mar. 4-6. 1989 Winter Simulation Confer­ 14-20. Nonlinear Evolution Equations, 1989, p. 315) ence, Washington, DC. (May fJun. 1989, Solitons and the Inverse Scattering Trans­ 18-24. Mathematische Modelle in Der p. 600) form, Oberwolfach, Federal Republic of Biologie, Oberwolfach, Federal Republic * 4-6. Studies on Decision Theory and Germany. (Mar. 1989, p. 314) of Germany. (Mar. 1989, p. 315) Their Related Topics, Research Institute 15-26. Workshop on Composite Me­ 20-22. Association for Computing Ma­ for Mathematical Sciences, Kyoto Uni­ dia and Homogenization Theory, Inter­ chinery 1990 Computer Science Confer­ versity, Japan. national Centre for Theoretical Physics, ence, Washington, D.C. (MayjJun. 1989, Trieste, Italy. (May I Jun. 1989, p. 600) p. 601) INFORMATION: T. Nakai, College of SIGCSE Technical Liberal Arts, Kobe Univ., Nada-ku, 17-20. Joint Mathematics Meetings, 22-23. Twenty-first (MayjJun. Kobe 657, Japan. Louisville, KY. {Including the annual Symposium, Washington, D.C. meetings of the AMS, AWM, MAA and 1989, p. 601) * 4-7. Research on Complex Analytic Ge­ NAM). 25-March 3. Eigenwertaufgaben In Natur ometry and Related Topics, Research In­ Und Ihre INFORMATION: H. Daly, AMS, P.O. Und lngenieurwissensachaften stitute for Mathematical Sciences, Kyoto Behandlung, Oberwolfach, Box 6248, Providence, RI 02940. Numerische University, Japan. Federal Republic of Germany. (Mar. INFORMATION: I. Naruki, Research 21-27. Modelltheorie, Oberwolfach, Fed­ 1989,p.315) Institute for Mathematical Sciences, eral Republic of Germany. (Mar. 1989, p. 314) Kyoto Univ., Sakyo-ku, Kyoto 606, March 1990 Japan. 22-26. Workshop on Applications of Al­ gebraic Topology to Geometry and Analy­ 4-10. Interval Methods for Numerical 4-8. Fifth Aerospace Computer Secu­ sis, Mathematical Sciences Research In- Computation, Oberwolfach, Federal Re­ rity Applications Conference, Tucson, AZ. public of Germany. (Mar. 1989, p. 315) (MayjJun. 1989, p. 600)

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 765 Meetings and Conferences

5-7. SIAM Conference on Applied Prob­ 25-31. Kontinuumsmechanik der Festen CHAIRMEN: Th. Beth, Karlsruhe; G.J. ability in Science and Engineering, New Korper, Oberwolfach, Federal Republic Simmons, Albuquerque. Orleans, LA. (Nov. 1988, p. 1389) of Germany. (Mar. 1989, p. 315) INFORMATION: Mathematisches For­ Oberwolfach Geschiifts­ 11-17. Mathematische Stochastik, Ober­ 26-April 6. Workshop on Group Theory schungsinstitut stelle: Albertstr. 24, D-7800 Freiburg. wolfach, Federal Republic of Germany. from a Geometrical Viewpoint, Interna­ for Theoretical Physics, (Mar. 1989, p. 315) tional Centre * 18-21. Sixty-eighth Annual Meeting of jJun. 1989, p. 60 I) * 13-16. Twenty-first Annual Iranian Math­ Trieste, Italy. (May the National Council of Teachers of Math­ ematics Conference, University of Isfa­ * 29-31. Mathematical Sciences Insti- ematics, Salt Lake City, UT. han, Iran. tute Symposium on Mathematics as Art, Associ­ Mathematics as a Consumer Good, Cor­ INFORMATION: NCTM, 1906 Chairman, Dept. of INFORMATION: nell University, Ithaca, NY. ation Dr., Reston, VA 22091; (703) Mathematics, P.O.Box 81745-163, 620-9840. Univ. of Isfahan, Isfahan, Iran. PuRPOsE: This symposium will be de­ voted to developing fruitful mecha­ 21-22. Northeast Section Meeting of 14-19. East European Category Semi­ nisms for education and research to the AMS, Pennsylvania State University, nar, Predela, Bulgaria. (May/Jun. 1989, best encourage the interplay of math­ University Park, PA. p. 60 I) applications in busi­ ematics and its INFORMATION: W. Drady, AMS, P.O. Section Meeting of the and government. 16-17. Central ness, industry, Box 6248, Providence, RI 02940. AMS, Kansas State University, Manhat­ INFORMATION: MSI at Cornell Univ., tan, KS. 201 Caldwell Hall, Ithaca NY 14853- * 22-28. Einhollende Algebren und Ringe 2602, 607/255-8005. Von Differentialoperatoren, Oberwolfach, INFORMATION: W. Drady, AMS, P.O. Republic of Germany. Box 6248, Providence, Rl 02940. Federal April1990 CHAIRMEN: W. Borho, Wuppertal; M. Oberwolfach, Fed­ 18-24. Masstheorie, Duflo, Paris; J. C. Jantzen, Eugene; of Germany. (Mar. 1989, eral Republic * 1-4. ENAR Spring Meeting, Baltimore, R. Rentschler, Orsay. p. 315) MD. INFORMATION: Mathematisches For­ Celebration of 18-24. Third Centenary SPoNsoRs: IMS, Sections of ASA. schungsinstitut Oberwolfach Geschiift­ Gesellschaft in Ham­ the Mathematische INFORMATION: ENAR: C. A. Rohde, sstelle: Albertstr. 24, D-7800 Freiburg. Hamburg. (Jan. 1989, burg, BundesstraBe, Dept. ofBiostat., Johns Hopkins Univ., * 29-May 5. Gruppentheorie (Pro-Endliche p. 71) 615 N. Wolfe St., Baltimore, MD Gruppen), Oberwolfach, Federal Repub­ * 19-22. Eleventh Annual National Graph­ 21205; IMS: L. Billard, Program Sec., lic of Germany. ics Association Conference and Exposi­ Dept. of Stat. & Computer Sci., Univ. tion, Anaheim, CA. of Georgia, Athens, GA 30602. CHAIRMEN: 0. H. Kegel, Freiburg; A. National Computer Lubotzky, Jerusalem. INFORMATION: * 1-7. Design and Codes, Oberwolfach, 2722 Merrilee INFORMATION: Mathematisches For­ Graphics Association, Federal Republic of Germany. Dr., Suite 200, Fairfax, VA 22031; schungsinstitut Oberwolfach Geschiift­ 703-698-9600. CHAIRMEN: D. Jungnickel, GieBen; J. sstelle: Albertstr. 24, D-7800 Freiburg. H. van Lint, Eindhoven. * 19-24. US-USSR Approximation Theory INFORMATION: Mathematisches For­ May 1990 Conference, University of South Florida, schungsinstitut Oberwolfach Geschaft­ Tampa, FL. sstelle: Albertstr. 24, D-7800 Freiburg. * 6-12. Geschichte der Mathematik, Ober- E.B. Saff; wolfach, Federal Republic of Germany. ORGANIZING CoMMITTEE: 4-7. Symposium on Distributions with A. Gonchar; P. Nevai. R. DeVore; Given Marginals (In Memory of Giuseppe CHAIRMEN: J. W. Dauben, New York; E. B. Saff, Institute for INFORMATION: Pompilj), Rome, Italy. (MayjJun. 1989, I. Schneider, Miinchen. Dept. of Constuctive Mathematics, p. 601) INFORMATION: Mathematisches For­ Mathematics, Univ. of South Florida, Oberwolfach Geschiift­ * 8-14. Arbeitsgemeinschaft Mit Aktuellem schungsinstitut Tampa, FL 33620. 24, D-7800 Frciburg. Thema (wird in den Mitteilungen der sstelle: Albertstr. 20-23. Directions in Matrix Theory, DMV Heft 1/1990 bekanntgegeben), Ober­ 7-June I. College on Recent Develop­ Auburn, AL. (MayjJun. 1989, p. 601) wolfach, Federal Republic of Germany. ments and Applications in Mathematics 23-24. Southeast Section Meeting of INFORMATION: Mathematisches For­ and Computer Science, International Cen­ the AMS, University of Arkansas, Fayet­ schungsinstitut Oberwolfach Geschiift­ tre for Theoretical Physics, Trieste, Italy. teville, AR. sstelle: Albertstr. 24, D-7800 Freiburg. (MayjJun. 1989, p. 601) INFORMATION: W. Drady, AMS, P.O. * 13-19. Abstrakte Konvexe Analysis, * 15-21. Mathematical Concepts of De­ Oberwolfach, Federal Republic of Ger­ Box 6248, Providence, RI 0240. Federal pendable Systems, Oberwolfach, many. Republic of Germany. CHAIRMEN: H. Konig, Saarbriicken; H. H. Schaefer, Tiibingen.

766 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

INFORMATION: Mathematisches For­ 6-9. Fifth Annual Conference of the INVITED SPEAKERs: H. W. Alt, Bonn; schungsinstitut Oberwolfach Geschaft­ European Consortium for Mathematics E. DiBenedetto, Northwestern Univ., sstelle: Albertstr. 24, D-7800 Freiburg. in Industry, Lahti, Finland. (Apr. 1989, IL.; C. Baiocchi, Palazzo Univ., Italy; p. 496) P. Benilan, Besan~on; H. Brezis, Paris 14-18. Conference on Nonlinear Anal­ * 6-12. 1990 Barcelona Conference on VI; L. Cafferelli, Princeton, NJ; M. ysis and Partial Differential Equations, Algebraic Topology, Centre de Recerca Chipot, Metz, France; A. Damiamian, Rutgers University, New Brunswick, NJ. Matematica, Barcelona, Spain. (Sept. 1988, Ecole Polytechnique, France; S. Davis, CoNFERENCE ToPics: Abstract non­ p. 1060) Northwestern; P. Fife, UT; A. Fried­ man, MN; J. Glimm, NYU-Courant; linear functional analysis; topological * 10-16. Reelle Algebraische Geometrie, S. Howison, Oxford; Jiang L.S., Suz­ and variational methods; nonlinear Oberwolfach, Federal Republic of Ger­ hou Univ., China; S. Kamin, Tel Aviv; elliptic equations and systems; pe­ many riodic solutions of Hamiltonian sys­ J. Keller, Stanford; D. Kinderlehrer, tems; evolution equations and dynam­ CHAIRMEN: E. Becker, Dortmund; L. MN; P. Knaber, Augsburg,Germany; ical systems; nonlinear equations in Brocker, Munster; M. Knebusch, Re­ S. Luckhaus, Heidelberg; E. Magenes, fluid mechanics. gensburg. Palazzo Univ., Italy; G. Meyer, Geor­ ORGANIZING COMMITTEE: A. Bahri, INFORMATION: Mathematisches For­ gia Tech; P. Ortoleva, IN; R. Pego, H. Brezis, L. Caffarelli, I. Ekeland, schungsinstitut Oberwolfach Geschaft­ MI; R. Ricci, Firenze; G. Sivashinsky, J.L. Lebowitz, L. Nirenberg, P. Rabi­ sstelle: Albertstr. 24, D-7800 Freiburg. Tel Aviv; I. Stakgold, DE. nowitz. INFORMATION: S. Chenevert, J. Roy, * 11-14. Fourteenth Rolf Nevanlinna Col­ Coordinators/Scientific Activities, INFORMATION: E. Oates, Conference loquium, University of Helsinki, Helsinki, on Nonlinear Analysis, Dept. of Math­ CRM, Universite de Montreal, C.P. Finland. (Please note changes from Apr. 6128-A, Montreal, Qc H3C 317 ematics, Hill Center, Rutgers Univer­ 1989, p. 496). sity, New Brunswick, NJ 08903. Canada. INVITED SPEAKERS: E. Arbarello, 17-23. Partial Differential Equations in * 20-26. The Schrodinger Equation and Roma; M. Atiyah, Oxford; F. Catanese, * Complex Analysis, Oberwolfach, Federal Its Classical Counterparts, Oberwolfach, Pisa; D. Drasin, West Lafayette; B. Republic of Germany. Federal Republic of Germany. Fuglede, Copenhagen; N. G. Makarov, CHAIRMEN: V. En13, Berlin. Leningrad; A. Marden, Minneapolis; CHAIRMEN: K. Diederich, Wuppertal; INFORMATION: Mathematisches For­ 0. Martio, Jyvaskyla; C. McMullen, J. J. Kohn, Princeton; I. Lieb, Bonn. schungsinstitut Oberwolfach Geschaft­ Princeton; J. Moser, Zurich; D. Sulli­ INFORMATION: Mathematisches For­ sstelle: Albertstr. 24, D-7800 Freiburg. van, NY. schungsinstitut Oberwolfach Geschaft­ ORGANIZERS: S. Rickman; 0. Lehto; sstelle: Albertstr. 24, D-7800 Freiburg. 21-25. Eleventh United States National 0. Martio; M. Seppala. Congress of Applied Mechanics, Tucson, 18-20. Joint WNAR-IMS Regional Meet­ AZ. (Nov. 1988, p. 1389) 11-14. World Organization of Systems ing, Montana State University, Bozeman, and Cybernetics Eighth International Con­ MT. (Mar. 1989, p. 315) 23-25. 1990 International Symposium gress, New York, NY. (Mar. 1989, p. 315) on Multiple-Valued Logic, Charlotte, NC. * 24-30. Mathematische Probleme in der (Apr. 1989, p. 496) * 11-15. Third International Conference on Nichtlinearen Elastizitat, Oberwolfach, Hyperbolic Problems, Uppsala, Sweden. Federal Republic of Germany. 25-31. Tenth International Conference on Pattern Recognition, Resorts Hotel, INFORMATION: B. Gustafason, Dept. CHAIRMEN: K. Kirchgassner, Stuttgart; Atlantic City, NJ. (Mar. 1988, p. 466) of Computer Sciences, Univ. of Upp­ J. E. Marsden, Berkeley. * 27-June 2. Lyapunov-Exponents, Ober- sala, Sturegatan 4 B 2 TR, S-Uppsala. INFORMATION: Mathematisches For­ Federal Republic of Germany. schungsinstitut Oberwolfach Geschaft­ wolfach, Quantum Dy­ 11-15. Rigorous Results in sstelle: Albertstr. 24, D-7 800 Freiburg. CHAIRMEN: L. Arnold, Bremen; J. P. namics, Liblice Castle, Czechoslovakia. Eckmann, Genf. (May/ Jun. 1989, p. 602) 27-30. Fourth International Congress INFORMATION: Mathematisches For­ 13-1 5. Seventh Annual Quality and Pro­ on Algebraic Hyperstructures and Ap­ schungsinstitut Oberwolfach Geschaft­ ductivity Research Conference, Madison, plications, Xanthi, Greece. (Apr. 1989, sstelle: Albertstr. 24, D-7800 Freiburg. WI. (Mar. 1989, p. 315) p. 496) * 13-22. Free Boundary Problems: Theory June 1990 and Applications, Centre de Recherches July 1990 Mathematiques, Universite de Montreal, * 3-9. Graphentheorie, Oberwolfach, Fed- Canada. 1-7. Modulfunktionen In Mehreren Vari­ eral Republic of Germany. ablen, Oberwolfach, Federal Republic of McMaster; ORGANIZERS: J. Chadam, Germany. (Apr. 1989, p. 497) CHAIRMEN: W. Mader, Hannover; G. F. Clarke, CRM; A. Friedman, MN; Summer Session on Ringel, Santa Cruz. P. Fife, UT; M. Glicksman, R.P.I.; 1-18. Twentieth Saint-Flour (Cantal), INFORMATION: Mathematisches For­ H. Rasmussen, Western Ontario; I. Probability Theory, schungsinstitut Oberwolfach Geschaft­ Stackgold, DE. France. (Mar. 1989, p. 315) sstelle: Albertstr. 24, D-7800 Freiburg.

JULY/ AUGUST 1989, VOLUME 36, NUMBER 6 767 Meetings and Conferences

* 2-6. Tenth Australian Statistical Confer­ 28-30. IMACS European Simulation ence/Second Pacific Statistical Congress, Meeting on Problem Solving by Simula­ August 1990 Sydney, Australia. tion, Esztergom, Hungary. (Mar. 1989, 5-11. Mathematical Methods in Tomog­ p. 316) INFORMATION: D. Shaw, Siromath raphy, Oberwolfach, Federal Republic of Pty. Ltd., 156 Pacific Hwy., St. * 28-31. Operations Research 1990, Inter­ Germany. (Apr. 1989, p. 497) Leonards, NSW 2065, Australia; national Conference Operations Research, Fax (02)4382574. 6-9. 1990 Joint Statistical Meetings, Vienna, Austria. Anaheim, CA. (Mar. 1988, p. 466) SPONSORS: The two German OR­ 8-14. Variationsrechnung, Oberwolfach, 8-11. Joint Mathematics Meetings, Ohio Societies, DGOR and GMOOR; Aus­ Federal Republic of Germany. (Apr. State University, Columbus, OH. (includ­ trian OR-Societies, OGOR; Swiss sis­ 1989, p. 497) ing the summer meetings of the AMS, ter society SVOR. * 9-11. "Universita'di Genova - The Ohio AWM, MAA and PME). This is the 75th ORGANIZING COMMITTEE: G. Feichtin­ State University Joint Conference" on Anniversary of the MAA. ger; W. Janco; W. E. Katzenberger; A. New Trends in Systems Theory, Genoa, INFORMATION: H. Daly, AMS, P.O. Stepan. Italy. Box 6248, Providence, RI 02940. INFORMATION: G. Feichtinger, Insti­ CONFERENCE TOPICS: Mathematical tut fiir Okonometrie, OR und Sys­ theory of linear and nonlinear dy­ 12-18. Algebraische Zahlentheorie, Ober­ temtheorie, Technische UniversiHit namical systems; adaptive and learn­ wolfach, Federal Republic of Germany. Wien, A-1 040 Wien, ArgentinierstraBe ing control; robustness; distributed (Apr. 1989, p. 497) 8. parameter systems; discrete events 12-18. Pre-Congress Topology Confer­ 30-September 4. International Confer­ dynamic systems; parallel and dis­ ence, University of Hawaii, Honolulu, ence on Potential Theory, Nagoya, Japan. tributed computing in process con­ HI. (Feb. 1989, p. 183) (May/Jun. 1989, p. 602) trol; control and decision aspects in: * 13-1 7. Fifth International Conference robotics, manufacturing, and commu­ on Hadronic Mechanics and Nonpoten­ nication networks. tial Interactions, University of Northern September 1990 CALL FoR PAPERS: Three(3) copies of Iowa, Cedar Falls, Iowa. a preliminary draft paper in English, Neuronet-90: IMACS International Sym­ not exceeding 10 double spaced pages, PuRPOSE: The conference will bring posium on Neural Nets and Neural Com­ together researchers from different should be received by the NTST Sec­ puters, Prague, Czechoslovakia. (May/Jun. fields in mathematics and physics to retariat by Sep. 30, 1989, at the ad­ 1989, p. 602) study the applications of geometry, dress given below. IMACS Symposium on Modelling and Lie theory, and related algebraic struc­ INFORMATION: NTST Secretariat, cfo Simulation of Electrical Machines, EN­ G. Conte, Dip. Mat. Univ. Genova, tures to mechanics, statistical physics, SEM -Nancy, France. (MayfJun. 1989, via L.B. Alberti 4, 16132 Genova­ and particle physics. There will be for­ p. 602) mal lectures as well as less structured Italy, email: [email protected], 2-8. Topologie, Oberwolfach, Federal sessions. Fax: + 39-10-3538769. Republic of Germany. (Apr. 1989, p. 497) CALL FOR PAPERS: Applicants wish­ 9-20. Geometry and Topology of Four­ ing to present papers are invited to 3-6. Fourth Asian Logic Conference, Manifolds, McMaster University, Hamil­ submit titles before October 1, 1989. Tokyo, Japan. (Mar. 1989, p. 316) ton, Ontario, Canada. (MayfJun. 1989, Abstracts will be requested at a later 3-7. IMACS Symposium on Intelligent p. 602) date. Models in Systems Simulation, Brussels, 15-21. Stochastic Image Models and Al­ INFORMATION: H. C. Myung, Dept. Belgium. (Mar. 1989, p. 316) gorithms, Oberwolfach, Federal Republic of Mathematics, Univ. of Northern * 3-7. Representation Des Groupes et of Germany. (Apr. 1989, p. 497) Iowa, Cedar Falls, Iowa 50614, (319) Analyse Complexe, Marseille, France. 273-6263. 15-23. Colloquium in Honor of Roland CHAIRMEN: M. Rais, Univ. Poitiers. Fraisse, Centre International de Recon­ 15-19. International Conference on Knot INFORMATION: A. Zeller-Meier, CIRM, tres Mathematiques, Luminy, France. Theory and Related Topics, International Luminy, Case 916, F-13288 Marseille (MayfJun. 1989, p. 602) House, Osaka, Japan. (Apr. 1989, p. 497) Cedex 9. 16-20. SIAM Annual Meeting, Chicago, 19-25. Mathematische Methoden Des IL. (Nov. 1988, p. 1389) 9-15. Surgery and L-Theory, Oberwol­ VLSI-Entwurfs Und Des Distributed Com­ fach, Federal Republic of Germany. (Apr. 22-28. Konvexgeometrie, Oberwolfach, putings, Oberwolfach, Federal Republic 1989, p. 498) Federal Republic of Germany. (Apr. of Germany. (Apr. 1989, p. 497) 1989, p. 497) 10-0ctober 5. School on Qualitative 21-29. The International Congress of Aspects and Applications of Nonlinear 29-August 4. Mechanik Und Algebrais­ Mathematicians 1990, Kyoto, Japan. Evolution Equations, International Centre che Geometrie, Oberwolfach, Federal Re­ (Nov. 1988, p. 1389) for Theoretical Physics, Trieste, Italy. public of Germany. (Apr. 1989, p. 497) 26-September 1. Komplexe Analysis, (MayfJun. 1989, p. 602) Oberwolfach, Federal Republic of Ger­ many. (Apr. 1989, p. 497)

768 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

* 10-14. Mathematiker-Kongress, Dres- den, German Democratic Republic. November 1990 July 1991 INFORMATION: G. Burosch, Sektion 2-3. Central Section Meeting of the 8-12. Second International Conference Mathematik, Wilhelm-Pieck-Univ., AMS, University of North Texas, Den­ on Industrial and Applied Mathematics, Universitiitsplatz 1, Rostock 1, 2500, ton, TX. Washington, DC. (Nov. 1988, p. 1389) German Democratic Republic. INFORMATION: W. Drady, AMS, P.O. 22-26. Thirteenth IMACS World Con­ 16-22. Risikotheorie, Oberwolfach, Fed­ Box 6248, Providence, RI 02940. gress on Computing and Applied Math­ eral Republic of Germany. (Apr. 1989, ematics, Trinity College, Dublin Univer­ p. 498) 18-24. Komplexitiitstheorie, Oberwol­ sity, Dublin, Ireland. (Mar. 1989, p. 316) * 17-22. DMV-Jahrestagung 1990, Bre- fach, Federal Republic of Germany. (Apr. men, Federal Republic of Germany. 1989, p. 498) August 1991 25-December 1. Stochastische Approx­ ORGANIZERS: J. Gamst; W. Fischer. imation Und Optimierungsprobleme In 8-11. Joint Mathematics Meetings, Uni­ INFORMATION: Mathematisches For­ Der Statistik, Oberwolfach, Federal Re­ versity of Maine, Orono, ME. (including schungsinstitut Oberwolfach Geschiift­ public of Germany. (Apr. 1989, p. 498) the summer meetings of the AMS, AWM, sstelle: Albertstr. 24, D-7800 Freiburg. * 25-December 1. Lineare Modelle und MAA, and PME) 23-29. Random Graphs and Combinator­ Multivariate Statistische Verfahren, Ober­ INFORMATION: H. Daly, AMS, P.O. ical Structures, Oberwolfach, Federal Re­ wolfach, Federal Republic of Germany. Box 6248, Providence, RI 02940. public of Germany. (Apr. 1989, p. 498) CHAIRMEN: H. Drygas, Kassel; 0. 19-22. 1991 Joint Statistical Meetings, * 24-28. International Symposium on Math- Krafft, Aachen; E. Sonnemann, Trier. Atlanta, GA. (Mar. 1988, p. 466) ematical Theories, San Sebastian, Spain. INFORMATION: Mathematisches For­ PuRPOSE: To offer an open platform schungsinstitut Oberwolfach Geschiift­ to mathematicians, philosophers of sstelle: Albertstr. 24, D-7800 Freiburg. January 1992 science and historians of science to discuss the singularity of mathemat­ 8-11. Joint Mathematics Meetings, Bal­ December 1990 timore, MD. (including the annual meet­ ical theories: their structures, histori­ ings of the AMS, AWM, MAA and NAM) cal evolutions, and interrelations with 2-8. Multigrid Methods, Oberwolfach, other sciences and technologies. Federal Republic of Germany. (Apr. INFORMATION: H. Daly, AMS, P.O. ORGANIZERS: Department of Logic 1989, p. 498) Box 6248, Providence, RI 02940. and Philosophy of Science at the Uni­ 3-7. 1990 Australasian Conference on versity of the Basque Country. Combinatorial Mathematics and Comput­ June 1992 INFORMATION: J. Echeverria, A. Ibarra, ing, Palmerston North, New Zealand. Departamento de L6gica y Filosofia (Feb. 1989, p. 183) 29-July 1. Joint Meeting with the Lon­ de Ia Ciencia, Universidad del Pais 9-15. Allgemeine Ungleichungen, Ober­ don Mathematical Society, Cambridge, Vasco/Euskal Herriko Unibertsitatea, wolfach, Federal Republic of Germany. England. (Mar. 1989, p. 316) Apartado 1249, 20080 San Sebastian (Apr. 1989, p. 498) (Spain). 16-22. Mathematische Logik, Oberwol­ January 1993 30-0ctober 6. Diophantische Approxi­ fach, Federal Republic of Germany. (Apr. mationen, Oberwolfach, Federal Republic 1989, p. 498) 13-16. Joint Mathematics Meetings, San of Germany. (Apr. 1989, p. 498) 25-January 1. Lineare Modelle Und Mul­ Antonio, TX. (including the annual meet­ tivariate Statistische Verfahren, Oberwol­ ings of the AMS, AWM, MAA, and fach, Federal Republic of Germany. (Apr. NAM) October 1990 1989, p. 498) INFORMATION: W. Drady, AMS, P.O. 7-13. Arbeitsgemeinschaft Mit Aktuellem Box 6248, Providence, RI 02940. Thema, Oberwolfach, Federal Republic of Germany. (Apr. 1989, p. 498) January 1991 January 1994 14-20. Geometrie, Oberwolfach, Fed­ 16-19. Joint Mathematics Meetings, eral Republic of Germany. (Apr. 1989, San Francisco, CA. (including the an­ 5-8. Joint Mathematics Meetings, Cincin­ p. 498) nual meetings of the AMS, AWM, MAA, nati, OH. (including the annual meetings 21-27. Mathematische Methoden In Der and NAM) of the AMS, AWM, MAA, and NAM) Robotik, Oberwolfach, Federal Republic INFORMATION: H. Daly, AMS, P.O. INFORMATION: H. Daly, AMS, P.O. of Germany. (Apr. 1989, p. 498) Box 6248, Providence, Rl 02940. Box 6248, Providence, RI 02940. 28-November 3. Mathematical Eco­ nomics, Oberwolfach, Federal Republic of Germany. (Apr. 1989, p. 498)

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 769 New AMS Publications

Combination book and videotape offer. Chaos and fractals: The Mathematics behind the computer graphics (PSAPM/39 above) and CHAOS AND FRACTALS: THE videotape Chaos, fractals and dynamics: Computer experiments MATHEMATICS BEHIND THE COMPUTER in mathematics, with Robert Devaney (VIDDEVANEY below) GRAPHICS ISBN 0-8218-0142-2 Individual member $58, List price $70, Robert L. Devaney and Linda Keen, Editors Institutional member $64 (Proceedings of Symposia in Applied Mathematics, To order, please specify CHAOSSET /N Volume 39) The following videotape is now available through the AMS. This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject CHAOS, FRACTALS AND DYNAMICS: of great interest in recent years and have proven to be COMPUTER EXPERIMENTS IN useful in a variety of areas of mathematics and the sciences. MATHEMATICS, WITH ROBERT DEVANEY The purpose of the short course was to provide a solid A Science Television Production introduction to the mathematics underlying the notions of over chaos and fractals. The papers in this book range In this captivating and richly illustrated videotape, Robert theory, Julia sets, the such topics as dynamical systems Devaney communicates his deep understanding as well calculus on Mandelbrot set, attractors, the Smale horseshoe, as his enthusiasm for chaos, fractals, and dynamical authors fractals, and applications to data compression. The systems. Starting at a level suitable for well-prepared high top experts in this field. represented here are some of the school students, he tells the mathematical story behind university Aimed at beginning graduate students, college and these fascinating topics. Equations and graphs are clearly mathematics instructors, and non-mathematics researchers, shown with computer-generated characters, and Devaney's exciting this book provides readable expositions of several explanations are lucid and instructive. Illustrating the topics of contemporary research. mathematics are forays into the colorful, unpredictable world Contents of fractals and Julia sets. Devaney explains how the computer Robert L. Devaney, Overview: Dynamics of simple maps is used to generate the pictures and shows how the various Philip J. Holmes, Nonlinear oscillations and the Smale colors are chosen for the graphical representations. As an horseshoe map instructional tool, this videotape would be particularly useful Kathleen T. Alligood and James A. Yorke, Fractal basin because it describes a current area of intense mathematical boundaries and chaotic attractors activity. Though the mathematical background required is Linda Keen, Julia sets elementary, those at the collegiate level and beyond will Bodil Branner, The Mandelbrot set appreciate this videotape for the clarity of exposition and the Jenny Harrison, Introduction to fractals sheer beauty of the graphics. function systems Michael F. Barnsley, Iterated 1980 Mathematics Subject Classification: 58 1980 Mathematics Subject Classifications: 58; 30, 51, 34, 39 VHS format, approx. one hour, 1989 ISBN 0-8218-0137-6, LC 89-7003 Price $59 ISSN 0160-7634 To order, please specify VIDDEVANEY /N 208 pages (hardcover), July 1989 Combination book and video tape offer. Individual member $19, List price $31, See CHAOSSET /N above. Institutional member $25 To order, please specify PSAPM/39N

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770 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

Kac-Moody Algebras THETA FUNCTIONS-BOWDOIN 1987 E. Arbarello, C. De Concini, and V. G. Kac, The infinite wedge Robert C. Gunning and Leon Ehrenpreis, representation and the reciprocity law for algebraic curves Editors Victor G. Kac and Minoru Wakimoto, Exceptional hierarchies of soliton equations (Proceedings of Symposia in Pure Mathematics, Volume 49) Andrew Pressley and Vyjayanthi Chari, Unitary representations of some infinite-dimensional Lie algebras Theta functions have a long and distinguished history and A. Rocha-Caridi, On highest weight and Fock space play a many-faceted and central role in a number of areas representations of the Virasoro algebra of mathematics. Interest in these functions has rekindled in Gregg J. Zuckerman, Modular forms, strings and ghosts recent years as a result of the wide variety of areas in which they have made major contributions. Crossing the lines of Lattice Models semi-simple Lie group theory and nilpotent Lie group theory, Helen Au-Yang and Jacques H. H. Perk, Solution of Hirota's theta functions are relevant to the arithmetic of quadratic discrete-time Toda lattice equation and the critical correlations forms and to partition theory, through which they relate to in the Z -invariant Ising model statistical mechanics and quantum field theory. In addition, Etsuro Date, Michio Jimbo, Tetsuji Miwa, and Masato Okado, they are used to study Riemann surfaces, abelian varieties, Solvable lattice models and solutions of differential equations from physics. In this Atsuo Kuniba, Theta function identities in a series of solvable way, they relate to partial differential equations and algebraic lattice models geometry. Jacques H. H. Perk, Star-triangle equations, quantum Lax pairs, and higher genus curves This two-volume collection contains the proceedings of an Craig A. Tracy, Introduction to exactly solvable models in AMS Summer Research Institute on Theta Functions, held in statistical mechanics July 1987 at Bowdoin College. With papers by some of the Physics top experts in this area, these volumes will provide readers Michio Jimbo, Introduction to holonomic quantum fields for with an excellent overview of the current research in and mathematicians applications of theta functions. Emil Martinec, Quantum field theory: a guide for mathematicians Contents Y. Namikawa, A conformal field theory on Riemann surfaces Infinite Analysis realized as quantized moduli theory on Riemann surfaces Takahiro Kawai, Systems of linear differential equations of A. Neveu, The physics of string theory infinite order: an aspect of infinite analysis Jacobian Varieties Masaki Kashiwara and Takahiro Kawai, A particular partition H. M. Farkas, Schottky-Jung theory of unity: an auxiliary tool in Hodge theory J. Fay, Schottky relations on 2 (c~C) H. P. McKean, Is there an infinite-dimensional algebraic R. C. Gunning, Analytic identities for theta functions geometry? Hints from KDV John B. Little, Translation manifolds and the Schottky problem Motohico Mulase, A correspondence between an infinite Henrik H. Martens, Mappings of closed Riemann surfaces Grassmannian and arbitrary vector bundles on algebraic curves Jose Ma Muiioz Porras, Geometric characterization of M. Sato, The KP hierarchy and infinite-dimensional Grassmann Jacobians and the Schottky equations manifolds Emma Previato and George Wilson, Vector bundles over Integrable systems curves and solutions of the K P equations Mark Adler, Some geometrical techniques in integrable Roy Smith and Robert Varley, Deformations of singular points systems on theta divisors N. Ercolani, Generalized theta functions and homoclinic L. A. Takhtajan, Uniformization, local index theorem, and varieties geometry of the moduli spaces of Riemann surfaces and vector Shirong Lu, Explicit equations for the KP and MKP hierarchies bundles Pierre van Moerbeke, Introduction to algebraic integrable Noriaki Yamawaki, Explicit actions of the theta groups for theta systems and their Pain/eve analysis divisors on Jacobian surfaces Robert L. Sachs, Polynomial r-functions for the AKNS hierarchy Prym Varieties Kanehisa Takasaki, Integrable systems as deformations of Arnaud Beauville, Prym varieties: a survey [)-modules Olivier Debarre, The trisecant conjecture for Pryms Vassil Kanev, Spectral curves, simple Lie algebras, and Prym-Tjurin varieties

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JULY/AUGUST 1989, VOLUME 36, NUMBER 6 771 New AMS Publications

Algebraic Geometry lacopo Barsotti, A new look for thetas THE MARKOFF AND LAGRANGE SPECTRA L. Breen, The cube structure on the determinant bundle Thomas W. Cusick and Mary E. Flahive Michael D. Fried and Helmut Volklein, Unramified Abelian (Mathematical Surveys and Monographs, Volume 30) extensions of Galois covers William L. Hoyt, On twisted Legendre equations and Kummer This book is directed at mathematicians interested in surfaces Diophantine approximation and the theory of quadratic B. Jijtchenko, On embedded tangent and secant varieties of A. forms and the relationship of these subjects to Markoff and projective algebraic varieties Lagrange spectra. The authors have gathered and systemized Modular Forms numerous results from the diverse and scattered literature, Siegfried Becherer, Siegel modular forms and theta series much of which has appeared in rather inaccessible Russian Ching-Li Chai, Arithmetic compactification of the Siegel moduli publications. space a comprehensive overview of the theory of L. Ehrenpreis, Fourier analysis, partial differential equations, Readers will find Lagrange spectra, starting with the origins of and automorphic functions the Markoff and subject in two papers of A. Markoff from 1879-80. Most of Jun-lchi lgusa, Problems on theta functions the that time has occurred in the last 20 years Marvin I. Knopp, On the Fourier coefficients of cusp forms the progress since so, when there has been a resurgence of interest in these having small positive weight or provide an excellent exposition of these John J. Millson, Intersection numbers of cycles on spectra. The authors in addition to presenting many new proofs locally symmetric spaces and Fourier coefficients new developments, various errors in the literature. of holomorphic modular forms in several complex and correcting variables Contents of Riccardo Salvati Manni, Vector-valued modular forms Older results on the Markoff spectrum weight g+~- 1 Vue Lin Lawrence Tong, Some nonzero harmonic forms and Markoff numbers and Markoff forms their geometric duals The Markoff and Lagrange spectra compared Number Theory Hall's ray D. V. Chudnovsky and G. V. Chudnovsky, Transcendental methods and theta-functions Gaps in the spectra Harvey Cohn, Singular moduli and modular equations for The measure of the spectra Fricke's cases The spectra via the modular group N. V. Kuznetsov, The sums of the Kloosterman sums I. I. Piatetski-Shapiro, The existence of Maass cusp forms and Alternative definitions of the spectra Kloosterman sums Facts about continuants Combinatorics Pell equations and automorphs of indefinite quadratic forms K. Aomoto, On the complex Selberg integral George E. Andrews, Mock theta functions 1980 Mathematics Subject Classifications: 11 J06, 11 J04; 11 009, Richard Askey, Orthogonal polynomials and theta functions 11H50, 11J70, 11K55 ISBN 0-8218-1531-8 C. Milne, The multidimensional '¥ sum and Macdonald S. 1 1 ISSN 0076-5376 identities for A~1 l 96 pages (hardcover), July 1989 Individual member $25, List price $42, Subject Classification: OOA 11 1980 Mathematics Institutional member $34 ISBN (Set) 0-8218-1485-0; (Part 1) 0-8218-1483-4; (Part 2) To order, please specify SURV /30N 0-8218-1484-2, LC 89-6723, ISSN 0082-0717 728 pages (part 1); 376 pages (part 2) (hardcover), July 1989 Set: Individual member $89, List price $149, Institutional member $119 Part 1: Individual member $59, List price $99, Institutional member $79 Part 2: Individual member $35, List price $58, Institutional member $46 To order, please specify PSPUM/49N (set), PSPUM/49.1 N (part 1), PSPUM/49.2N (part 2)

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772 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

REPRESENTATION THEORY AND HARMONIC A CENTURY OF MATHEMATICS ANALYSIS ON SEMISIMPLE LIE GROUPS IN AMERICA, Part Ill Paul J. Sally, Jr. and David A. Vogan, Jr., Peter Duren, Editor Editors with the assistance of Richard A. Askey, (Mathematical Surveys and Monographs, Volume 31) Harold M. Edwards, and Uta C. Merzbach (History of Mathematics, Volume 3) This book brings together five papers that have been influential in the study of Lie groups. Though published more than 15 The first volume in the History of Mathematics series was years ago, these papers made fundamental contributions that issued to commemorate the AMS Centennial in 1988. Originally deserve much broader exposure. In addition, the subsequent intended as a single volume, A Century of Mathematics in literature that has subsumed these papers cannot replace the America brought together a range of works-reminiscences, originality and vitality they contain. The editors have provided surveys and expositions, histories of the development a brief introduction to each paper, as well as a synopsis of the of American mathematics, and biographies-by some of major developments which have occurred in the area covered the century's eminent mathematicians and mathematical by each paper. historians. The first volume drew such an enthusiastic response from contributors that the editors decided to extend Included here are the doctoral theses of Arthur, Osborne, and A Century of Mathematics in America to include two more Arthur's thesis is closely related to Trombi's paper Schmid. volumes. insofar as both deal with harmonic analysis on real semisimple Lie groups, and, in particular, analysis on the Schwartz space The present book is the third and final volume in the A of Harish-Chandra. Arthur's thesis is concerned with the Century of Mathematics in America collection. The theme of image under the Fourier transform of the Schwartz space of a the second volume is continued here in articles describing semisimple Lie group of real rank one, while Trombi's paper the mathematics and the mathematical personalities in some provides an expository account of the harmonic analysis of the nation's prominent departments: Johns Hopkins, associated to the decomposition of the Schwartz space Clark, Columbia, MIT, Michigan, Texas, and the Institute for under the regular representation. In his thesis, Osborne Advanced Study. extends the Atiyah-Bott fixed point theorem for elliptic century describes complexes to obtain a fixed point formula for complexes The section on mathematics in the 19th development that are not elliptic. Schmid proves a generalization of the various aspects of this important era in the The article by Borei-Weil theorem concerning an explicit and geometric of mathematical research in this country. on American realization of the irreducible representations of a compact, Parshall and Rowe describes the influence and connected semisimple Lie group. Langlands's fundamental mathematics of two foreign mathematicians, Sylvester same era, but focus paper provides a classification of irreducible, admissible Klein. Cooke and Rickey write about the Hopkins and Clark representations of real reductive Lie groups. on the mathematics departments at Johns Universities, the premier departments in the country during 1980 Mathematics Subject Classification: 22 the 1880s. ISBN 0-8218-1526-1, LC 88-10301 ISSN 0076-5376 Some of the century's great mathematicians are represented 350 pages (hardcover), August 1989 particular, the article on Wiener presents Individual member $53, List price $88, in this volume. In Institutional member $70 a detailed biography of the life and work of this eminent To order, please specify SURV /31 N mathematician. The article on Zygmund describes his strong influence on the mathematical scene of his time and includes his ··family tree·· of thesis students and their students. Also noteworthy is an excellent article on the contributions of black mathematicians. Two articles-one by Mac Lane and one by Kelley-describe some of the work of American mathematicians in World War II. Articles on function algebras, function theory, probability, statistics, actuarial science, and the study of mathematical history provide a perspective on the range of scholarly activities of the mathematical sciences community.

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JULY/AUGUST 1989. VOLUME 36. NUMBER 6 773 New AMS Publications

Mathematicians, historians of science, and students alike J. L. Kelley, Once over lightly will find this book illuminating and rewarding. As a single Saunders Mac Lane, Mathematicians in World War II: The volume or part of this fine collection, the book makes an group at Columbia excellent addition to a library collection. That the lessons of Saunders Mac Lane, The education of Ph.D's in mathematics the past can guide the resolution of future problems makes Everett Pitcher, Off the record this book-and the entire series-important reading for all Probability, Statistics, and Actuarial Science who are concerned with the development of mathematics. Stephen M. Stigler, Mathematical statistics in the early states Contents [Reprint] The Nineteenth Century J. L. Doob, William Feller and twentieth century probability Karen V. H. Parshall and David E. Rowe, American [Reprint] mathematics comes of age, 1875-1900 Cecil C. Craig, Early days in statistics at Michigan [Reprint] Roger Cooke and V. Frederick Rickey, W. E. Story of Hopkins Churchill Eisenhart, S. S. Wilks's Princeton appointment and and Clark statistics at Princeton before Wilks George M. Rosenstein, Jr., The best method. American Morris H. DeGroot, A conversation with David Blackwell calculus textbooks of the nineteenth century [Reprint] Charlotte Angas Scott, Edwards' differential calculus [Reprint] Cecil J. Nesbitt, Personal reflections on actuarial science in North America from 1900 Mathematics at American Institutions History of Mathematics Armand Borel, The School of Mathematics at the Institute for Advanced Study Uta C. Merzbach, Article on American historians of mathematics Edgar R. Lorch, Mathematics at Columbia during adolescence Frederic F. Burchsted, Sources for the history of mathematics Dirk J. Struik, The MIT department of mathematics during its in the archives of American mathematics first seventy-five years. Some recollections 1980 Mathematics Subject Classifications: 01, 00 Wilfred Kaplan, Mathematics at the University of Michigan ISBN 0-8218-0136-8, LC 88-22155 Raymond L. Wilder, Reminiscences of mathematics at ISSN 0899-2428 400 pages (hardcover), August 1989 Michigan Individual member $45, List price $75, Albert C. Lewis, The building of the University of Texas Institutional member $60 mathematics faculty, 1883-1938 To order, please specify HMATH/3N Mathematics and Mathematicians Combination offer: A Century of Mathematics in America, Patricia Clark Kenschaft, Charlotte Angas Scott (1858-1931) Parts I, II, and Ill (HMATH/1 N, HMATH/2N, and HMATH/3N) as a set. ISBN 0-8218-0138-4 [Reprint] Individual member $109, List price $182, Institutional member $146 R. E. Langer and M. H. Ingraham, Edward Burr Van Vleck, To order, please specify HMATHSET /N 1863-1943 [Reprint] R. L. Wilder, The Mathematical Work of R. L. Moore; Its Combination offer: A Century of Mathematics in America, background, nature, and influence [Reprint] Parts II and Ill (HMATH/2N and HMATH/3N) as a set. Louise S. Grinstein and Paul J. Campbell, Anna Johnson Pel/ ISBN 0-8218-0152-X Individual member $79, List price $131, Institutional member $105 Wheeler (1883-1966) [Reprint] To order, please specify HMATHSET /2/3N Pesi Masani, Norbert Wiener: A survey of a fragment of his life and work Ronald Coifman and Robert Strichartz, The school of Antoni Zygmund INTRODUCTION TO ARRANGEMENTS Richard Askey, Handbooks of special functions Solomon Feferman, Patrick Suppes, and Jon Barwise, Peter Orlik Commemorative meeting for Alfred Tarski (CBMS Regional Conference Series, Constance Reid with Raphael M. Robinson, Julia Bowman Number 72) Robinson (1919-1985) [Reprint] John Wermer, Function algebras in the fifties and sixties An arrangement of hyperplanes is a finite collection Saunders Mac Lane, Addendum: Concepts and categories in of codimension one subspaces in a finite-dimensional perspective vector space. Arrangements occur in several branches of mathematics: combinatorics, braids, hypergeometric Surveys and Recollections functions, reflection groups, singularities, and coding theory. L. V. Ahlfors, The joy of function theory James A. Donaldson, Black Americans in mathematics

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774 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

This book, based on lectures presented by the author at positive operators, the characterization of homogeneous the CBMS Regional Conference held at Northern Arizona measure algebras, and disintegrations. In addition, there University in June 1988, provides the first introduction to the are research papers in ergodic theory, measure theory, study of the topology of the complement of an arrangement descriptive set theory, and the dynamics of measurable maps. in a complex vector space. The author discusses basic A number of the results in these papers are directly related to combinatorial tools, as well as algebras associated to the Stone's work. arrangement, differential forms, the cohomology and the Contents homotopy type of the complement, free arrangements, Thomas E. Armstrong, lnvariance of Renyi full conditional and reflection arrangements. With a particular emphasis probabilities under group actions on topological aspects, this book provides an excellent Joseph Auslander and Nelson Markley, Proximal roots of introduction to current activity in this area. minimal homeomorphisms Contents E. Barone and K. P. S. Bhaskara Rao, On the Los-Marczewski Combinatorics extension of charges and its uniqueness Jack B. Brown, Marczewski null sets and intermediate Baire Combinatorial algebras order Lattice homology Maxim R. Burke, Fixed points of automorphisms of IN 1 J. R. Choksi, S. J. Eigen, J. C. Oxtoby, and V. S. Prasad, The The complement M(A) work of Dorothy Maharam on measure theory, ergodic theory, The cohomology of M(A) and category algebras J. R. Choksi, S. J. Eigen, and V. S. Prasad, Ergodic theory on Differential forms homogeneous measure algebras revisited The topology of M(A) J. P. R. Christensen and C. Rasmussen, Axiomatic characterizations of inhomogeneous Poisson point processes Free arrangements (IPPP ), their mixtures and random translations Reflection arrangements John Coffey, Uniformly distributed D-sequences G. A. Edgar and L. Sucheston, On maximal inequalitites in 1980 Mathematics Subject Classifications: 57N65, 05835, 32C40, 57R45; 14F40, 14J99, 51A05 Orlicz spaces ISBN 0-8218-0723-6, LC 89-14893 Stanley J. Eigen and Cesar E. Silva, Finite full sets in 2-stack ISSN 0160-7642 structures 104 pages (softcover), August 1989 Nathaniel A. Friedman, Partial mixing, partial rigidity, and price $18 All individuals $11, List factors To order, please specify CBMS/72N Siegfried Graf and R. Daniel Mauldin, A classification of disintegrations of measures Jane M. Hawkins, Ratio sets of endomorphisms which preserve MEASURE AND MEASURABLE DYNAMICS a probability measure R. Daniel Mauldin, R. M. Shortt, and Cesar E. Jonathan L. King, An obstruction to K-fold splitting Silva, Editors W. A. J. Luxemburg, The work of Dorothy Maharam on kernel (Contemporary Mathematics, Volume 94) representations of linear operators R. Daniel Mauldin, One-to-one selections and orthogonal transition kernels Dorothy Maharam Stone's (1917-) contributions to operators M. G. Nadkarni, Descriptive ergodic theory and measure algebras has had a profound influence on this William Parry, Decoding with two independent processes area of research. Her career, which has spanned nearly half a William Parry, Temporal and spatial distribution of closed century, includes 40 research publications, some of them as orbits of hyperbolic dynamical systems recent as 1987. A Ph.D. student of Anna Pell Wheeler at Bryn Karl Petersen, Nonlinear sampling of a flow Mawr College, Stone has been an active force in mathematics S. T. Rachev and R. M. Shortt, Classification problem for research and various professional activities. probability metrics This volume contains the proceedings of the Conference on D. Ramachandran, A new proof of Hopf's theorem on invariant Measure and Measurable Dynamics, held in honor of Stone at measures the University of Rochester in September 1987. The papers in Daniel J. Rudolph, Markov tilings of IR" and representations of this collection represent contributions from some of the top IR" actions experts in this field. Stone's work is surveyed in a number of R. M. Shortt, Groups of measurable automorphisms for spaces articles which highlight her foundational results concerning of finite type

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JULY/AUGUST 1989, VOLUME 36, NUMBER 6 775 New AMS Publications

Michel Talagrand, A "regular oscillation" property of stable Aimed at the level of a beginning graduate student or sets of measurable functions advanced undergraduate, this book could serve well as a D. Tanny, A new proof of the strong law without first moment supplementary text for a course in finite field theory. Benjamin Weiss, Countable generators in dynamics-universal Contents minimal models A survey of some finite field theory 1980 Mathematics Subject Classifications: 28A05, 28C10, 60A05; 46A50, 03E05 Algebraic extensions of finite fields ISBN 0-8218-5099-7, LC 89-14914 ISSN 0271-4132 Iterated presentations and explicit bases July 1989 336 pages (softcover), Polynomials and polynomial functions Individual member $29, List price $48, Institutional member $38 Two applications To order, please specify CONM/94N 1980 Mathematics Subject Classifications: 12E20, 12F05, 12E05, 11T06, 11T30, 12-02; 05B15, 15A33, 12E10 ISBN 0-8218-5101-2, LC 89-14891 INFINITE ALGEBRAIC EXTENSIONS OF ISSN 0271-4132 1 04 pages ( softcover), July 1989 FINITE FIELDS Individual member $14, List price $24, Joel V. Brawley and George E. Schnibben Institutional member $19 (Contemporary Mathematics, Volume 95) To order, please specify CONM/95N

Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important BLASCHKE'S ROLLING THEOREM IN IRN applications in a number of diverse areas such as electronic J. N. Brooks and J. B. Strantzen communications, coding theory, combinatorics, designs, finite (Memoirs of the AMS, Number 405) geometries, cryptography, and other portions of discrete mathematics. In addition, a number of recent books have been Blaschke's rolling theorem in its original form dealt with the devoted to the subject. Despite the resurgence in interest, it problem of finding conditions under which a ball 0 would roll is not widely known that many results concerning finite fields 1 freely inside a compact convex set 0 with nonempty interior. have natural generalizations to abritrary algebraic extensions 2 More precisely, 0 is said to roll freely inside 0 if at each of finite fields. The purpose of this book is to describe these 1 2 frontier point of 0 there is a translation t such that t( 0 ) generalizations. 2 1 and 0 2 share a common tangent hyperplane at that point, and After an introductory chapter surveying pertinent results such that t(01) is contained in 0 2 . W. J. Firey introduced a about finite fields, the book describes the lattice structure of natural extension of the concept of free rolling whereby 0 1 is fields between the finite field GF(q) and its algebraic closure also a compact set. The aim of this book is to examine the r(q). The authors introduce a notion, due to Steinitz, of an problem in full generality in IR". extended positive integer N which includes each ordinary The book is divided into two parts. Part I is primarily positive integer n as a special case. With the aid of these concerned with producing local conditions sufficient to ensure Steinitz numbers, the algebraic extensions of GF(q) are that an arbitrary open convex set 8 1 is a subset of another represented by symbols of the form GF(qN). When N is an arbitrary open convex set 8 2 . These self-contained results ordinary integer this notation agrees with the usual notation n, follow contributions on the same theme by others, such as for a dimension extension of GF(q). The authors GF(q") n Koutroufiotis, Rauch, and Delgado. Part I also sets up the then show that many of the finite field results concerning machinery for Part II, where necessary and sufficient local GF(q") are also true for GF(qN). One chapter is devoted conditions are found for the general free rolling problem. to giving explicit algorithms for computing in several of the Part II also contains information regarding the nature of the infinite fields GF(qN) using the notion of an explicit basis for intersection of the frontiers of 8 1 and 8 2 , given that they GF(qN) over GF(q). Another chapter considers polynomials satisfy the conditions of containment derived in Part I. and polynomial-like functions on GF(qN) and contains a Contents description of several classes of permutation polynomials, including the q-polynomials and the Dickson polynomials. Also Local conditions for containment included is a brief chapter describing two of many potential Main result and sketch proof applications. The main result for curves Convex Regions in IR"

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776 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

The smooth case: applications to differential geometry ANR-fibrations: Basic lemmas Common boundaries of touching convex regions and Homeomorphism theory in Q-manifold bundles Blaschke's rolling theorem 1980 Mathematics Subject Classifications: 55R05, 55R1 0, 57N20; Existence of hyperplanes of support 54C55,57R99,58B05, 58099 Common boundaries results ISBN 0-8218-2471-6, LC 89-14913 Application to spheres and Blaschke's rolling theorem ISSN 0065-9266 75 pages (softcover), July 1989 1980 Mathematics Subject Classifications: 52A20; 51 N20 Individual member $9, List price $15, ISBN 0-8218-2466-X, LC 89-7017 Institutional member $12 ISSN 0065-9266 To order, please specify MEM0/406N 101 pages (softcover), July 1989 Individual member $10, List price $17, Institutional member $14 To order, please specify MEM0/405N REPRESENTATIONS DE LONGUEUR FINIE DES GROUPES DIE LIE RESOLUBLES Cloux FIBRATIONS AND BUNDLES WITH HILBERT Fokko du (Memoirs of the AMS, Number 407) CUBE MANIFOLD FIBERS H. Torunczyk and J. West The theory of finite-length (topological) representations of (Memoirs of the AMS, Number 406) Lie groups seems to hold a great deal of promise as one of the directions that representation theory might take in the Hilbert cube manifolds arise in a host of different contexts: ··post-classification" era. This book presents the theory of simultaneous stabilization of m-manifolds, polyhedra, finite-length representations of a solvable, type I Lie group G. CW-complexes, and absolute neighborhood retracts via The geometrical significance of this problem is explained in Cartesian products, function spaces and hyperspaces. These the framework of noncommutative differential geometry. In manifolds carry a great deal of information relating to the order to arrive at a satisfactory theory, the author introduces stabilized objects, such as simple-homotopy type. In several the concept of a ··schwartz space" for an irreducible unitary places, fibrations with Hilbert cube manifold fibers have come representation E of G. The computation of the appropriate up or seem likely to be used in the near future .. Ext-groups is reduced to a purely algebraic problem, which makes it possible to determine them explicitly in many This book analyzes Hurewicz fibrations over paracompact examples. Some properties of "g-finite cohomology," which spaces with locally compact absolute neighborhood retract should prove useful in other contexts, are developed in an fibers. The authors develop a fibred homeomorphism theory Appendix. and show that if the fibers are compact or the bases are semi-locally contractible, then a fibred version of Torunczyk's Representation theorists and specialists in operator algebras, characterization of Hilbert cube manifolds detects the locally as well as algebraists, will appreciate this book for the way trivial Hilbert cube manifold bundles. A corollary is that it highlights the geometrical significance of the theory of Hurewicz fibrations over CW-complexes with Hilbert cube finite-length modules. Readers will gain an understanding of manifold fibers are bundles. The authors provide several the problems and methods connected to the concept of a illustrative examples of non-bundle Hilbert cube manifold Taylor series in noncommutative differential geometry. fibrations. Contents Contents Le probleme des modules de longueur finie Characterization of Q-manifold bundles with compact fibers Vecteurs de Schwartz d'une representation unitaire Q-manifold bundles with non-compact fibers irreductible A non-trivial Hurewicz fibration Q-+ Q-+ Q Calcul des Ext" a l'aide d'operateurs differentials A trivial fibration with convex fibers Un modele algebrique pour Ia categorie ExtG(Es} Fibrations that satisfy fibred general position Exemples Fibred products of Hurewicz fibrations Q -+ Q -+ Q Appendice: Foncteurs derives des vecteurs g-finis A general position fibration that is not a bundle Fibred homeomorphism theory for general position fibrations

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JULY/AUGUST 1989, VOLUME 36, NUMBER 6 777 New AMS Publications

1980 Mathematics Subject Classifications: 22E25; 18E1 0, 17B30 The natural structures that occur give rise to continuous ISBN 0-8218-2470-8, LC 89-14898 generalizations of Fock space, and the numerical invariants ISSN 0065-9266 attached to them are a quantized form of the classical 78 pages (softcover). July 1989 Fredholm index. Individual member $9, List price $15, Institutional member $12 To order, please specify MEM0/407N Contents Product systems Semigroups of endomorphisms TWO-DIMENSIONAL TAME AND MAXIMAL Index and outer conjugacy ORDERS OF FINITE REPRESENTATION TYPE The covariance function The dimension of a product system ldun Reiten and Michel Van den Bergh (Memoirs of the AMS, Number 408) Divisible product systems Applications This book presents a classification of certain algebras of finite representation type. More specifically, letT= k[[x1 , x2]] be a Automorphisms series ring in two variables over an algebraically closed power 1980 Mathematics Subject Classifications: 46L40; 81 E05 field k of characteristic zero, and let A :::J T be a T -algebra ISBN 0-8218-2472-2, LC 89-6998 which is a finitely-generated T-module. The authors classify ISSN 0065-9266 the A such that the category ref A of finitely-generated 66 pages ( softcover), July 1989 A-modules has only a finite number of indecomposable Individual member $9, List price $15, Institutional member $12 of their Auslander-Reiten quivers. Such an modules, in terms To order, please specify MEM0/409N indecomposable T -algebra of finite representation type must be a tame order in a simple algebra A The authors show that the length of a maximal chain of a tower of tame overorders of A is given by the structure of the Auslander-Reiten quiver INTRODUCTION TO ALGEBRAIC CURVES f of A, as the rank of the Grothendieck group of f (which the authors define). In particular, this result gives a criterion for A Phillip A. Griffiths Volume 76) to be a maximal order, and this criterion is applied to obtain a (Translations of Mathematical Monographs, classification of maximal orders of finite representation type in division rings. Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion Contents of algebraic geometry. However, the majority of books Tame and maximal orders and their Grothendieck groups written on the subject discuss algebraic curves and compact The associated graded orders Riemann surfaces separately, as parts of distinct general The lattice of overlying orders theories. Most texts and university courses on curve theory Maximal orders of finite representation type generally conclude with the Riemann-Roch theorem, despite Passing from the graded to the complete case the fact that this theorem is the gateway to some of the most fascinating results in the theory of algebraic curves. 1980 Mathematics Subject Classifications: 16A 18, 16A48; 16A64 ISBN 0-8218-2469-4, LC 89-15024 This book is based on a six-week series of lectures presented ISSN 0065-9266 undergraduates and 72 pages (softcover), July 1989 by the author to third- and fourth-year Individual member $9, List price $15, graduate students at Beijing University in 1982. The lectures Institutional member $12 began with minimal technical requirements (a working To order, please specify MEM0/408N knowledge of elementary complex function theory and algebra together with some exposure to topology of compact surfaces) and proceeded directly to the Riemann-Roch and Abel theorems. This book differs from a number of CONTINUOUS ANALOGUES OF FOCK SPACE recent books on this subject in that it combines analytic and William Arveson geometric methods at the outset, so that the reader can (Memoirs of the AMS, Number 409) grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative This book presents a new approach to the classification algebra are not covered here, the book provides a solid theory of semigroups of endomorphisms of type I factors. foundation to proceed to more advanced texts in general

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778 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

algebraic geometry, complex manifolds, and Riemann ISBN 0-8218-4529-2, LC 89-6904 surfaces, as well as algebraic curves. Containing numerous ISSN 0065-9282 exercises and two exams, this book would make an excellent 245 pages (hardcover), July 1989 Individual member $59, List price $99, introductory text. Institutional member $79 Contents To order, please specify MMON0/77N Fundamental concepts The normalization theorem and its applications The Riemann-Roch theorem THIRTEEN PAPERS TRANSLATED Applications of the Riemann-Roch theorem FROM THE RUSSIAN S.D. Berman, K. Buzasi, V. K. Dubovoi, S. Yu. Abel's theorem and its applications Favorov, I. S. Kats, I. V. 1980 Mathematics Subject Classifications: 14, 14H ISBN 0-8218-4530-6 Lobarev, V. E. Lyantse, ISSN 0065-9282 Yu. I. Lyubarskii, Kh. B. Maiorga, 500 pages (hardcover), July 1989 A. A. Nersesyan, Individual member $56, List price $93, Institutional member $74 N. P. Pustovoitov, G. N. Zholtkevich To order, please specify MMON0/76N (American Mathematical Society Translations, Series 2, Volume 144)

This volume contains papers ranging over a broad variety VARIATIONAL PRINCIPLES FOR of topics, including group representations, HP-classes, NONPOTENTIAL OPERATORS approximation of functions, entire functions, the Laplace V. M. Filippov operator, and von Neumann algebras. (Translations of Mathematical Monographs, Volume 77) Contents This book develops a variational method for solving linear S. D. Berman and K. Buzasi, On modules over group algebras equations with B-symmetric and B-positive operators of groups containing an infinite cyclic subgroup of finite index and generalizes the method to nonlinear equations with S. D. Berman and K. Buzasi, Description of all finite­ nonpotential operators. The author carries out a constructive dimensional real representations of groups containing an extension of the variational method to ··nonvariational"" infinite cyclic subgroup of finite index equations (including parabolic equations) in classes of I. S. Kats, Connection between integral characteristics of functionals which differ from the Euler-Lagrange functionals. growth of entire functions and distributions of their zeros In this connection, some new functions spaces are considered. Yu. I. Lyubarskii, Representation of functions from HP in a Intended for mathematicians working in the areas of functional half-plane, and some of its applications analysis and differential equations, this book would also V. K. Dubovoi, Indefinite metric in Schur's interpolation problem prove useful for researchers in other areas and students in for analytic functions. I advanced courses who use variational methods in solving V. K. Dubovoi, Indefinite metric in Schur's interpolation problem linear and nonlinear boundary value problems in continuum for analytic functions. II mechanics and theoretical physics. A. A. Nersesyan, On uniform and tangential approximation by meromorphic functions Contents S. Yu. Favorov, On entire functions of completely regular growth of several variables Variational problems for linear equations with 8-symmetric V. E. Lyantse and Kh. B. Maiorga, On the theory of the and B-positive operators one-point boundary value problem for the Laplace operator. 1 Classes of functionals and function spaces v_ E- Lyantse and Kh. B. Maiorga, On the theory of the one-point boundary value problem for the Laplace operator. 11 Construction and investigation of variational principles for linear boundary value problems G. N. Zholtkevich, On the cohomology of von Neumann algebras Variational principles for nonlinear equations N. A- Pustovoitov, On approximate algebraic stability criteria, 1980 Mathematics Subject Classifications: 35A15, 47A50, 47H17; numerical-analytical methods for investigating the dynamics 46E35 and stability of complex systems

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JULY/AUGUST 1989, VOLUME 36. NUMBER 6 779 New AMS Publications

I. V. Lobarev, Eigenvalues and eigenfunctions of the Peierls result, he points to the advantages of various proofs and equation gives some wry commentary about why students prefer some proofs of the result over others. Extending the discussion 20C07, 20C32, 30015, 1980 Mathematics Subject Classifications: from Cauchy's proof of I'H6pital's rule, Boas discusses the 30020,30055, 30E10, 32A15, 34020,35J05,35J25, 45C05, 45K05, 46E15, 46L10, 65F15, 65H10; 15A52,46L35,47F05, 65H15 fact that the role of integration can be played by a general ISBN 0-8218-3125-9 linear operator that is the inverse of a differential operator, ISSN 0065-9290 such as a Laplace transform. He also points to a number of 152 pages (hardcover), July 1989 open topics of investigation in this area, showing how an $35, List price $58, Individual member rule can lead to the frontiers Institutional member $46 elementary result like I'H6pital's To order, please specify TRANS2/144N of mathematical research. 1980 Mathematics Subject Classifications: 26A06, 01 A45, 01 A50 VHS format, approx. one hour, 1989 Price $59 EUGENE ISAACSON, DEDICATION To order, please specify VIOBOAS/N Special Issue, Mathematics of Computation

This special issue of the journal Mathematics of Computation SOCIETE MATHEMATIQUE DE FRANCE, ASTERISQUE (Volume 52, Number 186, April 1989) is dedicated to the distinguished numerical analyst, Eugene Isaacson. The papers The AMS distributes Asterisque only in the U.S., Canada, and Mexico. in this special volume represent contributions by a range Orders from other countries should be sent to the SMF, B.P. 126-05, of well-established numerical analysts as well as younger 75226 Paris Cedex 05, France, or to OFFILIB, 48 rue Gay-Lussac, members of either AMS or researchers in the field, many of whom have been associates 75240 Paris Cedex 05, France. Individual SMF are entitled to the member price. (ISSN 0303-1179) of Isaacson in some capacity. As an Associate Editor since 1975 and Chairman of the Editorial Board from 1966 to 1975, Isaacson has made many important contributions to Mathematics of Computation, POINT SETS IN PROJECTIVE SPACES AND and his wise council has proven invaluable to the success THETA FUNCTIONS of the journal. Isaacson was a student of K. 0. Friedrichs I. Dolgachev and D. Ortland and worked primarily in the area of fluid flow and gas (Asterisque, Number 165) dynamics, with an emphasis on the numerical solution of partial differential equations. He has been on the faculty of This volume is concerned with some topics in classical the Courant Institute for most of his career and played an algebraic geometry related to the theory of invariants of important role in developing the Institute's computational finite ordered point sets in projective spaces, Cremona activities and computing facilities. With his former colleague, transformations, and theta functions. Most of the material can Herbert B. Keller, Isaacson wrote the influential text Analysis be found in the classical literature, especially, in A. Coble's of Numerical Methods. book ""Algebraic geometry and theta functions:· However, we 1980 Mathematics Subject Classifications: 65; 68 treat this subject from a modern point of view. Included are ISSN 0025-5718 discussions of such famous classical constructions as the set 721 pages ( softcover), April 1989 of 27 lines on a cubic surface, the set of 28 bitangents to a List price $50, Individual member $30, plane quartic curve, Del Pezzo and Kummer surfaces and Institutional member $40 To order, please specify ISAACSON/N their higher-dimensional analogs, nets of quadrics and Cayley dianode surfaces associated to them, Bertini and Geiser birational involutions. This is interrelated with such modern topics as geometric quotients, standard tableaux, infinite INDETERMINATE FORMS REVISITED root systems and their Weyl groups, group representations, Ralph P. Boas automorphism groups of rational surfaces, moduli spaces of abelian varieties, and others. In this insightful videotaped lecture, Ralph Boas, a well-known 14 mathematics, brings his more than 50 years 1980 Mathematics Subject Classification: figure in American ISSN 0303-1179 of mathematical experience to bear on questions growing out 212 pages (softcover), 1988 of the seemingly simple theorem of I'H6pital of elementary Individual AMS or SMF member $17, List price $24 calculus. As he sketches some of the history of this famous To order, please specify AST /165N

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780 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Miscellaneous

Personal Items a member of the Society for 59 State University, died on April 25, years. 1989, at the age of 78. He was Shimshon Avram Amitsur, of He­ H. W. Brinkmann, Professor a member of the Society for 25 brew University, was elected an Emeritus of Swarthmore College, years. Honorary Member of the London died on February 4, 1989. He was John W. Querry, of Raleigh, Mathematical Society. a member of the Society for 66 North Carolina, died on October Evelyn Boyd Granville, retired years. 11, 1988, at the age of 85. He was from California State University, Zauri Chanturiya, Tbilisi State a member of the Society for 55 Los Angeles, and currently teach­ University, died on February 20, years. ing at a small private college in 1989, at the age of 49. He was Veldanda V. Rao, University Texas, was awarded an honorary a member of the Society for 12 of Regina, died on February 27, doctor of science degree by Smith years. 1989, at the age of 58. He was College. Emil Grosswald, Professor a member of the Society for 24 Kazuyuki Hatada, Associate Emeritus of Temple University, years. Professor at Gifu University, Gifu died on April 11, 1989, at the Charles H. W. Sedgewick, of City, Japan, was awarded the In­ age of 76. He was a member of Dunedin, Florida, died on Novem­ ternational Cultural Diploma of the Society for 41 years. (See the ber 5, 1988, at the age of 86. He Honor and The Commemorative News and Announcements section was a member of the Society for Medal of Honor (Gold) by the of this issue of Notices.) 59 years. American Biographical Institute in Gottfried Kothe, Professor Abraham Seidenberg, Univer­ 1988. Emeritus of Johann-Wolfgang­ sity of California, Berkeley, died Chuan-Chih Hsiung, professor Goethe UniversiHi.t, died on April on May 3, 1988, at the age of 71. emeritus of mathematics, has had 30, 1989, at the age of 83. He He was a member of the Society an endowment fund established in was a member of the Society for for 49 years. his honor at Lehigh University. 32 years. (See the News and An­ Stefan E. Warschawski, Pro­ The C. C. Hsiung Fund for the nouncements section of this issue fessor Emeritus of the University Advancement of Mathematics is of Notices.) of California, San Diego, died on result of his excellent work the Robert R. McCready, retired May 5, 1989, at the age of 85. He over the last 20 years on Lehigh Professor of Dallas Baptist Uni­ was a member of the Society for University's Journal ofDifferential versity, died on February 2, 1989, 55 years. (See the News and An­ which was started by Geometry, at the age of 67. He was a member nouncements section of this issue Hsiung in 1967. The fund was of the Society for 34 years. of Notices.) made possible by proceeds from Edward J. McShane, Professor Hassler Whitney, Professor the journal over the past 22 years. Emeritus of the University of Vir­ Emeritus of the Institute for Ad­ ginia, died on June 1, 1989 at the vanced Study, died on May 10, age of 85. He was a member of 1989, at the age of 82. He was Deaths the Society for 61 years. (See the a member of the Society for 60 Robert L. Blair, Ohio University, News and Announcements section years. (See the News and An­ died on November 18, 1988, at of this issue of Notices). nouncements section of this issue the age of 61. He was a member Luna I. Mishoe, Delaware State of Notices.) of the Society for 3 7 years. College, died on January 16, 1989, Norbert J. Wielenberg, Univer­ Samuel Borofsky, Professor at the age of 72. He was a member sity of Wisconsin-Parkside,died on Emeritus of Brooklyn College of the Society for 42 years. May 2, 1989, at the age of 43. He (CUNY), died on November 16, Howard M. Nahikian, Profes­ was a member of the Society for 1988 at the age of 82. He was sor Emeritus of North Carolina 18 years.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 781 Visiting Mathematicians (Supplementary List)

The list of visiting mathematicians includes both foreign mathematicians visiting in the United States and Canada, and Americans visiting abroad. Note that there are two separate lists.

American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of Special Interest Period of Visit Baker, Mark D. (U.S.A.) Institut des Hautes Etudes Topology 9/89- 8/90 Scientifiques, France Baukston, Paul (U.S.A.) Queen Mary College; University Logic; Topology 1/90- 6/90 of London, United Kingdom Hemminger, Robert L. University of Otago, New Zealand Graph Theory 9/89- 8/90 (U.S.A.) Penner, Robert (U.S.A.) Universite Louis Pasteur, France Geometry 1/90- 6/90 Yandell, Brian (U.S.A.) Glasgow, United Kingdom; Statistics 1/90- 5/90 University of Strathclyde, United Kingdom

Visiting Foreign Mathematicians Boxler, Petra (West University of Southern California Dynamical Systems 9/89- 6/90 Germany) Braun, Ami (Israel) University of Southern California Ring Theory 9/89- 6/90 Chen, T-G (Taiwan) University of Toronto Several Complex Variables 7/89- 7/90 Corrector, Luis-Jaime (West University of Notre Dame Model Theory of Groups 8/89- 5/90 Germany) Dontchev, Asen (Bulgaria) University of Florida Optimal Control 1/90- 4/90 Gehrke, Mai (Denmark) Vanderbilt University Algebra 9/88- 8/90 Ghosh, Jayanta K. (India) Purdue University Decision Theory, Bayesian 7/89- 12/89 Analysis Giordano, Thierry University of Ottawa Algebras of Operators 4/89- 10/89 (Switzerland) Goncalves, Adilson (Brazil) University of Florida Groups & Geometry 8/89- 12/89 Gould, Jeremy (Wales) University of Ottawa Operators Algebras 10/89- 10/90 Hee, J.-Y. (France) University of Ottawa Algebra 6/89- 7/89 Jarrold, Timothy (England) University of Cincinnati Ring Theory 9/89- 6/90 Kozniewski, Tadeusz University of Notre Dame Topology 8/89- 5/90 (Poland) Lazar, A. J. (Israel) University of Cincinnati Functional Analysis 9/89- 1/90 Lazar, Aldo Joram (Israel) University of Georgia Analysis 1/89- 6/90 Lee, J. P. (Korea) University of Toronto Operator Algebras 7/89- 6/90 Lillest0l, Jostein (Norway) University of Wisconsin-Madison Statistics 7/89- 6/90 Lombard, Frederick (South Texas A&M University Statistics 9/89- 12/89 Africa) Maitra, Ashok (India) University of Minnesota Statistics 9/89- 6/90 Martelotti, A. (Italy) University of Florida Probability Theory 9/89- 10/89

782 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Visiting Mathematicians

Name and Home Countr.y Host Institution Field of S2ecial Interest Period of Visit Mogilski, Jerzy (Poland) University of Alabama Topology 8/89- 5/90 O'Hagan, Anthony Purdue University Bayesian Statistics 1/90- 5/90 (England) Opic, Bohumir University of Alabama Differential Equations 1/90- 5/90 (Czechoslavakia) Osborne, Michael (Australia) Texas A&M University Statistics 9/89- 12/89 Reents, Georg (West University of Florida Mathematical Physics 8/89 - 12/89 Germany) Royle, Gordon F. (Wales) Vanderbilt University Combinatorics 9/89- 8/91 Shen, C-K. {Taiwan) University of Toronto Differential Geometry 8/89- 8/90 Sigrist, F. (Switzerland) University of British Columbia Algebraic Topology 8/89- 8/90 Simanyi, Nandor (Hungary) University of Southern California Dynamical Systems 9/89- 6/90 Smith, Murray (New Purdue University Statistics; Bayesian Analysis 8/89- 5/90 Zealand) Sokolowski, J. (Poland) University of Florida Probability Theory 1/90- 2/90 Soltani, Ahmad {Iran) University of Ottawa Probability 9/89- 8/90 Stepanov, Vladimir University of Alabama Differential Equations l/90- 5/90 (U.S.S.R.) Tardive!, V. (France) University of British Columbia 8/89 - 12/89 Tougeron, Cl. (France) University of Toronto Analytical Geometry 1/90- 6/90 Traczyk, P. (Poland) University of Toronto Topology of Manifolds 9/89- 8/90 Triebel, Hans (German University of Alabama Differential Equations 1/90- 5/90 Democratic Republic) Vaienti, Sandro {Italy) University of Southern California Dynamical Systems 9/89- 6/90 Wlodzimierz, J. Charatonik West Virginia University Topology 8/88- 5/90 (Poland) Wood, Graham R. (New University of Wisconsin-Madison Statistics 8/89- 5/90 Zealand) Yoshino, T. (Japan) University of Toronto Operator Theory 3/89- 1/90 Zhang, Ji Ping (People's University of Florida Algebra 8/89- 4/90 Republic of China)

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 LC 88-39032 an uncountable homogeneous set? ISBN 0-8218-5091-1, an uncountable set have 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 probl-:!ms 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 S2. 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 S3. undergraduate student. The book may also be of interest SlOO 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.

JULY /AUGUST 1989, VOLUME 36, NUMBER 6 783 Reciprocity Agreements

Asia The American Mathematical Society has "reciprocity agree­ ments" with a number of mathematical organizations around ·Allahabad Mathematical Society the world. A current list appears below. Apply to: P. Srivastava, Secretary, Allahabad Mathemat­ These Reciprocity Agreements provide for reduced dues for members of these organizations who choose to join the AMS ical Society, 10, C.S.P. Singh Marg, Allahabad-211 001, and who reside outside of the U.S. and Canada. Reciprocally, India. members of the AMS who reside in the U.S. or Canada may join Dues: US $20 (annual), US $150 (life); payable to these organizations at a reduced rate. Summaries of the priv­ Allahabad Mathematical Society. ileges available to AMS members who join under the terms of Privileges: Indian Journal of Mathematics. reciprocity agreements are given on the following pages. Mem­ bers of these organizations who join the AMS as reciprocity Officers: Vachaspati (President), V. Kannan, B.S. Yadav members enjoy all the privileges available to ordinary mem­ (Vice-President), K. K. Azad (Treasurer), P. Srivastava bers of the Society. AMS dues for reciprocity members are $44 (Secretary). for 1989 and $46 for 1990. Each organization was asked to review and update its listing in the Spring. An asterisk(*) after the name of an organization indicates that no response to this Calcutta Mathematical Society* request had been received when the August Notices went to Apply to: U. Basu, Secretary, Calcutta Mathematical press. A disc (•) before the name of an organization indicates that application forms for that organization may be obtained Society, 92, Acharya Prafulla Chandra Road, Calcutta by writing the American Mathematical Society, P.O. Box 6248, 700 009, India. Providence, Rhode Island 02940. Dues: $2; payable to U. Basu, Secretary. Privileges: News Bulletin (free of cost). Officers: M. Dutta (President), P. C. Vaidya, B. R. Bhonsle, F. Harary, L. Debnath, S. P. Bandyopadhyay, (Vice-Presidents), B. K. Datta, (Treasurer), U. Basu (Secretary). Africa •Nigerian Mathematical Society* Indian Mathematical Society Apply to: Christopher 0. Imoru (Secretary), Nigerian Apply to: S. P. Arya, General Secretary, Indian Mathe­ Mathematical Society, Department of Mathematics, matical Society, Department of Mathematics, Maitreyi University of Ife, Ile-Ife, Nigeria. College, Bapu Dham Complex, Chanakyapuri, New Dues: $10; payable to the Treasurer, Nigerian Mathe­ Delhi 11 0 021, India. matical Society, Department of Mathematics, University Dues: $20; payable to V. M. Shah, Hon. Treasurer, of Benin, Benin City, Nigeria. IMS, Department of Mathematics, M. S. University of Privileges: Journal of the Nigerian Mathematical Society Baroda, Baroda, India. at the price normally charged to individual members. Privileges: Mathematics Student. Officers: A. Olubummo (President), J. 0. C. Ezeilo Officers: M. P. Singh (President), M. K. Singal (Immedi­ (Vice-President), C. 0. Nwachuku (Treasurer), C. 0. M. ate Past President), V. M. Shah (Treasurer), S. P. Arya Imoru (Secretary), S. A. Ilori (Assistant Secretary), H. 0. (General Secretary), J. N. Kapur (Academic Secretary), Tejumola (Editor-in-Chief). I. B. S. Passi (Editor of Journal of Indian Mathematical

784 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Reciprocity Agreements

Society), A. M. Vaidya (Editor of Mathematics Student), Punjab Mathematical Society* K. S. Padmanabhan (Hony. Librarian). Apply to: M. Rafique, Secretary, Punjab Mathematical Society, Department of Mathematics, University of the Korean Mathematical Society Punjab, Quaid-1-Azam Campus, Lahore 54590, Pakistan. Dues: US $25 for life membership; payable to M. Apply to: Hyunkoo Lee, 538 Dowha Dong, Mapo Ku, Secretary. Sung Ji Building, Room 706, Seoul 121-742, Korea. Rafique, Society Newsletter, Proceedings of the Con­ Dues: $15; payable to the Korean Mathematical Society. Privileges: ferences, Symposia, and Seminars arranged by the year) Privileges: Free receipt of Bulletin (two issues per Society. and Journal of the Korean Mathematical Society (two Roomani (President), Ch. Abdul issues per year). Officers: F. D. Anjum Hameed, S.M. Kalim (Vice-Presidents), Khalifa Rashid­ Officers: Jaihan Yoo (President), Heon Jae Lee (Vice­ ud-Din (Treasurer), M. Rafique (Secretary). President), Hong Oh Kim (Treasurer), Hyunkoo Lee (Secretary). Ramanujan Mathematical Society Malaysian Mathematical Society Apply to: Secretary, Ramanujan Mathematical Society, Department of Mathematics, Manasagangotri, Mysore Apply to: The Secretary, Malaysian Mathematical Society, University, Mysore-570006, India. cjo Department of Mathematics, University of Malaya, (annual), $150 (life); payable to Secretary 59100 Kuala Lumpur, Malaysia. Dues: $15 Ramanujan Mathematical Society. Dues: $5; payable to Malaysian Mathematical Society. Privileges: Journal of Ramanujan Mathematical Society. Privileges: MMS Newsletter, Bulletin of the Malaysian Officers: K. Ramachandra (President), N. Balasubrama­ Mathematical Society (two issues per year), reduced rate H. V. Krishna (Treasurer), E. for Menemui Matematik (three issues per year). nian (Vice-President), Sampathkumar (Secretary). Officers: Keng-Teh Tan (President), Sek-Wui Seah, Rosihan bin Mohd Ali (Vice-Presidents), Seng-Siong Book (Treasurer), Gek-Lin Chia (Secretary). Southeast Asian Mathematical Society* .Mathematical Society of Japan Apply to: Boon-Yian Ng, Southeast Asian Mathematical Society, cjo Department of Mathematics, University of Apply to: Setsuko lzawa, Secretary, Mathematical Society Malaya, Kuala Lumpur, Malaysia. of Japan, 25-9-203, Hongo 4-chome, Bunkyo-ku, Tokyo Dues: US $5; payable to Boon-Yiang Ng, Southeast 113, Japan. Asian Mathematical Society. Dues: US $40; payable to Mathematical Society of Japan. Privileges: SEAMS Newsletter, Southeast Asian Bulletin Privileges: Journal of the Mathematical Society of Japan; of Mathematics. Sugaku (in Japanese) for US $8 additional dues. Officers: Lim Chong Kong (President), Chong Chi Officers: Akio Hattori (President), Takuo lsa (Treasurer), Tat, Mari-Jo Ruiz (Vice-Presidents), Gek-Ling Chia Setsuko lzawa (Secretary). (Treasurer), Boon-Yian Ng (Secretary).

Mathematical Society • Vijnana Parishad of India of the Republic of China* Apply to: H. M. Srivastava, Foreign Secretary, VPI, Apply to: Mathematical Society of the Republic of China, Department of Mathematics, University of Victoria, P.O. Box 23-3, Taipei, Taiwan, Republic of China. Victoria, British Columbia, Canada, V8W 2Y2 or Dues: N.T. $200 (US $5.00); payable to Mathematical R. C. Singh Chandel, Secretary, VPI, Department of Society of the Republic of China. Mathematics, D. V. Postgraduate College, Orai-285001, Privileges: Chinese Journal of Mathematics (two to four U. P., India. issues per year). Dues: US $12 (annual), US $120 (life); payable to Officers: Simon C. Hsieh (President), Jau-D. Chen Vijnana Parishad, cjo Department of Mathematics, (Treasurer), Liang-Chi Tsao (Secretary). D. V. Postgraduate College, Orai-285001, U. P., India.

JULY/ AUGUST 1989. VOLUME 36, NUMBER 6 785 Reciprocity Agreements

Privileges: JfUinabha (an interdisciplinary mathematical Officers: Lars-Erik Lundberg (President), Mogens Esrom journal currently published once a year); back volumes Larsen (Vice-President), Erik Christensen (Treasurer), available at 25% discount. Mogens Esrom Larsen (Secretary), Ebbe Thue Poulsen, Officers: J. N. Kapur (President), R. P. Agarwal, M. Sten Markvorsen. K. Singal, R. S. Khare (Vice-Presidents), R. C. Singh Chandel (Secretary-Treasurer), H. M. Srivastava (Foreign Secretary). .Deutsche Mathematiker-Vereinigung e.V. Apply to: Deutsche Mathematiker-Vereinigung e.V., Al­ Europe bertstraBe 24, 7800 Freiburg, Federal Republic of Asociacion Matematica Espanola* Germany. Dues: DM 30.- (for reciprocity members); payable Apply to: Miguel de Guzman, President, Asociaci6n to Kreissparkasse Tubingen 16269 (BLZ 641 500 Matematica Espanola, Facultad de Matematicas, Uni­ 20), Federal Republic of Germany or Postscheckamt versidad Complutense, Madrid 3, Spain. Stuttgart 18517-706 (BLZ 600 100 70), Federal Republic Dues: US $15 for members of the American Math­ of Germany. ematical Society; payable to Asociaci6n Matematica Privileges: Mitteilungen der Deutschen Mathematiker­ Espanola. Vereinigung (four issues a year), Jahresbericht der Privileges: Boletin de Ia Asociaci6n Matemdtica Espanola; Deutschen Mathematiker- Vereinigung (four issues a Publicaciones de Ia Asociaci6n Matemdtica Espanola (at year). reduced prices). Officers: W. Tornig (President), K. P. Grotemeyer Officers: Miguel de Guzman, (President), Ireneo Peral (Treasurer), J. Flum (Secretary). (Treasurer), Maria T. Carrillo (Secretary). ·Edinburgh Mathematical Society ·Berliner Mathematische Gesellschaft e.V. Apply to: The Honorary Secretary, Edinburgh Mathe­ Apply to: R. D. Grigorieff, Fachbereich Mathematik, matical Society, James Clerk Maxwell Building, King's TU Berlin, StraBe des 17 .Juni 136, D-1 000 Berlin 12, Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scot­ Federal Republic of Germany. land. Dues: DM 12; payable to G. Preuss, Institut fur Dues: $8 (preferably £3 sterling); payable to the Honorary Mathematik I, FU Berlin, Arnimallee 3, D-1 000 Berlin Secretary. 33, Federal Republic of Germany. Privileges: Proceedings at reduced rate of $15 (preferably Privileges: One free copy of"Sitzungsberichte der BMG". £6 sterling) per annum. Officers: E.-J. Thiele (President), H.G.W. Begehr (Vice­ Officers: B. D. Sleeman (President), J. M. Ball (Vice­ President), G. Preuss (Treasurer), R. D. Grigorieff President), A. D. Sands (Treasurer), J. Martin, C. J. (Secretary). Shaddock (Secretaries).

Dansk Matematisk Forening* •Gesellschaft fUr Angewandte Mathematik Apply to: Mogens Esrom Larsen, Secretary, Dansk und Mechanik (GAMM) Matematisk Forening, Universitetsparken 5, 2100 K.eben­ havn 0, Denmark. Address for mail: Reinhard Mennicken, University of Dues: D.kr. 38; payable to Erik Christensen, Treasurer. Regensburg, D-8400 Regensburg, Federal Republic of Germany. Privileges: Mathematica Scandinavica (D.kr. 183 per volume), Nord. Mat. Tidss. (Normat) (N.kr. 120 per Apply to: R. Ansorge, Institut fUr Angewandte Math­ volume). (Members of the American Mathematical ematik, UniversiHit, Hamburg, Bundesstr. 55, D-200 Society do not have to join Dansk Matematisk Forening Hamburg 13, Federal Republic of Germany. to obtain the journals. Subscription orders should Dues: 25.-DM; payable to J. Siekmann, FB 12- Maschi­ be sent directly to the journals: Normat, Univer­ nentechnik, Universitiit- GHS Essen, Schiitzenbahn 70, sitetsforlaget, Avd. for tidsskrifter, Postbox 2959 Teyen, D-4300 Essen, Federal Republic of Germany. Oslo 6, Norway; Mathematica Scandinavica, Matematisk Privileges: Regular publications of GAMM and partici­ Institut, Aarhus Universitet, 8000 Aarhus C, Denmark.) pation in scientific meetings at a reduced rate.

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Officers: W. Walter (President), J. Zierep (Vice­ Matematikai Tanitasa (bimonthly). If sufficient interest President), J. Siekmann (Treasurer), R. Mennicken is expressed, a Bulletin in English will be available. In (Secretary), R. Ansorge (Vice-Secretary). addition, the JBMS is negotiating to obtain discounts for its reciprocity and sponsoring members on several serial publications and periodicals appearing in Hungary. Glasgow Mathematical Association Contact the JBMS secretary for more information Apply to: R. J. Steiner, Glasgow Mathematical As­ regarding this and other priviledges of membership. sociatiOn, Department of Mathematics, University of Officers: Akos Csaszar (President), Andras Hajnal (Secre­ Glasgow, University Gardens, Glasgow Gl2 8QW, tary General), Cecilia Szabados (Vice-Secretary General), Scotland. Andras Recski (Treasurer). Dues: £22; payable to Glasgow Mathematical Association. Privileges: Glasgow Mathematical Journal. London Mathematical Society Officers: R. J. Cole (President), R. Bailey (Vice­ Apply to: The Administrator, London Mathematical President), R. J. Steiner (Treasurer), S. J. Rowan Society, Burlington House, Piccadilly, London WI V (Secretary). ONL, United Kingdom. Dues: £5; payable to London Mathematical Society. Irish Mathematical Society (New members should not send payment until elected.) Address for mail: A. G. O'Farrell, Secretary, Maynooth Privileges: LMS Newsletter. Reduced rates for the Bul­ College, County Kildare, Ireland. letin, Journal, and Proceedings of the LMS; Nonlinearity; Journal ofApplied Probability; Mathematika; Mathemat­ Apply to: G. M. Enright, IMS Treasurer, Department ical Proceedings of the Cambridge Philosophical Society; of Mathematics, Mary Immaculate College, Limerick, Quarterly Journal of Mathematics; LMS Lecture Notes; Ireland. LMS Student Texts; LMS Monographs. (Please write to Dues: US $6; payable to G. M. Enright. the LMS for complete details.) Privileges: Right to receive the Bulletin of the Irish Math­ Officers: J. H. Coates (President), E. C. Lance, R. ematical Society; right to subscribe to the Proceedings of L. E. Schwarzeberger (Vice-Presidents), J.D.M. Wright the Royal Irish Academy (Section A) at a reduced rate. (Treasurer), C. J. Mulvey, A. R. Pears (Secretaries), D. Officers: F. Gaines (President), R. M. Timoney (Vice­ A. Brannan (Publications Secretary). President), G. M. Enright (Treasurer), A. G. O'Farrell (Secretary). Norsk Matematisk Forening islenzka Strer8frre8afelagi8* Apply to: Gerd Salter, Norsk Matematisk Forening, Matematisk Institutt, Postboks 1053 Blindern, N-0316 Apply to: President, Raunvisindastofnun Hask6lans, Oslo 3, Norway. Dunhaga 3, 107 Reykjavik, Iceland. Dues: N.kr. 50 or N.kr. 500 for permanent membership; Dues: $1 0; payable to islenzka Strerofrreoafelagio. payable to Gerd Salter, Norsk Matematisk Forening. Privileges: Newsletter (yearly). Privileges: Reduced subscription rate on Mathematica Officers: Halld6r I. Eliasson (President), Kristian Scandinavica and NORMAT (Nordisk Matematisk Tid­ J6nasson (Treasurer), Ragnar Sigurdsson (Secretary). skrift), free monthly information bulletin "infomat" about the activites of the Society. Officers: Ragni Piene (President), Tom Lindstrem (Vice­ Janos Bolyai Mathematical Society President), Bjern Jahren (Treasurer), Jon Reed (Secre­ Apply to: Secretary General, J. Bolyai Mathematical tary). Society, Anker Koz 1--3, Budapest, Hungary H-1061. Dues: Are voluntary but should minimally cover dupli­ eOsterreichische Mathematische cation and mailing costs; Reciprocity members (residing Gesellschaft outside Hungary) suggested fee is 1/8 of one percent of the member's net income; sponsoring members pay at Apply to: Werner Kuich, President, Osterreichische Ma­ least US $180 or equivalent per year. thematische Gesellschaft, Technische UniversiHit Wien, Privileges: Upon request-Matematikai Lapok (twice a Wiedner HauptstraBe 8-10, A-1 040 Wien, Austria. year), Kozepiskolai Matematikai Lapok (monthly), and Dues: oS 150; payable to Inge Troch, Treasurer.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 787 Reciprocity Agreements

Privileges: Internationale Mathematische Nachrichten Societat Catalana de Matematiques* (IMN). Apply to: Secretari de la Societat Catalana de Matema­ Ludwig Reich (Vice­ Officers: Werner Kuich (President), tiques, Carrer del Carme 4 7, 08001 Barcelona, Spain. President), lnge Troch (Treasurer), Hans Reichel (Secre­ tary). Dues: 1000 pessetes for members of the AMS, payable to the Societat Catalana de Matematiques. Privileges: But/ett( de Ia Societal Catalana de Matema­ Polskie Towarzystwo Matematyczne tiques, (2 numbers a year). Officers: J. Girbau (President), Carles Perell6 (Secretary), Apply to: Polskie Towarzystwo Matematyczne, Sniadec­ Rubi Corber6 (Associated Secretary). kich 8, 00-950 Warszawa, Poland. Dues: $8; payable to Polskie Towarzystwo Matematyczne. Societe Mathematique de Belgique Privileges: Participation in scientific conferences orga­ nized by the Polish Mathematical Society and in its sci­ Apply to: Guy Hirsch, Secretary, Societe Mathematique entific sessions; in addition, members receive one of the de Belgique, 317/11, Avenue Charles Woeste, 1090 following five series of the publication Annales Societatis Brussels, Belgium. Mathematicae Polonae: Commentationes Mathemati­ Dues: $25; payable to Societe Mathematique de Bel­ cae in congress languages, Wiadomosci Matematyczne gique, preferably by International Money Order, VISA, (Mathematical News) in Polish, Matematyka Stosowana MasterCard, or American Express. in Polish, Fundamenta Infor­ (Applied Mathematics) Privileges: Bulletin de Ia Societe Mathematique de congress languages, Dydaktyka Matematyki maticae in Belgique (6 numbers per year in 1989 and 1990). Series Mathematics) in Polish. (Didactics of A and Series B, totalling about 800 pages. Pelczar (President), Roman Duda, Officers: Andrzej Officers: A. Verschoren (President), L. Lemaire (Vice­ (Vice-Presidents), Maciej Brynski (Sec­ Adam Piskorek President), G. Hirsch (Secretary-Treasurer). retary), Janusz Kowalski (Vice Secretary), Maciej M~czyilski (Treasurer). Societe Mathematique de France Real Sociedad Matematica Espanola Address for mail: Societe Mathematique de France, B.P. 126-05, F 75226 Paris, Cedex 05, France. Apply to: J. Llovet, Secreta rio General de la Real Apply to: Madame Janine Le Peintre, S.M.F., B.P. Sociedad Matematica Espanola, Serrano 123, Madrid 126-05, F 75226 Paris, Cedex 05, France. 28006, Spain. Dues: $36; payable to American Mathematical Society Dues: $30; payable to Secretario, R. S.M. E. or S.M.F. Privileges: Gaceta Matemdtica and Revista Matemdtica Privileges: Individuals who pay dues of $33 are entitled Ibero Americana. to receive the Gazette. Other publications may be Officers: J. M. Aroca (President), Juan Llovet Verdugo purchased at the following prices: Officiel (surface (Secretary). mail) $17, Officiel (air mail) $25, Bulletin (without Memoirs) $33, Bulletin Ef Memoires $53. Asterique may be purchased at a discount price. (Members in the U.S., .Sociedade Portuguesa de Matematica Canada, or Mexico should order their copies from the AMS. See the AMS Catalogue of Publications.) de Apply to: J. E. Valen<;a, Sociedade Portuguesa Officers: G. Schiffmann (President), J. Detraz, J. M. o, 1000 Lis boa, Matematica, Av. da Republica 3 7 4 Lemaire, J. Stern (Vice-Presidents), A. Millet (Treasurer), Portugal. M. Chaleyat-Maurel, B. Helffer (Secretaries). Dues: 600 Portuguesa Escudos; payable to Sociedade Portuguesa de Matematica. .societe Mathematique Suisse Privileges: Boletim da Sociedade Portuguesa de Matemdti­ ca, free; discount of 70% in the subscription fees for Apply to: H. Holmann, Secretary SMS, lnstitut de Portugaliae Matemdtica. Mathematiques, Universite de Fribourg, CH-1700 Fri­ Officers: A. Ribeiro Gomes (President), J. E. Valen<;a, J. bourg, Perolles, Switzerland. C. Silva, J. F. Queir6 (Vice-Presidents), A. M. Cadete Dues: SFr. 15.- for members of the AMS residing outside (Treasurer). Switzerland; payable to H. Holmann.

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Privileges: Commentarii Mathematici Helvetici (reduced Unione Matematica Italiana* price); information concerning activities of SMS. Apply to: Segreteria della Unione Matematica Italiana, Stammbach (Vice­ Officers: N. A'Campo (President); U. Dipartimento di Matematica, Piazza Porta S. Donato, 5, (Treasurer-Secretary). President); H. Holmann 40127 Bologna, Italy. Dues: 40,000 lire; payable to Unione Matematica Italiana. Societe de Mathematiques Appliquees Privileges: Free Notiziario dell'UMI (monthly), Bollettino et Industrielles* dell'UMI, ser. A (3 issues a year), and membership list. Reduced fees for subscriptions to Bollettino dell 'UMI, Apply to: Societe de Mathematiques Appliquees et Ser. B. and discounts for other UMI publications. I_ndustrielles, Centre de Mathematiques Appliquees, Ecole Polytechnique, 91128 Palaiseau, France. Officers: Alessandro Figa-Talamanca (President), Benedetto Scimemi (Vice-President), Enrico Obrecht Dues: US $25; Societe de Mathematiques Appliquees et (Treasurer), Giuseppe Anichini (Secretary). Industrielles. Privileges: Free subscription to the News Bulletin, reduced rates at conferences organized by SMAI. Wiskundig Genootschap Officers: J. C. Nedelec (President), P. Lascaux, J. Periaux Address for mail: Wiskundig Genootschap, Delft Uni­ (Vice-Presidents), M. Lenoir (Treasurer), G. Meurant versity of Technology, Department of Mathematics (Secretary). and Informatics, P.O. Box 356, 2600 AJ Delft, The Netherlands. Apply to: Membership Department, Wiskundig Genoot­ •Suomen Matemaattinen Yhdistys schap, University of Utrecht, Postbus 80010, 3508 TA Utrecht, The Netherlands. to: Erik Valtonen, Secretary, Department of Apply Dues: Hfl 40.-; payable to Amro Bank, Utrecht, Mathematics, University of Helsinki, Hallituskatu 15, The Netherlands, Account 45.65.88.167, Penningmeester SF-00 100 Helsinki, Finland. Wiskundig Genootschap. Dues: 65 FIM; payable to Aatos Lahtinen Treasurer Privileges: Nieuw Archie! Voor Wiskunde (three issues a Department of Mathematics, University Helsinki: ~f year containing articles and a problem section), Med­ Hallituskatu 15, SF-00 100 Helsinki, Finland. edelingen (nine issues a year containing announcements Privileges: Arkhimedes (four issues a year) and Eukleides and book reviews), Proceedings of the Royal Academy of (newsletter). Sciences- "Indagationes Mathematicae" (can be obtained Officers: Seppo Rickman (President), Olli Martio (Vice­ at a reduced subscription rate of Hfl 120.-). President), Aatos Lahtinen (Treasurer), Erik Valtonen Officers: J. P. Murre (President), G. Y. Nieuwland (Vice­ (Secretary). President), J. Stegeman (Treasurer), R. W. Goldbach (Secretary).

Svenska Matematikersamfundet Latin America Apply to: Svenska Matematikersamfundet, Matematiska eSociedad Colombiana de Matematicas Institutionen, Umea Universitet, S-901 87 Umea, Swe­ den. Apply to: Sociedad Colombiana de Matematicas, Apartado Aereo 2521, Bogota, D.E., Colombia. Dues: 40 Skr. or 100 Skr. for permanent membership; payable to Svenska Matematikersamfundet, Ingegerd Dues: $16; payable to Sociedad Colombiana de Palmer, Saningsvagen 54, S-175 45 Jarfalla, Sweden. Matematicas. Privileges: Mathematica Scandinavica and Nordisk Privileges: Either Revista Colombiana de Matemdticas Matematisk Tidskrift at reduced rate. Information (four issues a year) or Lecturas Matemdticas (three about the meetings of the Society. issues a year). Officers: Urban Cegrell (President), Gert Almkvist (Vice­ Officers: Myriam Munoz de Ozak (President), Luis President), Ingegerd Palmer (Treasurer), Tord Sjodin Jorge Ferro (Vice-President), Luis Giraldo (Treasurer), (Secretary). Oswaldo Lezama (Secretary).

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 789 Reciprocity Agreements

Sociedad de Matematica de Chile Sociedade Brasileira de Matematica Aplicada e Computacional Apply to: Secretario, Sociedad de Matematica de Chile, Casilla 653. Santiago, Chile. Apply to: Comissao de Admissao da SBMAC, Rua Lauro Dues: US $1 0; payable to Sociedad de Matematica de Muller 455, 22290, Botafogo, Rio de Janeiro, RJ, Brasil. Chile. Dues: $16; payable to Sociedade Brasileira de Matematica Privileges: Receive: Gaceta de Ia Sociedad, Notas de Ia Aplicada e Computacional. Sociedad de Matemdtica de Chile (two issues per year). Privileges: Vote in election for officers of the Society, Officers: Gonzalo Riera (President), Jorge Billeke (Vice­ present papers at meetings of the SBMAC, receive the President), Renato Lewin (Treasurer), Victor H. Cortes Boletim and Matemdtica Aplicada e Computacional, and (Secretary). reduced registration fees at SBMAC Congress. Officers: Carlos A. de Moura (President), Leon R. Sinay (Vice-President), Joaquim Pereira Neto (Treasurer), Sociedad Matematica de Ia Republica Hilton V. Machado (Secretary). Dominicana Apply to: Eduardo Luna, Sociedad Matematica de .sociedade Paranaense de Matematica* P. 0. Box 797-2, Santo Ia Republica Dominicana, Apply to: C. Pereira da Silva, Sociedade Paranaense de Domingo, Dominican Republic. Matematica, Caixa Postal 1261, 80001, Curitiba-PR, Dues: US $6; payable to Isidro Rodriguez, Sociedad Brasil. Matematica de Ia Republica Dominicana. Dues: US $12; payable to Sociedade Paranaense de Privileges: Right to receive Notimat (bimonthly newslet­ Matematica. (twice a ter) and Revista Matemdtica Dominicana Privileges: Boletim da Sociedade Paranaense de Mate­ year). mdtica (two issues per year), Monografias da Sociedade Officers: Amado Reyes (President), Eduardo Luna (Vice­ Paranaense de Matemdtica (one issue per year). David Torres President), Isidro Rodriguez (Treasurer), Officers: C. Pereira da Silva (President), R. Petronzelli (Secretary). (Vice-President), E. Andretta (Treasurer), M. G. Borges (Secretary) . • Sociedad Matematica Mexicana* Union Matematica Argentina Apply to: Sra. Hilda C. de Villa, Apartado Postal 70-450, Mexico 20, D.F. Mexico 04510. Apply to: Secretary of the Union Matematica Argentina, Dues: US $1 0; payable to Sociedad Matematica Mexi­ Casilla de Correo 3588, 1000-Correo Central, Buenos cana. Aires, Argentina. Privileges: To be a regular member paying half of the Dues: US $16; payable to U ni6n Matematica Argentina. regular fee for persons living outside of Mexico. Privileges: Revista de Ia Union Matemdtica Argentina Officers: Alejandro Lopez-Yanez (President), Diego B. (two issues per year). Hernandez (Vice-President), Juan Morales (Treasurer), Officers: Roberto L. Cignoli (President), Juan A. Tirao, Luis Rivera-Gutierrez (Secretary). Roberto A. Macias (Vice-Presidents), Graciela Ana Canziani (Treasurer), Susana Elena Trione (Secretary) .

• Sociedade Brasileira de Matematica* Middle East Apply to: Cesar Camacho, Estrada Dona Castorina, .Iranian Mathematical Society* 110-Jardim Botanico, Rio de Janeiro, RJ, Brazil, 22460. Iranian Mathematical Society, P. 0. Dues: US $6; payable to Sociedade Brasileira de Mate­ Apply to: Secretary, matica. Box 13145-418, Tehran, Iran. Society, M. Privileges: 50% reduced membership rate; Boletim da Dues: $10; payable to Iranian Mathematical SBM; and up to a 25% discount of Society publications. Radjabalipour. Society Officers: Cesar Camacho (President), Paulo Roberto G. Privileges: Bulletin of the Iranian Mathematical annual Iranian Sad (Vice President), Carlos F. B. Palmeira (Treasurer), and reduced rate for participation in the Mario Jorge D. Carneiro (Secretary). Mathematics conferences.

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Officers: M. Toomanian (President-Secretary), M. Rad­ Mathematical Society of the Philippines jabalipour (Treasurer). Apply to: Membership Committee, Mathematical Society of the Philippines, Department of Mathematics, Ateneo Israel Mathematical Union de Manila University, P.O. Box 154, Manila, Philippines. Apply to: Israel Mathematical Union, c/o Abra­ Dues: $5; payable to Mathematical Society of the ham Berman, Secretary, Department of Mathematics, Philippines. Technion-Israel Institute of Technology, Haifa 32000, Privileges: Publications and newsletter of the Mathemat­ Israel. ical Society of the Philippines. Dues: $1 0; payable to Israel Mathematical Union. Officers: Jose Marasigan (President), Rene P. Felix Privileges: Newsletter; IMU-net, may attend and present (Vice-President), Aurora Trance (Treasurer), Rolando papers at meetings. Ramos (Secretary). Officers: Zvi Ziegler (President), Moshe Goldberg (Trea­ surer), Abraham Berman (Secretary).

South Pacific .New Zealand Mathematical Society Australian Mathematical Society Address for mail: Department of Mathematics and Address for mail: W. R. Bloom, Murdoch University, Statistics, Massey University, Palmerston North, New Murdoch, W A 6150 Australia. Zealand. Apply to: B. D. Jones, Department of Mathematics, Apply to: K. L. Teo, Department of Mathematics and University of Queensland, St. Lucia, Queensland 4067, Statistics, Massey University, Palmerston North, New Australia. Zealand. Dues: $A25; payable to B. D. Jones. Dues: $NZ 13.50; payable to K. L. Teo, Treasurer, Privileges: Free copies of The Gazette and copies of Department of Mathematics and Statistics, Massey Journal Series A and B, The Bulletin and the Lecture University, Palmerston North, New Zealand. Series at members' rates. Privileges: Newsletter of the NZMS (3 per year); Officers: G. I. Gaudry (President), D. Elliott, J. H. subscription to Mathematical Chronicle at reduced rate. Rubinstein, I. H. Sloan (Vice-Presidents), B. D. Jones Officers: G. L. Thornley (President), B. A. Woods (Vice­ (Treasurer), W. R. Bloom (Secretary). President), K. L. Teo (Treasurer), J. Giffin (Secretary).

FACTORIZATIONS OF b" ± 1, b = 2, 3, 5, 6, 7, 1 0, 11, 12 UP TO HIGH POWERS, SECOND EDITION John Brillhart, D. H. Lehmer, J. L. Selfridge, Bryant Tuckerman, and S. S. Wagstaff, Jr. (Contemporary Mathematics, Volume 22, Second Edition) This book is a revised and updated edition of a work that occurred since 1925. An update to the introduction is included originally appeared in 1983. It gives a historical account of the in this edition and discusses the major advances that have various methods and machines that have been used to factor, been made in the five years since the first edition appeared. and prove prime, the numbers b" ± 1. It is a revised version The introduction also discusses the multiplicative structure of an extension of a rare 1925 work by Cunningham and of b" ± 1 and explains the relation between the two kinds of brings together results going back to the seventeenth century. algebraic factorizations of these numbers. special form The factorizations and the very large primes of 1980 Mathematics Subject Classification: 11 are useful in group theory, number theory, discrete Fourier ISBN 0-8218-5078-4, LC 83-12316 transforms, random number generators, and cryptography. ISSN 0271-4132 The present edition contains more than 2000 large primes 320 pages (softcover), June 1988 $31, which have never been published before. Individual member $19, List price Institutional member $25 The book contains complete factorizations of b" ± 1 for the To order, please specify CONM/22NA given values of b and for all n ~ 100, and for many n > 100. Shipping/Handling: 1st book $2, each add') $1, $25 · Included is an extensive and valuable introduction which max. By air, 1st book $5, each add'l $3, $100 max. Prepayment required. Order from AMS, P.O. Box 1571, describes the developments in computing technology and Annex Station, Providence, RI 02901-1571, or call in methods of factoring and primality testing which have 800-556-7774 to use VISA or MasterCard.

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 791 New Members of the AMS

ORDINARY MEMBERS Farhood Pouryoussefi-Kermany, Tehran, NOMINEE MEMBERS Farid Aitsahlia, Stanford, CA Iran American University Nemat Akmalov, Univ of Washington, Peter P Raychev, Bulgarian Academy of Faisal Fakhri Awartani Seattle, WA Science, Sofia, Bulgaria Reza Modarres John A Barnes, Blacksburg, VA Jawaid H Rizvi, King Abdul Aziz Univ, Ahmad S Mokatrin Hans Werner Borchers, Heidelberg, Jeddah, Saudi Arabia Andrews University Federal Republic of Germany Judy A Roach, Midwest City HS, Midwest Jody Jay Marsh William R Breckon, Oxford Polytech, City, OK Michele J Pczet Oxford, England Donald D Rogers, Orlando, FL Darren L Slider David W Brown, V A Medical Center, Ashot A Shaginyan, Univ of Lowell, Auburn University Bronx, NY Lowell, MA Rebecca G Beverly Sandra A Bruesch, Lakewood, CA Heather P Stewart, Little Silver, NJ Bernard G Carlisle Michael L Bushnell, East Windsor, NJ Susan Palmer Tombes, Richmond, VA Saad I El-Zanati Alfred E Din, Upper Derby, PA Bjorn G Walther, Uppsala Univ, Uppsala, W Cory Eubanks Rodney Eastman, Stillwater, OK Sweden Robert B Gardner Jr Alan M Frieze, Carnegie Mellon Univ, Zhao Zhi Zhang, Academia Sinica, David A Grable Pittsburgh, PA Beijing, Peoples Republic of China Michael R Green Tahsin Mustafa Ghazal, King Saud Univ, Luis Neves de Almeida, Carcavelos, Linda Kay Lee Riyadh, Saudi Arabia Portugal Margaret E Moore James R Goetz, Freemont, CA Andries Petrus van der Walt, Univ of Maya C Mukherjee Leon A Gonzalez, Univ of Alcala de Stellenbosch, Stellenbosch, Republic Misty Anne Phillips Henares, Madrid, Spain of South Africa Ruben Rajas-Oviedo Leslie N Gruis, Washington, DC Ruby Elizabeth Rolling David E Hill, Montana College of Mineral Marion Stephenie Syer Sci-Tech, Butte, MT RECIPROCITY MEMBERS Michael S Walker Seana K Hogan, San Jose, CA Deutsche Mathematiker- Vereinigung e. V. Evan B Wantland Jeanne H Kenison, Manchester, NH Aloysius August Krieg Arminda Moehring Wey Hamidreza Khosrovi-Kamrani, Werner J A Stich Baylor University CTB/McGraw-Hill, Monterey, CA London Mathematical Society Sara A Barret John S Kintzinger, Dubuque, lA Yilmaz Akyildiz Boston University Gerhard Knieper, Freie Univ of Berlin, Aristides Katavolos James Edward Georges Berlin, Federal Republic of Germany Mathematical Society of Japan Joseph M Massaro Mark A Knobloch, West Hartford, CT Takao Matumoto Bowling Green State University Arnold Knopfmacher, Univ of Takao Yamaguchi Thilan U Hewage Witwatersrand, Johannesburg, Societe Mathematique de Belgique Brandeis University Republic of South Africa Stefaan Caenepeel Chungsim Han Donald E Lavigne, Killeen, TX Societe Mathematique de France Sung Won Park Alvaro Lecompte, Ponce, Puerto Rico Yves Carriere Brigham Young University Ahmad Mamourian, Univ of Tehran, Jacques Peyriere Joe M Simons Tehran, Iran Jean Pierre Tual California State University Fullerton Francisco Marcellan, Univ Politecnica, Societal Catalana de Ciencies Fisiques Alaina M Luisi Madrid, Spain Quimiques i Matemilliques Fariheh Towfiz Amos Nevo, Jerusalem, Israel J Carlos Naranjo-Del-Val California State University Hayward Andrew Chola Nyondo, Univ of Suomen Matemaattinen Yhdistys John David Morgenthaler Swaziland, Kwaluseni, Swaziland Hans-Olav Tylli California State University Long Beach Eamonn A O'Brien, Marquette Univ, Unione Matematica lta/iana Veronica S Richards Milwaukee, WI Sergio Stella California State University Los Angeles Kuo Chen Pan, Univ of South Florida, Brian P Dauzat Tampa, FL Leslie Lynne Lowes

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

California State University Northridge Marshall University Peter T Breznay Susan M Curtis Thomas Raymond Conforti Scott Allen Brown Vic Emerson Kim C Fleener Douglas P Brozovic Dhun Daruwala May Qian Fu Christine M Carrino Calvin College Dragan Glavasic Jianmou Chang Joel P DeJager Barbara A Miller Daniel Chi-Chong Chen William R Ericson Runaruk Ratanamalaya Ferenc Janos Pinter Paula K Pruis Eileen P Stitt Cheryl Diane Stitt Kevin N VanderMeulen Stephen M Wilkerson Ohio University Catholic University of America Memphis State University Timothy R Boyer Gregory V Clarke Robert Charles Yandell Oklahoma State University, Stillwater Claremont Graduate School Michigan State University David W Farmer Bruce C Abe Kelli Jo Brinks Jodie D Novak Zoe T Hoole New Jersey Ins/ of Tech Old Dominion University Clarkson University Lynette M De Souza James H Africa Kervin R Smith Christodoulos G Mavroyiakoumos Leon Michael Arriola College of William f~ Mary Richard J McNally Jay Casper David A Miller Clairie P Nicolaou Judith Dimond Kenneth Louis Sala Sudesh Kumar Srivastava Thomas R Gatlitfe Concordia University New York University, Courant Ins/ Anwar M Hossain Hoan Duong Pantaleao Silva Sophia Maggelakis Pankaj K Kamthan Nicholls State University Robert J McCarthy Boniface lwokwagh Madza Verna D Brown lain McKaig Claudio Todor James N Chapman III Carl J Thomsen Dannen College David Hanks Fabre Michael S Toner Dori L McGuire Frances French Moss Nizam X Uddin Dickinson College Mavis Marie Newchurch Thomas G Wangler David A Hastings Keith J Nuesslein Yuesheng Xu Eckerd College Kevin Paul Patureau Oregon State University Randy M Hall Robert E Pendzimaz David Eugene Lantis Georgetown University North Carolina State University Christopher E Milner Karen Lyn Bartolozzi Paul S Davenport III Xi Wang James F Frohnhofer Gregory Alan Gibson Marvin R Wilson Ellen M Walker Terri L Kammerer Pembroke State University Georgia Inst of Tech Jinhyo Kim Linda J Price Todd H Hoivik Arthur G Moore Lynae E Sakshaug Humboldt State University Dorothy Gayla Pait Pennsylvania State University, University Elizabeth S Bowman S Michael Sandler Park Michael Patrick Butler John Russell Taylor Alpana M Desai Stephen K Jackson North Dakota State University, Fargo Verne E Leininger Steven John McKay Paul A Flasch Portland State University Jon Derek Mitchem Northeastern Illinois University Robert L Garry Robert W Van Kirk Annie A Beckman Ying Wang Curtis Roger Voss Davar A Hamadani Purdue University Idaho State University Dale F Woods Chanakya Janak Wijeratne David L Gifford Northeastern University Rockefeller University Indiana University at Bloomington David E Mauu Erich D Jarvis Chrysalis Hartonas Steven F Morse Pratik Mukherjee Eung-11 Ko Abdelhaq Nadire SUNY at Albany Jennifer Woodworth Tony Yim-On Wong Venu P Addepalli Indiana-Purdue University, Fort Wayne Ying Xu Pietcr B Decker David A Gorrell Northern Michigan University David N Hardy Tammy J Hill Susan A Mcinnis Philip K Hotchkiss Kansas State University Oberlin College Susan 0 Jacobson Colin Jose Antonio Fernandes Kenichi Futamura Peter Kernwein Louisiana Tech University Occidental College Seokchan Kim Bashar A Attar Mee Young Kim Deborah A Lawrence Maharishi International University Ohio State University, Columbus JooSung Lee Maxwell V Rainforth Joe A Altobelli Qian Li Marquette University Michael R Anderson Kevin M Madigan Xiaoying Yan Gaurav Bhatnagar David J Moss William J Blatcher Charles Peter Murphy James P Braselton Stalo Georgiou Paschali

JULY/AUGUST 1989, VOLUME 36, NUMBER 6 793 New Members of the AMS

Burkard M Polster Lie Scott Lacey University of Georgia Jerilyn E Prentice Jonghoon Lee Katrina K Ashford Arsalan Saljoughy Chi-Kun Lin University of Guelph Mark D Tenney Carlos C Lizarraga Dominique Anfossi Stanislaus Suryadi Uyanto Maria Rosario Matas Kostas Gaitanos SUNY at Buffalo Heather L Nadelhoffer Grigorios A Mitsis Fred B Field Steve Nobe Rostant Ramlochan SUNY at Stony Brook Robert L Northcutt University of Hartford Fran~ois Lamontagne Bo Peng Kathleen M Driscoll Darko Mrakovcic Martin Peter Pokorny Donna J Fitzgibbon Sacred Heart University Hannah J Rasmussen University of Kansas Violette A Barasch Justine Marie Ritchie Melody L Southard Kathleen P Kingston Yvonne Marie Sandoval University of Kentucky San Francisco State University Jill A Savage Clayton T Brooks Kenneth D Owens Jr Xiangyang Shen Valerie L Crossfield WillS Parks Lori J Smellegar Scott G Cuccaro Bin Shao Kerny Jo Stanley Karen M Hart Stanford University Donald R Stark Samanthia Lea Israel Martin Scott Betz Chiung-Jue Sung Kevin A Roper Eduardo-Jose Chichilnisky Woody Jhishen Tsay Mark R Swetnam Suffolk University Taicheng Tso University of Massachusetts, Amherst Irina Kristy Paramanathan Varatharajah David Michael Hendrickson Ian C Westmacott Mariamma G Varghese University of Massachusetts, Boston Temple University Wen-Hui Wei Sheldon B Kovitz Abera Abay Tityik Wong University of Michigan Tennessee Tech University Tailiang Xie Dragan Vukotic Barry L Hamilton Bing Xu University of Mississippi Texas A f1 M University University of California, Davis Mahmoud Ali Abdurrahman Donald C Ratliff III Morris L Beatty Michael E Baldwin United States Coast Guard Academy Carlos Freitas Borges David Charles Bramlett Mark B Case University of California, Irvine Connie M Campbell United States Naval Academy Michael R Dowd Robert E Dawson Thomas P Farina University of California, Riverside Mark Alan Eaton University ofAlabama-Birmingham Martha Contreras Hong Gan Abdullah A Kamal Isabel Katarina Dazey David Alan Kelsey University ofArizona John Phelps Dibble Uma Devi Mallela James A Abolt Patty Kay George Tamara L McColgan Zakaria M Alawneh Donald Arthur Pedersen Alta Darlene Mills Eric Anson Michael Patrick Prophet Mary Elizabeth Norton Christian J Ballot University of Cincinnati John Carl Panetta Andrew Walcott Beckwith Scott R Clark Sharon R Simpson Ronald Frank Bellschweiler Xianggen Xia Cammy G Tidwell Edward James Bevan University of Colorado, Boulder Danny Ding Wang Marco Campini Daniel Lee Hansen George Clifton Wingard Chi-Wen Chen University of Connecticut, Storrs Nalin Linda Zhou Jian Cheng Hyeyoung Her University of Missouri, Columbia Yifen Cheng Kuo-Ching Jen Beata Dutkowska Marc Courtemanche William J Odendahl III Brian Patrick Kelly Haiyan Cui Guolin Pan Florence Lancien Michael P Elfendahl Karren R Taie Gilles Lancien Leobardo Fierro Nasser M Towghi Thomas P Lofaro Steve T Files Aihua Wang James R Nowell Matthew J Foraker Frank P Weber Xiaomin Peng Howard Frost Ding Xiao Narcisse Josoa Randrianantoanina Vinton E Geistfeld Wenhuan Yu Kevin K Schneider Rahman Ghamasaee Xun Yu David B Slavit David J Graser Minxie Zhang Donald R Vermillion Jorge E Guarin University of Delaware University of Montana David C Halpern Shannon E Wilson Matthew X Hunter Shi Jin University of Florida University of N C at Charlotte Wen-Fong Ke Christine Faye Hagan Joanne E De Ath Mohammed Ahmed Khan Dennis A Lange Louise E Farrow Matt Klassen Xinpei Lu

794 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members ofthe AMS

Jerry E Wright Richard Mercado Joseph Dolinak University of N Cat Greensboro Celia I Nunez Mirna Dzamonja Ralph Norman Hill Ruben Robles Jennifer Lynn Earles Michael P Lynch Gerardo H Rodriquez Paul E Fishback University of Nebraska at Omaha Luis A Soto Gonzalez Necdet Guner Stephen M Hart Pedro Vasquez Likang Guo Marcia S Molle Yliris Veza-Torres Kirk D Haller Karen L Schwartz Zoraida Villarrubia Thomas Allen Hogan University of New Brunswick, Fredericton University of Regina Matthew Oliver Ikle Ayse Alaca Baoyan Ding Kurt Nathan Johnson Saban Alaca University of South Carolina Jari Pekka Junikka Yanchao Li Gary Lee C De La Pefia University of Wise, Milwaukee University of Notre Dame University of Texas at Austin Adib Bagh Herman Jose Serrano Kathy E Gregoire University of Wise, Parks ide Zeljko M Sokolovic University of Texas at San Antonio John D Marter University of Oregon Donna E Jockers Virginia Commonwealth University Richard A Boro Andrew M Proefrock Susan Beers Browder Michel P Kovcholovsky Robert Stuart Vinson Jerry T Bryant Michael E Williams University of Washington Changsun Choi University of Pennsylvania Michael S Alexander Jeanne Marie Draper Andrew Hicks University of Waterloo Anne T Golden Miriam R Kantorovitz Richard J Atkins Kay Anita Harrell Ethan Lewis T John Fahey Karen L Jackson Xiaobo Liu Angele Marie Foley Randolph F Joe Anthony A Mikovsky Daniel A Ford Shirish Shankar Joshi Beth A Stahelin Stephen Thomas Gibbs Kimberly Jones Lukezic Zhenyu Zhang Lingli Jiang Thomas C Mosca III Guangjian Zhu Goansu Kim Mark L Perez University of Puerto Rico, Mayaguez Heather D Meek Rand V Pittman Luis Caceres Alfred John Menezes Washington State University Rolando D Cio Vargas Takis Merkouris David K Kern Pablo A Diaz Willem M Sluis Western Michigan University Rafael Augusto Diaz Jimenez Ping Yan Jiuqiang Lui Davila Edwin University of Winnipeg William Paterson College Milena Lucia Gomez Pabon Michael James Mackinnon Emily Rueda Blanca Nidia Loperena University of Wise, Madison Raul A Madrid Moreno Rebecca N Brady Cancafion Jaime Martinez Kequan Ding

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 logic exists upon which a systematic ISBN 0-8218-2459-7, LC 88-8130 of an algebraizable 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 $10 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 5 a congruence relation QT on the formula algebra. QT identifies all formulas that cannot be distinguished from one another, on the basis of T, by any property expressible in the language of 5. The characterization theorem states that a deductive system 5 is algebraizable if and only if n is one-to-one Shipping/Handling: 1st book $2. each add'l Sl. $25 and order-preserving on the lattice of 5-theories and also max. By air. 1st book $5. each add'l $3. $100 max. preserves directed unions. The authors illustrate these results Prepayment required. Order from AMS. P 0. Box 1571. with a large number of examples from modal and intuitionistic Annex Station. Providence. Rl 02901-1571. or call logic, relevance logic, and classical predicate logic. 800-556-7774 to use VISA or MasterCard.

JULY/ AUGUST 1989, VOLUME 36, NUMBER 6 795 INSTITUTIONS NOT SUBJECT TO U.S. LAWS may be required to execute and submit a copy of this form with the text of recruitment advertisements for the Notices (see Policy State­ ment below). Publication of recruitment advertisements not accompanied by the completed form may be delayed or denied. Employment at ______(Name of Institution) (City) (Country)

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No listing for a position will be printed if it expresses or implies any preference, limitation, specification, or discrimination based on age, color, race, religion, sex, or national origin in contravention of any federal or state statute prohibiting discrimination in employment on the basis of these criteria. The publisher reserves the right to edit any listing prior to publication which does not conform with federal or state law on discrimination in employment. All employers in the United States are required to abide by the requirements of Title VII of the Civil Rights Act of 1964, announcing a national policy of equal employment opportunity in private employment, without discrimination because of color, race, religion, sex, or national origin. All U.S. listings are accepted with the understanding that the employer complies with federal requirements. Advertisers not subject to U.S. laws may be required to sign a statement that they do not discriminate in employment on grounds of age, color, race, religion, sex, or national origin. Applicants should be aware that institutions outside the U.S. may not be legally bound to conform to these or similar requirements and the AMS cannot assume responsibility for enforcing compliance. Applicants are advised to inform themselves of conditions that may exist at the institutions to which they apply. In particular, readers should note that the Equal Employment Opportunity Act (42 U.S.C., §§2000e et seq.), which prohibits discrimination in employment on the basis of race, religion, sex, or national origin, contains (in §2000e-l) an exception from the provisions of the Act for any religious corporation, association, educational institution, or society with respect to employment of individuals of a particular religion to perform work connected with the carrying on by such corporation, association, educational institution, or society of its activities. The Age Discrimination Act of 1967 (29 U.S.C., §§621 et seq., as amended), makes it unlawful for an employer to discriminate against any individual between the ages of 40 and 70 because of age. Thus it is legal to seek as an employee someone who is "over 30," but not one "over 50"; neither is it legal to express a preference for someone who is "young," or is a "recent graduate," since the latter tend (on statistical grounds) to be young.

796 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

SUGGESTED USES for classified advertising are positions available, books or lecture notes UTAH SUPERCOMPUTING INSTITUTE 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 University of Utah Supercomputing from the top of the type; $18 for each additional 1/2 inch or fraction thereof. No discounts Institute invites applications for three for multiple ads or the same ad in consecutive issues. For an additional $10 charge, staff positions in the areas of (i) Correspondence will be forwarded. announcements can be placed anonymously. graphics, visualization and animation, Advertisements in the "Positions Available" classified section will be set with a minimum (ii) scientific computing, and (iii) devel­ one-line headline, consisting of the institution name above body copy, unless additional headline copy is specified by the advertiser. 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The objectives of the institute are inside front cover or may be obtained from the AMS DEADLINES are listed on the to pursue research and development in Advertising Department. above areas and to provide ser­ U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, the religion or national origin. "Positions Available" advertisements from institutions outside the vices in these areas to the faculty via U. S. cannot be published unless they are accompanied by a statement that the institution consulting and courses. Staff members does not discriminate on these grounds whether or not it is subject to U. S. laws. Details will be expected to pursue research in and specific wording may be found near the Classified Advertisements in the January and their area of expertise. Adjunct appoint­ July I August issues of the Notices. ments in academic departments will be SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians considered. are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and To apply send a curriculum vita to speak to Paula Montella for further information. Prof. Hans G. Othmer, Dir. of Academic Department, Attn: Paula Montella, AMS, P. 0. Box SEND AD AND CHECK TO: Advertising Supercomputing, Dept. of Mathematics, 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 University of Utah, Salt Lake City, UT, Charles Street, Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not required to do so. AMS FAX 401-331-3842. 84112 and arrange to have three letters of recommendation sent to this address. The University of Utah is an affirmative actionjequal opportunity employer. POSITIONS AVAILABLE BAYLOR UNIVERSITY Endowed Chair of Mathematics BROWN UNIVERSITY The Mathematics Department is accept­ OREGON STATE UNIVERSITY BROWN UNIVERSITY, Providence, Rl ing applications for the Ralph and Jean Assistant Professor positions in Alge­ 02912. Two professorships at the As­ Storm Chair for research in mathemat­ bra/Number Theory, Numerical Analysis, sociate Professor level or above, with ics. We are seeking a mathematician Geometric-Topology /Dynamical Systems, tenure, to begin July 1, 1990. Salary to with an established record of excel­ and Differential Geometry will become be negotiated. Preference to be given lence in research and a strong interest available September 16, 1990. Salary to applicants with research interests in teaching. The teaching load is three depends on qualifications. Closing date consonant with those of the present hours per semester. The starting date is December 15, 1989. Write to: members of the Department. For one of negotiable. Professor Bent Petersen the positions preference will be given to The Department offers the BA, BS, Staff Selection Committee those with research interest in Algebraic and MS degrees. The department has Department of Mathematics Geometry, Differential Geometry, or re­ an enrollment of 2500 students and the Oregon State University lated fields. Candidates should have University has 11 ,000 students. Baylor Corvallis, Oregon 97331-4605 a distinguished research record and a is located in Waco, Texas, which is 100 Oregon State University is an Affirma­ strong commitment to teaching. Qual­ miles from Dallas and 100 miles from tive Action/Equal Opportunity Employer ified individuals are invited to send a Austin. Baylor University is an Affirma­ and complies with Section 504 of the vita and at least three letters of rec­ tive Action/Equal Opportunity Employer Rehabilitation Act of 1973. OSU has a ommendation, no later than November and is under the patronage and general policy of being responsive to the needs 1, 1989, to Professor Robert Accola, direction of the Baptist General Conven­ of dual-career couples. Executive Officer, Department of Math­ tion of Texas. Send vita to Howard L. STAFF SELECTION COMMITTEE ematics, Brown University, Providence, Rolf, B.U. Box 7328, Baylor University, B. E. Petersen, Chair Rl 02912. Brown University is an Equal Waco TX 76798-7328. Opportunity I Affirmative Action employer. B. I. Fein R. Higdon R. M. Schori

JULY /AUGUST 1989, VOLUME 36, NUMBER 6 797 Classified Advertisements

POSITIONS AVAILABLE THE NORWEGIAN INSTITUTE The Norwegian Institute of OF TECHNOLOGY Technology UNIVERSITY OF UTAH Division of Mathematical Sciences Administration of Personnel Department of Mathematics N-7034 Trondheim, Norway for the FULL PROFESSOR OF MATHEMATICS invites applications In addition, reprints and preprints should following positions: (2 POSITIONS) be sent, in quadruplicate, to the same The Norwegian Institute of Technol­ full time tenure track address no later than one month after 1. At least four ogy invites applications for two tenured appointments on any of the professorial the closing date. Work in progress, positions as Full Professor of M~th­ is particularly in­ referred to in the letter of application, levels. The Department ematics. The Division of Mathematical work in the must arrive within three months after terested in applicants who Sciences is part of the Department of areas of geometry, algebra, topology, the closing date. Further information is Physics and Mathematics, and c~rrently available from the above address. group representation theory, app~ied has 23 faculty positions, 11 of wh1ch are scientific computing. mathematics, and full professorships. The Division offers a Selection will be based on research ex­ program in Industrial Mathematics. l~ad­ R. S. DOW NEUROLOGICAL ability. Applications pertise and teaching ing to the engineering degree of s1v.1ng. SCIENCE INSTITUTE until January 31, 1990 will be accepted (at M.S. level), and has a doctoral Postdoctoral Position in or until the positions are filled. program leading to the dr.ing. degr~e. Mathematical Neuroscience nonrenewable three­ 2. Two or more The program in Industrial MathematiCS Persons of any age The R.S. Dow Neurological Science In­ year Instructorships. consists of courses in mathematics, nu­ in 1989 or 1990 stitute in Portland, Oregon is seeking receiving Ph.D. degrees merical analysis and statistics, with a will be selected a Postdoctoral Fellow in Mathematical are eligible. Applicants general emphasis on mathematical mod­ ability and potential in Neuroscience. Candidates must be able on the basis of elling. Research interests of the current Starting salary to invent phenomenological descriptions teaching and research. faculty include algebraic coding theory, this academic year is $29,500; cost of drawing on methods from topology and algebraic geometry, hyperbolic ~onser­ are contingent on action abstract algebra, besides analysis. The living increases vation laws, non-linear systems, 1nverse Duties consist successful candidate will have primary by the State Legislature. problems, continued fractions, mathe­ courses during the three responsibility for own research project of teaching five matical physics, operator algebras, and will in sensorimotor control of posture or quarter academic year. Applications real and complex analysis. 31, 1989 or cerebellar studies. A Ph.D. in mathe­ be accepted until December Special emphasis will be placed on are filled. matics or mathematical physics is highly until the positions qualifications of candidates in areas of visiting positions of one desirable. Interested applicants should 3. One or more mathematics with relevance to mathe­ criteria are teach­ send statement of research interests, year or less. Selection matical modelling; in particular qualifica­ to curriculum vitae and three letters of ing ability and potential contrib~tio~ tions in partial differential equations and Applications reference to: Cheryl Cameron, Good our research environment. discrete mathematics. For at least one of will be accepted until January 31, 1990 Samaritan Hospital and Medical Center, the positions, candidates are sou~ht in are filled. 2169 NW Northrup, Portland, Oregon or until the positions the field of partial differential equat1ons. curriculum 97201. EOE/ AA. Applications must include Applicants are sought who show sig­ and three letters of vitae, bibliography nificant research accomplishments as applications reference. (Instructorship well as serious concern for teaching, CHAMINADE of the OF HONOLULU must also include an abstract and commitment to the initiating and UNIVERSITY and either a list of graduate Assistant Professor of Mathematics thesis promoting research. . courses completed or a transcript of The closing date for rece1pts of Applications are invited for tenure track graduate work.) applications is September 1, 1989. beginning August 1~· 1989 .. A Please send your application to: position The Professor is engaged on the Ph.D. (or a.b.d. with clear d1ssertat1on COMMITTEE ON STAFFING condition that he/she participates in the proposal) is required with a strong com­ DEPARTMENT OF teaching and examination work that is mitment to undergraduate teaching and MATHEMATICS in accordance with the relevant program an interest in scholarly activities. Salary UNIVERSITY OF UTAH of study at the time, and furthermore will depend on qualifications and teach­ 233JWB he/she must accept, without compen­ ing experience SALT LAKE CITY, UTAH 84112 sation, any revisions made by statutory Send vita and three letters of rec­ The University of Utah is an equal law or royal decree to curricula, pension ommendation, at least one testifying to opportunity-affirmative action employer. arrangements and retirement age. teaching ability, to Dr. Art Mori, Chair, A letter of application including a Department of Mathematics and Phys­ curriculum vitae and a list of publications ical Sciences, Chaminade University of should be addressed to The King and Honolulu, 3140 Waialae Avenue, Hon­ sent to: olulu, HI 96816. Deadline is August 1, The University of Trondheim 1989. (CUH is an EO/AAE.) continued

798 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE D Computing, T. Coleman, 607/255- OREGON STATE UNIVERSITY 9203 HOWARD UNIVERSITY The Andreotti Assistant Professor posi­ Department of Mathematics D Statistics and Applied Probability, R. tion in mathematics will become available Chairperson of Department Durrett, 607/255-8282 September 16, 1990. Salary depends on Details about each program can be qualifications. Closing date is December Applications and nominations for the obtained from the corresponding co­ 15, 1989. Write to: position of Chairperson for the Depart­ ordinator, whose name and telephone Professor Bent Petersen, Chair ment of Mathematics will be accepted number are shown above. Inquiries ad­ Andreotti Professorship Selection through November 15, 1989 for the term dressed to the appropriate program co­ Committee beginning August 1, 1990. ordinator also may be sent to: Department of Mathematics Viable candidates must have sev­ Mathematical Sciences Institute Oregon State University eral years of undergraduate teaching, a 201 Caldwell Hall Corvallis, Oregon 97331-4605 record of sustained research and pub­ Cornell University Oregon State University is an Affirma­ lications, evidence of active involvement Ithaca, NY 14853-2602 tive Action/Equal Opportunity Employer in professional societies, and adminis­ and complies with Section 504 of the trative experience and should qualify for Application Procedure for Rehabilitation Act of 1973. OSU has a a tenured appointment at the rank of Postdoctoral Visitors policy of being responsive to the needs professor. The Institute prefers scientists who of dual-career couples. Successful candidates will be ex­ are not more than five years beyond STAFF SELECTION COMMITTEE pected to provide leadership as the the doctoral degree. Candidates are el­ B. E. Petersen, Chair College and Graduate School continue igible for academic year appointments B. I. Fein to redefine and develop their academic at a salary of $28,500.00 plus bene­ R. Higdon programs to meet contemporary and Extensions to a second academic fits. R. M. Schori future challenges. year are possible, and candidates may Howard University, a historically black seek supplemental teaching positions. institution, is a private, comprehensive The deadline for '90-'91 applications is university in Washington, D.C. will be made research December 15, 1989; awards SITUATIONS WANTED with more than 12,000 students and over by January 31, 1990. In addition to a 2000 faculty. The College of liberal Arts curriculum vitae, three (3) letters of rec­ Mathematician or Math Instructor. Age has approximately 3000 students with ommendation are required, one of which 32. U.S. citizen; security clearance at­ over 350 faculty. should come from the thesis advisor. tained. Specialty: Combinatorics. Expe­ Letters of application or nomination, Reprints of published articles are ap­ rience: Several months tutoring minority a current curriculum vitae, names and preciated. The candidate should specify students, three years classroom teach­ addresses of three professional refer­ a mathematical scientist at Cornell with ing, three years service in communi­ ences should be sent to the Chairperson, whom (s)he expects to be associated. cations security. References and re­ Search Committee, Department of Math­ Applications for research in the following sume provided upon request. Phone: ematics, Box 103, Howard University, fields are particularly sought: (816)763-6790 or respond to: Applicant Washington, D.C. 20059. D Dynamical systems, nonlinear analysis Code 333, Advertising Department, AMS, An Equal Opportunity Employer and partial differential equations P.O. Box 6248, Providence, Rl 02940. D Parallel computation: numerical linear algebra, finite-element methods, numeri­ CORNELL UNIVERSITY cal optimization MATHEMATICAL SCIENCES D Probability INSTITUTE A list of mathematical scientists is available from the Institute office. Call MATHEMATICIAN seeking academic em­ The Mathematical Sciences Institute of 607/255-8005. ployment. Ph.D.; 25 published papers Cornell University is beginning its search The Administrative Associate (W. V. in analysis, numerical analysis; 2 joint for postdoctoral visitors for the academic Kone, 607 /255-7752) is available to an­ books, third in progress; 15 years year beginning August, 1990. The Insti­ swer remaining questions. teaching all levels (secondary-graduate); tute supports research in the following The Mathematical Sciences Institute broad experience; for resume, strong areas: is partially funded by the U.S. Army references call (216)746-1228, or re­ D Applied Analysis, J. E. Marsden, Research Office. Cornell University is spond to: Applicant Code 541 , Advertis­ 607/255-9957 an Equal Opportunity 1Affirmative Action ing Department, AMS, P.O. Box 6248, D Physical Mathematics, J. T. Jenkins, Employer. Providence, Rl 02940. 607/255-7185 D Numerical Analysis, L. Wahlbin, 607/255-2397

JULY/ AUGUST 1989, VOLUME 36, NUMBER 6 799 Classified Advertisements

SITUATIONS WANTED SERVICES ''MANDELBROT 3·· is a program de­ signed to make exploring the mathemat­ TECHNICAL TYPING AND EDITING. Ex­ RESEARCH MATHEMATICIAN available ical wonderland of fractals easy, fast and tensive experience and expert knowl­ fall 1989. Green card anticipated. lan. fun! It has fast math routines so images edge in the preparation of scientific D. Macdonald, 'Tiree··, 10 Middleton, are drawn in minutes, not hours, and manuscripts for publication in mathe­ Menstrie, FK11 7HA, Clackmannanshire, an incremental draw that lets you see matics, physics, and engineering. Call Scotland, UK. Telephone 011-44-259- what you're getting in seconds. Other or write for rates/free brochure. ARC 61601. features include ··point and click'' Julia Enterprises, P.O. Box 416, Hudson, MA sets, contrast-stretching algorithms to 017 49. ( 508) 568-0598. bring out details, multiple palettes, color FOR SALE cycling, mouse and 386 support. Man­ delbrot 3 requires an IBM-compatible CO-AUTHOR WANTED A Testable Unified computer with EGA, and is $25 from Field Theory Involving Emerald City Software, 1805A Felt St., Non-electromagnetic Lights Described Santa Cruz, CA 95062 (408)479-9916 Psych. prof./successful text author seeks and Mathematically Characterized math prof. as coauthor for text on math study habits. Contact: Dr. J. Nevid, 382 By John Lawrence Waters PUBLICATIONS CPW, New York, NY 10025. ABSTRACT A mathematical formula for the natural Jordan Rd., unity is derived as (a): the integration MATH SCI PRESS, 53 MA 02146, 617-738-0307, of two orthogonal vector functions each Brookline, PHYSICAL GEOMETRY, by perturbed by a well potential and (b): TOPICS IN $80. In Preparation: Geo­ as the product of two coplanar vectors R. Hermann, of Computer Science. which spin in opposite directions about metric Aspects a common point. The author hypothesizes a universe in which electromagnetic energy (EM) and material particles are transformed into a non-electromagnetic (NP) energy which involves neutrinos and the light seen by certain sensitive humans including speechless ··autistic·· children, one half of the available energy in the universe being EM and the other half NP energy. Black holes absorb EM and emit NP. Stars absorb NP and emit EM. The Technology author describes ways by which this The Swiss Federal Institute of applications for a theory can be tested. (The same paper in Zurich invites is advertised for sale in the AMS Notices Junior Faculty Position in Mathematics for March 1989) For a copy of this paper, send eight U.S. dollars to: John Waters, P.O.B. The initial appointment will be for three years, 706, Trinidad CA 95570-0706 U.S.A. No renewable for an additional three year term. personal checks. Foreign currency OK. Duties of the new professor include teach­ ing and research in mathematics, natural sci­ ences and engineering. GROUPS DISC: Disc with data of all Candidates should have a university degree groups of order up to 80 (not 64) and and successfully completed own research work. BASIC programs to analyze it. IBM or Willingness to teach at all university levels and Apple Macintosh, though data held as to cooperate with colleagues is expected. ASCII files which can easily be trans­ ferred to other machines. Introductory Applications with curriculum vitae and a list price US $100 with order. of publications should be submitted no later than From SUMS, Department of Math­ August 31, 1989, to the President of the ETH ematics, University College, SWANSEA Zurich, Prof. Hans BOhlmann, ETH-Zentrum, SA2 8PP, UK CH-8092 Zurich.

800 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Centre de Recherches Mathematiques

The term "nonsmooth analysis" was coined by the authorto convey the idea of the systematic study and application of the differential properties of functions not differentiable in the usual sense, together with a related nonsmooth geometry for sets. This book develops the theory as well as its applications, especially to optimization. Particular emphasis is placed upon the analytical theory of ~ OPTIMIZATION AND optimal control and the calculus of variations. NONSMOOTH ANALYSIS This is an unrevised reprinting (with corrections appended) of the complete text as originally published by Wiley lnterscience in 1983.

• "An outstandin9 scholarly work ... very well or9amze~ concise and written in ele9ant style". SIAM Review F.ILCLARKE • "Destined to become a classical reference". Mathematical Reviews • • Russian translation. Nauka Press, ;11oscow, I 988 2nd edition -1989 310 pages, ISBN: 2-921120-01-1 ,------, ORDER FORM I Send __ copy (ies) of Optimization and Specify credit card: Visa 0 or MasterCard 0 Name I Nonsmooth Analysis, $25 CON I $20 US. plus $2 per I I order for shipping. Card number Address------

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• PHYSICISTS • OCEANOGRAPHERS At the Swiss Federal Institute of XonTech. Inc. is expanding its ongoing efforts involving state­ of-the-art signal processing, data modeling and phenom­ Technology in Zurich a enology studies. We need bright, energetic and flexible mathematicians and physicists for these challenging as­ Chair of Mathematics signments. We have positions available for all levels of experience. Background in one or more of these tollowing is to be filled. areas is highly desirable: physical interpretation of sensor data, characterization and understanding of noise and signal phenomenology, advanced signal processing algorithm Duties of the new professor include teach­ development, algorithm design experience for parallel architectures, mathematical modeling of physical phenomena ing and research in mathematics. He will be re­ and sensor data. sponsible for undergraduate and graduate U.S. CITIZENSHIP REQUIRED courses for students of mathematics, natural sciences and engineering. We offer challenging assignments. competitive salaries, an outstanding benefits package, and a pleasant working environment. The openings for the above positions are at our Candidates should have a university degree, Van Nuys, CA headquarters facility. Qualified professionals successfully completed own research work and are invited to submit resumes and salary history to: Haman a proven ability to direct advanced research. Resources, Xon'lech, Inc., 686:1 Hayvenharst Ave., Willingness to teach at all university levels and Van Nays, CA 91406. to cooperate with colleagues is expected. Applications with curriculum vitae and a list ~ X onTech, Inc. of publications should be submitted no later than "People, Science and TechnolOCY" Los Anples Area • Oranp Coanty • Northem California August 31, 1989, to the President of the ETH Colorado Sprlnp • W..hlncton. D.C. • Hantsvllle, Alaballla Zurich, Prof. Hans BOhlmann, ETH-Zentrum, We are an equal opportunity employer M/F/H/V CH-8092 Zurich. UNIVERSITY OF CAPE TOWN Dept. of Mathematics Professor I Associate Professor/Senior Lecturer/Lecturer AppllcaHons are Invited for vacant posts In the Department of Mathematics. vacancies will exist from 1September 1989. Preference will be given to applicants In the fields Functional Analysis, Differential EquaHons, Algebra, Logic, Comblnatorlcs LECTURER/SENIOR and the Theory of Algorithms, or In closely related fields, but candidates In all fields of mathematics are Invited to apply. LECTURER IN~~~~~~ A negotiable salary package Includes anractlve staff benefits t: such as medical aid, a pension scheme and a housing MATHEMATIC . subsidy In certain circumstances. Further details concerning (One Tenured/Tenurable Appointment) remuneraHon will be supplied to applicants for the post. The ranks oflhe successful applicants will be decided upon the basis of qualifications and experience; candidates should Indicate In their LECTURERS leners of application for which post/s they wish to be considered. (FIELD UNSPECIFIED) ...... @i!tl Applicants should submit a full curriculum vitae and the names, addresses and telephone numbers of three referees (One Fixed Term Appointment) not later than 15 August 1989 to the Appointments Officer (ref: DP), University of Cape Town, Rondebosch, 7700, Republic of (OneTenured/ ~ South Africa (telephone no. (021) 65Q-2192; telefax no. (021) 65Q-2138). Further Information may be obtained from the Tenurable Appointment) ~ above, or from the Counsellor, Science and Technology, South African Embassy, Suite 350, 4801 Massachusetts Avenue, NW Appointments in the areas of pure mathematics, washington DC 20016. Applicants should furnish their referees applied mathematics or mathematical computer with copies of c.v:s and list of publlcaHons. Late applications will be considered If the position has not been filled. science are envisaged. Applicants should have a Ph.D or equivalent qualification and proven The nrm policy and practice of the University of Cape Town research achievement in an area that reinforces Is to oppose discrimination In any sphere of university life on grounds of gender, race or creed. ucr has consistently and extends existing strengths in the School. protested, and continues to protest, against apartheid laws The School currently has research strengths in and practices and Is commlned to a lust future tor our country. Information on this 11 available on request. many areas of pure and applied mathematics Bates Wells Recruitment CT • 876R-OS and statistics and is committed to further developing its involvement in mathematical computer science. An appointee with interests in the commercial or industrial applications of mathematics could be seconded for a fixed term as Director of the School's Industrial Mathematics and Statistics Group. The positions will be available from February 1990. Appointments to two positions will be either with tenure or on the basis of a contract with provision for conversion to tenure. Appointment to the other position will be for a At the the Swiss Federal Institute of fixed term of three years. Applicants should Technology in Zurich a indicate the type of appointment for which they wish to be considered by quoting the Chair of Mathematics appropriate Reference Number. is to be filled. Further information from Professor I H Sloan, Head of School [(02) 697 2957]. Applications close 15 August 1989. Duties of the new professor include teach­ Salary: Lecturer A$30,737 range A$40, 100 ing and research in the field of probability the­ Senior Lecturer A$40,937 range ory. He will be responsible for undergraduate A$47,564 and graduate courses for students of mathe­ matics, natural sciences and engineering. Applicants should forward TWO COPIES of: written application (quoting reference number, Candidates should have a university degree, business hours telephone number, together with successfully completed own research work in the names and addresses of two referees); curriculum vitae; and transcript of academic the area of probability theory and a proven abil­ record; to Academic Staff Office, P.O. Box 1, ity to direct advanced research. Willingness to Kensington, N.S.W. 2033. Australia. teach at all university levels and to cooperate with colleagues is expected. Applications with curriculum vitae and a list of publications should be submitted no later than August 31, 1989, to the President of the ETH Zurich, Prof. Hans BOhlmann, ETH-Zentrum, CH-8092 Zurich. '. Trust Saunders for mathe­ ELEMENTARY ALGEBRA AN INTRODUCTION TO LARRY MUGRIDGE. KUTZTOWN HISTORY OF MATHEMATICS6/E matics of unsurpassed UNIVERSITY/ JANUARY 1990 HOWARD EVES. UNIVERSITY ·'-·~~ OF quality. We are committed PREALGEBRA JAMES VAN DYKE OF MAINE AND UNIVERSITY JAMIE EVES. JACK BARKER. JAMES ROGERS. CENTRAL FLORIDA. to publishing the best ~ OF CONNECTICUT/ ALL OF PORTLAND COMMUNITY UNIVERSITY ~ 1989 authors, to maintaining the ~~ ii COLLEGE./MARCH 1990 SEPTEMBER highest standards of ~t. ~ PRECALCULUS WITH ABSTRACT ALGEBRA ~~~~ '"' THOMAS W HUNGERFORD. production and design, .~}! APPLICATION STANLEY I GROSSMAN \?' :' UNIVERSITY OF MONT ANA AND CLEVELAND STATE UNIVERSITY 1989 and to ensuring complete 1.\~l:ri r.;~ p UNIVERSITY COLLEGE. LONDON/ DECEMBER accuracy. As in the past, JANUARY 1990 INTRODUCTION TO ALSO BY GROSSMAN PROOF IN ABSTRACT this commitment is sus­ MATHEMATICS ANDI1EW tained by each book in COLLEGE ALGEBRA, WOHLGEMUTH. UNIVERSITY OF ALGEBRA AND TRIGONOMETRY, MAINE I DECEMBER 1989 our1990 set of mathematics COLLEGE TRIGONOMETRY MATHEMATICAL LOGIC: titles. From ancient founda­ APPLIED CALCULUS 2/E APPLICATION AND THEORY tions through contemporary DENNIS D. BE.RKEY. BOSTON JEAN E RUBIN. PURDUE UNIVERSITY I NOVEMBER 1989 higher mathematics, texts UNIVERSITY I DECEMBER 1989 CALCULUS FOR MANAGEMENT, INTRODUCTORY STATISTICS from Saunders harness the SOCIAL AND LIFE SCIENCES ANTHONY A SALVIA. THE I power of mathematics. I 2E, BERKEY/ NOVEMElER 1989 PENNSYLVIA STATE UNIVERSITY. BRIEF CALCULUS WITH ERIE I DECEMBER 1989 ' APPLICATIONS RAYMOND F 20/20 STATISTICS COUGHLIN AND DAVID E GEORGE W. BERGEMAN. ZITARELLI. BOTH OF TEMPLE NORTHERN VIRGINIA COMMUNITY I UNIVERSITY /SEPIEMBEf11989 COLLEGE. AND JAMES P SCOTT. 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New from the Wiley College Division METHODS OF FINITE CALCULUS: ONE AND SEVERAL MATHEMATICS VARIABLES John W. Brown & Donald Sherbert Sixth Edition 1-63003-9 668pp 1989 $49.50 Saturnino Salas & Einer Hille 1-61195-6 .1,232pp 1990 $60.00(tent)

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THE AVERAGED MODULI OF SMOOTHNESS With Applications in Numerical Methods and Approximation Blagovest Sendov & Vasil A. Popov Both of the Bulgarian Academy of Sciences 1-91952-7 181pp 1989 $57.95

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Archive for Mathematical Logic Constructive Approximation Continuation of Archiv fur mathematische Logik und Editors-in-Chief: R.A. DeVore, Columbia, SC and Grundlagenforschung E.B. Saff, Tampa, FL Managing Editor: H.D. Ebbinghaus, Freiburg An international mathematics journal dedicated to This journal publishes research papers and occasionally Approximations and Expansions and related research surveys or expository papers on mathematical logic. Related in Computation • Function Theory • Functional Analysis areas such as theoretical computer science and philosophy • Interpolation Spaces and Interpolation of Operators are covered as long as the methods of mathematical logic • Numerical Analysis • Spaces of Functions • Special play a significant role. Functions and applications. Abstracted/Indexed in: Mathematical Reviews, Science Abstracted/Indexed in: ASCA, lSI CompuMath, Abstracts, Philosophers' Index, Zentralblatt fur Mathematik Mathematical Reviews, Zentralblatt fur Mathematik ISSN 0933-5846 Title No. 153 ISSN 0176-4276 Title No. 365 1989, Vol. 28 (3 issues) $123.00 1989, Vol. 5 (4 issues) $114.00 Combinatorica Semigroup Forum An International Journal on Combinalorics and Managing Editors: K.H. Hofmann, Darmstadt, W. Germany; the Theory of Computing G.J. Lallement, University Park, Pennsylvania; N.R. Reilly, Editor-in-Chief: Laszlo Lovasz, Budapest Burnaby, Canada; B.M. Schein, Fayetteville Executive Editor: Laszlo Babai, Budapest Scope includes algebraic, topological and partially ordered Managing Editors: Peter Komjath, Budapest; semigroups, semigroups of measure and harmonic analysis Akos Seress, Budapest of semigroups, transformation semigroups, semigroups of Covers combinatorial structures (graphs, hypergraphs, operators, and applications of semigroup theory to other matroids, designs, permutation groups) • combinatorial topics such as ring theory, category theory, automata, logic optimization • combinatorial aspects of geometry and and more. number theory • the theory of algorithms • computational Abstracted/Indexed in: Current Contents, Mathematical complexity theory • randomization • explicit construction in Reviews, SCI, ASCA, Zentralblatt fi.ir Mathematik combinatorics and algorithms. ISSN 0037-1912 Title No. 233 An international quarterly of the J. Bolyai Mathematical 1989, Vols. 38-39 (6 issues total) $192.00 Society published jointly by Akademiai Kiad6 (publishers for the Hungarian Academy of Sciences) and Springer-Verlag. The Mathematicallntelligencer Abstracted/Indexed in: Current Contents, Mathematical Editor-in-Chief: S. Axler, East Lansing, Ml Reviews, Science Abstracts, CompuMath, International Here is the one mathematics journal you will enjoy reading Abstracts in Operations Research, Zentralblatt fi.ir from cover to cover. The Mathematical lntelligencer Mathematik informs and entertains a wide readership of professional ISSN 0209-9683 Title No. 493 mathematicians - especially those stimulated by 1989, Vol. 9 (4 issues) $123.00 discussion of developments in specialties other than their own. Each quarterly issue includes news items, Discrete and Computational Geometry book reviews, mathematical problems and a lively selection Editors-in Chief: J.E. Goodman, New York and of letters to the editor. R. Pollack, New York ISSN 0343-6993 Title No. 283 This international journal publishes significant articles 4 issues $30.50 in fields such as combinatorial geometry • design and analysis of geometric algorithms • convex polytopes • multi­ dimensional searching and sorting • extremal geometric Subscriptions are entered with prepayment only and filled problems • computational topology • geometry of numbers as issues are published. Prices include postage and • packing • covering • tiling. Other fields covered include handling. graph theory • mathematical programming • matroids To subscribe or request a free sample copy, write to: • solid modeling • generalized convexity theory • computer Springer-Verlag, New York, Inc., Attn: Michele Matozzo graphics • combinatorial optimization • image processing • (S238), 175 Fifth Avenue, New York, NY 10010 pattern recognition • cluster analysis • crystallography • VLSI/WSI design • robotics 7/89 8238 Abstracted/Indexed in: Engineering Index, Current Contents, lSI CompuMath, Mathematical Reviews, Zentralblatt fi.ir Mathematik Springer-Verlag ISSN 0179-5376 Title No. 454 . New York Berlin Heidelberg Vienna 1989, Vol. 4 (6 issues) $165.00 ' London Paris Tokyo Hong Kong New titles from Birkhauser Boston Your source for major mathematical developments

PROORESS IN MATHEMATICS PROORESS IN SYSTEMS AND CONTROL THEORY ENRIQUES SURFACES I COMPUTATION AND CONTROL Francois Cossec and Igor Dolgachev Proceedings of a Conference held in Bozeman, Montana, Enriques surfaces are key examples of the classification theory of complex Aug. 1988 algebraic surfaces. Using the arithmetic and combinatorial structures on Kenneth Bowers andjohn Lund the Picard group, this book explores the geometry of these surfaces by Sept. 89 I approx. 400 pages I 0-8176-3438-X I $49.00 I PSCT, Vol. I purely geometric methods, involving delicate combinatorial analysis, valid in arbitrary characteristics. Jan. 89 I 400 pages I 0-8176-3417-7 I $42.50 I PM, Vol. 76 SYSTEMS AND CONTROL: FOUNDATIONS & APPLICATIONS SURFACES DE RIEMANN Eric Reyssat Oct. 89 I approx. 256 pages I 0-8176-3441-X I $30.00 (tent.) I PM ESTIMATION TECHNIQUES FOR DISTRIBUTED PARAMETER SYSTEMS TOPOLOGICAL METHODS IN ALGEBRAIC H.T. Banks and K. 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The theoretical developments are illustrated by NILPOTENT ORBITS, PRIMITIVE IDEALS, numerous numerical examples and by applications of the techniques to AND CHARACTERISTIC CLASSES experimental data. W. Borho,j.L. Brylinski and R.L. Macpherson Sept. 89 I approx. 350 pages I 0-8176-3433-9 I $42.00 (tent.) I SC, Vol. I Nov. 89 I approx. 150 pages I 0-8176-3473-8 I $30.00 (tent.) I PM THE LENGTH SPECTRUM OF A RIEMANN SURFACE Peter Buser NORBERT WIENER: 1894-1964 Jan. 1990 I approx. 350 pages I 0-8176-3406-1 I $35.00 (tent.) I PM Pesi R. Masani This biography provides an incisive look into the life, work and times of one of the great American mathematicians of this Century. Starting with PROORESS IN NONLINEAR DIFFERENTIAL Wiener's childhood fascination for electricity and his early training in EQUATIONS & THEIR APPLICATIONS mathematical logic with Russell, it traces his profound understanding of the commonality of the functioning of the mind and the computer-to PARTIAL DIFFERENTIAL EQUATIONS his conception of the subject of cybernetics-to his penetrating insight into the impending age of automation in all its ramifications. Wiener's AND THE CALCULUS 011 VARIATIONS Essays in Honor of Ennio De Giorgi contributions to philosophy, science and engineering are documented and stress is laid on his considerable interaction with other great minds of }. Colombini, A. Marino, L. Modica, S. Spagnola the times. Volume I I approx. 450 pages I 0-8176-3424-X I $49.00 Volume 2 I approx. 450 pages I 0-8176-3424-8 I $49.00 Nov. 89 I approx. 340 pages I 0-8176-2246-2 I $65.00 (tent.) Aug. 89 I 2 volume set I 0-8176-3426-6 I $90.00 I PNLDE, Vols. I and 2 LINEAR REPRESENTATION OF GROUPS Ernst B. Vinberg PROPAGATION AND INTERACTION OF SINGULARITIES This text provides a comprehensive and detailed exposition of the fun­ IN NONLINEAR HYPERBOLIC PROBLEMS damentals of the representation theory of groups, especially of finite Michael Beals groups and compact groups. The exposition is based on the decompo­ This book presents the first expository overview of the use of microlocal sition of the two-sided regular representation. It is for students of analysis and commutator techniques in the study of solutions to nonlinear mathematics and theoretical physics, in particular quantum mechanics. wave equations. In a clear, comprehensive way the author synthesizes a June 89 I approx. 150 pages I 0-8176-2288-8 I $29.50 variety of research results from the last ten years, providing detailed proofs and descriptions of the central ideas behind the arguments and DIVISOR THEORY including a number of figures to illustrate the geometric aspects of Harold M. Edwards the theory. Divisor Theory is a concise and coherent account of the elements of the Oct. 89 I approx. 150 pages I 0-8176-3449-5 I $30.00 (tent.) I theory of algebraic numbers and algebraic functions as established by PNLDE, Vol. 3 Kronecker. The author, in a clear and interesting exposition, clarifies, simplifies, and extends the theory, providing applications to number fields and function fields. He points out and builds upon one of Kronecker's Available at your local scientific bookstore or order directly from the publisher: most valuable ideas, the definition of greatest common divisors, which Birkhiiuser Boston, Inc. are independent of the ambient field, as compared to factorization llc/o Springer-Verlag Distribution Center, P.O. Box 2485 into primes, which is not. Secaucus, NJ 07096-2491 (201) 348-4033 Nov. 89 I approx. 120 pages I 0-8176-3448-7 I $29.00 (tent.) Booth #201, joint Mathematics Meetings, Boulder, CO Vieweg Mathematics

New titles in our series Further titles in this series: Aspects of Mathematics ed. by Klas Diederich: Urban Cegrell Capacities in Complex Analysis 1988. XII, 153 pp. Softcover. US$ 27.00. The purpose of this book is to study plurisubharmonic and analytic func­ tions in ct" using capacity theory. Capa­ Jean-Pierre Serre cities can be thought of as a non-linear Lectures generalization of measures. The case on the Mordeii-Weil Theorem n =1 has been studied for a long time. In Translated and edited by Martin Brown this book the theory for ct n is developed. from notes by Michel Waldschmidt. 1989. X. 220 pp. Softcover. US $ 34.00. Gerd Faltings, Gisbert Wustholz et al. The book is based on a course given by Rational Points J.-P. Serre at the College de France in A Publication of the Max-Pianck-lnstitut 1980 and 1981. Basic techniques in Dio­ fUr Mathematik, Bonn. Adviser: Friedrich phantine geometry are covered, such Hirzebruch. as heights, the Mordeii-Weil theorem, 2nd Edition 1986. VIII, 268 pp. Soft­ Siegel's and Baker's theorem, Hilbert's cover. US $ 30.00. irreducibility theorem, and the large Contents: Moduli-Spaces (Gerd Fal­ sieve. Included are applications to, for tings) -Heights (Gerd Faltings) -Some example, Mordell's conjecture, the con­ Facts from the Theory of Group Sche­ struction of Galois extensions, and the mes (Fritz Grunewald) -Tate's Conjec­ classical class.number 1 problem. ture on the Endomorphisms of Abelian Varieties (Norbert Schappacher) - The Finiteness Theorems of Faltings (Gis­ bert Wustholz) - Complements (Gerd Yves Andre Faltings) -Intersection Theory on Arith­ G-Functions and Geometry metic Surfaces (Ulrich Stuhler). A Publication of the Max-Pianck-lnstitut This book consists of the notes from the To order these or other fur Mathematik, Bonn. Adviser: Friedrich seminar Bonn/Wuppertal 1983/84 Vieweg titles, Hirzebruch. about arithmetic algebraic geometry. It please contact: a proof for the Mordell-conjec­ GLP International 1989. XII, 231 pp. Softcover. US$ 30.00. contains Vieweg-Dept. The so-called G-functions were intro­ ture. On the way the reader may learn 560, Sylvan Avenue, duced as tools into the theory of dio­ about the pioneering work of S. Ara­ Englewood Cliffs, NJ 07622 phantine approximations by C. L. Siegel kelov, A. N. Parshin and J. G. Zarhin, Telephone (201) 871-1010 in 1929. Their importance for modern especially about S. Arakelov's new view telex (00230) 13-5368 arithmetic algebraic geometry became of diophantine geometry. The topics apparent by fundamental research of E. include moduli spaces, heights, finite Vieweg Publishing P. 0. Box 5829 Bombieri (1981). The present book is group schemes, Tate conjecture, Sha­ D-6200 Wiesbaden, F. R.G. the first systematic introduction into this farevich conjecture, and arithmetic sur­ telex 4186 928 field. faces. telefax (06121) 160229 Then, introduce yourself to the over­ Plus, your very own HP-288 cal­ head display for the HP-288. It allows culator free. (A $235 retail value.) you to project your calculations on an HP-288 for everyone in the class­ To learn more, and get free curric­ room to see. ulum materials, call (503) 757-2004 between Sam and 3pm, PT. Offer Now there's a better way to teach A scholastic offer for you. ends October 31, 1989. algebra and calculus in the class­ room. In fact, two ways. If your department or students There is a better way. purchase a total of 30 HP-288 cal­ First, introduce your students to the culators, we'll give you a classroom HP-288. It's the only calculator that overhead display for the HP-288 FJ/;'1 HEWLETT offers symbolic algebra and calculus. absolutely free. (A $500 retail value.) a:~ PACKARD

Calculator Support, Hewlett-Packard, 1000 NE Circle Blvd., Corvallis, OR 97330 Seven NEW Reasons to come to Academic Press New Software for Fractals! Number Theory, Vertex Operator Algebras The Desktop Fractal Trace Formulas and the Monster Design System and Discrete Groups 1.8. Frenkel, J. Lepowsky, and A. Meurman Michael Barnsley Symposium in Honor This work is motivated by and develops Designed to complement Michael of Atle Selberg, Oslo, Norway, connections between several branches of Barnsley's best selling text Fractals July 14--21, 1987 mathematics and physics-the theories of Everywhere, this software, which will Lie algebras, finite groups and modular edited by functions in mathematics, and string theo­ run on IBM and compatible PCs with an Karl Egil Aubert, Enrico Bombieri, enhanced graphics board and 640K mem­ and Dorian Goldfeld ry in physics. ory, will help to connect theoretical con­ One of the most powerful mathemati­ March 1989, 560 pages, $69.95 cepts with on-screen geometric modeling. cians of this century, Atle Selberg has al­ ISBN: 0-12-267065-5 Special features include interactive con­ most single handedly changed the course trol of complex images, graphics gener­ of modem analytic number theory. The Large Deviations ated by deterministic algorithms and by aim of the conference was to survey random iteration, a library of complex Selberg's principle contributions to mathe­ Jean-Dominique Deuschel images, a library of IFS codes, and maps matics in the areas of prime number theo­ and Daniel W. Stroock of parameter spaces and generalized ry and zeta functions, sieve methods, trace This book provides a survey of the Mandelbrot sets. formulas and discrete groups, and also to modem mathematical theory of large August 1989, c. 30 page manual and floppy focus on their most recent development. deviations. Starting from two classical disk, $39.95 (tentative)/ISBN: 0-12-079063-7 February 1989, 530 pages, $69.95 examples, Cramer's Theorem concerning ISBN: 0-12-067570-6 independent R-random variables and Fractals Everywhere Schilder's Theorem for rescaled Wiener measures, the authors develop general Michael Barnsley Elements of Differentiable principles. "If you want a genuine understanding of Dynamics and Bifurcation May 1989, 322 pages, $34.95 fractals as mathematics ... this is an excel­ ISBN: 0-12-213150-9 lent place from which to start." Theory -NATURE David Ruelle November 1988, 424 pages, $39.95 CALL TOLL FREE ISBN: 0-12-079062-9 Written by one of the eminent research­ ers in the field, this introductory text pre­ 1·800-321-5068 sents the elements of the theory of differ­ Quote this reference number for Lectures on Buildings entiable dynamical systems to students of free postage and handling on your prepaid order • 13089 Mark Ronan mathematics and the natural sciences in a lucid, yet rigorous way. The emphasis on The theory of buildings was developed, subjects such as infinite dimensional mainly by Jacques Tits in the 1950s, in an systems, non-invertible maps, attractors, attempt to develop a systematic interpreta­ and bifurcation theory is dictated by a tion of semi-simple Lie groups, particu­ view toward applications to natural phe­ ACADEMIC PRESS larly the exceptional groups. This book nomena. Harcourt Brace• Jovanovich, Publishers presents an up-to-date account of this Book Marketing Department #13089 theory, including such new developments February 1989, 200 pages, $27.50 1250 Sixth Avenue, San Diego, CA 92101 ISBN: 0-12-601710-7 Prices subject to change without notice. ©1989 by Academic Press, Inc. as the chamber systems. The book starts AU Rights Reserved. CBiLK -13089. from basic principles and later deals with important classes of buildings, particulary those of spherical and affine type. June 1989,214 pages, $27.95 ... and there are more at booths 206 & 207 ISBN: 0-12-594750-X at the Summer AMS Meeting Game-Theoretic and Mathematical Modeling

New Games and Economic Behavior

Games and Economic Behavior publishes original and survey papers dealing with game-theoretic modeling 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.

New IMPACT of computing in Science and Engineering

IMPACT of Computing in Science and Engineering focuses on articles from the areas of mathematical and scientific modeling, scientific computing, computer science, and scientific and engineering applications. The journal is interdisciplinary. Its papers will touch upon a combination of at least two of the four main areas. Articles typically will describe real-life problems attacked by a new or specifi­ cally adapted algorithm or by any other new computing technique.

Please enter my subscription for: When paying by credit card, please check one box: Games and Economic Behavior In the U.S.A. All other D Visa/Barclaycard D American Express D Volume 1 (1989), 4 issues and Canada countries D MasterCard/Access D Diner's Club ISSN 0899-8256 $100.00 $122.00 Expiration Date (Mo/Yr): ___ IMPACT of Computing in Science and Engineering Credit D Volume 1 (1989), 4 issues card ISSN 0899-8248 80.00 92.00 number: I I I I I Ill I II II I I I I Please send me: D A sample copy of ______D Privileged personal rate information. Personal sub- Signature: ------scription rates are available only on orders placed directly with the Publisher and paid for with per­ Total Amount: $ ____ sonal funds. Checks and money orders must be drawn against a U.S. bank. Name: ______Method of payment: D Purchase order D Check D Credit information is enclosed. is enclosed. is given. Address: ------D Enter as a Standing Order (institutions only) hereby authorizing Academic Press to service and bill our account each calendar year until cancelled. Please note: Payment or credit card information must City:------accompany order. Prices include postage, handling, and air freight where applicable, and are subject to State: ______Zip: ______change without notice. Payment must be in U.S. cur­ rency, U.S. Bank Draft, International Money Order, or UNESCO coupons. S9177B Country: ------NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF MATHEMATICS

Applications are invited for teaching appointments from candidates who are able to teach in one or more of the following areas: Pure Mathematics Applied Mathematics Operational Research Statistics

Candidates should possess a PhD degree in Mathematics or its equivalent. Gross annual emoluments range as follows: Lecturer ...... S$50,390 - 64,200 Senior Lecturer ...... S$58,680 - 100,310 Associate Professor .... S$88,650 - 122,870 (US$1 = S$1.94 approximately)

The commencing salary will depend on the candidate's qualifications, experience and the level of appointment offered. Leave and medical benefits will be provided. Depending on the type of contract offered, other benefits may include: provident fund benefits or an end-of-contract gratuity, a settling-in allowance of S$1 ,000 or S$2,000, subsidised housing at nominal rentals ranging from S$1 00 to S$216 p.m., education allowance for up to three children subject to a maximum of S$1 0,000 per annum per child, passage assistance and baggage allowance for the transportation of personal effects to Singapore. Staff members may undertake consultation work, subject to the approval of the University, and retain consultation fees up to a maximum of 60% of their gross annual emoluments in a calendar year. The Department of Mathematics is a department in the Faculty of Science. There are eight faculties in the National University of Singapore with a current student enrolment of some 14,000. All departments are well-equipped with a wide range of facilities to enhance the teaching and research activities of staff members. The University is linked to BITNET, an international network that interconnects almost 500 mainframe computers at 200 institutions of higher learning and research centres around the world. Application forms and further information on terms and conditions of service may be obtained from: The Director The Director Personnel Department North America Office National University of Singapore National University of Singapore 10 Kent Ridge Crescent 780 Third Avenue, Suite 2403 Singapore 0511 New York, N.Y. 10017, U.S.A. Tel: (212) 751-0331 Enquiries may also be sent through BITNET to: PERSDEPT@NUSVM Available from JPBM: MA'fHEMA 'fXCAJL lPOS'fERS AND POSTCARDS

On the occasion of Mathematics Awareness Week, the Joint Policy Board for Mathematics commissioned the printing of the posters and postcards that were designed to acquaint the public with this year's theme, "Mathematics: Discovering Patterns". Copies are still available of these well-designed objects:

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JPBM Visuals 818 Connecticut Ave., NW Suite 515 Washington, DC 20006 Anomalous Treatment of Submissions to Journal of Pure and Applied Algebra

A most unusual - one would guess unique - procedure can apparently be applied to papers submitted for publication in the JPAA. Ostensibly submissions are made to any of the editors who then handles the manuscript: sending it to referees, mediating between them and the author and (in case of acceptance) transmitting it to the Managing Editor to be sent for printing. This was in fact the procedure for the first two papers I had published in JPAA. The third, after undergoing a more than usually thorough examination by two independent referees (resulting in a revision which cleared up some obscurities and other details) was transmitted as accepted by the examining editor - but not sent on to North Holland by the Managing Editor. Instead, the latter sent me a rather formal letter in which he acknowledged receiving the manuscript as accepted for publication, but added that since it is Journal policy to publish only papers in English (this appears to be factually false by the way) he must reject the manuscript "on that ground" and would not accept it unless it had been "translated" so as to enable him to understand the result. My letters to the Managing Editor pointing out the ludicrousness of this dictum and its untenability in the face of the expressed opinions of the referees, the accepting editor and in fact of everyone who had looked at the paper remaining unanswered, I then circulated this Kafka­ esque exchange to the other editors on the Board. Some 90% of them elected to make no response - perhaps because they were used to similar shenanigans by their Managing editor? The two who acknowledged receiving copies of the correspondence claimed to be unable to comment by reason of not having seen the paper- thus found nothing objectionable in a Managing Editor's capriciously overriding the acceptance of a carefully refereed paper by firing off a patently preposterous pretext which he refuses to reconsider in a moment of possibly greater reasonable­ ness. I thereupon made a second attempt by sending around to the full Editorial Board just the Abstract of the paper (the Managing Editor's unique pronouncement purporting to require a translation only to the extent of obtaining "some understanding of the main result" - not of its proof). To their credit, none of the editors wrote back to confirm that the text was not in English; in fact, only one bothered to respond at all. He favored me with the tale of his own tri­ bulations as an Editor vis-a-vis referees who recommend badly written papers (thus the problems at the level of an examining rather than of a managing editor) volunteered to interpret the deter­ mination of not being in English - which he characterized as "an unfortunate choice of words" - as a request for a revision (without specification of what, if anything, needed it) and closed by finding the Abstract "totally incomprehensible" (I subsequently showed the Abstract to some non-mathematicians all of whom succeeded in correctly parsing the statements and grasping their content). The following finding seems to be warranted by the above: its Managing Editor runs the JPAA as an unopposed autocrat, consulting nothing but his momentary whim for his decisions, undeterred by the disjointness of his proclamations from any basis in reality or by the remoteness of his goings on from universally accepted standards of scholarly intercourse; and the other edi­ tors on the Board, insofar as they do not concur, are resigned to putting up with this state of affairs without objecting.

I. Fleischer

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Frobenius. Reiner's style is precise and agreeable to the Irving Reiner reader, his arguments always to the point, in one word, masterly."- Paulo Ribenboim, F.R.S.C., Queen's Univer­ Selected Works sity, Kingston, Ontario. Edited by Gerald}. Janusz "The subject matter of Reiner's work is still pursued inten- sively by a good part of the mathematical population, and ...._~ the availability of Reiner's important and original research The papers of Irving Reiner reproduced here represent a part of the life's work of a dedicated and influential math­ in one source will be appreciated by many working math­ ematician. His early papers were concerned with groups ematicians."- Morris Newman, University of California, of invertible matrices over integral domains and their Santa Barbara; author of Integral Matrices. studies led naturally to the study automorphisms. These "A richly deserved tribute to Professor Reiner's 1ife-long of integral representations of groups and orders with at­ research on integral representation theory, and to the deep tempts to classify their representations using Grothen­ dieck rings and their relative versions, Picard groups, and and lasting influence his work exerted on the modern class groups. His later papers dealing with zeta-functions development of that subject."- T. Y. Lam, University of r- _ -- bring quantitative methods and new ideas to the repre­ California, Berkeley. sentation theory. The influence of Reiner's work is most Cloth, $70.00. strongly felt by research mathematicians interested in problems related to integral representation theory. Order toll free 800/666-2211, or from ''This volume embodies work that is now classic and fol­ lows the tradition of the great masters, like Schur and e University of Illinois Press l MJII cJo CUP Services • P. 0. Box 6525 .Ithaca, NY 14851 I L l I American Mathematical Society

Translations Editor Position Open

The Translations Department of the Society is seeking applications for this position from mathemati­ cians with a reading knowledge of Russian. The person selected will work in the Society's Providence office, assisting on the Russian-to-English translation project. The project in question handles Russian language contributions to mathematics in all fields at the current research level. This means that applicants should have some aquaintance with the literature as it exists and is developing today. Ideally, the person filling the position will have a background that includes some research in mathematics. Qualified applicants will be given an opportunity to demonstrate their mathematical and linguistic skills on material that is representative of the actual textual matter dealt with in the project. Applications should be sent to: Human Resources American Mathematical Society P.O. Box 6248 Providence, Rl 02940 The Society is an equal opportunity employer and has a generous fringe-benefit program including TIAA/CREF.

MAPLE: Symbolic Now available from the AMS: Computation for Introducing Mathematica A Science Television Production the Macintosh This new videotape features Mathematica by The Symbolic Computation Group creator Dr. Stephen Wolfram demonstrating his Introductory price just $395! award winning new software on a Mac Ilx. Requiring only one megabyte of memory, ' MAPLE gives you the power to do a wide range Dr. Wolfram energetically leads the viewer of symbolic and numeric computations with through a variety of numerical calculations, astonishing speed. In fact, with two megabytes algebraic calculations and graphical renderings. of memory, you can solve problems that are He concludes with a discussion of programming virtually impossible by other methods. in the language of Mathematica. MAPLE features: • more than 1500 built-in mathematical functions that can be modified or extended • a complete on-line help system • Throughout this videotape, the computer screen two dimensional graphics • and much more! is clearly displayed showing the graphics in color and the commands in a large bold font for easy Order your MAPLE single user package today (Nine reading. It will serve as a brief survey of the 3.5 BOOK disks, tutorial, reference manual) by calling toll free (800) 354-9706 or writing to the address capabilities of this revolutionruy new below. No risk! Brooks/Cole offers a 30-day 100% mathematical software. money back guarantee. Questions? Call our software support representative at (408) 373-0728. VHS format. approximately one hour, 1989 Price $49 lei JBC002 To order, please specify VIDWOLFRAM/NA Publishing Company 1.:LJ Brooks/Cole Shlpptng/handltng: let tape $2, each add'! $1, $25 max. By air, let 511 Forest Lodge Rd. tape $5, each add'! $3, $100 msx. Prepqmeat reqaked. Order from Pacific Grove, CA 93950 AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call 800-556-7774 to use VISA or MasterCard. Application for Membership 1989

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Working Days OR telephone (313) 996-5268 and ask for MathDoc. And MathDoc has over a 95% success rate in quickly OR send your order via FAX (313) 996-2916 locating and supplying the articles in journals, collec­ OR send electronic mail (Internet) to tions, and conference proceedings listed in CMP, MR, [email protected] and MathSci...usually within two working days. All electronic mail will be acknowledged. Although MathDoc cannot ordinarily supply an entire OR order through the DIALOG DIALORDER or book, it often can give you information about the the BRS systems. book's availability through other sources. Infinite-Dimensional Topology Hypergraphs Prerequisites and Introduction Comblnatorlcs of Finite Sets by J. van Mill by C. Berge

(North-Holland Mathematical library, 43) (North-Holland Mathematical library, 45) 1989 xii + 402 pages 1989 Approx. 270 pages Hardbound Price: US $79.00/Dfl. 150.00 Price: US $79.00/Dfl. 150.00 ISBN 0-444-87133-0 ISBN 0-444-87489-5 Paperback Price: US $44.75/Dfl. 85.00 Translation of Hypergraphes: Combinatoires des Ensembles ISBN 0-444-87134-9 Finis (Bordas, Paris, 1987)

One can look upon this book as a complete and The idea of looking at a family of sets took shape around self-contained proof of Torunczyk's Hilbert cube manifold 1960.1n regarding each set as a "generalised edge· and in characterization theorem: a compact ANR X is a manifold calling the family itself a "hypergraph", the initial idea was to modeled on the Hilbert cube if and only if X satisfies the try to extend certain classical results of Graph Theory such disjoint-cells property. as the theorems of Turan and KOnig. In the process of proving this result several interesting and It was noticed that this generalisation often led to useful detours are made. simplification; moreover, one single statement, sometimes Contents: Extension Theorems. Elementary Plane Topology. remarkably simple, could unify several theorems on graphs. Elementary Combinatorial Techniques. Elementary This book presents what seems to be the most significant Dimension Theory. Elementary ANA Theory. work on hypergraphs. An Introduction to Infinite-Dimensional Topology. Cell-like Contents: General Concepts. Transversal Sets and Maps and a-Manifolds. Applications. What Next? Matchings. Fractional Transversals. Colourings. Bibliography.lndex. Hypergraphs Generalising Bipartite Graphs. Appendix: Matchings and Colourings in Matroids. References. Stochastic Differential Equations and Diffusion Graphs Processes Third Revised Edition Second Edition by C. Berge byN.Ikeda andS. Watanabe (North-Holland Mathematical library, 6) 1985 xiv + 414 pages (North-Holland Mathematical library, 24) Price: US $56.25/Dfl. 150.00 1989 568 pages ISBN 0-444-87603-0 Price: US $147.25/Dfl. 280.00 ISBN 0-444-87378-3 •... the revisions succeed admirably in bringing the reader up In Japan: Kodansha, Ltd. to date with the current situation in graph theory and then launching him or her on many interesting research ON THE FIRST EDITION: COMMENTS problems.· "This book has been eagerly awaited by experts ... The Mathematical Reviews authors are to be congratulated on a splendid piece of exposition.· Short Book Reviews •... has been carefully constructed and lucidly presented; it Advanced Calculus for Users will become a standard reference.· European Journal of Operational Research by A. Robert

A considerable number of corrections and improvements 1989 x + 366 pages have been made for the second edition of this classic work. Price: US $60.50/Dfl. 115.00 In particular, major and substantial changes are in Chapter ISBN 0-444-87324-4 Ill and Chapter V where the sections treating excursions of Co-Publisher and Distributor for Switzerland: Brownian Motion and the Malliavin Calculus have been PAN, Neuch/itel expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been This monograph is applications oriented, aimed at those who added. need to use advanced calculus in their work. Contents: Stochastic Integrals and Ito's Formula. Stochastic Contents: Differentiability. Integration of Differential Forms. Calculus. Stochastic Differential Equations. Diffusion Function Spaces. Fourier Series. Appendices: Convergence, Process on Manifolds. Theorems on Comparison and Definitions and Results. SAS Programs for a Few Figures. Approximation and their Applications. Bibliography. Index. Exercises. Bibliography. Index. NORTH-HOLLAND In the USA and Canada: For all other countries: Elsevier Science Publishing Co. Inc. Elsevier Science Publishers P.O. Box 886, Madison Square Station Book Order Department, P.0. Box 211 New York, NY 10159, USA 1000 AE Amsterdam, The Netherlands US $prices are valid only in the USA and Canada. In all other countries, the Dutch Guilder (Dtl.) price is defin~ive. Cuslomenl in The Netherlands, please add 6% BTW. In New York State, applicable sales tax should be added. All prices are subject to change without prior nolice. 407/B/0980 theory of these concepts, to the way in which they Classical Recursion Theory developed first in mathematical logic and computability theory and later in automata theory, and to the theory of The Theory of Functions and Sets formal languages and complexity theory. Priority is given to of Natural Numbers the new aspects of traditional questions, results and methods which have developed from the needs or by P .G. Odlfreddl knowledge of computer science and particularly of complexity theory. (Stucies in Logic and the Foundations of Mathematics, 125) 1989 xviii + 668 pages Price: US $110.50/Dfl. 210.00 Logic Colloquium '88 ISBN 0-444-87295-7 Proceedings of the Colloquium, Padova, Italy, August1988 1988 marks the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. This book edited by R. Ferro, C. Bonotto, S. Valentini is both a comprehensive reference for the subject and a textbook starting from first principles. and A. Zanardo Contents: Recursiveness and Computability. Basic Recursion Theory. Post's Problem and Strong (Stucies in Logic and the Foundations of Mathematics, 127) Reducibilities. Hierarchies and Weak Reducibilities. 1989 viii + 424 pages Turing Degrees. Many-One and Other Degrees. Price: US $110.50/Dfl. 210.00 Bibliography.lndex. ISBN 0-444-87455-0 "'difrecki has written a delightful yet scholarly treatise ... • G. E. Sacks, Harvard University and M.I.T. Contents: On the Model Theory of Free Metabelian Groups of Bounded Exponent (A. Baudisch). D.O.P. and n-Tuples of Models (E. Bouscaren). Algebra and Model Theory of Chain Fields: An Overview (M.A. Dickmann). A Lefschetz Principle Combinatorics for Integral Closures (A. Macintyre). The c'-Aigebras of Three-Valued Logic (D. Mundici). Some Problems and edited by A. Hajnal, L. Lovasz andV.T. Sos Results in the Theory of Actually Computable Functions (W.A. Maass, T.A. Slaman). Kleene-Spaces (D. Normann). (Colloquia Mathematica Societatis Janos Bolyai, 52) On Bounded Time Turing Reducibility on the Recursive Sets 1988 596 pages (T.A. Slaman). The n 1 ~Singleton Conjecture: An Price: US $223.75/Dfl. 425.00 Introduction (S. Friedman). The Descriptive Set Theory of ISBN 0-444-70345-4 a-Ideals of Compact Sets (A.S. Kechris). Solving Equation Distributed in the Socialist Countries by Kuhura, Budapest in Lambda-Calculus (C. 86hm, A. Piperno, E. Tronci). Comparative Logics and Abelian /-Groups (E. Casari). Leading combinatorialists from around the world contributed Finitary Inductively Presented Logics (S. Feferman). to this volume. The plenary lecturers were: Geometry of Interaction: Interpretation of System F J. Beck(on combinatorial games), B. Bollobas(on cycles in (J. Y. Girard). lntuitionistic Formal Spaces and their random graphs), A. Brouwer(on extremal design theory), Neighbourhood (G. Sambin). Probabilistic Models P. Erd6s (on problems and results in combinatorics), (R. Chuaqui). Logical Partial Functions and Extension C. Godsil (on the application of linear algebra in of Equational Logic (W. Craig). combinatorics), L. Lovasz(on matching theory), A.A. Razborov(on Boolean complexity), M. Saks (on collective coin flipping), and A. Schrijver(on disjoint paths in graphs). Iterative Methods for the Solution of Linear Systems Computability, Complexity, edited by A. Hadjldlmos Logic Reprinted from the Journal of Computational and Applied Mathematics, Volume 24, Nos. 1-2 edited by E. BOrger 1989 vi + 292 pages Price: US $84.25/Dfl. 160.00 (Studies in Logic and the Foundations of Mathematics, 128) ISBN 0-444-87277-9 1989 About610 pages Price: US $118.50/Dfl. 225.00 The iterative solution of linear systems of algebraic ISBN 0-444-87406-2 equations is a subject with numerous applications. This Translation of "Berechenbarkeit, Komplexitllt, Logik" collection of 20 papers includes: (i) extensions of the (V~eweg, Wiesbaden, 1985) classical iterative method of Jacobi, SOR etc., and others, e.g. the Semiiterative and the Conjugate Gradient methods The theme of this book is formed by a pair of concepts: the are developed, studied and applied, (ii) the consideration of concept of formal language as carrier of the precise square and rectangular coefficient of the linear system; in expression of meaning, facts and problems, and the concept the former case singular matrix coefficients are also treated, of algorithm or calculus, i.e. a formally operating procedure (iii) the description of new computer packages for classes of for the solution of precisely described questions and iterative methods, (iv) the proposition of algorithms for problems. The book is a unified introduction to the modem sequential and parallel computers. NORTH-HOLLAND In the USA and Canada: For all other countries: Elsevier Science Publishing Co. Inc. Elsevier Science Publishers P.O. Box 886, Madison Square Station Book Order Department, P .0 . Box 211 New York, NY 10159, USA 1000 AE Amsterdam, The Netherlands

US S price~- valid oriy in the USA and Canada. In all other oountriea, the Ould1 Guilder (Oft.) price ;. definilille. C..-s in The Nether~Mcll. please aid 8% BTW. In New Yook ~ • ..,._,.. ... lax should be added. AI prioel-.ubject 1o change~ prior notice. 4071t!10980a Choose Springer-Verlag Books for ill!l Your Research and Enjoyment! Collected Papers The Book of Prime Number Records Volume I Second Edition By A. Selberg By P. Ribenboim From the foreword: This new edition of The Book of Prime Number Records "The early work of Atle Selberg lies in the fields of analysis has been completely updated. As in the first edition, it devotes itself and number theory. It concerns the Riemann zeta-function, Dirichlet's to much more than presenting records concerning prime numbers. L-functions, the Fourier coefficients of modular forms, the distribu­ It moves on to explore the interface between computations and the tion of prime numbers, and the general sieve method. It is brilliant, theory of prime numbers. A current historical presentation of the and unsurpassed, and in the finest classical tradition. His later work main problems about prime numbers, as well as many fascinating cuts across many fields: function theory, operator theory, group topics, including primality testing , are included. In addition , it is theory, topology, differential geometry, and number theory. written in a language that is accessible to a broad audience - even It has enlarged and transfigured the whole concept and structure of non-mathematicians will enjoy it! arithmetic. It exemplifies the modern tradition at its sprightly best, 1989/app. 478 pp./Hardcover $54.00/ISBN 0-387-97042-8 and makes him one of the master mathematicians of our time." 19891711 pp./Hardcover $130.00 /ISBN 0-387-18389-2 Also available by the same author: 13 Lectures on Fermat's Last Theorem Coxeter Graphs and Towers of Algebras 1979/302 pp./Hardcover $45.00 ISBN 0-387-90432-8 By F.M. Goodman, P. de La Harpe, and V. Jones The authors address certain algebraic and von Neumann Weakly Differentiable Functions algebraic topics closely related to a recent paper on subfactors of Sobolev Spaces and Functions of Bounded Variation von Neumann factors which has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of By W.P. Ziemer this paper that certain algebras which are used there for the analysis The major thrust of this book is the analysis of pointwise of sub factors could also be used to define a new polynomial invar­ behavior of Sobolev functions of integer order and BV functions. iant for links. Recent efforts to understand the fundamental nature The analysis includes Lebesgue points and capacity, the comparison of the new link invariants has led to connections with invariant of distributional and approximate derivatives, and a development theory, statistical mechanics and quantum theory. In turn , the link that allows the approximation of Sobolev functions in a strong sense invariants, the notion of a quantum group, and the quantum Yang­ by smooth functions. Also included is a treatment of Sobolev­ Baxter equation have had great impact on the study of subfactors. Poincare type inequalities. 1989/288 pp., 3 illus.!Hardcover $32.00/ISBN 0-387-96979-9 Weakly Differentiable Functions is intended for graduate Mathematical Sciences Research Institute Publications, Volume I4 students and researchers whose interests may include aspects of approximation theory, the calculus of variations, partial differential equations, potential theory and related areas. The only prerequisite Commutative Algebra is a standard graduate course in real analysis. Edited by M. Hochster, C. Huneke, and J.D.Sally 19891app. 312 pp., 1 illus./Hardcover $49.00/ISBN 0-387-97017-7 This volume reflects a " Microprogram in Commutative Graduate Texts in Mathematics, Volume 120 Algebra:· The intent of the program was to survey recent major results and current trends in the theory of commutative rings , espe­ Algebra I commutative Noetherian rings. The papers represented in this cially Basic Notations of Algebra volume, some of which are expository, some strictly research, and some a combination, give a cross-section of what is happening now By I.R. Shafarevich in this area. Edited by A.l. Kostrikin translated from the Russian by M. Reid Contributors: K.Ak.in, D.A. Buchsbaum, M. Auslander, I. Rieten, L.L. Avramov , J. Backelin, J. Herzog, H. Bass, W. Bruns, This book is wholeheartedly recommended to every student S.P. Dutta, D. Eisenbud, J.-H. Koh, D. Eisenbud, D. Saltman, or user of mathematics. Although the author modestly describes his E.G. Evans, P.A. Griffith, R. Fedder, K.-i. Watanabe, S. Goto, book as "merely an attempt to talk about" algebra, he succeeds in E. Hamann, W. Heinzer, D. Lantz, M. Hochster, C. Huneke, writing an extremely original and highly informative essay on B. Ulrich, A. Iarrobino, W-E. Kuan, C. Rotthaus, G. Lyubeznik, algebra and its place in modern mathematics and science. S. McAdam, L.J. Ratliff, J.D. Sally, D. Rees, P. Roberts, From the fields , commutative rings and groups studied in J.D. Sally, R. Sharp, W.V. Vasconcelos, R. Wiegand. every university math course, through Lie groups and algebras to 1989/516 pp., 3 illus./Hardcover $49.80/ISBN 0-387-96990-X cohomology and category theory, the origins of each algebraic Mathematical Sciences Reasearch Institute Publications, Volume 15 concept can be related to attempts to "coordinatise" (or model) phenomena of physics or other branches of mathematics. 1989/app. 272 pp., 45 illus./Hardcover $59.80 ISBN 0-387-17006-5 Encyclopaedia of Mathematical Sciences, Volume 1 I P.S. 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