OTICES OF THE
AMERICAN MATHEMATICAL SOCIETY
Hoboken Meeting (October 21-22) page 1011
Muncie Meeting (October 27-28) page 1021
OCTOBER 1989, VOLUME 36, NUMBER 8 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences
This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub and annual meetings are joint meetings of the Mathematical Associ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet mathematics and from the headquarters office of the Society. Ab ing dates which fall rather far in the future are subject to change: this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. Meetings
Abstract Program Meeting# Date Place Deadline Issue 851 • October 21-22, 1989 Hoboken, New Jersey Expired October 852 • October 27-28, 1989 Muncie, Indiana Expired October 853 • November 18-19, 1989 Los Angeles, California Expired November 854 • January 17-20, 1990 Louisville, Kentucky October 11 December t (96th Annual Meeting) 855 • March 16-17, 1990 Manhattan, Kansas December 12 February 856 • March 23-24, 1990 Fayetteville, Arkansas December 12 February 857 • April 7-8, 1990 University Park, Pennsylvania January 25 March 858 • April 19-22, 1990 Albuquerque, New Mexico January 25 March 859 • August 8-11, 1990 Columbus, Ohio May 18 July I August (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 1083 for listing of special sessions. t Housing deadline is November 17
Conferences
June 7-July 4, 1990: Joint Summer Research Conferences in July 1990: AMS Summer Research Institute on Differential the Mathematical Sciences, University of Massachusetts at Geometry, location to be announced. Amherst, Massachusetts. January 16-17, 1989: AMS Short Course on Mathematical June/July 1990: AMS-Siam Summer Seminar on Vortex Questions in Robotics, Louisville, Kentucky. Dynamics and Vortex Methods, location to be announced. Deadlines
December Issue January Issue February Issue March Issue Classified Ads• Oct 27, 1989 Nov 27, 1989 Jan 10, 1990 Feb 8, 1990 News Items Nov 2, 1989 Nov 27, 1989 Jan 2, 1990 Feb 9, 1990 Meeting Announcements•• • Oct 23, 1989 Nov 20, 1989 Dec 21, 1989 Jan 29, 1990 • 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
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ARTICLES DEPARTMENTS
981 Modeling the Aids Epidemic: Mathematical Techniques Provide 979 LeHers to the Editor Qualitative Insights 1003 News and Announcements Mathematical models are useful in predicting the course of the AIDS epidemic and in understanding what measures are effective in stemming 1007 Funding Information for the its spread. This article describes the work of a group at Los Alamos Mathematical Sciences National Laboratories, whose models incorporate the social aspects of 1009 Meetings and Conferences the spread of the AIDS virus. of the AMS (Listing) 1090 1989 AMS Elections Candidates Election Information 1091 Mathematical Sciences Meetings and Conferences FEATURE COLUMNS 1100 New AMS Publications 1101 AMS Reports and Communications 984 Computers and Mathematics Jon Barwise Recent Appointments, 11 01 This month's column contains three reviews, one of APL *PLUS PC and Reports of Past Meetings, 1101 two of Milo. The two reviews of the same product are included in this column to illustrate the importance of perspective in the outcome of a 1105 Miscellaneous review. Also included is an informal exposition of some work of Gregory Personal Items, 11 05 Chaitin. Deaths, 11 05 Visiting Mathematicians (Supplement), 1106 1001 Washington Outlook Application Deadlines, 11 08 This month's column, written by Hans J. Oser, provides an overview of current events on Capitol Hill of interest to Notices readers. 1110 New Members of the AMS 1112 Classified Advertising 1131 Forms
OCTOBER 1989, VOLUME 36, NUMBER 8 977 Chaos and Fractals The Mathematics Behind the Computer Graphics Robert L. Devaney and Linda Keen, Editors AMERICAN MATHEMATICAL SOCIETY This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Provi dence, Rhode Island, in August, 1988. EDITORIAL COMMITTEE Chaos and fractals have been the subject of great interest in recent years and Robert J. Blattner, Michael G. Crandall Robert M. Fossum (Chairman) have proven to be useful in a variety of areas of mathematics and the sciences. Lucy J. Garnett, D. J. Lewis The purpose of the Short Course was to provide a solid introduction to the Nancy K. Stanton, Robert E. L. Turner mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Man INTERIM MANAGING EDITOR delbrot set, attractors, the Smale horseshoe, calculus on fractals, and applica James W. Maxwell tions to data com presion.
ASSOCIATE EDITORS Aimed at beginning graduate students, college and university mathematics in Ronald L. Graham, Special Articles structors, and non-mathematics researchers, this book provides readable exposi Jeffrey C. Lagarias, Special Articles tions of several exciting topics of contemporary research. SUBSCRIPTION INFORMATION 1980 Mathematics Subject Classifications: 58; 30, 51, 34, 39 Subscription prices for Volume 36 (1989) are 208 pages, July 1989 hardcover $1081ist; $86 institutional member; $65 individual ISBN 0-8218-0137-6, ISSN 0160-7634, LC 89-7003 member. (The subscription price for members is List $31, Inst Mcm $25, Indiv Mem $19 Included in the annual dues.) A late charge of To order, please use order code: PSAPM/39NA 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Add for post age: Surface delivery outside the United States and lndia-$1 0; to lndia-$20; expedited deliv ery to destinations in North America-$15; else where-$38. Subscriptions and orders for AMS publications should be addressed to the Amer ican Mathematical Society, P.O. Box 1571, An nex Station, Providence, Rl 02901-9930. All or ders must be prepaid.
ADVERTISING Special Combination Book and Videotape Offer ISBN 0-8218-0142-2 Notices publishes situations wanted and classi PSAPM/39NA (above) and VIDDEVANEY /NA (below) List $70, Inst Mem $64, Indiv Mem $58 fied advertising, and display advertising for pub To order, please use order code: CHAOSSET/NA lishers and academic or scientific organizations. Copyright @ 1989 by the American Mathemat ical Society. All rights reserved. Printed in the Now Available through the AMS United States of America. CHAOS, FRACTALS AND DYNAMICS: The paper used in this journal is acid-free and falls within the guidelines established to ensure Computer Experiments in Mathematics permanence and durability. €9 Most of this publi with Robert L. Devaney cation was typeset using the TEX typesetting sys A Science Television Production tem. In this captivating and richly illustrated videotape, Robert Devaney communi [Notices of the American Mathematical Society is cates his deep understanding as well as his enthusiasm for chaos, fractals, and published ten times a year (January, February, dynamical systems. As an instructional tool, this videotape will be particularly March, April, May/June, July/August, Septem ber, October, November, December) by the Amer useful because it describes a current area of intense mathematical activity. ican Mathematical Society at 201 Charles Street, Though the mathematical background required is elementary, those at the Providence, Rl 02904. Second class postage paid collegiate level and beyond will appreciate this videotape for the clarity of at Providence, Rl and additional mailing offices. exposition and the sheer beauty of the graphics. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, 19~0 Mathematics Subject Classification: 58 VHS format, approx one hour, 1989 Pnce $59 To order, please use order code: VIDDEVANEY/NA Membership and Sales Department, American Mathematical Society, P. 0. Box 6248, Provi dence, Rl 02940.] Publication here of the Soci All prices ~ubject to change. Shipment will be made by surface. ety's street address, and the other information in For ~ir dehvery add, 1st book $5, each additional book $3, brackets above, is a technical requirement of the maximum $100. Prepayment required. Order from American Mathematical Society, P. 0. Box 1571, Annex Station U. S. Postal Service. All correspondence should Providence, RI 02901-1571, or call toll free 800-566-7774 to charge be mailed to the Post Office Box, NOT the street with VISA or MasterCard. address.
978 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY their authors been asked for expla the other, but the classification dif nation? Aren't there better ways to fers among societies. Science is also Letters improve communication with those a product of culture. Thus when the outside our profession than by carica radical feminists write that science is to the Editor ture and abuse? There are significant masculine, they are reflecting the fact differences regarding issues of sci that Western society has declared sci ence among feminist researchers and ence to be masculine, not that women teachers working in many disciplines. are inherently incapable of doing sci Feminist Critiques of Science Would it not have been better to orga ence. (For a detailed discussion of nize a roundtable discussion, allow this topic and its implications for Your article "Feminist Critiques of ing important representative feminist science, see Evelyn Fox Keller's ar Science" displays far more interest critics to speak for themselves? ticle "The Gender/Science System: in attacking feminists than in explor Mathematicians seem puzzled or, Is Sex to Gender as Nature is to ing obstacles to the involvement of that more women don't pursue ca Science," Hypatia 2 37-49.) Many of more women in science and mathe reers in mathematics. Feminist critics us are working to increase the num matics. Feminist critiques have been suggest that some of the explanation ber of women in mathematics and made of all disciplines. Far from lies in narrowness, intolerance, and science. It is frustrating to have these discouraging women, these critiques insensitivity within the profession. efforts harmed by the inaccurate por encourage women to think seriously Your article displays these traits to trayal of the feminist critiques given about the nature and development of an alarming extent. disciplines and about difficulties and opportunities for women in them. Robert Bix The article totally distorts the ba The University of Michigan-Flint (Received July 31, 1989) Policy on Letters to the Editor sic point of view of feminist critics, Letters submitted for publication in Notices which is not that scientific results are reviewed by the Editorial Committee, should be overturned. Rather, fem I read the article "Feminist Critiques whose task is to determine which ones are inists and other critics argue that of Science" with great hope and ex suitable for publication. The publication scientists should examine more hon citement. I was pleased to see that schedule normally requires from two to estly the social forces that determine four months between receipt of the letter in the AMS was willing to discuss such Providence and publication of the earliest much of the direction of scientific a topic. However, I feel compelled to issue of Notices in which it could appear. investigation. They suggest that sci write to protest the alarmist nature Publication decisions are ultimately entists should assume more respon of the article. made by majority vote of the Editorial sibility for the social consequences Jackson warns of the effects of Committee, with ample provision for prior of their work. Feminists and oth discussion by committee members, by mail the feminist critiques of science as or at meetings. Because of this discussion ers assert that the professional struc reported in the popular press. I agree period, some letters may require as much ture of science and mathematics may that the statements are easy to mis as seven months before a final decision is discourage women by emphasizing interpret and can cause damage to made. Letters which have been, or may be, competition and individual mentor the effort to increase the numbers published elsewhere will be considered, but ing (where personal baises have a the Managing Editor of Notices should be of women in the sciences. Jackson, informed of this fact when the letter is sub- profound impact). They claim that unfortunately, has misinterpreted the mitted. we may discourage students by stress statements made by the radical fem The committee reserves the right to ing technical results rather than the inists in her article. edit letters. creative process and by presenting a The major problem is a misuse Notices does not ordinarily publish complaints about reviews of books or arti falsely monolithic view of science. of terminology. As mathematicians, cles, although rebuttals and correspondence Instead of honestly debating these we all know how important it is to concerning reviews in Bulletin of the Amer criticisms, your article tries to sup carefully define our terms. In the ican Mathematical Society will be consid press them through distortion and writings of the radical feminists, the ered for publication. All published letters ridicule. terms masculine and feminine have must include the name of the author. The very format of the article is Letters should be typed and in legible specific meanings that differ from form or they will be returned to the sender, unbalanced. Short quotations from the popular usage. The terms gen possibly resulting in a delay of publication. critics are chosen for sensational ef der and sex are not interchangeable. Letters should be mailed to the Editor fect, taken out of context, and at Masculine and feminine are cultural of Notices, American Mathematical Soci tacked as absurd. If these statements constructs, meaning that every so ety, P.O. Box 6248, Providence, RI 02940, are so incomprehensible, why haven't ciety classifies attributes as one or and will be acknowledged on receipt.
OCTOBER 1989, VOLUME 36, NUMBER 8 979 Letters to the Editor in the popular press, but it is perhaps pages of the AWM Newsletter, and we in short quotations that don't pro more frustrating to have the Notices felt it was important for the broader vide the full context of what's being commit the same errors. AMS membership to be informed of said. Space and style considerations It is evident that many of the it. limited the length of the quotations authors of the feminist critiques of The main points of both letters chosen, but I believe the quotations science are not knowledgeable about seem to me to center on the feminist I used accurately capture the tone the workings of science. I, myself, perspective of the cultural, sociologi and content of much of the writings am skeptical of some of the fem cal, and professional organization of in question and of the reaction of inist critiques of science. However, scientific fields. Professor Bix refers many women scientists and mathe I do find the area worthy of study to feminists' contributions to a better maticians. and discussion. What is needed is understanding of the "social forces," Professor Bix's idea of a round continued and increased communi "social consequences," and "profes table discussion is a good one. Such cation between the scientific commu sional structure" of science, and Pro a forum would further the discussion nity and those working in women's fessor Solow refers to the feminists' that we hoped to foster through this studies. Both sides have something examination of the societal declara article. to offer. tion that science is masculine. I don't question the validity of the critics' Allyn Jackson Anita E. Solow contributions in this area. However, Staff Writer Grinnell College my research led me to conclude that (Received August 3, 1989) some of them attempt to show that the nature of science itself has an Call for Examples EDITOR's NoTE: The Editors asked inherent masculine bias. That's an of Collaborative Research Allyn Jackson, AMS staff writer and ~interesting hypothesis to explore, but In the past twenty-five years, many author of the article "Feminist Cri by impression is that many who have important mathematical discoveries tiques of Science" (Notices, July I written in this vein have too little have been the result of collaboration August 1989, pages 669-672) if she understanding of science to make between two or more researchers. I wished to comment on the points persuasive arguments and therefore am in the process of preparing a raised in the previous two letters to rely on stereotypes of science and paper detailing interesting joint ef the editor. She supplied the following scientists. To point to a contrasting forts by contemporary mathemati comment. example, I have been told that femi cians. To this end, I would appre I'd like to thank both authors nist primatologists exposed a number ciate your readers sending me brief for taking the time to express their of masculine biases in the interpre accounts of the genesis and execu opinions. I think we all agree that tation of data in their field. They tion of significant and/or unusual discussion is the best way of dealing were successful in doing so because cooperation between them and their with the issues my article addresses. they understood the field they were colleagues. Indeed, that was the purpose of critiquing. the article: to stimulate discussion. I would like to thank Professor My intention was not to attack fem Solow for her clarification of termi Robert A. Melter inism, but rather to report on a nology. In response to Professor Bix's Professor of Mathematics controversy surrounding a particular perception that the article is unbal Long Island University thread of feminist scholarship. This anced, let me say that I recognize Southampton, New York 11968 controversy has been brewing in the the possibility of misunderstanding (Received July 14, 1989)
980 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Modeling the AIDS Epidemic
Mathematical Techniques Provide Qualitative Insights
A team of mathematicians at Los Alamos National exposure to HIV are not randomly distributed, but tend Laboratory has been using sophisticated mathematical to be confined to certain segments of the population. techniques and high-powered computing to formulate a set of models of the AIDS epidemic. Not only are 40.0 .-----.------,------r------, these models more consistent with exising data than TOTAL previous models, they also provide some advantages over statistical methods, which are based only on past trends. The qualitative insights the models provide allow £2 researchers to test various hypotheses about the disease 2 and pinpoint effective strategies to stem the spread of ~ 20.0 (/) 3 AIDS. In addition, the models can be used to unify 4 Cubic Growth of AIDS One of the most surprising aspects of the AIDS epidemic is that, unlike most epidemics, it does not exhibit exponential growth. Rather, the best fit to the data on the number of AIDS cases to date turns out to be a Figure I. Data reported by the CDC. Shown here is the cube root of cubic polynomial. This phenomenon was seen in the first the cumulative number of AIDS cases plotted versus time. Also shown models of the AIDS epidemic, formulated by the Centers are the same data broken down by racial subgroups: I. White, 2. Black, for Disease Control (CDC) in 1986. "I don't know of 3. Hispanic, and 4. Unknown. any other epidemic that's growing polynomially," says James M. Hyman, one of the Los Alamos modelers. Biased Mixing Model "Usually it's a very quick exponential, saturates out, and dies back down." Even when the population is The primary mechanisms for transmission of HIV are split into groups according to race, age, gender, or even sexual contact and sharing of intravenous needles. Since region of the country, the number of AIDS cases still little is known about needle-sharing habits, the Los exhibits this cubic polynomial behavior (Figure 1). "Cliff Alamos group has focused on modeling sexual contact. Qualls [a statistician at the University of New Mexico] The model divides the population into risk categories noticed that no matter how you cut the data, it always designated by different behaviors correlated with HIV had this cubic growth," remarks Hyman. "Whatever the infection, such as sexual partner exchange rate. They also mechanism that's keeping it from being exponential, it's adopted the assumption of "biased mixing"-the idea probably similar in the different categories." that people do not choose sexual partners at random, but Why does AIDS differ in this way? The main reason tend to choose from others in their own risk group. For appears to be the social factors that play a large role in example, the biased-mixing model assumes that those the spread of the human immunodeficiency virus (HIV, with a high partner-exchange rate tend to mix with the virus causing AIDS). For a disease like malaria, others having a large number of partners, while those transmission is randomly distributed over the popula who tend to be monogamous mix with others who also tion, essentially because mosquitos don't care who they have few sexual partners. Within each risk group, mixing bite. However, the behaviors that put people at risk of is assumed to be random. OCTOBER 1989, VOLUME 36, NUMBER 8 981 Modeling the AIDS Epidemic With these assumptions, "you get a completely differ on random infection. The team built their model by ent epidemic" than with random mixing, notes Hyman. successively modifying this equation to accomodate the The model predicts that people in the high-risk groups various parameters. become infected first, and they tend to infect others in their group. The peak of the number of infected people occurs first in the high-risk groups, and moves in a "satu ration wave" to lower-risk groups (Figure 2). The model 0.12 is consistent with the data, for it predicts the number of AIDS cases will increase like a cubic polynomial. "What happens is that the social behavior, once we put it into fi} 0.09 the model, slows the epidemic down tremendously" from 0w u.. the usual exponential growth, says Hyman. ~ 0.06 0.15 0.03 0.12 0 w 0.09 1- () w u.. Figure 3. Same as Figure 2, but with the assumption of random ~ 0.06 mixing. One of the parameters the model is most sensitive to 0.03 is transmissibility, a quantity, related to a, that measures the likelihood that an infected person will transmit the ·- .. - .. _ virus to another individual. Although the way transmis 0 0 25 50 75 100 sibility varies over time is not well understood, there RISK is evidence to suggest that HIV-carriers are most infec Figure 2. Numerical results of the biased mixing model, showing tious immediately after they have been infected. After the fraction of the population infected versus risk, defined here as the that, transmissibility drops off before rising again as the number of sexual partners per year. Each solid curve represents the virus begins to destroy the individual's immune system. distribution of infection at a particular time, with t measured in years. The time since infection strongly influences the way the The dotted line shows the distribution of risk in the population. virus spreads and therefore plays an important role in In contrast, if one assumes random mixing among modeling. The modelers have experimented with using people in high- and low-risk groups, then a very different functions with sharp initial peaks, constant functions, picture emerges. The epidemic actually spreads much and linear functions for the transmissibility of HIV. All more rapidly than if one assumes biased mixing. This is of these give strikingly different pictures of the distribu because the majority of the population is concentrated in tion of infection in the population. The sensitivity of the the lower-risk groups, and, with random mixing, many model to transmissibility indicates the crucial need for more of these people are exposed to the virus (Figure 3). more data on the probability of transmission of HIV. This model is inconsistent with current thinking about Data on sexual behavior and mixing patterns among the epidemic, because it shows the peak in the number and within various groups is also sorely lacking. In fact, of infected beginning and staying within the lower-risk the modelers have had to rely on the 1948 Kinsey report groups. In addition, this model predicts an exponential, for data on various aspects of sexual behavior, such rather than cubic, growth in the number of AIDS cases. as sexual outlet frequency, because more current data Because of these results, the modelers knew that simply are not available. Because of privacy concerns, social structure was crucial to their models. In addition gathering data on sexual behavior is rarely a simple to the number of partners per year, important parameters task. In the socially and politically charged atmosphere include age, sexual contact frequency, and the probability surrounding the AIDS epidemic, such concerns are even of infection. The Los Alamos team began with a logistic more pronounced. equation describing the change over time in the number of infected, I(t), dl Idt = a/( 1-I IN). Here, a is the rate Computing Power Imposes Limits at which an infected person passes on the virus and N is the size of the population. This is the basic equation Although the Los Alamos model can allow for a great deal of epidemiology describing the spread of a virus based of detail, current computing power imposes limitations. 982 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Modeling the AIDS Epidemic For a model with d parameters that typically range over money on condoms, or should we go after other [sexually 100 different values, the number of data points is 1ood. transmitted diseases]? Are clean needles more important Standard numerical techniques work well for solving the than a clean blood supply?" The models can be helpful differential equations in the model, but if d is larger than in predicting which strategies will be the most effective. 3 or 4, the size of the problem jumps out of the range Although he sees great promise in modeling, Hyman of current computing power. "You very quickly see that is cautious about overselling it. "Our biggest fear is when we add four more parameters [for a total of 7 or that people will take the numbers too absolutely," he 8], we run into trouble," says Hyman. "There's no way to says. "The main strength of models lies in predicting hit it with brute force. I'm using a Cray Y-MP and I can't qualitative behavior." Statistical extrapolation is still the even touch it. Three-dimensional fluid dynamics looks best way to predict the number of AIDS cases over the easy" compared to this. "What's needed are analytical next few years. The Los Alamos model has been very tools to reduce the complexity." Hyman says he and his accurate, with predictions that have matched the data Los Alamos colleague, E. Ann Stanley, are investigating within 2-3%, but the models' main advantage is that the use of a separation of variables technique that would they allow researchers to test various hypotheses. "With allow some of the degrees of freedom to be collapsed, extrapolation, you can't address such questions as, what if thereby reducing the computational load. They hope the we double the number of people who use condoms, how technique will allow problems now requiring the Cray to would that change the predictions?" Hyman remarks. be run on a Sun workstation. "There's no way to put that into your least-squares In addition to the Los Alamos team, several other fit." In addition, statistical extrapolations are probably mathematicians are working on AIDS epidemiology. The reliable only for predictions over 5 years, while the annual conference of the Society for Industrial and Ap models are capable of predicting qualitative trends over plied Mathematics, held in San Diego this past July, much longer periods. featured a minisymposium on the mathematical model Some researchers at the CDC and others in the ing of the AIDS epidemic. In addition to Stanley, who medical sciences community were at first skeptical of spoke on the work at Los Alamos, Herbert Hethcote of the usefulness and validity of the mathematical models. the University of Utah described his research, which ap "Good modelers in the field are really looking for plies dynamic simulation methods to early data on HIV qualitative understanding," says Hyman. "Models at this infection among gay men in San Francisco. Carl Simon point can't do better than extrapolation at guessing the of the University of Michigan spoke on sophisticated number of AIDS cases, which is what CDC in the past methods for modeling nonrandom mixing, and Carlos had been most interested in." But now, he says, attitudes Castilla-Chavez of Cornell University talked about aggre are changing. "The whole point of the model is to get gation and mixing in HIV transmission. Apart from the people to think in terms of the future, not just in terms epidemiology of AIDS, mathematicians are also working of how many AIDS cases we have now, but in terms on modeling other aspects of the disease, such as the way of how many infected people we have now, and what HIV mutates, its 3-dimensional structure, and the way it that's going to mean further down the road ... People destroys the immune system. are dying, people are getting infected every day. With The Los Alamos group is involved in a project to estimates of over one million people currently infected, develop user-friendly software that will allow public if mathematical models can give any new insights, it health workers to use the model to better understand the could result in a tremendous saving of lives." future of the epidemic. For this project, researchers at the University of Illinois are working on the software, Further reading: the Census Bureau is providing data, and the Air Force ''AIDS and a risk-based model,"' by Stirling A. Colgate, E. Academy will be testing the package. The package will Ann Stanley, James M. Hyman, Clifford R. Qualls, and Scott P. eventually be used as part of a demographic model Layne, Los Alamos Science, Fall1989. of Africa, in which the AIDS epidemic will be one ''Los Alamos Researchers Model AIDS Epidemic," by Stir component. ling A. Colgate, James M. Hyman, and E. Ann Stanley, SIAM News, May 1989. "The Science of Computing: Modeling the AIDS Epidemic," Qualitative Insights by Peter J. Denning, American Scientist, November/December, 1988. Hyman notes that the usefulness of the models lies "not so much in quantitative projections, but qualitative in Allyn Jackson sights for questions like, is it better for us to spend our Staff Writer OCTOBER 1989, VOLUME 36, NUMBER 8 983 Computers and Mathematics Edited by Jon Barwise Editorial notes exposition of some work of Gregory Chaitin. This work was mentioned by Boolos in his recent article How not to read a review containing a new proof of Godel's Theorem. The col It is a truism that reviews can tell one as much about umn also contains a review of the PC version of the the reviewer as about the item under review. This is language APL *PLUS. as true of computer programs as it is of movie and book reviews. But in what way is this so, and why? If reviewer A says this program is useful, but reviewer B says it is useless, surely one must be right and the other wrong. Right? Wrong. No more so than Informal Exposition if A says the salt is left of the pepper while B that the salt is not left of the pepper. If A and B are on opposite sides of the table, they can both be right. The content of the two claims depends in some crucial way on the vantage points of the two speakers. And so too Cbaitin'~ Equation: if they are reviewers. Whether a book is interesting, An Extension of Godel's Theorem a movie relevant, or a computer program is useful depends on the perspective of the critic. I may have Jean-Paul Delahaye* no use for a spreadsheet program, but many people do. I may find a program natural to use because of The science of the 20th century has a fascinating my previous experience, where another person finds it characteristic: it has been discovering its own limita very unnatural. tions. The best known example of this is in quantum The perspectival relativity of reviews has long mechanics, where Heisenberg's uncertainty principle fascinated me. In reading reviews of novels and imposes limits on what can be measured. Perhaps movies, I always try to figure out how similar the even more disconcerting are the mathematical results reviewers perspective is to my own. It seems to me a demonstrated since 1930 concerning the impossibility good review should make this perspective clear. of certain demonstrations, because they can assign a This month, due to odd circumstances, I happened sort of limit to thought itself. A new step in this to find myself with two reviews of the same program, direction has just been taken by G. Chaitin, of IBM's MILO. Both the reviews are good reviews, in the research center near New York: using computer sci above sense, even though a casual reading would ence techniques he has constructed an equation that suggest that they seem to differ significantly in their surpasses the power of formal mathematics [1], [2]. conclusions about MILO. I have decided to publish At the origin of these researches is found the both of them, since they are both useful, and since very legitimate desire to clarify completely the notion they nicely illustrate the importance of perspective in of proof. At the end of the 19th century and the the outcome of a review. beginning of this one, this goal led mathematicians This month's column *This article orginally appeared in French in La Recherche, 200, June 1988, pp. 860-862. Jean-Paul Delahaye is from the Laboratoire In addition to the two reviews of MILO just men d'Informatique Fondamentale de Lille, Univ. des Sciences et Tech. tioned, this month's column contains an informal de Lille, Bat. M3, 59655 Villeneuve d'Ascq, France. 984 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics as famous as Frege, Peano, Hilbert and Russell, and 0101 01. . . is simple. The string of the first hundred many others, to attempt to formulate, much more thousand decimals of 1t is more complex, but also precisely than Euclid had done, the rules of reasoning relatively simple itself, because it can be generated and the systems of axioms (or postulates) with which by a program that is clearly shorter than it is. Such it is possible to reproduce all of known mathematics. a string of digits or of symbols, having a complexity Once the internal contradictions in the first demon smaller than its length, is redundant; consequently it strative systems that were proposed were eliminated, is possible to simplify it. it remained to assure oneself that the new systems The complexity of a string or, just as well, of that were retained were really not contradictory and a statement, thus measures its incompressible infor were complete. In other words, could one be sure that mation, thermodynamicists would say its "disorder." one could demonstrate in this manner all mathemat Contrary to intuition, almost all strings are complex, ical truths, past, present, and future, without falling in other words incompressible, the same as almost all one day into a contradiction? The logicians and the real numbers are irrational or even transcendental. mathematicians who worked on this project did not Chaitin has exploited this property and applied the at all expect that one day it would be announced to concept of complexity to the strings of symbols that them that they were wasting their time. Nevertheless, form the axioms of a formal system or demonstrative this is what happened in 1930, when the Austrian system. First of all, he proved in 197 4 that one can mathematician Kurt Godel established that "any for never demonstrate, in a given formal system, that a mal system that only demonstrates true arithmetical string has a complexity greater than a certain fixed statements is necessarily incomplete, because certain constant. More precisely, in order to show that a string true arithmetical statements cannot be proven within is of complexity m, it is necessary to use axioms which it." already have complexity greater than m+c, where cis a The existence of these unprovable or undecidable constant independent of the axioms. Thus, in a certain statements profoundly troubled certain eminent math sense, an axiomatic system cannot produce theorems ematicians like John von Neumann, but this was not richer in complexity than the axioms themselves. the case for the majority, who considered them to be exceptional singularities that are not encountered in "real mathematics," or in any case in arithmetic. Chaitin's diophantine equation One could therefore ignore them, the same way that encodes the random number Q continuous curves without a derivative "do not exist" for a physicist. However, today fractal curves have In 1987 Chaitin wrote his unsolvable equation, by invaded the natural sciences. Similarly, undecidable transporting to elementary arithmetic the incomplete statements are far from being rare. G. Chaitin uses ness theorems that he had discovered in the field techniques from algorithmic information theory to of complexity theory. This exponential diophantine show that they are very frequent, sometimes very equation-such an equation involves only whole num simple, and that some of them reside in the very heart bers, additions, multiplications and elevations to a of the most elementary arithmetic. power-has 17,000 variables and is parameterized by a number k, the same as Fermat's equation xk + yk = zk has three variables and is parameterized by the num Algorithmic information theory ber k. The information contained in the solution of a Since 1965 the mathematicians A. Kolmogorov, R. finite number of cases of the equation is not usually Solomonoff, G. Chaitin and P. Martin-Lof have been at all useful in solving other cases. Mathematical for interested in the "information content," also called the mal reasoning is powerless to link the different cases, complexity, of a statement composed of a finite string in other words, no method of solution is essentially of symbols [3). In the field of algorithmic information better than the one that consists in directly putting in theory, this complexity is quantitatively defined, to be the axioms the results that one wants to obtain! More equal to the size of the smallest computer program precisely, to solve his equation for m values of the pa that permits one to generate the given statement. If a rameter kin a given formal system, Chaitin showed in sufficiently powerful programming language is chosen, 1987 that the axioms must have a complexity superior this notion of complexity has a precise meaning: to to m + c', where c' is a constant that, as before, doesn't show that a string of symbols is simple, it is sufficient depend on the axioms. This extraordinary parameter to exhibit a small program which is capable of writing ized diophantine equation thus surpasses what can be it. It is thus that the string of a thousand digits achieved by any formal system, which necessarily is of OCTOBER 1989, VOLUME 36, NUMBER 8 985 Computers and Mathematics limited complexity and thus cannot treat more than a The property of the incompressibility of the in finite number of cases. formation contained in n implies that statistically it The techniques used by Chaitin to carry out his possesses as many 1's as O's and more generally that all slightly mad enterprise have their origin in the work blocks of n bits appear in 0 with the same frequency. developed during the past thirty years concerning D. Moreover, n is not computable, that is to say, there Hilbert's tenth problem, [4], [5] which Y. V. Mati is no program that permits one to calculate its first n jasevic finally solved in 1970. The answer to this bits in a determined time Tn, for any given n. One problem is negative, contrary to Hilbert's initial idea. easily deduces that 0 is transcendental. On the other The answer stipulates that there is no algorithm that hand, the number n is transcendental but computable: enables one to state if a diophantine equation has solu there are many algorithms that permit us to effectively tions. As is often the case in mathematics, the concepts calculate the first n bits in a determined time. and tools developed to treat a problem reveal them How has Chaitin encoded Q in his equation? selves to be useful to resolve other questions. Here, the Because the number n measures a probability, it is a agility acquired in the manipulation of diophantine real number between zero and one, thus it is written in equations has notably served to construct polynomials base two in the form O.a 1a 2a3a4 ••• ak . . . Here the bit whose positive values are the prime numbers. This ak is equal to 1 or to 0 depending on whether or not train of research about diophantine equations led Chaitin's equation has an infinite number of solutions Jones and Matijasevic in 1984 to give a new proof for the value k of the parameter. Since it is impossible of the solution of Hilbert's tenth problem, and it is to deduce the value of a bit a; from the values of the this simplified proof which has permitted Chaitin to others, the solution of Chaitin's equation for the value explicitly write his undecidable equation, since before i of the parameter is completely independent from the him one was content to demonstrate the existence of solutions for the other cases. This equation is thus so such equations by describing a way to construct them, complex that the only way to resolve m cases is to put without ever carrying the constructions through to the an amount of information equal to m into the system end [4], [5]. of axioms that one starts with. The diophantine equations which have been used encode, that is to to resolve Hilbert's tenth problem A beautiful computer science effort say, they represent indirectly, problems known to be undecidable. In an analogous manner, Chaitin has For reasons of practicality, Chaitin wrote his equation encoded in his equation (we will see how later) a in several stages. Inspiring himself in the methods number which is incompressible, so that the different of Jones and Matijasevic, he first defined a low-level cases of the equation are independent and it is programming language, a sort of abstract machine lan impossible to formulate axioms adapted to all the guage, and a translator which transforms each program cases. written in this language into an associated diophan What is an incompressible number? A number tine equation. Then he defined a simplified version of which when written in base two has absolutely nothing the LISP language and wrote in his abstract machine redundant; more precisely, its k first bits have a language a program that permits one to utilize his complexity approximately equal to k. Such a number LISP. This manner of proceeding by nesting languages is also called random, and there is no method better is very common in computer science, because it is than tossing a coin in order to bet on the bits that the only way to bridge the distance between what is comprise it. simple for the machine but impractical for us, and In fact, Chaitin chose an incompressible number what is powerful and easy to use. Chaitin then wrote 0 which he had discovered in 1974. Its definition a LISP program not intended for execution, but to involves the notion of a universal Turing machine, be translated into a diophantine equation via the named after the British mathematician Alan Turing machine language. What would this program do if it who introduced it in 1936. A universal Turing machine were actually executed? If one let it run indefinitely, is an abstract computer with potentially infinite storage it would calculate values closer and closer to 0. How that can simulate the functioning of any computer. ever, the number 0 is not computable; in fact, it is The random number 0 is equal to the probability that altogether impossible to calculate an amount of time a particular universal Turing machine halts within Tn by which the program will furnish n correct bits a finite number of steps after being fed a random of 0. The principle of this LISP program is very sim program. ple. Because the number n measures the probability 986 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics that a universal Turing machine halts when it is [4] M. Davis, H. Putnam and J. Robinson, "The de fed a random program, the LISP program simulates cision problem for exponential diophantine equa for more and more time in turn all the possible tions," Ann. Math. 74, 425-436, 1961. programs keeping track of all those that halt. From [S] J. P. Jones and Y. V. Matijasevic, "Register the machine language program deduced from the machine proof of the theorem on exponential text of this LISP program, the translator constructs diophantine representation of enumerable sets," the redoubtable diophantine equation with 17,000 Journal of Symbolic Logic 49, 818-829, 1984. variables that occupies two hundred pages of listing. It is amusing that several investigators in a com mercial enterprise have devoted months of work and important computing equipment for the sole purpose of explicitly writing an equation whose existence was Reviews of Mathematical Software proved by Chaitin's theoretical results and whose es sential property is that it is altogether impossible to solve it. Until now, the undecidables of Godel seemed ex Milo: The Math Processor ceptional and pathological and many thought that for the Macintosh they could be ignored. The work of Chaitin shows not only that these undecidables are numerous, but Raymond F. Smith* even that they are close to us and "palpable."* Ed itor's Note: Starting with work of Paris and Kirby Introduction. I currently use Expressionist and a word (see J. Paris and L. Harrington, "A mathematical in processor (usually Microsoft Word) to produce hand completeness in Peano arithmetic," pp. 1133-1142 in outs and tests for most of my classes. This combination J. Barwise, Handbook of Mathematical Logic, North produces very nice documents when used on a laser Holland, 1977) in the late 1970's, continuing with the printer. Though it is not of the quality produced by program of "reverse mathematics" of H. Friedman, TEX, the ease of use makes it appropriate to my needs. there has been a whole line of work extending Godel's I am also beginning to learn the Maple computer al in another direction, of finding genuine mathematical gebra system, and will be using it in courses in the statements independent of particular axiom systems. fall. Maple does lots of wonderful things for me, but These two hundred pages of listing where this produces poor mathematical output and takes some terrifying equation is written signify perhaps that our time to learn. In would be nice to have something intuition about the whole numbers is far from being that lies between these two options that I could use clear and precise as we all thought. It seems that it is to prepare examples and that my students could use irremediably limited, incomplete and vague. Any effort to produce nicely written up homework. Milo is an to formalize it will collide with Chaitin's equation and attempt to fill that gap on Macintosh computers. In will not be able to elucidate more than a few cases this review I will first discuss what an ideal program leaving the infinity of others unknown and random. to fill that gap should look like, and then look at how And Chaitin to conclude: "Nonlinear dynamics and Milo measures up to that ideal. quantum mechanics have shown that randomness is The Ideal Program. This discussion will, of course, present in nature. I believe that I have shown that it is reflect my biases. I am a faculty member at a liberal also present in pure mathematics, in fact even in the arts college that emphasizes the importance of writing most elementary branches of the theory of numbers." in all disciplines. Thus I would like for my students [1] G. Chaitin, Algorithmic information theory, Cam- to be able to discuss mathematical ideas in English bridge University Press, 1987. [See also G. Chaitin, as well as to write decent mathematics. Thus my "Randomness in arithmetic," Scientific American ideal program would allow a reasonable amount of 259:1, 80-85, July 1988.] [2] G. Chaitin, "Incompleteness theorems for random reals," Advances in Applied Mathematics 8, 119- *Raymond F. Smith is Associate Professor of Mathematics at Whittier College, where the mathematics department is establishing 146, 1987. an NSF funded Macintosh lab for use in calculus, and eventually, in [3] G. Chaitin, Information, randomness and incom other mathematics courses. He has also been deeply involved in the pleteness. Papers on algorithmic information the development of the college's writing across the curriculum program. ory, World Scientific Publishing Company, 1987. OCTOBER 1989, VOLUME 36, NUMBER 8 987 Computers and Mathematics flexibility in the presentation of written English. On Text. When Milo is in the text mode, the options the other hand, as I begin to use a computer algebra on the menu bar are "File", "Edit", "Style", and system in classes, I assume that my students will be "Font". The "File", "Edit", and "Font" menus are doing much of their work on such a system, and standard, and the "Style" menu allows for minimal so will be assigning them homework that takes that selection (plain text, bold, italic, underline, outline, into account. In particular, I will expect them to shadow, type size). Tabs are set at about three spaces, deal with more challenging derivatives, integrals, and and margins are set automatically to give lines about calculations than in the past. 6.5 inches wide, beginning at the left-hand edge of My ideal program, then, would allow me to inte the page. No modifications can be made in either tab grate text and mathematical symbols in a format that settings or margins. There are no other formatting allows for reasonable amounts of algebraic manipu possibilities. Although various fonts and styles can lation, including symbolic integration and differentia be chosen, each new text block begins in Geneva tion. I should be able to create most mathematical sym 12 point regardless of what style was in force in bols, though I certainly don't expect everything. The the previous section. Consistently using any font manipulation should leave me with standard mathe other than Geneva is difficult. In summary, the word matical forms, and should be consistent. I should be processing capabilities of Milo are minimal. (There is able to create graphs and to include graphics in my a restriction that text blocks cannot be longer than document. I should be able to do minimal text editing about 4000 words. Given the purpose of Milo, this and formatting, including setting margins and tabs, restriction is not significant.) using a variety of fonts and text formats, setting page Graphics. Graphics blocks allow for the use of breaks, and creating headers and footers. I shouldn't either graphs of expressions created in Milo or of expect such more difficult things as creating footnotes. graphics created elsewhere and copied from the clip (I really would like this sort of thing, but there are board or scrapbook. Graphics are pasted in on the memory restrictions.) Finally, I should be able to left margin in the same size as the original. Once a mix text and symbols freely within the document graphic element has been inserted, it cannot be resized so that what is produced is a professional looking or modified except by deleting it. Thus, the user must mathematical document. make sure that the object is the correct size before it Overview of Milo. The Milo document consists of is pasted in. text, graphics, and expression sections. A document Graphs are created by selecting the expressions to consists of any number of these sections in any order, be graphed and then choosing the "graph" option. but each section starts on a new line. Thus, a Milo The user may assign titles to the graph and axes, expression cannot be put in the middle of a line of and select the domain, among other options. The text. Text sections look like standard word proces graph is then drawn in a separate window. Once a sor documents with minimal editing and formatting graph is created, it may be resized and pasted into a possibilities. Expression sections consist of expres Milo document. Parametric equations are graphed by sions created and manipulated using keyboard and placing the definitions of the two parameters on the menu commands. Graphics sections consist either of same line. Several functions may be graphed in the graphics imported from some other application or of same window by placing their definitions on separate graphs created from Milo expressions. A typical Milo lines and selecting them all. It is not possible to label document consists of alternating text and expression the graphs of individual functions. There is no facility sections with graphics included where appropriate. for graphs in three dimensions. The text and expression sections have their own cur The graphs are drawn quickly and are of nice sors (the usual 1-bar for text, and a question mark for quality; the graphing option may be Milo's best. expressions). The user jumps from one to the other by Expressions. The expression block is the heart of either using the "enter" key to create a new section of Milo. The options on the menu bar in this mode are the type different from the current one or by using the "File", "Edit", "Templates", "Diacritical", "Simplify", mouse to move to an existing section. New sections of "Transform", and "Rules". The "Templates" option any type may be inserted at any place in a document. allows for the creation of mathematical symbols and In general, then, Milo meets my specifications for expressions. The symbols available include most of an integrated mathematical word processor. In the the standard ones, though set notation is not included. next portion of this review I shall discuss each of the Diacritical marks may be added to characters or ex sections of Milo in more detail, and comment on how pressions. The "Simplify" and "Transform" menus they meet the ideal. include a wide variety of options for simplifying and 988 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics transforming expressions; among them are various The next step is to apply a rule selected from the algebraic manipulations, differentiation of most func integral tables to give tions, integration of polynomials, and some matrix n n algebra. The "Rules" menu allows for the transfor 2 2 mation of expressions according to predefined rules /sin xdxlx=o=-cos xlx=O entered from files or created by the user. Many of the menu options may be performed by key strokes. Milo expressions, then, are created using the key The "evaluate" option gives board and the "Templates" and "Diacritical" menus. The remaining menus are used to manipulate them. n To give a feel for the process, let me describe how I 2 integrated sin(x) on the interval [0, n/2]: -cos xlx=o=-cos xL=~--cos xlx=o I first selected "definite Integral" from the "Tem 2 plates" menu. This produced an integral sign with cursors indicating entry points for the function, vari Now we "substitute", giving able of differentiation, and end points. The cursor for the function was selected, so I next typed "sin". After -cos xl --cos xl =-cos ~--coso I typed the "n", the entire term was italicized, and x=-n x=O 2 a new cursor indicated the position of the variable. 2 I then typed in an x, followed by a "tab" which moved me to the variable of integration. The next Finally, "simplify" and two applications of "number tab took me to the lower end-point, and then to the crunch" give upper end-point. The "n /2" was entered by typing "optionjp", "/", "2". The fraction was displayed in 1l 1l -19 vertical format. Once this was done, I was ready to -cos ---cos 0=-cos -+cos 0=-2.1684xiO + 1.= 1. manipulate. I selected the entire expression and copied 2 2 it (via "command/C"), typed "=", was given an equal sign and a new cursor on the right-hand side. Pasting This is an example of Milo's differentiation and ("command/W") gave me a copy of the expression simplification options. to manipulate. (From now on I will not describe the "copy, equal, paste" maneuver which is the key to creating strings of equalities.) The next stage was to select "Evaluate Integrals" from the "Simplify" menu. This removed the end points, putting them rather in the evaluate "F(b) - F(a)" notation, leaving the rest of the integral unchanged. At this stage I needed to use the Milo rule evaluation routine to evaluate the integral. I opened (in the standard Macintosh fashion) the file "Table of Integrals" and selected the formula for the sine integral. I then used the "Enter Applying the "differentiate" option gives Rule" option on the "Rules" menu. Going back to my document, I selected the integral and used the "Apply Rule" option. This replaced the integral with "-cosx". The "evaluate", "simplify", and "number crunch" options left me with the correct result. A Milo document illustrating this process is shown below. This is a sample Milo document. I want to compute The idea now is to cancel out some of the terms. an integral. I first create the integral, copy it and use The next several steps illustrate the changes that take the "evaluate Integral" command. place. We first factor the x - 5 ~ n 2 2 (Cx-5) 3 (~(><-2) (x-3r +3(x-2) 2 (x-3Y) (x-5)-4(1) (x-3) 3 (><-2Y)) Jsin x dx = Jsin x dx Ix = 0 8 0 (x-5) OCTOBER 1989, VOLUME 36, NUMBER 8 989 Computers and Mathematics If we now use "simplify", we get is the general problem with Milo, it will do much of what you want it to, but it often takes longer than it would by hand. 5 3 3 {x-5) - ((x-5) (z(x-3) (x-2) + 3(x-2)2 {x-3)2) -4{x-3) {x-zJ2) Bugs and Glitches. There are a number of problems in the version of Milo that I reviewed. Chief among Factoring out the x - 2 gives my minor complaints is that the Milo window always opens somewhat to the right side of the screen, and is not wide enough to contain an entire line. Thus it needs to be moved and resized. Several times I found myself in a position where the window "froze up"; and then pulling out x - 3, we get that is, the program was still running, but nothing was echoing to the screen. A major bug in the text option is that the screen does not automatically scroll (x-5>-5 (x-2) (x-3) 2 ((x-5) {z(x-3) +3(x-z)) 1-4(x-2) {x-3)) when typing goes past the bottom of the window. This feature works in the expression mode. I can put everything into a positive exponent from Although it is not a bug, there is what I would describe as a major problem in the "rules" option. Milo's rules are simply symbolic substitutions, replac {x-3) 2 (x-2) ((x-5) {z(x-3) +3(x-z))-4(x-2) {x-3)) ing dummy variables in a formula with the corre sponding symbols in an expression to be manipulated. {x-5) 5 Thus Milo's "Table of Integrals" looks exactly like a printed table of integrals. The problem with this is I can also multiply out the messy term in the numera that the term to be manipulated must look exactly tor like the formula that defines a rule. For example, you cannot use the formula for the integral of sinn(ax) to integrate sinn x. Both the parentheses and a symbol {x-3) 2 (x-2) {x 2-17 x+36) corresponding to the "a" must be there for it to work. Another problem is the look of some of the {x-5r symbols. I have a particular problem with the "lim" template. When Milo displays the limit of a fraction, As the reader may discern, this was a considerable the "lim" stays near the denominator in the fraction, amount of work for a relatively insignificant result. In rather than being centered. This gives me a rather general, this is the way one uses Milo. An expression uncomfortable feeling. Milo's parenthesis template is or formula is entered, copied, and manipulated by also poorly done. It does change size appropriately, use of the menus or key commands. The process is but is too bold for my taste. It is also not possible to carried through the necessary steps which are chosen change the spacing of expressions on a line; you must by the user. Although Milo will calculate derivatives follow Milo's rules. directly, integrate polynomials and sums of powers of Conclusion. These concluding comments reflect x, and simplify expressions in a variety of ways, it views as to the usefulness of Milo to the mathema is still limited in its overall capabilities. For instance, tician or mathematics student. Milo is clearly a first it does not know how to factor x 2 - 5x + 6 into a step towards the ideal combination program for this product of linear terms. There is a limit template, but audience, but it has a long way to go. Many of the Milo does not know how to evaluate limits. There are problems with Milo can be fixed as later versions come also a variety of frustrations in that certain operations out, but there are a number of more serious difficulties are impossible to do with Milo. For instance, I was that show up that are due not so much to program not able to figure out any manipulations that would design problems as to memory limitations. change 3n;nn into (3/n)n. I started this review by describing a program It is possible, though somewhat difficult, to simplify that combined the worlds of computer algebra and complicated rational expressions like those that result word processing, a program that might not have all from differentiation using the quotient rule. I have of either, but many of the best features of both. included such an example. Although Milo made the As I complete the review, I am not sure that that differentiation easy, the simplification could have been is feasible. I can certainly do without many of the done much more quickly with pencil and paper. This features of an advanced word processor, but Milo's 990 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics half loaf of partial symbolic manipulation is simply something like Mathematica. While Milo's range as not adequate to my needs. I cannot really think of a symbolic algebra program is limited relative to full a situation where I would realistically use Milo; I grown systems like Maple or Mathematica, what it can have come to the conclusion that I will have to stick do it does elegantly and swiftly. to a computer algebra system like Maple for doing I first saw Milo when its author, Ron Avitzur, mathematics and a word processor for writing up showed an early version to my instructional & research mathematics. When inexpensive machines with very software group, the Course Authoring Tools project large memories become available, I will start to look under AIR at Stanford, in the summer of 1987. Since for the successor to Milo that can do the job I want then I have seen several other symbolic manipulation it to. Milo is certainly a reasonable first attempt at an and geometric visualization systems, but none as light integrated program, but there is much that needs to be on its feet, as compact, and none that use the mouse done before a really satisfactory program is feasible. so intelligently. This last point bears emphasis because I believe one of the most serious obstacles to general use of symbolic algebra systems by mathematicians and stu dents has been that, typically, the user cannot directly manipulate mathematical objects in his or her cus tomary way. There are those, usually a small superset Milo of the authors, who will argue that the operators in a Sha Xin Wei* given SMS are rationally chosen and named, but they overlook the fact that a mapping from the set of math Introduction. Milo, a symbolic math and graphing ematical operations & syntax to their particular set of program, is available from Paracomp for $200. It SMS operators & syntax is by no means necessarily comes on a single disc with 1 7 files of rewrite rules unique or natural. In reply to Charlie Gunn, who pro (mostly integral tables) and 9 help files, and runs on a posed in the April Computer & Mathematics column, Mac 512K under System 4.2 or later. It will also run "that the translation of mathematics into a com under MultiFinder on the Mac II. puting environment is one of the leading challenges for mathematics," one might say tradurre e tradire. General Remarks Moreover, this "translation" is more complex than a It's important to understand, first of all, that Milo is matter of translating notions between notational sys billed as a "math processor" rather than a symbolic tems (as between the languages of differential forms manipulation system (SMS); it is an intelligent piece of and of tensors in local coordinates). Potential users are paper which remembers certain common mathemati stymied because they must learn yet another language, cal syntactic structures like polynomials or matrices, the symbol manipulator's interface, in order to shape and helps accelerate algebraic manipulations. Like their own expressions. full-blown symbolic algebra systems, e.g. Macsyma, For example, to extract or insert an element of a Maple or Mathematica, Milo depends on rewrite rules matrix in a general SMS like Mathematica, requires which transform one expression to another. Besides typing in several brackets, structure and assignment a compact core of routines which handle arithmetic, statements, all extraneous to the mathematical pur polynomial algebra and calculus, Milo can be fed pose. By contrast, Milo allows you to either select rewrite rules directly from the keyboard. Its main that entry with a mouse or "walk" into it using one design goal was to be a speedy and compact aid to the key, then type in an expression. Mathematica does calculations characteristic of undergraduate & first have very good help facilities like pop-up menus year graduate physics through the level of Jackson's of keywords, but Milo's direct manipulation interface Electromagnetism, so don't expect the generality of makes common symbol pushing operations completely transparent, obviating the need for any extra verbiage altogether. We'll see examples of this later. *Sha Xin Wei is currently a graduate student in mathematics Milo's principal advantages compared to other at Stanford, working on a dissertation in differential geometry. He SMS are direct manipulation of expressions via an has been a project leader and consultant in the development of extremely intelligent harmony of mouse and keyboard Tools mathematical and scientific software at the Course Authoring technique, easy to use rule-based symbolic manipula Project, Academic Information Resources, Stanford University. tion, and streamlined graphing. OCTOBER 1989, VOLUME 36, NUMBER 8 991 Computers and Mathematics Symbolic Manipulation and then across the equality: Milo has arguably one of the smoothest structured expression editors on the Macintosh; the structured 2 editor guarantees that there are no syntactic errors, ~e-ror =2(-zr+l) an important feature which distinguishes it from l command-line SMS like Maple, Mathematica and lt Scratchpad. Unlike the math layout desk accessory, Expressionist™, which requires you to poke through fig 3. transposing across equality panels of templates, Milo provides three ways to enter expression template structures: by menu selections, Milo's own Solve For command is quite primitive, by command key equivalents, or by typing their however: selecting the first x in (x- a) 2 + x = 0 to be English names (macros). Milo's templates, e.g. an solved, yields x = I JX + a. elastic (resizable, see below) matrix or a loop integral, The general method of symbolic manipulation is appear with blank positions (denoted by question to select all or part of an expression, then operate marks) through which you can tab as in standard upon it with rewrite rules. Typical rewrite rules are Macintosh dialogs. identities like ? ? 1T~ ?:? which can be reversed by a mouseclick, or assignments like fig. 1 some standard templates 1 1 1 You can create templates of expressions to be invoked by name, such as \boostx, which expands 2 3 4 into the 4 x 4 matrix 1 1 1 T~--- I~ 0 I 0 3 4 5 01 ~0 0 I y~ 0 0] 1 1 I y~ y 0 0 4 5 6- i0 0 1 0 0 0 0 1 You teach Milo a set of rules by selecting and entering the assignments, then apply them to some representing a generator of the poincare group. other selected expression. You can build a menu of Most remarkably, you can shift terms in a sum your own rules during a session, but unfortunately, or product, and factor out an expression simply by Milo provides no way for you to save or automatically dragging selections around with your mouse. As a install whole menus as a structured dictionary of rule simple example of this elegant action, selecting the sets. exponential factor in figure 2, you can option-drag it For example, let's define a characteristic polyno across the + to transpose it, across the left parenthesis mial ofT by first writing p(x) = IT- mil, selecting to factor it out of the expression, it, and applying the first rule shown above, which expands to the following equality I 1 1 p(m)= 1 ~~~-m~3 4 5 ~Jo 0 0 1 1 I 1 fig 2. factoring by dragging a selection with the mouse 456 992 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics Then by a cycle of Matrix Algebra and Simplify op One of Milo's loveliest features is the ability to erations, we transform the selected expression through scale up a subrectangle of a graph simply by dragging the following sequence a mouse over the plot. This allows extremely simple graphical approximation of real roots. Magnifying five times around the origin took seconds and produced 1 1 1 1 1 1 1 1 1 --- -m+-- - 2 3 4 2 3 4 2 3 4 1 1 1 1 1 1 1 1 1 -m 0 1 0 = ----0 m 0 = - -m+-- 3 4 5 345 OJ 3 45 0 0 1 r0 0 m 1 1 1 1 1 1 1 1 1 r~ ------m+- 456 4 56 4 5 6 At this point, we open a file of determinant rules, enter a rule into Milo by highlighting it, and apply it to the current selection to obtain ·0.0006 fig 5. magnification of previous graph near origin and after three rescalings around the most positive which we reduce by selecting subexpressions and root: applying various factoring and simplifying operators: 1 1 1 -m+- -m+- -m+- 3 m2 m2 m m2 m m 2 6 4 13 -m +-+---+------+-= 2 4 8 6 12 24 25 9 16 240 3 11m2 131m 1 =-m +-----+-- 12 3600 43200 ·0.00 but with no further (alphanumeric) typing. fig 6. magnification of graph in fig. 4 about positive root Graphing Milo handles graphing with exemplary simplicity: just select the expression and choose the Graph command, To graph a parametrized curve just requires selecting Graphs appear in separate windows, can be resized two expressions in one cell with automatically refined axes, then copied out as -SJ/i~ :·+1 C~...i.3" ~. regular pictures into other Macintosh documents. For example, by selecting our cubic polynomial, we can call up its graph in one stroke fig 4. graph of a cubic fig 7. parametric plot OCTOBER 1989, VOLUME 36, NUMBER 8 993 Computers and Mathematics Composition of plots is equally simple - just select One of Milo's most serious weaknesses is its depen consecutive cells: dence on the macintosh's machine arithmetic. While floating point operations are as accurate and speedy as -f1_;p.·;. :·(::+1) f1 .. -._;._; :: any other Mac application which uses Apple's SANE 80 bit extended precision arithmetic library, arith - _; ·' .. , ':. ( : + 1) .. -._;._; :. :: metic with integers exceeding 232 will overflow and yield nonsense. On the same hand, Milo does not seem to take advantage of the Mac II's 881 floating point which yields accelerator, so that number crunching is speeded up by only the same 4x factor over the Mac Plus as the rest of the program. As for linear algebra, Milo does not support ma trix inversion and general determinant functions in this version. However, Milo already has a quite good matrix interface: you can expand any given matrix as you go simply by creating new entries, and as men tioned above, the structured editor allows you to walk through components without any special commands. It would be nice to see more work along this line, per haps allowing the user to select, insert or redimension arrays simply by mouse. By turning off various commutativity options for addition and multiply, one can mimic some com fig 8. composition of plots putations over noncommutative rings, but this is a global behavior; Milo sacrifices the notion of general object typing, which is supported for example by Mathematica, in favor of speed and simplicity. However, Milo-blithely assuming that all graphs There are no booleans and no inequality tests, are nicely continuous-attempts no adaptive sampling, which is a pity. so the graphs of tan(x) and sin(l/x) appear badly mangled. Analysis Algebra and Arithmetic Milo does perform the usual partial and total differen tiation, and comes with 22 pages of integral formulas In keeping with its compact design, we've seen how cast in the form of rewrite rules, some of which may Milo's algebraic functions (like Simplify, Factor, Mul seem rather cavalier, e.g. tiply Out) often work on a finer grain than Mathemat ica 's operators. 10 Milo understands the usual trigonometric and tran sin (ax)dx=~ (axyi-1 scendental functions. It comes with a file of trig iden I tities which may be loaded in via the rewrite rule X L.(2i -1)(2i -1)! menu. Full unit conversion files allow you to perform i=1 the kind of back of the envelope dimensional analysis dear to physicists. And Milo does give e, p, and i their You will probably have to massage an expression usual senses. It can transform sums and products with quite a bit before you can apply an integration rule limited success but cannot evaluate any limits. because Milo performs lazy pattern matching and does Generally, however, Milo's algebraic power is not automatically support change of variables. Milo strictly limited, partly because it assumes that all shares with Mathematica the weakness of assuming computation is performed over Z and R. Milo will not that all calculus is performed over (products of) solve for roots symbolically, or automatically factor the real line; this confines its vector analysis to polynomials or integers. Though it will evaluate the line integrals, div grad curl (in the usual coordinate factorials and combination functions, Milo does not systems) and all that. As for series expansion, I would provide even a mod function to tease budding number say that it is rather optimistic to have a "Taylor theorists. Expansion" operator that recognizes only sine, cosine 994 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics and exponential functions. To be fair, however, Milo's Consider the conformal change of metric designers were careful to provide a basis for analysis by including transformations (Trig->Base Trig, Trig ~t-eug. >Exponential) that reduce transcendental functions to exponentials or sums of sines and cosines. Hatted quantities will be defined with respect to the Milo does support a slew of syntactic structures conformal metric. The christoffel symbols for those who have the patience to compose their own rewrite rules for more sophisticated analysis; these include notation for commutator, bra-ket formalism, covariant derivative semicolon, expectation. can be written in terms of the original metric & Pattern Matching connection. So for a specific triplet (/; ij), applying vs Procedural Programming the expressions for the christoffel symbols, we obtain Having become accustomed to Mathematica 's hybrid 1.. i+giku i-giiu k)+r1.. language which accommodates APL-like array man t IJ =~glkfgiku2 \ , , , IJ agement, LISP-like list management, and C-like con trol structures in a general pattern matching rewrite or, applying the contraction rule for the metric, language with variables and functions, I chafed slightly under the absence of variables and procedural control ~i =Hu.loil+u.i o~~-gklgiJ u.k)+rli structures (no iteration!) in Milo. We can continue similarly using Milo to compute Example the derivatives of the conformal chrisoffel symbols and As a less trivial example of what can abe accomplished consequently the conformal scalar curvature relative in a short time with Milo, I defined the Riemann cur to the original metric. vature tensor with its symmetries, its contractions, the Ricci and scalar curvature, and then computed some Final remarks corresponding expressions under a conformal change of metric. By turning off multiplicative commutativity, It's too bad that a direct manipulation interface de I was able to work with coordinate indices as super signed around Milo's paradigm hasn't been fitted scripts or subscripts, and define operations on tensors. onto a powerful SMS like Mathematica or Maple. However teaching Milo the einstein convention on Nonetheless, for all its many limitations and despite repeated indices was complicated because the same its idiosyncratically shallow representation of mathe global noncommutativity applied to the components matical operations, Milo has proved to be the only as well as their indices. immediately usable and useful "supercalculator" for The general expression for the Riemann curvature pesky intricate but easy algebraic computations. In a tensor is given by short time, I hope to see an improved version which will retain the compactness and the elegance of the Rkl i =ri k .1-rl k .i +rl m Ijk +rim rfk. original. It should prove useful for undergraduates in the physical sciences and is sufficiently "lazy" (or Here, the boldface variables are the dummy vari fine-grained) to encourage some intelligent heuristics ables in the rewrite rule's pattern; plain variables must (on the part of the student!) while providing a check match literally. Starting with the expression for the against minor algebraic errors, signs errors, dropped covariant derivative of the curvature, i i k . m R 1 terms and the like, but I would not entrust inhu it's quite easy to apply a permutation,' say, manly long calculations to the current version of the k t-1 I t- m m .. k to obtain for example program. While its larger cousins have lumbered on Rij kl;m+Rij lm;k+Rij,kl;m. (Reversing the boldfacing to "automate" calculations in more sophisticated do allows the pattern matcher to recognize the indices.) mains, Milo is one of the few to have taken a step The scalar curvature expands to toward natural, transparent and direct manipulation ij ( kl R \ ij .-.k ij (....Jc ....Jc rm....Jc rm....Jc \ of mathematical objects. R=g \g ijk~=g Ki]k=g 1 'i],k_1 .i.k,i+ ij 1 km+ 1 ik 1 .fmJ. OCTOBER 1989, VOLUME 36, NUMBER 8 995 Computers and Mathematics APL*PLUS PC - A Review To compute the ordinary (inner) product of A and B, we could type: Fernando Tuse/1* A+.xB 1. An introduction to APL. which would display the result immediately. Alterna tively, we could assign the result to a variable C by APL is an acronym for A Programming Language, typing: C +-A+. B. APL provides a wealth of o~ a language designed by Dr. Iverson over twenty-five x erators. Matrix inversion is a primitive operation, as ts years ago. It runs on a large number of machines least squares fit. Many operators can take an array of and, despite its name, it is quite unlike any other any size as argument. For example, we could type *A ( programming language. It will appeal to those who * is the exponential function, so 1 = e = 2. 71828 ... ) have ever felt the need of a "matrix calculator", for * to get a two by three matrix each of whose elements it is in matrix calculus and more generally in the would be e raised to the corresponding element of A. handling of arrays that APL excels. For this reason, As a matter of fact, very rarely one has to code a loop I have been using APL for over five years, as both in APL. a teaching and research tool in statistics, where APL One of the aspects in which APL departs from is particularly suitable in areas such as multivariate most computer languages is the order of evaluation: analysis or categorical data. right to left. This takes some getting us~d to, ~ut Although APL is pretty well known by the mathe makes it easier to evaluate complex expressiOns savmg matical community, I will briefly describe some of its partial results along the way. For example, one can general features, to put in perspective the particular write A+- 3 B +- *C +- 5 7. This would store the implementation that is reviewed here. + vector ( 5 7) in take the exponential of each term APL is an interpreted language. Although com c, and store the result in B, and then add 3 to each pilers do exist, much of the beauty and usefulness element and store the result in A. of APL stems from its interactive nature. A user Besides having the full range of usual mathe knowing nothing about programming could still use. a matical functions predefined, APL provides ways to computer with an APL interpreter to perform matnx manipulate arrays by extracting portions, "pasting" computations and see the results on the spot. arrays together (along any conformable dimension), APL uses a special character set, which takes some an extremely powerful generalized transpose operator getting used to. Once past this hurdle, though, APL (which includes as a particular case the usual trans notation is tremendously concise and elegant. It is pose of a two dimensional array), and even a random amazing what can be done with a few keystrokes. For number generator. example, All of the above can be used interactively -typing an expression to get an immediate result. Nonethe A+- 2 3 p 3 2 3.4 2.1 3 7 less, APL offers the possibility of defining functions B+-4 3 2 which can take arguments (and produce results) much like subroutines or procedures in more conventional defines A to be the matrix ( 2~ 1 ~ 3:.,4 ) and Bas the languages. Functions are fully recursive -they can call themselves. Variables can be global (available to all three dimensional vector ( 4 3 2). There is no need to functions), or local to a function. declare or dimension A before use; arrays are created There is a useful concept in APL which differs "on the fly", just as scalar variables in FORTRAN. from what is usual in other programming languages: For a vector, only a list of values is needed. Each that of a workspace. A workspace is a collection of computation or assignment is performed as soon as variables and functions which is loaded and saved as the RETURN key is pressed. Arrays are not limited to a unit. Thus, a researcher working in APL can save his any particular number of dimensions - a_ltho~gh. the entire working environment as a whole, rather than size of available memory imposes a practical hmtt to having to keep data on program files separately. This the use of multidimensional arrays. is extremely convenient. Further, the current status of computation is stored in the workspace, so it is *Fernando Tusell is a member of the Department of Economic possible to stop a computation befor~ completion, s~ve Analysis at the University of Pais Vasco. the workspace with the function whtch was executmg "pending", and resume the computation later! 996 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics 2. Hardware needed. generator installed on a CGA adapter at home, and work with a soft character set at my office, with a APL *PLUS PC is an implementation of APL for machine having an Hercules graphics card. There are the IBM PC and compatible machines, marketed by drivers for a wide range of graphics cards on IBM STSC Inc., a major provider of APL products and compatible and not-so-compatible machines. services. The version I am reviewing is a bit old: Finally, APL *PLUS PC can be run in a "key version 6.0 released in 1986. I will refer to some new word" mode; each of the non-ASCII characters is features later, which, although they are of very little replaced by a keyword which can be entered on a stan use to me (this is why I never felt any need to upgrade dard ASCII keyboard. For example, instead of typing beyond version 6.0) can be a big boost to other users. A +- 2 2 p 1 2 4 6 one can type: A #is 2 2 APL *PLUS PC can be comfortably run on an IBM #rho 1 2 4 6. This loses some of the conciseness and PC. Version 6.0 is a 141,573 bytes program. DOS beauty of the APL notation, but may be useful in 3.30, which I continue to use, is (depending on the some situations. number of buffers and files you specify at boot time) APL*PLUS PC is a reasonably well behaved pro about 57,000 bytes long. A few thousand bytes are gram. I run it at home on an old vintage IBM PC taken by communications buffers, window scrolling under DOS 3.30, and at different places on an IBM AT memory, and the type ahead buffer. Therefore, one machine under DOS 3.00 with a CGA adapter and on needs at the very least over 200K to load and run a cheap Taiwanese AT-clone under MS-DOS 3.20 with APL *PLUS PC. Anything above that is the size of an Hercules card. I have a ROM character set installed your workspace. In practice, especially if one is using in the IBM PC, and use the soft character set on the DOS 4.00 (which is much larger than DOS 3.30) or other two machines; with a CGA, the characters are is not willing to forego the use of memory resident merely readable, while on an Hercules card the quality programs, 512K or 640K would sound as a reasonable is much better. In all cases I have had absolutely no configuration. Bear in mind that, although one can problems with the program. use data files, much of the effectiveness of APL stems The use of the APL character set again requires from having at once in memory all of your variables special printer support. A variety of devices are sup and functions. ported. In general, there should be no problem with Besides memory, one is well advised to mount IBM graphics or Epson-compatible pin printers (I have a numeric coprocessor (an Intel 8087 for the IBM used an NEC Pinwriter and a Star Gemini 10 with no PC class machines, and 80287 or 80387 coprocessors problems, although spacing among lines is different in for AT-class or larger machines), since this makes a the latter, and graphics dumps appear in unconnected big difference if your work involves heavy numeric pieces). The HP Laserjet series II printer is also sup computation. However, this is not a requirement. ported. If one only has access to a daisywheel printer, More on that below. it may still be possible to find a wheel with the APL As I said in the previous section, APL uses a character set. Remember also that one can get along special character set. STSC Inc. provides a variety of pretty well with any kind of printer unless one wants solutions to this problem which I will describe briefly. to list APL source. Printing results is not a problem, First, if you specify the kind of graphics adapter that except that the minus sign (which in APL is different your computer has, you can get the software bundled from the minus operator) may be printed strangely. with a ROM chip. All you have to do is replace a chip in your graphics card with the one provided -a fairly 3. The APL*PLUS PC interpreter. simple undertaking. With this chip, you will have your 3.1 Data types and memory limits. usual character set plus the APL character set. The only problem is that this restricts the use of APL *PLUS PC supports four data types; boolean, the APL character set to the computer where the chip integers, reals, and character. Strings are arrays of is installed -something inconvenient if you carry your characters. There is no need to worry about declaring floppies with you and wish to work at different places. variables -even arrays are created on the fly when Fortunately, soon after first releasing APL *PLUS PC, first referenced. Reals can be of the order of 10308 • STSC Inc. adopted a different, complementary solu The type of an array is determined on the basis of tion. On the one hand, it began to supply drivers which the types of the elements. One real element forces the provide a "soft" character set. Whatever graphics card whole array to be real. you may happen to have, a simple installation will Since all conversions are done automatically, one provide you APL characters. I have a ROM character can freely mix variables and arrays, integer or real, OCTOBER 1989, VOLUME 36, NUMBER 8 997 Computers and Mathematics in any expression. The only practical consideration is "component file". This is a file written in a special that integers take up less storage than reals; integers format, from which we can retrieve elements by up to 32767 take 2 bytes, while larger integers and position (e.g., the second array in the file). In general, reals take 8 bytes, providing about the same precision a workspace is easier to deal with. Not only can we as FORTRAN's double precision. save and retrieve a workspace as a whole, but we can The size of the largest array used to be a constraint also retrieve selected variables or functions by name, with APL interpreters targeted at the microcomputer with a command such as: ) COPY LINEAR JACOBI, which market; back in 1984 the two major contenders in the would retrieve a function named JACOBI from the APL market limited the size of the largest array to workspace of name LINEAR. 32K and 64K. This restriction has disappeared from Although much can be done in APL, sometimes APL *PLUS PC version 6.0 and later. One can have we need to interface to other programs, or use a pre now an array as large as memory will permit. I found existing set of data. APL*PLUS PC makes it easy, by a problem though with version 6.0; although a matrix providing a set of functions to deal with "native" (or as large as 100 x 100 (and even larger, if you have DOS) files. Fiies are read (or written) as a stream of enough memory) can be defined and made part of a characters, which can be readily converted to numbers computation, an operator such as the matrix inversion if required. The only thing to take care of is the APL (which is a primitive operation in APL, requiring only "minus" sign (different from the usual - sign, which a keystroke) will fail with a NONCE ERROR. This will in APL is an operator), which usually maps into some happen with any matrix larger than about 62 x 62. strange character when written to a native DOS file. It is easy however to circumvent this problem by The usual procedure I follow when writing results for writing- a small function which performs a partitioned use by some other program is to format them to my inversion. liking within APL, replace any_ minus signs, and then Since a real number takes 8 bytes of storage, it write to a DOS file by using the functions provided. follows that a 640K machine with a 440K workspace can hold simultaneously in memory over 55,000 real 3.3 Full screen editor. numbers in one or more arrays. When planning a Although it offers an enhanced version of the however, one has to consider that partial computation, traditional "del" editor available with all APL systems, results need memory, so a cramped workspace will APL *PLUS PC also offers a screen editor that is a joy prevent us from performing computations requiring to use. It provides all the services that we have come storage. For instance, if A. B and sizable temporary c to expect from modern editors; global replace, block of respective orders 1 x 100, 100 x 1, were matrices copy and cut-and-paste operations, and can be used and 1 x 100, we can easily write an expression of to edit both functions and other APL objects. It is A x B x C to compute the product the form + . + . invoked like its older "del" counterpart from within an of the three matrices. The fact that APL evaluates APL session, using the command )EDIT. For anyone to left implies, however, that when the from right planning a lot of development, it is a considerable of B and is performed, a temporary result product c productivity booster. is generated of dimension 100 x 100, requiring some 80,000 bytes. Unless we have that much storage free, 3.4 Speed and precision. the computation will abort with a ws FULL message. A pair of parenthesis will solve the problem in the Reals are stored in the IEEE 64 bit standard example just shown, and, in general, rewriting an format, with a 52 bit significand and 11 bit exponent. expression can go a long way in avoiding large size Precision will not be a concern for most users. Being temporary results. an interpreter, computation is slower -in some cases much slower- than what can be achieved on the same machine with a compiled language (i.e., FORTRAN management. 3.2 Workspace and file or Pascal). As an example of what can be expected, The workspace is the most often used way to save I ran some benchmarks which attempted to measure and retrieve data and functions. In APL *PLUS PC we floating-point performance. They are presented in the can save data and functions in a workspace or in a following table: 998 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics Time in seconds for different machines using functions for the most usual kinds of graphs; the APL *PLUS PC Version 6.0 system functions provided are well thought out. There is one commercial package for statistics (STATGRAPHICS) which builds upon the graphic IBM PC 4.77 MHz. AT-clone 8 MHz. Compaq 20 MHz. capabilities of APL*PLUS PC. It provides good 8087 No 8087 80287 No 80287 80387 No 80387 bi-dimensional and tri-dimensional graphics among Matrix inverse 30x 30 many other things, and is a good example of how far 26.5 153.4 14.8 42.5 3.1 13.8 one can go using APL*PLUS PC. Matrix inverse 60x 60 180.0 1057.5 99.8 292.9 20.7 95.2 3.6 Utility workspaces and other features. Matrix product 30x 30 27.5 80.8 14.4 23.0 3.4 7.4 A number of utility workspaces came with version Matrix product 60x 60 6.0 of APL *PLUS PC. I will only briefly describe some 186.2 423.4 87.2 121.0 20.9 38.1 of them. There are interactive tutorials, to assist in Natural log l 0,000 reals learning APL and particular features of APL*PLUS PC 5.1 126.1 3.3 35.9 0.8 11.3 (graphics, communications, etc.). Other workspaces provide functions to drive HP Laserjet printers and These figures, besides showing what can be attained Epson-compatible printers. The utilities provided en with APL, show the dramatic improvement in times able the user to download an APL font and set various achieved by the use of a floating point coprocessor. printer parameters. A workspace named UTILITY This improvement is particularly noticeable when provides functions to convert numbers (hex to deci the computation involves evaluation of trascendental mal), do workspace maintenances, time function exe functions, as was to be expected. cution, and other various chores. There are other util ities in the workspace ASMFNS, containing functions 3.5 Graphics. which, aside from their stated purpose, provide exam Graphics are not a standard feature of the APL ples on how to interface assembly language functions language. They are part however of the APL *PLUS to APL. Other workspaces provide communications PC system. I have tested graphics only on a CGA and tools, and translation to/from IBM APL PC. an Hercules graphics adapter (in fact, an inexpensive Regarding communications, one can with the touch Taiwanese look-alike). They worked flawlessly. Many of a key convert a PC into a (dumb) APL terminal other graphics boards and output devices are sup from within an APL session. I have found this feature ported, according to the manual, including Amdek, extremely useful. If one has a direct serial connection Scion, Tecmar, and EGA adapters. Even with no to a mainframe (or a modem connection), one can graphics screen, one can draw a graph in memory set switch back and forth between an APL session and aside previously (when loading APL), for later print a host session without leaving APL. For instance, ing on a suitable printer. Epson compatible printers one can start a long computation in a host, come and the HP Laserjet+ printer are both supported in back to APL and continue working while the remote version 6.0 of APL *PLUS PC. This however reduces computation completes; or interrupt momentarily the the size of the available workspace in the amount of work to send mail through a host without having to memory set aside for graphics. save and then retrieve the active workspace. Not only APL *PLUS PC graphics are implemented through terminal mode, but also any kind of DOS operation or a set of system functions which enable the programmer program can be executed from within APL, provided to think in terms of an ideal easel or sheet bearing no the free memory in the workspace is large enough. direct relationship to the actual output device used. Among the workspaces provided, some are of di Then, one can draw on a coordinate system having rect appeal to the mathematical community. There is 1024 points along both the X and the Y axis, regardless one to perform complex arithmetic (including complex of the fact that a CGA screen in four color mode only matrix inversion, and finding the roots of a complex supports a resolution of 200 x 320 points, and other polynomial). Another one provides functions to com adapters have likewise different resolutions. pute the eigenvalues and eigenvectors of various kinds There are system primitives for drawing lines, of matrices. Again, they provide good examples of circles (and arcs and ellipses), for painting, shading, APL programs. I missed with version 6.0 a workspace zooming, and also for putting text in a graphic screen. named HELZER, which was included with a previous I have found it pretty easy to program a set of version, and contains the linear algebra routines in OCTOBER 1989, VOLUME 36, NUMBER 8 999 Computers and Mathematics the book Applied Linear Algebra with APL, by Garry experience with version 6.0 is that if a larger workspace Helzer. Both the workspace and the book are well than a 640K machine will provide is really needed, worth a look, and demonstrate the potential of APL one should consider buying a larger machine. Use of in teaching, besides providing useful mathematical virtual memory adds overhead, and is likely to result routines. in less that acceptable performance. APL *PLUS PC is marketed for 386-based machines with DOS extenders 3.7 Documentation. providing a much larger address space, and one should documentation quite good in general. It is I found probably consider one of those machines if very large the form of loose-leaf binders, with full provided in workspaces are needed more than incidentally. indexing and tutorials on graphics, files, formatting, editors, and an installation guide. An alphabetical listing of system functions is provided for reference 4. Conclusion. purposes, with a full description of each command or There is always room for improvement. I already function and examples. A separate APL Quick Guide mentioned the fact that some functions (like the booklet contains much of the information one is likely matrix inverse) do not work for very large arrays. to need. On top of that, a help facility, which makes Since I usually have to generate random numbers, it nearly unnecessary to resort to the manuals, is I soon realized that the standard APL function ? a keystroke away. Documentation is certainly not a generates random integers in the 0-32767 range only. weak point of the APL*PLUS PC package. This is to short a range for simulation purposes. I also 3.8 Newer versions. found the description of ARBIN (the system function As I mentioned, APL*PLUS PC Version 6.0 is which performs arbitrary input-output) hard to grasp, not the most current. Since first released, APL*PLUS and the function itself hard to use. PC has undergone continuous improvements (version Aside from that, and some other very minor 1.0 was a 69,000 byte program, while version 6.0 is annoyances, APL*PLUS PC must be described as a more that twice that size, which gives an idea of the solid, mature product. The retail price is $695, but extensive changes made). Besides other improvements, can be easily bought for about $550 from discount newer versions try to increase the size of the available dealers. A reduced price version (Pocket APL, limiting workspace by: i) Using LIM/EMS memory. ii) Using the size of the workspace) is also available for $95. a virtual memory scheme, which swaps to disk objects. For anyone needing a fast, simple way to perform This allows a workspace limited only by available disk matrix computations, or a language to write one-of-a space. kind programs for which speed of execution is not the I have not tested these features. My impression primary issue, APL *PLUS PC is a tool that deserves from the benchmarks I have seen and from my consideration. 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; 03845, 03855, have an algebraic counterpart, no general and precise notion 03860, 03C05, 08C15 LC 88-8130 which a systematic ISBN 0-8218-2459-7, of an algebraizable logic exists upon ISSN 0065-9266 investigation cf 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 nT on the formula algebra. nT identifies all formulas that cannot be distinguished from one another, on the basis of T, by any property expressible in the language of 5. The characterization theorem states that a deductive system 5 is algebraizable if and only if n is one-to-one All prices subject to change. Shipment will be made by surface. For and order-preserving on the lattice of 5-theories and also air delivery add, 1st book $5, each additional book $3, maximum $100. Society, P.O. preserves directed unions. The authors illustrate these results Prepayment required. Order from American Mathematical Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free with a large number of examples from modal and intuitionistic 800-566-7774 to charge with VISA or MasterCard. logic, relevance logic, and classical predicate logic. 1000 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook Ratchford, number two at the AAAS, is mentioned as This month's column is written by Hans J. Oser, a candidate for the deputy director's position there. who is a consultant to the Office of Governmental Senate approval for both should be swift. and Public Affairs of the Joint Policy Board for Alarming numbers of vacancies continue to exist Mathematics in Washington, D.C. in the administration. There are around 400 appoint ments a new president can make. As of 9 August, 156 appointees have been confirmed by the Senate, plus As this column is being written, the Nation's 16 more who had served in the Reagan administra Capital is still reflecting the general laziness that ac tion. Sixty nominations are currently pending, 2 were companies the wait for Labor Day weekend, the signal rejected by the Senate (Secretary of Defense and in of summer's end. Until the town returns to normal, the the Justice Department), but 160 positions are still government runs on autopilot - the President is holed without any nominees. So, if you know somebody ... up in Kennebunkport, Maine, and his staff has been Congress is tied in knots over the defense budget, billeted in rather sparse quarters, some even without not to mention the mounting number of ethics cases telephones. Quite a come-down from the days of the they have to deal with, including sex offenses by mem Reagan Administration, when the staff was kept in the bers. Defense Secretary Cheney's former colleagues in best hotels in Santa Barbara. In the meantime, world the House decided to reject his proposals for cutting politics is hot in South Africa, Lebanon, Poland, and two defense weapons systems. Apparently, there is China. Only Columbia seems to get some attention just too much pork involved. On the stealth bomber, from the vacationing administration. On the domestic it boils down to "B2 or not B2, that is the question?", side, the only pronouncements on pending legislation as one Congressman put it. express the President's promise to lower the capital No "profiles in courage" on Capitol Hill in this gains tax. Nothing is said about that other campaign season of budgeting. The Gramm-Rudman-Hollings promise, to boost support for education in our schools. Law (GRH) turns out to have fewer teeth than During his confirmation hearings, D. Allan Brom its authors expected. By making it apply only to ley had to answer a lot of questions about his expected the following fiscal year, our lawmakers simply shift relationship with the President and OMB, but the expenditures back to the current fiscal year (e.g., the Senate, on 3 August, approved him overwhelmingly payday for the defense department)- after compliance to be the new Director of the Office of Science and with the GRH-targets has been confirmed in mid Technology Policy (OSTP) in the White House. Sworn summer. What a way to balance your checkbook! in the next day, Bromley went on vacation for two The NSF budget was supposed to double in five weeks. With no one to talk to in Washington, it was years, starting back in FY 88. The appropriations probably the best thing for him to do. Bromley hopes subcommittee in the House of Representatives rejected to rebuild the office which had dwindled to about that administration proposal for the third time and a half dozen people during Graham's term in office. suggested instead a modest 6% increase for 1990. This With most of the budget decisions for 1990 already far action is contrary to the repeated endorsements by down the line, his opportunity to make any changes the authorization subcommittee which is chaired by may not come until next year. Current rumor in Doug Walgren. At the 6% rate, the doubling would Washington has it that James B. Wyngaarden, former occur in 12 years (without inflation), but it would NIH director, is still interested in the job for Asso take 35 years with inflation kept to 4% for the entire ciate Director for Biomedical Matters at OSTP. Tom period. Do we really want to wait that long? The OCTOBER 1989, VOLUME 36, NUMBER 8 1001 Washington Outlook Senate still has not acted on the NSF budget, but will class computer with 64 kilobytes of memory, and do so after Labor Day. But the budget constraints put producing color pictures of remarkable clarity in on the HUD-Independent-Agencies subcommittee are comparison to the pictures transmitted from the lunar such that little, if any, relief can be expected from the Apollo mission twenty years ago. The ~ effect puts the Senate's budget actions. received energy at one twenty-billionth that of a digital The Air Force Office of Scientific Research (AFOSR) wrist watch to peel off the information contained in awarded nine new University Research Initiatives in that signal. Credit goes not only to the astronomers mathematics last May, beginning in the current fiscal who conceived of building the necessary antennas, year and totalling $1.24 million. These contracts run but also to the engineers and mathematicians who for three years. (See the News and Announcements carried through with the signal processing schemes, section of this issue of Notices.) The Department of algorithms and computer programs, to make this Defense expects to initiate $5 million worth of new possible. With judicious energy conservation, Voyager starts in the URI program in FY 90, but how much should transmit pictorial information for another 30 of that will go into mathematics support is not known years. What an accomplishment! at this time. The rich colors from Voyager 2 suggest to some as Congressman John Dingell, the indefatigable Demo tronomers that there is organic chemistry on Neptune crat from Michigan, continues his investigations into andfor its moons, leading to speculation that NASA's scientific misconduct. His hearings have provoked low-key SETI program, the search for extraterrestrial David Baltimore, Nobelist at the Whitehead Insti intelligence, may eventually discover something out tute in Massachusetts, to write a stinging defense there in the vastness of space. The New York Times, of the practice of scientific research in the National not known for recklessness, rhapsodized in an editorial Academy's Summer-1989 volume of "Issues in Sci "Bach to Bach", that we should send music into the ence and Technology". His paper there, "Baltimore's universe to get ourselves acquainted with others out Travels", is well worth reading. there. The chief astronomer of the Paris Observatory, The American Association of University Profes Jean Heidmann, in the context of the proposed 1992 sors is also concerned about Congress' invasion of the International Space Year, offers his cooperation for a academic sphere. In their annual meeting they passed massive international global SETI network. Congress a resolution that expressed the AAUP position: "The will have to deal with this proposal after Labor Day Meeting protests ... the tendency of legislative investi when it deliberates on the 1990 NASA budget request. gations toward equating scientific errors or omissions The American Physical Society chipped in $500 with misconduct, and in the process to impugn the for the reelection of Congressman Don Ritter (R-PA), professional integrity of individual scientists." Pre one of the few scientists in the House. This won't buy cisely David Baltimore's point. The AAUP also " ... much legislation but it's enough to get an invitation urges Congress, in the furtherance of its purposes, to to the next prayer breakfast. The mathematicians, refrain from actions that, in the name of legislative meanwhile, do their praying off-line. But, do we oversight, encroach upon the freedom of scientists mathematicians really concern ourselves enough with to impart the findings of research without fear of the future of the discipline, where the next generation political reprisal." Strong words indeed! of teachers is coming from, what should be taught, Things have gone much better elsewhere in the what one should fight for? universe. Voyager 2 just completed its spectacular Fortunately, the summer doldrums have some good flyby of Neptune and its moons and, in the process, side effects as well. Apparently, the computers in York produced the most extraordinary photography. The town Heights were idle enough to let the Chudnovsky discovery of the nine rings-five new ones-and brothers (Columbia University) calculate 1C to an un the eight moons circling the blue planet made the precedented 1,011,196,691 digits. hearts of all astronomers beat faster. Voyagers' feat Next month we should know more about the budget is remarkable for its primitive technology: A 20 in the agencies for 1990. After all, the new fiscal year Watt transmitter sending data, processed on a PC- begins on 1 October! 1002 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements Important NSF Proposal To reflect these emphases, the fol an association as thesis advisor and Format Changes lowing proposal format changes will postdoctoral scholars sponsored by be effective for proposals submitted the P.I. over the past five years, with The National Science Foundation on or after October 1, 1989. a summary of the total numbers of (NSF) is announcing two important I. Education and Human Re graduate students advised and post changes in proposal format to reflect sources. A statement must be in doctoral scholars sponsored. two emphases of proposal evaluation. cluded specifying the potential of the • to avoid potential conflicts of These changes apply to all proposals proposed research to contribute to interest in merit review, a list of submitted to the Foundation, includ the education and the development scientists with whom the investiga ing those submitted to the Division of human resources in science and tor has had a long-term association of Mathematical Sciences. engineering at the postdoctoral, grad and/or with whom he/she has collab The first emphasis is the impor uate, and undergraduate levels. This orated on a project or a book, article, tance of education and human re statement may include, but is not report or paper within the last 48 sources within research supported by limited to, the role of the research in months; and the investigator's own the NSF. One established criterion student training, course preparation, graduate and postdoctoral advisors. in NSF's merit review of proposals and seminars, particularly for un These changes will be incorpo is the effect of the proposed research dergraduates. Special effectiveness or rated into the next revision of Grants on the infrastructure of science and achievement in the area of producing for Research and Education in Sci engineering. Reviewers are asked to professional scientists and engineers ence and Engineering. consider the potential of the proposal from groups presently underrepre to improve the quality, institutional sented should be described. Major Computer Research distribution, or effectiveness of the 2. Biographical Sketches. In ad Facilities at Five Nation's scientific and engineering dition to data on educational back Universities Funded by NSF research, education, and work force. ground and career, these must now The NSF is particularly concerned include the following information: Multi-year projects to help establish, about the development of scientists • a list of up to five publications enhance, and operate major experi and engineers for the future. To make most relevant to the research pro mental research facilities at five uni this more explicit, principal investi posed and up to five other significant versities have been funded by the gators will now be asked to specify research publications. Patents, copy National Science Foundation. The the relationship of the project to the rights, or software systems developed grants are expected to total over education and development of hu may be substituted for publications. $8,000,000 by the end of the five-year man resources. These publications may overlap the grant period. The NSF Institutional The second emphasis is the im continuing requirement for a list of Infrastructure awards are aimed at portance of quality of publications all publications resulting from and developing computer research facili in the merit review process. Evalu citing prior NSF support. A com ties at major universities. ation of scientific productivity must plete list of publications for the past The award to the University of emphasize quality of published work five years is no longer required. Only Arizona in Tucson, Arizona, provides rather than quantity. To ensure this the list of ten will be used in merit $577,911 in the first year of the grant. emphasis, NSF will now limit the review. Over the entire five-year period, ten number of publications considered • a list of the names of graduate facilities will be supported, involving in reviewing a grant application. students with whom the PI has had research in the areas of programming OCTOBER 1989, VOLUME 36, NUMBER 8 1003 News and Announcements languages, software for molecular ge maintenance, technical support staff, gence methodologies in flight-related netics, and graphical user interfaces and other associated costs will en differential game, control, and op for scientific visualization. able it to perform significantly more timization problems, $156, 194; I. The University of Chicago has or better research than would sep LASIECKA, University of Virginia, been granted $378,948 in the first arate support, at the same funding Control and stabilization of distrib year of its five-year award to pro level, for individual research projects uted parameter systems: Theoretical mote experimental research in a wide or equipment acquisition. and computational aspects, $146,205; variety of areas, including computer -NSF News Release J. WALKER, Lehigh University, Com vision and graphics, and computer putational and analytical methods in science theory. University Research Initiative nonlinear fluid dynamics, $136, 186; A first year grant of $576,612 will Awards R. A. DEVORE, University of South be made to the University of Pennsyl Carolina, Application of the ¢ vania as part of a five-year award that The Department of Defense (DOD) transform and wavelets, $125,000; B. will fund facilities for five research has announced awards in its Univer NICOLAENKO, Arizona State Univer areas: artificial intelligence and lan sity Research Initiative (URI) pro sity, Spatio-temporal complexity and guage processing; machine percep gram. The URI is designed to large-scale structures in problems of tion and robotics; graphic interfaces, strengthen the ability of universi continuum mechanics, $90,000; R. movement description, and anima ties to conduct research and educate PFEFFER, Florida State University, tion; computer communication; and graduate and undergraduate students Nonlinear dynamics underlying at logic and computation, including the in areas important to national de mospheric predictability, $85,000; D. ory of computation, database sys fense. The first awards, which con W. BREWER, University of Arkansas, tems, and programming languages. sisted mostly of large, multiyear Computational algorithms for identi The University of Rochester in grants for teams of investigators, fication of distributed parameter sys Rochester, New York, will be awarded were made in 1986. tems, $60,223. $365,879 in the first year of its five The 1989 competition was specif year grant. The funds will help the ically directed toward institutions Math Staff in university's scientists develop a labo that have the capability to perform NSF's Education Directorate ratory for real-time vision consisting defense research, but may lack re of key robotic components: a "head" sources to assemble multidisciplinary The directorate for Science and En containing cameras for visual input; teams. In addition, only academic in gineering Education (SEE) at the an arm or "neck" that supports and stitutions receiving less than $4 mil National Science Foundation (NSF) moves the "head"; and a general pur lion from the DOD for research and sponsors a range of programs that pose processor for high-level vision development in 1986 or 1987 were support educational projects in math and planning. eligible. ematics, science, and engineering. The State University of New York Among the five DOD agencies Listed below are the names and tele at Stony Brook will receive a first that fund academic research in the phone numbers of those SEE pro year grant of $334,000 as part of mathematical sciences, the Air Force gram officers whose background is a three-year award that will pro Office of Scientific Research (AFOSR) in the mathematical sciences. These vide funds for a network of high was the only agency to receive URI individuals can provide information performance graphics workstations. funds for awards in the mathemati about their own programs, as well The goal of the research is to create cal sciences. The Mathematical Sci as information about other programs tools that can be used to rapidly gen ences Directorate at AFOSR made within SEE. erate application-specific, visually URI grants totaling $1.24 million for Materials Development oriented computing environments on 1989. Listed below are the princi Thomas Berger high-performance workstations. pal investigators, their institutions, 202-357-7066 These institutions have made a the titles of their projects, and the Calculus Curriculum Development substantial commitment to support amounts that will be granted in each John S. ("Spud") Bradley the researchers and their projects, of the three years of the grants. 202-357-7051 and will assume an increasing share FRED S. ROBERTS, Rutgers Uni of the project costs each year through versity, Discrete applied mathemat Teacher Enhancement out the grant period in anticipa ics, $250,000; A. S. FoK.As, Clarkson Joan Ferrini-Mundy tion of the facilities becoming self University, Nonlinear wave phenom 202-357-7074 sufficient. In addition, each institu ena related to interaction in the iono Teacher Preparation tion has demonstrated that the sup sphere, $191,192; B. RoDIN, Wash Glenda Lappan port provided by NSF for equipment, ington University, Artificial intelli- 202-357-7069 1004 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements Teacher Enhancement cal communication theory, quantiza Sciences will be among the topics to Carroll Wilde tion, information theory, and coding. be studied. 202-357-7539 N~ws.-~rom the Berger, a continuing rotator from News from the Mathematics! Sciences Institute the University of Minnesota, has Cometf University moved from the Teacher Enhance Institute for Mathematics ment program to Materials Develop and Its Applications In addition to a semester-long pro ment. The new rotators are Ferrini University of Minnesota gram on Hamiltonian Systems (de Mundy, from the University of New scribed in the September Notices), Hampshire; Wilde, from the Naval The Institute for Mathematics and this fall the Mathematical Sciences Postgraduate School in Monterey; Its Applications (IMA) program for Institute (MSI) is sponsoring a work and Lappan, from Michigan State 1989-1990 is "Dynamical Systems shop on Large-Scale Numerical Op University. and Their Applications". The pro timization. The workshop will exam The community expresses its gram will begin September 5 with an ine the impact of parallel computing thanks for a job well done to out opening workshop that will feature on optimization problems. Tom F. going mathematics staff from SEE: introductory lectures by Rutherford Coleman is organizing the workshop T. Christine Stevens, who completed Aris, Shui-Nee Chow, Paul Fife, Mar to be held at Cornell University, Oc her term of service in the Teacher tin Golubitsky, John Mallet-Paret, tober 19-20, 1989, directly after the Enhancement program and is now Kenneth R. Meyer, Richard Moeckel, ORSA/TIMS meeting in New York at the University of St. Louis, and Grisha Sivashinsky, and Forman A. City. His co-organizer, Yuying Li, Florence Fasanelli, who finished her Williams. The topics of concentra is a computer science post doctoral term in the Young Scholars program. tion for the period September to De fellow at Cornell. Program officers in SEE can be cember are Chemical Reactions and The field of numerical optimiza reached via electronic mail. To form Combustion Dynamics. The organiz tion deals with the minimization of an individual's address, take the first ers include Rutherford Aris, Donald an "objective" function (usually real initial and last name, and append Aronson, Paul Fife, Amable Linan, valued) possibly subject to constraint @note.nsf.gov for Internet, or @nsf Harry Swinney, and Forman Williams. functions. Linear programming is for Bitnet. For example, to contact There will be a workshop on "Pattern a special case where the objective Tom Berger on Internet, use the ad and Dynamics in Reactive Media" and constraint functions are all lin dress [email protected]. during October 16-20, 1989 and a ear. Large-scale numerical optimiza The address is Directorate for Sci workshop on "Dynamical Issues in tion focuses on problems with many ence and Engineering Education, Na Combustion Theory" during Novem variables-perhaps 1000 or more. Such tional Science Foundation, 1800 G ber 13-17, 1989. problems are typically sparse, i.e., Street, NW, Washington, DC 20550. The winter program will concen many zero coefficients, and efficient trate on Hamiltonian Dynamics and techniques must exploit this prop Neil Gerr Named Head of the Mathematical Physics; L. Kadanoff, erty. Office of Naval Research R. McGehee, K. Meyer, J. Moser, C. Mathematical modeling of many Math Program Robinson, and E. Zehnder will be the physical situations in engineering and organizers. the sciences leads to large-scale opti Neil Gerr has been named direc During March-April, 1990 there mization problems. Applications are tor of the Mathematics Division of will be a concentration on Mathe numerous and diverse: for example, the Office of Naval Research (ONR), matical Physiology and Differential design of bridges and structures, pro after serving several months as act Delay Equations. A series of lectures tein folding and the conformation ing director. Gerr received his Ph.D. in Neural Networks and Develop of molecules, operation of a factory in statistics from the University of mental Biology is planned. (See the to maximize profit subject to vari North Carolina at Chapel Hill. He advertisement in this issue of Notices ous pollution constraints, and even was an associate at Daniel H. Wag for more information.) automatic cartoon animation. ner Associates until 1984, when he During April-June, 1990 the con One of the important themes of joined ONR as a scientific officer centration will be on Fluid Flow and the workshop will be the impact of in the signal analysis program. His Convection Dynamics. Turbulence in parallel computing on the area. Cole research interests include stochastic Fluid Flows, Nonlinear Phenomena man says that parallel computers processes and random fields, signal in Atmospheric and Oceanic Sciences offer the opportunity to solve big processing, spectral analysis, statisti- and Chaotic Processes in Geological ger optimization problems and solve OCTOBER 1989. VOLUME 36, NUMBER 8 1005 News and Announcements them faster, but questions need to mization, solving sparse linear prob linear systems to see if it can be used be asked. Can sequential algorithms lems on multiprocessors, optimiza as a stepping stone in non-linear be modified to yield efficient parallel tion and medical image reconstruc optimization research. methods? Can new parallel methods tion, quadratic programming, and in The emphasis of the workshop for solving these problems on par terior point methods for linear pro will be on current research. There allel computers be designed? What gramming. fore, it will be of most interest to parallel optimization issues are there Coleman says the workshop is scientists who design algorithms and beyond linear algebra? One session timely partially because of the large to scientists from the oil and air of the workshop will be devoted to amount of recent work on how to craft industries and government labs discussing the questions optimizers solve sparse linear systems on par where active research groups need to should be asking about the parallel allel computers; however, relatively keep abreast of developments in this computing environment. little has been done on non-linear field. Other topics to be addressed at optimization. The time is right to Scientists interested in attending the workshop include: linear pro examine the body of existing knowl or receiving more information should gramming, partially separable opti- edge on parallel methods for sparse contact MSI at 607-255-7763. 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 ISDN 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 $307, Institutional member $246, blended. Although the beginnings of a secondary classification in Global Individual member $184, Reviewer $154 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 $491, Institutional member $393, the subject has attained its present global analysis. Individual member $295, Reviewer $246. 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 manifolds; Infinite-dimensional manifolds; relativity-as ~ell as within mathematics All prices subject to change. Shipment will itself. Calculus on manifolds; nonlinear operators; be made by surface. For air delivery add, Spaces and manifolds of mappings; 1st book $5, each additional book $3, maxi Today, this vital and active field is Volume 2: Variational problems in infinite mum $100. Prepayment required. Order from American Mathematical Society, P.O. Box undergoing a virtual explosion of new dimensional spaces; Ordinary differential 1571, Annex Station, Providence, RI 02901- and important results. Reviews in equations on manifolds; dynamical systems; 1571, or call toll free 800-566-7774 to charge Global Analysis makes information about Volume 3: Ordinary differential equations with 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. 1006 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information for the Mathematical Sciences Travel Grants nine months. In addition, there will Mathematical Sciences for ICM-90, Kyoto be an expense allowance of $1 ,000. Postdoctoral Research Fellowships Applicants must be citizens or per U. S. mathematicians wishing to manent residents of a country in The NSF Mathematical Sciences Post apply for travel support to attend North America. The fellowship may doctoral Research Fellowship pro the 1990 International Congress of be combined with other stipends gram is designed to permit recipients Mathematicians in Kyoto, Japan, are and/or part-time teaching; this op to choose research environments that reminded that an application form tion can be used to extend the award will have maximal impact on their fu can be found at the back of the to cover a period of up to two years. ture scientific development. Awards September 1989 issue of Notices. For further information about the will be made for appropriate research Deadline for receipt of applications acceptability of such arrangements, in pure mathematics, applied mathe in Providence is November 1, 1989. individuals should contact the Secre matics and operations research, and The first announcement for ICM-90 tary of the Society. statistics at an appropriate nonprofit also appeared in the September issue. The number of fellowships to be United States institution. awarded is small and depends on the The fellowships will be offered AMS Centennial Fellowships amount of money contributed to the only to persons who 1. are U.S. cit Invitation for Applications, program. The Trustees have arranged izens or nationals as of January 1, 1990-1991 a matching program from general 1990; 2. will have earned, by the be Deadline December 1, 1989 funds in such fashion that funds for ginning of their fellowship tenure, a at least one fellowship are guaran doctoral degree in one of the mathe These fellowships are intended to teed. Because of the generosity of the matical sciences; 3. will have held the provide enhanced opportunities for AMS membership it was possible to doctorate for no more than five years research to talented mathematicians award two fellowships for 1987-88, as of January 1, 1990; and 4. will not who have had relatively few such three fellowships for 1988-89, and previously have held any other NSF opportunities in the past. These fel three fellowships for 1989-90; how postdoctoral fellowship. The evalu lowships are open to any individual ever, in the several preceding years, it ation of applicants will be based, who is seven to twelve years past the was not financially possible to award in part, on ability as evidenced by Ph.D.; i.e., has received the Ph.D. more than one fellowship. past research work and letters of rec degree between January 1, 1978, and The deadline for receipt of appli ommendation, likely impact on the December 31, 1983. It is expected cations is December 1, 1989. Awards future scientific development of the that applicants will have had a min will be announced in February 1990, applicant, and scientific quality of imum of three years of full-time or earlier if possible. the research likely to emerge. Appli teaching or comparable industrial ex For application forms, write to cants' qualifications will be evaluated perience. In addition, the selection the Executive Director, American by a panel of mathematical scientists. committee will give preference to ap Mathematical Society, P.O. Box 6248, For copies of the application bro plicants who have not had extensive Providence, RI 02940. (It should be chure or further information, contact postdoctoral research support. noted that completed application and the Special Projects Program, Divi The stipend for fellowships award reference forms should NOT be sent sion of Mathematical Sciences, Na ed in 1990-91 has been set by the to this address, but to the address tional Science Foundation, 1800 G Trustees ofthe Society at $36,000 for given on the forms.) Street, NW, Washington, DC 20550; OCTOBER 1989, VOLUME 36, NUMBER 8 1007 Funding Information tel. 202-357-3453; or the American The Selected Professions Fellow tions must be received by AAUW two Mathematical Society at tel. 401-272- ships are awarded to women who weeks before the application dead 9500. are citizens or permanent residents line. The deadline for applications is of the U.S. in designated fields. For November 15, 1989. 1990-1991, a new focus was placed Computing Research Equipment on science and technology fields to Program Deadline University Fellowships for Women address the continuing low partic ipation of women in these areas. The American Association of Uni Fellowships for master's degree can SCREMS (Scientific Computing Re versity Women (AAUW) Educational didates, including those enrolled in search Equipment in the Mathemat Foundation has awarded more than one-year programs, are available for ical Sciences) is a program of the 5000 fellowships since 1888. This the final year of study in com Division of Mathematical Sciences year, 197 fellowships were awarded puter/information science and math of the National Science Foundation. for a total of $1.7 million. AAUW ematics/statistics. The fellowships, The program will make a limited provides graduate fellowships and which range from $5000 to $7500, number of awards for the purchase grants to women who have demon are for full-time study. The deadline of scientific computing equipment strated scholarly excellence. is December 15, 1989. for mathematical sciences research. AAUW offers three different kinds International Fellowships are SCREMS is designed to provide for of fellowships that may be of interest awarded to women of outstanding the kind of equipment that is re to women in the mathematical sci academic ability who are not citi quired by several (two to five) re ences. The first category is the Amer zens or permanent residents of the search projects and that would be ican Fellowships, postdoctoral and U.S. for full-time graduate or post difficult to justify for a single project. for women graduate study in the U.S. Applicants dissertation fellowships Eligible institutions include U.S. or permanent resi must hold the equivalent of a U.S. who are citizens educational institutions with ongoing dents of the U.S. Applicants for the bachelor's degree by December 1, research programs in mathematics, postdoctoral fellowships must hold 1989. Upon completion of studies, applied mathematics, or statistics. by the applica fellowship recipients must return to a doctoral degree Proposals involving more than one November 15, 1989. their home countries to pursue pro tion deadline, institution or department are wel fellowship provides fessional careers. Previous and cur The Founders come. Significant cost-sharing on the senior scholar in any rent recipients of AAUW fellowships $25,000 for a part of the institution(s) is expected. field; the other fellowships provide are not eligible. The fellowships pro $20,000, and some have disciplinary vide $13,000 each. The deadline is The deadline for proposals for restrictions. The dissertation fellow December 1, 1989. SCREMS is December 4, 1989. For ships provide stipends of $12,500, For more information, contact: further information, contact Debo for the final year of writing the dis AAUW Educational Foundation, rah Lockhart, Program Director for sertation. An applicant must have 2401 Virginia Avenue, NW, Wash Special Projects, Division of Math completed all coursework, passed all ington DC 20037; telephone 202- ematical Sciences, Room 339, Na examinations, and have had the dis 728-7603. You may request only one tional Science Foundation, 1800 G sertation proposal or plan approved application and may apply for only Street, N.W., Washington, DC 20550; by the application deadline. one fellowship. Requests for applica- telephone 202-357-3453. 1008 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences oftheAMS FUTURE MEETINGS Hoboken, New Jersey October 21-22 1011 Muncie, Indiana October 27-28 1021 Los Angeles, California November 18-19 1035 Louisville, Kentucky January 17-20 1039 Mathematical Sciences Employment Register 107 6 Invited Speakers and Special Sessions 1083 FUTURE CONFERENCES Joint Summer Research Conferences in the Mathematical Sciences University of Massachusetts, Amherst, June 7-July 4 1087 OCTOBER 1989, VOLUME 36, NUMBER 8 1009 I ...... I A Century of ACe !Jf: ACen 1n ofMa A Century in Am of Mathematics Part I Mathematics in America Edlled by I' Part II with the as Edited hy Pete Part III with the assls 1-:dited by l'eter Dun·n. with the asslstanC'r or Rit'hard A. Askry in America Harold M. Edward!> Olfl1 Uta C. Mrn:harh VOJ.l Olfl.f11 QHISTORYOF vow~ MATHEMATICS AN EXCELLENT ADDITION TO VOLUME 3 YOUR UBRARY COLLECTION PART I edited by Peter Duren with the assistance of Richard A. Askey and Uta C. Merzbach This volume brings together a variety of perspectives on the political, social, and mathematical forces that have shaped the American mathematical community in the past century. Humorous, edifYing, and poignant, this book presents the personal recollections of a number of mathematicians who have influenced the development of mathematics in this country. ISBN 0-8218-0124-4, LC 88-22155, ISSN 0899-2428; 486 pages (hardcover). 1988 List price $57, Institutional member $46, Individual member $34, Code HMATH/lNA PART II edited by Peter Duren with the assistance of Richard A. Askey and Uta C. Merzbach Similar in perspective to Part I but differing in organization and emphasis, this volume focuses on some key elements in the making of mathematics in America. The first section of the book deals with some of the influential mathematics departments in the United States. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's bicentennial. In the last section, various aspects of America's mathematical past are explored on the political, social, and scientific levels. ISBN 0-8218-0130-9, LC 88-22155, ISSN 0899-2428; 578 pages (hardcover), 1989 List price $70, Institutional member $56, Individual member $42, Code HMATH/2NA PART III edited by Peter Duren with the assistance of Richard A. Askey, Harold M. Edwards, and Uta C. Merzbach The third and final volume of this collection. The theme of the second volume is continued here in articles describing the mathematics and the mathematical personalities in some of the nation's prominent departments. ISBN 0-8218-0136-8, LC 88-22155, ISSN 0899-2428; 400 pages (hardcover), 1989 List price $75, Institutional member $60, Individual member $45, Code HMATH/3NA COMBINATION OFFERS A Century of Mathematics in America, Parts I, II, and III as a set. A Century of Mathematics in America, Parts II and III as a set. ISBN 0-8218-0138-4 ISBN 0-8218-0152-X List price $182, Institutional member $146, List price $131, Institutional member $105, Individual member $109 Individual member $79 Code HMATHSET/NA Code HMATHSET/2/SNA Prepayment required. Order from AMS, Annex Station, P.O. Box 1571, Providence, RI 02901-1571 or caiiS00-556-7774 to use VISA or MasterCard. For optional air delivery, please add $5 first book, $3 each additional, $100 maximum. Hoboken, New Jersey Stevens Institute of Technology October 21-22 Program The eight-hundred-and-fifty-first meeting of the Ameri Finite groups, RICHARD N. LYONS and MICHAEL E. can Mathematical Society will be held at Stevens Institute O'NAN, Rutgers University, New Brunswick. 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. Stevens Institute of Technology and Insti Invited Addresses TRETKOFF, tute for Advanced Study, Princeton University. By invitation of the Eastern Section Program Commit tee, there will be four invited one-hour addresses. The Contributed Papers speakers, their affiliations, the titles of their talks, and the scheduled times of presentation are: There will also be sessions for contributed ten-minute RussEL CAFLISCH, Courant Institute of Mathematical papers. Late papers will not be accommodated. Sciences and the University of California, Los Angeles, Dynamics and singularity formation for vortex sheets, Registration 1:30 p.m. Sunday. BRUCE KITCHENS, IBM Thomas J. Watson Research The meeting registration desk will be located in the lobby Center, Yorktown Heights, Symbolic dynamics, 11:00 of the Stevens Center and will be open from 8:00 a.m. to a.m. Sunday. 5:00 p.m. on Saturday, October 21, and from 8:00 a.m. FANG HuA LIN, Courant Institute of Mathematical to 12:00 noon on Sunday, October 22. Sciences, New York University, Level sets of soiutions of The registration fees are $30 for members of the elliptic and parabolic equations, ll :00 a.m. Saturday. AMS, $45 for nonmembers, and $10 for students or SHELDON E. NEWHOUSE, University of North Car unemployed mathematicians. olina, Chapel Hill, Geometric aspects of topological en tropy, l :30 p.m. Saturday. Social Event reception and dinner will be held Saturday Special Sessions A special evening, October 21, in the S. W. Williams Library. By invitation of the same committee, there will be eight The event will include cocktails and a buffet dinner special sessions of selected twenty-minute papers. The appropriate to the harvest season. Participants can make topics, and the names and affiliations of the organizers, reservations by sending a check for $25 per person to are as follows: Denise Ryan, Department of Mathematics, Stevens In Geometry related to computer vision, PRABIR BHAT stitute of Technology, Hoboken, NJ 07030. Reservations TACHARYA, University of Nebraska, Lincoln, and ROBERT should be made by the first week in October. Participants A. MELTER, Long Island University. having any questions regarding the dinner should call Algebraic semantics, STEPHEN L. BLOOM, Stevens In Ms. Ryan at 201-420-5448. stitute of Technology. Mathematical fluid dynamics, RUSSEL CAFLISCH. Petition Table Low-dimensional topology, MARK E. FEIGHN, LEE D. MOSHER, and ULRICH OERTEL, Rutgers University, A petition table will be set up in the registration area. Newark. Additional information about petition tables can be Smooth dynamical systems, BRUCE P. KITCHENS and found in a box in the Louisville meeting announcement SHELDON E. NEWHOUSE. in this issue of Notices. OCTOBER 1989, VOLUME 36, NUMBER 8 1011 ~ ~ !. !. ~· ~· Technology Technology of of COMPLEX COMPLEX CENTER CENTER Institute Institute STEVENS STEVENS MORTON-PIERCE-KIDDE MORTON-PIERCE-KIDDE ,~ ,~ #1. #1. #6. #6. Stevens Stevens ~ ~ ~ ~ ~ ~ r r s:: s:: ~ ~ m m :I: :I: s:: s:: m m :D :D -i -i (/) (/) > > m m (/) (/) g g z z (") (") :I: :I: ~ ~ m m z z s:: s:: ., ., 0 0 g g N N ...... 0 0 ...... Meetings Accommodations marked Hoboken. Proceed south over a viaduct and turn left onto 14th Street. Go about four blocks to Washington Street A block of rooms has been reserved at the Holiday Inn and turn right. Take Washington Street for five blocks and turn Harmon Meadow for Friday, October 20, and Saturday, left onto 9th Street. Go two blocks to Castle Point Terrace, turn October 21, at a special rate of $69 per night for a right and park in the 8th Street Lot directly ahead. The special rate may be available for single or double. To Stevens from the north: Take the New York State Thruway Sunday, October 22, but this is not guaranteed. The to the Garden State Parkway south. Take Exit 153 to Route rooms will be held until October 7, 1989. To reserve 3 east toward the Lincoln Tunnel. Exit to the right at a sign a room at this special rate, individuals must call the marked Last Exit in New Jersey and turn right at the second Holiday Inn Harmon Meadow at 201-348-2000, ask for traffic light. Proceed south over the viaduct as above. the sales office, and identify themselves as participants To Stevens from the south and west: Take the New Jersey of the AMS meeting at Stevens Institute of Technology. Turnpike to Exit 16E and follow signs toward the Lincoln Tun The Holiday Inn provides free return transportation nel. Exit to the right at a sign marked Last Exit in New Jersey to Newark Airport or Penn Station in Newark. Par and turn right at the second traffic light. Proceed south over the ticipants must ask for this service when making room viaduct as above. reservations. To the Holiday Inn from New York City: Take the Lincoln The Holiday Inn is located in a pleasant outdoor mall Tunnel. Follow I-495 west to Route 3 west. Follow the signs with several stores and restaurants and 14 movie theaters. for Harmon Meadow Boulevard, and make the second right It is approximately four miles from the Stevens campus (immediately before an EXXON station). Continue around the to the mall and the Holiday Inn provides free shuttle complex and make a right at the first stop sign. Make a left at service. The Holiday Inn has an exercise room and a car the next stop sign. The entrance to the Holiday Inn is one half rental agency which offers cars for approximately $30 block ahead on the right. per day. To the Holiday Inn from the north: From Routes 80 and 95 or the George Washington Bridge take the New Jersey Turnpike Travel south; where the turnpike divides take the eastern spur (toward From Newark Airport the Lincoln Tunnel). Leave the turnpike at Exit 17. After the toll stay right and follow the service road marked by a sign for The Newark Airport is located about ten miles from Route 3-Secaucus straight through the first light and turn right both the Stevens campus and the Holiday Inn Harmon at the first stop sign. The entrance to the Holiday Inn is one Meadow. Taxi service is available to both the Stevens half block ahead on the right. campus and the Holiday Inn for approximately $25- Take $30. By bus, participants should take the #300 New To the Holiday Inn from the south and Newark Airport: Jersey Turnpike north; where the turnpike divides take Jersey Transit Airport Express to the Port Authority Bus the New the eastern spur (toward the Lincoln Tunnel). Leave the turn runs Terminal in Manhattan at a cost of $7. This service pike at Exit 16E. After the toll follow the service road marked every ten to fifteen minutes and takes approximately by a sign for Secaucus straight through the first light and turn thirty minutes depending on the traffic. From the Port right at the first stop sign. The entrance to the Holiday Inn is Authority Bus Terminal take the #126 New Jersey Transit one half block ahead on the right. bus to Hoboken ($1. 70), or the #320 New Jersey Transit To the Holiday Inn from the west: Take Route 3 east and exit hour bus to Harmon Meadow ($2.15), with service every onto a service road at the sign marked Secaucus-N.J.Turnpike beginning at 8:20 a.m. until 9:20 p.m. Exit Only. Follow the service road and turn right onto Harmon From Penn Station Manhattan Meadow Boulevard immediately after passing under the New Go to the Port Authority Bus Terminal at 8th Avenue Jersey Turnpike. Continue through a traffic light and turn right and 42nd Street and proceed as above, or take a PATH at the first stop sign. The entrance to the Holiday Inn is one train from 6th Avenue and 33rd Street to Hoboken ($1 half block ahead on the right. exact fare in bill or coins required). From the Hoboken terminal it is a walk of approximately one-half mile to Parking the Stevens Center. The taxi fare to Stevens Center is $2.75. Free parking is available in the 8th Street and 6th Street parking lots. (Please refer to the campus map). By Car Hoboken is located on the Hudson river across from Manhattan between the Lincoln and Holland Tunnels. Weather is located off Route The Holiday Inn Harmon Meadow October weather is usually pleasant in the Hoboken area. three miles west of the Lincoln Tunnel. #3 approximately Meteorological averages for the month are 57°F and 3.1 To Stevens from New York City: Take the Lincoln Tunnel. At inches of rain. the tunnel exit bear to the extreme right through the underpass OCTOBER 1989, VOLUME 36, NUMBER 8 1013 Program of the Sessions The time limit for each contributed paper in the sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in the sessions at this meeting will be found in the October 1989 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. Saturday, October 21 AMS Special Session on Mathematical Fluid Dynamics, I AMS Special Session on Geometry 9:00 a.m.-10:50 a.m. Room 218, Pierce Hall Related to Computer Vision, I 9:00 a.m. A boundary-value problem for the stationary (8) Vlasov-Poisson equations: the plane diode. 9:00 a.m.-10:50 a.m. Room 219, Kidde Hall Claude Greengard, IBM T. J. Watson Research Center, Yorktown Heights, New York (851-76-84) 9:00a.m. Encoding rectilinear polygonal arcs. 9:30 a.m. Convergence of a point vortex method for vortex (1) Prabir Bhattacharya*, University of Nebraska, Lincoln, and Azriel Rosenfeld, University of (9) sheets. Thomas Hou, Courant Institute of Mathematical Maryland, College Park (851-68-59) Y. Sciences, New York University (851-65-48) 9:30 a.m. Discretized straight lines: Parameters, primitives and 10:00 a.m. Solitary water waves with capillary ripples at infinity. (2) properties. (1 0) Thomas Beale, Duke University (851-76-72) Leo Dorst, Technical University Delft, The J. Netherlands and North American Philips Corporation, 10:30 a.m. Computation of solitary internal waves in stratified Briarcliff Manor, New York (851-68-81) (Sponsored (11) fluids. by Robert A. Malter) Bruce Turkington*, Alexander Eydeland and Sheng 10:00 a.m. Discussion Wang, University of Massachusetts, Amherst (851-76-99) 10:30 a.m. Orthogonal polygons: Convexity and visibility. (3) Derick Wood, University of Waterloo (851-51-86) (Sponsored by Robert A. Malter) AMS Special Session on Low-dimensional Topology, I AMS Special Session on Algebraic Semantics, I 9:00 a.m.-10:50 a.m. Room 203, Morton Hall 9:00 a.m.-10:50 a.m. Room 216, Pierce Hall 9:00 a.m. Geometric finiteness of certain Kleinian groups. (12) Preliminary report. 9:00 a.m. Matrix and matricial iteration theories. Peter Scott*, University of Michigan, Ann Arbor, and (4) Stephen L. Bloom, Stevens Institute of Technology (851-68-68) G. A. Swarup, University of Melbourne, Australia (851-57-24) 9:30 a.m. Algebraic semantics and data directed design. 9:30 a.m. The boundary of outer space in rank two. (5) Eric G. Wagner, IBM T. J. Watson Research Center, (13) Marc Culler, University of Illinois, Chicago, and Karen Yorktown Heights, New York (851-68-66) Vogtmann*, Cornell University (851-20-14) 10:00 a.m. Boolean categories: A foundation for assertion (6) semantics. Preliminary report. 10:00 a.m. Thin triangles in finite volume hyperbolic group (14) graphs. Preliminary report. Ernest G. Manes, University of Massachusetts, Amherst (851-68-45) (Sponsored by Frank A. Kay Tatsuoka, Rutgers University, Newark Wattenberg) (851-20-28) (Sponsored by Mark E. Feighn) 10:30 a.m. Sequential structures. Preliminary report. 10:30 a.m. The anti-length spectrum for hyperbolic 3-manifolds. (7) Michael W. Mislove, Tulane University, and Frank J. (15) Preliminary report. Oles*, IBM T. J. Watson Research Center, Yorktown Robert Meyerhoff, Boston University (851-57-46) Heights, New York (851-68-67) (Sponsored by Eric G. Wagner) 1014 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions AMS Special Session on Algebraic AMS Special Session on Geometry Geometry, P-adic Aspects, I Related to Computer Vision, II 9:00 a.m.-10:50 a.m. Room 224, Kidde Hall 2:45 p.m.-5:05 p.m. Room 219, Kidde Hall 9:00a.m. Formal Mellin transform in the arithmetic of function 2:45p.m. Discrete multidimensional Jordan surfaces. (16) fields. (25) Gabor T. Herman, University of Pennsylvania David Goss, Ohio State University, Columbus (851-57-01) (851-11-56) 3:15p.m. Two approaches to digital topology. Preliminary 9:30a.m. Rigid subanalytic sets. Preliminary report. (26) report. (17) Leonard Lipshitz, Purdue University, West Lafayette T. Y. Kong, Queens College, City University of (851-14-57) New York (851-68-08) (Sponsored by Prabir 10:00 a.m. Duality theorems in rigid analytic spaces. Preliminary Bhattacharya) (18) report. 3:45p.m. Pattern matching as a basis for programmatic feature Bruno Chiarellotto, Princeton University (851-14-65) (27) recognition. (Sponsored by Marvin D. Tretkoff) Thomas J. Peters, University of Connecticut, Storrs 10:30 a.m. Logarithmic decay and overconvergence of the unit (851-68-74) (19) root zeta function. Preliminary report. 4:15p.m. Combinatorial and computational aspects of B. Dwork*, Princeton University, and S. Sperber, (28) Minkowski decompositions. University of Minnesota, Minneapolis (851-14-64) Ruth Silverman•, University of the District of Columbia, and David Mount, University of Maryland, College Park (851-51-58) (Sponsored by Robert A. AMS Special Session on Melter) Computational Algebra, I 4:45p.m. Discussion 9:30 a.m.-10:50 a.m. Room 116, Pierce Hall AMS Special Session on Algebraic Semantics, II 9:30 a.m. What can be computed in algebraic geometry? (20) Dave Bayer, Columbia University (851-14-103) 2:45 p.m.-4:05 p.m. Room 216, Pierce Hall (Sponsored by Charles C. Sims) 10:00 a.m. Faster base changes for groups, and their 2:45 p.m. Step bisimulation can be truly concurrent. (21) applications. (29) Douglas R. Troeger, Syracuse University (851-68-69) Gene Cooperman, Northeastern University 3:15p.m. A general framework for models of type (851-20-75) (30) polymorphism. 10:30 a.m. Fast Fourier analysis for finite groups. Badri R. Narayanan, Stevens Institute of Technology (22) Daniel N. Rockmore, Columbia University (851-68-80) (851-20-60) 3:45 p.m. Discussion AMS Invited Address AMS Special Session on Mathematical Fluid Dynamics, II 11:00 a.m.-noon Room 228, Kidde Hall (23) Level sets of solutions of elliptic and parabolic 2:45 p.m.-4:35 p.m. Room 218, Pierce Hall equations. 2:45 p.m. Some experiments on a vortex redistribution method. Fang-Hua Lin, Courant Institute of Mathematical (31) Leon L. Van Dommelen, Florida A & M University Sciences, New York University (851-35-93) (851-76-55) (Sponsored by Russel Caflisch) 3:15p.m. Discussion AMS Invited Address 3:45p.m. On the smallest scale estimates for the incompressible (32) Navier-Stokes equations. William D. Henshaw, IBM T. J. Watson Research 1:30 p.m.-2:30 p.m. Room 228, Kidde Hall Center, Yorktown Heights, New York, Heinz-Otto Kreiss, University of California, Los Angeles, and (24) Geometric aspects of topological entropy. Luis G. Reyna•, IBM T. J. Watson Research Center, Sheldon E. Newhouse, University of North Carolina, Yorktown Heights, New York (851-76-38) (Sponsored Chapel Hill (851-58-47) by Craig C. Douglas) OCTOBER 1989, VOLUME 36, NUMBER 8 1015 Program of the Sessions Saturday, October 21 (cont'd) AMS Special Session on Smooth Dynamical Systems, I 2:45 p.m.-5:05 p.m. Room 120, Pierce Hall 4:15p.m. Stieltjes integral representation and effective diffusivity and iterated integrals. (33) bounds for turbulent transport. 2:45 p.m. Asymptotic homotopy cycles Marco Avellaneda*, Courant Institute of (43) Diego Benardete•, Tufts University, and John Mathematical Sciences, New York University, and Mitchell, Prime Computer, Bedford, Massachusetts Andrew J. Majda, Princeton University (851-76-100) (851-58-89) 3:15 p.m. Markov partitions for expanding maps of the circle. (44) Matt Stafford, University of Minnesota, Minneapolis AMS Special Session on (851-58-37) Low-dimensional Topology, II-A 3:45 p.m. Invariant measures for smooth maps on manifolds. (45) Preliminary report. Jane Hawkins, University of North Carolina, Chapel 2:45 p.m.-5:05 p.m. Room 203, Morton Hall Hill (851-28-71) 2:45 p.m. Deformations of length functions in groups. 4:15p.m. Zero prime end rotation number implies a fixed point. (34) Richard K. Skora, Columbia University (851-20-12) (46) Preliminary report. 3:15p.m. A one-parameter Lefschetz fixed point theorem. Marcy Barge* and Richard Gillette, Montana State (35) Ross Geoghegan, State University of New York, University (851-58-91) Binghamton (851-57-22) 4:45 p.m. Linear differential equations with a quasi-periodic, matrix. Preliminary report. 3:45 p.m. Examples of discrete groups acting on complex (47) skew-Hermitian coefficient (36) hyperbolic 2-space. Preliminary report. Marek Rychlik, University of Arizona (851-58-61) William M. Goldman, University of Maryland, College Park (851-57-40) 4:15p.m. On Haken-and Heegaard-spectra for 3-manifolds. AMS Special Session on (37) Klaus Johannson, University of Tennessee, Knoxville Computational Algebra, II (851-57-26) 4:45 p.m. Closed braid representatives of split and composite 2:45 p.m.-4:35 p.m. Room 116, Pierce Hall (38) links. Joan S. Birman•, Institute for Advanced Study, and 2:45 p.m. Polynomial factorization and applications. Polytechnic Institute William W. Menasco, State University of New York, (48) Erich Kaltofen, Rensselaer Buffalo (851-57-30) (851-12-62) (Sponsored by Charles C. Sims) 3:15p.m. Shrinking lattice polyhedra. (49) John Cremona, University of Exeter, England, and AMS Special Session on Susan Landau•, Wesleyan University and University Low-dimensional Topology, 11-B of Massachusetts, Amherst (851-51-63) 3:45 p.m. Structures for computational algebra in scratchpad. (50) Stephen M. Watt, IBM T. J. Watson Research Center, 2:45 p.m.-4:35 p.m. Room 201 , Morton Hall Yorktown Heights, New York (851-68-95) (Sponsored 2:45 p.m. The orthogonal spectrum of a hyperbolic surface. by Charles C. Sims) (39) Ara Basmajian, University of Oklahoma (851-30-06) 4:15 p.m. The computation of Galois groups. Watson Research 3:15p.m. Limit volumes of hyperbolic three-orb/folds. (51) Clifton J. Williamson, IBM T. J. (40) Colin Adams, Williams College (851-57-15) Center, Yorktown Heights, New York (851-11-97) (Sponsored by Charles C. Sims) 3:45 p.m. A parameter space for immersed incompressible (41) surfaces in 3-manifolds. John Hempel, Rice University (851-57-85) AMS Special Session on Algebraic ·4:15p.m. Integral formulae for the enhancement of links and (42) singularities. Preliminary report. Geometry, P-adic Aspects, II Lee Rudolph, Clark University (851-53-23) 2:45 p.m.-5:05 p.m. Room 224, Kidde Hall 2:45 p.m. Fundamental groups over the p-adics and modulo p. (52) Preliminary report. David Harbater, University of Pennsylvania (851-14-52) 3:15p.m. p-Adic local zeta functions and Newton polyhedron. (53) Preliminary report. Diane Meuser, Boston University (851-14-101) 1016 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 3:45 p.m. Distinctness of Kloosterman sums. Preliminary report. (54) Benji Fisher, Princeton University (851-14-102) Sunday, October 22 4:15p.m. Monodromy of Kloosterman F-crystals, I. Preliminary (55) report. Richard Crew, University of Minnesota, Minneapolis AMS Special Session on Geometry (851-14-96) (Sponsored by Marvin D. Tretkoff) Related to Computer Vision, Ill 4:45 p.m. Discussion 8:30 a.m.-10:50 a.m. Room 219, Kidde Hall AMS General Session 8:30 a.m. Object detection in images by probing. Preliminary (65) report. 2:45 p.m.-4:55 p.m. Room 220, Pierce Hall David M. Mount, University of Maryland, College Park (851-51-94) (Sponsored by Robert A. Melter) 2:45 p.m. A bouquet of congruences. Preliminary report. 9:00 a.m. Global distances from local operations. (56) Joseph Arkin*, David C. Arney and Rickey A. Kolb, (66) Gunilla Borgefors, Swedish Defence Research United States Military Academy (851-11-05) Establisment, Sweden (851-51-53) (Sponsored by 3:00 p.m. Systems of super sequential numbers. Preliminary Robert A. Melter) (57) report. 9:30 a.m. Illuminating line segments from beyond. Joseph Arkin, David C. Arney*, Lee S. Dewald and (67) Wei-Ping Liu and Ivan Rival*, University of Ottawa Frank R. Giordano, United States Military Academy (851-68-73) (851-11-02) 10:00 a.m. Computational geometry and computer vision. 3:15p.m. Lusin's theorem for absolutely continuous functions. (68) Preliminary report. (58) Preliminary report. Godfried Toussaint, McGill University (851-68-82) Casper Gottman, Purdue University, West Lafayette (Sponsored by Robert A. Melter) (851-26-19) 10:30 a.m. Discussion 3:30 p.m. Rational reciprocity. (59) Charles Helou, Pennsylvania State University, Delaware County Campus (851-11-18) AMS Special Session on 3:45 p.m. A nonlinear recurrence yielding binary digits. Low-dimensional Topology, 111-A (60) Stanley Rabinowitz*, Westford, Massachusetts, and Peter Gilbert, Digital Equipment Corporation, Nashua, New Hampshire (851-11-88) 8:30 a.m.-10:50 a.m. Room 203, Morton Hall 4:00p.m. Regular lattices and weakly replete lattices. 8:30a.m. Not all/inks are concordant to boundary links. (61) George M. Eid, John Jay College of Criminal Justice, (69) Preliminary report. City University of New York (851-28-51) Tim D. Cochran*, Northwestern University, and Kent 4:15p.m. A sequence of knot groups and their centers. E. Orr, Indiana University, Bloomington (851-57-54) (62) Preliminary report. 9:00 a.m. Knot polynomials and boundary slopes. Preliminary Francis D. Lonergan, Webster, Massachusetts (70) report. ( 851-55-35) D. Cooper and D. D. Long*, University of California, 4:30p.m. Classifying cellular automata. Santa Barbara (851-57-04) (63) Klaus Sutner, Stevens Institute of Technology 9:30 a.m. Volumes of hyperbolic 3-orbifolds. (851-68-42) {71) William Dunbar*, Pennsylvania State University, Erie, 4:45 p.m. n-tuple hulls in uniform algebra spectrum. Preliminary and G. Robert Meyerhoff, Boston University (64) report. (851-57-13) Tome V. Tonev, Bulgarian Academy of Science, 10:00 a.m. State models and the Alexander polynomial. Bulgaria (851-46-17) (72) Preliminary report. Kenneth C. Millett, University of California, Santa Barbara (851-57-20) 10:30 a.m. Progress on the Tait flyping conjecture. (73) Morwen B. Thistlethwaite, University of Tennessee, Knoxville (851-57-27) OCTOBER 1989, VOLUME 36, NUMBER 8 1017 Program of the Sessions 10:30 a.m. i-invariance for Galois representations. Preliminary Sunday, October 22 (cont'd) (83) report. Michael Larsen* and Richard Pink, Princeton University (851-11-87) (Sponsored by Marvin D. AMS Special Session on Tretkoff} Mathematical Fluid Dynamics, Ill AMS Special Session on 9:00 a.m.-10:50 a.m. Room 218, Pierce Hall Low-dimensional Topology, 111-B 9:00 a.m. Invariant helical subspaces of the Navier-Stokes (74) equations. 9:30 a.m.-10:50 a.m. Room 201, Morton Hall Sidney Leibovich, Alexis Mahalov, Cornell 9:30a.m. The second homology of discrete groups of University, and Edriss S. Titi*, University of (84) diffeomorphisms. California, Irvine (851-76-32) Alexander Suciu* and Solomon Jekel, Northeastern 9:30a.m. Combinatorics and invariant tori in vortex dynamics. University (851-57-25} (75) Chjan Lim, Rensselaer Polytechnic Institute 10:00 a.m. lmbeddings of three-manifold groups. (851-76-50) (85) F. Gonzalez-Acuna, Universidad Nacional Autonoma 10:00 a.m. A steady state solution of nonlinear diffusion a de Mexico, and Wilbur Whitten*, University of process. Preliminary report. (76) Southwestern Louisiana (851-57-16} Raymond Michalek, Stevens Institute of Technology 10:30 a.m. Algebraic surfaces and exotic smooth structures. (851-35-49) (86) Robert E. Gompf, University of Texas, Austin 10:30 a.m. Discussion (851-57-10} AMS Special Session on AMS Special Session on Finite Groups, I Smooth Dynamical Systems, II 9:30 a.m.-10:50 a.m. Room 116, Pierce Hall 9:00 a.m.-10:50 a.m. Room 120, Pierce Hall 9:30 a.m. A proof of the Kegei-Wielandt conjecture. 9:00a.m. Multiple bifurcation in a predator-prey system. (87) Peter Kleidman, Rutgers University, New Brunswick (77) Preliminary report. (851-20-76) (Sponsored by Richard N. Lyons) Douglas S. Shafer, University of North Carolina, 10:00 a.m. Regular orbits of nilpotent groups. Charlotte (851-58-43} (88) Walter Carlip, University of Chicago (851-20-34} 9:30a.m. Parameter spaces of shift-/ike rational maps of degree 10:30 a.m. Some lattices and their groups. Preliminary report. (78) 2. (89) John Conway, Princeton University (851-20-77) Linda Keen, Herbert H. Lehman College, City (Sponsored by Richard N. Lyons) University of New York (851-99-104) 10:00 a.m. Cellular automata can have non-recursive dynamics. (79) Lyman P. Hurd, University of Maryland, College Park AMS Invited Address (851-58-79) 10:30 a.m. Connect-the-dots and topological entropy. Preliminary 11:00 a.m.- noon Room 228, Kidde Hall (80) report. Ethan M. Coven, Wesleyan University (851-58-44) (90) Symbolic dynamics. (Sponsored by James T. Campbell) Bruce P. Kitchens, IBM T. J. Watson Research Center, Yorktown Heights, New York (851-99-106) AMS Special Session on Algebraic Geometry, P-adic Aspects, Ill AMS Invited Address 9:00 a.m.-10:50 a.m. Room 224, Kidde Hall 1:30 p.m.-2:30 p.m. Room 228, Kidde Hall 9:00 a.m. Discussion (91) Dynamics and singularity formation for vortex sheets. 9:30 a.m. A Gauss-Bonnet type formula for certain Mumford Russel Caflisch, Courant Institute of Mathematical (81) curves. Sciences, New York University and University of Richard M. Freije, Mount Holyoke College California, Los Angeles (851-76-33) (851-14-92) 10:00 a.m. L-functions and differential equations, II. Preliminary (82) report. Peter F. Stiller, Institute for Advanced Study (851-14-90) 1018 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 3:15 p.m. The group of outer automorphisms of a free product. AMS Special Session on Geometry (99) Preliminary report. Related to Computer Vision, IV Darryl McCullough and Andy Miller*, University of Oklahoma (851-57-21) 2:45 p.m.-4:05 p.m. Room 219, Kidde Hall 3:45 p.m. Geodesic laminations with transverse distributions. (1 00) Preliminary report. 2:45 p.m. A Jordan surface theorem for three-dimensional digital Francis Bonahon, University of Southern California (92) spaces. (851-57 -03) Ralph Kopperman, City College, City University of New York, Paul R. Meyer* and Richard G. Wilson, Herbert H. Lehman College, City University of New AMS Special Session on York (851-54-11) Smooth Dynamical Systems, Ill 3:15p.m. A general Voronoi diagram as a spatial metric. (93) John D. Radke, University of Pennsylvania (851-51-98) (Sponsored by Robert A. Melter) 2:45 p.m.-4:05 p.m. Room 120, Pierce Hall 3:45 p.m. A survey of metrics used in digital geometry. 2:45 p.m. Do steady fast magnetic dynamos exist? (94) Robert A. Melter, Long Island University, (101) lttai Kan*, George Mason University, Edward Ott, Southampton College (851-51-09) John M. Finn, University of Maryland, College Park, and James D. Hanson, Auburn University, Auburn (851-99-1 05) AMS Special Session on 3:15p.m. Unstable chaos and symbolic dynamics. Mathematical Fluid Dynamics, IV (102) Denis Blackmore, New Jersey Institute of Technology and Courant Institute of Mathematical 2:45 p.m.-4:05 p.m. Room 218, Pierce Hall Sciences (851-58-29) 3:45 p.m. Linking and the shadowing property for piecewise 2:45 p.m. Dynamics of small numbers of hydrodynamically (103) monotone maps. (95) interacting spheres under the influence of gravity. Liang Chen, Tufts University (851-58-41) Preliminary report. Jonathan H. C. Luke, New Jersey Institute of Technology (851-76-83) (Sponsored by Denis L. AMS Special Session on Finite Groups, II Blackmore) solutions to the Euler equations. 3:15 p.m. Complex approximate 2:45 p.m.-4:05 p.m. Room 116, Pierce Hall (96) Preliminary report. Vladimir Scheffer, Rutgers University, New 2:45 p.m. Revision of the classification of the finite simple Brunswick (851-76-70) (104) groups: A status report. 3:45 p.m. Approximation of an initial-boundary value problem for Daniel Gorenstein, Rutgers University, New (97) a Bingham fluid. Brunswick (851-20-78) Jong Uhn Kim, Virginia Polytechnic Institute and 3:15p.m. Discussion State University (851-76-31) 3:45 p.m. Finite groups and the multiplicative structure of (105) subfields. Robert M. Guralnick*, University of Southern AMS Special Session on California, and Roger Wiegand, University of Low-dimensional Topology, IV Nebraska, Lincoln (851-20-07) W. Wistar Comfort 2:45 p.m.-4:05 p.m. Room 203, Morton Hall Associate Secretary 2:45 p.m. Topology of curves in compact complex surfaces. Middletown, Connecticut (98) Walter D. Neumann, Ohio State University, Columbus (851-32-39) OCTOBER 1989, VOLUME 36, NUMBER 8 1019 Presenters of Papers Numbers following the names indicate the speakers' positions on the program. • AMS Invited Lecturer * AMS Special Session Speaker *Adams, C., 40 Eid, G. M., 61 * Larsen, M., 83 *Rychlik, M., 47 Arkin, J., 56 * Fisher, B., 54 *Lim, C., 75 *Scheffer, V., 96 Arney, D. C., 57 *Freije, R. M., 81 • Lin, F.-H., 23 *Scott, P., 12 *Avellaneda, M., 33 *Geoghegan, R., 35 * Lipshitz, L., 17 *Shafer, D. S., 77 * Barge, M., 46 Goffman, C., 58 Lonergan, F. D., 62 *Silverman, R., 28 * Basmajian, A., 39 *Goldman, W. M., 36 *Long, D. D., 70 *Skora, R. K., 34 *Bayer, D., 20 * Gompf, R. E., 86 *Luke, J. H., 95 *Stafford, M., 44 *Beale, J. T., 10 * Gorenstein, D., 104 *Manes, E. G., 6 *Stiller, P. F., 82 * Benardete, D., 43 *Goss, D., 16 * Melter, R. A., 94 * Suciu, A., 84 *Bhattacharya, P., I * Greengard, C., 8 *Meuser, D., 53 Sutner, K., 63 *Birman, J. S., 38 * Guralnick, R. M., I 05 *Meyer, P. R., 92 •Tatsuoka, K., 14 *Blackmore, D., I 02 * Harbater, D., 52 * Meyerhoff, R., 15 * Thistlethwaite, M. B., 73 * Bloom, S. L., 4 *Hawkins, J., 45 *Michalek, R., 76 * Titi, E. S., 74 * Bonahon, F., I 00 Helou, C., 59 * Miller, A., 99 Tonev, T. V., 64 * Borgefors, G., 66 *Hempel, J., 41 * Millett, K. C., 72 *Toussaint, G., 68 •Caflisch, R., 91 *Herman, G. T., 25 *Mount, D. M., 65 *Troeger, D. R., 29 * Carlip, W., 88 * Hou, T. Y., 9 *Narayanan, B. R., 30 *Turkington, B., II *Chen, L., I 03 *Hurd, L. P., 79 *Neumann, W. D., 98 *Van Dommelen, L. L., 31 * Chiarellotto, B., 18 *Johannsen, K., 37 • Newhouse, S. E., 24 * Vogtmann, K., 13 *Cochran, T. D., 69 * Kaltofen, E., 48 * Oles, F. J., 7 *Wagner, E. G., 5 *Conway, J., 89 * Kan, 1., 101 *Peters, T. J., 27 *Watt, S. M., 50 * Cooperman, G., 21 *Keen, L., 78 Rabinowitz, S., 60 *Whitten, W., 85 *Coven, E. M., 80 *Kim, J. U., 97 *Radke, J.D., 93 *Williamson, C. J., 51 *Crew, R., 55 • Kitchens, B. P., 90 *Reyna, L. G., 32 *Wood, D., 3 * Dorst, L., 2 * Kleidman, P., 87 *Rival, I., 67 *Dunbar, W., 71 *Kong, T. Y., 26 *Rockmore, D. N., 22 * Dwork, B., 19 * Landau, S., 49 *Rudolph, L., 42 GROUP ACTIONS AND INVARIANT THEORY I A. Bialynicki-Birula, J. Carrell, P. Russell, and D. Snow, Editors (Conference Proceedings, Canadian Mathematical Society, Volume 10) This volume contains the proceedings of a conference, 1980 Mathematics Subject Classifications: 14-02, 14L30, 1406, 2006; sponsored by the Canadian Mathematical Society, on 20G05, 14025 Group Actions and Invariant Theory, held in August, 1988 in ISBN 0-8218-6015-1, LC 89-17605 ISSN 0731-1036 Montreal. The conference was the third in a series bringing 240 pages (softcover), September 1989 together researchers from North America and Europe Individual member $20, List price $33, (particularly Poland). The papers collected here will provide Institutional member $26 an overview of the state of the art of research in this area. The To order, please specify CMSAMS/10NA conference was primarily concerned with the geometric side of invariant theory, including explorations of the linearization All prices subject to change. Shipment will be made by surface. problem for reductive group actions on affine spaces (with For air delivery add, 1st book $5, each additional book $3, a counterexample given recently by J. Schwarz), spherical maximum $100. Prepayment required. Order from American and complete symmetric varieties, reductive quotients, Mathematical Society, P.O. Box 1571, Annex Station, Provi automorphisms of affine varieties, and homogeneous vector dence, RI 02901-1571, or call toll free 800-566-7774 to charge bundles. with VISA or MasterCard. 1020 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Muncie, Indiana Ball State University October 27-28 Program The eight-hundred-and-fifty-second meeting of the Amer Otero, Margaret Robinson, Karl Rubin, Alice Silverberg, ican Mathematical Society will be held at Ball State Marie A. Vitulli, Daqing Wan, Lawrence C. Washington, University in Muncie, Indiana on Friday, October 27, Akihiko Yukie, and Xiao-Wei Zhu. and Saturday, October 28, 1989. This meeting will be Statistics and probability, M. MASOOM ALI, Ball State held in conjunction with the Indiana Section of the University. Mir M. Ali, L. Billard, John Coffey, Miklos Mathematical Association of America. Csorgo, Randy L. Eubank, Donald A. S. Fraser, Anant P. Godbole, Shanti S. Gupta, Hira L. Koul, Ian B. Joint Invited Addresses Macneill, George P. McCabe, Joseph W. McKean, G. P. Patil, Madan Puri, Vijay K. Rohatgi, Andrew L. Rukhin, By invitation of the Central Section Program Committee, A. K. Md. E. Saleh, H. Salehi, J. N. Srivastava, W. J. and the Mathematical Association of America, there will Studden, George P. H. Styan, Derrick S. Tracy, Grace be one joint invited address as follows: Wahba, and Douglas A. Wolfe. SHELDON AXLER, Michigan State University, Writing Complex analysis, DAVID E. BARRETT, University mathematics, 12:30 p.m. Saturday. of Michigan, Ann Arbor, and LASZLO LEMPERT. H. Alexander, Eric Bedford, John Bland, Terrence J. Napier, Invited Addresses Zbigniew Slodkowski, and Sai Kee Yeung. spaces and their applications, By invitation of the Central Section Program Commit Extremally disconnected Missouri State University. tee, there will be four invited one-hour addresses. The ANANDA GUBBI, Southwest M. Friedler, Peter Greim, speakers, their affiliations, the titles of their talks, and Thomas E. Armstrong, Louis Henriksen, Neil Hindman, the scheduled times of presentation are: Ananda V. Gubbi, Melvin M. Rajagopahtn, K. Sun LASZLO LEMPERT, Purdue University, Imbedding pseu Thomas Jech, Karel Prikry, and Robert F. Wheeler. doconvex domains into a ball, 10:30 a.m. Saturday. daresan, Andrzej Szymanski, in geometry and arithmetic, KENNETH R. MEYER, University of Cincinnati, Sta Noncommutative algebra University. Ricardo Alfaro, bility and chaos in almost periodic systems, 1:45 p.m. DARRELL E. HAILE, Indiana Carolyn A. Saturday. Eli Aljadeff, Allen D. Bell, Jeffrey Bergen, Jeanne Wald Kerr, Leonid PAULS. MUHLY, University oflowa, Iowa City, Some Dean, Timothy J. Hodges, L. S. Levy, Martin Lorenz, Peter advances in operator algebra, 1:30 p.m. Friday. Krop, David B. Leep, Ian M. Musson, and J. STEVEN SPERBER, University of Minnesota, Min Malcolmson, Patrick J. Morandi, neapolis, Exponential sums and p-adic analysis, 11:30 T. Stafford. DAVID R. LARSON, Texas a.m. Friday. Triangular operator algebras, A&M University. Alvaro Arias, Richard L. Baker, David P. Blecher, Xingde Dai, Kenneth R. Davidson, Timothy Special Sessions G. Feeman, John Froelich, Frank L. Gilfeather, Donald By invitation of the same committee, there will be eight W. Hadwin, Elias Katsoulis, Jon Kraus, Richard Mercer, special sessions of selected twenty-minute papers. The Robert L. Moore, John Lindsay Orr, Justin Peters, David topics, the names and affiliations of the organizers, and R. Pitts, Stephen C. Power, Zhong-Jin Ruan, Norberta speakers are as follows: Salinas, Roger Smith, Baruch Solei, Belisario A. Ventura, Number theory and algebraic geometry, ALAN Bruce Wagner, and Warren R. Wogen. ADOLPHSON, Oklahoma State University, and STEVEN Function spaces and topology, KATHRYN FROST SPERBER. Ted Chinburg, Richard Crew, David R. Dor PoRTER, Ball State University. Gerald Beer, Beverly man, B. Dwork, David Goss, Ben Lichtin, William L. Brechner, Edwin Duda, Jo Heath, James Keesling, G. McCallum, Diane Meuser, Kyungho Oh, Daniel E. Kenneth R. Kellum, Judy Kennedy, John S. Kulesza, OCTOBER 1989, VOLUME 36, NUMBER 8 1021 Meetings Panos Lambrinos, W. Marciszewski, Robert A. McCoy, found in a box in the Louisville meeting announcement S. A. Naimpally, M. Zuhair Nashed, Prem Sharma, in this issue of Notices. Robert K. Tamaki, Terence E. Wilson, and J. S. Yang. Differential equations, JOHN F. PORTER and T. K. Accommodations PUTTASWAMY, Ball State University. F. V. Atkinson, set aside in several area Deborah Brandon, Fred Brauer, Robert Stephen Cantrell, Blocks of rooms have been should make their own Dean A. Carlson, David Eberly, B. F. Esham , Jr., Harry motels and hotels. Participants the hotel or motel of their Gingold, Po-Fang Hsieh, Anthony W. Leung, Yi Li, reservations directly with as AMS members in Warren S. Loud, Lawrence Markus, Hiroshi Matano, M. choice, and identify themselves given below. Reservations Zuhair Nashed, Robert Ochs, T. K. Puttaswamy, James order to obtain the special rates than September 27, 1989. Serrin, Ratnasingham Shivaji, R. E. Showalter, Yasutaka should have been made no later will be accepted on a space Sibuya, Robert T. Smith, H. M. Srivastava, Alastair D. After that date reservations The rates are subject to a ten percent tax. Wood, and Yuncheng You. available basis. Distances given below are driving distances measured from the Student Center. Contributed Papers Days Inn (three miles) ten-minute There will also be sessions for contributed 2000 North Broadway, Muncie, IN 47303 papers. Late papers will not be accommodated. Telephone: 317-288-9953 Toll Free: 1-800-325-2525 MAA Program Single $30 Double $37 The MAA program will begin on Saturday, October 28, at Lees Inn (two-and-one-half miles) 9:00a.m. The MAA Business Meeting will begin at 3:05 3302 North Everbrook Lane, Muncie, IN 47304 p.m. In addition to the jointly sponsored Invited Address, Telephone: 317-282-7557 Toll Free: 1-800-733-5337 are scheduled: the following MAA Invited Addresses Single $43 Each additional occupant: $6 Santa Clara University, GERALD L. ALEXANDERSON, Includes continental breakfast. Gaussian binomial coefficients. DANIEL H. GOTTLIEB, Purdue University, Topology Muncie Inn (one-and-one-half miles) and the robot arm. 414 North Madison Street, Muncie, IN 47305 RoBERT J. LOPEZ, Rose-Hulman Institute of Technol Telephone: 317-282-5981 equations with the ogy, Teaching calculus and differential Single $25 Double $34 Waterbed $35 computer algebra system MAPLE. Includes morning coffee. GLORIA OLIVE, Anderson University and the Univer sity of Otago, Does Rudolf Steiner have the answer? Radisson Hotel (one-and-one-half miles) GARY J. SHERMAN, Rose-Hulman Institute of Tech 420 South High Street, Muncie, IN 47305 nology, REU students get results in group theory-say Telephone: 317-741-7777 Toll Free: 1-800-333-3333 CAYEY essential! 1-2 persons $42 3-4 persons $48 Includes buffet breakfast and two cocktails Registration per occupant per evening. The meeting registration desk will be located in the Signature Inn (two-and-one-half miles) east end of the second floor corridor of the Pittenger 3400 Chadam Lane, Muncie, IN 47305 Student Center on the Ball State University campus. The Telephone: 317-284-4200 Toll Free: 1-800-822-5252 campus is located at the corner of University Avenue and McKinley Avenue. All sessions will be held in the Single $43 Each additional occupant $6 Student Center. The meeting registration desk will be Includes continental breakfast. p.m. on Friday, October 27, open from 8:00a.m. to 5:00 Student Center Pittenger Hotel Saturday, October 28. and from 8:00 a.m. to noon on Ball State University, Muncie, IN 47306 for members of the The registration fees are $30 Telephone: 317-285-1555 Use SUVON from Indiana $10 for students and AMS, $45 for nonmembers, and campuses. unemployed mathematicians. Single $33 Double $38 Petition Table Each additional occupant $4 Located on the Ball State University campus. A petition table will be set up in the registration area. Additional information about petition tables can be 1022 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings MUNCIE, INDIANA TO GASTON II DELAWARE O)UNfY AIRPORT RIGGIN ROAD t CENTENNIAL N JACKSON TO WINCHESTER BY-PASS TO COWAN TO NEW CASTLE TO ANDERSON TOI-70 1. BALL STATE UNIVERSITY CAMPUS SCALE 2. STUDENT CENTER AND PITTENGER HOTEL 2.25 ern.= 1 mile 3.DAYSINN 4. LEES INN 5. MUNCIE INN 6. RADISSON HOTEL [£] -STATEffiGHWAYS 7. SIGNATURE INN 8. SUPER 8 MOTEL OCTOBER 1989, VOLUME 36, NUMBER 8 1023 Meetings Super 8 Motel (two-and-one-half miles) There is direct bus service from the Indianapolis 3601 West Foxridge Lane, Muncie, IN 47304 Airport to Muncie. Three buses per day are scheduled, Telephone: 317-286-4333 Toll Free: 1-800-843-1991 leaving the airport at 11:20 a.m., 5:30 p.m., and 9:15 p.m., arriving in Muncie at 1:50 p.m., 7:35 p.m., and One person/one bed $30.88 11:20 p.m. respectively. The bus will be marked either Two persons/one bed $34.88 "ABC" or "Summit". A university van will meet all three Two persons/two beds $37.88 bus arrivals on Thursday, October 26, at the Muncie Each additional occupant: $3 bus station. Those arriving by bus on other days should inform the Department of Mathematical Sciences, Ball Food Service State University, Muncie, Indiana, 47306, or call 317- There are a number of restaurants on campus and in 285-8640 to make arrangements for service. The van will the surrounding area. Complete listings will be available also meet the American Eagle flights from Chicago to the at the meeting registration desk. There will be several Muncie Airport on Thursday, October 26. hundred visitors on campus on Friday, October 27, and it is anticipated that campus area dining facilities will Parking be used to their capacities during the noon hour only. Parking near the Student Center on Friday, October 27, A buffet lunch will be served for participants and their will be limited. Vans marked "AMS" will make stops at guests in the Student Center at noon on Friday, October the hotel, motels, and Stadium Parking Lot starting on 27, and Saturday, October 28. The cost of the luncheon Friday morning at 7:45 a.m. The Stadium Parking Lot is is $7.25 per meal. It is recommended that participants west of the Ball State Stadium. The stadium is located have lunch at these buffets due to the tight schedule. at the northeast corner of Bethel and Tillotson Avenues, There are no formal evening meals planned. and is accessible from either east or west via McGalliard Road. From the west, McGalliard Road is also State Travel Road 332 connecting with I-69. Please note: Eastern Standard Time is in effect in Indi On Saturday, October 28, there should be no difficulty ana all year. Muncie is located approximately 60 miles parking near the Student Center. There is a parking northeast of downtown Indianapolis, and 75 miles from structure south of the building, and a parking lot west Indianapolis International Airport. A number of major of the building. Additional university lots are a block airlines and several regional airlines serve Indianapo further south. lis. The American Eagle Commuter Airline flies twice daily each way between Chicago and the Muncie Air Weather port, which is approximately four miles from campus. Autumn weather in Muncie is likely to be clear, with Interstate I-69 is approximately eight miles west of the cool days and crisp nights. The average daily maximum campus and runs north from Indianapolis into Michigan. temperature at this time is 60°F, and the average daily The shortest route from I-69 to the campus is from the minimum temperature is 38°F. The average rainfall for exit at State Road #332. the month of October is 2.56 inches. 1024 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions The time limit for each contributed paper in the sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in the sessions at this meeting will be found in the October 1989 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. 10:00 a.m. An algebraic identity arising in the computation of an Friday, October 27 (9) lgusa local zeta function. Preliminary report. Margaret Robinson, Mount Holyoke College (852-11-118) AMS Special Session on Differential Equations, I 10:30 a.m. Shintani zeta functions for GL(2). (10) Akihiko Yukie, Oklahoma State University and Institute for Advanced Study (852-12-134) Room 308 A & B, Pittenger 8:00 a.m.-10:50 a.m. (Sponsored by Alan C. Adolphson) Student Center 11:00 a.m. The classification of spinors under GSpin(14) over 8:00 a.m. Global dynamics of nonlinear evolution equations. (11) finite fields and its application. (1) Yuncheng You, University of Minnesota, Minneapolis Xiao-Wei Zhu, University of Oklahoma (852-11-74) (852-35-116) 8:30 a.m. An optimization problem in electromagnetic wave (2) propagation. AMS Special Session on Noncommutative Robert Ochs, University of Toledo (852-78-132) Algebra in Geometry and Arithmetic, I 9:00 a.m. A three dimensional inverse scattering problem in (3) acoustics. 9:00 a.m.-10:50 a.m. Pine Shelf Room, Pittenger Robert T. Smith, Millersville University of Student Center Pennsylvania (852-35-71) 9:30 a.m. Boundary conditions for a one-dimensional problem in 9:00 a.m. State spaces, finite algebras and skew group rings. (4) viscoelasticity. (12) Ricardo Alfaro, University of Michigan, Flint R. J. Weinacht, University of Delaware, and B. F. (852-16-53) Esham, Jr.•, State University of New York, College at 9:30a.m. Enveloping algebras of nilpotent Lie superalgebras. Geneseo (852-35-143) (13) Preliminary report. 10:00 a.m. Global existence of smooth shearing motions of Allen D. Bell* and lan M. Musson, University of (5) K-BKZ fluids. Wisconsin, Milwaukee (852-16-69) Deborah Brandon, Virginia Polytechnic Institute and 10:00 a.m. Morita equivalence of primitive factors of the State University (852-76-26) (14) enveloping algebra U(s1(2)). 10:30 a.m. Effects of spatial arrangement of heterogeneous Timothy J. Hodges, University of Cincinnati (6) environments in population dynamics. (852-16-104) Robert Stephen Cantrell* and Chris Cosner, 10:30 a.m. Enveloping fields of non-split three dimensional University of Miami (852-92-62) (15) semisimple Lie algebras. Preliminary report. Peter Malcolmson, Wayne State University (852-16-66) AMS Special Session on Number Theory and Algebraic Geometry, I AMS Special Session on 9:00 a.m.-11:20 a.m. Room 301 , Pittenger Student Triangular Operator Algebras, I Center 9:00 a.m.-11 :20 a.m. Forum, Pittenger Student 9:00 a.m. Asymptotics of a lattice point problem and D-modules. Center (7) Ben Lichtin, University of Rochester (852-11-119) 9:30a.m. On a functional equation of lgusa's local zeta function. 9:00 a.m. Compactness and complete distributivity of lattices. (8) Diane Meuser, Boston University (852-14-146) (16) Kenneth R. Davidson•, University of Waterloo, and David R. Pitts, University of California, Los Angeles (852-47-82) OCTOBER 1989, VOLUME 36, NUMBER 8 1025 Program of the Sessions Friday, October 27 (cont'd) AMS Special Session on Function Spaces and Topology, I 9:00 a.m.-11:20 a.m. Room 306, Pittenger Student 9:30 a.m. lsometries of certain reflexive operator algebras. Center (17) Preliminary report. Robert L. Moore* and Tavan T. Trent, University of 9:00a.m. Irrational rotations on simply connected domains. Alabama, Tuscaloosa (852-47-31) (26) Preliminary report. Beverly L. Brechner, University of Florida 10:00 a.m. Triangular subalgebras of groupoid C*-algebras. (852-54-44) (18) Baruch Solei, University of Haifa, Israel and University of North Carolina, Charlotte (852-46-42) 9:30a.m. Discrete dynamical systems and homeomorphism (27) groups. Preliminary report. 10:30 a.m. Direct integrals and invariant subspaces. Judy Kennedy, University of Delaware (852-54-123) (19) Donald W. Hadwin, University of New Hampshire (852-47-83) 10:00 a.m. The dimension of the space of homeomorphisms. (28) James Keesling, University of Florida (852-54-97) 11 :00 a.m. On joint quasitriangularity. (20) Norberto Salinas, University of Kansas (852-47-102) 10:30 a.m. Span and open mappings. Preliminary report. (29) Edwin Duda, University of Miami (852-54-25) 11:00 a.m. Informal Discussion AMS Special Session on Statistics and Probability, I AMS Special Session on Complex Analysis, I 9:00 a.m.-11:20 a.m. Room 303, Pittenger Student Center 9:30 a.m.-10:15 a.m. Room 305, Pittenger Student Center 9:00 a.m. Hypergeometric and related distributions of order k. (21) Preliminary report. 9:30 a.m. Hulls of graphs. Anant P. Godbole, Michigan Technological University (30) H. Alexander, University of Illinois, Chicago (852-60-32) (852-32-1 08) 9:30a.m. Adjustment for the reporting delay of AIDS and (22) estimation of the size of the HIV infected population in the USA. AMS Invited Address lan B. Macneill*, L. Liu, University of Western Ontario, Q. P. Duong, Bureau of Management 11:30 a.m.-12:30 p.m. Room 301-302, Pittenger Consulting, Canada, and V. K. Jandhyala, University Student Center of California, Irvine (852-62-34) (Sponsored by M. Masoom Ali) (31) Exponential sums and p-adic analysis. of Minnesota, 10:00 a.m. Nonparametric rank based main effects test Steven Sperber, University (23) procedures for the two-way layout in the presence of Minneapolis (852-12-90) interaction. Douglas A. Wolfe*, Angela M. Dean, M. Dirk Wiers and Bradley A. Hartlaub, Ohio State University, AMS Invited Address Columbus (852-62-49) (Sponsored by M. Masoom Ali) 1:30 p.m.-2:30p.m. Ballroom, Pittenger Student 10:30 a.m. Probing encountered data, meta analysis and Center (24) weighted distribution methods. G. P. Patil* and C. Taillie, Pennsylvania State (32) Some advances in operator algebra. University, University Park (852-62-52) (Sponsored Paul S. Muhly, University of Iowa (852-46-40) by M. Masoom Ali) 11 :00 a.m. On shrinkage estimation of the parameters of an (25) autoregressive Gaussian process. Preliminary report. AMS Special Session on Number A. K. Md. E. Saleh, Carleton University (852-62-37) Theory and Algebraic Geometry, II (Sponsored by M. Masoom Ali) 3:00 p.m.-6:20 p.m. Room 301 , Pittenger Student Center 3:00 p.m. Additive Galois structure of global function fields. (33) Preliminary report. Ted Chinburg, University of Pennsylvania (852-11-55) 1026 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 3:30 p.m. Factorization of singular moduli for rank 2 Drinfeld (34) modules. Preliminary report. AMS Special Session on Noncommutative David R. Dorman, Middlebury College and Harvard Algebra in Geometry and Arithmetic, II University (852-11-12) 4:00p.m. L-series of Grossencharacters of type Ao for function 3:00 p.m.-4:50 p.m. Pine Shelf Room, Pittenger (35) fields. Student Center David Goss, Ohio State University, Columbus (852-11-75) 3:00 p.m. Decommutatizations of group rings and some of their properties. 4:30p.m. Kolyvagin's classes in Shafarevich-Tate groups. (47) Eli Aljadeff, University of Illinois, Urbana-Champaign (36) William G. McCallum, University of Arizona (852-11-128) (852-16-81) 3:30 p.m. Cyclic homology and Grothendieck groups of crossed 5:00 p.m. Arithmetic of elliptic curves. (48) products. (37) Karl Rubin, Ohio State University, Columbus Martin Lorenz, Temple University (852-16-80) (852-11-149) 4:00p.m. Differential operators on some affine cones. 5:30p.m. Canonical models and adelic representations. (49) lan M. Musson, University of Wisconsin, Milwaukee (38) Alice Silverberg, Ohio State University, Columbus (852-16-68) (852-14-78) 4:30 p.m. Algebraic structure of Skylanin algebras. Preliminary 6:00 p.m. Kummer's lemma for prime-power cyclotomic fields. (50) report. (39) Lawrence C. Washington, University of Maryland, S. P. Smith, University of Washington, and J. T. College Park (852-11-135) Stafford*, University of Michigan, Ann Arbor (852-16-79) AMS Special Session on Complex Analysis, II AMS Special Session on 3:00 p.m.-5:45 p.m. Room 305, Pittenger Student Triangular Operator Algebras, II Center 3:00p.m. Iteration of polynomial automorphisms of c2. 3:00 p.m.-6:20 p.m. Forum, Pittenger Student Center (40) Eric Bedford*, Indiana University, Bloomington, and John Smillie, Cornell University (852-32-14) 3:00 p.m. Cohomology in operator algebras. I. Preliminary (51 ) report. 4:00 p.m. Compactification of Kahler manifolds and integrality of Frank L. Gilfeather*, University of New Mexico, and (41) characteristic numbers. Roger Smith, Texas A&M University, College Station Sai Kee Yeung, Massachusetts Institute of (852-46-150) Technology (852-32-70) 3:30 p.m. Cohomology in operator algebras. II. 5:00 p.m. A moduli space for pointed convex domains. (52) Frank L. Gilfeather, University of New Mexico, and (42) John Bland*, University of Toronto, and Tom Roger Smith*, Texas A&M University, College Duchamp, University of Washington (852-32-1 09) Station ( 852-46-151 ) 4:00p.m. The weak closures in 11 1 hyperfinite factors of AMS Special Session on Extremally (53) canonical nest subalgebras of UHF algebras. Richard L. Baker, University of California, Berkeley Disconnected Spaces and their Applications, 1 (852-47-64) (Sponsored by Paul R. Chernoff) 4:30 p.m. Norm-principle bimodules of nest algebras. 3:00 p.m.-4:50 p.m. Room 219A, Pittenger Student (54) Xingde Dai, Texas A&M University, College Station Center (852-47-153) Triangular operators. Preliminary report. 3:00 p.m. No-projective spaces. 5:00 p.m. (55) Warren R. Wogen, University of North Carolina, ( 43) Louis M. Friedler*, University of Bridgeport, and Hill (852-47-101) Stephen Willard, University of Alberta (852-54-54) Chapel A survey of non-commutative thin sets. 3:30 p.m. Some cardinality issues concerning Boolean algebras 5:30 p.m. (56) John Froelich, University of Houston, University Park (44) and Boolean spaces. (Sponsored by Vern I. Paulsen) Karel Prikry, University of Minnesota, Minneapolis (852-47-65) (852-54-121) 6:00p.m. Triangular subalgebras of UHF C*-a/gebras. Preliminary report. 4:00 p.m. Boolean topology and convergence. (57) Belisario A. Ventura, University of California, Irvine (45) Thomas Jech, Pennsylvania State University, and California State University, San Bernardino University Park (852-54-154) (852-46-142) 4:30 p.m. Completeness of measure-type algebras for finitely (46) additive measures. Thomas E. Armstrong, University of Maryland, Baltimore County (852-28-22) OCTOBER 1989, VOLUME 36, NUMBER 8 1027 Program of the Sessions Friday, October 27 (cont'd) AMS Special Session on Differential Equations, II AMS Special Session on 3:00 p.m.-5:20 p.m. Room 308 A & B, Pittenger Statistics and Probability, II Student Center 3:00 p.m. A bifurcation problem at a singular limit. 3:00 p.m.-6:20 p.m. Room 303, Pittenger Student {70) James Serrin, University of Minnesota, Minneapolis Center {852-35-115) 3:30 p.m. Diffusion models with micro-structure. 3:00 p.m. Inference for exponential autogressive processes. {71) R. E. Showalter, University of Texas, Austin {58) L. Billard, University of Georgia {852-60-76) {852-35-86) {Sponsored by M. Masoom Ali) 4:00 p.m. Algebraic and topological selections of multivalued 3:30 p.m. Second order corrections to limiting normality. {72) adjoints of differential operators. Preliminary report. {59) Donald A. S. Fraser, University of Toronto Sun J. Lee, University of South Florida, and M. {852-62-88) Zuhair Nashed*, University of Delaware {852-34-111) 4:00 p.m. On spectral domain of harmonizable processes. 4:30 p.m. Profile of finite extinction in a one-dimensional {60) A. G. Miamee, Hampton University, and H. Salehi*, {73) nonlinear diffusion equation. Michigan State University {852-60-20) Hiroshi Matano, University of Tokyo, Japan 4:30 p.m. Interpretation of the analysis of complex experimental {852-35-131) {Sponsored by Takushiro Ochiai) {61) designs: a case study. 5:00 p.m. On the symmetry of solutions of semilinear elliptic George P. McCabe, Purdue University, West {74) equations on Rn. Lafayette {852-62-92) {Sponsored by M. Masoom Ali) Vi Li*, University of Chicago, and Wei-Ming Ni, 5:00 p.m. Statistical inference for nonregular families of University of Minnesota, Minneapolis {852-35-127) {62) densities. {Sponsored by T. K. Puttaswamy) Vijay K. Rohatgi, Bowling Green State University 5:30 p.m. Superlinear semipositone problems. {852-62-19) {Sponsored by M. Masoom Ali) {75) Ratnasingham Shivaji, Mississippi State University 5:20p.m. Testing the Goodness-of-fit of a linear model via {852-35-73) {63) nonparametric regression techniques. 6:00 p.m. Finite time blowup in a model of solar Randy L. Eubank* and Clifford H. Spiegelman, {76) magnetohydrostatics. Texas A &M University, College Station {852-62-45) David Eberly, University of Texas, San Antonio {Sponsored by M. Masoom Ali) {852-85-85) 6:00 p.m. Matrix derivatives and multivariate moments. {64) DerrickS. Tracy, University of Windsor {852-62-50) {Sponsored by M. Masoom Ali) AMS Session on Analysis AMS Special Session on 3:00 p.m.-4:50 p.m. Room 311 , Pittenger Student Function Spaces and Topology, II Center 3:00 p.m. A numerical method for the diffusion equation subject 3:00 p.m.-5:20 p.m. Room 306, Pittenger Student (77) to moving boundary nonlocal specification. Center Shingmin Wang, Northeast Missouri State University {852-35-117) {Sponsored by John F. Porter) 3:00 p.m. Compact open, Isbell and bounded open topology on 3:20 p.m. Positive solutions to a general competition model. {65) function spaces. {78) Roger Logan* and Lige Li, Kansas State University Panos Lambrinos, University of Central Florida {852-35-58) {852-54-133) 3:40 p.m. Parameter function determination in boundary value 3:30 p.m. Properties of C(X) with the epi-topology. (79) parabolic equation. Preliminary report. {66) Robert A. McCoy, Virginia Polytechnic Institute and Morteza Shafii-Mousavi, Indiana University, South State University {852-54-96) Bend {852-35-1 07) 4:00 p.m. New topologies on convex functions. 4:00 p.m. Strong porosity and Brownian motion. (67) Gerald Beer, California State University, Los Angeles {80) Casper Goffman, Purdue University, West Lafayette {852-54-04) {852-26-122) 4:30 p.m. Mosco convergence and function spaces. 4:20 p.m. Higher regularity of solutions to the p-Laplacian {68) Robert K. Tamaki* and Gerald Beer, California State {81) obstacle problem. University, Los Angeles {852-54-05) Jun Mu, Indiana University, Bloomington {852-35-03) 5:00 p.m. On automorphism groups of locally compact groups. {69) T. S. Wu, Case Western Reserve University, and J. S. Yang*, University of Southern California {852-22-13) 1028 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 4:40 p.m. Artificial boundary conditions for elastodynamics. (82) Douglas B. Meade, Purdue University, West AMS Special Session on Lafayette (852-35-136) Statistics and Probability, Ill 8:00 a.m.-10:20 a.m. Room 303, Pittenger Student Center Saturday, October 28 8:00 a.m. The Galton-Watson predator-prey process. (93) John Coffey, Purdue University, Calumet Campus (852-60-02) AMS Special Session on Extremally 8:30a.m. Diagnostics for R-estimates of regression coefficients. Disconnected Spaces and their Applications, II (94) Joseph W. McKean, Western Michigan University (852-62-91) (Sponsored by M. Masoom Ali) 8:00 a.m.-10:20 a.m. Room 219A, Pittenger Student 9:00a.m. Some limit theorems for perturbed empirical Center (95) distribution functions evaluated at a random point. Madan Puri, Indiana University, Bloomington 8:00a.m. Maximal subgroups of {3N can be small. (852-62-95) (83) Neil Hindman, Howard University (852-22-16) 9:30a.m. Path properties of infinite series of independent 8:30a.m. A characterisation of {3N. (96) Ornstein-Uhlenbeck processes. (84) M. Rajagopalan, Tennessee State University Miklos Csorgo, Carleton University (852-60-89) (852-54-1 0) 10:00 a.m. A characterization of spherically symmetric 9:00 a.m. New techniques for constructing non-normal (97) distributions. (85) subspaces. Preliminary report. Mir M. Ali, University of Western Ontario (852-60-77) Andrzej Szymanski, Slippery Rock University of (Sponsored by M. Masoom Ali) Pennsylvania (852-54-141) 9:30 a.m. Hyperstonean methods in vector-valued function (86) spaces. AMS Special Session on Function Peter Greim, The Citadel (852-54-155) Spaces and Topology, Ill 10:00 a.m. The Stonian transform of a vector-valued function. (87) Preliminary report. Robert F. Wheeler, Northern Illinois University 8:00 a.m.-10:20 a.m. Room 306, Pittenger Student (852-46-09) Center 8:00 a.m. lnvariance of continuity. (98) Prem Sharma, Butler University (852-54-33) on AMS Special Session 8:30a.m. Proximal graph topologies. Preliminary report. Triangular Operator Algebras, Ill (99) S. A. Naimpally*, Kuwait University, Kuwait, and G. Di Maio, University of Naples, Italy (852-54-17) 8:00 a.m.-10:20 a.m. Forum, Pittenger Student 9:00a.m. On topoplogical classification of funtion spaces Cp(X) Center (100) of low Borel complexity. T. Dobrowolski, University of Warsaw, Poland, W. 8:00a.m. Classification of triangular AF algebras. Marciszewski*, University of Kansas and University (88) Stephen C. Power, University of Lancaster, England of Warsaw, Poland, and J. Mogilski, University of (852-47-11) Alabama, Tuscaloosa and University of Warsaw, 8:30a.m. Triangular AF algebras and nest subalgebras of UHF Poland (852-54-36) (Sponsored by Andy R. Magid) (89) algebras. 9:30 a.m. Informal Discussion Justin Peters, Iowa State College, Ames 10:00 a.m. k-to-1 mappings. Preliminary report. (852-46-156) (101) Jo Heath, Auburn University, Auburn (852-54-140) 9:00a.m. Triangular AF algebras and nest subalgebras of UHF (90) algebras. Bruce Wagner, Iowa State University (852-46-1 00) AMS Special Session on 9:30a.m. Compactness and complete distributivity for Differential Equations, Ill (91) commutative subspace lattices. Kenneth R. Davidson, University of Waterloo, and David R. Pitts*, University of Nebraska, Lincoln and 8:00 a.m.-10:20 a.m. Room 308 A & B, Pittenger University of California, Los Angeles (852-06-08) Student Center a.m. of triangular algebras. 10:00 On the closure 8:00a.m. Existence of positive solutions for elliptic systems, John Lindsay Orr, University of Lancaster, England (92) (1 02) degenerate and nondegenerate ecological models. C. Power) (852-47-24) (Sponsored by Stephen Anthony W. Leung* and Guangwei Fan, University of Cincinnati (852-35-72) OCTOBER 1989, VOLUME 36, NUMBER 8 1029 Program of the Sessions 10:00 a.m. An approximation theorem for noncommutative Saturday, October 28 (cont'd) ( 112) valuation rings. Patrick J. Morandi, Indiana University, Bloomington (852-16-48) 8:30 a.m. An algorithm for globally analytic triangularization of a (103) matrix function. AMS Session on Algebra and Geometry Harry Gingold, West Virginia University, and Po-Fang Hsieh*, Western Michigan University (852-15-18) 9:00 a.m.-10:30 a.m. Room 311, Pittenger Student 9:00a.m. Some characteristic equations arising in epidemic Center (104) models. Fred Brauer, University of Wisconsin, Madison 9:00a.m. Algorithmic results for Hermite's problem. Preliminary (852-92-28) (113) report. Malvina Baica, University of Wisconsin, Whitewater 9:30 a.m. A remark on the Gevrey property of formal solutions. (852-11-124) (1 05) Preliminary report. Yasutaka Sibuya, University of Minnesota, 9:20a.m. Orderings and nonring CMC subsets of a ring. Minneapolis (852-34-60) (114) Preliminary report. Kenneth G. Valente*, Colgate University, and Marie 10:00 a.m. Fuchsian quasi-differential equations. Preliminary A. Vitulli, University of Oregon (852-13-87) (1 06) report. Lawrence Markus, University of Minnesota, 9:40 a.m. Embedding analytic manifolds in uniform algebra Minneapolis (852-34-112) (Sponsored by T. K. (115) spectrum. Puttaswamy) Toma V. Tonev, Bulgarian Academy of Science, Bulgaria (852-32-15) 10:00 a.m. Geometry of the dual ball of the spin factor. AMS Special Session on Number (116) Yaakov Friedman, Jerusalem College of Technology, Theory and Algebraic Geometry, Ill Israel, and Bernard Russo•, University of California, Irvine (852-46-106) 10:20 a.m. Distinguishing certain Brieskorn manifolds. 9:00 a.m.-10:20 a.m. Room 1 01, Burkhardt Hall (117) John W. Emert, Ball State University (852-57-120) 9:00 a.m. Monodromy of Kloosterman F-crystals, II. Preliminary (1 07) report. Richard Crew, University of Minnesota, Minneapolis MAAWelcome (852-14-145) (Sponsored by Alan C. Adolphson) 9:30 a.m. Effective bounds for order of p-adic growth of 9:00 a.m.-9:05 a.m. Room 301, Pittenger Student (108) solutions at a regular singularity. Preliminary report. Center G. Christal, University of Paris VI, France, and B. Dwork*, Princeton University (852-34-1 05) 10:00 a.m. The Newton polygon and P-adic analytic variation of MAA Invited Address (109) L-functions over finite fields. Preliminary report. Daqing Wan, University of Washington (852-11-21) 9:05 a.m.-9:25 a.m. Room 301, Pittenger Student Center AMS Special Session on Noncommutative ( 118) Does Rudolf Steiner have the answer? Algebra in Geometry and Arithmetic, Ill Gloria Olive, University of Otago, New Zealand and Anderson University 9:00 a.m.-10:20 a.m. Pine Shelf Room, Pittenger Student Center MAA Invited Address 9:00 a.m. The level of division algebra over local and global (11 0) fields. 9:25 a.m.-10:15 a.m. Room 301, Pittenger Student David B. Leep*, University of Kentucky, and Nicole Center Vast, Universite Catholique de Louvain, Belgium (852-11-41) (119) Gaussian binomnial coefficients. 9:30 a.m. Wild representation type and failure of direct-sum Gerald L. Alexanderson, Santa Clara University (111) cancellation. R. M. Guralnick, University of Southern California, L. S. Levy*, University of Wisconsin, Madison, and R. B. Warfield, Jr., University of Washington (852-13-144) 1030 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions AMS Invited Address AMS Special Session on Number Theory and Algebraic Geometry, IV 10:30 a.m.-11:30 a.m. Ballroom, Pittenger Student Center 3:00 p.m.-4:20 p.m. Room 101 , Burkhardt Hall (120) Imbedding pseudoconvex domains into a ball. 3:00 p.m. On topoplogy of quasi-ordinary singularities. Laszlo Lempert, Purdue University, West Lafayette (126) Preliminary report. (852-32-06) Kyungho Oh, Purdue University, West Lafayette (852-14-27) 3:30p.m. The nonring CMC subsets of a commutative ring. MAA Invited Address (127) Kenneth G. Valente, Colgate University, and Marie A. Vitulli*, University of Oregon (852-13-23) 10:45 a.m.-11:30 a.m. Room 301 , Pittenger Student 4:00p.m. Waring's problem in matrix rings over fields. Center (128) Daniel E. Otero, Xavier University (852-15-147) (121) REU students get results in group theory-say CAYEY essential. AMS Special Session on Complex Analysis, Ill Gary J. Sherman, Rose-Hulman Institute of Technology 3:00 p.m.-5:45 p.m. Room 305, Pittenger Student Center AMS-MAA Invited Address 3:00 p.m. Polynomially convex hulls over the circle. (129) Zbigniew Slodkowski, University of Illinois, Chicago 12:30 p.m.-1:30 p.m. Room 301 , Pittenger Student (852-32-137) (Sponsored by David E. Barrett) Center 4:00 p.m. Convexity properties of coverings of smooth projective (130) varieties. (122) Writing mathematics. Terrence J. Napier, Massachusetts Institute of University Sheldon Axler, Michigan State Technology (852-32-11 0) 5:00 p.m. Informal Discussion MAA Invited Address AMS Special Session on Extremally p.m. Room 301, Pittenger Student 1:40 p.m.-2:25 Disconn~cted Spaces and their Applications, Ill Center (123) Topology and the robot arm. 3:00 p.m.-4:20 p.m. Room 219A, Pittenger Student Daniel H. Gottlieb, Purdue University, West Lafayette Center 3:00 p.m. Ultrapowers of Banach spaces C(X). Preliminary AMS Invited Address (131) report. K. Sundaresan, Cleveland State University (852-54-07) 1:45 p.m.-2:45 p.m. Ballroom, Pittenger Student 3:30 p.m. Bases for a class of spaces containing basically Center (132) disconnected spaces and spaces of minimal prime (124) Stability and chaos in almost periodic systems. ideals: the locally compact case. Kenneth R. Meyer, University of Cincinnati Melvin Henriksen, Harvey Mudd College (852-58-35) (852-54-148) 4:00p.m. On the projective cover of Sw-11. (133) Ananda V. Gubbi, Southwest Missouri State MAA Invited Address University (852-54-01) 2:30 p.m.-3:00 p.m. Room 301 , Pittenger Student Center (125) Teaching calculus and differential equations with the computer algebra system MAPLE. Robert J. Lopez, Rose-Hulman Institute of Technology OCTOBER 1989, VOLUME 36, NUMBER 8 1031 Program of the Sessions Saturday, October 28 (cont'd) AMS Special Session on Statistics and Probability, IV AMS Special Session on Noncommutative 3:00 p.m.-6:20 p.m. Room 303, Pittenger Student Algebra in Geometry and Arithmetic, IV Center 3:00 p.m. Multivariate model building with partial, additive and 3:00 p.m.-4:50 p.m. Pine Shelf Room, Pittenger (145) interaction splines. Student Center Grace Wahba, University of Wisconsin, Madison (852-62-84) 3:00 p.m. Actions of Lie algebras and Hopf algebras on 3:30p.m. On the asymptotic optimality of certain empirical (134) associative rings. (146) Bayes simultaneous testing procedures. Jeffrey Bergen, DePaul University (852-16-103) Shanti S. Gupta* and Tachen Liang, Purdue 3:30 p.m. Commutativity and primitivity in the enveloping algebra University, West Lafayette (852-62-51) (135) of the Virasoro algebra, I. 4:00p.m. A limit theorem for moment sequences. Carolyn A. Dean, University of Michigan, Ann Arbor (147) Fu-Chuen Chang, Purdue University, West Lafayette, (852-16-126) J. H. B. Kemperman, Rutgers University, New 4:00 p.m. Commutativity and primitivity in the enveloping algebra Brunswick, and w. J. Studden*, Purdue University, ( 136) of the Virasoro algebra, II. West Lafayette (852-60-38) (Sponsored by M. Jeanne Wald Kerr, Michigan State University Masoom Ali) (852-16-125) 4:30p.m. Three useful expressions for expectations involving a 4:30 p.m. Tensor algebra of a relatively free group. (148) Wishart matrix and its inverse. (137) Leonid Krop, DePaul University (852-16-67) George P. H. Styan, McGill University (852-62-93) 5:00p.m. Inference regarding the dispersion matrix under the (149) Hierarchical multivariate model, and related AMS Special Session on distribution theory. Triangular Operator Algebras, IV J. N. Srivastava, Colorado State University (852-62-158) (Sponsored by M. Masoom Ali) 3:00 p.m.-6:20 p.m. Forum, Pittenger Student Center 5:30 p.m. Asymptotica/ estimation of variance. (150) Andrew L. Rukhin, University of Maryland, Baltimore 3:00 p.m. On non-self adjoint operator algebras. County (852-62-46) (Sponsored by M. Masoom Ali) (138) Edward G. Effros, University of California, Los 6:00 p.m. A weak convergence result useful in autoregression. Angeles, and Zhong-Jin Ruan*, University of Illinois, (151) Hira L. Koul, Michigan State University (852-62-94) Urbana-Champaign (852-46-39) (Sponsored by M. Masoom Ali) 3:30 p.m. Nest algebras and the Dunford-Pettis property. (139) Preliminary report. Timothy G. Feeman, Villanova University AMS Special Session on Function (852-47-139) Spaces and Topology, IV 4:00 p.m. Nests of subspaces in Banach space. (140) Alvaro Arias* and Jeff Farmer, Texas A & M University, College Station (852-46-152) 3:00 p.m.-5:20 p.m. Room 306, Pittenger Student 4:30 p.m. A new duality for spaces of operators. Center (141) David P. Blecher, University of Houston-University 3:00p.m. Generalized semicontinuous functions. Park (852-47-63) (152) JohnS. Kulesza, George Mason University 5:00 p.m. On reflexive operator algebras. (852-54-43) (142) Elias Katsoulis, University of Athens, Greece 3:30p.m. Function space topologies for Darboux and related (852-47-138) (Sponsored by David R. Larson) (153) functions. 5:30 p.m. Extensions of isometric isomorphisms. Preliminary Kenneth R. Kellum, San Jose State University ( 143) report. (852-54-98) Richard Mercer, Wright State University (852-47-30) 4:00 p.m. Toward a function space topology for variational 6:00 p.m. The tensor product problem for reflexive algebras. ( 154) calculus in Sobo/ev and related function spaces. (144) Jon Kraus, State University of New York, College at M. Zuhair Nashed, University of Delaware Buffalo (852-47-56) (852-49-99) 4:30 p.m. A note on umbra/ spaces. (155) Terence E. Wilson, Mississippi State University (852-54-157) (Sponsored by Kathryn Frost Porter) 5:00 p.m. Informal Discussion 1032 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Program of the Sessions 5:00 p.m. Contour integral solutions of certain systems of AMS Special Session on (160) hypergeometric partial differential equations and their Differential Equations, IV applications. Preliminary report. H. M. Srivastava, University of Victoria (852-34-129) 3:00 p.m.-6:20 p.m. Room 308 A & B, Pittenger 5:30 p.m. The existence of optimal controls for infinite horizon Student Center (161) hereditary Lagrange problems with state and control dependent discount factors. 3:00p.m. Estimates of oscillations for the prescribed mean Dean A. Carlson, University of Toledo (852-49-47) ( 156) curvature equation. 6:00 p.m. Asymptotic behavior of the solutions of a certain nth F. V. Atkinson, ~niversity of Toronto (852-34-114) (162) order ordinary homogeneous differential equation in 3:30 p.m. Lyapunov functions for quadratically truncated plane the vicinity of an irregular singular point. (157) autonomous systems. T. K. PuHaswamy, Ball State University (852-34-61) Warren S. Loud, University of Minnesota, Minneapolis (852-34-29) 4:00 p.m. Asymptotic& beyond all orders in an eigenvalue MAA Business Meeting (158) problem. Alastair D. Wood, Dublin City University, Republic 3:05 p.m.-3:30 p.m. Room 301, Pittenger Student of Ireland (852-34-130) (Sponsored by T. K. Center Puttaswamy) 4:30 p.m. On large time behaviour of linear degenerate Andy Roy Magid (159) hyperbolic systems. Associate Secretary Harry Gingold*, West Virginia University, and Norman, Oklahoma Victor Trutzer, University of Lowell (852-35-113) (Sponsored by Po-Fang Hsieh) ·· ...... I·' REPRESENTATION THEORY AND NUMBER This volume contains the proceedings of the conference THEORY IN CONNECTION WITH THE LOCAL ··Representation Theory and Number Theory in Connection LANGLANDS CONJECTURE with the Local Langlands Conjecture;· held in December 1985 at the University of Augsburg. The program of the J. Ritter, Editor conference was divided into two parts: (i) the representation (Contemporary Mathematics, Volume 86) theory of local division algebras and local Galois groups, The Langlands Program summarizes those parts of and the Langlands conjecture in the tame case; and (ii) new mathematical research belonging to the representation theory results, such as the case n = p, the matching theorem, of reductive groups and to class field theory. These two principal orders, tame Deligne representations, classification topics are connected by the vision that, roughly speaking, the of representations of GL(n), and the numerical Langlands irreducible representations of the general linear group may conjecture. The collection of papers in this volume provides an well serve as parameters for the description of all number excellent account of the current state of the local Langlands fields. In the local case, the base field is a given p-adic field Program. K and the extension theory of K is seen as determined by the irreducible representations of the absolute Galois group 1980 Mathematics Subject Classifications: 11537, 11540, 11545, GK of K. Great progress has been made in establishing 20G25, 22E50 correspondence between the supercuspidal representations ISBN 0-8218-5093-8, LC 88-39030 of GL(n, K) and those irreducible representations of GK ISSN 0271-4132 280 pages (softcover), January 1989 whose degrees divide n. Despite these advances, no book Individual member $17, List price $28, or paper has presented the different methods used or even Institutional member $22 collected known results. To order, please specify CONM/86NA All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-566-7774 to charge with VISA or MasterCard. OCTOBER 1989, VOLUME 36, NUMBER 8 1033 Presenters of Papers Numbers following the names indicate the speakers' positions on the program. <> AMS-MAA Invited Lecturer * AMS Special Session Speaker • AMS Invited Lecturer o MAA Invited Lecturer *Alexander, H., 30 * Gilfeather, F. L., 51 *McCabe, G. P., 61 oSherman, G. J., 121 o Alexanderson, G. L., 119 *Gingold, H., 159 *McCallum, W. G., 36 * Shivaji, R., 75 *Alfaro, R., 12 *Godbole, A. P., 21 *McCoy, R. A., 66 *Showalter, R. E., 71 *Ali, M. M., 97 Goffman, C., 80 *McKean, J. W., 94 * Sibuya, Y., 105 * Aljadeff, E., 47 * Goss, D., 35 Meade, D. B., 82 *Silverberg, A., 38 * Arias, A., 140 o Gottlieb, D. H., 123 *Mercer, R., 143 * Slodkowski, Z., 129 *Armstrong, T. E., 46 *Greim, P., 86 *Meuser, D., 8 *Smith, R. T., 3 *Atkinson, F. V., 156 * Gubbi, A. V., 133 • Meyer, K. R., 124 * Smith, R., 52 <> Axler, S., 122 *Gupta, S. S., 146 *Moore, R. L., 17 *Solei, B., 18 Baica, M., 113 *Hadwin, D. W., 19 *Morandi, P. J., 112 • Sperber, S., 31 *Baker, R. L., 53 *Heath, J., 101 Mu, J., 81 *Srivastava, H. M., 160 * Bedford, E., 40 *Henriksen, M., 132 • Muhly, P. S., 32 *Srivastava, J. N., 149 *Beer, G., 67 *Hindman, N., 83 * Musson, I. M., 49 *Stafford, J. T., 50 * Bell, A. D., 13 *Hodges, T. J., 14 *Naimpally, S. A., 99 *Studden, W. J., 147 *Bergen, J., 134 *Hsieh, P.-F., 103 *Napier, T. J., 130 * Styan, G. P., 148 * Billard, L., 58 * Jech, T., 45 * Nashed, M. Z., 72, 154 * Sundaresan, K., 131 *Bland, J., 42 * Katsoulis, E., 142 *Ochs, R., 2 *Szymanski, A., 85 *Blecher, D. P., 141 *Keesling, J., 28 *Oh, K., 126 * Tamaki, R. K., 68 * Brandon, D., 5 *Kellum, K. R., 153 o Olive, G., 118 Tonev, T. V., 115 * Brauer, F., I 04 *Kennedy, J., 27 *Orr, J. L., 92 *Tracy, D. S., 64 * Brechner, B. L., 26 *Kerr, J. W., 136 *Otero, D. E., 128 Valente, K. G., 114 * Cantrell, R. S., 6 *Koul, H. L., 151 * Patil, G. P., 24 *Ventura, B. A., 57 *Carlson, D. A., 161 *Kraus, J., 144 *Peters, J., 89 *Vitulli, M. A., 127 *Chinburg, T., 33 *Krop, L., 137 *Pitts, D. R., 91 *Wagner, B., 90 *Coffey, J., 93 *Kulesza, J. S., 152 *Power, S. C., 88 * Wahba, G., 145 *Crew, R., 107 * Lambrinos, P., 65 * Prikry, K., 44 *Wan, D., I 09 * Csorgo, M., 96 * Leep, D. B., 110 * Puri, M., 95 Wang, S., 77 *Dai, X., 54 • Lempert, L., 120 * Puttaswamy, T. K., 162 *Washington, L. C., 39 *Davidson, K. R., 16 *Leung, A. W., 102 * Rajagopalan, M., 84 *Wheeler, R. F., 87 * Dean, C. A., 135 *Levy, L. S., Ill *Robinson, M., 9 *Wilson, T. E., 155 * Dorman, D. R., 34 *Li, Y., 74 * Rohatgi, V. K., 62 * Wogen, W. R., 55 * Duda, E., 29 * Lichtin, B., 7 * Ruan, Z.-J ., 138 *Wolfe, D. A., 23 * Dwork, B., I 08 Logan, R., 78 *Rubin, K., 37 *Wood, A. D., 158 *Eberly, D., 76 oLopez,R.J., 125 * Rukhin, A. L., 150 *Yang, J. S., 69 Emert, J. W., 117 *Lorenz, M., 48 Russo, B., 116 *Yeung, S. K., 41 *Esham, B. F., Jr., 4 *Loud, W. S., 157 *Saleh, A. K., 25 *You, Y., 1 * Eubank, R. L., 63 *Macneill, I. B., 22 * Salehi, H., 60 * Yukie, A., 10 * Feeman, T. G., 139 *Malcolmson, P., 15 *Salinas, N., 20 * Zhu, X.-W., 11 * Fraser, D. A., 59 * Marciszewski, W., 100 * Serrin, J., 70 * Friedler, L. M., 43 *Markus, L., 106 Shafii-Mousavi, M., 79 *Froelich, J., 56 * Matano, H., 73 *Sharma, P., 98 1034 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Los Angeles, California University of California, Los Angeles November 18-19 Second Announcement The eight-hundred-and-fifty-third meeting of the Ameri Contributed Papers can Mathematical Society will be held at the University There will also be sessions for contributed ten-minute of California, Los Angeles on Saturday, November 18, papers. and Sunday, November 19, 1989. This meeting will be held in conjunction with the Southern California Section MAA Program of the Mathematical Association of America. All sessions The Southern California Section of MAA will meet on will take place in the Mathematical Sciences Building on Saturday, November 18. Among the invited speakers the UCLA campus. will be THOMAS M. LIGGETT, University of California, Los Angeles. There will also be two special sessions titled Calculus and computers, and Minority programs in Invited Addresses mathematics. By invitation of the Far Western Section Program Com mittee, there will be four invited one-hour addresses. The Registration speakers, their affiliations, and the titles of their talks, if The meeting registration desk will be located in the available, are: Faculty Lounge in the Mathematical Sciences Building. BURTON I. FEIN, Oregon State University, Recent The desk will be open from 8:00 a.m. until 4:00 p.m. on work in potential theory. Saturday, and from 8:30 a.m. to noon on Sunday. The STEPHEN M. GERSTEN, University of Utah, Salt Lake registration fees are $30 for members of the AMS, $45 City, Automatic and hyperbolic groups. for nonmembers, and $10 for students and unemployed NICOLAS SPALTENSTEIN, University of Oregon, Eu mathematicians. There is a special one-day fee of $15 gene. for MAA members on Saturday only. THOMAS H. WoLFF, California Institute of Technol ogy, Galois groups and rational division algebras. Petition Table A petition table will be set up in the registration area. Special Sessions Additional information about petition tables can be found in a box in the Louisville meeting announcement By invitation of the same committee, there will be four in this issue of Notices. special sessions of selected twenty-minute papers. The topics, and the names and affiliations of the organizers, Accommodations are as follows: Geometric methods in combinatorial group theory, Blocks of rooms are being held until October 17 at ROGER C. ALPERIN, San Jose State University, and the following locations. Participants should make their KAREN VOGTMANN, Cornell University. own arrangements directly with the hotel of their choice Algebraic topology, JAMES P. LIN, University of Cali and be sure to mention the joint AMS-MAA meeting fornia, San Diego. at UCLA. Note that the rates do not include applicable Quadratic forms and simple algebras, DAviD J. SALT taxes. The Claremont and Royal Palace hotels are located MAN, University of Texas, Austin, and MuRRAY M. in Westwood Village within walking distance, adjacent ScHACHER, University of California, Los Angeles. to the south side of campus. The UCLA Guest House is Harmonic analysis, THOMAS H. WOLFF. on the campus. OCTOBER 1989, VOLUME 36, NUMBER 8 1035 Meetings 0 INFORMATION 0 ENTRANCE * EMERGENCY REPORTING SYSTEM(ERS)BOOTHS .. ACCESSIBLF TO N THE DISABLED 1036 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings Participants must refer to the AMS-MAA meeting when summoned by dialing number 35 from the courtesy making reservations at the following hotels to obtain the phones in the baggage claim area. The bus should arrive rates that are listed. within 15 minutes; the fare is $12 for one passenger plus tip. For information or advance reservations call Claremont Hotel 213-777-8000. From courtesy phones dial number 35. 90024 1044 Tiverton Avenue, Westwood The most economical transportation is via public Telephone: 213-208-5957 bus from the LAX Transit Center at 96th Street and Single $35.50 Double $37.50 Vicksburg Avenue ( 1I 4 mile northeast of the main airport Twins $41.50 exit). To reach the Transit Center from the terminal, wait next to the lower level roadway under a SHUTTLE Royal Palace Westwood BUS sign, which lists buses as A, B, C, etc. Board the 1052 Tiverton Avenue, Westwood 90024 free Cor Lot C bus and exit the airport, getting off at its Telephone: 213-208-6677 or 800-248-6955 (Califor first stop outside of the airport just after it enters Parking nia) or 800-631-0100 (Outside California) Lot C. Walk 100 yards east to the LAX Transit Center. Single $67 Double $73 The fastest and most frequent service to UCLA is by the All rooms have kitchenettes. RTD #560 bus, which takes approximately 30 minutes to reach the campus and costs $1.20. (NOTE: Exact Participants must refer to Reference #2905 when making change in coins is required; no bills accepted!) Direct reservations at the following hotel to obtain the rates service to UCLA is also available Monday through Friday listed. on the Culver City #6 bus, which takes approximately UCLA Guest House 50 minutes; the fare is 50 cents. All buses approach (on UCLA campus) the campus from the south, up Westwood Boulevard, Telephone: 213-825-2923 turning right (east) at LeConte Avenue. Exit the bus at the corner and walk north up Westwood to the Mathematical Queen bed $71 Sciences Building (Boelter Hall, approximately 3I 4 mile Two twin beds $71 on the right, beyond parking structure #9.) Participants Parlor room (sofa sleeper and kitchenette) $66 planning to stay at the UCLA Guest House should stay Two room suite (kitchenette, queen on the bus to the end of the line. and sofa sleeper) $99 Parking Food Service Permits costing $4 per day are required for any cars Information will be provided at the meeting registration parking on campus between the hours of 7:00 a.m. and desk regarding availability of food service within walking 9:00 p.m. daily and may be obtained at any of the several distance. parking kiosks around the campus. Visitors with permits from other University of California campuses may use Travel these to park at UCLA, but must check in at a kiosk. The parking area closest to the Mathematical Sciences The UCLA campus is located approximately 12 miles Building is Structure #9 on Westwood Boulevard; its north of Los Angeles International Airport (LAX), which kiosk is in the center of the Boulevard. is served by all of the major airlines. The taxi fare from the airport to the UCLA campus is approximately Lance W. Small $20 plus tip. There is no extra charge for additional Associate Secretary passengers going to the same destination. The Super La Jolla, California Shuttle, which provides door-to-door service, can be OCTOBER 1989, VOLUME 36, NUMBER 8 1037 Look what's new in Mathematical Surveys and Monographs The Mathematical Surveys and Monographs series is one you're already familiar with. It's been around since 1943, when The Problem of Moments by J. A. Shohat and J.D. Tamarkin was pub lished. The series has grown over the years and includes important mathematical monographs that cover a broad spectrum of areas such as function theory, analysis, approximation theory, algebra, and topology. Each of the books is designed to give a survey of the subject and a brief introduction to its recent developments and unsolved problems. The editorial committee••. Victor W. Guillemin M. Susan Montgomery (Chairman) David Kinderlehrer ------... invites you to participate in the development of this classic series by • consulting them as reference books • using books in this series in your courses • recommending them to your library • submitting manuscripts for publication to begin a standing order to the Director of Publication at the AMS New and Recent Publications in Mathematical Surveys and Monographs Each new title is exceptional. All are the high quality mathematical publications you've grown to expect in the Mathematical Surveys and Monographs series. Yet the variety of topics and areas of mathematical interest make them perfect reference books or possible textbooks for graduate level courses. ;:::) Representation theory and harmonic analysis on :.J Asymptotic behavior of dissipative systems by semisimple Lie groups. edited by Paul J. Sally. Jr. Jack K. Hale, 1988, 198 pp. (LC 87-33495; ISBN 0-8218- and David A. Vogan. Jr., 1989. 350 pp. (ISBN 0-8218- 1527-X). List $58, Inst. mem. $46, Indiv. mem. $35, 1526-1). List $88, Inst. mem. $70, Indiv. mem. $53, Code SURV /25NA Code SURV/31NA 0 Noetherian rings and their applications, edited by :J The Markhoff and Lagrange spectra by Thomas W. Lance W. Small, 1987, 118 pp. (LC 87-14997; ISBN Cusick and Mary E. Flahive, 1989, 96 pp. (ISBN 0- 0-8218-1525-3). List $41, Inst. mem. $33, Indiv. mem. 8218-1531-8). List $42, Inst. mem. $34, Indiv. mem. $25, Code SURV/24NA $25, Code SURV/30NA 0 Introduction to various aspects of degree theory in 0 Amenability by Alan L. T. Paterson, 1988, 416 pp. Banach spaces by E. H. Rothe, 1986, 254 pp. (LC 86- (ISBN 0-8218-1529-6). List $95, Inst. mem. $76, 8038; ISBN 0-8218-1522-9). List $66, Inst. mem. $53, Indiv. mem. $57, Code SURV/29NA Indiv. mem. $40, Code SURV /23NA 0 Direct and inverse scattering on the line by :J Noncommutative harmonic analysis by Michael E. Taylor, Richard Beals, Percy Deift, and Carlos Tomei, 1988, 1986, 344 pp. (LC 86-10924; ISBN 0-8218-1523-7). List 209 pp. (LC 88-14487; ISBN 0-8218-1530-X). List $74, Inst. mem. $59, Indiv. mem. $44, Code SURV/22NA $57, Inst. mem. $46, Indiv. mem. $34, Code SURV/28NA 0 The Bieberbach conjecture: Proceedings of the symposium on the occasion of the proof, edited by 0 Basic hypergeometric series and applications by Nathan J. Fine, 1988, 144 pp. (LC 88-6235; ISBN 0-8218- Albert Baernstein, David Drasin, Pe.ter Duren, and 1524-5). List $42, Inst. mem. $34, Indiv. mem. $25, Albert Marden, 1986; reprinted 1987, 260 pp. (LC 86-10843; Code SURV/27NA ISBN 0-8218-1521-0). List $50, Inst. mem. $40, Indiv mem. $30, Code SURV/21NA 0 Operator theory and arithmetic in H"" by Hari Bercovici, 0 Partially ordered abelian groups with interpolation 1988, 275 pp. (LC 88-10344; ISBN 0-8218-1528-8). List by Kenneth R. Goodearl, 1986, 358 pp. (LC 86-7876; $71, Inst. mem. $57, Indiv. mem. $43, Code SURV/26NA ISBN 0-8218-1520-2). List $74, Inst. mem. $59, Indiv. mem. $44, Code SURV/20NA Standing orders are accepted for this and any other series published by the Society. Proforma invoices are sent to standing order customers prior to the publication of each new volume. Shipment is made upon receipt of payment and publication. To begin a standing order, please contact the Customer Services Department of the AMS. PREPAYMENT REQUIRED. Order from the American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or callB00-556-7774 from within the continental U.S. (40I-272-9500, elsewhere) to use VISA or MasterCard. Prices subject to change. For optional air delivery, please add: first book $5, each additional $3, $100 maximum. For informa tion on numbers 1-19, please refer to the AMS Catalogue of Publications. Louisville Meetings January 17-20, 1990 Preliminary Announcement Founded in 1778 by George Rogers Clark at the Falls of the Ohio, Louisville grew into a major trading and industrial city during the 19th century. It continues that tradition along with its growing health and ser IMPORTANT DEADLINES vice industries. Louisville is a city of horses, fine architecture, friendly people and delicious food. Its Historic Main Street, Victorian Man AMS Abstracts sions, Center for the Arts and Health Center make it a great place to For consideration for special sessions Expired visit and live. The metropolitan area's three public and two private Of contributed papers October 11 colleges and universities and its two major seminaries provide a wide variety of educational opportunities. MAA Abstracts Of contributed papers Expired WHERE TO FIND IT PAGE For Special Computer Session October 20 Employment Register How to preregister and get a room 1052 (Applicants & Employers) November 17 AMS-MAA Invited Addresses 1041 EARLY Preregistration and Housing October 31 November 17 Annual Meeting of the AMS 1041 ORDINARY Preregistration and Housing MAA Minicourse Preregistration November 17 AMS Short Course 1080 FINAL Preregistration December 18 Annual Meeting of the MAA 1044 Motions for AMS Business Meeting December 18 Other Organizations 1050 Preregistration cancellations (50% refund) January 3 Housing Changes/Cancellations with Housing Other Events of Interest· 1051 Bureau December 15 Timetable 1061 AMS Banquet (50% refund) January 3 Employment Register 1076 NAM Banquet (50o/o refund) January 3 Miscellaneous Information 1056 OCTOBER 1989, VOLUME 36, NUMBER 8 1039 A Year of National Dialo,gue A series of 1990 events coordinated by the Mathematical Sciences Education Board to promote discussion of fundamental issues in mathematics education Special Events at LouisviUe Wednesday, January 17 8:30 a.m.- 9:50 a.m. AMS-MAA Panel Discussion Mathematics and public policy: How can we make a difference? Panelists: Philip Daro, Executive Director of the American Mathematics Project; Kenneth M. Hoffman, MIT; Harvey B. Keynes, University of Minnesota, Minneapolis; Paul J. Sally, Jr., University of Chicago, and John A. Thorpe, SUNY at Buffalo (organizer) 9:30a.m. -10:55 a.m. Panel Discussion: Humanistic Mathematics Lynn V. Cheney, Head of the National Endowment for the Humanities; Ubiratan D'Ambrosio, Universidade Estadual de Campinas, Brazil; Philip J. Davis, Brown University; and Alvin M. White, Harvey Mudd College (moderator) 4:25 p.m.- 5:30 p.m. AMS-MAA Science and Government Speaker Mathematics: Keystone of modern science and technology D. Allan Bromley, Assistant to the President for Science and Technology Policy 7:15p.m.- 8:15p.m. AMS-MAA Science and Government Speaker Revitalizing mathematics education: A national imperative Admiral James D. Watkins, Secretary of Energy Thursday, January 18 Joint Policy Board for Mathematics: Communicating Mathematics 6:00 p.m.- 6:45 p.m. Reception- Cash Bar 6:45 p.m.- 8:15 p.m. Breaking the code {The life ofAlan Turing) Reading by the playwright Hugh Whitemore, Reminiscences by Peter J. Hilton, SUNY at Binghamton, Presentation of the second annual JPBM Communications Award Friday, January 19 12:15 p.m.- 2:15p.m. Mathematicians and Education Reform/Mathematical Sciences Educational Board Workshop: The mathematician as gatekeeper of educational reform 7:00 p.m.- 9:00 p.m. Joint Policy Board for Mathematics: National Meeting of Department Heads The David Report Revisited: A dialogue with Edward E. David, Jr. Evaluation of teaching MAA Committee on Accreditation 9:00 p.m.- 10:30 p.m. AMS-MAA Panel Discussion: Teaching undergraduate mathematics: Insights from education research Ronald G. Douglas, SUNY at Stony Brook (moderator); Alan H. Schoenfeld, University of California, Berkeley, (principle speaker); Respondents: Paul J. Sally, Jr., University of Chicago, and Guido L. Weiss, Washington University Saturday, January 20 1:30 p.m.- 2:30p.m. A preview ofthe MS 2000 study, William E. Kirwan, Chair of MS 2000 Committee and President, University of Maryland For information about other events in the Year of National Dialogue, contact: Robert Kansky, MSEB, 2101 Constitution Avenue, NW, Washington, DC 20418, 202-334-3294. 1040 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings The Scientific Program The January 1990 Joint Mathematics Meetings, including the 96th Annual Meeting of the AMS, the 73rd Annual Meeting of the Mathematical Association of America, and the 1990 annual meetings of the Association for Women in Mathematics and the National Association for Mathematicians, will be held January 17-20 (Wednesday- Saturday), 1990, in Louisville, Kentucky. Sessions will take place in the Commonwealth Convention Cen ter and Hyatt Regency. AMS-MAA Invited Addresses By invitation of the AMS-MAA Joint Program Commit tee (Hugh L. Montgomery, David P. Roselle, Mary Ellen Rudin, and Peter Sarnak, chairman), four speakers will address the AMS and MAA on some history or devel opment of mathematics. The names of the speakers, their affiliations, the titles, dates, and times of their talks follow: JoN BARWISE, Stanford University, Nonwellfounded sets and their applications, 11:10 a.m. Friday; CHARLES W. CuRTIS, University of Oregon, A century of representation theory of finite groups, 11:10 a.m. Saturday; Shlomo Sternberg, Colloquium Lecturer BARRY SIMON, California Institute of Technology, Fifty years of eigenvalue perturbation theory, 11: 10 a.m. 96th Annual Meeting of the AMS Wednesday; January 17-20, 1990 NOLAN R. WALLACH, Rutgers University, title to be announced, 11: 10 a.m. Thursday; Sixty-Third Josiah Willard Gibbs Lecture: The 1990 Gibbs Lecture will be presented at 8:30 p.m. on Wednes day, January 17, by GEORGE B. DANTZIG of Stanford University. The title of his lecture is The wide world of pure math which goes by other names. Colloquium Lectures: A series of three Colloquium Lectures will be given by SHLOMO STERNBERG of Harvard University. The title of this lecture series is Some thoughts on the interaction between group theory and physics (tentative). The lectures will be given at 1:00 p.m. daily, Wednesday through Friday, January 17-19. Prizes: The 1990 Frank Nelson Cole Prize in Algebra will be awarded at 4:25 p.m. on Thursday, January 18. Invited Addresses: By invitation of the Program Com mittee for National Meetings, there will be six fifty minute invited addresses. The names of the speakers, their affiliations, the dates, times and titles (if available) of their talks follow: SuN-YUNG ALICE CHANG, University of California, Los Angeles, title to be announced, Saturday 2:15 p.m.; ISRAEL C. GORBERG, Tel Aviv University, Linear operators, matrix functions and control, Thursday 2: 15 p.m.; MIKE HOPKINS, University of Chicago, title to be George B. Dantzig, Gibbs Lecturer announced, Friday 9:00 a.m.; OCTOBER 1989, VOLUME 36, NUMBER 8 1041 Meetings HENRYK IWANIEC, Rutgers University, Problems and Semigroup theory, INESSA LEVI and W. WILEY methods in analytic number theory, Friday 10:05 a.m.; WILLIAMS, University of Louisville, Wednesday and JANOS KoLLAR, University of Utah, The structure of Thursday 8:00 a.m. algebraic threefolds, Thursday 3:20 p.m.; Function theoretic methods in differential equations, ISRAEL M. SIGAL, University of Toronto, title to be PETER A. McCoY, United States Naval Academy, Wed announced, Wednesday 10:05 a.m.; nesday and Thursday 8:00 a.m. Optimization and nonlinear analysis, LYNN McLIN Special Sessions: By invitation of the same commit DEN, University of Illinois, Urbana, and JAYS. TREIMAN, tee, there will be eighteen special sessions of selected Western Michigan University, Friday 1:00 p.m., Saturday twenty-minute papers. The topics of these special ses 8:00 a.m. and 1:00 p.m. sions, the names and affiliations of the mathematicians Analytic number theory, HuGH L. MoNTGOMERY, arranging them, and the dates and times they will meet, University of Michigan, Ann Arbor, Wednesday 2:15 are as follows: p.m., Friday 1:00 p.m., and Saturday 8:00 a.m. Linear operators, matrix functions and control, JosEPH Geometric spectral and inverse spectral problems, PE A. BALL, Virginia Polytechnic Institute and State Univer TER A. PERRY, University of Kentucky, Wednesday 2:15 sity and ISRAEL C. GORBERG, Friday 1:00 p.m., Saturday p.m., Thursday and Saturday 8:00 a.m. 8:00 a.m. and 1:00 p.m. Markov processes and stochastic analysis, PHILIP E. The Schrodinger equation, JosEPH G. CoNLON, Uni PROTTER, Purdue University, Wednesday 2:15 p.m. and versity of Michigan, Wednesday 2:15 p.m., Thursday Friday 8:00 a.m. 8:00 a.m., and Friday 1:00 p.m. Abstracts for consideration for these sessions should Multivariable operator theory, RAUL E. CuRTO and have been submitted by the September 20 deadline. PAULS. MuHLY, University of Iowa, Wednesday 2:15 This deadline was previously published in the Calendar p.m., Thursday and Friday 8:00 a.m. of AMS Meetings and Conferences and in the Invited Homotopy theory, ETHAN S. DEVINATZ and MIKE Speakers and Special Sessions section of the Notices. HoPKINS, University of Chicago, Wednesday 2:15 p.m., Friday and Saturday 1:00 p.m. Contributed Papers: There will be sessions for con Group representations and operator algebras, ROBERT tributed papers on Wednesday, Thursday, Friday and S. DoRAN, Texas Christian University, Wednesday 8:00 Saturday. a.m. and Friday 1:00 p.m. Abstracts should be prepared on the standard AMS Functional equations and their applications, BRUCE R. form available from the AMS office in Providence or EBANKS, University of Louisville, Thursday and Friday in departments of mathematics, and should be sent to 8:00a.m. Abstracts, Editorial Department, American Mathemati History of mathematics, FLORENCE D. FASANELLI, cal Society, Post Office Box 6248, Providence, Rhode National Science Foundation, and VIcToR J. KATz, Uni Island 02940, so as to arrive by the abstract deadline versity of the District of Columbia, Wednesday 8:00a.m. of October 11, 1989. A charge of $16 is imposed for and Friday 1:00 p.m. retyping abstracts that are not in camera-ready form. Control of infinite dimensional systems, RoBERT E. Late papers will not be accepted. FENNELL, Clemson University, and SuzANNE MARIE LENHART, University of Tennessee, Friday and Saturday Electronic Submission of Abstracts: This service is 8:00a.m. now available to those who use the TEX typesetting Geometric function theory in one and several complex system and can be used for abstracts of papers to be variables, CARL H. FITZGERALD, University of Califor presented at this meeting. Requests to obtain the pack nia, San Diego, and TED J. SUFFRIDGE, University of age of files may be sent electronically on the Internet Kentucky, Wednesday 2:15 p.m., Thursday and Saturday to [email protected]. Requesting the files elec 8:00a.m. tronically will likely be the fastest and most convenient Oscillation theory in ordinary differential equations, way, but users may also obtain the package on IBM or GARY D. JoNES, Murray State University, Friday and Macintosh diskettes, available free of charge by writing Saturday 1:00 p.m. to: Rosanne Granatiero, American Mathematical Soci Topology in computer graphics and image process ety, Publications Division, P.O. Box 6248 Providence ing, EFIM D. KHALIMSKY, New York, New York, YUNG ' ' RI 02940, USA. When requesting the Abstracts package, KONG, Queens College, and RALPH D. KOPPERMAN, City users should be sure to specify whether they want the College, CUNY, Wednesday and Saturday 8:00 a.m. plain TEX, A.MS-TEX, or the Jb.TEX package. Again, late Algebraic geometry, JANOS KoLLAR, Friday 8:00 a.m. papers will not be accepted. and 1:00 p.m. and Saturday 8:00 a.m. 1042 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings Other AMS Sessions organized by NAOMI FISHER, University of Illinois at Mathematical Reviews' 50th Birthday: The first issue of Chicago, HARVEY B. KEYNES, University of Minnesota, Mathematical Reviews (MR) appeared in 1940; therefore Minneapolis, and PHILIP D. WAGREICH, University of the year 1990 will be MR's 50th year of publication. To Illinois at Chicago. This session will take place both mark this anniversary, there will be a session on Fifty on Thursday, January 18, and Saturday, January 20, years of Mathematical Reviews on Thursday, January 18, beginning at 8:00 a.m. at 8:30 p.m. All persons interested in MR (in particular, semi reviewers for the journal) are invited to attend this YEAR OF NATIONAL DIALOGUE centennial event. Reviewers are asked to please check the SPECIAL EVENTS box on the Pregistration/Housing Form so that special Teaching Undergraduate Mathematics: The AMS mention of their status can be made on their meeting on Science Policy and the MAA Science badge. Committee Policy Committee are cosponsoring a panel discussion Council Meeting: The Council of the Society will meet on Teaching undergraduate mathematics: Insights from at 2:00 p.m. on Tuesday, January 16. education research on Friday, January 19 at 9:00 p.m. Business Meeting: The Business Meeting of the Society Several recent reports have described better ways to will take place immediately following the award of the teach undergraduate mathematics. The claims were Cole Prize at 4:25 p.m. on Thursday, January 18. For based on new research in mathematics education additional information on the Business Meeting, please which is little known in the mathematics community. refer to the box titled Committee on the Agenda for The panel will present and examine this research Business Meetings. from a mathematician's viewpoint. Both believers and skeptics are encouraged to attend. An open ended opportunity for comments and questions will Other AMS- MAA Sessions follow the formal presentation. RoNALD G. DouGLAS, SUNY at Stony Brook is the moderator. ALAN H. ScHOENFELD, University of California, Berkeley, is YEAR OF NATIONAL DIALOGUE the principal speaker. Respondents are PAUL J. SALLY, SPECIAL EVENTS JR., University of Chicago, and Gumo L. WEiss, The Society and the Association are jointly sponsoring Washington University. two invited addresses of major importance to the Year Mathematics and Public Policy: These same com of National Dialogue on Wednesday, January 17. mittees are also cosponsoring a panel discussion on Policy: How can we make AMS-MAA Science and Government Speaker: At Mathematics and Public panel discussion is scheduled from 4:25 p.m. D. ALLAN BROMLEY, Assistant to the Pres a difference? The a.m. on Wednesday. In this "Year ident for Science and Technology, will speak on 8:30 a.m. to 9:50 the mathematics community is Mathematics: Keystone of modern science and technol of National Dialogue," asked to participate actively in a discussion of ogy. being mathematics education throughout the United States, AMS-MAA Science and Government Speaker: At to help shape changes in the schools, and to com 7:15 p.m. ADMIRAL JAMES D. WATKINS, Secretary municate clearly and forcefully with others about the of Energy, will speak on Revitalizing mathematics need for change and the directions of that change. But education: A national imperative most mathematicians are inexperienced in the process of interaction with those who make public policy. Preparation for College Teaching: The AMS-MAA This session will provide examples of successful in SIAM Committee on Preparation for College Teaching is teractions between mathematicians and public policy sponsoring a forum on How Should Mathematicians Pre makers at the local, state, and national levels. JoHN pare for College Teaching? This forum is scheduled from A. THORPE, SUNY at Buffalo and Chair of the MAA 10:00 a.m. to 10:55 a.m. on Friday. BETTYE ANNE CASE, Science Policy Committee, is the organizer and mod Florida State University, is the moderator. Panelists erator. Panelists will include PHILIP DARO, Executive include DONALD W. BUSHAW, Washington State Univer Director of the American Mathematics Project; KEN sity; MICHAEL C. REED, Duke University; RICHARD D. NETH M. HoFFMAN, Massachusetts Institute of Tech RINGEISEN, Clemson University; and GUIDO L. WEISS, nology; HARVEY B. KEYNES, University of Minnesota, Washington University. Minneapolis; and PAUL J. SALLY, JR., University of Mathematics and Education Reform: This session is Chicago. jointly sponsored by the AMS and MAA and is being OCTOBER 1989. VOLUME 36, NUMBER 8 1043 Meetings 73rd Annual Meeting of the MAA well as discussion of what topics can be handled and January 17-20, 1990 how. Software and detailed lecture notes will be sent to participants after the course on request (for a nominal Retiring Presidential Address: Past President LEONARD handling fee). GILLMAN, University of Texas, will give his Retiring Presidential Address on Teaching programs that work at Minicourse #2: Finite-Pak-Software for Linear Pro 3:20 p.m. on Friday. gramming is being organized by MARVIN L. BITTINGER Invited Addresses: There will be five invited fifty and J. CoNRAD CROWN, Indiana University-Purdue Uni minute addresses. The names of the speakers, their versity at Indianapolis. Part A is scheduled from 8:30 affiliations, the dates, times, and titles follow: a.m. to 10:30 a.m. on Wednesday, January 17, and part JANOS D. AczEL, University of Waterloo, New de B from 8:30 a.m. to 10:30 a.m. on Thursday, January velopments in solving the second part of Hilbert's fifth 18. Enrollment is limited to 30. problem, 3:20p.m. Wednesday; A new integer based method for solving systems of MICHAEL BARNSLEY, Iterated Systems, Inc., Teaching equations will be introduced and applied to solving of mathematics through fractals and chaos, 2:15p.m. Friday; systems and to the basic simplex algorithm for solving maximum-type linear programs. Then a new method for THOMAS KAILATH, Stanford University, Displacement structure of matrices and some applications, 10:05 a.m. solving linear programs with mixed constraints, called Saturday; Crown's Method, will be delineated. Crown's Method is JuDITH D. SALLY, Northwestern University, What's easy to apply and avoids the cumbersome and out-of between a domain and its quotient field?, 2: 15 p.m. date techniques of the Big M and Two-Phase Methods. Wednesday; Software will be presented for carrying out each of the procedures. Each participant will receive a disk and PETER WINKLER, Emory University and Bellcore, On the (sometimes) strange behavior of large random things, printed materials. 10:05 a.m. Thursday; Minicourse #3: Random mappings will be presented Minicourses: Seventeen Minicourses are being offered by BERNARD HARRIS, University of Wisconsin. Part A is by the MAA. The names and affiliations of the organizers, scheduled from 8:30a.m. to 10:30 a.m. on Wednesday, the topics, the dates and times of their meetings, and the January 17, and part B from 8:30a.m. to 10:30 a.m. on enrollment limitations of each are as follows: Thursday, January 18. Enrollment is limited to 80. The subject of random mappings employs proba Minicourse #1: Computer based discrete mathematics bilistic methods to study combinatorial structures and is being organized by NANCY Hooo BAXTER, Dickinson algebraic systems. Specifically, let X be a finite set with College, ED DUBINSKY, Purdue University, and DONALD lXI = n. Let T n be a set of mappings from X into X. MuENCH, St. John Fisher College. Part A is scheduled Let P be a probability measure on T n. The set of such from 7:00p.m. to 9:00p.m. on Tuesday, January 16; part mappings is in one-to-one correspondence with the set of B is scheduled from 2: 15 p.m. to 4: 15 p.m. on Wednes labelled directed graphs for which every vertex has out day, January 17; and part C is scheduled from 2: 15 p.m. degree one. Various specializations of P and/or Tn lead to 4:15 p.m. on Thursday, January 18. Enrollment is to various types of combinatorial structures and alge limited to 30. braic systems. These include trees, the symmetric group This Minicourse is about a new way of teaching Sn on n elements (and various subgroups), the symmetric discrete mathematics. The content agrees with what semigroup on n letters (and various subsemigroups). is generally recommended. The method is based on The goal of the course is to demonstrate the utility of contemporary research in learning abstract mathematics probabilistic methods in studying combinatorial struc and makes use of a very high level programming language tures and algebraic systems. The course will be largely ISETL. ISETL is interactive and its syntax is close self-contained with prerequisites restricted to combina to mathematical notation. Participants will learn to torics, probability and abstract algebra contained in a understand several mathematical programs that express typical undergraduate course in discrete mathematics. complicated mathematical ideas and will write their Exercises which can be solved using pocket calculators own. The point for teaching is that students learn to use and tables of standard probability distributions (such as important mathematical constructs (such as set formers, the normal distribution) will be used. Registrants should quantifiers, function definitions) in the context of getting bring a "good" scientific calculator to the course. their programs to do the right thing. The syntax is sufficiently simple that most of their mental energy is Minicourse #4: Lagrange first year calculus is being devoted to understanding mathematical processes that organized by FRANCESCA SCHREMMER, West Chester become realities for them. The course includes "hands University and ALAIN SCHREMMER, Community College on" experience with ISETL and discrete mathematics, as of Philadelphia. Part A is scheduled from 8:30 a.m. 1044 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings to 10:30 a.m. on Wednesday, January 17, and part B from 2:15 p.m. to 4:15 p.m. on Thursday, January 18. from 8:30a.m. to 10:30 a.m. on Thursday, January 18. Enrollment is limited to 80. Enrollment is limited to 80. The purpose of this Minicourse is to encourage and The conventional approach to the first year calcu prepare faculty members to serve as advisors for a lus depends from the outset on the notion of limit, team of undergraduate modelers. They will be told and whether explicitly or implicitly. In contradistinction, La shown how to do it. The emphasis throughout will grange's approach depends only on Taylor expansions be on the Mathematical Contest in Modeling as an obtained immediately from the definition of the func educational experience, one that will help increase the tion. Continuity, differentiability, extremes, concavity, ... applied presence on campus. Participants will receive a and two-sided limits are then seen systematically as copy of the MCM89 special issue of the UMAP Journal, attributes of Taylor expansions. The Minicourse will as well as an MCM Advisor's Handbook. concentrate mostly on the Differential Calculus. In the Minicourse #7: Derive workshop is being organized first session, the approach will be presented in the usual by WADE ELLIS, JR., West Valley College. Part A is expository manner and systematically contrasted with scheduled from 4:30 p.m. to 6:30 p.m. on Wednesday, the conventional approach. The second session will be January 17, and part B from 7:00p.m. to 9:00p.m. on devoted to an implementation of Lagrange's approach Thursday, January 18. Enrollment is limited to 30. particularly suited for "just plain folks" as it does not re Derive (successor to muMATH) is a computer alge quire the usual precalculus. This consists in first treating bra system developed by David Stoutemyer and Albert the complete calculi of affine functions [a(x) =ax+ b], Rich and is based on a LISP-like programming language. 2 quadratic functions [q(x) = ax +bx+c], and the homo The system contains many specialized mathematically graphic functions [h(x) = (ax+b)j(cx+d)] to introduce oriented functions and operators. In the Minicourse, most of the basic questions and ideas. The course then each participant will use Derive on an IBM Personal continues with (Laurent) polynomial, rational functions Computer. No prior knowledge of computer program and irrational and transcendental functions introduced ming will be assumed. The first session will begin with a as solutions of differential equations. The presentation demonstration of the Derive formula entry conventions will be based on materials already used by students for and computing environment. Participants will then work several years, complete with exams. through hands-on guided exercises to become familiar Minicourse #5: Teaching mathematical modeling is with Derive's built-in operations. The second session will being organized by FRANK R. GIORDANO, U.S. Military be devoted to Derive modules on calculus, linear algebra, Academy and MAURICE D. WEIR, Naval Postgraduate and differential equations. A discussion period including School. Part A is scheduled from 8:30a.m. to 10:30 a.m. a brief comparison of Derive with other mathematical on Wednesday, January 17, and part B from 8:30 a.m. computer environments will conclude the workshop. to 10:30 a.m. on Thursday, January 18. A third optional Minicourse #8: Using history in teaching calculus session, part C, will use the microcomputer facility and is being organized by V. FREDERICK RICKEY, Bowling is scheduled from 12:15 p.m. to 2:00 p.m. on Thursday, Green State University and the U.S. Military Academy. January 18. Enrollment is limited to 40. Part A is scheduled from 4:30 p.m. to 6:30 p.m. on In 1981 the MAA Committee on the Undergraduate Wednesday, January 17, and part B from 2:15 p.m. to Program in Mathematics recommended that "Students 4:15 p.m. on Thursday, January 18. Enrollment is limited should have an opportunity to undertake 'real world' to 80. mathematical modeling projects ... " as part of the com Students of the calculus instinctively ask many pen mon core curriculum for all mathematical science majors. etrating questions: What is the calculus? What good is This is because many applications of problems in sci it? Why are the concepts presented the way they are? ence, industry and government are best approached using When the calculus reform movement eliminates the com mathematical modeling techniques. This Minicourse pro putational drudgery to concentrate on the fundamental vides an introduction to the modeling process and to ideas of the calculus, it will be even more imperative to several topics underlying the construction of mathemat respond to these questions. The answers are inherently ical models, as well as addresses issues related to the historical, and so by interjecting a historical vein into our design of an undergraduate course in modeling. The teaching we can respond to these questions in meaningful optional third session will consist of demonstrations and and inspiring ways. A wide variety of ideas for using the "hands-on" running of models on microcomputers. history of the calculus that have been successfully used to Minicourse #6: Coaching a team for the modeling motivate students will be presented. Some samples: The contest is being organized by B. A. FusARO, Salisbury geographical origins of the integral of the secant, an idea State University. Part A is scheduled from 2:15 p.m. of Fermat for integrating xn, a trick of Euler's for max to 4:15 p.m. on Wednesday, January 17, and part B min problems, and how an analysis of a wrong proof of OCTOBER 1989, VOLUME 36, NUMBER 8 1045 Meetings Cauchy leads to the definition of uniform convergence. Minicourse #11: Writing in mathematics courses is Bibliographies and historical notes will be provided. being organized by GEORGE D. GOPEN and DAVID A. SMITH, Duke University. Part A is scheduled from 8:30 Minicourse #9: How to use inexpensive graphing calcu a.m. to 10:30 a.m. on Friday, January 19, part B from lators to enhance the teaching and learning ofprecalculus 1:00 p.m. to 3:00p.m. on Friday, January 19, and part mathematics and calculus is being organized by BERT K. C from 3:30p.m. to 5:30p.m. on Saturday, January 20. WAITS and FRANKLIN DEMANA, Ohio State University. Enrollment is limited to 60. Part A is scheduled from 2: 15 p.m. to 4: 15 p.m. on The organizers will present an effective strategy Thursday, January 18, and part B from 8:30 a.m. to for incorporating writing assignments into mathemat 10:30 a.m. on Friday, January 19. Enrollment is limited ics courses, for helping students improve their writing, to 40. and for keeping the grading burden within reasonable Inexpensive ($75 or less) graphing calculators are bounds. This strategy is based on Reader Expectation dramatically changing the way we teach precalculus Theory, a new way of viewing the composition and revi mathematics. Participants will learn how to use "state sion process. We will present the elements of the theory of the art" graphing calculators. Built-in features such and explore (not just assume) the connections between as zoom-out and zoom-in will be explored. Graphing writing and thinking that it implies. Where possible, calculators are powerful tools that permit the user to examples will be based on tests written by students in make and test generalizations by looking at a large calculus courses. The theory and its practical applica number of examples in a short period of time, to easily tions are not limited to calculus, of course, not even to solve difficult equations and inequalities graphically, mathematics; it is the basis for an efficient and effective and to deal with problems and applications that are Writing Across the Curriculum program that has already not contrived. Mathematical topics will include solving been implemented at the University of Chicago, Harvard equations and inequalities, theory of equations, analytic Law School, and Duke University. geometry, polar and parametric equations, maximum and Minicourse #12: An introduction to the mathematical minimum problems, systems of equations, and motion elements of computer graphics is being organized by simulation. Demonstrations of the use of "state of the JOAN WYZKOSKI WEISS, Fairfield University. Part A is art" computer software for three dimensional graphics scheduled from 8:30 a.m. to 10:30 a.m. on Friday, will also be presented. January 19, and part B from 1:00 p.m. to 3:00p.m. on Minicourse # 10: A seminar on women in mathematics Saturday, January 20. Enrollment is limited to 30. is being organized by MIRIAM P. CooNEY esc, Saint Graphs and illustrations of geometrical objects are Mary's College, Notre Dame, Indiana. Part A is scheduled useful tools in the teaching of mathematics. Computer from 8:30a.m. to 10:30 a.m. on Friday, January 19, and graphics simplifies the production of these teaching aids. part B from 1:00 p.m. to 3:00p.m. on Saturday, January This Minicourse will present some of the mathematical 20. Enrollment is limited to 32. techniques used to produce realistic pictures on graph The goal of this Minicourse is to prepare participants ics display devices. Some of the topics to be discussed to conduct a seminar that identifies women mathemati are curve and surface sketching, 2D and 3D transfor cians (past and present), studies their lives and the mations, perspective drawing, and hidden line removal. mathematical times as a context for their work, and Suggestions will be given for the use of these techniques reveals mathematics as a human pursuit. Applying the to complement mathematics instruction. Since IBM per assumption that social-emotional aspects of learning are sonal computers will be available for demonstrations and important to students of mathematics, the Minicourse in-class experimentation, some programming experience will provide strategies for creating a seminar that pro is necessary. Participants will receive a copy of the notes, vides a support group to encourage potential mathematics references and program listings and a disk containing the majors, both women and men. demonstration programs. The content of the Minicourse, like the seminar, will Minicourse # 13: A survey of educational software is include history and stories of women mathematicians, being presented by VIRGINIA E. KNIGHT and VIVIAN YOH gender bias and its historic causes, research on gender KRAINES, Meredith College. Part A is scheduled from differences, alternative teaching/learning styles, and re 1:00 p.m. to 3:00p.m. on Friday, January 19, and part search on "women's ways of knowing." The format will B from 7:00 p.m. to 9:00 p.m. on Friday, January 19. follow seminar-style discussions, including consideration Enrollment is limited to 30. of the difficulties in learning the discussion process as a An increasing variety of software is available for the mode of teaching. Readings and a syllabus will be sent IBM PC and compatibles which enhance the instruction to participants prior to the meeting. of college mathematics courses. The organizers will demonstrate ways to use various programs in precalculus, 1046 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings calculus, linear algebra, differential equations and other such laboratories by three or four faculty who have courses. Then the participants can try these and other been involved in them in a variety of settings: a small programs themselves. Handouts and brochures will be college, a private university, a large state university, and provided which give more information on the software. a two-year college. The presentations will describe the No computer experience is required. curricular innovations that have been made possible by the availability of a mathematics computer laboratory, # 14: Creating order out of chaos in fresh Minicourse the software that has been found useful, and the means man mathematics: instituting a mathematics placement by which the laboratories obtained their initial funding program is being organized by LINDA H. BoYD, DeKalb and continuing support. Part of the Minicourse will out College and is sponsored by the Committee on Placement line sources of funding and methods for increasing the Examinations. Part A is scheduled from 1:00 p.m. to probability of success for proposals for such funding. 3:00 p.m. on Friday, January 19, and part B from 3:30 Participants who want a copy of the instructional soft p.m. to 5:30 p.m. on Saturday, January 20. Enrollment ware should bring their own disks (ten 5 1/4 inch, 360K is limited to 40. MS DOS disks). Members of the MAA Committee on Placement Examinations will use lectures, worksheets, and question Minicourse # 17: The informed consumer's instruc and answer sessions to present an overview of the tional guide to graphing calculators is being presented by task of establishing a mathematics placement program. JOHN W. KENELLY and IRIS B. FETTA, Clemson Univer Topics covered will include: reasonable expectations of sity. Part A is scheduled from 8:30a.m. to 10:30 a.m. on a placement program, tests available through the MAA Saturday, January 20, and part B from 1:00 p.m. to 3:00 Placement Test Program (PTP), selection or creation of p.m. on Saturday, January 20. Enrollment is limited to a placement test or series of tests, statistical analysis 50. of test items and tests, methods of establishing a cutoff Graphing calculators add a significant dimension to score, and administration of a placement program. mathematics instruction. For individual considerations and external recommendations, one should understand Minicourse #15: Mathematica and college teaching the instructional roles of the current and future products. is being presented by STAN WAGON, Smith College With overhead projector versions of the Casio, Hewlett and visiting the University of Washington. Part A is Packard and Sharp calculators and with individual loan scheduled from 8:30 a.m. to 10:30 a.m. on Saturday, units of at least the last two, the course will compare the January 20, and part B from 3:30 p.m. to 5:30 p.m. on instructional advantages of each. Calculus and statistics Saturday, January 20. Enrollment is limited to 80. material, as well as inservice teacher training syllabi, will Because of its wide-ranging abilities, heretofore not be distributed. Input will be collected and relayed to seen in a single software package, Mathematica is an industrial contacts. Participants are urged to bring their ideal tool for illustrating diverse topics at the undergrad own calculators to the course, especially Casios if they uate level. This Minicourse will be an introduction to have them, so that they can enter and save programs. Mathematica, with examples (animations, high-precision number-crunching, plotting of contours and surfaces, Participants interested in attending any of the MAA symbolic differentiation and integration, etc.) taken from Minicourses should complete the MAA Minicourse Pre various areas of college-level mathematics. Techniques registration Form and send it directly to the MAA office for using the package efficiently, both in short sequences at the address given on the form so as to arrive prior of instruction and in longer programs, will be discussed. to the November 17 deadline. DO NOT SEND THIS Knowledge of programming in BASIC or a similar lan FORM TO PROVIDENCE. Please note that these MAA guage is a prerequisite. Handouts will be available at the Minicourses are NOT the AMS Short Course. After the course. deadline, interested participants are encouraged to call the MAA headquarters at 800-331-1622. Minicourse # 16: Starting, funding and sustaining Please note that prepayment is required. Payment can mathematics laboratories is being organized by STAVROS be made by check payable to MAA (Canadian checks must N. BusENBERG, Harvey Mudd College, and is sponsored be marked "in U.S. funds") or VISA or MASTERCARD by the MAA Science Policy Committee. Part A is sched credit cards. uled from 8:30a.m. to 10:30 a.m. on Saturday, January The MAA Minicourses are open only to persons who 20, and part B from 3:30 p.m. to 5:30 p.m. on Saturday, register for the Joint Mathematics Meetings and pay the January 20. Enrollment is limited to 30. Joint Meetings registration fee. If the only reason for This Minicourse will familiarize participants with registering for the Joint Meetings is to gain admission successful examples of the use of computer laborato to a MAA Minicourse, this should have been indicated ries in the undergraduate mathematics curriculum. The by checking the appropriate box on the MAA Minicourse course will feature descriptions of ongoing examples of Preregistration Form. Then, if the Minicourse is fully OCTOBER 1989, VOLUME 36, NUMBER 8 1047 Meetings subscribed, full refund can be made of the Joint Meetings Other MAA Sessions preregistration fee. Otherwise, the Joint Meetings prereg istration will be processed, and then be subject to the 50 percent refund rule. Participants should take care when YEAR OF NATIONAL DIALOGUE cancelling Minicourse preregistration to make clear their SPECIAL EVENT intention as to their Joint Meetings preregistration, since Humanistic Mathematics: A panel discussion on Hu if no instruction is given, the Joint Meetings registration manistic Mathematics is scheduled from 9:30 a.m. to will also be cancelled. PREREGISTRATION FORMS 10:55 a.m. on Wednesday. The moderator is ALVIN FOR THE JOINT MEETINGS SHOULD BE MAILED M. WHITE, Harvey Mudd College. Other participants TO PROVIDENCE PRIOR TO THE DEADLINE OF include LYNNE V. CHENEY, Head of the National En NOVEMBER 17. dowment for the Humanities; UBIRATAN D'AMBROSIO, The registration fee for MAA Minicourses # 1, 2, 7, Universidade Estadual de Campinas in Brazil; and 12, 13, and 16 is $50 each. The registration fee for all PHILIP J. DAVIS, Brown University. other MAA Minicourses is $30 each. Contributed Papers: Contributed papers have been Calculus Revision: The CUPM Subcommittee on Cal accepted on six topics in collegiate mathematics. The culus Reform and the First Two Years (CRAFTY) is topics, the names and affiliations of the organizers, and organizing a "poster session" on Calculus Revision on days they will meet are: Wednesday, from 2:15 p.m. to 6:00 p.m. This session will provide an afternoon open house of informal discus • Prognostic and diagnostic testing: Helping high school sion with up to forty "exhibitors" representing various students get ready for college-level mathematics, spon new calculus projects now underway. Each exhibitor sored by the Committee on Placement Examinations will have a table to display handouts, but facilities for BERT K. WAITs, Ohio State University. Wednesday participant-provided hardware (outlets for computers) and/or Thursday. will be limited. A wide range of projects is being sought, NSF supported and not. There may not be enough room • Recent developments in placement-RAY E. for everyone who wants to be an exhibitor. Anyone CoLLINGS, Tri-County Technical College, South Car interested in being an exhibitor should write Thomas W. olina, JoHN W. KENELLY, Clemson University, and Tucker, Mathematics Department, Colgate University, ELIZABETH J. TELES, Montgomery College, Maryland, Hamilton, NY 13346 prior to November 10, 1989. Please Friday andjor Saturday. include a brief description of the project indicating • Discrete mathematics: Has the bubble burst?- MAR its scope, level of involvement (individual, department, THA J. SIEGEL, Towson State University, Maryland, consortium), and present status. Wednesday andjor Thursday. Assessment: The Committee on Two-Year Colleges is sponsoring a panel discussion on Assessment in the First • Classic classroom calculus problems- ANTHONY BAR Two Years of College Mathematics, which is scheduled California, Friday CELLOS, American River College, from 2:15 p.m. to 3:45 p.m. on Thursday. The organiz morning and/or Saturday morning. ers are RAy E. COLLINGS, Tri-County Technical College, • A core in mathematics- KAY B. SoMERS, Moravian South Carolina; JoHN W. KENELLY, Clemson University; College, Pennsylvania, Friday andjor Saturday. and ELIZABETH J. TELES, Montgomery College, Mary land. The moderator is RAY E. CoLLINGS. The panelists The deadline for submitting papers for these sessions and topics are: WILLIAM H. CALDWELL of the Univer was September 28. In addition, there will be the following sity of North Florida and Florida Board of Regents, special computer session on Saturday. on Mathematics and the college level academic skills test in Florida; DAVID LovELOCK of the University of • Computers in the classroom: The time is right, Arii.ona, on The are you ready project; TINA H. STRALEY DAVID P. KRAINES, Duke University, and VIVIAN Y. at Kennesaw State College in Georgia, on Computerized KRAINES, Meredith College. Presentations are invited testing in college algebra: advantages and pitfalls; and on the use of microcomputers to enhance undergrad JoHN TRIPP of Central Piedmont Community College, uate mathematics classroom instruction. Proposals sponsored by the College Board, on Computer adaptive should be sent to Vivian Y. Kraines, Department testing. of Mathematics and Computer Science, Meredith Computer Algebra Systems as Teaching Tools: The College, Raleigh, NC 27607-5298 by October 20. CUPM Subcommittee on Symbolic Manipulation is sponsoring this panel discussion from 2: 15 p.m. to 1048 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings 4:15 p.m. on Thursday. The moderator is DoNALD B. matics by ANDREW 0DLYZKO, AT&T Bell Laboratories. SMALL, Colby College. The panelists and their topics The presentation is scheduled from 1: 15 p.m. to 2:05 are: MICHAEL G. HENLE, Oberlin College on Classroom p.m. on Friday. experiences; ZAVEN A. KARIAN, Denison University, on Unity in Diversity- Challenge for Change: The Com Hardware issues; ARNOLD M. OsTEBEE, St. Olaf College mittee on Participation of Women is sponsoring a panel on Pedagogical issues; and the moderator on CAS labs in discussion on this topic from 7:45 p.m. to 8:45 p.m. on calculus. Friday. The moderator will be FRANCES A. RosAMOND, CAS Workshop Reunion: A CAS Workshop Reunion is National University. being organized by DoNALD B. SMALL, Colby College, Providing Computer Resources for Mathematics: The and is scheduled from 7:30p.m. to 9:30p.m. on Friday. Committee on Computers in Mathematics Education (CCIME) is sponsoring this panel discussion. The orga Is Graduate Education Meeting the Needs of Mathe nizers are JoHN S. DEVITT, University of Saskatchewan, maticians? This panel discussion is scheduled from 8:30 and WADE ELLIS, JR., West Valley College. The session a.m. to 9:50a.m. on Friday. The focus will be on whether is scheduled for 8:00a.m. to 9:50a.m. on Saturday. The graduate education is meeting the needs of college teach moderator will be DAVID A. SMITH, Duke University. ing and industry. The moderator is ALFRED B. WILLCOX, interim Director of the Office of Governmental Af The Development of Calculator-based Placement Test fairs. The panelists are RHONDA J. HuGHES, Bryn Mawr ing: The Committee on Placement Examinations is spon College; STEPHEN B. Rom, Austin Community College; soring this panel discussion. This panel is scheduled IVAR STAKGOLD, University of Delaware; and WILLIAM from 1:30 p.m. to 3:00 p.m. on Saturday. The organizer P. THURSTON, Princeton University. is JoHN G. HARVEY, University of Wisconsin, Madison. The panel members are MARY M. LINDQUIST, Columbus Calculus Texts in a Time of Reform: The Textbook College in Georgia, BERNARD L. MADISON, University of Authors Association is sponsoring an open forum on Arkansas, ROBERT NoRTHCUTT, Southwest Texas State Calculus texts in a time of reform: The roles of au University, and THOMAS W. TucKER, Colgate University. thors, publishers and emerging technologies from 9:00 Since 1986 the MAA Calculator-Based Placement Test a.m. to 10:55 a.m. on Friday. LoUis C. LEITHOLD is the Project has been developing new placement tests that will moderator. Panel members are DAVID P. GEGGIS, Man require students to use scientific calculators when taking aging Editor for Mathematics at PWSeKent Publishing them. John Harvey directs this project; the panelists are Co.; MIKE KEEDY, President of the Textbook Authors the chairs of the first four test panels. The panelists Association; BRUCE PETERSON, Middlebury College and will discuss the development of calculator-based tests chairman of A. P. Calculus Test Development Commit and calculator-active items, in general, and will describe tee of the College Board; and the following textbook the development of the calculator-based Arithmetic and authors: HOWARD ANTON at Drexel University, JAMES F. Skills Test, the Basic Algebra Test, the Algebra Test, and HURLEY at the University of Connecticut, MARGARET L. the Calculus Readiness Test. LIAL at American River College, EARL W. SWOKOWSKI at Models of Two- Year Four- Year Dialogues: This panel Marquette University, GEORGE B. THOMAS, JR. at Mas discussion is scheduled from 1:30 p.m. to 3:00 p.m. on sachusetts Institute of Technology, and the moderator. Saturday. It is sponsored by the Committee on Two The panel's presentation, of approximately one hour, Year Colleges and organized by CAROLE ANN BAUER, will be followed by questions and comments from the Triton College, Illinois. The panel members are DAVID audience. E. BoLIVER, JR., Trenton State College; WILLIAM H. MAA Section 5-day Workshops: MARVIN L. MANZER, Western Wyoming College; ALBERT D. OTTO, BRUBAKER, Messiah College in Pennsylvania, and B. Illinois State University, Normal; and ERNEST R. Ross, A. FusARO, Salisbury State University, Maryland, are JR., St. Petersburg Junior College. organizing a panel discussion on these workshops, which Calculus for the Twenty-First Century: SHELDON P. is scheduled from 9:00a.m. to 10:55 a.m. on Friday. The GoRDON, Suffolk County Community College, is orga panel will address the planning of 5-day workshops: how nizing this panel discussion. It is scheduled from 1:30 to obtain support, choose speakers, and recruit partici p.m. to 3:00 p.m. on Saturday. The panelists will be pants. Among the panelists will be an NSF representative the moderator, ANDREW M. GLEASON, Harvard Univer and several directors of successful workshops. sity; DAVID A. SMITH, Duke University; and GILBERT STRANG, Massachusetts of Technology. The speakers will Mathematics: The CUPM Subcommittee on Symbolic look beyond the current projects for calculus reform to Symbolic Computation is sponsoring a special presenta focus on the state of calculus in the next century. They tion on Applications of Symbolic Mathematics to Mathe- OCTOBER 1989, VOLUME 36, NUMBER 8 1049 Meetings will share their visions and predictions for the direc tions by recent doctoral recipients, moderated by DoN tions of calculus, its applications, its instruction and the HILL, Florida A&M University, and GERALD CHACHERE, impact of technology on the subject. Howard University. Two- Year College Reception: The Committee on Two The NAM Business Meeting will take place at 10:00 Year Colleges is sponsoring an informal reception for a.m. on Saturday, January 20. RoGER NEWMAN, Southern two-year college faculty from 4:30 p.m. to 6:00 p.m. on University, will preside. Wednesday, January 17. Prize Session and Business Meeting: The MAA Prize YEAR OF NATIONAL DIALOGUE Session and Business Meeting is scheduled from 4:25 SPECIAL EVENTS p.m. to 5:30 p.m. on Friday, January 19. The Chauvenet The Joint Policy Board for Mathematics (JPBM) is Prize, the Yueh-Gin Gung & Dr. Charles Y. Hu Award sponsoring a reception with cash bar on Thursday, Jan for Distinguished Service to Mathematics and several uary 18, from 6:00 p.m. to 6:45 p.m. The reception Certificates of Meritorious Service will be presented. will be followed by a session from 6:45 p.m. to 8: 15 This meeting is open to all members of the Association. p.m. on Breaking the code (The Life of Alan Turing), to include readings by the playwright HuGH WHITE Board of Governors: The MAA Board of Governors will meet at 8:30 a.m. on Tuesday, January 16. This MORE, reminiscences by PETER J. HILTON, SUNY at meeting is open to all members of the Association. Binghamton. At the conclusion of this session the second annual JPBM Communications Award will be Section Officers: There will be a Section Officers' presented. meeting at 4:30p.m. on Tuesday, January 16. The JPBM Committee for Mathematics Department Heads has organized a National Meeting of Depart Activities of Other Organizations ment Heads on at 7:00 p.m. on Friday, January 19. From 7:00 p.m. to 8:00 p.m. there is a session on The The Association for Women in Mathematics (A WM) David Report Revisited: A Dialogue with Edward E. will sponsor the eleventh annual Emmy Noether Lecture David, Jr. at 9:00 a.m. on Thursday, January 18. This will be followed at 8:00 p.m. by three parallel The A WM will also sponsor a panel discussion on discussion sessions as follows: Wednesday, January 17, at 3:20p.m. 1. The David Report Revisited (continued) The A WM Business Meeting will be held at 4:20 p.m. 2. Evaluation of teaching on Wednesday, January 17. 3. MAA Committee on Accreditation An open reception is planned for 9:30 p.m. on Wednesday, January 17. The 1990 International Congress of Mathematicians to be held August 21 - 29 in Kyoto, Japan will be YEAR OF NATIONAL DIALOGUE represented in Louisville by the Japan Travel Bureau. SPECIAL EVENT Participants should be sure to visit this booth in the ex The Mathematicians and Education Reform (MER) hibit area to pick up a copy of the Second Announcement and the Mathematical Sciences Education Board and other pertinent information. (MSEB) are cosponsoring a Workshop on The mathe In Louisville, The National Association of Mathe matician as gatekeeper of educational reform at 12: 15 maticians (NAM) will celebrate its 20th anniversary. In p.m. on Friday. honor of the occasion, a banquet is planned for Fri day evening. Further information can be found in the The National Science Foundation (NSF) invites partic following section. ipants at the Joint Mathematics Meetings to meet infor NAM will receive the William W. S. Claytor Lecture at mally with staff members over the lunch hour (noon to 1:00 p.m. on Friday, January 19, by SCOTT W. WILLIAMS, 1:00 p.m.) daily, Wednesday- Saturday, January 17-20. SUNY at Buffalo, on The box product problem. Short presentations on proposal writing and processing NAM is also sponsoring a panel discussion on How to and Foundation priorities will be followed by the op make mathematics work for minorities on Saturday, Jan portunity for individual questions. Please bring a lunch uary 20, at 9:00a.m. BEVERLY ANDERSON, University of (or not) and join us. Wednesday and Friday sessions the District of Columbia and the Mathematical Sciences will focus on research projects; Thursday and Saturday Education Board, will serve as moderator. sessions will focus on education projects. Friday will NAM will also sponsor a contributed paper session also provide an opportunity to discuss priorities and at 2:15 p.m. on Thursday, January 18, titled Presenta- 1050 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings processes at other Federal agencies funding mathematics registration, a 50% refund of the amount paid for the research. ticket will be made if written notification is received The NSF will also be represented at a booth in the in Providence prior to January 3. After that date, no exhibit area. NSF staff members will be available to refund can be made. Although it is expected that some provide counsel and information on NSF programs of tickets will be available for purchase at the meeting, interest to mathematicians. The booth will be open the interested participants are urged to purchase their tick same days and hours as the exhibits. ets through preregistration. No refund can be made for tickets purchased at the meeting. YEAR OF NATIONAL DIALOGUE NAM Banquet: In recognition of NAM's 20th an SPECIAL EVENT niversary, a banquet will be held on Friday, January 19, The National Research Council project, Mathematical from 6:00 p.m. to 8:00 p.m. The Talbot-Cox Address Sciences in the Year 2000 (MS 2000), is sponsoring and other special presentations will be featured. The a panel discussion titled A preview of the MS 2000 address will be given by JoHNNY L. HousTON, Executive study, on Saturday, January 20, from 1:30 p.m. to Secretary of NAM, on Some milestones of the past; Some 2:30 p.m. The program will begin with a presentation challenges of the future. The menu consists of bluegrass by the Chair of the MS 2000 Committee, WILLIAM salad, boneless chicken breast with sauce chasseur, rice E. KIRWAN, President, University of Maryland, and pilaf, vegetable, rolls with butter, coffee/tea/decaf, and will be followed by a question and answer period caramel pecan cheesecake. between the audience and members of the MS 2000 Tickets are $20 each; the price includes the gratuity. Committee. This forum will be an opportunity to Interested participants should complete the appropri discuss the preliminary findings and recommendations ate section of the Preregistration/Housing Form. In the of the MS 2000 Project, and to receive the input of event of cancellations of tickets purchased through pre the mathematical community in shaping the project's registration, a 50% refund of the amount paid for the final report, which is due for publication in the fall of ticket will be made if written notification is received 1990. in Providence prior to January 3. After that date, no refund can be made. Although it is expected that some tickets will be available for purchase at the meeting, The Rocky Mountain Mathematics Consortium interested participants are urged to purchase their tick (RMMC) Board of Directors will meet on Friday, January ets through preregistration. No refund can be made for 19, from 2:15p.m. to 4:10p.m. tickets purchased at the meeting. No-Host Cocktail Party: There will be a no-host Other Events of Interest cocktail party on Friday evening, January 19, from 8:00 Social Events p.m. to 10:00 p.m. Participants are encouraged to use this occasion to spend some time with old and new AMS 25-Year-Member Banquet: All meeting partic friends. ipants are invited to attend the AMS's second annual banquet to honor individuals who have been members of the Society for twenty-five years or more. This banquet provides an excellent opportunity to socialize with fellow Book Sales and Exhibits participants in a relaxed atmosphere. The banquet will be AMS Information Booth: All meeting participants are held on Saturday, January 20, with a cash bar reception invited to visit the AMS Information Booth in the exhibit at 7:00 p.m. and dinner at 7:30 p.m. The location and area during the meeting. Complimentary coffee and tea further details will be announced at a later date. will be served. An attractive pin with the AMS logo The menu includes Kentucky bibb salad with sliced will be available for participants, compliments of the tomatoes in vinaigrette, baked stuffed chicken breast AMS. Carol-Ann Blackwood, Membership Manager of (vegetable stuffing served with red pepper sauce on the Society, will be at the booth to answer questions the side), potato and vegetable, rolls and butter, cof about membership in the Society. fee/tea/decaf, and white chocolate mousse served in Book Sales: Books published by the AMS and MAA a chocolate cup with raspberry sauce. Special meals will be sold at discounted prices somewhat below the cost available upon request, including vegetarian. for the same books purchased by mail. These discounts Tickets are $20 each; the price includes the gratuity. will be available only to registered participants wearing Interested participants should complete the appropri the official meeting badge. VISA and MASTERCARD credit ate section of the Preregistration/Housing Form. In the cards will be accepted for book sale purchases at the event of cancellations of tickets purchased through pre- OCTOBER 1989, VOLUME 36, NUMBER 8 1051 Meetings meeting. The book sales will be open the same days and ORDINARY Preregistration: Those who preregister hours as the exhibits. by the ORDINARY deadline of November 17 will also and program in the mail two to Exhibits: The book, educational media and software receive their badge prior to the meeting, unless they check the exhibits are open Wednesday through Saturday, January three weeks appropriate box on the Preregistration/Housing Form. 17-20. The hours they are open are 1:00 p.m. to 5:00 So, it is extremely important that the mailing address p.m. on Wednesday, 9:00 a.m. to 5:00 p.m. Thursday given on the Preregistration/Housing Form be one at and Friday, and 9:00 a.m. to noon on Saturday. All can receive this mailing. There will participants are encouraged to visit the exhibits during which the participant desk at the meeting to assist individuals who the meeting. Participants visiting the exhibits will be be a special either do not receive this mailing or who have a problem asked to display their meeting badge or acknowledgment of with their badge. Unfortunately, it will not be possible to preregistration from the Mathematics Meetings Housing make changes to badges before the meeting. Also, it will Bureau in order to enter the exhibit area. not be possible to include any tickets to special events Mathematical Sciences Employment Register: Those purchased through preregistration in the mailing with wishing to participate in the Employment Register at the the badge and program. There will be a special ticket Louisville meetings should read carefully the important section at the Joint Mathematics Meetings Registration article about the Register which follows this meeting Desk where prepurchased tickets to the AMS and/ or announcement. NAM Banquets may be picked up. Please note that requests for housing assignments How to Preregister and Get a Room through the Mathematics Meetings Housing Bureau and How to Preregister preregistrations for the Employment Register must be received by the ORDINARY deadline of November 17. The importance of preregistration cannot be overem phasized. Those who preregister pay fees considerably FINAL Preregistration: Those who preregister by the lower than the fees that will be charged for registration FINAL deadline of December 18, will pick up their badge at the meeting, and receive typeset badges instead of and program at the meeting. Unfortunately, it is not typewritten. possible to provide FINAL preregistrants with housing All preregistrations will be acknowledged. or tickets to special events, although the latter may still In order to make preregistration for the Louisville be available for purchase at the meeting. Please note that meetings more convenient, a new FINAL preregistration the December 18 deadline is firm and any forms received deadline has been established. There are now three after that date will be returned and full refunds issued. separate preregistration deadlines, each with its own It is essential that the Preregistration/Housing Form advantages and benefits: (found at the back of this issue) be completed fully and clearly. In the case of several preregistrations from the EARLY Preregistration October 31 same family, each family member who is preregistering ORDINARY Preregistration November 17 should complete a separate copy of the Preregistra FINAL Preregistration December 18 tion/Housing Form, but all preregistrations from one EARLY Preregistration: Those who preregister by the family may be covered by one payment. Please print or EARLY deadline of October 31 will be eligible for a type the information requested, and be sure to complete drawing to select the winners of complimentary hotel all sections. Absence of information (missing credit card rooms in Louisville. Multiple occupancy of these rooms numbers, incomplete addresses, etc.) causes a delay in is permissible. The location of rooms to be used in this the processing of preregistration for that person. lottery will be based on the number of complimentary Please provide your nickname if you wish this infor rooms available in the various hotels. Therefore, the free mation to be printed on your badge. Also, it is planned room may not necessarily be in the winner's first choice to make available at the meeting a list of preregistrants hotel. Winners will be randomly selected from the names by area of interest. If you wish to be included in this list, of all participants who preregister by October 31. The please provide the Mathematical Reviews classification winners will be notified by mail prior to December 31. number of your major area of interest on the Preregis So preregister early! (A list of the winners in Phoenix tration/Housing Form. A list of these numbers appears appears in the section titled How to Get a Room). EARLY on the back of the AMS abstract form. The master copy preregistrants will receive their badge and program by of this list will be available for review by participants at mail two to three weeks before the meeting (see the the Message Center section of the registration desk. next paragraph for more details), unless they check the appropriate box on the Preregistration/Housing Form. Electronic Preregistration: Preregistration through elec tronic mail is also available. Anyone wishing to prereg- 1052 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings ister through this method should send a message to MAA Minicourses [email protected] requesting this service. A (if openings available) message will be sent back within 24 hours with instruc Minicourses# 1, 2, 7, 12, 13, 16 $ 50 tions on how to complete the format required. Credit Minicourses # 3, 4, 5, 6, 8, 9, cards will be the ONLY method of payment accepted for 10,11,14,15,17 $30 electronic preregistration. Formats received through this will be imposed for all invoices prepared method will be treated in the same manner as forms A $5 charge are submitted without ac received through postal mail. when preregistration forms companying check(s) for the preregistration fee or are Receipt of the Preregistration/Housing Form and pay accompanied by an amount insufficient to cover the ment will be acknowledged by the Mathematics Meetings total payments due. Unfortunately, it is not possible for Housing Bureau. Participants are advised to bring a copy the Mathematics Meetings Housing Bureau to refund of this acknowledgement with them to Louisville. The amounts less than $2. Preregistration forms received same deadlines apply as for normal preregistration. well before the deadline of November 17 which are not accompanied by correct payment will be returned to the Registration fees: Modes of payment which are ac participant with a request for resubmission with full ceptable, provided they are payable in U.S. dollars to the payment. This will, of course, delay the processing of order of the American Mathematical Society, are U.S. any housing request. Postal Money Orders, certified U.S. bank checks, U.S. An income tax deduction is allowed for education bank money orders, personal checks drawn on a U.S. expenses, including registration fees, cost of travel, meals or Canadian banks, or credit card (Visa or MasterCard and lodging incurred to (i) maintain or improve skills only). in one's employment or trade or business or (ii) meet The Joint Meetings registration fees at the meeting express requirements of an employer or a law imposed will be 30% higher than the preregistration fees listed as a condition to retention of employment, job status, below. or rate of compensation. This is true even for education Participants wishing to attend sessions for one day that leads to a degree. However, the Tax Reform Act of only may take advantage of a one-day fee which is 1986 has introduced significant changes to this area. In equal to 55% of the on-site registration fees for members general, the deduction for meals is limited to 80% of the or nonmembers. The one-day fee is not applicable to cost. Unreimbursed employee educational expenses are student, unemployed, or emeritus participants, nor is it subject to a 2% of adjusted gross income floor. There are available through preregistration. exceptions to these rules; therefore, one should contact one's tax advisor to determine the applicability of these At the time of this writing, the location of the Joint provisions. Mathematics Meetings Registration is Hall C of the There is no extra charge for members of the families Commonwealth Convention Center. Registration will be of registered participants, except that all professional open on Tuesday, January 16, from 3:00 p.m. to 7:00 mathematicians who wish to attend sessions must register p.m. Registration for the AMS Short Course is outside independently. of the Regency Ballroom South in the Hyatt Regency, Nonmembers who preregister or register at the meet and is open on Tuesday from 8:00 a.m. to 2:30 p.m. ing and pay the nonmember fee will receive mailings from AMS and MAA, after the meeting is over, contain Joint Mathematics Meetings ing information about a special membership offer. Member of AMS, Canadian Mathematical Society, MAA $ 68 How to Get a Room Emeritus Member of AMS, MAA $ 21 Nonmember $105 Participants must preregister by the ORDINARY dead Student/Unemployed $ 21 line of November 17 in order to obtain hotel accom modations through the Mathematics Meetings Housing Employment Register Bureau. Be sure to complete the Housing section of the Employer $ 7 5 Preregistration/Housing Form completely, after reading Additional interviewer (each) $ 35 the information in this section thoroughly. Participants Applicant $ 15 are asked to rank all hotels on the form after reviewing Employer posting fee $ 10 the following page. AMS Short Course Student/Unemployed $ 15 All Other Participants $ 40 OCTOBER 1989, VOLUME 36, NUMBER 8 1053 s· ~ 3:: ~ - ~ final should insure 195 275 245 325 400 200 225 300 200 accepted all changes Seelbach, $ deadline. to Suites Providence American get also in reservations Galt, changes 1989 to are VIP VIP Exec Exec the however, hotel 26 17, date, accepted. number Suite for 2-Bed 1-Bed 1-Bed 2-Bed Type* of preference Parlor checks be 1-Bed 2-Bed 1-Bed 2-Bed that of 1989; time will 15, After telephone December November order Personal wfcot cards Checkin to in 85 The $95 the N/A N/A N/A Quad cancellations hotels. 16 beds to cards. credit a.m. or 2 December the 1989. L__ to to prior 11:00 other credit 15, -- 85 numbered after 68 beds 70 64 58 $ No Quad sent 2 December be '--- major changes Brown Bureau - all only). all the from changes form changes December wfcot -- 85 for 80 $ N/A Housing N/A handicapped. N/A and make accept - beds housing and accept 2 the Bureau before lists (for hotels for noon Please Meetings is 75 the beds cannot 64 53 65 $ preregistration Triple Triple housing 2 Housing Express 1989. Providence equipped the in final the Seelbach 26, Bureau of beds also all payments, Mathematics 2 63 63 58 and 53 60 $65 American are get Double or allow Bureau the back - 1 or room to and Accommodations Housing Hyatt, 26 the December For them. 60 Please Housing through on 59 58 55 49 on The $ Galt, Single Hotel after the MasterCard, 1989. availability, December listed 1989. for until free free free free Meetings to numbers - 26, Obtain 15, reservations 15 VISA, space time hotels to check on preregistration. the younger younger younger younger with directly day all & & & & for How day day have make suites.* above. based per Mathematics free December December Checkout December that yrs. yrs. yrs. hotel yrs. not per per all also the 18 16 18 16 pool Privileges) Privileges) $4 guarantee must $4 $4.50 listed tax. from the are Pool rooms, after and parking parking with children should card through hotels suites only (In/Out Description Restaurants Indoor Bureau Parking (In/Out Children Restaurants Outdoor Children Restaurants Free Rooms Restaurants Parking Any Children Restaurants Free Parking Children calling imperative of hotels credit is by Checks a the nonsmoking It following reservations sales/occupancy to East) Housing OR made Providence have p.m. the guarantees the backup. hotel descriptions In be for hotels. check House of 2:00 that River percent card 40202 40202 40202 by 40202 directly allow at the venue 9.2 Galt In A detailed a housing KY hotels $50 KY Bureau KY KY to Brown Jefferson Broadway to credit to for Please Street a CANNOT for reservations -the sent West cancellations West called Fourth service and for 290). or hotel. subject used Housing be Location 320 502-587-3434 Bureau Fourth Louisville, (adjacent Louisville, 502-589-5200 500 335 Louisville, 502-585-3200 502-583-1234 Louisville, hotels full to and the are be confirmed are can changes these p.m. with assignments. may Housing below East (extension Tower changes REQUIREMENTS: at and -- hotels identification 3:00 desiring all the is Regency hotel Mathematics listed cards lists House House directly Suite" Brown call make the cancellations personal rates following Hyatt "All Hyatt Galt The Galt Seelbach made 401-272-9500 Please Reservations The and Participants housing and accurate with Please be is GUARANTEE Express with The * .... .,. 0 Ul z m -i m -i 0 ::t: (5 (f) 0 ., m )> s: s: z ~ :0 (f) m s: ~ ::t: (5 )> )> () r 0 () iii ::;! Meetings Downtown Louisville RIVER ROAD cao ~ 1iJ' L- ~ L.. MAIN I-l STREE~ l__ ~ ,-- JARKJ 111111111111111 TROLLEY LOOP ln-- .. ~-= 1 COMMONWEALTH Jl_JJEFFERSON STREETo~ CONVENTION CENTER -uBERTY ~CRlr: 2 HYATT REGENCY HOTEL SEELBACH HOTEL 3 1 4 4 BROWN HOTEL 5 GALT HOUSE 6 GALT HOUSE EAST MUHAMMAD): 'ALI BLVD 7 LOUISVILLE GALLERIA Q)D o ll + N ~-l[ - CHESTNUT STREET~- - 0 BROADWAY OCTOBER 1989, VOLUME 36, NUMBER 8 1055 Meetings Participants should be aware that it is general hotel deadline. Since these rooms can be occupied by as many practice in most cities to hold a nonguaranteed reser as four persons, this represented a considerable savings. vation until 6:00 p.m. only. When one guarantees a All participants wishing to preregister for the Louis reservation by paying a deposit or submitting a credit ville meetings are urged to consider the EARLY deadline card number as guarantee in advance, however, the hotel of October 31 in order to qualify for the Louisville Room usually will honor this reservation up until checkout Lottery. (See the section titled How To Preregister.) time the following day. If the individual holding the Inn San Carlos reservation has not checked in by that time, the room is Days then released for sale, and the hotel retains the deposit Donald Josephson George Lang or applies one night's room charge to the credit card Sheraton number submitted. Dan Britten Mary T. Treanor If you hold a guaranteed reservation at a hotel, but Gael T. Mericle Carolyn Tucker are informed upon arrival that there is no room for you, Lee Stout there are certain things you can request the hotel do. First, they should provide for a room at another hotel in Holiday Inn Financial Center town for that evening, at no charge. (You have already Paul D. Ivers.on Richard G. Montgomery paid for the first night when you made your deposit.) Sheldon H. Katz Robert Treger They should pay for taxi fares to the other hotel that Bernard Mair evening, and back to the meetings the following morning. They should also pay for one telephone toll call so that Holiday Inn Airport East you can let people know you are not at the hotel you H. Thomas Banks John C. Longnecker expected. They should make every effort to find a room Lynn E. Garner Paul Milnes for you in their hotel the following day, and if successful, Aziz T. Ibrahim pay your taxi fares to and from the second hotel so that Executive Park you can pick up your baggage and bring it to the first Paul M. Cook, II hotel. Not all hotels in all cities follow this practice, so your request for these services may bring mixed results, or none at all. The AMS-MAA Joint Meetings Committee always Miscellaneous Information endeavors to obtain the lowest possible sleeping room Audio-Visual Equipment: Standard equipment in all rates for participants at annual meetings. The committee session rooms is one overhead projector and screen. (In is also responsible for maintaining a sound fiscal position vited 50-minute speakers are automatically provided with for these meetings, and, until recently, has been able two overhead projectors.) Blackboards are not available. to keep the deficits at a reasonable level, while still AMS speakers requiring additional equipment should providing the very best meeting facilities available to the contact the Audio Visual Coordinator for the meeting, participants. at the AMS office in Providence at 401-272-9500, ext. As the meetings have grown in scope and complexity 239, or electronic mail [email protected] by over the years, however, it has been necessary to find November 1. larger facilities with more and more session rooms. MAA speakers requiring additional equipment may Unfortunately, the cost of these facilities is higher than make written request for one additional overhead projec can be covered by the registration fees, and the committee tor/screen, 35mm carousel slide projector, 16mm sound has arranged for all of the hotels in Louisville to collect film projector, or VHS video cassette recorder with one an extra $3 per room per night from participants, which color monitor. Such requests should be addressed to the will be used to offset the rental cost of the Commonwealth Audio Visual Coordinator for the meeting who will for Convention Center. (The rates above include this extra ward them to the MAA Secretary for possible approval. charge.) The committee hopes that these extra funds will These requests should also be received by November 1. not be necessary at future annual meetings, and therefore chose this method over an increase in the registration Child Care: The following are day care centers (all in fees. area code 502): Camp Hyatt (for Hyatt guests only). 587-3434. Donna The following participants received a complimen Rees or Kent Berman. For ages 3 to 15 (limited to 15 tary hotel room during the Phoenix meetings. They children). Staffed by Hyatt personnel. $4 per child per qualified for these rooms by submitting their Prereg hour. Hours are flexible but 24 hour advance notice istration/Housing Form by the EARLY preregistration required. 1056 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY I 0 2 Greater Louisville Area .g 8 a0 al m ::0 ~ J 3: < !II 0 r c ~- s:: m ~= !"c.> z c s:: al m ::0 CX> £ N :i,. ~ s ~IIroquois Park T .... 0 Ul ...... Meetings "We Sit Better" agency (on-site children sitting). 583- 4. Announcements of events competing in time or 9618 or 58 5-4 712. Starks Building. $5 per hour plus place with the scheduled scientific program will not be $3 transportation. Information on number and ages of accepted. children, time of day, and location required when calling. 5. Copies of an accepted announcement for either ta Calico Child Development Center (same day drop-in ble are to be provided by the proponent. Announcements service), 1211 East Broadway ( 1 mile east of Convention are not to be distributed in any other way at the meeting Center). 581-1020. Mrs. Shafer. State licensed, infants (for example, not by posting or personal distribution of to 9 years old (maximum of 35 children). 6:00 a.m. to handbills). midnight. $2 per hour ($3.50 for two children) 6. It may be necessary to limit the number of events or In addition, a Parent-Child Lounge will be located the quantity of announcements distributed at a meeting. near the Joint Meetings registration area. It will be 7. At the close of registration, both tables will be furnished with casual furniture, crib, a changing area, swept clean. A proponent who wishes the return of extra some assorted toys and a televison set. Any child using copies should remove them. MUST be accompanied by a parent (not this lounge Mail: All mail and telegrams for persons attending the simply an adult) who must be responsible for supervision meetings should be addressed as follows: Name of Partic of the child. This lounge will be unattended and parents ipant, Joint Mathematics Meetings, cfo Commonwealth assume all responsibility for their children. This lounge Convention Center, 221 Fourth Avenue, Louisville, KY be open during the hours of registration and all will only 40202. Mail and telegrams so addressed may be picked must leave the lounge at the close of registration persons up at the mailbox in the registration area during the each day. hours the registration desk is open. U.S. mail not picked Information Distribution: A table is set up in the up will be forwarded after the meeting to the mailing registration area of Joint Mathematics Meetings for dis address given on the participant's registration record. of information of a nonmathematical nature semination Telephone Messages: A telephone message center is of possible interest to the members. located in the registration area to receive incoming calls table is set up in the exhibit area for the A second for participants. The center is open from January 17 of information of a mathematical nature dissemination through 20, during the hours that the Joint Mathematics not promoting a product or program for sale. Meetings registration desk is open. Messages will be taken If a person or group wishes to display information of and the name of any individual for whom a message has a mathematical nature promoting a product or program been received will be posted until the message has been they may do so in the exhibit area at the Joint for sale, picked up at the message center. Once the registration Journals and Promotional Materials exhibit for a Books, desk has closed for the day there is no mechanism for $30 per item. fee of contacting participants other than calling them directly person or group would like to display material in If a at their hotel. The telephone number of the message area separate from the Joint Books table, the the exhibit center is 502-583-6931. proponent must reimburse the AMS and MAA for any extra furnishings requested (tables, chairs, easels, etc.) in Travel Agent: For some years now, the AMS-MAA addition to payment of the $30 per item fee. Joint Meetings Committee has engaged a travel agent for The administration of these tables is in the hands the January and August Joint Meetings in an effort to of the AMS-MAA Joint Meetings Committee, as are ensure that everyone attending these meetings is able to all arrangements for Joint Mathematics Meetings. The obtain the best possible airfare. This service is presently following rules and procedures apply. being performed by Meetings, Incentives, Conventions can be 1. Announcements submitted by participants should of America, Inc. (MICA); their advertisement announcement. Although ordinarily be limited to a single sheet no more than found elsewhere in this meeting any travel agent can obtain Supersaver or other such X 1411• 8!" can obtain 2. A copy of any announcement proposed for either published promotional fares, only MICA discount over and above table is to be sent to the Director of Meetings, American the special additional 5 percent off regular roundtrip coach Mathematical Society, Post Office Box 6248, Providence, these fares, and the 45 percent beneficial only Rhode Island 02940 to arrive at least one week before fare. The latter, of course, is financially of the promotional the first day of the scientific sessions. when one does not qualify for one attention to the 3. The judgment on the suitability of an announce fares. Participants should pay particular stated in the ad. ment for display rests with the Joint Meetings Commit restrictions and cancellation policies tee. It will make its judgments on a case-by-case basis to Weather: A thirty-year average temperature during establish precedents. January is 33°F with a normal maximum of 41°F and 1058 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings normal minimum of 24°F. There is an average of 3.4 inches of precipitation and if it snows in Louisville, it Committee on the Agenda for Business Meetings may do so in January. Dial 502-581-WAVE in Louisville The Society has a Committee on the Agenda for Business Meetings. for current weather information. The purpose is to make Business Meetings orderly and effective. The committee does not have legal or administrative power. It is intended that the committee consider what may be called "quasi Local Arrangements Committee political" motions. The committee has several possible courses of action on a proposed motion, including but not restricted to The members of the Local Arrangements Committee are (a) doing nothing; Martin J. Brown, Joseph A. Cima (ex-officio), William E. (b) conferring with supporters and opponents to arrive at a mu tually accepted amended version to be circulated in advance of the Fenton, William H. Jaco (ex-officio), Leon Harkleroad, meeting; John A. Oppelt (Chairman), Kenneth A. Ross (ex-officio), (c) recommending and planning a format for debate to suggest Carl Russell, Elaine M. Salvo, Sandy A. Spears, W. Wiley to a Business Meeting; (d) recommending referral to a committee; Williams, and Jeffrey Allen Wright. (e) recommending debate followed by referral to a committee. There is no mechanism that requires automatic submission of a motion to the committee. However, if a motion has not been sub Petition Table mitted through the committee, it may be thought reasonable by a At the request of the AMS Committee on Human Rights of Mathe Business Meeting to refer it rather than to act on it without benefit maticians, a table will be made available in the meeting registration of the advice of the committee. area at which petitions on behalf of named individual mathemati The secretary notes the following resolution of the Council: Each the Society shall be willing cians suffering from human rights violations may be displayed and person who attends a Business Meeting of and able to identify himself as a member of the Society. In further acting in their individual capacities. signed by meeting participants explanation, it is noted that each person who is to vote at a meeting Signs of moderate size may be displayed at the table, but must is thereby identifying himself as and claiming to be a member of the not represent that the case of the individual in question is backed American Mathematical Society. by the Committee on Human Rights unless it has, in fact, so voted. The committee consists of M. Salah Baouendi, Robert M. Fos Volunteers may be present at the table to provide information on sum (chairman), and Carol L. Walker. individual cases, but notice must be sent at least seven (7) days in In order that a motion for the Business Meeting of January 18, advance of the meeting to the Director of Meetings in Providence 1990, receive the service offered by the committee in the most effec (telephone 401-272-9500). Since space is limited, it may also be tive manner, it should be in the hands of the secretary by December necessary to limit the number of volunteers present at the table at 18, 1989. any one time. The Committee on Human Rights may delegate a Robert M. Fossum, Secretary person to be present at the table at any or all times, taking precedence over other volunteers. Any material which is not a petition (e.g., advertisements, resumes) will be removed by the staff. When registration closes, any material on the table will be discarded, so individuals placing petitions on the table should be sure to remove them prior to the close of registration. THE FLOWERING OF APPLIED MATHEMATICS IN AMERICA PETER D. LAX This perceptive and wide-ranging videotaped lecture provides a perspective on the development of applied mathematics in America from one who has been at the forefront of research in this field for almost forty years. Asserting that mathematics doesn't "trickle down" to the sciences but rather lives in partnership with them, Lax elucidates certain themes in applied mathematics by describing some of the field's highlights in such areas as fluid dynamics, mathematical physics, and optimization. He indicates the ways in which other sciences have stimulated developments in mathematics and describes some of the decisive mathematical contributions made by scientists from other fields. In addition, he turns his experienced eye to issues of science policy, undergraduate education, and the role of computation in mathematical research. All prices subject to change. Shipment will be made by surface. For air delivery add, $3, maxi 1980 Mathematics Subject Classification: 00 1st book $5, each additional book mum $100. Prepayment required. Order from VHS format, approx. one hour, American Mathematical Society, P.O. Box January 1989 1571, Annex Station, Providence, Rl 02901- Price $59 1571, or call toll free 800-566-7774 to charge To order, please specify VIDLAX/ NA with VISA or MasterCard. OCTOBER 1989, VOLUME 36, NUMBER 8 1059 Meetings A8 DELTA AIRLINES + JOINT MATHEMATICS MEETINGS SPECIAL AIRFARES 1-800-888-6422. MICA, Inc., the official travel management firm for the Joint Mathematics Meet ings to be held in Louisville, Kentucky, January 17-20, 1990, has arranged for special discounts aboard Delta Air Lines.* Save 5% off the lowest published promotional fares, meeting all restrictions, or 45% off regular roundtrip coach fares, with a seven day advance purchase. The lowest fares require a Saturday night stay, are subject to airline change/cancella tion penalties, and must be purchased at least 30 days prior to departure. Each Joint Mathematics Meetings participant will also receive $100,000 flight insurance with each ticket purchased through MICA aboard any airline. *Delta Air Lines has been designated as the official airline carrier for the Louis ville Meetings because it provides the most convenient service for the majority of participants from across the country. However, if Delta does not provide conven ient service from your area, MICA will inform you of the most convenient flights and lowest available airfare on other airlines. Call Today Toll-Free and Save: 1-800-888-6422 Monday-Friday, 8:30 am-6:00 pm EST Meetings, Incentives, Conventions of America, Inc. (MICA, Inc.) 37 Jerome Avenue, Bloomfield, CT 06002 1060 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Timetable (Eastern Standard Time) The purpose of this timetable is to provide assistance to preregistrants in the selection of arrival and departure dates. The program, as outlined below, is based on information at press time. Tuesday, / •matioal January 16 / Ma~::atical/''"" Society / As~=~~ation of America MORNING SHORT COURSE SERIES MATHEMATICAL QUESTIONS IN ROBOTICS 8:00 a.m. - 2:30 p.m. SHORT COURSE REGISTRATION Outside Regeny Ballroom South, Hyatt Regency 8:30 a.m. - 4:00 p.m. BOARD OF GOVERNORS' MEETING 9:00 a.m. - 10:15 a.m. SHORT COURSE LECTURE #1 Introduction Roger W. Brockett 10:45 a.m. - noon SHORT COURSE LECTURE #2 Kinematics of manipulators Madhusudan Raghavan AFTERNOON 2:00 p.m. - 3:15 p.m. SHORT COURSE LECTURE #3 Resolution of kinematic redundancy John B. Baillieul 2:00 p.m. - 7:00 p.m. COUNCIL MEETING 3:00 p.m. - 7:00 p.m. REGISTRATION FOR JOINT MEETINGS Hall C, Commonwealth Convention Center 3:45p.m.- 5:15p.m. SHORT COURSE LECTURE #4 Control and programming of multi fingered robot hands Shankar Sastry 4:30 p.m. - 6:30 p.m. SECTION OFFICERS' MEETING EVENING 7:00 p.m. - 9:00 p.m. MINICOURSE #1 (Part A) Computer based discrete mathematics Nancy Hood Baxter Ed Dubinsky Donald Muench OCTOBER 1989, VOLUME 36, NUMBER 8 1061 TIMETABLE Wednesday, /hamatioal /, January 17 /Ma~::atical/'"" Society / As::~:tion of America /_or~zations MORNING 7:30 a.m. - 4:00 p.m. REGISTRATION Hall C, Commonwealth Convention Center 8:00 a.m. - 1 0:55 a.m. SPECIAL SESSIONS Group representations and operator algebras, I History of mathematics, I Topology in computer graphics and image processing, I Semigroup theory, I Function theoretic methods in differential equations, I 8:00 a.m. - 10:55 a.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS PAPERS Prognostic and diagnostic testing: Helping high school students get ready for college-level mathematics, Part A Bert K. Waits Discrete mathematics: Has the bubble burst?, Part A Martha J. Siegel 8:30 a.m. - 9:50 a.m. AMS-MAA PANEL DISCUSSION Mathematics and public policy: How can we make a difference? Philip Daro Kenneth M. Hoffman Harvey B. Keynes Paul J. Sally, Jr. John A. Thorpe, moderator/organizer 8:30a.m.- 10:30 a.m. MINICOURSE #2 (Part A) Finite-Pak - Software for linear programming Marvin L. Bittinger J. Conrad Crown MINICOURSE #3 (Part A) Random mappings Bernard Harris MINICOURSE #4 (Part A) Lagrange first year calculus Francesca Schremmer Alain Schremmer MINICOURSE #5 (Part A) Teaching mathematical modeling Frank R. Giordano Maurice D. Weir NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1062 TIMETABLE Wednesday, /,oan / homa""" /., January 17 (cont'd} /Ma~::atical Society / As::~~tion of America / Or~~~:zations MORNING (cont'd) 9:00a.m. - 9:30 a.m. EMPLOYMENT REGISTER ORIENTATION SESSION 9:30a.m. - 4:00p.m. EMPLOYMENT REGISTER REGISTRATION Hall A, Commonwealth Convention Center 9:30 a.m. - 10:55 a.m. PANEL DISCUSSION Humanistic mathematics Lynne V. Cheney Ubiratan D'Ambrosio Philip J. Davis Alvin M. White, moderator 10:05 a.m.- 10:55 a.m. INVITED ADDRESS Title to be announced Israel M. Sigal 11 :10 a.m. - noon AMS-MAA INVITED ADDRESS Fifty years of eigenvalue perturbation theory Barry Simon AFTERNOON noon - 1 :00 p.m. NATIONAL SCIENCE FOUNDATION Informal Discussion Group 1 :00 p.m. - 2:00 p.m. COLLOQUIUM LECTURE I Some thoughts on the interaction between group theory and physics (tentative) Shlomo Sternberg 2:15p.m.- 3:05p.m. INVITED ADDRESS What's between a domain and its quotient field? Judith D. Sally 2:15p.m.- 3:30p.m. SHORT COURSE LECTURE #5 Planning and executing robot assembly strategies in the presence of uncertainty Bruce R. Donald SPECIAL SESSIONS 2:15 p.m. - 6:00 p.m. The Schrodinger equation I Multivariable operator theory I Homotopy theory I Geometric function theory in one and several complex variables I Analytic number theory I Geometric spectral and inverse spectral problems I Markov proceses and stochastic analysis I OCTOBER 1989, VOLUME 36, NUMBER 8 1063 TIMETABLE Wednesday January 11 {cont'd) ~~ommloal 4:'=matical Society ation of America ~~·zations AFTERNOON (cont'd) 2:15p.m.- 4:15p.m. MINICOURSE #1 (Part B) Computer based discrete mathematics Nancy Hood Baxter Ed Dubinsky Donald Muench MINICOURSE #6 (Part A) Coaching a team for the modeling contest B. A. Fusaro 2:15p.m.- 6:00p.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS PAPERS Prognostic and diagnostic testing: Helping high school students get ready for college-/eve/ mathematics, Part B Bert K. Waits Discrete mathematics: Has the bubble burst?, Part B Martha J. Siegel 2:15p.m.- 6:00p.m. CUPM SUBCOMMITTEE ON CALCU- LUS REFORM AND THE FIRST TWO YEARS POSTER SESSION Calculus Revision Thomas W. Tucker 3:20p.m.- 4:10p.m. INVITED ADDRESS New developments in solving the second part of Hilbert's fifth problem Janos D. Aczel 3:20p.m.- 4:20p.m. ASSOCIATION FOR WOMEN IN MATHEMATICS (AWM) PANEL DISCUSSION 4:00p.m.- 5:15p.m. SHORT COURSE LECTURE #6 Symbolic description of movement Roger W. Brockett 4:20p.m.- 4:50p.m. AWM BUSINESS MEETING 4:25p.m.- 5:30p.m. AMS-MAA SCIENCE AND GOVERNMENT SPEAKER Mathematics: Keystone of modern science and technology D. Allan Bromley 4:30p.m.- 6:30p.m. MINICOURSE #7 (Part A) Derive workshop Wade Ellis, Jr. MINICOURSE #8 (Part A) Using history in teaching calculus V. Frederick Rickey 4:30p.m.- 6:00p.m. TWO-YEAR COLLEGE RECEPTION 1064 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Wednesday, /,'"" /hamalioal / .. January 17 (cont'd) /Ma~::atical Society /As::~~tion of America / ~r~~~:zations EVENING 7:15 p.m. - 8:15 p.m. AMS-MAA SCIENCE AND GOVERNMENT SPEAKER Revitalizing mathematics education: A national imperative Admiral James D. Watkins 8:30 p.m. - 9:30 p.m. JOSIAH WILLARD GIBBS LECTURE The wide world of pure math which goes by other names George B. Dantzig 9:30 p.m. - 11 :00 p.m. AWM OPEN RECEPTION Thursday, (rican /hematical /,er January 18 / Ma~:~atical Society / As::~ation of America / Or~~~izations MORNING 7:30a.m. - 4:00 p.m. REGISTRATION Hall C, Commonwealth Convention Center 8:00a.m.- 10:55 a.m. SPECIAL SESSIONS The Schriidinger equation II Multivariable operator theory II Functional equations and their applications I Geometric function theory in one and several complex variables II Semigroup theory II Function theoretic methods in differential equations II Geometric spectral and inverse spectral problems II 8:00a.m.- 10:55 a.m. AMS-MAA SESSION Mathematics and education reform Naomi Fisher Harvey B. Keynes Philip D. Wagreich 8:00 a.m. - 1 0:55 a.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS PAPERS Prognostic and diagnostic testing: Helping high school students get ready for college-level mathematics, Part C Bert K. Waits Discrete mathematics: Has the bubble burst? Part C Martha J. Siegel OCTOBER 1989, VOLUME 36, NUMBER 8 1065 TIMETABLE Thursday, /,;,., /hamatloal /., January 18 (cont'd) /Ma~::atical Society / As::~~tion of America / Or~~;zations MORNING (cont'd) 8:30a.m.- 10:30 a.m. MINICOURSE #2 (Part B) Finite-Pak - Software for linear programming Marvin L. Bittinger J. Conrad Crown MINICOURSE #3 (Part B) Random mappings Bernard Harris MINICOURSE #4 (Part B) Lagrange first year calculus Francesca Schremmer Alain Schremmer MINICOURSE #5 (Part B) Teaching mathematical modeling Frank R. Giordano Maurice D. Weir AWM EMMY NOETHER 9:00 a.m. - 9:50 a.m. LECTURE OF SCHEDULES 9:00a.m. EMPLOYMENT REGISTER DISTRIBUTION 9:30 a.m. - 5:30 p.m. EMPLOYMENT REGISTER INTERVIEWS 10:05 a.m.- 10:55 a.m. INVITED ADDRESS On the (sometimes) strange behavior of large random things Peter Winkler 11 :10 a.m. - noon AMS-MAA INVITED ADDRESS Title to be announced Nolan R. Wallach L AFTERNOON noon - 1 :00 p.m. NATIONAL SCIENCE FOUNDATION Informal Discussion Group 1 :00 p.m. - 2:00 p.m. COLLOQUIUM LECTURE II Some thoughts on the interaction between group theory and physics (tentative) Shlomo Sternberg 2:15p.m.- 3:05p.m. INVITED ADDRESS Linear operators, matrix functions and control Israel C. Gohberg 1066 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Thursday, /rioac /hematioal /., January 18 (cont'd) /M:.::atical Society / As::~~tion of America / Or~~~:zations AFTERNOON (cont'd) 2:15p.m.- 4:15p.m. MINICOURSE #1 (Part C) Computer based discrete mathematics Nancy Hood Baxter Ed Dubinsky Donald Muench MINICOURSE #6 (Part B) Coaching a team for the modeling contest B. A. Fusaro MINICOURSE #8 (Part B) Using history in teaching calculus V. Frederick Rickey MINICOURSE #9 (Part A) How to use inexpensive graphing calcu lators to enhance the teaching and learning of precalculus mathematics and calculus Bert K. Waits Franklin Demana 2:15 p.m. - 4:10 p.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS NATIONAL ASSOCIATION OF PAPERS Prognostic and diagnostic testing: MATHEMATICIANS (NAM) Helping high school students get ready CONTRIBUTED PAPER for college-level mathematics, Part D SESSIONS Bert K. Waits Presentations by recent doctoral recipients Discrete mathematics: Has the bubble Don Hill burst?, Part D Gerald Chachere Martha J. Siegel 2:15 p.m. - 3:45 p.m. COMMITIEE ON TWO-YEAR COLLEGES PANEL DISCUSSION Assessment in the first two years of college mathematics William H. Caldwell Ray E. Collings (organizer/moderator) John W. Kenelly (organizer) David Lovelock Tina H. Straley Elizabeth J. Teles (organizer) John Tripp 2:15p.m.- 4:15p.m. CUPM SUBCOMMITIEE ON SYMBOLIC MANIPULATION PANEL DISCUSSION Computer algebra systems as teaching tools Michael G. Henle Zaven A. Karian Arnold M. Ostebee Donald B. Small (moderator) OCTOBER 1989, VOLUME 36, NUMBER 8 1067 TIMETABLE .. Thursday, / "'"" /hemotloaJ / January 18 (cont'd) /Ma~::atical Society / As::~:tion of America / Or~~~:zations AFTERNOON (cont'dl 3:20 p.m. - 4:10 p.m. INVITED ADDRESS The structure of algebraic threefolds Janos Kollar 4:25 p.m. - 6:00 p.m. COLE PRIZE SESSION AND BUSINESS MEETING EVENING 6:00p.m.- 8:15p.m. JOINT POLICY BOARD FOR MATHEMATICS 6:00p.m. RECEPTION 6:45p.m. SESSION Breaking the code (The life of Alan Turing) Peter J. Hilton Hugh Whitemore Presentation of JPBM Communications Award 7:00 p.m. - 9:00 p.m. MINICOURSE #7 (Part B) Derive workshop Wade Ellis, Jr. 8:30 p.m. - 10:00 p.m. HAPPY BIRTHDAY MATHEMATICAL REVIEWS! Fifty years of Mathematical Reviews Friday, /homatioal /., January 19 / /''"'"Ma~::atical Society / As::~~tion of America / Or~~~izations MORNING 7:30 a.m. - 4:00 p.m. REGISTRATION Hall C, Commonwealth Convention Center 8:00 a.m. - 10:55 a.m. SPECIAL SESSIONS CONTRIBUTED PAPER SESSIONS Multivariable operator theory Ill Recent developments in placement, Part A Functional equations and their Elizabeth J. Teles applications II Ray E. Collings John W. Kenelly Control of infinte dimensional systems I Classic classroom calculus problems, Algebraic geometry I Part A Anthony Barcellos Markov processes and stochastic analysis II A core in mathematics, Part A Kay B. Somers 8:00 a.m. - 10:55 a.m. SESSIONS FOR CONTRIBUTED PAPERS 1068 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Friday, /hematiooJ / .. January 19 (cont'd) /Ma~::atical/""" Society / As::~~tion of America / Or~~~:zations MORNING (cont'd) 8:30 a.m. - 10:30 a.m. MINICOURSE #9 (Part B) How to use inexpensive graphing calculators to enhance the teaching and learning of precalculus mathematics and calculus Bert K. Waits Franklin Demana MINICOURSE #1 0 (Part A) A seminar on women in mathematics Miriam P. Cooney esc MINICOURSE #11 (Part A) Writing in mathematics courses George D. Gopen David A. Smith MINICOURSE #12 (Part A) An introduction to the mathematical elements of computer graphics Joan Wyzkoski Weiss 8:30 a.m. - 9:50a.m. PANEL DISCUSSION Is graduate education meeting the needs of mathematicians? Rhonda J. Hughes Stephen B. Rodi lvar Stakgold William P. Thurston A. B. Willcox (moderator) 9:00 a.m. - 9:50 a.m. INVITED ADDRESS Title to be announced Mike Hopkins 9:00 a.m. - 10:55 a.m. CALCULUS TEXTS OPEN FORUM Calculus texts in a time of reform: the roles of authors, publishers and emerging technologies Howard Anton David P. Geggis James F. Hurley Mike Keedy Louis C. Leithold (moderator) Margaret L. Lial Bruce Peterson Earl W. Swokowski George B. Thomas, Jr. 9:00 a.m. - 10:55 a.m. 5-DAY WORKSHOPS PANEL DISCUSSION MAA section 5-day workshops Marvin L. Brubaker (organizer) B. A. Fusaro (organizer) OCTOBER 1989, VOLUME 36, NUMBER 8 1069 TIMETABLE Friday, /_ /hematloal /., January 19 (cont'd) /Ma~::atical Society / As::~~tion of America · / Or~;~;zations MORNING (cont'd) 9:00a.m. EMPLOYMENT REGISTER DISTRIBUTION OF SCHEDULES 9:30 a.m. - 5:30 p.m. EMPLOYMENT REGISTER INTERVIEWS 10:00 a.m. - 10:55 a.m. AMS-MAA-SIAM COMMITTEE ON PREPARATION FOR COLLEGE TEACHING FORUM How should mathematicians prepare for college teaching? Donald W. Bushaw Bettye Anne Case (moderator) Michael C. Reed Richard D. Ringeisen Guido L. Weiss 10:05 a.m.- 10:55 a.m. INVITED ADDRESS Problems and methods in analytic number theory Henryk lwaniec .------~------, 11:10 a.m.- noon AMS-MAA INVITED ADDRESS Nonwellfounded sets and their applications Jon Barwise AFTERNOON noon - 1 :00 p.m. NATIONAL SCIENCE FOUNDATION Informal Discussion Group 12:15 p.m. - 2:15p.m. MATHEMATICIANS AND EDUCATION REFORM/ MATHEMATICAL SCIENCES EDUCATION BOARD WORKSHOP The mathematician as gatekeeper of educational reform 1 :00 p.m. - 2:00p.m. COLLOQUIUM LECTURE Ill NAM CLAYTOR LECTURE Some thoughts on the interaction The box product problem between group theory and Scott W. Williams physics (tentative) Shlomo Sternberg 1 :00 p.m. - 4:05 p.m. SPECIAL SESSIONS Linear operaors, matrix functions and control/ The Schrodinger equation Ill Homotopy theory II Group representations and operator algebras II History of mathematics II Oscillation theory in ordinary differential equations I 1070 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Friday, ~,;.,., /hemal;"' /OK January, 19 (cont'd) /Ma~::atical Society / As::~:tion of America / ~r~~:zations AFTERNOON (cont'd) 1:00 p.m. - 4:05p.m. SPECIAL SESSIONS Algebraic geometry II Optimization and nonlinear analysis I Analytic number theory II 1 :00 p.m. - 3:00p.m. MINICOURSE #11 (Part B) Writing in mathematics courses George D. Gopen David A. Smith MINICOURSE #13 (Part A) A survey of educational software Virginia E. Knight Vivian Yoh Kraines MINICOURSE #14 (Part A) Creating order out of chaos in freshman mathematics: instituting a mathematics placement program Linda H. Boyd 1:00 p.m. - 4:05p.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS PAPERS Recent developments in placement, Part B Elizabeth J. Teles Ray E. Collings John W. Kenelly A core in mathematics, Part B Kay B. Somers 1 :15 p.m. - 2:05 p.m. CUPM SUBCOMMITTEE ON SYMBOLIC COMPUTATION SPECIAL PRESENTATION Applications of symbolic mathematics to mathematics Andrew Odlyzko 2:15p.m.- 3:05p.m. INVITED ADDRESS Teaching mathematics through fractals and chaos Michael Barnsley 2:15p.m.- 4:10p.m. ROCKY MOUNTAIN MATHEMATICS CONSORTIUM BOARD OF DIRECTORS' MEETING 3:20 p.m. - 4:10 p.m. RETIRING PRESIDENTIAL ADDRESS Teaching programs that work Leonard Gillman 4:25 p.m. - 5:30 p.m. PRIZE SESSION AND BUSINESS MEETING OCTOBER 1989, VOLUME 36, NUMBER 8 1071 TIMETABLE Friday, /hematiooJ /., January 19 (cont'd) / "'"" /Ma~::atical Society / As::~~tion of America / Or~~~;zations EVENING 6:00 p.m. - 8:00 p.m. NAM BANQUET Some milestones of the past; Some challenges of the future Johnny L. Houston 7:00 p.m. - 9:00 p.m. NATIONAL MEETING OF DEPARTMENT HEADS 7:00p.m. The David Report Revisited: A dialogue with Edward E. David, Jr. PARALLEL SESSIONS 8:00p.m. The David Report Revisited (continued) 8:00p.m. Evaluation of Teaching 8:00p.m. MAA Committee on Accreditation 7:00 p.m. - 9:00 p.m. MINICOURSE #13 (Part B) A survey of educational software Virginia E. Knight Vivian Yoh Kraines 7:30 p.m. - 9:30 p.m. COMPUTER ALGEBRA SYSTEMS SESSION CAS workshop reunion Donald B. Small (organizer) 7:45 p.m. - 8:45 p.m. COMMITTEE ON PARTICIPATION OF WOMEN PANEL DISCUSSION Unity in diversity - Challenge for change Frances A. Rosamond (moderator) 8:00p.m.- 10:00 p.m. NO-HOST COCKTAIL PARTY 9:00 p.m. - 1 0:30 p.m. AMS-MAA PANEL DISCUSSION Teaching undergraduate mathematics: Insights from education research Ronald G. Douglas (moderator) Paul J. Sally, Jr. Alan H. Schoenfeld (principal speaker) Guido L. Weiss Saturday, /homatloal /., /rioan 1 January 20 / Ma:::atical Society / As::~ ation of America / Or~~~izations MORNING 7:30 a.m. - 3:00 p.m. REGISTRATION Hall C, Commonwealth Convention Center 1072 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Saturday ' , A:American /homatloal / .. 20 January , (cont d) Mathematical Society / As~:~~tion of America / Or~~~:zations MORNING {cont'd) 8:00a.m.- 10:55 a.m. SPECIAL SESSIONS CONTRIBUTED PAPER SESSIONS Linear operators, matrix functions and Recent developments in placement, control// Parte Elizabeth J. Teles Control of infinite dimensional systems II Ray E. Collings John W. Kenelly Geometric function theory in one and several complex variables Ill Classic classroom calculus problems, Part B Topology in computer graphics and Anthony Barcellos image processing II A core in mathematics, Part C Algebraic geometry Ill Kay B. Somers Optimization and nonlinear analysis II Analytic number theory Ill Geometric spectral and inverse spectral problems Ill 8:00a.m.- 10:55 a.m. AMS-MAA SESSION Mathematics and education reform Naomi Fisher Harvey B. Keynes Philip D. Wagreich 8:00 a.m. - 10:55 a.m. SESSIONS FOR CONTRIBUTED PAPERS 8:00 a.m. - 9:50 a.m. COMMITIEE ON COMPUTERS IN MATHEMATICS EDUCATION PANEL DISCUSSION Providing computer resources for mathematics John S. Devitt (organizer) Wade Ellis, Jr. (organizer) David A. Smith (moderator) 8:30 a.m. - 10:30 a.m. MINICOURSE #15 (Part A) Mathematica and college teaching Stan Wagon MINICOURSE #16 (Part A) Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg MINICOURSE #17 (Part A) The informed consumer's instructional guide to graphing calculators John W. Kenelly Iris B. Fetta 9:00 a.m. - 10:00 a.m. NAM PANEL DISCUSSION How to make mathematics work for minorities Beverly Anderson (moderator) OCTOBER 1989, VOLUME 36, NUMBER 8 1073 TIMETABLE Saturday, /hematioal /., January 20 (cont'd) L~;;atical/''"" Society L As;~~tion of America L_o;_~zations MORNING (cont'd) 10:00 a.m. - 10:55 a.m. NAM BUSINESS MEETING 10:05 a.m. - 10:55 a.m. INVITED ADDRESS Displacement structure of matrices and some applications Thomas Kailath 11:10 a.m.- noon AMS-MAA INVITED ADDRESS A century of representation theory of finite groups Charles W. Curtis AFTERNOON noon - 1 :00 p.m. NATIONAL SCIENCE FOUNDATION Informal Discussion Group 1 :00 p.m. - 5:30 p.m. SPECIAL SESSIONS Linear operators, matrix functions and control Ill Homotopy theory Ill Oscillation theory in ordinary differential equations II Optimization and nonlinear analysis Ill 1 :00 p.m. - 3:00 p.m. MINICOURSE #1 0 (Part B) A seminar on women in mathematics Miriam P. Cooney esc MINICOURSE #12 (Part B) An introduction to the mathematical elements of computer graphics Joan Wyzkoski Weiss MINICOURSE #17 (Part B) The informed consumer's instructional guide to graphing calculators John W. Kenelly Iris B. Fetta 1 :00 p.m. - 5:30 p.m. SESSIONS FOR CONTRIBUTED CONTRIBUTED PAPER SESSIONS PAPERS Recent developments in placement, Part D Elizabeth J. Teles Ray E. Collings John W. Kenelly A core in mathematics, Part D Kay B. Somers Computers in the classroom: The time is right, Part A David P. Kraines Vivian V. Kraines 1074 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY TIMETABLE Saturday, January 20 (cont'd) ~:omotlool izations ~ri~omatical Society ation of America ~~' AFTERNOON (cont'd) 1:30 p.m.- 3:00p.m. COMMITIEE ON PLACEMENT EXAMINATIONS PANEL DISCUSSION The development of calculator-based placement testing John G. Harvey (organizer) Mary M. Lindquist Bernard L. Madison Robert Northcutt Thomas W. Tucker 1:30 p.m.- 3:00p.m. COMMITIEE ON TWO YEAR COLLEGES PANEL DISCUSSION Models of two-year four-year dialogues Carole Ann Bauer (organizer) David E. Boliver, Jr. William H. Manzer Albert D. Otto Ernest A. Ross, Jr. 1:30 p.m.- 3:00p.m. CALCULUS PANEL DISCUSSION Calculus for the twenty-first century Andrew M. Gleason (moderator) Sheldon P. Gordon (organizer) David A. Smith Gilbert Strang 1:30 p.m.- 2:30p.m. NATIONAL RESEARCH COUNCIL MS2000 PANEL DISCUSSION A preview of the MS 2000 study William E. Kirwan 2:15p.m.- 3:05p.m. INVITED ADDRESS Title to be announced Sun-Yung Alice Chang 3:30p.m.- 5:30p.m. MINICOURSE #11 (Part C) Writing in mathematics courses George D. Gopen David A. Smith MINICOURSE #14 (Part B) Creating order out of chaos in freshman mathematics: instituting a mathematics placement program Linda H. Boyd MINICOURSE #15 (Part B) Mathematica and college teaching Stan Wagon MINICOURSE #16 (Part B) Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg EVENING 7:00 p.m. - 10:00 p.m. 25-YEAR-MEMBER BANQUET OCTOBER 1989, VOLUME 36, NUMBER 8 1075 Mathematical Sciences Employment Register January 1990 Meetings in Louisville The Mathematical Sciences Employment Register ( MSER), views will be held on Thursday and Friday, January 18 held annually at the Joint Mathematics Meetings in January, and 19. No interviews will be held on Wednesday. provides opportunities for mathematical scientists seeking pro Fifteen-minute intervals are allowed for interviews, fessional employment to meet employers who have positions including two or three minutes between successive inter to be filled. Job listings (or descriptions) and resumes prepared views. The interviews are scheduled in half-day sessions: by employers and applicants are assigned code numbers. and Thursday morning and afternoon, and Friday morning displayed at the meeting so that members of each group may and afternoon, amounting to four half-day sessions for determine which members of the other group they would like to a.m.) have an opportunity to interview. Requests for interviews are interviews. There are ten time periods (9:30-11:45 then submitted, and a computer program assigns the appoint in which interviews can be scheduled in the morning and ments, matching requests [not areas of interest] to the extent fourteen time periods (I: 15- 5:00 p.m.) in the afternoon. possible, using an algorithm which maximizes the number of It is possible that an applicant or employer may be sched interviews which can be scheduled subject to constraints deter uled for the maximum number of interviews in a session. mined by the number of time periods available, the numbers Requests for interviews will be accommodated depend of applicants and employers, and the pattern of requests. The ing on the availability of participants. The scheduling report below outlines the operation of the register, indicating program does not have a provision allowing participants some of the procedures involved for the benefit of those not to specify particular times for interviews beyond the familiar with its operation. choice of session (day, and morning or afternoon). Such The Mathematical Sciences Employment Register is appar requests cannot be accommodated. ently unique among employment services offered by profes Requests for interviews taking place during the two ses sional organizations in the sciences. engineering and the hu sions on Thursday MUST BE SUBMITTED on Wednes manities. The computer programs used are constructed around day between 9:30 a.m. and 4:00 p.m. Requests for inter a matching program, devised by Donald R. Morrison, and based views to take place during the Friday sessions must be on an algorithm described in his paper "Matching Algorithms" submitted on Thursday before 4:00 p.m. Those who fail in Journal of Combinatorial Theory, volume 6 ( 1969). pages 20 to do so cannot be included in the pool of available par to 32; see also "Matching Algorithms" (abstract) Notices, Au ticipants when the matching program which schedules the gust 1967, page 630. The number of interviews arranged by interviews is run on the computer that night. This applies the program is significantly greater than the number possible at to all employers and applicants both preregistered and the employment registers of other organizations, in many cases on-site registrants. Forms submitted with preregistration greater by an order of magnitude. achieve registration for the Employment Register only. 1990 Employment Register in Louisville Background of Applicants The Employment Register will be held on Wednesday, Thursday, and Friday, January 17, 18, and 19, 1990. Statistics from previous Employment Registers have shown A short (optional) orientation session will be conducted employers sought to fill approximately 180 positions. I 0 of by the AMS-MAA-SIAM Committee on Employment which were nonacademic jobs. For 98% of the positions. Opportunities at 9:00 a.m. on Wednesday, January 17. holders of doctoral degrees were preferred, for 65% of the applicants with doctorates were acceptable, The purpose of the orientation session is to familiarize positions only for 30% of the positions, holders of masters degrees were participants with the operation of the Register and with considered eligible. Few of the nonacademic employers the various forms involved. Following orientation, par indicated an interest in holders of bachelors degrees in ticipants should pick up their material for participating mathematics. in the Employment Register. Computer-scheduled inter- 1076 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings These forms do not automatically include the participant the services of the Mathematics Meetings Houstng Bu in the interviewing process. The interview request forms reau and has the further advantage of helping to reduce handed out at the Employment Register must be turned waiting times at the meeting in Louisville. in before the 4:00 p.m. deadline in order to receive a Employer forms received after the November 17 computer printed schedule the next day. deadline cannot be included in the printed lists. For de On Thursday and Friday mornings at 9:00 a.m. all tails on registration and preregistration for the Louisville schedules for applicants and employers for the day (both Joint Mathematics Meetings, please refer to the informa morning and afternoon sessions) will be available for tion on these subjects which may be found elsewhere in distribution. this issue. The Friday afternoon session is the annual "employ Employers and applicants who have preregistered for ers' choice" session. For this session interviews will be the Employment Register must pick up their MSER scheduled on the basis of requests made by employers. material after 9:30 a.m. on Wednesday, January 17. Applicants do not submit specific interview requests for (This material includes the interview request forms wbich this session; but, in order to participate, they must in are handed out at the meeting only.) These are not the dicate their availability for the session by returning the forms that are submitted with preregistration. Interview Request Form for Friday, indicating that they Employers' job listings and applicants' resumes will be will attend the afternoon session that day. posted at the meeting, so that applicants and employers Applicants should be aware of the fact that interviews may review them. arranged by the Employment Register represent only an Material for the Employment Register will not be initial contact with employers and that hiring decisions mailed in advance. are not ordinarily made during or immediately following Preregistered Applicants to bring a number such interviews. Applicants are advised In addition to the Joint Meetings preregistration fet;, of their vitae or resumes so that they may leave of copies there is an applicant fee of $15 payable prior to the employers. them with prospective November 17 deadline. These fees must accompany the Employment Register is The Mathematical Sciences Preregistration/Housing Form. Late preregistration for by the American Mathematical Society, the sponsored the Employment Register is not possible. and the Society Mathematical Association of America, Applicants' resumes will be made available to employ it is operated for Industrial and Applied Mathematics; ers at the Employment Register in printed form, so that· under the general su by members of the AMS staff they may be studied carefully at leisure. The December pervision of the joint AMS-MAA-SIAM Committee on issue of Employment Information in the Mathematical Employment Opportunities. Sciences (ElMS) will contain photographic reproductions the Employment Regis Anyone with questions about of the resumes of applicants who have preregistered by ter should contact the Employment Register Coordinator November 17. Forms not received in time cannot be American Mathematical Society at 401-272-9500, at the included in this issue. See the section on preparation of extension 286 or by e-mail: [email protected]. resumes elsewhere in this announcement. after the Register The telephone number to be used Employers' job listings and applicants' resumes will be should note that begins is 502-583-6970. Participants posted at the meeting, so that applicants and employers will be participating this number will be for those who may review them. in the Employment Register and is not for contacting participants or taking messages. Those who wish to Preregistered Employers leave messages should call the message center telephone In addition to the Joint Meetings preregistrauon fee, number found in the Louisville meeting announcement. there is a separate charge for each employer who wi}! be interviewing applicants at the register. There i:; no Preregistered Employers/ Applicants additional charge for posting more than one posilioll, provided they are in the same department. Preregistration for the Mathematical Sciences Employ Please refer to the Preregistration/Housing Form fo~ ment Register must be completed by November 17, 1989. a list of the Joint Mathematics Meetings and Employ. Applicants and employers (including all interviewers) ment Register fees. These fees must accompany the who wish to preregister for the Employment Register Preregistration/Housing Form. The registration fee for must also register for the Joint Mathematics Meetings. employers covers the cost of a copy of the Decerpber Forms for preregistration, housing, the applicant resume Issue of ElMS. This publication (distributed at the ni~et form, and the employer form are located in the back of ing) contains printed copies of the resumes of applicqnts this issue. Preregistration for the Employment Register, who preregistered prior to the deadline. Please note: The in addition to permitting inclusion in the printed winter Winter List of Applicants will no longer be prepared 1\fld, lists of Employers, has the advantage of reduced fees and therefore, will not appear in ElMS or be distributed af the OCTOBER 1989, VOLUME 36, NUMBER 8 1077 Meetings meeting as in previous years. It is requested that employers of Applicants will no longer be prepared and, therefore, submit both employer and Preregistration/Housing Forms will not appear in ElMS or be distributed at the meeting with appropriate fees in the same envelope. It would also as in previous years. be helpful if the names of cointerviewers are listed on the After registration has been completed, applicants and employer form. If possible, these individuals should also employers should come to fill out the forms necessary preregister at the same time. to participate in the Employment Register. Employers' It is the policy of some institutions to pay for em job listings and applicants' resumes will be posted at the ployer fees. These payments do not always accompany the meeting, so that applicants and employers may review preregistration forms but are sent in after the deadline them. has passed, or when the meeting is over. It is important Nonparticipating Employers that the institution's fiscal department indicate the name Employers who do not plan to participate in the Employ of the participating employer with their remittance advice ment Register, but wish to display job descriptions, may or payment order so that proper credit can be made in obtain special forms from Carole Kohanski, MSER, P. 0. Providence. Box 6248, Providence, RI 02940. These job descriptions, Employers are encouraged to provide more than one subject to approval, must be received in the Providence interviewer, when they are able to do so, in order office by November 17 in order to qualify for the reduced to increase the number of interviews which may be fee of $10. There is a $15 fee for listings received after scheduled. Please take care to indicate on the form the the November 17 deadline. number and names of interviewers for whom simultaneous Employers who attend the Joint Mathematics Meet interviews may be scheduled. (If all interviewers will be ings, but do not want to interview, can post job descrip interviewing for the same position, or for the same set of tions, subject to approval, at the Employment Register. positions, only one form should be submitted and only Poslings will not be allowed i]l the Joint Meetings reg one employer code number will be assigned; therefore, istration area. A fee of $15 will be charged and must each interviewer would then receive a separate computer be paid at the Joint Mathematics Meetings registration schedule and separate table number.) More than one desk. Participants should be sure to inform the cashier employer code will be required if some interviewers will that they would like to post a job description but are not interview for all positions. Thus, if there are two not planning to interview and obtain the proper receipt disjoint sets of positions, two forms are required and in order to receive the form necessary for posting at the two employer codes will be assigned. Employment Register desk. A coded strip at the bottom of the form summarizes the information on each form. All employers are required Applicants Not Planning to Attend to complete the Summary Strip. This is used to prepare Applicants for professional positions in the mathematical a computer-printed list of preregistered employers for sciences, who do not plan to attend the meeting in distribution to the applicants at the meeting. Louisville and participate in the Employment Register, may submit resumes for publication in the December N onpreregistered Applicants and Employers issue if they use the MSER Form for Applicants at the Employers and applicants who wish to participate in back of this issue and observe the deadline of November the Register who have neither preregistered nor paid 17. (It is, of course, not necessary to preregister for the the Employment Register fee must first go to the Joint meeting or pay the Employment Register registration fee Mathematics Meetings registration desk, in order to if one is not attending the meeting. Resumes will not be complete their registration. No provision will be made to posted at the Employment Register if the participant is handle cash transactions at the site of the Employment not attending the meeting.) Register. Registration for the Joint Meetings is required Lists of Employers for participation in the Employment Register. It is also Winter required that all participating employer interviewers The Winter List of Employers consists of summaries of register for the Joint Mathematics Meetings. the position listings submitted by the employers who Please refer to the Preregistration/Housing Form for preregistered for the meeting; it will be distributed to onsite registration fees. the applicants participating in the Register. Others may Onsite registration for the Employment Register is purchase the Winter List of Employers at the AMS $100 for employers and an additional $50 for each Exhibits and Book Sale at the meeting or from the additional interviewer and $20 for applicants. The reg Providence office after the meeting. The price at the istration fee for employers covers the cost of a copy of meeting is $5 each. Any copies remaining after the the December Issue of ElMS. This publication contains meeting will be available from the Providence office of printed copies of the resumes of applicants who preregis the Society for $7 each. tered prior to the deadline. Please note: The Winter List Please note that this list will not be updated with 1078 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings onsite employers after the Employment Register has The forms must be carefully typed using a new black concluded. ribbon. The best results are obtained by using a modern typewriter with a carbon-coated polyethylene film ribbon December Issue of Employment but satisfactory results may be obtained with a ribbo~ Information in the Mathematical Sciences made of nylon or other woven fabric if suitable care is exercised. It is important that the keys be clean and make For several years the periodical ElMS has published a sharp, clear impression, which must be a uniform dark six issues per year listing open positions in academic black. Gray, blue, or other colors will not reproduce and governmental and industrial organizations, primarily i~ should, therefore, not be used. Do not use an eraser as it ~orth America, along with a few listings from countries wdl. cause smudges which reproduce when photographed.' m other parts of the world. ElMS is a joint project Use a correcting typewriter, or correction tape or fluid of the American Mathematical Society (publisher), the if necessary. ' Mathematical Association of America, and the Society Only an original copy of the form should be submitted, for Industrial and Applied Mathematics. a photocopy or xerographic reproduction will not reproduce The December issue of ElMS contains resumes of as well and may not be accepted for publication. It is persons seeking professional positions in the mathemat therefore important to exercise care in order to assure that ical sciences. Resumes of applicants taking part in the the results are satisfactory. ~mploym~nt Register and those not attending will be Submission of copy of good quality is entirely the mclude~ m the December 1989 issue provided they responsibilty of the applicant. The Society (which will are recetved before the November 17 deadline and are print this material) must be the final judge of what copy in satisfactory condition. Other mathematical scientists is capable of being reproduced adequately and therefore ~ho wish to be included may have their resumes printed of what is acceptable for inclusion in the printed booklet. tf the same deadline is observed and if the copy supplied The Society will not correct or replace inadequate copy meets the same technical requirements described in the and cannot prepare original copy. In the event the quality following section. of a resume, submitted by an applicant participating in Copies of the December issue of ElMS will be the Employment Register, does not meet the necessary ?istributed in Louisville to the employers who participate m the Employment Register. conditions for inclusion in the December issue, the resume will be returned if time allows; otherwise the Job applicants planning to participate in the Employ resume will be posted at the Employment Register in ment Re~ister in Louisville are therefore strongly urged Louisville, along with those of the other participants. to preregtster so that their resumes can appear in the December issue. Forms received past the deadline of November 17 will be returned. Additional copies of the December Issue of ElMS will be available for sale at the AMS Exhibits and Book Sale at the meeting. Prices at the meeting are $8 each List of Retired Mathematicians for the December issue. Any copies remaining after the Available for Employment meeting will be available from the Providence office of The annual List of Retired Mathematicians will be included in the the Society for $13. December and January issues of the publication Employment Infor mation in the Mathematical Sciences. Retired mathematicians who Preparation of Applicants' Resumes are interested in being included in the list may send the follow for the December issue of ElMS ing information to the Mathematical Sciences Employment Regis ter, American Mathematical Society, P. 0. Box 6248, Providence, The December issue of ElMS will be printed using Rhode Island 02940. photographic reproductions of forms completed and I. Full Name submitted by applicants. For this reason, special care 2. Mailing Address must be exercised by those who prepare the forms in 3. Highest degree, year, university 4. Most recent employment: institution order ~o assure that the results are of good quality, 5. Type of position desired and wtll be clear and legible after they have been 6. Academic or industrial employment preferred photographed, reduced in size, and printed. 7. Date available for employment (month/year) Because an employer's first impressions of an appli 8. Geographic location preferred cant are likely to be based on the appearance of the The deadline for receipt of this information is November 17. Off printed form, applicants are strongly advised to study prints of the list will be available from the Mathematical Sciences Employment Register, American Mathematical Society, P.O. Box the suggestions given below, before the forms are filled 6887, Providence, Rhode Island 02940. out, so that the original copy will be neither marred nor damaged. OCTOBER 1989, VOLUME 36, NUMBER 8 1079 American Mathematical Society Short Course Series Introductory Survey Lectures on Mathematical Questions in Robotics Louisville, Kentucky, January 16-1 7, 1990 The American Mathematical Society, in conjunction The lectures will require no advanced background in with its ninety-sixth Annual Meeting, will present a robotics. Some familiarity with basic differential geome two day Short Course entitled "Mathematical Questions try and elimination theory will be useful. In addition to in Robotics" on Tuesday and Wednesday, January 16- the specific reference material listed by the speakers, the 17, 1990, at the Hyatt Regency Hotel in Louisville, book by Richard Paul, Robotic Manipulators: Mathemat Kentucky. The program is under the direction of Roger ics, Programming and Control, MIT Press, Cambridge, W. Brockett, Harvard University. Mass., 1981, provides a useful perspective. Applications of robotics ranging from the exploration Advance registration fee: $40 ($15 student/unem of distant planets to the manufacture of automobiles have ployed). Onsite registration fee: $50 ($20 student/unem caught the imagination of the public. What is seldom ployed). Registration and housing information can be suggested in popular accounts, however, is the fact that found in this issue of Notices, see sections Preregistration, behind the operation of even the simplest robot is a Housing and Registration at the Meetings. great deal of computational and geometric analysis. The The Short Course series is under the direction of purpose of this Short Course is to expose the audience the Short Course Subcommittee of the AMS-MAA Com to a range of mathematical problems and techniques mittee on Employment and Educational Policy (CEEP): which have been used in the study of robot kinematics, Stefan A. Burr (chair), R. Peter DeLong, Lisl Novak dynamics and motion planning. Specific topics to be Gaal, Robert P. Kurshan, Barbara L. Osofsky, Marjorie discussed include kinematic chains, grasping and motion L. Stein, and James J. Tattersall. control. The speakers will address both the physical and the computational aspects of these topics, using ideas from geometry, algebra and computer science. Synopses and Reading Lists Tuesday, January 16: RoGER W. BROCKETT, Harvard University, Introduction Introduction (Roger W. Brockett). The introduction will MADHUSUDAN RAGHAVAN, General Motors Research be devoted to establishing a framework for the study Laboratories, Kinematics of Manipulators of robot kinematics, compliance and task description. JoHN B. BAILLIEUL, Boston University, Resolution of We will select a few highlights from the literature and Kinematic Redundancy give enough background so as to make it possible to SHANKAR SASTRY, University of California, Berkeley, appreciate their mathematical context and their practical Control and Programming of Multifingered Robot significance. Examples will include a physical and math Hands ematical formulation of the idea of a kinematic chain, a discussion of compliance, the treatment of a basic Wednesday, January 17: result on grasping and a result on optimal kinematic BRUCE R. DoNALD, Cornell University, Algorithms for configurations. Motion Planning (tentative) ROGER W. BROCKETT, Harvard University, Symbolic 1. Richard Paul, Robotic Manipulators: Mathemat Description of Movement ics, Programming and Control, MIT Press, Cambridge, Mass., 1981. Synopses of the talks and accompanying reading lists 2. R. W. Brockett, Robotic Manipulations and the follow. Lecture notes will be mailed to those who prereg Product of Exponentials Formula, in Lecture Notes in ister and will be available at the Short Course registration Control and Information Sciences, Proceedings of the desk for those registering on site. International Symposium on Mathematical Theory of 1080 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Short Course Series Networks and Systems (P. A. Fuhrman, ed.), Springer 4. J. J. Craig, Introduction to robotics, mechanics and Verlag, Berlin, 1984, pp. 120-127. control, Addison-Wesley Publishing Co., 1986, chapters 3. K. H. Hunt, Kinematic Geometry of Mechanisms, 1-4. Oxford University Press, Oxford, 1978. 5. L.-W. Tsai and A. Morgan, Solving the kinematics 4. R. W. Brockett and Josip Loncaric, The Geometry of the most general six- and five-degree-offreedom ma of Compliance Programming, in Theory and Application nipulators by continuation methods, Transactions of the of Nonlinear Control Systems (C. I. Byrnes and A. ASME, Journal of Mechanisms Transmissions and Au Lindquist, eds.), North Holland, Amsterdam, 1986, pp. tomation in Design, Vol. 107, June 1985, pages 189-200. 35-42. 6. H.-Y. Lee and C.-G. Liang, A new vector theory for the analysis of spatial mechanisms, Mechanisms and Kinematics of Manipulators (M. Raghavan). The two Machine Theory, Vol. 23, No. 3, 1988, pages 209-217. classical problems in manipulator kinematics are: (a) 7. H.-Y. Lee and C.-G. Liang, Displacement analysis the forward kinematics problem: given the manipulator of the general spatial 7-/ink 7R mechanism, ibid, pages geometry (i.e. base location, link lengths, twist angles, 219-226. offsets) and values of the joint variables, find the position and orientation of the hand, (b) the inverse kinematics Resolution of Kinematic Redundancy (J. Baillieul). problem: given the manipulator geometry and the desired Kinematic redundancy can be a design feature or an position and orientation of the hand, find the values of artifact of a particular mode of operation in robotics. the joint variables which will place the hand in that In either case, motion programming of devices such as desired configuration. robotic hands, manipulator arms, etc. presents both chal For manipulators comprised of rigid bodies, the above lenge and opportunity since the task does not uniquely problems may be formulated as principal systems of mul determine the trajectories of all degrees of freedom. For tivariate polynomials over the reals. Algebraic methods a variety of practical reasons, it is desirable to resolve for solving such systems usually proceed by eliminating kinematic redundancy in a rational fashion, and there variables and reducing the problem to one involving sev is a growing contemporary body of literature on various eral univariate polynomials over the reals. Manipulator aspects of such resolution. kinematics therefore relies heavily on elimination algo A very basic example of the problems which are rithms. In this lecture, we describe Sylvester's dyalitic studied involves a robot arm which has more joints than method, an elimination procedure which exploits the necessary to move the end effector or hand into an arbi sparsity and structure evident in polynomials arising in trary configuration (=position and orientation). A simple manipulator kinematics. abstraction of the problem involves an analytic function The equations describing a manipulator exhibit some f : 8 -+ X associating joint configurations () E 8 to Let be the position vector of interesting properties. p end effector configurations x E X. X will typically be (a a point on the hand of a n-revolute jointed spatial subset of) the group of proper rigid motions of 3-space, function series manipulator. When p is expressed as a S£(3, R), and if, say, the robot arm has only revolute of the manipulator parameters, one may show that it joints, 8 is (a subset of) an n-torus. Kinematic redun is linear in sinO; and cosO;, where 0;, i = 1, ... , n are dancy is typically an issue if dim 8 > dim X in which the joint variables. Interestingly enough, the function case we face the problem of the equation f( 0) = x being pTp is also linear in sinO; and cosO;. We present a list underdetermined. One rational approach to associating a of such functions in the ideal associated with revolute joint configuration to a given end effector configuration jointed manipulators. We then show how they may be x is to seek that value () which optimizes some crite used with the dyalitic elimination procedure to solve the rion function g( ()) subject to satisfying the constraint problem for the six-revolute jointed inverse kinematics f(O) = x. Under reasonable assumptions, the mathe series manipulator of general geometry. This was once matics underlying such pointwise optimization needn't considered the most difficult problem in manipulator involve more than multivariable calculus. If as is typical kinematics. in robotic applications, however, there is given a path 1. G. Salmon, Lessons introductory to the modern of configurations x(t), it is not always straightforward higher algebra, Chelsea Publishing Co., 1885, pages 79- to generate a corresponding path O(t) by optimizing 90. some function along the path. Generally, one wants 2. J. F. Canny, The complexity of robot motion the algorithms for generating O(t) to be cyclic (closed planning, MIT Press, 1988, chapter 3. x-paths lift to closed 0-paths), and it has been shown 3. F. S. Macaulay, The algebraic theory of modular that in many robotic applications there are topologi systems, Stechert-Hafner Service Agency, 1964, pages cal obstructions to globally valid implementations of 1-17. cyclic algorithms. These obstructions (called algorithmic OCTOBER 1989, VOLUME 36, NUMBER 8 1081 Short Course Series singularities in the robotics literature) manifest them In the first part I will discuss the modelling of selves physically in nonsmooth motions and the robot's the low-level control problem for a multifingered hand being unable to move in certain directions to first order. manipulating an object under a variety of contact types: The lecture will consist of a historical introduction fixed, sliding, rolling and soft fingered or rhealogical. to redundancy in robots and a look at the current state The nonholonomies associated with rolling make it of algorithms which resolve kinematic redundancy by particularly interesting. We discuss the use of control instantaneously optimizing a function of the joint con laws for explicit linearization of these control systems figurations. We shall also discuss resolution of kinematic under state feedback. We show simulations and discuss redundancy by means of optimizing nonholonomic and implementation considerations. path-integral criteria. The latter approach has practical I will discuss in the second part of the talk how advantages in certain applications, but it leads to a class results from the (differential) geometric control theory of two point boundary value problems which, if solved literature can be brought to bear on the problem of by standard numerical procedures, are substantially more changing grasps on an object. Some connections with complex than the previously mentioned resolution tech Berry's phase formula will also be given. Finally, I will niques based on optimizing instantaneous functions of discuss a neurophysiologically motivated environment the joint configurations. Recent research has shown that, which we are developing for the specification, control using the theory of exponential dichotomies, we may and programming of multifingered hands. develop continuation methods which render these prob The talk is based on collaborative work with my lems more manageable while at the same time relating students: Li Zexiang (NYU), Ping Hsu (University of their solution to well understood instantaneous methods. Illinois), Arlene Cole (AT&T Bell Labs), John Hauser (USC), Richard Murray, Curt Deno and Kris Pister. l. J. Baillieul, 1985. Kinematic Programming Alter natives for Redundant Manipulators, IEEE International Symbolic Description of Movement (Roger W. Brock MO, Conference on Robotics and Automation, St. Louis ett). It can be very tedious to specify the instructions March 25-28, pp. 722-728. which will enable a robot to carry out a useful task. the 2. D. R. Baker and C. W. Wampler, 1988. On In order to make this process as efficient as possible it Inverse Kinematics of Redundant Manipulators, Interna is desirable to have a precise, yet flexible, language for Research, vol. 7, no. 2, pp. tional Journal of Robotics man-machine interaction. Since movement is central to 3-21. what a robot does, this means that one needs a conve Baillieul, and J. M. Hollerbach, 3. D. P. Martin, J. nient language for describing motion in a 3-dimensional Transactions on Robotics and 1989. Resolution, IEEE world populated by objects. In short, one needs a motion Automation, v. S, no. 4, pp. 529-533. description language. In this talk we will give examples of current practice, drawing on work in various areas Algorithms for Motion Planning (tentative) (Bruce R. outside and within robotics. We will discuss the role of Donald). Synopsis will appear in the November Notices. feedback (force and vision) and investigate robustness and stability based on idealized models. We will study in Control and Programming of Multifingered Robot some detail a formal language (in the sense that this term Hands (Shankar Sastry). In this talk, I will discuss is used in computational theory) for motion description the dynamics, control, planning of motions and design and illustrate its use with a video. of multifingered hands. The talk will be in two parts 1. H. R. Lewis and C. H. Papadimitriou, Elements with extensive videotape footage (to be shown after of the Theory of Computation, Prentice-Hall, Englewood the talk) illustrating both animated simulations and Cliffs, NJ, 1981. experiments. The talk is a blend of recent advances 2. R. W. Brockett, On the Computer Control of in our understanding of classical mechanics, computer Movement, Proceedings of the 1988 IEEE Conference on graphics as well as some neurophysiology. Robotics and Automation, April 1988. 1082 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions Invited Speakers at the time this issue of Notices went to the printer. at AMS Meetings The section below entitled Information for Organizers describes the timetable for announcing the existence The individuals listed below have accepted invitations of Special Sessions. to address the Society at the times and places in dicated. For some meetings, the list of speakers is incomplete. November 1989 Meeting in Los Angeles, California Far Western Section Associate Secretary: Lance W. Small Los Angeles, CA, November 1989 Deadline for organizers: Expired Burton I. Fein Nicolas Spaltenstein Deadline for consideration: Expired Stephen M. Gersten Thomas H. Wolff Roger C. Alperin and Karen Vogtmann, Geometric methods in combinatorial group theory Louisville, KY, January 1990 James P. Lin, Algebraic topology Jon Barwise (AMS-MAA) Henryk lwaniec David J. Saltman and Murray M. Schacher, Quadratic Chang Janos Kollar Sun-Yung Alice forms and simple algebras Charles W. Curtis Israel M. Sigal Thomas H. Wolff, Harmonic analysis (AMS-MAA) Barry Simon (AMS-MAA) George B. Dantzig Shlomo Sternberg (Gibbs Lecture) (Colloquium Lectures) January 1990 Meeting in Louisville, Kentucky Israel C. Gohberg Nolan R. Wallach Associate Secretary: Joseph A. Cima Mike Hopkins (AMS-MAA) Deadline for organizers: Expired Deadline for consideration: Expired Fayetteville, AK, March 1990 Joseph A. Ball and Israel C. Gohberg, Linear operators, Marcel F. Neuts Mark A. Stern matrix functions and control Vladimer I. Oliker Jonathan M. Wahl Joseph G. Conlon, The Schrodinger equation Manhattan, KS, March 1990 Raul E. Curto and Paul S. Muhly, Multivariable J. Brian Conrey Jean-Pierre Rosay operator theory Stewart B. Priddy Jang-Mei Wu Ethan S. Devinatz and Mike Hopkins, Homotopy University Park, PA, April1990 theory Robert S. Doran, Group representations and operator Robert T. Glassey Lowell Jones algebras Carsten Grove Gang Tian Bruce R. Ebanks, Functional equations and their ap Columbus, OH, August 1990 plications Michael G. Crandall Florence D. Fasanelli and Victor J. Katz, History of (Progress in Mathematics Lecture) mathematics Denton, TX, November 1990 Robert E. Fennell and Suzanne Marie Lenhart, Control Avner D. Ash of infinite dimensional systems Organizers and Topics Carl H. FitzGerald and Ted J. Suffridge, Geometric function theory in one and several complex variables of Special Sessions Gary D. Jones, Oscillation theory in ordinary differen The list below contains all the information about tial equations Special Sessions at meetings of the Society available Janos Kollar, Algebraic geometry OCTOBER 1989, VOLUME 36, NUMBER 8 1083 Invited Speakers and Special Sessions Efim D. Khalimsky, Yung Kong and Ralph D. George E. Strecker, Applications of category theory Kopperman, Topology in computer graphics and image processing Apri11990 Meeting in University Park, Pennsylvania lnessa Levi and W. Wiley Williams, Semigroup theory Eastern Section Peter A. McCoy, Function theoretic methods in differ Associate Secretary: W. Wistar Comfort Deadline for organizers: Expired ential equations Deadline for consideration: January 4, 1990 Lynn McLinden and Jay S. Treiman, Optimization Donald M. Davis, Algebraic topology and nonlinear analysis Hugh L. Montgomery, Analytic number theory April 1990 Meeting in Albuquerque, New Mexico Peter A. Perry, Geometric spectral and inverse spectral Far Western Section problems Associate Secretary: Lance W. Small Philip E. Protter, Markov processes and stochastic Deadline for organizers: Expired analysis Deadline for consideration: January 4, 1990 August 1990 Meeting in Columbus, Ohio March 1990 Meeting in Fayetteville, Arkansas Associate Secretary: W. Wistar Comfort Southeast Section Deadline for organizers: November 15, 1989 Associate Secretary: Joseph A. Cima Deadline for consideration: April 27, 1990 Deadline for organizers: Expired Eiichi Bannai, Thomas A. Dowling, Dijen Ray Deadline for consideration: November 21, 1989 Chaudhuri and Neil Robertson, Combinatorics Singular Geraldo Soares De Souza and Gary Sampson, Zita M. Divis and David Terman, Dynamics of bio- integral operators and related areas logical systems algebras J. Duncan and A. L. T. Patterson, Banach John S. Hsia and Warren M. Sinnott, Number theory Probability Colm A. O'Cinneide and ltrel E. Monroe, S. P. Jain and T. Rizvi, Ring theory and applications distributions of phase-type Surinder K. Sehgal and Ronald Solomon, Group theory Karl H. Hofmann and Jimmie D. Lawson, Semi-groups in geometry and analysis November 1990 Meeting in Denton, Texas Dima Khavinson, On complex function theory of one Central Section and several complex variables Associate Secretary: Andy Roy Magid David R. Morrison and Jonathan M. Wahl, Algebraic Deadline for organizers: February 15, 1990 geometry Deadline for consideration: July 16, 1990 Vladimir I. Oliker and Andrejs E. Treibergs, Geometry, physics and nonlinear PDE's Information for Organizers James G. Oxley, Combinatorics William L. Pardon and Mark A. Stern, Differential Special Sessions at Annual and Summer Meetings are geometry held under the supervision of the Program Committee for National Meetings (PCNM). They are adminis tered by the Associate Secretary in charge of that March 1990 Meeting in Manhattan, Kansas meeting with staff assistance from the Meetings and Central Section in the Society office in Provi Associate Secretary: Andy Roy Magid Editorial Departments Deadline for organizers: Expired dence. Deadline for consideration: November 21, 1989 According to the "Rules for Special Sessions" of Andrew G. Bennett, Harmonic analysis and probability the Society, Special Sessions are selected by the PCNM theory from a list of proposed Special Sessions in essentially David J. Foulis and Richard J. Greechie, Orthostruc the same manner as Invited Speakers are selected. The tures number of Special Sessions at a Summer or Annual David H. Hamilton and John F. Rossi, Geometric Meeting is limited. The algorithm that determines the function theory number of Special Sessions allowed at a given meeting, Lige Li, Partial differential equations while simple, is not repeated here, but can be found in Satyagopol Mandai, Commutative algebra "Rules for Special Sessions" on page 614 in the April Alexander G. Ramm, Inverse problems and scattering 1988 issue of Notices. theory Each Invited Speaker is invited to generate a Spe Joseph M. Rosenblatt, Ergodic theory cial Session, either by personally organizing one or Richard H. Schelp, Graph theory by having a Special Session organized by others. Pro- 1084 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions posals to organize a Special Session are sometimes Far Western Section (Pacific and Mountain) requested either by the PCNM or by the Associate Lance W. Small, Associate Secretary Secretary. Other proposals to organize a Special Ses Department of Mathematics sion may be submitted to the Associate Secretary in University of California, San Diego La Jolla, CA 92093 charge of that meeting (who is an ex-officio member e-mail: [email protected] of the committee and whose address may be found (Telephone 619-534- 3590) below). These proposals must be in the hands of the Central Section PCNM well in advance of the meeting and, in any Andy Roy Magid, Associate Secretary case, at least nine (9) months prior to the meeting at Department of Mathematics which the Special Session is to be held in order that University of Oklahoma the committee may consider all the proposals for Spe 601 Elm PHSC 423 Norman, OK 73019 cial Sessions simultaneously. Proposals that are sent e-mail: [email protected] to the Providence office of the Society, to Notices, or (Telephone 405- 325- 2052) directed to anyone other than the Associate Secretary Eastern Section will have to be forwarded and may not be received in W. Wistar Comfort, Associate Secretary time to be considered for acceptance. De)Jilrtment of Mathematics It should be noted that Special Sessions must Wesleyan University be announced in Notices in such a timely fashion Middletown, CT 06457 e-mail: [email protected] that any member of the Society who so wishes may (Telephone 203- 347-9411) submit an abstract for consideration for presentation Southeastern Section in the Special Session before the deadline for such 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 e-mail: [email protected] Meetings and can usually be accommodated. They are (Telephone 919-962- I 050) As a general rule, members who anticipate organizing Special selected by the Section Program Committee. The pro Sessions at AMS meetings are advised to seek approval at least cessing of proposals for Special Sessions for Sectional nine months prior to the scheduled date of the meeting. No Special Meetings is handled by the Associate Secretary for Sessions can be approved too late to provide adequate advance the Section, who then forwards the proposals to the notice to members who wish to participate. Section Program Committee, which makes the final selection of the proposals. Each Invited Speaker at Information for Speakers a Sectional Meeting is invited to organize a Special Session. Just as for national meetings, no Special A great many of the papers presented in Special Ses Session at a Sectional Meeting may be approved so sions at meetings of the Society are invited papers, but late that its announcement appears past the deadline any member of the Society who wishes to do so may after which members can no longer send abstracts for submit an abstract for consideration for presentation consideration for presentation in that Special Session. in a Special Session, provided it is received in Prov The Society reserves the right of first refusal for idence prior to the special early deadline announced the publication of proceedings of any Special Ses above and in the announcements of the meeting at sion. These proceedings appear in the book series which the Special Session has been scheduled. Con Contemporary Mathematics. tributors should know that there is a limitation in More precise details concerning proposals for and size of a single special session, so that it is sometimes organizing of Special Sessions may be found in the true that all places are filled by invitation. Papers "Rules for Special Sessions" or may be obtained from not accepted for a Special Session are considered as any Associate Secretary. ten-minute contributed papers. Abstracts of papers submitted for consideration for presentation at a Special Session must be received by Send Proposals for Special Sessions to the the Providence office (Editorial Department, American Associate Secretaries Mathematical Society, P. 0. Box 6248, Providence, The programs of sectional meetings are arranged by the Associate RI 02940) by the special deadline for Special Sessions, Secretary for the section in question: which is usually three weeks earlier than the dead- OCTOBER 1989, VOLUME 36, NUMBER 8 1085 Invited Speakers and Special Sessions line for contributed papers for the same meeting. The be sure to specify whether they want the plain TE)(, Council has decreed that no paper, whether invited or A.MS-TEX, or the g\TEX 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 electron tion of joint authorship may be accepted, provided ically via the Internet to [email protected]. no individual speaks more than once. An author can Requesting the files electronically will likely be the speak by invitation in more than one Special Session fastest and most convenient way, but users may also at the same meeting. obtain the package on IBM or Macintosh diskettes, An individual may contribute only one abstract by available free of charge by writing to: Rosanne Gra title in any one issue of Abstracts, but joint authors natiero, American Mathematical Society, Publications are treated as a separate category. Thus, in addition Division, P.O. Box 6248, Providence, RI 02940, USA. to abstracts from two individual authors, one joint When requesting the Abstracts package, users should abstract by them may also be accepted for an issue. Some Mathematical Questions in Biology: 1····· I MODELS IN POPULATION BIOLOGY ••••••••••••· = Alan Hastings, Editor difference equations form a common theme. The topics (Lectures on Mathematics in the Life Sciences, Volume 20) covered are cultural evolution, multilocus population genetics, spatially structured population genetics, chaos and the Population biology has had a long history of mathematical dynamics of epidemics, and the dynamics of ecological modeling. The 1920s and 1930s saw major strides with communities. the work of Lotka and Volterra in ecology and Fisher, Haldane, and Wright in genetics. In recent years, much more 1980 Mathematics Subject Classifications: 92A 10, 92A 15 sophisticated mathematical techniques have been brought ISBN 0-8218-1170-3, LC 89-15119 ISSN 0075-8523 to bear on questions in population biology. Simultaneously, 136 pages (softcover), September 1989 advances in experimental and field work have produced a Individual member $17, List price $28, wealth of new data. While this growth has tended to fragment Institutional member $22 the field, one unifying theme is that similar mathematical To order, please specify LLSCI/20NA questions arise in a range of biological contexts. All prices subject to change. Shipment will be made by surface. This volume contains the proceedings of a symposium on For air delivery add, 1st book $5, each additional book $3, Some Mathematical Questions in Biology, held in Chicago in maximum $100. Prepayment required. Order from American 1987. The papers all deal with different aspects of population Mathematical Society, P.O. Box 1571, Annex Station, Provi biology, but there are overlaps in the mathematical techniques dence, RI 02901-1571, or call toll free 800-566-7774 to charge used; for example, dynamics of nonlinear differential and with VISA or MasterCard. 1086 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences in the Mathematical Sciences University of Massachusetts at Amherst, MA, June 7 to July 4, 1990 The 1990 Joint Summer Research Conferences in the Summer Research Conference Coordinator, Meetings Mathematical Sciences will be held at the University Department, American Mathematical Society, Post of Massachusetts at Amherst, from June 7 to July 4. Office Box 6248, Providence, RI 02940 or by E-Mail: It is anticipated that the series of conferences will [email protected] on the Internet. be supported by grants from the National Science Please type or print the following: Foundation and other agencies. 1. Title and dates of conference desired There will be six conferences in six different areas of mathematics. The topics and organizers for the 2. Full name address conferences were selected by the AMS-IMS-SIAM 3. Mailing 4. Telephone number and area code for office and Committee on Joint Summer Research Conferences in home the Mathematical Sciences. The selections were based of AMS, IMS, or SIAM? If AMS, please on suggestions made by the members of the committee 5. Member member code and individuals submitting proposals. The committee give scientific background relevant to the topic of considered it important that the conferences represent 6. Your diverse areas of mathematical activity, with emphasis the conference assistance requested; please estimate cost on areas currently especially active, and paid careful 7. Financial attention to subjects in which there is important of travel and if interested interdisciplinary activity at present. 8. Indicate if support is not required in attending even if support is not offered. The conferences are similiar in scientific structure to those held throughout the year at Oberwolfach. The deadline for receipt of applications is February These conferences are intended to complement the 23, 1990. Requests for invitations will be forwarded Society's program of annual Summer Institutes and to the Organizing Committee for each conference Summer Seminars, which have a larger attendance and for consideration after February 23, 1990. Applicants are substantially broader in scope. The conferences are selected will receive formal invitations and notifica research conferences, and are not intended to provide tion of financial assistance from the AMS. Requests an entree to a field in which a participant has not received past the deadline will be returned. Funds avail already worked. able for these conferences are limited and individuals It is expected that funding will be available for who can obtain support from other sources should a limited number of participants in each conference. do so. Women and members of minority groups are Others, in addition to those funded, will be welcome, encouraged to apply and participate in these confer within the limitations of the facilities of the campus. ences. In the spring a brochure will be mailed to all who Any questions concerning the scientific portion of are invited to attend the conferences. The brochure the conference should be directed to the chair or any will include information on room and board rates, the member of the Organizing Committee. residence and dining hall facilities, travel and local The Joint Summer Research Conferences in the information and a Residence Housing Form to use Mathematical Sciences are under the direction of to request on-campus accommodations. Information the AMS-IMS-SIAM Committee on Joint Summer on off-campus housing will also be included in the Research Conferences in the Mathematical Sciences. brochure. Participants should make their own housing The following Committee members chose the topics and travel arrangements. Each participant will be for the 1990 conferences: William B. Arveson, John required to pay nominal registration and social fees. A. Bums, Martin Golubitsky, Daniel J. Kleitman, Those interested in attending one of the confer Anthony W. Knapp, Ingram Olkin, Mary Ellen Rudin, ences should send the following information to the Stephen Simpson and Gregg J. Zuckerman. OCTOBER 1989, VOLUME 36, NUMBER 8 1087 Joint Summer Research Conferences Thursday, June 7 to Wednesday, June 13 commutative algebra of operators, the infinitesimal Probability models and statistical analysis deformation being specified in terms of a Poisson for ranking data bracket on the original algebra. Perhaps the first ex ample is the Moyal quantization (deformation) of the MICHAEL A. FLIGNER (The Ohio State University), algebra of smooth functions on a symplectic mani Co-Chair, fold. The formulas involved have been abstracted and JosEPH S. VERDUCCI (The Ohio State University), extended to coalgebras and to Hopf algebras. Co-Chair In the past decade, a new source of examples has Probability models for rankings have been derived come from the physics of completely integrable sys from several sources including: tems and from the inverse scattering method, calling ( 1) the rank order of jointly distributed random attention, in particular, to the Yang- Baxter equations. variables, Recent work, particularly in the USSR, has revealed (2) models for paired comparisons, the relation between these equations and "quantum (3) decompositions of metrics on the permutation groups", which are not groups at all but deformations group, of certain classical Hopf algebras, some coming from (4) linear representations of the permutation group, algebraic groups and some from closely related Lie and algebras. Recently, homological machinery has helped (5) regression models onto "unfolding" surfaces. to determine what kinds of deformations are possible. Many of the models may be motivated by physical A serious problem in this rapidly developing area processes related to disciplines as diverse as psychol is the language gap between those who have come to ogy, business, medicine, zoology, etc. Additionally, it from the different directions of physics, analysis, some of the basic models can be extended to incorpo and algebra. Part of the purpose of this conference rate covariates, either associated with the items being is to narrow that gap with various expository talks. ranked or with the individuals making the rankings. Workers in the US and USSR seem, moreover, to The conference will address both probabilistic prop have approached the topic with different but comple erties of various models and procedures for statistical mentary mathematical methods, the relations between inference. Many related topics will also be discussed, which will be explored. including computer algorithms and packages for im Members of the Organizing Committee: David A. plementing the methodologies. Vogan, Jr. (Massachusetts Institute of Technology) Members of the Organizing Committee: Persi Di and Yurii I. Manin (University of Moscow). aconis (Harvard University), Paul Feigin (Technion Israel Institute of Technology) and Colin Mallows Thursday, June 21 to Wednesday, June 27 (AT&T Bell Labs). Strategies for sequential search and selection Thursday, June 7 to Wednesday, June 13 in real time Inverse scattering on the line THOMAS S. FERGUSON (University of California, Los Co-Chair DAVID SATTINGER (University of Minnesota, Angeles), Minneapolis), Chair STEPHEN M. SAMUELS (Purdue University), Co-Chair Description of conference will appear in the The focus of this conference is on problems related November issue of the Notices. to sequential observation of random variables and selection of actions in real time. There has been a Thursday, June 14 to Wednesday, June 20 continuing development in both breadth and depth Deformation theory of algebras and quantization of the research in a number of areas that contributes with applications to physics to this subject. It is hoped that the conference will clarify the relations and promote interaction among MURRAY GERSTENHABER (University of the areas. These topics include the following: Pennsylvania), Co-Chair 1. Generalizations of the classical secretary prob JAMES D. STASHEFF (University of North Carolina), lems, including partial information models, backward Co-Chair solicitation, unknown population size, random arrival One of the oldest forms of algebraic quantiza time, etc. tion amounts to the study of deformations of a 2. The more general area of discrete stopping rule commutative algebra of classical observables to a non- problems such as selling an asset, the burglar problem, 1088 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences detecting a changepoint, the proofreading problem, Members of the Organizing Committee: Ron Don etc. agi (University of Pennsylvania) and Hershel M. 3. Problems of sequential search for a lost object Farkas (Hebrew University of Jerusalem). and of allocation of search effort. 4. Sequential allocation of experiments including Thursday, June 28 to Wednesday, July 4 bandit problems as the most important case. 5. Multi-criteria problems involving the theory of Logic, local fields, and subanalytic sets choice in sequential problems. Lou VAN DEN DRIES (University of Illinois at 6. Competitive versions or game theoretic models Urbana-Champaign), Chair of the above problems. This concerns applications oflogic (in combination 7. Prophet inequalities. with other ideas) to algebraic and analytic objects 8. Records and extreme values. defined over complete fields. The subject originates The conference will bring together leading re with Tarski's elimination theory for real closed fields searchers in these areas, allowing those from Japan ( 1948). One particular corollary, the so-called Tarski and the Soviet Union to interact with those from the Seidenberg projection property of semi-algebraic sets, Western nations. is widely known and used. In the sixties, Ax & Members of the Organizing Committee: Boris A. Kochen and Ersov extended much of Tarski's work Berezovskiy (Institute of Control Sciences, USSR), to nonarchimedean complete fields of characteristic F. Thomas Bruss (Facultes Universitaires de Namur, 0. Their main result is a reduction, uniform for all Belgium, and University of California, Los Angeles) Henselian fields of equicharacteristic 0, of a given and Lawrence A. Shepp (AT&T Bell Laboratories). elementary statement about such fields to elementary statements about their residue field and value group. Ax and Kochen gave a remarkable application to forms over p-adic fields. June 27 Thursday, June 21 to Wednesday, In later influential papers by P.J. Cohen, A. Mac Schottky Problems intyre and J. Denef, emphasis shifted from analyzing LEON EHRENPREIS (Temple University), Co-Chair individual statements to the study of statements de ROBERT C. GUNNING (Princeton University), pending on parameters, using techniques of quantifier Co-Chair elimination and cell decomposition. This greatly ex tended the range of applications, as shown by Denef's The Schottky problem is that of determining which striking proof of the rationality of Poincare series principally polarized Abelian varieties are the Jacobi of p-adic algebraic sets ( 1984). More recently p-adic varieties of compact Riemann surfaces, or equiva analytic sets could be handled similarly by means of lently, of determining which matrices in the Siegel "piecewise uniform Weierstrass preparation for power upper half space are the period matrices of compact series with parameters" (Denef-van den Dries, 1988). Riemann surfaces of genus g. There are a number What emerges is a theory of subana1ytic sets over ar of approaches to this problem, and there has been a bitrary complete fields of characteristic 0, generalizing considerable amount of research undertaken in this and simplifying the classical theory over the reals, due area in the recent past. The goal of this confer to Lojasiewicz, Gabrielov, Hironaka and Hardt. ence is to reexamine the Schottky problem in the The aim of the conference is to survey these light of current research, to seek additional syntheses developments, stressing algebraic, arithmetic and ana of the various approaches that have been taken to lytic applications, for example to Poincare series, zeta the problem, and to consider anew the fundamental functions of nilpotent groups, Lojasiewicz inequali mathematical structures that underlie these various ap ties, polynomials with few terms, and to stimulate proaches. There are some very fundamental properties further work in this area. Open problems, like the of Riemann surfaces involved in these investigations characteristic p case, will be discussed. and some remarkably interesting open problems that Members of the Organizing Committee: Jan Denef remain. (University of Leuven, Belgium), Leonard Lipshitz (Purdue University), and Angus Macintyre (Oxford University, England). OCTOBER 1989, VOLUME 36, NUMBER 8 1089 1989 AMS Elections Candidates Reports and Communications section of the September 1989 issue of OFFICERS Notices for the list of current members of the Council and Board of President Elect* Trustees. Members are requested to write their suggestions for such Michael Artin candidates in the appropriate spaces below. REPLACEMENT BALLOTS Vice President (two to be elected) James G. Arthur James B. Serrin This year ballots for the AMS election will be mailed September I 0, Lenore Blum Dennis P. Sullivan 1989, or within a day or two thereafter. The deadline for receipt of Phillip A. Griffiths ballots in Providence is November 10, 1989. There has been a small but recurring and distressing problem concerning members who state that they have not received ballots Associate Secretaries* in the annual election. It occurs for several reasons, including fail Andy Roy Magid Lance W. Small ure of local delivery systems on university or corporate properties, (Central) (Far Western) failure of members to give timely notice of changes of address to the Providence office, failures of postal services, and other human Member-at-Large of the Council (five to be elected) errors. Sheldon Axler Charles Herbert Clemens To help alleviate this problem, the following replacement proce Joan S. Birman Amassa C. Fauntleroy dure has been devised: A member who has not received a ballot by James W. Cannon Edwin E. Floyd October I 0, 1989, or who has received a ballot but has accidentally Alexandre J. Chorin Carl Pomerance spoiled it, may write after that date to the Secretary of the AMS, Post Frank H. Clarke Shing-Tung Yau Office Box 6248, Providence, RI 02940, asking for a second ballot. The request should include the individual's member code and the Board of Trustees (one to be elected) address to which the replacement ballot should be sent. Immediately Ramesh A. Gangolli John C. Polking upon receipt of the request in the Providence office, a second ballot, which will be indistinguishable from the original, will be sent by first NOMINATING COMMITTEE FOR 1990 class or air mail. It must be returned in an inner envelope, which (Preferential Ballot, three to be elected) will be supplied, on the outside of which is the following statement Sylvain E. Cappel! Ray A. Kunze to be signed by the member: Robert M. Hardt Paul C. Roberts The ballot in this envelope is the only ballot that I am submitting Barbara Lee Keyfitz Robert F. Williams in this election. I understand that if this statement is not correct then no ballot of mine will be counted. EDITORIAL BOARDS COMMITTEE FOR 1990 (Preferential Ballot, two to be elected) signature Linda Keen Andrew M. Odlyzko Carlos E. Kenig Barry Simon Although a second ballot will be supplied on request and will be sent *Uncontested offices by first class or air mail, the deadline for receipt of ballots will not be extended to accommodate these special cases. SUGGESTIONS FOR 1990 NOMINATIONS Election Information Council and Board of Trustees The ballots for election of members of the Council and Board of Vice President (I) Trustees of the Society for 1990 will be mailed on or shortly after September 10, in order for members to receive their ballots well in advance of the November I 0 deadline. Prior to casting their ballots Associate Secretaries (2) members are urged to consult the following articles and sections of the Bylaws of the Society: article I, section I; article II, sections I, 2; article III, sections I, 2, 3; article IV, sections I, 2, 4; article VII, sections I, 2, 5. The complete text of the Bylaws appears on pages Members-at-large of the Council (5) 1155-1160 of the November 1987 issue of Notices. A list of the members of the Council and Board of Trustees serving terms during 1989 appears in the AMS Reports and Communications section of the September 1989 issue of Notices. SUGGESTIONS FOR 1990 NOMINATIONS Each year the members of the Society are given the opportunity to Member of the Board of Trustees (I) propose for nomination the names of those individuals they deem both qualified and responsive to their views and needs as part of the mathematical community. Candidates will be nominated by the The completed form should be addressed to AMS Nominating Com Council to fill positions on the Council and Board of Trustees to mittee, Post Office Box 6248, Providence, RI 02940, to arrive no replace those whose terms expire December 31, 1990. See the AMS later than November 10, 1989. 1090 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) 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, Instituto Per Le Applicazioni Del Cal colo, Rome, Italy. (Jan. 1989, p. 63) 1989-1990. Academic Year Devoted to Hyperbolic Geometry and Quasiconformal Mappings, Mittag-Leffler Institute, Djur of interest to sho1m, Sweden. (Dec. 1988, p. 1584) THIS SECTION contains announcements of meetings and conferences some segment of the mathematical public, including ad hoc, local, or regional meetings, * 1989-1990. Special Year in Geometry, and meetings or symposia devoted to specialized topics, as well as announcements University of Maryland, College Park, of regularly scheduled meetings of national or international mathematical organizations. MD. (Information on meetings of the Society, and on meetings sponsored by the Society, will found inside the front cover.) of Mary be SPONSORS: The University AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, land and the National Science Foun and specifies the place, date, subject (when applicable), and the speakers; a second dation. full announcement will be published only if there are changes or necessary additional CONFERENCE THEMES AND INFORMA information. Once an announcement has appeared, the event will be briefly noted in each TION: Activities besides the "Folia issue until it has been held and a reference will be given in parentheses to the month, tions conference in memory of Bruce year, and page of the issue in which the complete information appeared. Asterisks (*) Reinhart" (Jul./ Aug. 1989, p. 762) mark those announcements containing new or revised information. and the annual "Geometry Festival" IN GENERAL, announcements of meetings and conferences held in North America carry will include workshops on the topics: only date, title of meeting, place of meeting, names of speakers (or sometimes a general for abstracts or contributed papers, and source "Spaces of Riemannian manifolds" statement on the program), deadlines of further information. Meetings held outside the North American area may carry more - contact K. Grove, 301-454-7075; detailed information. In any case, if there is any application deadline with respect to "Moduli spaces" - contact B. Gold participation in the meeting, this fact should be noted. All communications on meetings man, 301-454-2929; "Cyclic Homol and conferences in the mathematical sciences should be sent to the Editor of Notices, ogy" - contact J. Schafer, 301-454- care of the American Mathematical Society in Providence. 3535. DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged January !-December 23, 1989. Math to submit information for these listings early enough to allow them to appear in more than ematisches Forschungsinstitut Oberwol one issue of Notices prior to the meeting in question. To achieve this, listings should be fach (Weekly Conferences), Federal Re received in Providence SIX MONTHS prior to the scheduled date of the meeting. public of Germany. (Apr. 1988, p. 629 and Nov. 1988, p. 1381) 16-20. Sixth World Congress on Medical * 20-24. Hamiltonian Systems, Transfor Informatics, Beijing, China. (Feb. 1989, mation Groups, and Special Transform October 1989 p. 182) Methods, Montreal, Canada. 15-18. Fourth International Workshop on 16-20. Workshop: Patterns and Dynam INFORMATION: F. H. Clarke, CRM, High-Level Synthesis, Kennebunkport, ics in Reactive Media, Institute for Math Universite de Montreal, CP 6128-A, ME. (Dec. 1988, p. 1590) ematics and its Applications, Minneapo Montreal, Quebec, H3C 3J7, Canada. 15-21. Geometrie, Oberwolfach, Federal lis, MN. (Feb. 1989, p. 182) 20-26. Hamiltonian Systems, Trans Republic of Germany. (Jul./ Aug. 1989, 17-20. Hyperfunctions and Differential Groups and Special Trans p. 763) Equation, Research Institute for Mathe formation Centre de Recherches matical Sciences, Kyoto University, Japan. form Methods, 16-18. Second International Conference (CRM) Universite de (Jul./ Aug. 1989, p. 763) Mathematiques on Data and Knowledge Systems for Man Montreal. (Please note date change from In ufacturing and Engineering, National 19-20. Workshop on Large-Scale Numer Jan. 1989, p. 70) stitute of Standards and Technology, ical Optimization, Mathematical Sciences 21-22. Eastern Section Meeting of the Gaithersburg, MD. (Apr. 1989, p. 495) Institute, Cornell University, Ithaca, NY. AMS, Stevens Institute of Technology, the (May /Jun. 1989, p. 599) 16-20. Workshop on Set Theory and Hoboken, NJ. Continuum, Mathematical Sciences Re 19-21. Journees Mathematiquesflnforma search Institute, Berkeley, CA. (May/Jun. tique, Marseille, France. (Jul./ Aug. 1989, INFORMATION: W. Drady, AMS, P.O. 1989, p. 599) p. 763) Box 6248, Providence, RI 02940. OCTOBER 1989, VOLUME 36, NUMBER 8 1091 Meetings and Conferences 22-28. Linear Operators and Applica 30-December l. College on Differen University, St. Cloud, MN. (Jul./ Aug. tions, Oberwolfach, Federal Republic of tial Geometry, Trieste, Italy. (Mar. 1989, 1989, p. 764) Germany. (Jul./ Aug. 1989, p. 763) p. 313) 12-15. National Computer Graphics As 22-28. Second Osterreichisches Sym sociation Mapping and Geographic Infor posium Zur Geschichte der Mathematik, mation Systems, Los Angeles, CA. (Apr. November 1989 Neuhofen a.d. Ybbs, Austria. (Jul./ Aug. 1989, p. 494) 1989, p. 763) 2-4. Second Annual Conference on Tech 13-17. Workshop on ·Logic Related to 23-26. Beijing International Confer nology in Collegiate Mathematics, Ohio Computer Science and Programming Lan ence on System Simulation and Scientific State University, Columbus, OH. (Mar. guage Theory, Mathematical Sciences Re Computing, Beijing, China. (Mar. 1989, 1989, p. 313) search Institute, Berkeley, CA. (MayfJun. p. 313) 2-5. Third International Conference on 1989, p. 600) Expert Systems in Law, Florence, Italy. 13-17. Workshop: Dynamical Issues in * 24-26. IEEE Computer Society Design, (MayfJun. 1989, p. 599) Combustion Theory, Institute for Mathe Office and Personal Workstation Sympo 3-5. Conference on Low Dimensional matics and its Applications, Minneapolis, sium and Tutorials, Laurel, MD. Topology and Combinatorial Group The MN. (Dec. 1988, p. 1591) INFORMATION: C. Daly, Johns Hop ory, SUNYA, Albany, NY. (Sep. 1989, 13-17. Supercomputing '89, Reno, NV. kins University, Applied Physics Lab p. 913) (Jul./Aug. 1989, p. 764) oratory, Johns Hopkins Rd., Laurel, * 4-5. Twenty-sixth Midwest Partial Dif 15-l 7. Geometry of Manifolds, Research MD 20707-6099; 301-953-3565. ferential Equations Seminar, Argonne, Institute for Mathematical Sciences, Ky Illinois. oto University, Japan. (Jul./ Aug. 1989, Appli 25-27. Evolution Equations and INVITED SPEAKERS: R. Beals, J. Bona, p. 764) Research cations to Nonlinear Problems, G.-Q. Chen, C. Coffman, F. Gesztezy, 17-20. Workshop on Classical and Quan for Mathematical Sciences, Ky Institute W.-M. Ni, B. Peletier, P. Takac. tum Transport in Hamiltonian Systems, oto University, Japan. (Jul./ Aug. 1989, INFORMATION: M. K. Kwong, Math Mathematical Sciences Institute, Cornell 764) p. ematics and Computer Science Di University, Ithaca, NY. (MayfJun. 1989, 25-28. Workshop on Numerical Meth vision, Argonne National Laboratory, p. 600) ods for Elliptic Systems, Espoo, Finland. Argonne, IL 60439, 312-972-7486 18-19. Far Western Section Meeting of (MayfJun. 1989, p. 599) ([email protected] ). 26-28. The Riccati Equation In Control, the AMS, University of California, Los Systems and Signals, Villa Gallia, Como, 4-8. Workshop on Geometric and Alge Angeles, CA. Italy. (Jan. 1989, p. 70) braic Integration Algorithms, Mathemati INFORMATION: W. Drady, AMS, P.O. cal Sciences Institute, Cornell University, Box 6248, Providence, RI 02940. 27-28. Central Section Meeting of the Ithaca, NY. (MayfJun. 1989, p. 599) AMS, Ball State University, Muncie, IN. 5-ll. Fastringe und Fastkorper, Ober 19-25. Random Partial Differential Equa (May /June 1988, p. 732) Germany. wolfach, Federal Republic of tions, Oberwolfach, Federal Republic of INFORMATION: W. Drady, AMS, P.O. (Jul./Aug. 1989, p. 764) Germany. (Jul./Aug. 1989, p. 764) Box 6248, Providence, RI 02940. 6-8. On the Structure of Solutions to 20-24. Seminaire Sud-Rhodanien de Ge Research Partial Differential Equations, ometrie Differentielle, Marseille, France. Ky 27-28. Fourth Annual Pi Mu Epsilon Re Institute for Mathematical Sciences, (Jul./Aug. 1989, p. 764) gional Undergraduate Mathematics Con oto University, Japan. (Jul./ Aug. 1989, p. 764) 26-December 2. Methoden und Ver ference, De Pere, WI. (Sep. 1989, p. 913) fahren der Mathematischen Physik, Ober 29-November 4. Computational Methods 6-9. International Conference on wolfach, Federal Republic of Germany. Clara, CA. in Solid Mechanics, Oberwolfach, Fed Computer-Aided Design, Santa (Jul./ Aug. 1989, p. 764) (Apr. 1989, p. 495) eral Republic of Germany. (Mar. 1989, 27-29. Computer Algebra and Its Ap Applied Ge p. 313) 6-10. SIAM Conference on plication to Investigations for Mathemat 30-November l. Thirtieth Foundations ometry, Tempe, AZ. (Nov. 1988, p. 1388) ics, Research Institute for Mathemati of Computer Science (FOCS), Research 6-l 0. SIAM Conference on Geometric cal Sciences, Kyoto University, Japan. Park, NC. (Sep. 1989, p. 913) Design, Tempe, AZ. (Mar. 1989, p. 314) (Jul./Aug. 1989, p. 764) 30-November 2. Workshop on Ho 8-10. Conference for Mathematics in 27-29. The Recent Developments of High motopy Theory, Mathematical Sciences Chemistry, College Station, TX. (Jul./ Aug. Technology and Mathematical Science Research Institute, Berkeley, CA. (Mar. 1989, p. 764) (II), Research Institute for Mathemat 1989, p. 313) l 0-l I. Eighteenth Midwest Differential ical Sciences, Kyoto University, Japan. 30-November 2. Differential Analysis Equations Conference, Southern Illinois (Jul./ Aug. 1989, p. 765) and Differential Topology, Research In University, Carbondale, IL. (Apr. 1989, 29-December l. Numerical Analysis and stitute for Mathematical Sciences, Ky p. 495) Scientific Computing, Research Institute oto University, Japan. (Jul./ Aug. 1989, l 0-ll. Conference on Women in Mathe for Mathematical Sciences, Kyoto Uni p. 764) matics and the Sciences, St. Cloud State versity, Japan. (Jul./ Aug. 1989, p. 765) 1092 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 17-23. Theory and Numerical Meth 8-13. Workshop on Variational Meth ods for Initial-Boundary Value Problems, ods in Hamiltonian Systems and Elliptic December 1989 Oberwolfach, Federal Republic of Ger Equations, L'Aquila, Italy. (Please note 3-9. Wiener-Hopf-Probleme, Topelitz many. (Mar. 1989, p. 314) changes from Sep. 1989, p. 914) Anwendungen, Oberwol Operatoren und 27-31. Holiday Symposium on Braids PROGRAM: The workshop will consist of Germany. fach, Federal Republic and Knots, New Mexico State University, of 1-hour invited lectures which sur p. 765) (Jul./ Aug. 1989, Las Cruces, NM. (Sep. 1989, p. 914) vey the field and/or describe current 4-6. 1989 Winter Simulation Confer research. Shorter 15-20 minutes com ence, Washington, DC. (MayfJun. 1989, munications are welcome, as well as p. 600) informal discussions on open ques 1990. IMACS International Workshop 4-6. Studies on Decision Theory and tions, future directions of research, on Massively Parallel Methods in Com Their Related Topics, Research Institute etc. putational Physics, Boulder, Colorado. for Mathematical Sciences, Kyoto Uni CALL FOR PAPERS: The organizing (Sep. 1989, p. 914) versity, Japan. (Jul./ Aug. 1989, p. 765) committee should be contacted by 1990. IMACS Conference on Computer * 4-6. First International Conference on participants before Oct. 30, 1989. Aided Design, Yugoslavia. (Sep. 1989, Deductive and Object-Oriented Databases, People intending to give a short talk p. 914) Kyoto, Japan. should send a summary before Oct. 15, 1989. INFORMATION: W. Kim, MCC, 3500 W. Balcones Ctr. Dr., Austin, TX January 1990 * 9-13. Stable Processes and Related Top- 78759; Phone: 512-338-3439. ics Workshop, Ithaca, NY. l-6. Zeitreihenanalyse, Oberwolfach, PuRPOsE: The purpose of the work 4-7. Research on Complex Analytic Ge Federal Republic of Germany. (Mar. shop is to bring together researchers ometry and Related Topics, Research In 1989, p. 314) stitute for Mathematical Sciences, Ky working on different aspects of the on Arti oto University, Japan. (Jul./ Aug. 1989, * 3-5. International Symposium area to discuss both the state of the p. 765) ficial Intelligence and Mathematics, Fort art and future directions of the math Lauderdale, FL. 4-8. Fifth Aerospace Computer Secu ematical theory of stable processes rity Applications Conference, Tucson, AZ. PuRPOsE: The symposium is the first and their statistical analysis. (MayfJun. 1989, p. 600) of a biennial series featuring applica CONFERENCE TOPICS: Dependence structure of stable laws, sample paths 6-9. Algebraic Number Theory, Research tions of mathematics in artificial intel of stable processes, self-similar stable Institute for Mathematical Sciences, Ky ligence as well as artificial intelligence processes, multiple stable integrals, oto University, Japan. (Jul./ Aug. 1989, techniques and results in mathemat extrema of stable processes. p. 765) ics. There has always been a strong relationship between the two disci ORGANIZERS: G. Samorodnitsky 9. Boston Celebration of the ASA150 plines, however, the contact between (Chair), Cornell Univ.; S. Cambanis, Sesquicentennial, Boston, MA. (Sep. 1989, practioners of each has been lim Univ. of North Carolina; M. Taqqu, p. 914) ited, partly by the lack of a forum in Boston Univ. 10-16. Asymptotic Methods for which the relationship could grow and INVITED SPEAKERs: E. Gine, R. LeP Computer-Intensive Procedures in Statis flourish. This symposium represents a age, J. Levy, W. Linde, M. Maejima, tics, Oberwolfach, Federal Republic of small step towards improving contacts V. Mandrekar, M. Marcus, D. Mason, Germany. (Mar. 1989, p. 314) and promoting cross-fertilization be J. Mijnheer, S. Rachev, B. Rajput, I. 11-13. Fourth SIAM Conference on Par tween the two areas. Rosinski, J. Szulga, W. Vervaat, A. allel Processing for Scientific Computing, SPONSORs: Florida Atlantic Univ., and Weron, W. Woyczynski, J. Yukich. Chicago, IL. (Mar. 1989, p. 314) IJCAI. INFORMATION: D. Drake, Mathemati 11-14. Number Theory- Studies Related INVITED SPEAKERs: D. Mumford, Har cal Sciences Institute, Cornell Univer to Automorphic Forms, Research Institute vard Univ. (Keynote speaker); M. sity, 201 Caldwell Hall, Ithaca, NY for Mathematical Sciences, Kyoto Uni Davis, Courant Institute; Z. Manna, 14853-2602, 607-255-7740. versity, Japan. (Jul./ Aug. 1989, p. 765) Stanford Univ.; D. McDermott, Yale 10-13. International Conference on Dif Univ.; A. Robinson, Syracuse Univ.; 12-14. Second Australian Supercomputer ferential Equations and Applications to L. Valiant, Harvard Univ. Conference, University of Wollongong, Biology and Population Dynamics, Har INFORMATION: F. Hoffman, Dept. of NSW, Australia. (Sep. 1989, p. 914) vey Mudd College, Claremont, CA. (Sep. Math., Florida Atlantic Univ., Boca * 13-15. Twenty-eighth IEEE Conference 1989, p. 914) on Decision and Control, Tampa, FL. Raton, FL 33431, Tel: 407-367-3345; email: [email protected] or 14-20. Nonlinear Evolution Equations, INFORMATION: L. Shaw, Dept. of Elec golumbic@israearn. bitnet. Solitons and the Inverse Scattering Trans trical Engineering and Computer Sci form, Oberwolfach, Federal Republic of ence, Polytechnic University, 333 Jay 7-13. Mathematische Optimierung, Ober Germany. (Mar. 1989, p. 314) St., Brooklyn, NY 11201; 718-260- wolfach, Federal Republic of Germany. 15-26. Workshop on Composite Me 3590. (Mar. 1989, p. 314) dia and Homogenization Theory, Inter- OCTOBER 1989, VOLUME 36, NUMBER 8 1093 Meetings and Conferences national Centre for Theoretical Physics, sity of Berlin, Federal Republic of Ger PROGRAM: Topics expected to be em Trieste, Italy. (May I Jun. 1989, p. 600) many. (Jul./ Aug. 1989, p. 765) phasized include wave phenomena, 16-17. AMS Short Course on Mathe 11-15. The Twenty-sixth Australian Ap spectral methods, scattering theory, matical Questions in Robotics, Louisville, plied Mathematics Conference, Coolan dynamical systems, critical point the KY. gatta, Queensland, Australia. (Sep. 1989, ory, nonlinear analysis and related p. 915) applications to the equations of math INFORMATION: M. Foulkes, AMS, P.O. ematical physics. Box 6248, Providence, RI 02940. 11-1 7. Funktiontheorie, Oberwolfach, Federal Republic of Germany. (Mar. INVITED SPEAKERS: J. Hale, M. 17-20. Joint Mathematics Meetings, 1989, p. 315) Lapidus, E. Lieb, P.-L. Lions, R. New Louisville, KY. (Including the annual ton, P. Rabinowitz, K. Schmitt, B. 15-20. American Association for the Simon, J. Sjostrand. meetings of the AMS, AWM, MAA and Advancement of Science Annual Meeting, NAM). INFORMATION: C. Bennewitz, Y. Saito, New Orleans, LA. (Sep. 1989, p. 915) J. Ward, Dept. of Math., University INFORMATION: H. Daly, AMS, P.O. 18-24. Mathematische Modelle in Der of Alabama at Birmingham, Birming Box 6248, Providence, RI 02940. Biologie, Oberwolfach, Federal Republic ham, Alabama 35294, 205-934-2154. of Germany. (Mar. 1989, p. 315) 21-27. Modelltheorie, Oberwolfach, Fed 20-22. Association for Computing Ma 16-1 7. Central Section Meeting of the eral Republic of Germany. (Mar. 1989, chinery 1990 Computer Science Confer p. 314) AMS, Kansas State University, Manhat ence, Washington, D.C. (May I Jun. 1989, tan, KS. 22-24. ACM/SIAM Symposium on Dis p. 601) INFORMATION: W. Drady, AMS, P.O. crete Algorithms, San Francisco, CA. 22-23. Twenty-first SIGCSE Technical Box 6248, Providence, Rl 02940. (Sep. 1989, p. 915) Symposium, Washington, D.C. (May/Jun. 22-26. Workshop on Applications of Al 1989, p. 601) 18-24. Masstheorie, Oberwolfach, Fed gebraic Topology to Geometry and Analy 25-March 3. Eigenwertaufgaben In Natur sis, Mathematical Sciences Research In eral Republic of Germany. (Mar. 1989, Und lngenieurwissensachaften Und Ihre p. 315) stitute, Berkeley, CA. (MayfJun. 1989, Numerische Behandlung, Oberwolfach, p. 600) Federal Republic of Germany. (Mar. * 18-24. Third Centenary Celebration of 28-February 3. Regelungstheorie, Ober 1989, p. 315) the Mathematische Gesellschaft in Ham wolfach, Federal Republic of Germany. 26-March 2. IEEE Computer Society burg, BundesstraBe, Hamburg. (Please (Mar. 1989, p. 314) COMPCON Spring '90, San Francisco, note changes from Jan. 1989, p. 71) 29-February 16. Second College on Vari CA. (Sep. 1989, p. 915) INVITED SPEAKERS: K.-R. Biermann ational Problems in Analysis, Interna (Berlin, DDR); J.S. Birman (New tional Centre for Theoretical Physics, York, NY); P.L. Butzer (Aachen); Trieste, Italy. (May I Jun. 1989, p. 600) March 1990 E.W. Dijkstra (Austin, TX); S. Gel 4-10. Interval Methods for Numerical bart (Rehovot); G.H. Golub (Stan February 1990 Computation, Oberwolfach, Federal Re ford, CA); K.P. Hadeler (Tiibingen); public of Germany. (Mar. 1989, p. 315) J. Hartmanis (Ithaca, NY); S. Helga * 3. Eighty-seventh Ontario Mathematics son (Cambridge, MA); F. Hirzebruch Meeting, Ottawa, Ontario, Canada. 5-7. SIAM Conference on Applied Prob ability in Science and Engineering, New (Bonn); J. Hoschek (Darmstadt); K. CALL FOR PAPERS: Papers to be sent Orleans, LA. (Nov. 1988, p. 1389) Jacobs (Erlangen); A. Jaffe (Cam to: A.B.M. Lutful Kabir. bridge, MA); V. Kac (Cambridge, 5-7. Symposium on Symbolic Computa MA); K. Krickeberg (Paris); H. Lenz INFORMATION: Eighty-seventh Ontario tion (on the occasion of the sixtieth birth Mathematics Meeting, Dept. of Math. (Berlin); M.P. Malliavin (Paris); Y.I. day of Erwin Engeler), ZUrich, Switzer Manin (Moscow); C. Procesi (Rome); and Stat., Carleton University, Ot land. (Sep. 1989, p. 915) tawa, Ontario, Canada, K1S 5B6. V. Ptak (Prag); A. Salomaa (Turku); 11-17. Mathematische Stochastik, Ober J.W. Schmidt (Dresden); C.J. Scriba 4-10. Funktiontheoretische Methoden wolfach, Federal Republic of Germany. (Hamburg); M. Vergne (Paris); R. Bei Partiellen Differential Und Integral (Mar. 1989, p. 315) Wilson (New Brunswick, NJ); E. Ch. gleichungen, Oberwolfach, Federal Re 13-16. Twenty-first Annual Iranian Math Wittmann (Dortmund); D. Zagier public of Germany. (Mar. 1989, p. 314) ematics Conference, University of Isfa (Bonn/Maryland). 4-10. Nukleare Frechet-Riiume, Ober han, Iran. (Jul./ Aug. 1989, p. 766) wolfach, Federal Republic of Germany. 14-1 9. East European Category Semi 19-22. Eleventh Annual National Graph (Mar. 1989, p. 314) nar, Predela, Bulgaria. (MayfJun. 1989, ics Association Conference and Expo 5-10. Eighth International Seminar on p. 601) sition, Anaheim, CA. (Jul./Aug. 1989, Model Optimization in Exploration Geo * 15-21. International Conference on Dif p. 766) physics, with a Workshop on Geophysical ferential Equations and Mathematical 19-24. US-USSR Approximation Theory Data Inversion in Environmental Research Physics, University of Alabama at Birm Conference, University of South Florida, and Planning, Berlin-West, Free Univer- ingham, Alabama. Tampa, FL. (Jul./ Aug. 1989, p. 766) 1094 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 20-23. Directions in Matrix Theory, Laval, Quebec; S. Kotz, Univ. of Auburn, AL. (MayjJun. 1989, p. 601) Maryland; R.B. Nelsen, Lewis and May 1990 23-24. Southeast Section Meeting of Clark College; L. Ruschendorf, Westf. the AMS, University of Arkansas, Fayet Wilhelms Univ., Munster, DDR; A. 3-4. Twenty-first Annual Pittsburgh Con teville, AR. Sampson, Univ. of Pittsburgh; H. ference on Modeling and Simulation, Uni Sherwood, Univ. of Central Florida; versity of Pittsburgh, Pittsburgh, PA. INFORMATION: W. Drady, AMS, P.O. B. Schweizer, Univ. of Massachusetts; (Sep. 1989, p. 916) Box 6248, Providence, RI 0240. V. Benes, Czech. Tech. Univ., Prague. 6-12. Geschichte der Mathematik, Ober * 23-24. University of Arkansas' Four wolfach, Federal Republic of Germany. teenth Annual Lecture Series in Math 8-14. Arbeitsgemeinschaft Mit Aktuellem (Jul./ Aug. 1989, p. 766) ematical Sciences, Univ. of Arkansas, Thema (wird in den Mitteilungen der * 7-9. 1990 IEEE Symposium on Research Fayetteville, Arkansas. DMV Heft 1/1990 bekanntgegeben), Ober in Security and Privacy, Oakland, CA. wolfach, Federal Republic of Germany. CONFERENCE THEME: The theme of (Jul./ Aug. 1989, p. 766) PuRPOSE: The purpose of this sympo these lectures is probability distribu sium is to bring together researchers tions of phase type and applications. 15-21. Mathematical Concepts of De and developers who work on secure The principle lecturer will be M.F. pendable Systems, Oberwolfach, Federal computer systems. The symposium Neuts. This series will be held in con Republic of Germany. (Jul./Aug. 1989, will address advances in the the junction with the AMS Southeastern p. 766) ory, design, implementation, evalu Regional Meeting. ation and application of secure com INFORMATION: I. Monroe, University 18-21. Sixty-eighth Annual Meeting of puter systems. of Arkansas, Fayetteville, Arkansas the National Council of Teachers of Math CONFERENCE ToPics: Math Related: 72701; 501-575-3351. ematics, Salt Lake City, UT. (Jul./ Aug. Cryptology and Formal Models. 1989, p. 766) CALL FOR PAPERS: Send five copies 25-31. Kontinuumsmechanik der Festen of your paper or panel proposal to 21-22. Eastern Section Meeting of the Korper, Oberwolfach, Federal Republic D. Cooper, Program Co-Chair at the of Germany. (Mar. 1989, p. 315) AMS, Pennsylvania State University, Uni address given below. Papers must be versity Park, PA. (Note change in name 26-29. Workshop on Number Theory and received by November 6, 1989. from Sep. 1989, p. 916) Algorithms, Berkeley, CA. (Sep. 1989, p. INFORMATION: D. Cooper, Program 916) INFORMATION: W. Drady, AMS, P.O. Co-Chair, Unisys Corp., 5731 Slauson 26-April 6. Workshop on Group Theory Box 6248, Providence, RI 02940. Ave., Culver City, CA 90230; Tel: from a Geometrical Viewpoint, Interna 213-338-3727, Fax: 213-338-0327. tional Centre for Theoretical Physics, * 22-27. Tenth Conference on Analytic Trieste, Italy. (May/Jun. 1989, p. 601) Functions, Kozubnik, Poland. 7-10. SIAM Conference on Applications 29-31. Mathematical Sciences Insti of Dynamical Systems, Orlando, FL. (Sep. tute Symposium on Mathematics as Art, CoNFERENCE ToPics: Geometric func 1989, p. 916) Mathematics as a Consumer Good, Cor tion theory of one complex variable, quasiconformal mappings, complex 7-June l. College on Recent Develop nell University, Ithaca, NY. (Jul./Aug. ments and Applications in Mathematics 1989, p. 766) analysis in several variables, complex analytic geometry and potential the and Computer Science, International Cen ory in en. tre for Theoretical Physics, Trieste, Italy. (MayfJun. 1989, p. 601) April1990 PROGRAM: The conference will con sist of invited lectures (4 5 minutes) 13-19. Abstrakte Konvexe Analysis, 1-4. ENAR Spring Meeting, Baltimore, and short communications (20 min Oberwolfach, Federal Republic of Ger MD. (Jul./ Aug. 1989, p. 766) utes). many. (Jul./ Aug. 1989, p. 766) 1-7. Design and Codes, Oberwolfach, ORGANIZERs: J. Siciak, Jagiellonian 14-18. Conference on Nonlinear Anal Federal Republic of Germany. (Jul./ Aug. Univ., Krakow; J. Lawrynowicz, Pol ysis and Partial Differential Equations, 1989, p. 766) ish Academy of Sciences, L6di. Rutgers University, New Brunswick, NJ. 1-14. NATO Advanced Study Institute INFORMATION: K. Rusek, Instytut (Jul./ Aug. 1989, p. 767) on "Generators and Relations in Groups Matematyki UJ, ul. Reymonta 4, 17-19. Interface '90 (formerly Computer and Geometries", Castelvecchio Pascoli 30-059 Krakow, Poland. Science and Statistics: Symposium on In (Lucca), Italy. (Sep. 1989, p. 916) terface), East Lansing, MI. (Sep. 1989, 4-7. Symposium on Distributions with 22-28. Einhollende Algebren und Ringe p. 916) Given Marginals (In Memory of Giuseppe Von Differentialoperatoren, Oberwolfach, 20-26. The Schrodinger Equation and Pompilj), Rome, Italy. (Please note Federal Republic of Germany. (Jul./ Aug. Its Classical Counterparts, Oberwolfach, changes from MayfJun. 1989, p. 601) 1989, p. 766) Federal Republic of Germany. (Jul./ Aug. 1989, p. 767) INVITED SPEAKERS: S. Cambanis, 29-May 5. Gruppentheorie (Pro-Endliche Univ. of North Carolina; M.J. Frank, Gruppen), Oberwolfach, Federal Repub 21-24. The Simulation of Random Pro Univ. of Chicago; G. Genest, Univ. lic of Germany. (Jul./ Aug. 1989, p. 766) cesses and Fields - Mathematics and OCTOBER 1989, VOLUME 36, NUMBER 8 1095 Meetings and Conferences Applications, Portofino, Italy. (Sep. 1989, 3-9. Graphentheorie, Oberwolfach, Fed 11-14. Fifth SIAM Conference on Dis p. 916) eral Republic of Germany. (Jul./ Aug. crete Mathematics, Atlanta, GA. (Sep. 21-25. Eleventh United States National 1989, p. 767) 1989, p. 917) Congress of Applied Mechanics, Tucson, 4-7. Fifth Annual IEEE Symposium on 11-15. Third International Conference on AZ. (Nov. 1988, p. 1389) Logic in Computer Science, Philadelphia, Hyperbolic Problems, Uppsala, Sweden. 23-25. 1990 International Symposium PA. (Sep. 1989, p. 917) (Jul./ Aug. 1989, p. 767) on Multiple-Valued Logic, Charlotte, NC. 4-8. Workshop on Model Theory, Berke 11-15. Rigorous Results in Quantum Dy (Apr. 1989, p. 496) ley, CA. (Sep. 1989, p. 917) namics, Liblice Castle, Czechoslovakia. 25-31. Tenth International Conference 6-9. Fifth Annual Conference of the (MayjJun. 1989, p. 602) on Pattern Recognition, Resorts Hotel, European Consortium for Mathematics 13-15. Seventh Annual Quality and Pro Atlantic City, NJ. (Mar. 1988, p. 466) in Industry, Lahti, Finland. (Apr. 1989, ductivity Research Conference, Madison, 27-June 2. Lyapunov-Exponents, Ober p. 496) WI. (Mar. 1989, p. 315) wolfach, Federal Republic of Germany. 6-12. 1990 Barcelona Conference on 13-22. Free Boundary Problems: Theory (Jul./ Aug. 1989, p. 767) Algebraic Topology, Centre de Recerca and Applications, Centre de Recherches * 29-June I. Eleventh Annual Conference Matematica, Barcelona, Spain. (Sept. Mathematiques, Universite de Montreal, of the Canadian Applied Mathematics 1988, p. I 060) Canada. (Jul./ Aug. 1989, p. 767) Society, Halifax, Nova Scotia. * 6-1 5. Third Logical Biennial (in honour 17-23. Partial Differential Equations in of S.C. Kleene), Chaika (near Varna), Complex Analysis, Oberwolfach, Federal INFORMATION: M. Meidell, Confer Bulgaria. Republic of Germany. (Jul./ Aug. 1989, ence Coordinator, Continuing Educa p. 767) tion Div., Technical Univ., of Nova PROGRAM: Kleene '90 is the third 18-20. Joint WNAR-IMS Regional Meet Scotia, P.O. Box 1000, Halifax, Nova edition of the Logical Biennial, suc ing, Montana State University, Bozeman, Scotia, B3J 2X4 Canada. ceeding Goede) '86 and Heyting '88. Its scientific programme includes a MT. (Mar. 1989, p. 315) Summer School with invited lectures, * 18-22. Fourteenth Mathematical Sci Lecture Series on Partially Ordered June 1990 a Conference with selected contribu ences tions, discussions and informal semi Sets, Johns Hopkins University, Balti more, Maryland. June 1990. AMS-SIAM Summer Sem nars. inar on Vortex Dynamics and Vortex CONFERENCE TOPICS: Recursion the INVITED SPEAKER: T. Trotter, Arizona Methods, Location on the west coast ory, modal and nonclassical logic, State University. to be announced. proof theory, logic in theoretical com INFORMATION: E.R. Scheinerman, puter science, applications of logic to Dept. of Mathematical Sciences, Balti INFORMATION: B. Verducci, AMS, P.O. mathematics, Kleene session. more, MD 21218 USA; 301-338-7210; Box 6248, Providence, Rl 02940. CALL FOR PAPERS: Five copies of a Email: [email protected] or draft full paper of no more than 15 June/July 1990. International IMACS mcs_ wers@j h unix. double-spaced standard pages accom Conference on Mathematical Modelling panied by one-page camera-ready Ab 24-30. Mathematische Probleme in der and Applied Mathematics, Vilnius, USSR. stract should reach the PC Chairman Nichtlinearen Elastizitiit, Oberwolfach, (Sep. 1989, p. 917) according to the following deadlines: Federal Republic of Germany. (Jul./ Aug. 1-8. Third International IMACS Sym Nov. 15, 1989- submission; Mar. 15, 1989, p. 767) posium on Orthogonal Polynomials and 1990- notification; May 20, 1990- final * 25-29. International Symposium on Fuzzy Their Applications, Erice-Trapani (Sicily), version due. Approach to Reasoning and Decision Mak Italy. (Sep. 1989, p. 917) ORGANIZING COMMITTEE: V. Goranko, ing, Bochyne, Czechoslovakia. * 1-10. Fourth Annual Meeting of the L. Ivanov, S. Passy, P. Petkov (Chair International Workshop in Analysis and man). INFORMATION: V. Novak, Minin In its Applications, Dubrovnik-Kupari, Yu INFORMATION: Kleene '90, Mathemat stitute, Czechoslovakia Academy of goslavia. ics Faculty, Blvd. Anton Ivanov 5, Sciences, A. Rimana 1768, 70800 Ostrava-Poruba, Czechoslovakia. CONFERENCE THEME: Inner product Sofia 1126, Bulgaria; phone: (+359.2) and convexity structures in analysis, 62561, exts. 598, 524. 27-30. Fourth International Congress mathematical physics and economics. I 0-16. Reelle Algebraische Geometrie, on Algebraic Hyperstructures and Ap INFORMATION: C.V. Stanojevic, Dept. Oberwolfach, Federal Republic of Ger plications, Xanthi, Greece. (Apr. 1989, of Mathematics and Statistics, Uni many. (Jul./ Aug. 1989, p. 767) p. 496) versity of Missouri-Rolla, Rolla, MO 11-14. Fourteenth Rolf Nevanlinna Col 65401. loquium, University of Helsinki, Helsinki, July 1990 3-6. 1990 Annual Meeting of the Sta Finland. (Jul./ Aug. 1989, p. 767) tistical Society of Canada, St. John's, 11-14. World Organization of Systems 1-7. Modulfunktionen In Mehreren Vari Newfoundland, Canada. (Sep. 1989, and Cybernetics Eighth International Con ablen, Oberwolfach, Federal Republic of p. 917) gress, New York, NY. (Mar. 1989, p. 315) Germany. (Apr. 1989, p. 497) 1096 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 1-15. International Symposium on Alge INFORMATION: J.G. Gimbel, Univer - Adams Memorial Sympo sity of Alaska, Fairbanks, AK 99775. braic Topology August 1990 sium, University of Manchester, England. 13-1 7. Fifth International Conference (Sep. 1989, p. 918) 5-11. Mathematical Methods in Tomog Mechanics and Nonpoten raphy, Oberwolfach, Federal Republic of on Hadronic 1-18. Twentieth Summer Session on of Northern Germany. (Apr. 1989, p. 497) tial Interactions, University Probability Theory, Saint-Flour (Cantal), Iowa, Cedar Falls, Iowa. (Jul./ Aug. 1989, Conference on Ap- France. (Mar. 1989, p. 315) * 5-11. International p. 768) proximation Theory, Hungary. 2-6. Tenth Australian Statistical Con 13-1 7. Eleventh IFAC World Congress, ference/Second Pacific Statistical Con ORGANIZER: Janos Bolyai Mathemat Tallin, USSR. (Sep. 1989, p. 918) gress, Sydney, Australia. (Jul./ Aug. 1989, ical Society. 13-1 7. Algebraic Geometry and Ana p. 768) CoNFERENCE ToPics: Fourier analy lytic Geometry, Tokyo, Japan. (Sep. 1989, 2-6. The Jonsson Symposium, Laugar sis, approximation procedures, inter p. 919) vatn, Iceland. (Sep. 1989, p. 918) polation theory, function spaces. 13-18. Institute of Mathematical Statis INFORMATION: Janos Bolyai Mathe * 2-6. Thirty-fourth Annual Meeting of the tics Fifty-third Annual Meeting(jointly matical Society, Budapest, Anker Koz Australian Mathematical Society, Towns with the Second World Congress of the 1-3. I. Ill., H-1061. ville, Queensland, Australia. Bernoulli Society), Uppsala, Sweden. (Sep. ORGANIZERS: R. Hosking, L. Marsh, 6-9. 1990 Joint Statistical Meetings, 1989, p. 919) B. Newman. Anaheim, CA. (Mar. 1988, p. 466) 14-18. The Asian Mathematical Con INFORMATION: R.J. Hosking, Dept. 8-11. Joint Mathematics Meetings, Ohio ference 1990, Hong Kong, China. (Sep. of Math., James Cook University, State University, Columbus, OH. (includ 1989, p. 919) Townsville, Queensland 4811, Aus ing the summer meetings of the AMS, 15-19. International Conference on Knot tralia. AWM, MAA and PME). This is the 75th Theory and Related Topics, International of the MAA. House, Osaka, Japan. (Apr. 1989, p. 497) 3-6. Eleventh Dundee Conference on Or Anniversary dinary and Partial Differential Equations, INFORMATION: H. Daly, AMS, P.O. * 16-18. SIGAL International Symposium Dundee, Scotland. (Sep. 1989, p. 918) Box 6248, Providence, RI 02940. on Algorithms, Tokyo, Japan. 8-14. Variationsrechnung, Oberwolfach, PROGRAM: The Symposium will con 12-18. Algebraische Zahlentheorie, Ober Federal Republic of Germany. (Apr. sist of several invited talks and con wolfach, Federal Republic of Germany. 1989, p. 497) tributed papers. Proceedings will be (Apr. 1989, p. 497) 9-11. "Universita'di Genova - The Ohio available at the Symposium. The of 12-18. Pre-Congress Topology Confer State University Joint Conference" on ficial language is English. The Sym of Hawaii, Honolulu, New Trends in Systems Theory, Genoa, ence, University posium will be held before the Inter HI. (Feb. 1989, p. 183) Italy. (Jul./ Aug. 1989, p. 768) national Congress of Mathematicians Conference, Quo Vadis, 9-20. Geometry and Topology of Four * 13-16. Alaska 1990 at Kyoto, Japan. University of Alaska, Manifolds, McMaster University, Hamil Graph Theory?, ORGANIZERS: Special Interest Group ton, Ontario, Canada. (May 1Jun. 1989, Fairbanks, AK. on Algorithms (SIGAL) of the Infor Japan. p. 602) PuRPOSE: The conference is devoted mation Processing Society of CHAIRMEN: A. Nozaki, ICU; T. 15-21. Stochastic Image Models and Al to seeking optimal directions for the Nishizeki, Tohoku U. gorithms, Oberwolfach, Federal Republic study of graph theory. A principle ob CALL FOR PAPERS: Authors are re of Germany. (Apr. 1989, p. 497) jective will be to construct a list of quested to send twelve copies of a de 15-23. Colloquium in Honor of Roland questions whose resolution will signif icantly contribute to the development tailed abstract of at most ten double Fraisse, Centre International de Recon Dead of graph theory and its applications. spaced pages by Feb. 15, 1990. tres Mathematiques, Luminy, France. 1990. The format will entail informal pre line of Submissions: Feb. 15, (May I Jun. 1989, p. 602) Osaka sentations, much discussion, and the INFORMATION: T. Asano, 16-20. SIAM Annual Meeting, Chicago, Univ., Hatsu free exchange of topics that partici Electro-Communication IL. (Nov. 1988, p. 1389) Japan. pants are currently exploring. cho, Neyagawa, Osaka 572, 22-28. Konvexgeometrie, Oberwolfach, CONFERENCE TOPICS: Algorithmic 19-25. Mathematische Methoden Des Federal Republic of Germany. (Apr. graph theory, practical applications 1989, p. 497) VLSI-Entwurfs Und Des Distributed Com of graphs, impact of graph theory on putings, Oberwolfach, Federal Republic 26-29. International Conference on New education, combinatorial and topo of Germany. (Apr. 1989, p. 497) Trends in Geometric Function Theory logical methods, random graphs and 21-29. The International Congress of and Applications, University of Madras, enumeration. Mathematicians 1990, Kyoto, Japan. Madras, India. (Sep. 1989, p. 918) ORGANIZERS: P.Z. Chinn, Humboldt (Nov. 1988, p. 1389) 29-August 4. Mechanik Und Algebrais State Univ.; J.G. Gimbel, Univ. of che Geometrie, Oberwolfach, Federal Re Alaska; J.W. Kennedy, Pace Univ.; 26-September 1. Komplexe Analysis, public of Germany. (Apr. 1989, p. 497) L.V. Quintas, Pace Univ.; F.S. Roberts, Oberwolfach, Federal Republic of Ger Rutgers Univ. many. (Apr. 1989, p. 497) OCTOBER 1989, VOLUME 36, NUMBER 8 1097 Meetings and Conferences 28-30. IMACS European Simulation 23-29. Random Graphs and Combinator CHAIRMEN: H. Heyer, Tiibingen; L. Meeting on Problem Solving by Simula ical Structures, Oberwolfach, Federal Re Schmetterer, Wien. tion, Esztergom, Hungary. (Mar. 1989, public of Germany. (Apr. 1989, p. 498) INFORMATION: Mathematisches For p. 316) 24-28. International Symposium on Math schungsinstitut Oberwolfach Geschaft 28-31. Operations Research 1990, Inter ematical Theories, San Sebastian, Spain. sstelle: Alberstrasse 24 D-7800 national Conference Operations Research, (Jul./ Aug. 1989, p. 769) Freiburg im Breisgau. Vienna, Austria. (Jul./ Aug. 1989, p. 768) 30-0ctober 6. Diophantische Approxi 5-7. Second SIAM Confernce on Linear 30-September 4. International Confer mationen, Oberwolfach, Federal Republic Algebra in Signals, Systems & Controls, ence on Potential Theory, Nagoya, Japan. of Germany. (Apr. 1989, p. 498) San Francisco, CA. (Sep. 1989, p. 920) (May I Jun. 1989, p. 602) 12-16. Supercomputing '90, New York, October 1990 NY. (Sep. 1989, p. 920) September 1990 18-24. Komplexitiitstheorie, Oberwol 7-13. Arbeitsgemeinschaft Mit Aktuellem fach, Federal Republic of Germany. (Apr. Federal Republic September/October 1990. IMACS Thema, Oberwolfach, 1989, p. 498) GAMM Conference on Computer Arith of Germany. (Apr. 1989, p. 498) 25-December 1. Stochastische Approx metic, Scientific Computation and Fed 14-20. Geometrie, Oberwolfach, imation Und Optimierungsprobleme In Mathematical Modelling, Bulgaria. (Sep. eral Republic of Germany. (Apr. 1989, Der Statistik, Oberwolfach, Federal Re 1989, p. 919) p. 498) public of Germany. (Apr. 1989, p. 498) IMACS Symposium on Modelling and Der 21-27. Mathematische Methoden In 25-December 1. Lineare Modelle und Simulation of Electrical Machines, EN Robotik, Oberwolfach, Federal Republic Multivariate Statistische Verfahren, Ober SEM - Nancy, France. (May I Jun. 1989, of Germany. (Apr. 1989, p. 498) wolfach, Federal Republic of Germany. p. 602) * 21-27. Arithmetik der Korper, Oberwol- (Jul./ Aug. 1989, p. 769) 2-7. Twelfth International Conference on fach, Federal Republic of Germany. Nonlinear Oscillations, Cracow, Poland. P. (Sep. 1989, p. 919) CHAIRMEN: M. Jarden, Tel Aviv; December 1990 Roquette, Heidelberg. Federal 2-8. Topologie, Oberwolfach, INFORMATION: Mathematisches For 2-8. Multigrid Methods, Oberwolfach, 1989, p. 497) Republic of Germany. (Apr. schungsinstitut Oberwolfach Geschaft Federal Republic of Germany. (Apr. 3-6. Fourth Asian Logic Conference, sstelle: Alberstrasse 24 D-7800 1989, p. 498) Tokyo, Japan. (Mar. 1989, p. 316) Freiburg im Breisgau. * 3-5. First International Symposium on 3-7. IMACS Symposium on Intelligent Uncertainty and Analysis: Fuzzy Reason Analysis Models in Systems Simulation, Brussels, * 21-2 7. International Functional ing, Probabilistic Methods and Risk Man on the Occasion of the Sixti Belgium. (Mar. 1989, p. 316) Meeting agement, College Park, Maryland. eth Birthday of Professor M. Valdivia, 3-7. Representation des Groupes et Anal Spain. INFORMATION: B.M. Ayyub, Dept. of yse Complexe, Marseille, France. Peiiiscola, Civil Engineering, Univ. of Maryland, (Jul./ Aug. 1989, p. 768) K.D. Bier ORGANIZING COMMITTEE: College Park, Maryland 20742. 8-12. Neuronet-90: IMACS International stedt, Paderborn; J. Bonet, Valencia; Symposium on Neural Nets and Neu J. Horvath, Maryland; M. Maestre, 3-7. 1990 Australasian Conference on ral Computers, Prague, Czechoslovakia. Valencia. Combinatorial Mathematics and Comput (Please note change from May/Jun. 1989, INFORMATioN: J. Bonet, Univ. Politec ing, Palmerston North, New Zealand. p. 602) nica de Valencia, E.T.S. Arquitectura, (Feb. 1989, p. 183) 9-15. Surgery and L-Theory, Oberwol Dept. Matematica Aplicada, C. de 9-15. Allgemeine Ungleichungen, Ober fach, Federal Republic of Germany. (Apr. Vera, E-46071 Valencia, Spain. wolfach, Federal Republic of Germany. 1989, p. 498) 28-November 3. Mathematical Eco (Apr. 1989, p. 498) 10-0ctober 5. School on Qualitative nomics, Oberwolfach, Federal Republic 16-22. Mathematische Logik, Oberwol Aspects and Applications of Nonlinear of Germany. (Apr. 1989, p. 498) fach, Federal Republic of Germany. (Apr. Evolution Equations, International Centre 1989, p. 498) for Theoretical Physics, Trieste, Italy. 25-January 1. Lineare Modelle Und Mul (MayjJun. 1989, p. 602) November 1990 tivariate Statistische Verfahren, Oberwol 10-14. Mathematiker-Kongress, Dres 2-3. Central Section Meeting of the fach, Federal Republic of Germany. (Apr. den, German Democratic Republic. AMS, University of North Texas, Den 1989, p. 498) (Jul./ Aug. 1989, p. 769) ton, TX. 16-22. Risikotheorie, Oberwolfach, Fed INFORMATION: W. Drady, AMS, P.O. January 1991 eral Republic of Germany. (Apr. 1989, Box 6248, Providence, RI 02940. p. 498) 16-19. Joint Mathematics Meetings, 17-22. DMV-Jahrestagung 1990, Bre * 4-10. WahrscheinlichkeitsmaBe aufGrup San Francisco, CA. (including the an men, Federal Republic of Germany. pen, Oberwolfach, Federal Republic of nual meetings of the AMS, AWM, MAA, (Jul./ Aug. 1989, p. 769) Germany. and NAM) 1098 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences INFORMATION: H. Daly, AMS, P.O. 19-22. 1991 Joint Statistical Meetings, Box 6248, Providence, RI 02940. Atlanta, GA. (Mar. 1988, p. 466) January 1993 13-16. Joint Mathematics Meetings, San July 1991 January 1992 Antonio, TX. (including the annual meet 8-12. Second International Conference 8-11. Joint Mathematics Meetings, Bal ings of the AMS, AWM, MAA, and on Industrial and Applied Mathematics, timore, MD. (including the annual meet NAM) Washington, DC. (Nov. 1988, p. 1389) ings of the AMS, AWM, MAA and NAM) INFORMATION: W. Drady, AMS, P.O. 22-26. Thirteenth IMACS World Con INFORMATION: H. Daly, AMS, P.O. Box 6248, Providence, RI 02940. gress on Computing and Applied Math Box 6248, Providence, RI 02940. ematics, Trinity College, Dublin Univer sity, Dublin, Ireland. (Mar. 1989, p. 316) January 1994 June 1992 5-8. Joint Mathematics Meetings, Cincin nati, OH. (including the annual meetings August 1991 29-July l. Joint Meeting with the Lon don Mathematical Society, Cambridge, of the AMS, AWM, MAA, and NAM) 8-11. Joint Mathematics Meetings, Uni England. (Mar. 1989, p. 316) INFORMATION: H. Daly, AMS, P.O. versity of Maine, Orono, ME. (including Box 6248, Providence, RI 02940. the summer meetings of the AMS, AWM, MAA, and PME) INFORMATION: H. Daly, AMS, P.O. Box 6248, Providence, RI 02940. The Collected Papers of /R. H. BING/ Sukhjit Singh, Steve Armentrout, Robert J. Daverman, Editors A powerful mathematician and a great historical background on Bing's life and 1980 Mathematics Subject Classifications: problem solver, R. H. Bing laid the achievements. 57, 54, 26 LC 88-14445 foundation for a number of areas of ISBN 0-8218-0117-1, will appeal to 2 volumes, 1680 pages (hardcover), July topology. Many of his papers have This collection mathematicians in all areas, and 1988 continued to serve as a source of major , Institutional member $130 , especially those in topology, as well as List price $162 theoretical developments and concrete Individual member $97 and educators in the applications in recent years. One students, historians, To order, please specify COLBING/NA mathematical sciences, for it provides outstanding example was Michael H. a complete historical summary of the Freedman's use of Bing's Shrinking mathematical events in the life of the Criterion to solve the four-dimensional man and the mathematician, R. H. Bing. Poincare Conjecture. All prices subject to change. Shipment Contents: will be made by surface. For air deliv This two-volume set brings together I. R. H. Bing: An introduction; An editorial ery add, 1st book $5, each additional over one hundred of Bing's research, preface; R. H. Bing: A study of his life, book $3, maximum $100. Prepayment expository, and miscellaneous papers. by S. Singh; A chronology of R. H. Bing; required. Order from American Mathe These works range over a great variety of Ph.D. students of R. H. Bing; R. H. Bing: matical Society, P.O. Box 1571, Annex topics in topology, including the topology October 20, 1914-April 28, 1986, by R. D. Station, Providence, RI 02901-1571, or of manifolds, decomposition spaces, Anderson and C. E. Burgess; Abstracts call toll free 800-566-7774 to charge with continua, metrization, general topology, by R. H. Bing; II. Papers of R. H. Bing; VISA or MasterCard. and geometric topology. In addition, III. Classifications of works of R. H. Bing; there are a number of papers in the Publications of R. H. Bing: Classified by the areas of convex functions, linearity, and year; Publications of R. H. Bing: Classified conformal varieties. The introductory by subject matter; Works not included in section in the first volume provides these volumes; Permissions. OCTOBER 1989, VOLUME 36, NUMBER 8 1099 New AMS Publications 1980 Mathematics Subject Classification: 05C15 ISBN 0-8218-5103-9, LC 89-15011 EVERY PLANAR MAP IS FOUR COLORABLE ISSN 0271-4132 K. Appel and W. Haken 768 pages (softcover), October 1989 (Contemporary Mathematics, Volume 98) Individual member $48, List price $80, Institutional member $64 To order, please specify CONM/98N In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained The American Mathematical Society is now distributing the exposition accessible to a general mathematical audience. following title. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of THE LIBRARY & INFORMATION SCIENCE the authors' proof. In addition, the authors have added an CUMINDEX appendix which treats in much greater detail the argument Frederick G. Kilgour for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a This index is now available through the AMS as Volume 7 proof that four coloring can be accomplished in polynomial in the Information Access Series. The first six volumes in time. the series, also available through the Society, consist of indexes covering the literature of statistics and probability Contents from 1902-1968. The Cumlndex is a cumulation of the ··back-of-the-book·· Introduction index entries from 96 English-language books in the field of History librarianship and information science. It provides an index to a C- and D-Reducibility corpus of literature in far greater depth than would a library's Unavoidable Sets and our Discharging Procedure subject catalog or an index to periodical articles. With 90,000 Details of the Proof entries, this book provides a novel information retrieval tool. Our Checking Procedure Contents Part 1: Discharging How to Use a Cumlndex Introduction D-429 Background of the Cumlndex System The Discharging Procedure D-435 The Set U of Reducible Configurations D-459 Author's Preface Probabilistic Considerations D-478 Cumulative List of Index Entries from 96 Books on Library Possible Improvements D-486 and Information Science Part II: Reducibility List of Books in the Cumulation Arranged by Book Code Introduction R-491 1980 Mathematics Subject Classification: 00 The Computer Programs R-492 ISBN 0-88274-006-7, LC 72-86076 Immersion Reducibility R-493 722 pages (hardcover), 1973 The Unavoidable Set U of Reducible Configurations R-503 Individual member $33, List price $55, Institutional member $44 Appendix to Part II To order, please specify TUKEY /7N Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. 1100 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications Recent Appointments four invited one-hour addresses, S. Beiler, J. Birman, R. Meyerhoff, as follows: SAMUEL WEINBERGER, R. Craggs, R. Penner, S. Kwasik, University of Chicago, Flexibility L. Taylor, M. Kreck, P. Shalen, Committee members' terms of and rigidity of stratified spaces, in J. Davis, R. Skora, J. Hoste, D. office on standing committees troduced by Melvin Rothenberg; Long, C. Gordon, and J. Hillman. expire on December 31 of the HENRI GILLET, University of Illi Quadratic forms and real al year given in parentheses fol nois, Chicago, Analogies between gebraic geometry, VICTORIA Pow lowing their names, unless oth function fields and number fields, ERS, Emory University and CoLM erwise specified. introduced by Paul Vojta; RICHARD MuLcAHY, Spelman College. RocHBERG, Washington Univer Speakers were D. Lewis, D. Leep, sity, Estimates for singular num A. Hahn, T. Smith, R. Fitzgerald, Alexandre Chorin ( 1991) has bers of integral operators, intro C. Delzell, T. Craven, R. Brown, been appointed chairman of the duced by Richard Maher; and F. Kalhoff, L. Walter, V. Powers, Committee on Proceedings ofSym NICHOLAS LERNER, Purdue Uni S. Barton, R. Robson, J. Mad posia in Applied Mathematics by versity, Microlocal analysis and den, G. Stengle, I. Alarcon, B. President William Browder. Con applications to tomographic prob Alpers, B. Reznick, J. Shick, J. tinuing members of the committee lems, introduced by Georg Hetzer. Hale, A. Earnest, D. Hung, and are Giles Auchmuty ( 1989), and M. Kruskemper. Special Sessions Bjorn E. J. Dahlberg ( 1991 ). Codes and designs, NEAL Michael Artin, Walter Feit, and By invitation of the same Com BRAND, University of North Texas, Melvin Hochster have been ap mittee, there were thirteen spe and CARY HUFFMAN, Loyola Uni pointed to the Committee to Se cial sessions of selected twenty versity of Chicago. Speakers in lect the Winner ofthe Cole Prize by minute papers. The topics, orga cluded W. Arlinghaus, H. Park, President William Browder. Pro nizers, and speakers follow: Se J. Beder, N. Brand, E. Bannai, fessor Hochster will serve as chair quence spaces and summability, N. Sloane, J. Key, E. Assmus, K. man. MARTIN BUNTINAS, Loyola Uni Phelps, J. Leon, J. Goldman, C. versity of Chicago, and BILLy Salwach, C. Coburn, Y. Chee, A. RHOADES, Indiana University. Rosa, L. Teirlinck, J. Hall, D. Reports of Past Meetings Speakers were J. Connor, P. Nara Newhart, H. Ward, H. Mattson, yanaswami, M. Macphail, C. Goff W. Huffman, and J. Wood. The May Meeting man, G. Goes, A. Snyder, B. Noncommutative ring theory, in Chicago Rhoades, J. Fridy, G. Bennett, D. JEFFREY BERGEN, DePaul Univer The eight-hundred-and-forty-ninth Borwein, S. Chang, J. Boos, A. sity. Speakers were M. Beattie, meeting of the American Mathe Freedman, J. Sember, G. Bauer, A. Bell, A. Berele, J. Bergen, D. matical Society was held at Loyola L. Baric, W. Ruckle, J. Magee, J. Burkholder, W. Chin, D. Haile, University of Chicago on Friday, DeFranza, D. Fleming, A. Jaki T. Hodges, S. Jain, M. Kleiner,C. May 19, and Saturday, May 20, movski, H. Henig, J. Siddiqi, J. Lanski, G. Letzer, L. Levy, A. 1989. There were 387 registrants, Lee, and N. Mohapatra. Lichtman, M. Lorenz, L. Makar including 351 members of the So Geometric topology, TIM CocH Limanov, P. Malcolmson, W. Mar ciety. RAN, Northwestern University. tindale, I. Musson, J. O'Neill, J. Speakers included W. Neumann, Osterburg, E. Taft, M. Wright, S. Invited Addresses S. Akbulut, R. Gompf, P. Kirk, Khuri, and J. Dauns. By invitation of the Committee R. Stern, A. Edmonds, D. Ruber Numerical methods in harmonic to Select Hour Speakers for Cen man, N. Habegger, T. Cochran, K. analysis, JoNATHAN CoHEN, De tral Sectional Meetings, there were Orr, L. Simolinsky, W. Menasco, Paul University. Speakers were OCTOBER 1989, VOLUME 36, NUMBER 8 1101 AMS Reports and Communications G. Beylkin, R. Coifman, B. Jaw I. Hambleton, M. Rothenberg, R. technic Institute and State Univer erth, S. Mallat, R. DeVore, G. Schultz, and R. Fintushel. sity (VPI), May 29-June 9, 1989. Weiland, J. Lewis, J. Daly, and L. Nonlinear analysis and its ap The topic of the seminar was The Greengard. plications, S. P. SINGH, Memorial Mathematics of Random Media. Kazhdan-Lusztig theory andre University of Newfoundland. The seminar was supported by the lated topics, VINAY DEODHAR, Uni Speakers were M. Martelli, V. Mu Air Force Office of Scientific Re versity of Indiana. Speakers were stonen, S. Park, B. Rhoades, G. search, the Army Research Office, L. Scott, L. Casian, B. Boe, T. Beer, E. Fadell, G. Fournier, D. and the National Science Founda Enright, V. Lakshmibai, S. Ku Roux, V. Sehgal, W. Takahashi, J. tion. mar, D. Peterson, 0. Mathieu, E. Whitfield, and L. De Michele. The AMS-SIAM Committee on Neher, B. Parshall, R. Irving, D. Applied Mathematics selected the Collingwood, J. Carrell, M. Dyer, Contributed Papers topic of this conference. Members J. Du, V. Deodhar, and L. Renner. There were 4 sessions for con of the committee at the time were Algebraic groups and related tributed papers. The session times, Constantine M. Dafermos, James topics, STEPHEN DOTY, Loyola Uni numbers of papers, and names of M. Hyman, Donald E. McClure, versity of Chicago. Speakers were presiders follow: Friday morning, George C. Papanicolaou, Francis H. Tiwari, R. Dabrowski, S. Co 7 papers, Richard Maher of Loy Sullivan, and Robert F. Warming. hen, F. Grosshans, M. Berry, D. ola University of Chicago presid The Organizing Committee for White, L. Krop, L. Tan, J. Lah ing. Friday afternoon, 8 papers, the seminar included Martin Day, tonen, J. Wang, J. Humphreys, S. Robert Reisel of Loyola Univer Richard Durrett, Werner Kohler Smith, E. Friedlander, G. Seitz, B. sity of Chicago presiding, Saturday (Co-Chairman), Graeme Milton, Srinivasan, R. Dipper, and Z. Lin. morning, 9 papers, Joseph Mayne and Benjamin S. White (Co Arithmetic geometry and in and Alan Saleski of Loyola Uni Chairman). tersection theory, HENRI GILLET, versity of Chicago presiding. Sat There were 52 invited addresses. University of Illinois at Chicago. urday afternoon, 4 papers, Anne There were 118 mathematicians Speakers were C. Soule, E. Kani, Hupert of Loyola University of who registered for the seminar. Ac P. Vojta, W. McCallum, D. Har Chicago presiding. cording to the registration cards of bater, T. Chinburg, J. Jorgenson, Local Arrangements those who attended, 20 attended and R. Rumely. for the first week only, 39 dur W. Cary Huffman of Loyola Uni Recursion theory, CHRISTINE ing the second week only, and versity of Chicago chaired the Lo HAUGHT, University of Chicago. 59 for up to the full period of cal Arrangements Committee. He Speakers were R. Shore, T. Sla the seminar. Six countries not in was assisted by the following fac man, S. Ahmad, T. Millar, G. North America were represented ulty, A. Hupert, T. Kazan, M. Li, Sacks, H. Ye, M. Groszek, A. by the following numbers of par R. Maher, D. Maher, J. Mayne, Nerode, A. Kucera, M. Kumabe, ticipants: Australia ( 1), France (2), A. McDonald, G. McDonald, M. M. Stob, C. Jockusch, J. Knight, Israel (2), Italy (1), USSR (4), Yu Paleczny, R. Reisel, and A. Saleski. W. Calhoun, M. Lerman, and A. goslavia ( 1 ) Loyola University gave a wine and Kechris. Forty-nine papers were repro cheese reception for the meeting Partial differential equations, duced and distributed to partici Friday evening. NICHOLAS LERNER, Purdue Uni pants during the seminar totaling versity. Speakers were J. Manfredi, Andy Roy Magid 1,061 pages of notes plus a three A. Himonas, H. Bellout, X. Saint Associate Secretary page Table of Contents. Raymond, G. Hetzer, K. Kimura, Norman, Oklahoma As with previous summer sem N. Hanges, D. White, A. Tzavaras, inars, the Society will publish for S. Berhanu, G. Roberts, and S. mal proceedings in the series Lec Chanillo. 1989 AMS-SIAM tures in Applied Mathematics. Algebraic topology and vari Summer Seminar on eties, RONNIE LEE, Yale University The Mathematics The Council in Boulder and STEVEN WEINTRAUB, Louisi of Random Media ana State University. Speakers The Council met at 2:00 p.m. on 6 were S. Yau, A. Durfee, W. Neu The twentieth AMS-SIAM Sum August 1989 in the Century Room mann, J. Wood, J. Wolper, I. Dol mer Seminar on Applied Mathe of the Clarion Harvest Hotel in gachev, F. Cohen, F. Raymond, matics was held at Virginia Poly- Boulder. There were twenty-five 1102 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications members in attendance. President the Board of Trustees, and the year for three year terms. It post William Browder was in the chair. Council's Executive Committee, poned to the next Council meet The Council approved the min the Council established an "Award ing the question of terms of office utes of the April 1989 Council. for Distinguished Public Service" for the Treasurer and Associate While sitting in Executive Ses to be presented every two years Treasurer. sion, the Council made the follow to a research mathematician who A few items of new business ing additional nominations for the has made a distinguished contribu were considered by the Council. It election of 1989: tion to the mathematics profession passed a resolution congratulating through public service during the Pi Mu Epsilon for its Diamond Vice-President preceding five years. This award, Jubilee. And it asked its officers to {Two to be elected) in the amount of $2500, will be pursue the matter of overturning Lenore Blum, Berkeley presented at the Business Meeting the contempt of Congress citation (Already nominated were of the Society in even numbered of H. Chandler Davis. James G. Arthur, Toronto; Phillip years upon the recommendation In response to a report from the A. Griffiths, Duke; James B. Ser of a committee app,ointed by the MAA Committee on Preparation rin, Minnesota; and Dennis P. Sul President. for College Teaching and letters livan, CUNY Graduate Center.) The Council also established received by the Council concern a "Citation for Public Service", ing the current job situation, the Member at Large one to three of which will be Council discussed many aspects of (Five to be elected) presented each year for notable graduate education. Sheldon Axler, Michigan State contributions to the mathematics The Council was honored to Alexandre J. Chorin, Berkeley profession through public service. hear a presentation by Lida Bar James W. Cannon, Brigham Young These citations together with a rett, President of the Mathemati {Those nominated already were monetary award of $500 will be cal Association of America, on the Joan S. Birman, Columbia; Frank presented each year at the Busi activities of the MAA, especially H. Clarke, Montreal; Charles Her ness Meeting of the Society upon those related to AMS activities. bert Clemens, Utah; Edwin E. the recommendation of the same The Council adjourned at 7:15 Floyd, Virginia; Amassa C. Faunt committee. p.m. leroy, North Carolina State; Carl The Council continued its work Robert M. Fossum Pomerance, Georgia; and Shing on election reforms. It rescinded Secretary Tung Yau, Harvard.) its policy in which it limited to Urbana, Illinois The Council also elected mem twice in any ten year period ap bers of editorial boards that were proval of nominations by petition proposed by the Editorial Boards for the same individual. It referred The Business Meeting Committee. problems regarding the Nominat in Boulder The Council received reports ing Committee to a committee The Business Meeting of 8 Au from several Society committees, to be appointed by the President. gust 1989 began about 5: 10 and including an AMS-MAA Commit It decided to implement a con followed immediately upon the tee on Employment and Educa tested election for the position of award of the Steele Prizes. Presi tional Policy (CEEP) report which President-elect on a trial basis (for dent Browder presided. contained recommendations that three presidential elections begin The Secretary informed the its Data Subcommittee be made ning in 1991) by requesting that its membership of items of business into a self-standing committee, Nominating Committee send two transacted by the Council at the an action which the Council en nominations for the position to meeting of 6 August 1989. dorsed. The Council requested that the Council in those years when a The President opened the floor a FORUM section be established president-elect will be elected. The for questions. The meeting ad in the Notices and it agreed to es Council requested that the Secre journed about 5:30 p.m. tablish a "Collected Works Book tary prepare amendments to the Series". Bylaws for action by the January Robert M. Fossum On the advice of the Soci 1990 Council to allow for elec Secretary ety's Science Policy Committee, tion of two Vice-Presidents each Urbana, Illinois OCTOBER 1989, VOLUME 36, NUMBER 8 1103 AMS Reports and Communications 1989 AMS-SIAM-SMB was sponsored by the American The theme of the symposium Symposium on Some Mathematical Society, the Society was Sex allocation and sex change: Mathematical Questions for Industrial and Applied Mathe Experiments and models. There in Biology matics, and the Society for Math were two half-day sessions, includ ematical Biology. The AMS-SIAM ing three one-hour lectures in the The twenty-third annual Sympo Committee on Mathematics in the morning and four one-hour lec sium on Some Mathematical Ques Life Sciences served as the Orga tures in the afternoon. tions in Biology was held on Mon nizing Committee for the sympo Support was provided by a day, August 7, 1989, in Room sium. The committee at the time grant from the National Science 161 of the Lashmiller Chemical consisted of Kenneth L. Lange, Foundation. Building on the campus of the Michael C. Mackey, Marc Man The Society will publish formal University of Toronto. The sym gel, Hans G. Othmer, Alan S. proceedings in the series Lectures posium was held in conjunction Perelson, Richard E. Plant (Chair on Mathematics in the Life Sci with the annual meeting of the man), and John Rinzel. Professor ences. American Institute of Biological Mangel served as the symposium Sciences (AIBS). The symposium organizer. DYNAMICS AND CONTROL OF MULTIBODY SYSTEMS J. E. Marsden, P. S. Krishnaprasad, and J. C. Sima (Contemporary Mathematics, Volume 97) The study of complex, interconnected mechanical systems These kinds of considerations motivated the organization with rigid and flexible articulated components is of growing of the AMS-IMS-SIAM Joint Summer Research Conference interest to both engineers. and mathematicians. Recent on Control Theory and Multibody Systems, held at Bowdoin work in this area reveals a rich geometry underlying the College in August, 1988. This volume contains the proceedings mathematical models used in this context. In particular, Lie of that conference. The papers presented here cover a range groups of symmetries, reduction, and Poisson structures play of topics, all of which could be viewed as applications of a significant role in explicating the qualitative properties of geometrical methods to problems arising in dynamics and- multibody systems. In engineering applications, it is important control. The volume contains contributions from some of the to exploit the special structures of mechanical systems. For top researchers and provides an excellent overview of the example, certain mechanical problems involving control of frontiers of research in this burgeoning area. interconnected rigid bodies can be formulated as Lie-Poisson systems. The dynamics and control of robotic, aeronautic, and 1980 Mathematics Subject Classifications: 55FXX, 70HXX, 70QXX space structures involve difficulties in modeling, mathematical ISBN 0-8218-5104-7, LC 89-15019 analysis, and numerical implementation. For example, a new ISSN 0271-4132 (softcover), August 1989 with large, flexible components 488 pages generation of spacecraft Individual member $28, List price $46, are presenting new challenges to the accurate modeling Institutional member $37 and prediction of the dynamic behavior of such structures. To order, please specify CONM/97NA Recent developments in Hamiltonian dynamics and coupling of systems with symmetries has shed new light on some of these issues, while engineering questions have suggested new mathematical structures. All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional b?ok $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Statton, Providence, RI 02901-1571, or call toll free 800-566-7774 to charge with VISA or MasterCard. 1104 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Miscellaneous Personal Items tween the Argonne National Lab Jack R. Meagher, Professor oratory and the University of Chi Emeritus of Western Michigan Uni Lamberto Cesari, R. L. Wilder cago and to assist young scientists versity, died on July 30, 1989, at Professor Emeritus of the Uni engaged in numerical or analytical the age of 76. He was a member versity of Michigan, Ann Arbor, mathematics research. of the Society for 21 years. has given a series of lectures at the Richard N. Draper, of the Su Charles E. Mullan, of Tuscon, "Academia dei Lincei" in Rome percomputing Research Center, Arizona, died on July 11, 1989, at and at the Universities of Palermo, was appointed Fellow at that in the age of 81. He was a member Catania and Messina on BV so stitution based upon his research of the Society for 18 years. lutions in the calculus of vari into the use of Cayley graphs for E. J. Oglesby, Professor Emer ations. Cesari has also given a multiprocessor network architec itus of the University of Virginia, lecture at the ninth centenary of tures. died on May 20, 1989, at the age the University of Bologna, and has Arjun K. Gupta, of Bowling of 97. He was a member of the been the inaugural speaker at the Green State University, has been Society for 68 years. GAMM International Conference elected a Fellow of the American Antonio Pignedoli, of the Uni on "Problems involving change" Statistical Association. versity of Bologna, died on August in Stuttgart. 7, 1989, at the age of 71. He was a Gui-Quiang Chen, of New York member of the Society for 5 years. University, has been named the Deaths Jean-Louis Verdier, of the Uni first recipient of the Argonne Mark J. Mason, of Colorado State versity of Paris VII, died on Au University of Chicago Fellowship University, died on April22, 1989, gust 25, 1989, at the age of 54. He in Mathematics. The Fellowship at the age of 25. He was a member was a member of the Society for was created to strengthen ties be- of the Society for 6 years. 23 years. ALGEBRAIC TOPOLOGY Mark Mahowald and Stewart Priddy D (Contemporary Mathematics. Volume 96) D This book will provide readers with an overview of some of the 1980 Mathematics Subject Classifications: 55-06; 55P42, 55P45, major developments in current research in algebraic topology. 55R45,55T15, 18F25 LC 89-15023 leading researchers in the field, the ISBN 0-8218-5102-0, Representing some of the ISSN 0271-4132 book contains the proceedings of the International Conference 368 pages (softcover), August 1989 on Algebraic Topology, held at Northwestern University in Individual member $25, List price $41, March, 1988. Several of the lectures at the conference were Institutional member $33 expository and will therefore appeal to topologists in a broad To order, please specify CONM/96NA range of areas. The primary emphasis of the book is on homotopy theory and its applications. The topics covered include elliptic All prices subject to change. Shipment will cohomology, stable and unstable homotopy theory, classifying be made by surface. For air delivery add, spaces, and equivariant homotopy and cohomology. 1st book $5, each additional book $3, maxi Geometric topics-such as knot theory, divisors and mum $100. Prepayment required. Order from American Mathematical Society, P.O. Box configurations on surfaces, foliations, and Siegel spaces-are 1571, Annex Station, Providence, RI 02901- also discussed. Researchers wishing to follow current trends 1571, or call toll free 800-566-7774 to charge in algebraic topology will find this book a valuable resource. with VISA or MasterCard. OCTOBER 1989, VOLUME 36, NUMBER 8 1105 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 Marathe, Kishore B. Centro Nazionale delle Ricerche, Differential Geometry, 9/89- 1/90 (U.S.A.) Italy Mathematical Physics Visiting Foreign Mathematicians Aljadeff, Eli (Israel) University of Illinois, Urbana Algebra 8/89- 5/90 Alvarez-Lopez, Jesus A. University of Illinois, Urbana Differential Geometry 8/89- 5/90 (Spain) Arai, Toshiyasu (Japan) University of Illinois, Urbana Logic 8/89- 5/90 Bhargava, S. (India) University of Illinois, Urbana Number Theory 8/89- 5/90 Golumbic, Martin (Israel) IBM T.J. Watson Research Center Algorithmic Graph Theory, 9/89- 8/90 Discrete Mathematics Gordon, Yehoram (Israel) University of Illinois, Urbana Analysis 8/89- 5/90 Khachiyan, L.G. (U.S.S.R.) Cornell University Computational Optimization 9/89- 2/90 Ko, Ki Hyoung (Korea) Louisianna State University Topology: Link Theory 8/89- 5/90 Kreinovich, Vladikya Stanford University Logic, Computer Science, 9/89- 12/89 (U.S.S.R.) Mathematical Foundations of Physics Leader, Imre (England) Louisianna State University Graph Theory, Functional 8/89- 12/89 Analysis Pheidas, Thanases (Greece) University of Illinois, Urbana Logic 8/89- 5/90 Ryan, David (New Zealand) Cornell University Optimization Theory 8/89- 10/89 Sarkozy, Andras (Hungary) University of Illinois, Urbana Number Theory 8/89- 5/90 Strelitz, Shlomo (Israel) University of Illinois, Urbana Analysis 8/89- 5/90 Top, Jakov (The Queen's University Arithmetical Algebraic Geometry 9/89- 8/90 Netherlands) Vargas Jarillo, Cristobal Cornell University Applied Mathematics 9/89- 12/89 (Mexico) 1106 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AUTHOR AND SUBJECT INDEXES OF MATHEMATICAL REVIEWS, 1980-84 This comprehensive 12-volume set contains both author and subject listings for all of the reviews that appeared in Mathematical Reviews during the years 1980 to 1984. Containing over 9600 pages, it is an important addition to any mathematics library. With this set of indexes at hand, readers can: • access fully, by both author and subject area, the mathematical literature of five years, 1980 through 1984 • discover listings for approximately 200,000 papers, books, and conference proceedings -all the items reviewed in Mathematical Reviews during these years • obtain information about approximately 8000 additional items that were not reviewed individually. but which are fully classified and cross-referenced in these indexes • find complete bibliographic information for each article under any author associated with the article, and cross-references for the names of editors, translators, and other persons associated with an item • access, via a key index, all those publications that do not have named authors or editors • locate, under each subject index heading, all items having this classification as either a primary or a secondary classification ISBN 0-8218-0105-08, LC 42-4221 12 volumes, 9653 pages; 1986 List $1943, Inst. mem. $1554, Indiv. mem. $1166, Rev. $972 To order, please specify MREVIN/80/84NA Combination offer. A special price is offered when the Author and Subject Indexes of Mathe matical Reviews, 1980-84 (MREVIN/80/84) is purchased together with the Author and Subject Indexes ojMathematicalReviews, 1973-79 (MREVIN/73/79). ISBN 0-8218-0151-1 List $3055, lnst. mem. $2444, Indiv. mem. $1833, Rev. $1528 To order, please specify MRCIN/73/84NA Prepayment required. Order from the American Mathematical Society, Annex Station, P. 0. Box 1571, Providence, RI 02901-1571 or call401-272-9500 (800-556-7774 from within the continental U. S.) to use VISA or MasterCard. Application Deadlines for Grants and Assistantships Many fellowship programs have deadlines for receipt of appli November 15 cations. These deadlines are noted in news items and in the • AAUW Educational Foundation (American Fellowships) [GS], Stipends Section of the December Notices. They are listed below [PS] (See funding news item in this issue of Notices) for your convenience, and as a reminder since many of these Kosciuszko Foundation [SFN] deadlines occur before the publication date of the December Kosciuszko Foundation (Graduate and Postgraduate Exchange issue. Dates taken from the December 1988 issue have been with Poland) [TSA] updated with information received in preparation for the De Los Alamos National Laboratory (J. Robert Oppenheimer cember 1989 issue. For information about the various programs Research Fellowship) [PS] the reader is referred to the appropriate part of the Stipends Sec • NSF Mathematical Sciences Postdoctoral Research Fellow tion of the December 1988 Notices as follows: [GS] = Graduate ships [PS] (See news item in this issue of Notices) Support Section; [PS] =Postdoctoral Support Section; [TSA] = • NSF Visiting Professorships for Women [PS] (See Sep. 1989 Travel and Study Abroad Section; [SFN] = Study in the U.S. Notices, p. 865) for Foreign Nationals. November 30 North Atlantic Treaty Organization [TSA] * Information from the December 1988 issue not yet confirmed this year. December 1 • Refers to a news item in a recent issue of Notices. • AAUW Educational Foundation (Selected Professions Fel lowships) [GS] (See the funding news item in this issue of October 1 Notices) American Philosophical Society [PS] · • AMS Centennial Fellowships [PS] (See news item in this issue John Simon Guggenheim Memorial Foundation Fellowships of Notices) [PS] American Philosophical Society [PS] Institute for Advanced Study Memberships [PS] October 2 Lady Davis Fellowship Trust [TSA) Bunting Institute of Radcliffe College (Science Scholar Fel Lady Davis Visiting Professorships [TSA] lowships) [PS] Sigma Delta Epsilon, Graduate Women in Science [GS], [PS] * University of Illinois at Urbana-Champaign (The Chancel October 18 lor's Postdoctoral Fellowship Program) [PS] Kennedy Scholarships [SFN] December 15 November 1 • AAUW Educational Foundation (International Fellowships) American-Scandinavian Foundation [TSA) [SFN] (See the funding news item in this issue of Notices) Fannie and John Hertz Foundation Fellowships [GS] IBM Thomas J. Watson Research Center (Postdoctoral Fel • NSF Postdoctoral Fellowships in Japan [PS] (See Sep. 1989 lowships for Research in Mathematical Sciences) [PS] Notices, p. 865) Mathematical Sciences Research Institute [PS] University of Michigan (Michigan Society of Fellows Post Natural Sciences and Engineering Research Council of Canada doctoral Fellowships) [PS] (Visiting Fellowships) [TSA) President's Commission on White House Fellowships [PS] November 4 (See Dec. 1988 Notices, p. 1619) North Atlantic Treaty Organization (Postdoctoral Fellowships) [TSA) December 31 Massachusetts Institute of Technology (C.L.E. Moore Instruc November 9 torships in Mathematics) [PS] National Research Council (Ford Foundation Predoctoral and University of Utah (Instructorship in Mathematics) [PS] Dissertation Fellowships for Minorities) [GS] University of Wisconsin, Madison (Van Vleck Assistant Pro NSF Graduate Fellowships [GS] fessorship in Mathematics) [PS] NSF Minority Graduate Fellowships [GS] Zonta International (Amelia Earhart Fellowship Awards) [GS] 1108 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Application Deadlines January 1 January 25 Brown University (Jacob David Tamarkin Assistant Profes American Society for Engineering Education (Navy-ASEE sorship) [PS] (See Dec. 1987 Notices, p. 1317) Summer Faculty Research Programs) [PS] California Institute of Technology (Division Research Fel January 27 lowship) [PS] (See Dec. 1987 Notices, p. 1318) California Institute of Technology (Harry Bateman Research * Office of Naval Research (Graduate Fellowship Program) [GS] Instructorships) [PS] January 31 Courant Institute (Instructorships in Mathematics) [PS] Office of Technology Assessment (Congressional Fellowship Courant Institute (Postdoctoral Visiting Memberships) [PS] Program) [PS] Harvard University (Benjamin Peirce Lectureships) [PS] * Indiana University, Bloomington (Vaclav Hlavaty Research February 1 Assistant Professorships) [PS] AAAS Summer Fellowship [GS] University of California, Los Angeles (Earle Raymond Hedrick American Philosophical Society [PS] Assistant Professorships in Mathematics) [PS] American Society for Engineering Education (NASA-ASEE University of Chicago (Leonard Eugene Dickson Instructor Summer Faculty Fellowships) [PS] ships in Mathematics) [PS] * American Society for Engineering Education (ONR Graduate University of Pennsylvania (Hans Rademacher Instructor Fellowship Program [GS] ship) [PS] University of Cincinnati (Charles Phelps Taft Postdoctoral University of Texas (R H Bing Faculty Fellowships) [PS] Fellowships) [PS] Weizmann Institute of Sciences (Feinberg Graduate School Postdoctoral Fellowships [TSA) February 28 Weizmann Institute of Sciences (Openings for Scientists) [TSA) Australian Institute of Nuclear Science and Engineering (Re Yale University (Josiah Willard Gibbs Instructorships) [PS] search Fellowship) [PS] Centro de Investigacion del lPN (Solomon Lefschetz Research January 4 Instructorships) [TSA) University of California, San Diego (S. E. Warschawski As March 1 sistant Professorships) [PS] Royal Norwegian Council for Scientific and Industrial Re January 6 search (Postdoctorate Fellowships) [TSA] * Committee on Institutional Cooperation (Minorities Fellow March 2 ships in the Sciences, Mathematics and Engineering) [GS] * California State Graduate Fellowships [GS] * University of Michigan, Ann Arbor (T. H. Hildebrandt Re search Assistant Professorships) [PS] March 15 * Hubert H. Humphrey Doctoral Fellowships [GS] January 8 Purdue University (Research Assistant Professorships) [PS] March 31 North Atlantic Treaty Organization [TSA] January 12 National Center for Atmospheric Research (Advanced Study April1 Program) [PS] American Philosophical Society [PS] National Research Council (Ford Foundation Postdoctoral May 15 Fellowships for Minorities) [PS] Weizmann Institute of Sciences (Feinberg Graduate School January 15 Postdoctoral Fellowships [TSA] * AAAS Science, Engineering and Diplomacy Fellowships [PS] Weizmann Institute of Sciences (Openings for Scientists) [TSA] Dartmouth College (John Wesley Young Research Instructor June 15 ships) [PS] Indo-American Fellowship Program [TSA] Institute for Mathematics and its Applications [PS] • Institute for Mathematics and its Applications (Postdoctor August 1 ates in Industrial Mathematics) [PS] (See advertisement at American Philosophical Society [PS] the back of this issue of Notices) Kosciuszko Foundation [GS] August 15 Michigan State University (MSU Postdoctoral Research Po North Atlantic Treaty Organization [TSA] sitions in Mathematics) [PS] August 31 * National Research Council (Research Associateship Programs) Australian Institute of Nuclear Science and Engineering (Re [PS] search Fellowship) [PS] Rice University (Griffith Conrad Evans Instructorships) [PS] * Rutgers University (Hill Assistant Professorships) [PS] September 1 University of Pittsburgh (Andrew Mellon Postdoctoral Fel Royal Norwegian Council for Scientific and Industrial Re lowships) [PS] search (Postdoctorate Fellowships) [TSA) OCTOBER 1989, VOLUME 36, NUMBER 8 1109 New Members of the AMS ORDINARY MEMBERS Zhong Ge, Mathematics Science Res Inst, Muralidharan Nair, Arlington, TX lssam Mohamed Ali, Mosul Univ, Iraq Berkeley, CA Kamil R Nemr, Seattle, WA Douglas M Andrews, Iowa State Univ, James R Gorson, Arlington, VA Avital Y Ohayon, Haifa, Israel Ames Carol Sachiko Grams, Chesapeake, VA Eddie C Paramore Jr, Tuskegee Univ, Marek Antonowicz, Univ of Warsaw, Ronald P Green, Linwood, MA Alabama Poland S. JamesMarie Gross, Dubuque, lA Glenn L Pfeifer, Albuquerque, NM Juan Elias Badilla, San Jose, Costa Rica Youzhong Guo, Wuhan, People's Tao Qian, Flinders Univ, Bedford Park, Wojciech Bartoszek, Bydgoszcz, Poland Republic of China Australia Donald G Beane, College of Wooster, OH Nathaniel Shawn Hellerstein, Oakland, Jiri Rachounek, Palacky Univ, Olomouc, Asher Ben-Artzi, Univ of California San CA Czechoslovakia Diego, La Jolla Steve W Horton, Long Beach, CA George D Raikov, Bulgarian Acad of George W Bergeman, Round Hill, VA Alan R Jacobs, Phoenix, AZ -Science, Sofia, Bulgaria Jan Bernert, Nurnberg, Federal Republic Teresa Janiak, Higher College of Eng, Istvan Ratko, Hungarian Acad of Science, of Germany Zielona Gora, Poland Budapest, Hungary A N Bezdenezhnykh, Gorky N I Krzysztof Jarosz, Southern Illinois Univ, Italo Rebecchi, Jackson Heights, NY Lobachevskii State Univ, USSR Edwardsville Lois E Reed, Flagstaff, AZ Robert J Blodgett, Allen, MD Vivakanand Kadarnauth, Scarborough, Ryozi Sakai, Kariya-Higashi Senior HS, Joseph E Carroll, Arcata, CA Ontario, Canada Aichi Kariya, Japan Ji Cheng Chen, Zhongshan Univ, Maysoon Fathi Khalaf, Riyadh, Saudi Dinesh G Sarvate, College of Charleston, Guangzhou, People's Republic of Arabia sc China Seunghwan Kim, Cornell Univ, Ithaca, Nicholas I Shepherd-Barron, Univ of Yubo Chen, Shandong Normal Univ, NY Illinois, Chicago People's Republic of China YoungS Kim, Duluth, MN Zhongzhou Shu, Southwestern Jiaotong Gabriel Ciobanu, Univ Al I Cuza, lasi, Marek Aleksander Kowalski, Univ of Univ, Sichuan; People's Republic of Romania Warsaw, Poland China Jack Clark, Western Maryland College, Yaya Sukjaya Kusumah, Jurusan Andrzej Sierocinski, Warsaw Tech Univ, Westminster, MD Pendidikan Mathematics, Bandung, Poland Roza Dabrowska, Pedagogical Univ, Indonesia Rumen Simeonov, Sofia, Bulgaria Zielona Gora, Poland Alexandr M Kytmanov, lnst of Physics, Marvin A Solberg, Edgewater, MD Johanna Danos, Kaneohe, HI Krasnoyarsk, USSR Max A Stafford, Colorado Springs, CO Tilak Ananda De Alwis, Univ of Stanley C M Leung, Eugene, OR Vojislav Stojkovic, Laguna Hills, CA Mississippi, University Simon N Litsyn, Perm, USSR David L Stout, Univ of West Florida, RenDing, Hebei Teachers Univ, Hebei, Jiang-Hua Lu, Univ of California Pensacola People's Republic of China Berkeley Dorothy Lee Stowers, Houston, TX Robert D Dolan, Elizabethtown College, Zhikang Lu, Southern Illinois Univ, Timothy B Straney, Albuquerque, NM PA Edwardsville Zhila Tabatabai, Fayetteville, AR Kurt Drummond, Univ of the West Christopher Michael Luczynski Cheshire, Judith F Tavel, Vassar College, Indies, Kingston, Jamaica MA Poughkeepsie, NY Nancy R Dunn, Univ of New Orleans, LA Lawrence J Marx, Univ of California Philip Uri Treisman, Univ of California Kenneth J Dykema, Univ of California Davis Berkeley . Berkeley Valentin Matache, Univ of Timisoara, Charles Tresser, IBM, Yorktown Heights, John D Earle, Scottsdale, AZ Romania NY JeffreyS Ely, Westerville, OH Daniel Mayost, Ottawa, Ontario, Canada Lau P Van den Dries, Univ of Illinois, Katherine S Eskew, Martin, TN David W McLaughlin, Univ of Arizona, Urbana Eugene A Feinberg, Hamden, CT Tucson Tony F Von Sadovszky, Reno, NV Elzbieta Ferenstein, Tech Univ of Kentaro Mikami, Akita Univ, Japan Relja Vulanovic, Univ of Novi Sad, Warsaw, Poland Paraskevoula M Mina, Limassol, Cyprus Yugoslavia John L Friese, Anchorage, AK Ngaiming Mok, Columbia Univ, New Stanislaw Walczak, Lodz Univ, Poland York, NY 1110 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS Richard H Wallis, Academic Press, San Heinrich Voss NOMINEE MEMBERS Diego, CA Indian Mathematical Society California St Polytech University Yue Yun Wang, Shanghai Jiao Tong Harvansh L Manocha Nancy Heywood Albert of China Univ, People's Republic Iranian Mathematical Society City College (CUNY) Di Wei, Sichuan Univ, People's Wan Assad Niknam Kemaul N Ally of China Republic Israel Mathematical Union Steve Bobea Donald Ferguson Winter, Redlands, CA Yehuda Pinchover Raquel Can6 de Zdzislaw Wojtkowiak, Univ Autonoma Korean Mathematical Society Ruby Anne E Deveras Spain Barcelona, Young Hyun Cho David W Felts D Wolden, Beaver, UT Lohra Mathematical Society of Japan Damon L Gang Stephen Wolfram, Wolfram Research, Tsuyoshi Hayashida GengXin Huang IL Champaign, Yasushi Matsuoka Mini! Lee Wood, Seattle Pacific Univ, WA Dick A Tadayoshi Mizvtani Fenton Li Shi Wujie, Southwest China Teachers New Zealand Mathematical Society Lifoma Salaam Univ, Sichuan, People's Republic of Margaret J Morton Rob Schneiderman China Polskie Towarzystwo Matematyczne Phillip G Shirts Frederico Xavier, Univ of Notre Dame, Marian Kwapisz Tai-Ho Wu IN Donghui Zhang Christian L Yankov, Bulgarian Acad of Societe Mathematique de France Oklahoma State Univ, Stillwater Science, Sofia, Bulgaria Jean-Luc Archambault Cindy H Clements Lily Yen, Burnaby, British Columbia, Augustin Blaquiere Canada Mireille B Campana Pan American University Weian Zheng, East China Normal Univ, Robert Domain John E Bernard Shanghai, People's Republic of China Robert A Gergondey St Lawrence University Qi Ji Zhu, Zhejiang Univ, People's Michel Roger Hare! George L Ashline Republic of China Salah-Eddine Kabbaj Mark H Hays Wan Zhuang, Shandong Normal Univ, Francoise Michel James P Hoyt People's Republic of China Paul Sablonniere Karen J Kobasa Michael T Zubal, Parma, OH Suomen Matemaattinen Yhdistys University of California, Riverside Magnus Steinby Chong Liang Svenska Matematikersamfundet University of California, San Diego RECIPROCITY MEMBERS Torbjorn Sigurd Kolsrud Mark K Yasuda Deutsche Mathematiker- Vereinigung e. V. Unione Matematica lta/iana University of Massachusetts, Boston Franz B Kalhoff Luigi Favella Sidney S Atwood Hanno Lefmann Franco Giannessi Margaret V Zaleskas PARTITION PROBLEMS IN TOPOLOGY Stevo Todorcevic (Contemporary Mathematics, Volume 84) This book presents results on the case of the Ramsey problem 1980 Mathematics Subject Classifications: 04-02, 03E05, 03E50; 50-02, for the uncountable: When does a partition of a square of 54A25 an uncountable set have an uncountable homogeneous set? ISBN 0-8218-5091-1 , LC 88-39032 ISSN 0271-4132 This problem most frequently appears in areas of general 130 pages ( softcover), January 1989 topology, measure theory, and functional analysis. Building on Individual member $13, List price $22, his solution of one of the two most basic partition problt:~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 All prices subject to change. Shipment will be made by surface. theory at the level of a first year graduate or advanced For air delivery add, lst book $5, each additional book $3, undergraduate student. The book may also be of interest maximum $1 00. Prepayment required. Order from American to the exclusively set-theoretic reader, for it provides an Mathematical Society, P.O. Box 1571, Annex Station, Provi excellent introduction to the subject of forcing axioms of set dence, RI 02901-1571, or call toll free 800-566-7774 to charge theory, such as Martin's axiom and the Proper forcing axiom. with VISA or MasterCard. OCTOBER 1989, VOLUME 36, NUMBER 8 1111 Classified Advertisements SUGGESTED USES for classified advertising are positions available, books or lecture notes UNIVERSITY OF CALIFORNIA for sale, books being sought, exchange or rental of houses, and typing services. LOS ANGELES THE 1989 RATE IS $42.50 per inch on a single column (one-inch minimum), calculated Department of Mathematics from the top of the type; $18 for each additional 1/2 inch or fraction thereof. No discounts for multiple ads or the same ad in consecutive issues. For an additional $10 charge, TEMPORARY POSITIONS announcements can be placed anonymously. Correspondence will be forwarded. (1) Two E. R. Hedrick Assistant Pro Advertisements in the ··positions Available·· classified section will be set with a minimum fessorships. Applicants must show very one-line headline, consisting of the institution name above body copy, unless additional strong promise in research and teaching. headline copy is specified by the advertiser. Advertisements in other sections of the classified pages will be set according to the advertisement insertion. Headlines will be centered in Salary $37,000. Three year appointment. boldface at no extra charge. Classified rates are calculated from top of type in headline to Teaching load: four quarter courses per bottom of type in body copy, including lines and spaces within. Any fractional text will be year, which may include one advanced charged at the next 1/2 inch rate. Ads will appear in the language in which they are submitted. course in the candidate's field. Pref Prepayment is required of individuals but not of institutions. There are no member erence will be given to applications discounts for classified ads. Dictation over the telephone will not be accepted for classified completed by January 1 , 1990. advertising. (2) Two or three Research Assistant DEADLINES are listed on the inside front cover or may be obtained from the AMS Professorships in Computational and Advertising Department. Applied Mathematics. Applicants must U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, show very strong promise in research religion or national origin. ··positions Available·· advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution and teaching. Salary $37,000. Three year does not discriminate on these grounds whether or not it is subject to U. S. laws. Details appointment. Teaching load: four quarter and specific wording may be found near the Classified Advertisements in the January and courses per year, which may include one July/August issues of the Notices. advanced course in the candidate's field. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians Preference will be given to applications are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and completed by January 1, 1990. speak to Paula Montella for further information. (3) One or two Assistant Profes SEND AD AND CHECK TO: Advertising Department, Attn: Paula Montella, AMS, P. 0. Box sorships in the Program in Comput 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 ing (PIC). Applicants must show very Charles Street, Providence, Rhode Island 02904. Individuals are requested to pay in advance, strong promise in teaching and research, institutions are not required to do so. AMS FAX 401-331-3842. preferably in the general area of Logic, Language and Computation. Teaching load: four quarter programming courses POSITIONS AVAILABLE and an advanced quarter course of the NORTHERN ILLINOIS UNIVERSITY candidate's choice per year. Two year Department of Mathematical Sciences COMMUNITY COLLEGE Fall1990 appointment, possibly renewable once OF PHILADELPHIA or twice. Salary range: $37,000-$44,000. Several anticipated tenure-track posi Preference will be given to applications The Mathematics Department invites ap tions in pure and applied mathemat completed by January 1, 1990. plications for an anticipated 1990 tenure ics at assistant professor level begin (4) One or two Lectureships in the track position. Candidates must have at ning Fall 1990. Applicants should have Program in Computing (PIC). Applicants least a Master's Degree in Mathematics, strong research record or potential and must show very strong promise in the a commitment to quality teaching both strong commitment to teaching. Math teaching of programming. Teaching load: remedial and college level students, and ematicians in any area of pure and five quarter programming courses per a serious interest in curriculum develop applied mathematics may apply. Ap year. One year appointment, possibly ment. plicants should anticipate completion renewable up to four times. Salary de The department is actively engaged of the Ph.D. by August 1990. Prefer pends on experience, begins at $31 ,200. in developing new mathematics courses. ence for research complementing that (5) Subject to administrative approval, It has recently received grants from NSF of present faculty. Salary range com a few adjunct assistant professorships. and CASET. Outstanding benefits. Send petitive. Research-oriented department, Two year appointments. Strong re curriculum vitae and 3 letters of recom offers Ph.D. Two-course teaching load. search and teaching background re mendation to: William Clee, Head, Dept. Send vita and three letters of reference quired. Salary $32,400-$36,500 per year. of Mathematics, COMMUNITY COL by January 15, 1990 (this deadline may Teaching load: five quarter courses per LEGE OF PHILADELPHIA, 1700 Spring be extended) to: year. Garden Street, Philadelphia, PA 19130. Dr. J. L. Selfridge, Chair (6) Several positions for visitors and Women and minorities are encouraged to Department of Mathematical lecturers. To apply, write to Alfred W. apply. CCP is an affirmative action/equal Sciences Hales, Chair, Department of Mathemat opportunity employer. Applications due Northern Illinois University ics, University of California, Los Angeles, November 3, 1989. DeKalb, IL 60115-2888 CA 90024-1555. Attn: Staff Search. Northern Illinois University is an Affirma UCLA is an equal opportunity/affirm tive Action/Equal Opportunity Employer. ative action employer. 1112 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements AVAILABLE POSITIONS THE AIR FORCE FLIGHT tory, the use of modern computers, and DYNAMICS LABORATORY other service support will be provided UNIVERSITY OF and for the visiting professor and may in WISCONSIN-MADISON THE AIR FORCE INSTITUTE clude support for a limited number of the Department of Mathematics OF TECHNOLOGY visiting professor's doctoral students. Employment Opportunities announce the PERIOD OF APPOINTMENT AND SALARY 1990-1991 The initial period of appointment is The Department of Mathematics at the FLIGHT CONTROL one full year. A shorter period and University of Wisconsin-Madison solicits DISTINGUISHED VISITING for but applications for the following positions PROFESSOR PROGRAM the starting date are negotiable, to begin fall 1990. should be prior to October 1, 1990. Tenure and Tenure Track Positions. The Air Force Institute of Technology Extension for a second year may be Force Appointments will be made at the Assis (AFIT) at Wright-Patterson Air possible. Salary is commensurate with tant Professor level unless qualifications Base, Dayton, Ohio announces the op qualifications. A per diem allowance is and experience require appointment at portunity to join the AFIT graduate fac also paid. higher rank. Deadline for applications is ulty as a Distinguished Visiting Profes APPLICATION November 30, 1989. sor in the Department of Electrical and A resume of qualifications and ex of Van Vleck Assistant Professorships. Computer Engineering in the School perience, including a list of significant Appointments are for a specified term of Engineering. publications and any need for support of three years at an academic year salary of RESPONSIBILITIES Ph.D students can be submitted anytime at least $31 ,500. The usual teaching load The responsibilities of the AFIT Distin prior to February 28, 1990 to: is two courses per semester. Ordinarily guished Visiting Professor include pro Capt RANDALL N. PASCHALL teaching only those applicants who have received viding academic leadership in Department of Electrical and their doctorate since 1987 and prior and research in association with AFIT Computer Engineering to September 1990 will be considered. faculty and students, and initiating and Air Force Institute of Technology Preference will be given to candidates conducting research and consultation (AFIT/ENG) Air who are likely to interact well with other with the Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio members of the Department. Deadline Force Wright Research and Development 45433-6583 for applications is December 31, 1989. Center. Phone:(513) 255-3576 Candidates should provide clear evi QUALIFICATIONS The Flight Control Distinguished Visit dence of teaching ability and excellence The person appointed as Distin ing Professor Program is made possible be an in mathematical research. Supporting guished Visiting Professor should through a grant from the Air Force materials should include a vita, and eminent faculty member at a prestigious Wright Research and Development Cen three or four recommendation letters, at university. Selection will be based upon ter's Flight Dynamics Laboratory: least one of which discusses, in detail, the individual's experience, proposed AFIT is an Equal Opportunity and the candidate's teaching qualification. teaching program and research areas. Affirmative Action Employer. Van Vleck applicants are also required Areas of special interest and activity at to submit a one to three page abstract AFIT are: Flight Control Systems, Con of their dissertation. trol Systems for Reconfigurable Aircraft, Control Application forms are available from Design of Robust Multivariable FAIRFIELD UNIVERSITY Theory the Hiring Committee, Department of Systems, Quantitative Feedback Tenure-track Position in Mathematics Mathematics, 223 Van Vleck Hall, 480 Design, Output Digital Feedback De level Assistant Professor is Lincoln Drive, Madison, WI, 53706. Appli sign Technique for Multivariable Track An entry and to start in September 1990 cations will be accepted for all positions ing Systems, Hoc Control Theory, sought have a Ph.D. in Mathematics until they are filled; however, in order to Adaptive Control and Estimation. Appli who must of teaching ability. Normal ensure full consideration, the application cants are expected to have a Ph.D. and and evidence the area load is 3 courses per semester and all supporting materials should be be a professional contributor in teaching Salary is competitive and received by the above deadlines. The of flight control. Consideration will be plus research. consideration is given to dossiers University of Wisconsin is an AA/EOE given to applicants who have extensive full industry by February 1 , 1990. Please employer. flight control experience within completed and three letters of The Immigration Reform and Control and government. send a resume to Joseph B. Dennin, Chair, Act of 1986 requires the University to RESEARCH SUPPORT reference (EAI of Math and Computer Science, verify the identity and work authorization Two powerful hybrid computers Dept. Fairfield, CT 06430- of the successful applicant. Offer of em SIMSTARS) are the heart of AFIT's Fairfield University, fidelity, is a Jesuit University ployment is contingent upon verification. flight control laboratory. A high 7524. Fairfield full flight envelope, real-time aircraft sim located 60 minutes from New York City. ulator is developed for academic and It is an Equal Opportunity I Affirmative research use. Overall, AFIT's computer Action Employer. resources equal or exceed those found at other universities. An office, labora- OCTOBER 1989, VOLUME 36, NUMBER 8 1113 Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF UTAH UNIVERSITY OF CALIFORNIA Department of Mathematics SANTA CRUZ NORTH CAROLINA STATE UNIVERSITY invites applications for the Department of Mathematics following positions: The Mathematics Department at the University of California, Santa Cruz is A junior-level tenure-track position in 1. At least four full time tenure track recruiting for a position in algebra or probability and stochastic processes will appointments on any of the professorial number theory. The teaching load is become available July 1, 1990. Require levels. The Department is particularly in 4 one-quarter courses per year. Rank: ments include records in or strong po terested in applicants who work in the Assistant Professor 1-111. Minimum Quali tential for research and instruction. To areas of geometry, algebra, topology, fications: Ph.D. in Mathematics. Demon apply, send resume, any reprints or pre group representation theory, applied strated achievements in, or potential prints, and thesis abstract, and arrange mathematics, and scientific computing. for, research, teaching and professional to have three letters of reference sent to: Selection will be based on research ex service, commensurate with experience. J. W. Bishir, Department of Mathematics, pertise and teaching ability. Applications Salary: $32,400-$34,900. Effective: July Box 8205, North Carolina State Univer will be accepted until January 31, 1990 1, 1990. Applicants should send vitae, sity, Raleigh, NC 27695-8205. AA/EOE. or until the positions are filled. information about their research and Applications from women and minorities 2. Two or more nonrenewable three teaching experience and four letters of are especially encouraged. year Instructorships. Persons of any age recommendation commenting on their receiving Ph.D. degrees in 1989 or 1990 teaching and research, to-Recruitment are eligible. Applicants will be selected Committee, Mathematics Department, on the basis of ability and potential in University of California, Santa Cruz, teaching and research. Starting salary CA 95064. Closing Date: December 31, this academic year is $29,500; cost of 1989. Please refer to #190-890 in your living increases are contingent on action reply. UCSC IS AN EEO/AA/IRCA EM by the State Legislature. Duties consist PLOYER MARYVILLE COLLEGE-ST. LOUIS of teaching five courses during the three MATHEMATICS/ ACTUARIAL SCIENCE quarter academic year. Applications will (Search Re-Opened) be accepted until December 31, 1989 or until the positions are filled. Louis invites appli Maryville College-St. 3. One or more visiting positions of one position beginning cations for a faculty year or less. Selection criteria are teach in mathematics re January, 1990. Ph.D. ing ability and potential contribution to 1, 1989. Education WESTERN ILLINOIS UNIVERSITY quired by December our research environment. Applications experience must be compatible with DEPARTMENT OF MATHEMATICS and will be accepted until January 31, 1990 of the mathematics the curricular needs or until the positions are filled. Applications and nominations for the undergraduate pro and actuarial science Applications must include curriculum position of chairperson with associate The successful candidate is ex grams. vitae, bibliography and three letters of or full professor faculty rank are in to teach a wide range of courses, pected reference. (Instructorship applications vited. The doctorate in mathematics, in ac including upper division courses must also include an abstract of the statistics, or mathematics education is Strong commitment tuarial mathematics. thesis and either a list of graduate required. Evidence of excellence in un Rank and salary to teaching is required. courses completed or a transcript of dergraduate and graduate teaching, a qualifications and commensurate with graduate work.) record of substantial research/scholarly experience. Please send your application to: achievement, and the demonstration of Louis is a pri Maryville College-St. COMMITTEE ON STAFFING appropriate administrative ability is ex with a student vate, liberal arts college DEPARTMENT OF pected. The selection process will begin in West St. enrollment of 3,000 located MATHEMATICS November 1, 1989 and continue until the Louis County. UNIVERSITY OF UTAH position is filled. Send application, vita, letter, resume, Please send cover 233JWB photocopies of transcripts, and at least by and the names of three references SALT LAKE CITY, UTAH 84112 three letters of reference to: Chairperson to: November 1 , 1989 The University of Utah is an equal Search Committee; Department of Math B. Lammert Mrs. Dianna opportunity-affirmative action employer. ematics; Macomb, II 61455. WIU IS AN Director of Human Resources EQUAL OPPORTUNITY AFFIRMATIVE LOUIS MARYVILLE COLLEGE-ST. ACTION EMPLOYER. WOMEN, MINORI 13550 Conway Road TIES, AND HANDICAPPED PERSONS St. Louis, Missouri 63141 ARE ESPECIALLY ENCOURAGED TO AA/EOE. APPLY. 1114 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE THE UNIVERSITY OF FLORIDA BEMIDJI STATE UNIVERSITY Department of Mathematics CARNEGIE MELLON UNIVERSITY Applications are invited for a tenure A Zeev Nehari Assistant In each of the next several years, the track position in mathematics beginning Professorship in Department of Mathematics intends to August 30, 1990. A doctorate with em Mathematics fill a substantial number of tenure-track phasis in any area of pure or applied faculty positions with mathematicians of mathematics or doctoral candidate with The Zeev Nehari Assistant Professor exceptional caliber. Outstanding candi an emphasis in any area of pure or ap ships have been instituted in the De dates from all academic ranks and all plied mathematics with degree expected partment of Mathematics of Carnegie areas of pure and applied mathematics by August 30, 1990, is required. Commit Mellon University to honor the memory are invited to apply for these positions. ment to quality teaching will be expected of Professor Zeev Nehari, a member Applications from junior candidates with of all candidates. Candidates for this of the Department from 1954 to his post-doctoral experience are especially position will be expected to teach a wide death in 1978. The position available welcome. variety of mathematics courses ranging is for an initial period of one or two First preference will be given to can from precalculus level courses to upper academic years, beginning in September didates who will facilitate Department level courses in pure andjor applied 1990, and extendable for one additional goals of establishing strong working mathematics. In addition to teaching, the year when mutually agreeable. It car groups in partial differential equations, person who fills this position will be ries a reduced academic year teaching algebraic geometry and number theory. required to work with other faculty mem load of six hours per week during one Secondary preference will be given to bers and students in curriculum devel semester and three hours per week dur candidates who will fit well into currently opment, student placement, and student ing the other. Applicants are expected functioning groups. In particular, it is advising. All applicants must be able to to show exceptional research promise, likely that one position will be filled this lawfully accept long term employment in as well as clear evidence of achieve year by an algebraist. the United States at the time of an offer ment and should have research inter Senior candidates should have dis of employment. Appointments will gen ests which intersect those of current tinguished research records, and junior erally be at the assistant professor level faculty of the Department. Applicants candidates are expected to have made although in exceptional cases a more should send a vita, list of publications, significant research contributions. Every senior appointment is possible. Starting and a statement describing current and candidate is expected to possess a salary range is $28,000 to $35,000. For planned research, and arrange to have strong commitment to teaching. Candi information about the position contact at least three letters of recommenda dates should forward a resume (includ Dr. Tom Richard, Department of Math tion sent to the committee. Applications ing a list of publications) and should ematics and Computer Science, Bemidji also should include at most three two arrange for at least four letters of rec State University, Bemidji, MN 56601- digit mathematics subject classification ommendation to be sent to: 2699. Submit letter of application, re numbers (as displayed in Mathematical David A. Drake, Chair sume, transcripts of all graduate course Reviews) corresponding to the primary Department of Mathematics work (official transcripts are required at area( s) of research of the applicant. All University of Florida the time of employment), and three (3) communications should be addressed 201 Walker Hall letters of reference submitted directly by to: Zeev Nehari Assistant Professorship Gainesville, Florida 32611 referrer to Dr. Frank Saccoman, Dean Committee, Department of Mathematics, All applications for the academic year of Science and Mathematics, Bemidji Carnegie Mellon University, Pittsburgh, 1990-1991 should be complete by De State University, Bemidji, MN 56601- PA 15213. Carnegie Mellon University is cember 31, 1989. The University of 2699. Postmarked deadline is December an Affirmative Action/Equal Opportunity Florida is an equal opportunity employer 1, 1989, applications will be accepted Employer. and energetically solicits applications after that date if the position is still from women and minority candidates. open. Equal Opportunity Educator and Employer. OCTOBER 1989. VOLUME 36, NUMBER 8 1115 Classified Advertisements POSITIONS AVAILABLE UTAH STATE UNIVERSITY DARTMOUTH COLLEGE Department of Mathematics and UTAH STATE UNIVERSITY Statistics Senior Position in Mathematics. Asso Department of Mathematics and ciate or Full Professor position avail Statistics Applications and nominations are invited able beginning in 1990-91. Candidates for tenured or tenure-track positions should have established and recognized Applications and nominations are invited in mathematics and statistics beginning research program, proven ability to at for tenured or tenure-track positions in September, 1990. Applications in all ar tract external research support, and nonlinear partial differential equations eas and at all ranks will be considered. interest in building and leading a strong and/or dynamical systems, beginning Excellence in research and a demon research group. Appointee will partici September, 1990. Applications for all strated commitment to both graduate pate in the recruitment for several junior ranks will be considered. and undergraduate teaching are sought. positions. Proven record of excellence Excellence in research and a demon Successful applicants in applicable ar in teaching at both the undergraduate strated commitment to both graduate eas will be expected to interact with and graduate levels and commitment and undergraduate teaching are re the mathematics, statistics and applied to professional interaction with faculty quired. Successful applicants will be science faculty at USU. The ability to and Ph.D. students required. Applica expected to interact with the applied provide broad scholarly leadership is tions are welcome in all fields of math science faculty at USU, as well as col essential for senior-level applicants. ematics. Department has special inter leagues in mathematics and statistics. Utah State University, located in the ests in algebra, combinatorics, geom The ability to provide broad scholarly Wasatch Range of the Rocky Mountains, etry /topology, and probability /statistics. leadership is essential for senior-level offers competitive salaries and excel Dartmouth provides grants to new fac applicants. lent medical, retirement and professional ulty members for research-related ex Utah State University, located in the benefits. penses, a generous sabbatical program, Wasatch Range of the Rocky Montains, Applications, including resume and and moderate teaching loads. The review offers competitive salaries and excel three letters of reference, should be of applications will begin on January 1, lent medical, retirement and professional submitted to: Search Committee, De 1990. Send a letter of application, a benefits. partment of Mathematics and Statistics, curriculum vitae, the names of four peo Applications, including resume and Utah State University, Logan, UT 84322- ple who have agreed to write letters three letters of reference, should be sub 3900. Preference will be given to appli of recommendation, and a description mitted to: Michael P. Windham, Search cations completed by January 31, 1990, of research interests to: Mathematics Committee, Department of Mathematics but all will be considered until available Senior Search Committee Chair, De and Statistics, Utah State University, Lo positions are filled. partment of Mathematics and Computer gan, UT 84322-3900. Preference will be Utah State University is an equal Science, Bradley Hall, Dartmouth Col given to applications completed by Jan opportunity /affirmative action employer. lege, Hanover, NH 03755. Dartmouth is uary 1990, but all will be considered 31, firmly committed to Affirmative Action until available positions are filled. and strongly encourages applications Utah State University is an equal from minorities and women. opportunity/affirmative action employer. TEXAS TECH UNIVERSITY Texas Tech University seeks applica tions for a position in the Department UNIVERSITY OF GEORGIA Mathematics opening in the Fall of of Department of Mathematics 1990. To qualify applicants must 1) have Athens, GA 30602 THE JOHNS HOPKINS UNIVERSITY a Ph.D. from a recognized university, 2) have a strong dedication to both teach The department may have some tenure Applications are invited for a junior po ing and research, 3) exhibit research track positions available for the 1990-91 sition in statistics, to begin in Fall 1990. interests that are compatible with ongo academic year at the assistant and as Selection is based on demonstration and ing programs in the department and 4) sociate professor levels. The rank and promise of excellence in research, teach be willing and able to work with students salary will be commensurate with the ing, and innovative application. AA/EOE. at both the undergraduate and graduate applicant's abilities and experience. The Applicants are asked to furnish a vita, level. To apply send resume and have principle requirement is excellence in transcripts, a letter describing profes three letters of recommendation sent teaching and research. Some prefer sional interests and aspirations, and to Harold Bennett, Chairman of Hiring ence will be given to areas in which arrange for three letters of recommen Committee, Department of Mathematics, the department is already well repre dation to be sent to Prof. John C. Texas Tech University, Lubbock, Texas sented. Send curriculum vitae and four Wierman, Chairman, Mathematical Sci 79409. Applications are to be received letters of recommendation to Richard ences Department, The Johns Hopkins no later than November 15, 1989. Texas A. Bouldin Head (address above) by University, Baltimore, MD 21218. Tech University is an equal opportunity January 15, 1990. UGA is an Equal Op employer. EOE/ AA. portunity I Affirmative Action Employer. 1116 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE WAKE FOREST UNIVERSITY TRINITY UNIVERSITY The Z. Smith Reynolds Position Announcement CALIFORNIA STATE Professorship in Mathematics UNIVERSITY, NORTHRIDGE Trinity University invites applications and Wake Forest University announces the nominations for a tenure-track position Applications are invited for four tenure establishment of a distinguished profes in mathematics, appointment beginning track positions for the Fall of 1990. Three sorship made possible by the Z. Smith August, 1990. The appointment will be positions at the assistant professor level Reynolds Foundation. The scholar se made at the rank of Assistant Professor. in areas of interest to the faculty and lected to fill this position must have an Responsibilities include teaching nine possibly one at the associate profes established record of recognized schol credit hours per semester, continuing sor level, will be available. A Ph.D. by arship and a commitment to teaching scholarly activity, assisting in curriculum the Fall of 1990 is required. Candidates and research in a university setting. development, advising, and committee in Mathematics Education and Applied Duties include teaching, continuing a service. Minimum qualifications are the mathematics (especially with experience program of research, contributing to Ph.D. in Mathematics with excellence in in industry) are encouraged to apply, but the intellectual life of the Department and strong commitment to teaching. candidates in all areas of mathematics of Mathematics and Computer Science, Founded in 1869, Trinity University with a commitment to both teaching and and fostering the mathematical growth occupies a modern campus overlook research will be considered. Responsi of gifted undergraduates. The position, ing the San Antonio skyline. Purposely bilities include teaching 9-12 hours, de which carries both tenure and the rank small and selective, with about 2500 pending on research and/or other con of professor, could be filled as early as students, Trinity stresses a high quality, tributions. Send vita and three letters of the fall semester of 1990. undergraduate liberal arts and science recommendation to Jerry Rosen, Hiring Wake Forest University is a compre program; in particular, the Mathemat Committee Chair, Dept. of Mathematics, hensive university with 5000 students, ics Department does not offer graduate California State University, Northridge, 3500 of whom are in the undergraduate courses. San Antonio is a city of ap CA 91330 by Feb. 15 for full con college. The Department of Mathematics proximately 850,000 people situated in a sideration. Women and minorities are and Computer Science has 17 per metropolitan area of 1.2 million. especially encouraged to apply. CSUN manent positions, 13 of which are in Closing date for applications is De is located in a Northwestern suburb of mathematics, and offers majors in math cember 29, 1989. Send vita, graduate Los Angeles and is in close proximity ematics and computer science and an transcripts and three letters of reference to Cal. Tech., U.S.C., and U.C.L.A. (15 MA in mathematics. to: mins. away). Inquiries, nominations, and applica Professor William F. Trench AFFIRMATIVE ACTION/EQUAL OP tions should be directed to: Department of Mathematics PORTUNITY EMPLOYER Professor Richard Carmichael, Trinity University Chair 715 Stadium Drive Department of Mathematics and San Antonio, Texas 78212 MACALESTER COLLEGE Computer Science Trinity University is an equal opportunity Mathematics/Computer Science P.O. Box 7311 affirmative action employer. 1600 Grand Ave. Wake Forest University St. Paul, MN 55105 Winston-Salem, NC 27109 USA Evaluation of applicants will begin in late THE OHIO STATE UNIVERSITY Applications are invited for two approved winter and will continue until the position Department of Mathematics tenure-track positions in Mathematics, is filled. AA/EO employer. and one position, subject to adminis Research Instructorships in Mathematics trative approval, in Computer Science, beginning in September, 1990. Candi Applications are invited for the position WILLIAMS COLLEGE dates should have a Ph.D. and an of research instructor in mathematics for interest in a career of teaching and re Department of Mathematics Williamstown, Massachusetts 01267 the academic year 1990-91. Candidates search in a four-year liberal arts college. should hold a Ph.D. (or equivalent) in Teaching load is 6-9 hours a week. Three anticipated positions, probably at mathematics and show strong research Competitive salary scale, good benefits, the rank of assistant professor, for promise. pleasant urban residential location. Ap Fall 1990. Strong Commitment to both Please send credentials and have plicants should supply resume and three teaching and scholarship is essential. letters of recommendation sent to Pro references to Professor Wayne Roberts, Please have a vita and three letters fessor Joseph Ferrar, Department of address above. Applications received un of recommendation on teaching and Mathematics, The Ohio State Univer til positions filled. Macalester is an equal research sent to Frank Morgan, Chair. sity, 231 W. 18th Avenue, Columbus, opportunity, affirmative action employer. Evaluation of applications will continue Ohio 4321 0. The Ohio State University is Women and minorities are especially until positions are filled. an Equal Opportunity1 Affirmative Action encouraged to apply. AA/EOE Employer. OCTOBER 1989, VOLUME 36, NUMBER 8 1117 Classified Advertisements AVAILABLE POSITIONS UNIVERSITY OF CALIFORNIA MILLS COLLEGE LOS ANGELES Oakland, California STEPHEN F. AUSTIN Department of Mathematics STATE UNIVERSITY The Department of Mathematics and Department of Mathematics and REGULAR POSITIONS IN Computer Science invites applications Statistics PURE AND APPLIED MATHEMATICS for a tenure track position as an As Nacogdoches, Texas 75962 Four to six regular positions in pure and sistant Professor of Mathematics, to applied mathematics. Areas of specific commence in the fall of 1990 (subject Applications are invited for the position interest include logic; algebra, algebraic to final budgetary approval). Applicants of Chairman of the Department of Math geometry, number theory and combi must have a Ph.D. in mathematics and ematics and Statistics. Desired qualifica natorics; geometry and topology; anal should submit evidence of exceptional tions include earned doctorate, proven ysis, functional analysis, mathematical teaching ability and strong research po leadership and administrative capabil physics and dynamical systems; prob tential. Mills is a small liberal arts college ity. Also, demonstrated teaching excel ability, statistics and game theory; lin for women, located in the San Francisco lence, research accomplishments, and ear and non-linear differential equations; Bay Area, and is known for its innovative other qualifications suitable to appoint applied mathematics, numerical analy mathematics and ::omputer science pro ment at a senior rank in a department sis and mathematical computer science. grams. Applications should include a vita of mathematics and statistics. Salary Very strong promise in research and and three letters of reference (address is competitive. Eleven-month appoint teaching required. Positions initially bud ing both teaching ability and research ment. Duties to begin Summer of 1990 geted at the assistant professor level. potential). Please have all materials sent or Fall Semester 1990. Submit letter Sufficiently outstanding candidates at to: of application, resume, transcripts and higher levels will also be considered. Head of the Mathematics Search three letters of recommendation post Teaching load: Averaging 1.5 courses Committee marked by January 1, 1990 to: Dr. R. G. per Quarter, or 4.5 Quarter courses per Department of Mathematics and Dean, Chairman of Search Committee, year. Computer Science Department of Mathematics and Statis To apply, write to Alfred W. Hales, Mills College tics, Stephen F. Austin State University, Chair, Department of Mathematics, Uni 5000 MacArthur Blvd. Nacogdoches, Texas, 75962. EOE/ AA. versity of California, Los Angeles, CA Oakland, California 94613 90024-1555. Attn: Staff Search. UCLA is The deadline for completed applications an equal opportunity/affirmative action is January 20, 1990. Mills College is UNIVERSITY OF VIRGINIA employer. an affirmative actionjequal opportunity employer. The Department of Applied Mathemat ics at the University of Virginia seeks OREGON STATE UNIVERSITY with a strong in a numerical analyst OREGON STATE UNIVERSITY terest in partial differential equations Assistant Professor positions in Alge and their physical applications. The De bra/Number Theory, Numerical Analysis, The Andreotti Assistant Professor posi partment, which cooperates closely with Geometric-Topology /Dynamical Systems, tion in mathematics will become available other departments within the School of and Differential Geometry will become September 16, 1990. Salary depends on Engineering and Applied Science where available September 16, 1990. Salary qualifications. Closing date is December it is located and with the Mathematics depends on qualifications. Closing date 15, 1989. Write to: Department in the College of Arts and December 15, 1989. Write to: Professor Bent Petersen, Chair Science, has active research progams Professor Bent Petersen Andreotti Professorship Selection in continuum mechanics, control theory, Staff Selection Committee Committee and numerical analysis/scientific com Department of Mathematics Department of Mathematics puting. The successful candidate will be Oregon State University Oregon State University able to support and direct doctoral stu Corvallis, Oregon 97331-4605 Corvallis, Oregon 97331-4605 dents in this latter area, to collaborate Oregon State University is an Affirma Oregon State University is an Affirma with faculty, and to teach a range of tive Action/Equal Opportunity Employer tive Action/Equal Opportunity Employer applied mathematics courses. EOE/ AA. and complies with Section 504 of the and complies with Section 504 of the Applications should be sent to Rehabilitation Act of 1973. OSU has a Rehabilitation Act of 1973. OSU has a James G. Simmonds, Chair policy of being responsive to the needs policy of being responsive to the needs Department of Applied of dual-career couples. of dual-career couples. Mathematics STAFF SELECTION COMMITTEE STAFF SELECTION COMMITTEE Thornton Hall B. E. Petersen, Chair B. E. Petersen, Chair University of Virginia B. I. Fein B. I. Fein Charlottesville, VA 22903 R. Higdon R. Higdon R. M. Schori R. M. Schori 1118 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE UNIVERSITY OF CALIFORNIA ILLINOIS INSTITUTE OF TECHNOLOGY IRVINE THE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS The Department of Mathematics invites John Jay College of Criminal Justice IRVINE, CALIFORNIA 92717 applications for two tenure-track fac Department of Mathematics ulty positions at the Assistant Professor Applications for an Assistant Profes level beginning August, 1990. Strong Professor, tenure-track posi Assistant sorship opening in the academic year preference will be given to candidates 1990. Requirements: Ph.D.; tion, January 1990-91 are invited: who specialize in Statistics or Numerical potential for research; demonstrated Candidates for the position must have Analysis and who are interested in solv commitment to teaching. Com strong a Ph.D. and a research record in either ing scientific or engineering problems. numer. ~al analysis or op puter science, Mathematical Physics or Differential Ge Requirements are a Ph.D. degree, evi background preferred. erations research ometry. Duties include research, under dence of outstanding research potential of Criminal Justice, John Jay College graduate and graduate teaching. Send and teaching ability, and U.S. citizenship is a senior col located in Manhattan, applications, curriculum vitae, work in or resident status. Send resume, graduate lege in CUNY. print or in preparation, and three let Submit a letter of application and a relevant reprints, dissertation transcript, ters of recommendation to: Professor curriculum vitae, and arrange for three three letters of reference to abstract and Abel Klein, Chairman of the Recruitment letters of recommendation to be sent, to: Department Samuel Graff, Chairperson, Committee, Department of Mathematics, M. J. Frank, Chairman John Jay College of of Mathematics, University of California, Irvine, CA 92717. Department of Mathematics 445 West 59 Street, Criminal Justice, Appointment begins on July 1, 1990. Illinois Institute of Technology 0019 by December 1, New York, NY 1 UC Irvine is an Affirmative Action/Equal Chicago, Illinois 60616 and women are encour 1989. Minorities Opportunity Employer. Applications received by December 15, AA/EOE Employer. aged to apply. If no qualified candidates apply, there 1989 will be considered first. I.I.T. is is a possibility that the position may be an Equal Opportunity I Affirmative Action upgraded. Employer. BROWN UNIVERSITY BROWN UNIVERSITY, Providence, Rl BOSTON UNIVERSITY THE OHIO STATE UNIVERSITY at the As 02912. Two professorships DEPARTMENT OF MATHEMATICS Department of Mathematics sociate Professor level or above, with tenure, to begin July 1, 1990. Salary to The Department of Mathematics at The Department of Mathematics of The be negotiated. Preference to be given Boston University invites applications Ohio State University hopes to fill several to applicants with research interests for two anticipated positions in the area positions, both visiting and permanent, consonant with those of the present of Dynamical Systems. One position effective Autumn Quarter 1990. Candi members of the Department. For one of is a permanent position at the Assistant dates in all areas of applied and pure the positions preference will be given to Professor level or higher. The successful mathematics are invited to apply. Sig those with research interest in Algebraic applicant should be a recognized scholar nificant research accomplishments or Geometry, Differential Geometry, or re in the field of dynamics and should have exceptional research promise, and evi lated fields. Candidates should have research interests which complement dence of good teaching ability, will be a distinguished research record and a those of current members of the Dynam expected of successful applicants. strong commitment to teaching. Qual ics group at Boston University. Salary Please send credentials and have ified individuals are invited to send a and academic rank are negotiable. The letters of recommendation sent to Pro vita and at least three letters of rec Department also seeks applications for fessor Joseph Ferrar, Department of ommendation, no later than November a two year visiting Assistant Professor Mathematics, The Ohio State University, 1, 1989, to Professor Robert Accola, ship in this field. Applications should 231 W. 18th Avenue, Columbus, Ohio Executive Officer, Department of Math be sent to: Search Committee, Depart 43210. Review of resumes will begin ematics, Brown University, Providence, ment of Mathematics, Boston University, immediately. Rl 02912. Brown University is an Equal 111 Cummington St., Boston, MA 02215. The Ohio State University is an Equal Opportunity 1Affirmative Action employer. AA/EOE. . Opportunity1 Affirmative Action Employer. OCTOBER 1989, VOLUME 36, NUMBER 8 1119 Classified Advertisements POSITIONS AVAILABLE RUTGERS UNIVERSITY-NEWARK THE CHINESE UNIVERSITY OF Professor of Mathematics HONG KONG OHIO UNIVERSITY Department of Mathematics The Department of Mathematics and THE CHINESE UNIVERSITY OF HONG Computer Science anticipates an open KONG invites applications for the post The Department of Mathematics antic ing at the Rank of Professor I or Profes of Lecturer in Mathematics-The post ipates the appointment of one tenure sor II beginning Fall 1990. Candidates is tenable in August 1990. Applicants track assistant professor in the area of should exhibit outstanding research ac should possess a Ph.D. degree in Math algebra or analysis beginning September complishments. Salary and teaching load ematics. Preference will be given to 1, 1990. Salary will be competitive. Du are negotiable. Applicants from all fields candidates working on Optimization and ties include research and teaching at the are invited. Areas of research inter Control Theory, Nonlinear Partial Differ undergraduate and graduate level. Appli est in the department include number ential Equations. Strong candidates in cants must have a Ph.D. in Mathematics theory, representation theory and auto all fields are, however, encouraged to and have research interests compatible morphic forms, Lie algebras, transfor apply. In addition to participation in the with the current faculty in algebra or mation groups, low dimensional topol activities of the Board of Studies in analysis. Send resume and have three ogy and Teichmuller theory. Nominations Mathematics, the appointee is expected letters of recommendation sent to Shih and applications should be sent to: Jane to undertake research in his/her field liang Wen, Chairman, Department of Gilman, Chair, Department of Mathemat of specialisation and be responsible for Mathematics, Ohio University, Athens, ics, Rutgers University, Newark, New teaching at the undergraduate and post Ohio 45701. The deadline for applica Jersey 071 02. The closing date for appli graudate level. Annual Salary (currently tions is January 1, 1990. cations is 1/15/90 but applications will under review): HK$206,040-233,820 by Ohio University is an Equal Opportu be considered until the position is filled. 2 increments BAR HK$247,680-344,400 nity and Affirmative Action Employer. AA/EOE. by 7 increments (approx. exchange rate: £1=HK$12.59; US$1=HK$7.8). Starting salary will depend on qualifications and experience. Conditions of Service: Ben efits include long leave, annual leave, sick leave, superannuation (University 15% of salary; appointee 5%), med ical benefits, education allowance for children, and housing allowance for an appointee whose annual salary is UNIVERSITY AT ALBANY BRYN MAWR COLLEGE HK$219,960 or above. An appointee State University of New York on overseas terms of service is enti are invited for two posi School of Public Health Applications tled to have passage benefits for him in Mathematics, to start September tions self/herself and his/her dependants. Ap We anticipate at least one appointment one open as to rank and tenured 1990, plication procedure: Applications should at the level of Professor in the Depart tenure-track, and one at Assistant or be made out in duplicate, giving full ment of Biometry and Statistics starting rank, tenure-track. One of the Professor particulars, experience as well as the Fall 1990. Candidates must have a Ph.D. person positions must be filled with a names and addresses of three referees, in Statistics or closely related field, an in the joint com taking responsibility with copies of certifi outstanding research record, research and sent together puter science program with Haverford and recent interests compatible with the ongoing cates/diplomas, testimonials College. Preferred specialties: geometry, publications to the Personnel Section, programs in the department, experience applied mathematics, or com algebra, The Chinese University of Hong Kong, in teaching graduate courses and in di research record puter science. Strong before December 31, recting graduate students. Applications Shatin, Hong Kong and excellence in teaching expected. 1989. Please quote reference number and 3 letters of recommendations must Women and minority candidates are es 72/509/2/89 and mark 'Recruitment' on be received by November 15, 1989. encouraged to apply. Please pecially cover. Applications from women and minori direct application and three letters of ties are encouraged. Apply to Lloyd recommendation to: F. Cunningham, Jr., Lininger, Chair, Department of Biometry Faculty Search, Department of Mathe and Statistics, School of Public Health, matics, Bryn Mawr College, Bryn Mawr, University at Albany, Empire State Plaza, PA 19010. Closing date January 1, 1990. Corning Tower Room 2523, Albany, New Bryn Mawr College is an EO/AA em York, 12237. EOE/AA. ployer. 1120 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements POSITIONS AVAILABLE BOSTON UNIVERSITY DEPARTMENT OF MATHEMATICS MathSciSM The Department anticipates two posi BOSTON UNIVERSITY tions in pure mathematics for Fall 1990. DEPARTMENT OF MATHEMATICS One at the Full or Associate Profes WHEN MathSci IS ONLINE sor level. The other level depending The Department of Mathematics at MATHEMATICS IS on candiates. Record of distinguished Boston University anticipates an op achievements in research and commit ON THE SCREEN pening for an Assistant Professor in ment to excellence in teaching required. Probability for Fall 1990. Outstanding Preference will be given to candidates Entries in Seconds candidates should be able to teach 800,000 in Number Theory and/or Algebraic Ge MathSci is the online database that finds, courses in Operations Research. Prefer ometry. Send applications to: Search in a matter of seconds, any information ence given to applicants with a strong published in Mathematical Reviews (MR), Committee, Department of Mathematics, theoretical background and a commit Current Mathemat1cal Publications (CMP}, 111 Cummington St., Boston, MA 02215. Current Index to Statistics (CIS}, and the ment to teaching. Send vita and 3 letters AA/EOE. Index to Statistics and Probability by John of reference to: Murad Taqqu, Depart 1\Jkey and Ian Ross. These combined ment of Mathematics, Boston University, sources give you over 800.000 entries in all 111 Cummington St., Boston, MA 02215. areas of the mathematical sciences. PUBLICATIONS AA/EOE. Monthly Updates MathSci is updated monthly, with over MATH SCI PRESS, 53 Jordan Rd., 3, 700 new entries from MR and 4,000 from Brookline, MA 02146, 617-738-0307, CMP; also quarterly updates of 750 new TOPICS IN PHYSICAL GEOMETRY, by entries from CIS. NEW MEXICO STATE UNIVERSITY R. Hermann, $80. In Preparation: Geo metric Aspects of Computer Science. Visiting and tenure-track positions for Easy Fingertip Access When can you use MathSci? Anytime ... 24 Fall 1990, primarily assistant professor hours a day. Now you can search for all level. Under very special circumstances, the information from MR. CMP, CIS, and the FOR SALE appointments at higher rank may be pos 1\Jkey Index when you want it and need it. to research From your office. From your home. Any sible. Strong commitment where you can connect a modem to a and teaching required. Preference given Symbolism: Sculptures and Tapestries, microcomputer (or terminal) and dial a to applicants with research interests re by John Robinson. Catalogue produced local number. lated to strengths in the department. for the POP Maths Roadshow, Leeds, NMSU meets NSF criteria for classi Sept., 1989. Colour photographs of 4 Where to Get Online with fication as a minority institution and tapestries: 14 symbolic and 5 represen MathSci welcomes applications from women and tational sculptures. Beautifully crafted, MathSci is produced by the American members of minority groups. Arrange for mainly in bronze. Includes trefoil, (8, Mathematical Society, a source of materials vita, short research description, and at for the mathematical community. MathSci 3) and (15, 4) torus knots. Comments can be accessed on BRS, DIALOG, Compu least three reference letters to be sent by John Robinson and Ronnie Brown. Serve. EasyNet, and the European Space to: Order from: Mathematics and Knots, Agency (ESA). To learn more about Hiring Committee, Dept. of Mathemat MathSci, contact Taissa Kusma at the AMS University of Wales, Bangor, Gwynedd by calling 800-556-7774 in the continental ical Sciences, New Mexico State Univer LL57 1UT, U.K. Fax: (248)361429:email: United States. sity, Las Cruces, New Mexico 88003. An R.Brown&U K.AC.Bangor. VAXA EO/AA Employer. (£6 sterling, P/P £1.20 Surface, £2.60 Air: Mastercard/VISA to home address). Coming in 1989 Computing Reviews (CR} and the annual ACM Guide to Computing Literature (GCL) from the Association of Computing Machin ery is being added to MathSci in 1989. These ACM publications provide compre hensive coverage of the international research literature in computing and computer science. American Mathematical Society P. 0. Box 6248 Providence, RI 02940 (401) 272-9500 ""' • MathSd ... oenlce mark mthe American MathemaUcal Society OCTOBER 1989, VOLUME 36, NUMBER 8 1121 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN 31261, SAUDI ARABIA MATHEMATICAL SCIENCES DEPARTMENT Needs FACULTY MEMBERS FOR TEACHING GRADUATE AND UNDERGRADUATE COURSES IN ALL AREAS OF MATHEMATICAL SCIENCIES. PH.D. IN MATHEMATICS IS REQUIRED. CANDIDATES MUST HAVE STRONG RESEARCH POTENTIAL OR ACCOMPLISHMENTS AND DEMONSTRATED EXCELLENCE IN TEACHING. PREFERRED AREAS OF RESEARCH ARE APPLIED MATHEMATICS AND NUMERICAL ANALYSIS. KFUPM offers attractive salaries commensurate with qualifications and experience, and benefits that include free furnished air-conditioned accommodation on campus, yearly repatriation tickets, ten months duty each year with two months vacation salary. Minimum regular contract for two years, renewable. Interested applicants are requested to send their Curriculum Vitae with supporting information not later than one month from the date of this publication, to: DEAN OF FACULTY AND PERSONNEL AFFAIRS KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPT NO. MATH/540/AP-01 DHAHRAN 31261, SAUDI ARABIA POSTDOCTORAL APPOINTMENTS NATIONAL UNIVERSITY NONLINEAR DYNAMICS AND FRACTALS OF SINGAPORE $34,000 to $38,000 The Naval Surli-u:n Warlitre Center, Silver Spring. Maryland. is seeking post DEPARTMENT OF MATHEMATICS doctoral research mathematicians and physicists in dynamical systems. fractals AppiK:at'ons are invited for teaching appointments from candidates who are able to teach in one or more ot the and tlwir physical applications. One or two appointments. sponsored hy tho foiiOYiing areas: Office or Naval Tm:hnology (ONT} Fellowship Program. are available in NSWC's Nonlinear Dynamics Croup. Usually, appointments arc extended a st~ • Pure Mathematics • Applied Mathematics • Operational Research • Statlatics cond ymtr and possibly a third. Candidates should possess a PhD Degree in Matllemalics or ils equivalent. NSWC's basic research program is divided t~qually between physics applica Gross annua emoluments range as follows: tions and the underlying pure mathematics of dynamical systems and fractals. Lecturer S$50,390 - 64,200 Emphasis is placed upon balance among thnoreti,:al. expt!rinwntal. and mameri Senior Lecturer S$58,680 - 100,310 cal work. Associate Profesaor S$88,650 - 122,870 (US$1 = S$2.00 approximately) The Croup's current interests are: The carmencing salary ..11 depend on !t1e candidates quallicalions, experience and lhe kM!I ct appointment clfered. • Dynamical systems theory • Fractals. fractal measures. and dinwnsion theory l.eale and medical benelils _..II be provided. Depending on lhe type ct conlract offered, olher benefits may include: provident fund benelils or an end-of-contract gratuity, a seltling-in allawance of S$1 ,000 or S$2,000, sut> • Applications of geometric topology and nwasum theory ~dised hou~ng at nominal rentals ranging from S$100 to S$216 p.m., education allowance for up to lhree children • Data analysis: detection of chaos and its separation from noise subject to a maximum of S$10,000 per annum per child, passage ~stance and baggage allowance for lhe 1ransportation ct personal effects to Singapore. Staff members may undertake consultation work, subject to lhe • Fractal analysis and modeling of cloud radiance and ocean wave data app.roval of the University, and ~n consultalion fees up to a maximum of 60% of lheir gross annual emoluments • Applications of dynamical systems and fractals to cloud modeling in a calendar year • Nonlinear dynamics of magnetonlastir: ribbons and columns The Dep.artment ct Matllematics is a dep.artment in lhe Faculty cl Science. There are 8 facu~es in lhe National • Nonlinear dynamics of lluids: wave breaking. coupled fluid mechanical University ot Singapore ~ a cunent student enrolment of SOITle 14,000. All departments are well-equipped with systems a wide range cl lacil~es for teaching and research. Interested individuals. write or call: All academic staff have access to lhe fciiOYiing computer and teeoommunication resources: an individual microcomputer (an IBM AK:ompatible or Apple Macintosh); an IBM mainframe computer with 16 MIPS ot com· NAVAL SURFACE WARFARE CENTER puting pa.yer; an NEC SX supercomputer wilh 650 MFLOPS ot computing power, departmental laser prinlers; Attn: Dr. Robert Cawley (Code R41] a wide spectrum ot mainframe and microcomputer software; voicemail, BITNET to access academic institutions 10901 New Hampshire Avenue world-wide In add~on, a proposed campus nei'Mlrk based on slat&d-lhe-an optical fibre technology _..II be ® Silver Spring, Maryland 20903-5000 installed by 1990 to facilitate resource sharing and efeclronic communication for the academic communi!y. Telephone: [202) 394-2256 or AUTOVON Application forms and further information on terms and concfoons of service may be oblained from: 2!10-2256 The Director .The Diteetor For application information and materials, write to: Peraonnel Department North America Office American Society for Engineering Education NATIONAL UNIVERSITY OF SINGAPORE NATIONAL UNIVERSITY OF SINGAPORE 10 Kent Ridge Crescent, Singapore 0511 780 Thinl Avenue, Suite 2403 fASEE] N- 'lbrk, N.Y. 10017, U.S.A. Projects Office, Suite 200 Tel: (212) 751-11331 11 Dupont Circle Washington, DC 20036 Enquiries may also be sent lhrough BITNET to PERSDEPT@ NUSVM or through li!iellx: (65) m3948 Telephone: (202] 293-7080 • An Equal Opportunity Employer • iJ[I]IIill Le savoir universitaire, Functions UQAM une valeur sure! Bowdoin 1987 Professeurs n!guliers ou invites Robert C. Gunning and Departement de mathematiques Leon Ehrenpreis, Editors et d•informatique Theta functions have a long and distin Le departement de mathematiques et guished history and play a many-faceted and d'informatique sollicite des candidatures pour central role in a number of areas of mathe matics. Interest in these functions has re deux postes de professeur regulier ou invite. Le kindled in recent years as a result of the wide premier, dans les domaines de Ia geometrie variety of areas in which they have made major contributions. differentielle et de Ia topologie, debutera le 1er juin 1990; pour l'eventuel deuxieme paste, Crossing the lines of semi-simple Lie group theory and nilpotent Lie group theory, theta toutes les candidatures seront considerees, functions are relevant to the arithmetic of mais Ia preference ira au secteur des groupes quadratic forms and to partition theory, through which they relate to statistical et algebres de Lie. Les candidats devront mechanics and quantum field theory. In posseder une experience ou des capacites addition, they are used to study Riemann surfaces, abelian varieties, and solutions of reconnues en recherche, et etre en mesure differential equations from physics. In this d'enseigner en franc;ais aux trois cycles way, they relate to partial differential equations and algebraic d'etudes. geometry. This two-volume collection contains the pro Cette oflre s'adresse egalement aux femmes et aux ceedings of an AMS Summer Research Insti hommes et, conformement aux exigences relatives tute on Theta Functions, held in July 1987 at Bowdoin College. With papers from some of ill'immigration au Canada, Ia priorite sera accordee the top experts in this area, these volumes aux citoyens canadiens et aux residents permanents. will provide readers with an excellent oveiView of the current research in and applications of theta functions. Les curriculum vitae rediges de preference en franc;ais et trois lettres de recommandation postees directement par les signata ires doivent 1980 Mathematics Subject Clasaification: 00 ISBN (set) 0.8218-1485-Q; (Part 1) 0.8218-1483-4; parvenir avant le 15 janvier 1990 a l'adresse (Part 2) 0.8218-1484-2, LC 89-6723, ISSN 0082- suivante : 0717 728 pages (Part 1), 376 pages (Part 2) hardcover 1989 Set: List $149, Instmem $119,lndiv mem $89 Robert V. Anderson, directeur Part 1 only: List $99, Inst mem $79, Indiv mem $59 Part 2 only: List $58, Inst mem $46, Indiv mem $35 Departement de mathematiques To order, please use PSPUM/49NA (Set) et d'informatique PSPUM/49.1NA(Part 1) PSPUM/49.2NA (Part 2) Universite du Quebec a Montreal C.P. 8888, succursale A Montreal (Quebec) Canada H3C 3P8 Prepayment required. Onler from American ,,, Universite du Quebec a Montreal Mathematical Society, P. 0. 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Phillips The theory of buildings was developed, edited by mainly by Jacques Tits in the 1950s, in an Jean Della Dora and John Fitch This revised edition reflects the wealth of A Volume in the COMPUTATIONAL MATHE new results discovered in the intervening attempt to develop a systematic interpreta MATICS AND APPLICATIONS Series years since the first edition established tion of semi-simple Lie groups, particu larly the exceptional groups. This book This volume assembles papers describ scattering theory as an important and fruit ing the present state of development of ful area of research. This new, revised presents an up-to-date account of this theory, including such new developments practical parallelism for computer al edition will continue to inspire researchers gebra. Subjects covered include vectori as chamber systems. to expand the application of the original zation, loosely coupled systems, and a ideas proposed by the authors. CONTENTS: Chamber Systems and Examples. Coxeter Complexes. Buildings. variety of algorithmic developments and December 1989, c. 304 pages Local Properties and Coverings. BN-Pairs. software tools, with an emphasis on $39.95 (tentative)/ISBN: 0-12-440051-5 Buildings of Spherical Type and Root Groups. finding solutions to real problems and A Construction of Buildings. The Classification producing usable algebra systems. The Conformal Invariance and of Spherical Buildings. Affine Buildings I. volume is based on the papers from The String Theory Affine Buildings II. Appendixes. Index. Computer Algebra and Parallelism June 1989,214 pages, $27.95 Workshop, held at the TIM3 Laboratory edited by of the University of Grenoble. Petre Dita and Vladimir Georgescu ISBN: 0-12-594750-X October 1989, c. 272 pages This book contains the lectures deliver $39.95 (tentative)/ISBN: 0-12-209042-X ed at the Summer School on Conformal Spinors and Calibrations Invariance and String Theory, held at F. Reese Harvey Computational Aspects of Poiana Brasov, Romania in September This book is a collection of examples 1987. and counter-examples illustrating the Commutative Algebra CONTENTS: Conformal Invariance in mathematical infrastructure of spinors edited by Statistical Mechanics: l.T. Todorov, Finite and calibrators. The following table of Lorenzo Robbiano Temperature Two-Dimensional QFT Models contents describes its breadth and reveals Recent results on computational prob of Conformal Current Algebra. V. Rittenberg, the underlying motivation-differential lems in commutative algebra and related Operator Contents of Some c= 1 Models in geometry-in its many facets: Rieman areas are the features of this volume. All Statistical Mechanics. H. Saleur and P. di nian, symplectic, Kahler, hyper-Kahler, contributors deal directly or indirectly Francesco, Two Dimensional Critical Models with the notion of a Grobner (or stan on a Torus. R. Flume, Wess-Zumino-Witten as well as complex and quatemionic. CONTENTS: Classical Groups I. The Eight dard) basis and improvements to algo Model and Othe Two-Dimensional Critical Types of Inner Product Spaces. Classical rithms for computing such bases. This Systems. P. Bouwknegt, Kac-Moody Algebras collection of papers has been reprinted in 2D Conformal Field Theories. M. Henkel, Groups II. Euclidean/Lorentzian Vector Conformal Algebras and Defects in the Quan Spaces. Differential Geometry. Normed Alge from the special double issue of the tum Ising Chain. M. Karowski, Conformal bras. Calibrations. Matrix Algebras. Spinors: Journal of Symbolic Computation, The Clifford Algebras. The Groups Spin and Quantum Field Theories and Integrable Sys Volume 6, Numbers 2 and 3. tems. String Theory and Related Topics: Pin. The Clifford Algebras Cl(r,s) as Algebras. In Paperback: $32.50/ISBN 0-12-589590-9 l.Ya. Aref eva, String Field Theory. J.-L. The Split Case Cl(p,p). Inner Products on the August 1989, 264 pages Gervais, Liouville Superstring. R. Kerner, Spaces of Spinors and Pinors. Low Dimen Geometry of the Kaluza-Klein Theory. Yu.l. sions. Manin, Reflections on Arithmetical Physics December 1989, c. 336 pages Determinants of Laplacians on Riemann Sur $39.95 (tentative)/ISBN: 0-12-329650-1 faces. H.P. Nilles, String on Orbifolds: An In ACADEMIC PRESS troduction. S. Paycha, Quantization of Bosonic Harcourt Brace •Jovanovich, Publishers Closed Strings and the Liouville Model. W. Book Marketing Department #24109 Lerche and A.N. Schellekens, The Covariant 1250 Sixth Avenue, San Diego, CA 92101 Lattice Construction of Four-Dimensional Strings. P. Cartier, A Course on Determinants. CALL TOLL FREE July 1989, 576 pages, $59.95 1-800-321-5068 ISBN: 0-12-218100-X Quote this reference number for free postage and handling on your prepaid order .. 24109 Prices subject to change without notice. ©':989 by Academic Press, Inc. All Rights Reserved. CBIKA- 24109. 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Mathematical Society Lecture Note Series London 19891450 pp./24119-7/Hardcover $79.50 I 28446·5/Paper $29.95 19891200 pp./37823-Q/Paper $29.95 Differential Equations: Their Solution Using Symmetries At bookstores or order from Hans Stephani Cambridge University Press This text emphasizes how to find and use the symmetries on which nearly all 40 West 20th Street, New York, NY 10011. methods of constructing closed form solutions rely. Call toll·free, 800872·7423, outside NY State. 800·227·0247, NY State only. 19891256 pp./35531-1/Hardcover $39.50 MasterCard and VISA accepted. Prices subject to change. INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS JUST RELEASED announces a workshop on .. Mathematical Physiology and Srinivasa Ramanujan Birth Centenary Volumes Volumes 51 & 52 (1987) of Differential-Delay Equations .. 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Box 6248 Providence, RI 02940 111 ..... 1.11.1 ••• 1•• 111 ••• 1.1 •• 1.1 ••• 1•• 1•• 11.11 ••• 1 Fold here Fasten PAYMENT securely MAA Minicourse Preregistration Form, Louisville, Kentucky January 17-20, 1990 NOTE: This Ia NOT an AMS Short Course Form. Please use the Joint Meetings Preglatratlon/Houaing Form to preregister for the AMS Short Course. To register for MAA Mlnlcourae(a), please complete THIS FORM or a PHOTOCOPY OF THIS FORM and return It with your payment to: Susan Wilderson Mathematical Association of America 1529 Eighteenth Street, N. W. Washington, DC 20036 Telephone: 202-387-5200 Telephone: ------(Please print) Surname First Middle Street address City State Zip • Deadline for MAA Minicourse preregistration: November 17, 1989 (After this date, potential participants are encouraged to call the MAA headquarters at 800-331-1622.) • Deadline for cancellation in order to receive a 50% refund: January 3, 1990 • Each participant must fill out a separate Minicourse Preregistration form. • Enrollment is limited to two Minicourses, subject to availability. • Please complete the following and send both form and payment to Susan Wilderson at the above address: I would like to attend D 1 Minicourse D 2 Minicourses Please enroll me in MAA Minicourse(s): #--and#-- In order of preference, my alternatives are: #-- and #-- • PAYMENT Check enclosed: $ __ Credit card type: D MasterCard D Visa Credit card#------Expiration date:------ Your Employing Institution Signature (as it appears on credit card) Minicourse Number and Name Organized by Fee 1. Computer based discrete mathematics Nancy Hood Baxter, Ed Dubinsky & Donald Muench $50 2. Finite-Pak - Software for Linear Programming Marvin L. Bittinger & J. Conrad Crown $50 3. Random mappings Bernard Harris $30 4. Lagrange first year calculus Francesca Schremmer & Alain Schremmer $30 5. Teaching mathematical modeling Frank R. Giordano & Maurice D. Weir $30 6. Coaching a team for the modeling contest B. A. Fusaro $30 7. Derive workshop Wade Ellis, Jr. $50 8. Using history in teaching calculus V. Frederick Rickey $30 9. How to use inexpensive graphing calculators to enhance Bert K. Waits & Franklin Demana $30 teaching and learning of precalculus mathematics and calculus 10. A seminar on women in mathematics Miriam P. Cooney $30 11. Writing in mathematics courses George D. Gopen & David A. Smith $30 12. An introduction to the mathematical elements of computer graphics Joan Wyzkoski Weiss $50 13. A survey of educational software Virginia E. Knight & Vivian Yoh Kraines $50 14. Creating order out of chaos in freshman mathematics: Linda H. Boyd $30 instituting a mathematics placement program 15. Mathematica and college teaching Stan Wagon $30 16. Starting, funding and sustaining mathematics laboratories Stavros N. Busenberg $50 17. The informed consumer's instructional guide to graphing calculators John W. Kenelly & Iris B. Fetta $30 n I plan on preregistering for the Louisville, Kentucky meetings ONLY in order to attend the MAA Minicourse(s) indicated above. It is my understanding tnat, should the course(s) of my choice be filled, full refund of the Louisville meetings preregistration fee will be made. ALGEBRAIC K-THEORY AND ALGEBRAIC NUMBER THEORY Michael R. Stein and R. Keith Dennis, Editors (Contemporary Mathematics, Volume 83) Instructions for Applicant's Form This volume contains the proceedings of a seminar on on facing page Algebraic K-theory and Algebraic Number Theory, held at the The form. Applicants' forms submitted for the Em East-West Center in Honolulu in January 1987. The seminar, ployment Register will be photographically reproduced which hosted nearly 40 experts from the U.S. and Japan, in the December 1989 issue of Employment Informa was motivated by the wide range of connections between the tion in the Mathematical Sciences (ElMS). Resumes of two topics, as exemplified in the work of Merkurjev, Suslin, those attending will be posted at the meeting. Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, The forms must be carefully typed using a fresh Thomason, and lhara. As is evident from the diversity of topics black ribbon. The best results are obtained with a represented in these proceedings, the seminar provided an carbon-coated ,polyethylene film ribbon, but satisfac opportunity for mathematicians from both areas to initiate tory results may be obtained using a ribbon made of further interactions between these two areas. nylon or other woven fabric if suitable care is exer cised. It is important that the keys be clean and make 1980 Mathematics Subject Classifications: 20G35, 20E07 a sharp, clear impression. ISBN 0-8218-5090-3, LC 88-38151 Do not erase-it causes ISSN 0271-4132 smudges which reproduce when photographed. Use a 450 pages ( softcover), January 1989 correcting typewriter or correction tape or fluid if nec Individual member $28, List price $46, essary. Submit the original typed version only. Copies Institutional member $37 will not reproduce properly and are not acceptable. To order, please specify CONM/83NA Hand lettered forms will be returned. Applicants' forms must be received by the Society All prices subject to change. Shipment will be made by surface. For by air delivery add, 1st book $5, each additional book $3, maximum $100. November 17, 1989 in order to appear in the spe Prepayment required. Order from American Mathematical Society, P.O. cial issue of ElMS and must be accompanied by the Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free Preregistration/Housing Form printed in this issue, if 800-566-7774 to charge with VISA or MasterCard. attending the meeting. Forms received past the dead line or not completed will be returned. @ Specialties AL = Algebra AN = Analysis Bl = Biomathematics BS = Biostatistics ...... CB = Combinatorics CM = Communication CN = Control CS = Computer Science BANACH SPACE THEORY CT = Circuits DE = Differential Equations EC = Economics ED = Mathematical Education Bor-Luh Lin, Editor FA =Functional Analysis FI =Financial Mathematics (Contemporary Mathematics, Volume 85) FL = Fluid Mechanics GE = Geometry HM = History of Math LO = Logic This volume contains the proceedings from a Research MB = Mathematical Biology ME = Mechanics Workshop on Banach Space Theory held at the University MO =Modelling MP =Mathematical Physics MS =Management Science of Iowa in Iowa City in July 1987. The workshop provided NA =Numerical Analysis NT =Number Theory OR= Operations Research participants with a collaborative working atmosphere in which PR = Probability SA = Systems Analysis ideas could be exchanged informally. Several papers were ST = Statistics TO= Topology initiated during the workshop and are presented here in their final form. Also included are contributions from several @ Career Objectives experts who were unable to attend the workshop. None of AR = Academic Research AT = Academic Teaching the papers will be published elsewhere. During the workshop, NR = Nonacademic R&D NC = Nonacad. Consulting two hours each day were devoted to seminars on current NS =Nonacademic Supervision problems in such areas as weak Hilbert spaces, zonoids, @ CD Duties analytic martingales, and operator theory, and these topics T =Teaching U =Undergraduate are reflected in some of the papers in the collection. G =Graduate R =Research C = Consulting A = Administration 1980 Mathematics Subject Classifications: 46-06, 46B10, 46B20, 46B22, 46B25 S = Supervision IND =Industry ISBN 0-8218-5092-X, LC 88-38106 GOY = Government DP = Data Processing ISSN 0271-4132 Location 536 pages (softcover), January 1989 E =East S =South Individual member $29, List price $48, C =Central M =Mountain Institutional member $38 W =West To order, please specify CONM/85 NA 0 = Outside U.S. I = Indifferent All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free ...•...... 800-566-7774 to charge with VISA or MasterCard . MATHEMATICAL SCIENCES EMPLOYMENT REGISTER APPLICANT FORM JANUARY 17-19, 1990 LOUISVILLE, KENTUCKY The form must be typed. (Please see instructions on facing page) APPLICANT: Name'------ Mailing address (include zip code)------ @ Specialties______@ Career objectives and accomplishments ACADEMIC: 0 Research, 0 Teaching NON-ACADEMIC: 0 Research and Development, 0 Consulting, 0 Supervision Near-term career goals•------ Significant achievements or projects, including role'------ Honors and offices•------• Other (e.g., paper to be presented at THIS meeting)------ Selected titles of papers, reports, books, patents______ @Degree Year Institution ------@ No. of abstracts, internal reports______@ No. of papers accepted______® No. of books and patents______EMPLOYMENT HISTORY: Present Previous Previous @ Employer~------ Position @Duties Years ______to'------______to'------______to ______DESIRED POSITION:: ______Q) Duties; ______Q) Available mo. __ /yr.__ Location______Salary______@ References (Name and Institution) © Citizenship: (check one) 0 U.S. Citizen 0 Non-U.S. Citizen, Permanent Resident 0 Non-U.S. Citizen, Temporary Resident ~AVAILABLE FOR INTERVIEWS: (Interviews for Session 4 scheduled on the basis of employer's request only.) Session 1 0 Session 2 0 Session 3 0 Session 4 0 Thurs. AM 9:30-11:45 Thurs. PM 1:15-5:00 Fri. AM 9:30-11:45 Fri. PM 1:15-5:00 I do not plan to attend the Louisville meetings 0 one be yr. 1990 printed Please only will I ( scheduled. code below. Sessions above. the 17-19, computer mo. be <[} @start Equations=DE, a on positions, notes @ may of Statistics=ST, FORM Unknown the employer set Govemment=GOV, • 01/90; prepare the section in which one Interviewers to ®No. ' e.g. see Differential the @ JANUARY same Biology=MB, Supervised ( ) 1:15-5:00 4, to than 4 ( ) used Position the No provided Analysis=SA, be PM, for refer interviews More People and/or are @Date Industry=IND, or will Track of 3, Restriction of Fri. Session position ( ) Circuits=CT, 2, used Mathematical Systems ' of I, (Please be number.) Yes position, Tenure number to complete) Title Number Scientist); the Check to table same Citizenship assigned. Supervision=S, Logic=LO, Science=CS, Experience sure the be ® ® Probability=PR, increase (Research for (be separate will Q) abbreviations to interviews: and Computer for Interviewers Possible RESC State Impossible codes STRIP ( ) order KENTUCKY 9:30-11:45 STRIP; Dept. ' ' 2. 4. in ( ) Administration=A, ( ) interviewing Mathematics=HM, schedule so, Research=OR, AM, available be of do employer Controi=CN, IIICDIIIIIIIIII[D[DJD] to will Fri. Sesslon3 SUMMARY two I SUMMARY computer Periods History able Renewal The Operations Duties and (Project Engineer), the Positions are Consulting=<:, LOUISVILLE, {!) @ of and Experience Q) separate they PREN interviewers a required submiued. all (j) are FOR..\1 Theory=NT, as when (If Geometry=GE, Number Communication=CM, receive the Analyst), City in forms yrs. restriction=NR; 111111 @ then @ exactly Number __ two No Interviewers 1:15-5:00 scheduled. items interviewer ( ) @ would be (Operations one 2 Register Graduates=G, Research=R, PM, Mechanics=FL, may the positions, than Combinatorics=CB, at Fluid of Analysis=NA, REGISTER OPAN Q)Duties resident=CP, Session Thurs. interviewer corresponding more sets Appointment StafO, display interviews each of on Numerical identify provide disjoint permanent Undergraduates=U, to or two Term Biostatistics=BS, ' placed Mathematics=FI, Technical 111111111 leuers therefore, are be simultaneous I EMPLOYMENT Citizen @ only. will Science=MS, there encouraged I Circled Teaching=T, Financial (Member U.S. whom if assigned; Sought are I itself for be (J) request 9:30-11:45 Interviewers MTS Accepted Thus, below. I will 1. 3. (!) 1 ( ) sought SCIENCES FORM Biomathematics=BI, eyers Management AM, I Citizen¥ form Open, pi announcement.) Employers Analysis=FA, Degree Specialties The em U.S. interviewers number positions. Dean, of of II Session all Thurs. ® @ Doctor=D; code @ meeting sessions. for I completing Salary--- Specialities bans Physics=MP, Functional Analysis=AN, suggested. number I the Prof, Prof, are ® before lnterviewer(s) on the Zip employer Register I Master=M, Louisville interview of Asso the one required=N; MATHEMATICAL Fonn not the capitals at State, ---yr.- session Mathematical Algebra=AL, carefully Prof, the Institution only I Name Education=ED, will this on City, Block ® Ill read and in Asst Bachelor=B, Institution following experience Interviews I ink. distribution no ---rna:- Lect, Please indicate for I hrs./wk for FORM orintervlewers interviewers black to ofPosition(s) Modeling=MO, @® Preferred Mathematical submilled CODE scheduled Inst, Register I in be are care some I TO; (A) type if Date Title(s) take Teaching Degree Available Number summaries or I should ® Processing=DP, of I ©Starting @ @ @) Interviews @ Please EMPLOYER INSmUCTIQNS· print Employment list form required EMPLOYER NOTES: Possible=P;bnpossible=I; Economics=EC, Data • Mechanics=ME, Topology= @ D,D,DJITJITJITJDJ,DJITJITJITJITJ,D,D,IIIIliiiii,IIIII,IIIII,CD,DDDD I Preregistration/Housing Form, Louisville, Kentucky January 17-20, 1990 Please complete this form and return it with your payment to Mathematics Meetings Housing Bureau P.O. Box 6887, Providence, Rhode Island 02940- Telephone: (401) 272-9500, Ext. 290-Telex: 797192 DEADLINES: Room Lottery Qualification October 31, 1989 Preregistration/Employment Register /Hotel Reservations November 17, 1989 Final Preregistration ONLY December 18, 1989 Housing Changes/Cancellations December 15, 1989 50% Refund on Preregistration/Employment Register /Banquets January 3, 1990 (no refunds after this date) REGISTRATION FEES Preregistration by At Meeting December 18, 1989 JOINT MATHEMATICS MEETINGS $ $ Member of AMS, CMS, MAA 68 88 Nonmember 105 136 * Student, Unemployed, or Emeritus 21 27 AMS SHORT COURSE Member/Nonmember 40 50 * Student or Unemployed 15 20 EMPLOYMENT REGISTER -Employer fee (1st Interviewer) 75 100 -Employer fee (2nd / 3rd Interviewer) 35 50 - Applicant fee 15 20 - Posting fee for job descriptions for noninterviewing employers 10 15 (N.B.: A separate form appears in this issue for preregistration for MAA Minicourses) * All full-time students currently working toward a degree or diploma qualify for the student registration fees, regardless of income. The unemployed status refers to any person currently unemployed, actively seeking employment, and who is not a student; it is not intended to include persons who have voluntarily resigned from their latest position. The emeritus status refers to any person who has been a member of the AMS or MAA for twenty years or more and is retired on account of age or on account of long term disability from his or her latest position. 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AT availability, THE children. etc. Rates of 3, credit ON space Suites) a 2, REQUIRE available at on rate. 1, STAYING ages (All OR HOUSING (Headquarters next NOT BE based IF East the writing check available NAME at by WILL WILL by Regency House House indicating rooms, Brown INFORMATION EVEN $50 next hotel YOU YOU FULL Galt Hyatt Seelbach Galt The THIS IF IF the preference of of another nonsmoking occupants; with at HERE HERE Order choice SUPPLY order have room in hotel room a requests: REQUIREMENTS: (date) CHECK CHECK hotels SECTION: hotels PLEASE other on list assigned housing rank unranked arrive PLEASE PLEASE following be an will HOUSING Please 0 at 0 The will GUARANTEE guarantees. Please Special I JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY The Journal of the American Mathematical Society is a quarterly journal containing research articles of the highest quality in all areas of pure and applied mathematics. Editors Michael Artin H. Blaine Lawson, Jr. Richard Melrose Wilfried Schmid Robert E. Tarjan ISSN 0894-0347 Quarterly, Volume 3, 1990 Code 90JAMS/NA 1990 Subscription Prices: List $116*, Institutional Member $93*, Individual Member $70* * Add for postage: Surface delivery to destinations outside the U.S. and India-- $8; to India- $18. Expedited delivery to destinations in North America $12; elsewhere -- $25. Note: Subscriptions to AMS joum!\IS are sold only on a calender year basis (January-December); split year and multiple year subscription orders are not accepted. Subscription orders received from nonmember institutions and organizations after January 1 of the subscription year will be sold at list price plus a I 0% late charge (rounded); the maximum late charge for any subscrip tion is $200. Subscription cancellations from nonmembers will not be accepted after March I of the subscription year. Cancella tion refunds are computed by deducting an $8 cancellation fee, and the price of each issue already shipped, from the price paid. To order: Prepayment required in U.S. funds. Mail to AMS, Annex Station, P. 0. Box 1571, Providence, Rhode Island 02901-1571 U.S.A. or call800-556-7774 in the continental U.S. to use VISA or MasterCard. A New Translation Journal in Mathematics SUGAKU EXPOSITIONS Sugaku Expositions is a new translation journal now available from the American Mathe matical Society. The journal is published biannually, and began in 1988. Volume 3 is the 1990 volume. Each issue of Sugaku Expositions contains several expository articles, translated from the Japanese journal Sugaku, which provide highly informative accounts of a variety of current areas of research. As with all AMS publications, Sugaku Expositions is printed on acid-free paper to ensure long life for your mathematical collection. ISSN 0898-9583 1990 Subscription Prices List price $70, Institutional member $56, Individual member $42 To order, please specify 90SUGA/NA (Vol. 3) 1989 Subscription Prices List price $60, Institutional member $48, Individual member $36 To order, please specify 89SUGA/NA (Vol. 2) 1988 Back Volume Prices List price $60, Institutional member $48, Individual member $36 To order, please specify 88SUGA/NA (Vol. 1) Add for postage: for destinations outside U.S. and India $8, to India $13; air delivery to North America $12, elsewhere $17. Prepayment required. Mail to: American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571 or call800-556-7774 to use VISA or MasterCard. Sample Copies: To request a sample copy, use order code SUGAEXAM/NA. Mail to AMS, ATTN: Cus tomer Services, P. 0. Box 6248, Providence, RI 02940-6248 Note: Subscriptions to AMS journals are sold only on a calendar year basis (January-December). Split year and multiple year subscription orders will not be accepted. The Latest North-Holland Publications Methods of Differential Geometry Logic Colloquium '87 in Analytical Mechanics Proceedings of the Colloquium, Granada, Spain, July 1987 edited by M. de Leon and P.R. Rodrigues edited by H.D. Ebbinghaus, J. Fernandez-Prlda, M. Garrido, D. Lascar (North-Holland Mathematics Studies, 158) and M. Rodriguez Artalejo 1989 x + 484 pages Price: US $110.50/Dfl. 210.00 (Studies in Logic and the Foundations of Mathematics, 129) ISBN 0-444-88017-8 1989 x + 376 pages Price: US $105.251DII. 200.00 The differential geometric formulation of analytical ISBN 0-444-88022-4 mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical Contents: Model Theory of Henselian Valued Fields content from a mathematical viewpoint. (F. De/on). On the Foundations of Mathematics in 1987 (F.R. Drake). Logic and Natural Language Systems Topics covered in this volume include differential forms, the (J.E. Fenstad). Model Theory of Regular and Compact differential geometry of tangent and cotangent bundles, Spaces (J. Flum). Categoricity and ~ermutation Gro~ps almost tangent geometry, symplectic and pre-symplectic (W. Hodges). Unidimensional Theones. A~ Introduction to Lagrangian and Hamiltonian formalisms, tensors and Geometric Stability Theory (E. Hrushovski). Unbounded connections on manifolds, and geometrical aspects of Filters on oo (J.I. /hoda). Type Theory and Explicit variational and constraint theories. Mathematics (G. Jliger). An Introduction to Extenders and Core Models for Extender Sequences (P. Koepke). Logical Contents: Differential Geometry. Almost Tangent Structures Aspects of the Axiomatic Method: On Their Significance in and Tangent Bundles. Structures on Manifolds. Connections (Tradition) Foundations and in Some (Now) Common or in Tangent Bundles. Symplectic Manifolds and Cotangent Garden Varieties of Mathematics (G. Kreisel). On the Use of Bundles. Hamiltonian Systems. Lagrangian Systems. Diagonally Nonrecursive Functions (A. Kucera~. Some Presymplectic Mechanical Systems. Appendices. Aspects of lmpredicativity: Notes on Weyl's Philosophy of Bibliography. Index. Mathematics and on Today's Type Theory (G. Longo). General Logics (J. Meseguer). Semantic Parallels in Natural Language and Computation (J. Van Benthem). Approximation Problems in Analysis and Probability Topics in General Topology byM.P. Heble editedbyK. Morita andJ. Nagata (North-Holland Mathematics Studies, 159) (North-Holland Mathematical Ubrary, 41) 1989 xii + 246 pages Price: US $92.00/Dfl. 175.00 ISBN 0-444-88021-6 1989 About 760 pages Price: US $197.251DII. 375.00 ISBN 0-444-70455-8 This is an exposition of some special results on analytic or c·-approximation of functions in the strong sense, in finite Being an advanced account of certain aspects of general and infinite-dimensional spaces. topology, the primary purpose of this volume is to provide the reader with an overview of recent developments. The papers cover basic fields It starts with H. Whitney's theorem on strong approximation such as metrization and extension of maps, as well as newly-developed by analytic functions in finite-dimensional spaces and ends fields like categorical with some recent results by the author on strong topology and topological dyna':"ics. . . Contents: Extensions of Mapp1ngs c·-approximation of functions defined in a separable Hilbert I (K. Manta). Extensions of Mappings II (T. Hoshina). Normality space. The volume also contains some special results on of Product S~aces I approximation of stochastic processes. (M. Atsuji). Normality of Product Spaces II (T. Hoshma). Generalized Paracompactness (Y. Yasui). The Tychonoff Functor and Related Topics (T. Ishii). Metrization I Contents: Weierstrass-Stone Theorem and Generalisations A Brief Survey. Strong Approximation in Finite-Dimensional (J.-1. Nagata). Metrization II (Y. Tanaka). Generalized Metric Spaces. Strong Approximation in Infinite-Dimensional Spaces 1 (J. -1. Nagata). Generalized Metric Spaces II (K.-1. Tamano). Function Spaces. Approximation Problems in Probability. Spaces (A. Okuyama, T. Terada). Appendices: Topological Vector Spaces. Differential N-Compactness and Its Applications (~. E~a. T. Kiyo~':wa, Calculus in Banach Spaces. Differentiable Banach H. Ohta). Topological Games and Apphcat1ons. (Y. YaJimar Manifolds. Probability Theory. Bibliography. Index. Categorical Topology (R. Nakagawa). Topological Dynamics (N. Aoki). NORTH-HOLLAND In the USA and Canada: For all other countries: Elsevier Science Publishing Co. Inc. Elsevier Science Publishers P .0. Box 886, Madison Square Station Book Order Department, P.0. Box 211 New York, NY 10159, USA 1000 AE Amsterdam, The Netherlands us$ pr;c. are valid only in the !!SA and Canada. In all other counlties, the Dulch Guildeo: (011.) price is ~onilive. ~us~ in The Nelhet'lands, please add 6% BTW. In New York Stale, applicable sales tax should be added. All prices are subject lo change wilhoul pnor ncl1011. 407/B/0983 Mathematics Update from Springer-Verlag Winner-1989 Award for New! Best Mathematics Package! Matroid Theory and its Applications in Differential and Difference Electric Network Theory and in Statics Equations through By Andras Recski Computer Experiments Gives an introduction to matroid theory (after presenting the With a Supplementary Diskette Containing PHASER: necessary background about graphs and algebra); with An Animator/Simulator for Dynamical Systems for IBM special emphasis on 1ts algorithmic aspects and on the Personal Computers applications in electrical engineering and in statics. One Second Edition feature of the book is the presentation of new concepts in the By Hiiseyin Ko~ak language of graphs, matrices and geometrical objects "Both the book and its accompanying software are of the wherever possible. 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