OF THE

1994 AMS Election Special Section page 7 4 7

Fields Medals and Nevanlinna Prize Awarded at ICM-94 page 763

SEPTEMBER 1994, VOLUME 41, NUMBER 7

Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences

This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe· January 1994 issue of the Notices on page 43. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island, on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings

Abstract Program Meeting# Date Place Deadline Issue 895 t October 28-29, 1994 Stillwater, Oklahoma Expired October 896 t November 11-13, 1994 Richmond, Virginia Expired October 897 * January 4-7, 1995 (101st Annual Meeting) San Francisco, California October 3 January 898 * March 4-5, 1995 Hartford, Connecticut December 1 March 899 * March 17-18, 1995 Orlando, Florida December 1 March 900 * March 24-25, 1995 Chicago, Illinois January 9 April 901 May 24-26, 1995 Jerusalem, Israel February 9 May (Joint Meeting with the lsreali Mathematical Union) 902 August 6-8, 1995 (97th Summer Meeting) Burlington, Vermont May 18 August 903 October 7-8, 1995 Boston, Massachusetts July 24 October 904 November 3-4, 1995 Kent, Ohio August 15 November November 17-18, 1995 Greensboro, North Carolina August 15 November January 10-13, 1996 (1 02nd Annual Meeting) Orlando, Florida March 22-23, 1996 Iowa City, Iowa April13-14, 1996 New York, New York April19-21, 1996 Baton Rouge, Louisiana November 1-3, 1996 Columbia, Missouri January 8-11, 1997 (103rd Annual Meeting) San Diego, California May 2-4, 1997 Detroit, Michigan January 7-10, 1998 (104th Annual Meeting) Baltimore, Maryland March 27-28, 1998 Manhattan, Kansas *Please refer to page 835 for listing of special sessions. t Please refer to the Table of Contents for further information.

Conferences

January 2-3, 1995: Short Course on Coding Theory, and Short Course on Knots and Physics, San Francisco, California June 25-July 27, 1995: Joint Summer Research Conferences in the Mathematical Sciences, University of Washington, Seattle, Washington July 9-29, 1995: AMS Summer Institute on Algebraic Geometry, University of California, Santa Cruz, California July 16-August 12, 1995: AMS-SIAM Summer Seminar in Applied Mathematics on the Mathematics of Numerical Analysis: Real Number Algorithms, Park City, Utah

Other Events Cosponsored by the Society

October 8-14, 1994: Symposium on the Legacy of Norbert Wiener: A Centennial Symposium, Massachusetts Institute of Technology, Cambridge, Massachusetts October 16-18, 1994: Women in Probability Workshop, Cornell University, Ithaca, New York November 27-December 3, 1994: Norbert Wiener Centenary Congress, Michigan State University, East Lansing, Michigan

Deadlines

November-December Issue*** January Issue Classified Ads* October 3, 1994 November 8, 1994 News Items September 21, 1994 November 3, 1994 Meeting Announcements** September 21, 1994 October 31, 1994 * 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. *** Please note December dates are earlier than previously published due to combined issue. ,_,_,,,,,...... _.,., ... ,.... _,, ...... ,_.,_,_,.. ,...... -...... ------OTICES OF THE AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS ARTICLES 739 Letters to the Editor 744 Academic Employment 763 Fields Medals and Nevanlinna Prize Awarded at ICM-94 Application Cover Sheet Winners of the Fields Medals and the Nevanlinna Prize were announced at 747 1994 AMS Election Special the International Congress of Mathematicians 1994 in August in Zurich, Section Switzerland. Allyn Jackson profiles the prize winners and reports on other 770 Forum ICM activities. 792 News and Announcements 766 The Tyranny of the Mean: Gender and Expectations Marcia C. Linn 804 Funding Information for the Mathematical Sciences In the tyranny of the mean referred to in the title, all members of the group with larger membership are expected to be more competent than all 806 For Your Information members of the group with smaller membership. Marcia C. Linn expands on 810 Acknowledgment of the theory and relates it to a number of areas in mathematics education. Contributions 830 Meetings and Conferences of FEATURE COLUMNS the AMS Stillwater, OK October 28-29, 830 772 Computers and Mathematics Keith Devlin Richmond, VA George Gratzer leads off this month's column with the fourth in his series November 11-13, 831 of articles on TE)<. Then Eugene Lehman describes a method of solving San Francisco, CA quartic equations on a pocket calculator. Next Edward Spitznagel looks January 4-7, 832 at the group theory package GAP; Eric Schweitzer reports on jspell, a Invited Addresses, Special TE)<-compatible spell checker; and Maurino Bautista reviews the software Sessions, and Contributed Papers, HiQ 2.02. The column concludes with a commentary by W. A. Beyer on a 835 previous Macsyma review and a note regarding an update of Mathematics AMS-SIAM Summer Seminar in Help Stack. Applied Mathematics, 839 841 Mathematical Sciences Meetings 790 Inside the AMS and Conferences John W. Morgan, chair of the Committee on Science Policy, outlines the 850 New Publications Offered by the three major areas of emphasis at the committee's April 1994 meeting. He AMS also reports on committee discussion of some National Science Foundation 855 Publications of Continuing questions and committee goals. Interest 856 Officers and Committee Members 869 Miscellaneous Personal Items, 869 Deaths, 869 870 Visiting Mathematicians 871 New Members of the AMS 875 Classified Advertising 891 Forms

SEPTEMBER 1994, VOLUME 41, NUMBER 7 737 ------·------·------·------..----·----·-----·-··------......

From the Executive Director ... NQ.:tiCES CHANGES Beginning with the January 1995 issue, there will be a change in the Notices. This AMERICAN MATHEMATICAL SOCIETY change implements the recommendations of a committee formed nearly two years ago to review member publications. The committee recommended an ''enhanced" Notices led by a full-time editor and a committee of associate editors. These editors will have EDITORIAL COMMITTEE au~ority over and responsibility for the content of the Notices and are expected to Sheldon Axler acttvely engage in acquisition and editorial oversight. In addition to anticipated content Amassa C. Fauntleroy Robert M. Fossum (Chairman) changes, there will be changes in format and style. There is an air of excitement as we Susan J. Friedlander (Forum Editor) await a livelier, more informative, mathematically enriched, enhanced Notices. Carolyn S. Gordon A consequence of the change in theNotice sis that this column, "From the Executive Carl R. Riehm (Letters Editor) Director", will no longer appear. It will, quite naturally, be replaced by an editorial page MANAGING EDITOR featuring articles written by the editor or possibly other writers selected by the editor. John S. Bradley ASSOCIATE EDITORS This column started in early 1989 shortly after I became Executive Director. It Jeffrey C. Lagarias, Special Articles was envisioned as a mechanism to inform readers of the Notices about timely issues before the mathematics community and about the various plans and activities of the ASSOCIATE MANAGING EDITOR Society. About sixty such articles have appeared. I hope the intent of the column has Allyn Jackson been achieved. Because this column will cease with the new Notices, and because I will SUBSCRIPTION INFORMATION be leaving the position of Executive Director next year, I want to take these last few Subscription prices for Volume 41 (1994) are columns to reflect on the activities of the Society over the past five or six years. $146 list; $117 institutional member; $88 individ­ ual member. (The subscription price for members I feel fortunate to have served as Executive Director of the Society during very is included in the annual dues.) A late charge of exciting and challenging times. It has been a period in which the AMS has taken an 10% of the subscription price will be imposed upon active approach toward achieving its mission of supporting mathematical research and orders received from nonmembers after January 1 scholarship. It has been a time in which the Society has taken actions to provide more of the subscription year. Add for postage: Surface delivery outside the United States and lndia-$15; op~nness and broader member participation in the deliberations of Society policy and to lndia-$28; expedited delivery to destinations in actions. North America-$32; elsewhere-$67. Subscrip­ Through surveys and interviews with the membership and others from the math­ tions and orders for AMS publications should be addressed to the American Mathematical Society, ematical community, the AMS reexamined how it might best serve the community P.O. Box 5904, Boston, MA 02206-5904. All orders and support mathematical research and scholarship. Following an intensive period of must be prepaid. information-gathering, the AMS Strategic Planning Task Force (SPTF) presented its ADVERTISING report to the Society in early 1991. This consensus report set a course of action for the Notices publishes situations wanted and classified AMS. Borrowing from the recent AMS National Policy Statement, the consensus is advertising, and display advertising for publishers that "researc~ within mathematics, the application of mathematics in other disciplines, and academic or scientific organizations. and the teaching of mathematics are interdependent-nourishing each other with ideas, @ Copyright 1994 by the American Mathematical methods. and inspiration." To support mathematical research and scholarship, "math­ Society. All rights reserved. ematics must be viewed as a synergistic system in which none of these components can be neglected without weakening the others." The SPTF then put forth several goals Printed in the United States of America. for the AMS and recommended the mechanism of annual operating plans to organize § The paper used in this journal is acid-free and strategies, set priorities, and allocate resources to achieve these goals. This has been a falls within the guidelines established to ensure per­ time of intense activity toward realizing the goals the SPTF set for the Society. manence and durability. 0 Printed on recycled paper. As Executive Director, one also has responsibility for the administration of the Most of this publication was typeset using the TEl{ affairs of the Society. The time of my tenure has been particularly interesting. The typesetting system. dominant business activity of the Society is publication, and this is a time of enormous change in publication-a time of complete reevaluation of the role of the publisher [Notices of the American Mathematical Society is published monthly except bimonthly in May/June, and of myriad challenges posed by the electronic delivery of information. The business July/August, and November/December by the Amer­ affairs of the Society are an interesting intellectual challenge, as they are international ican Mathematical Society at 201 Charles Street, in scope and quite complex and varied. Providence, Rl 02904-2213. Second class postage paid at Providence, Rl and additional mailing of­ I believe that the two major tasks that will face the next Executive Director are that fices. POSTMASTER: Send address change no­ the Society stay on course in the direction set forth by the SPTF, and that the financial tices to Notices of the American Mathematical Soci­ foundation of the Society remain sound during these times of rapid and uncertain change. ety, Customer Service Department, American Math­ Neither will be an easy task. ematical Society, P. 0. Box 6248, Providence, Rl 02940-6248.] Publication here of the Society's street In my next two columns, I will reflect on these two major issues before the Society. address, and the other information in brackets above, is a technical requirement of the U.S. Postal Ser­ William J aco vice. All correspondence should be mailed to the Post Office Box, NOT the street address. Tel: 401- 455-4000. e-mail: ams@math. ams. erg.

-·----.... - ..... ·------738 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY gents of UC asking that the AWM ideas sitions taken under oath or confidential Letters be applied in my case-as indeed they documents sealed under court order. A were. A new Tenure Review Commit­ "trial'" in the Notices is not only undesir­ to the Editor tee of seven was chosen from a list of able, but legally prohibited. Therefore, I over forty distinguished mathematicians chose not to waste space in this letter cor­ and scholars from around the country. recting the numerous errors in FFfAV After weighing large amounts of in­ (some minor, some not so minor) and Response to "Fighting for Tenure: formation, including ten new letters of concentrated instead on explaining some Another View" recommendation and material about oth­ of the issues surrounding my settlement. This is my response to the article ''Fight­ ers promoted to tenure at Berkeley that (Corrections of some of these errors are ing for Tenure: Another View", by is not generally available, the commit­ available at math. berkeley. edu by Lenore Blum and Lisa Goldberg (FF­ tee unanimously recommended me for gopher or anonymous ftp.) TAV) published in the July/August 1994 tenure as a full professor. (See the July In conclusion, I wanted a fair hearing issue of the Notices. I wanted to re­ 16, 1993 and October 15, 1993 issues and a fair review of my work, that's all. spond in the same issue, but the editors of Science for more details of the re­ I didn't think I had gotten one the wouldn't extend me that courtesy. view process and the conclusions of the first time, so I fought hard for another In 1986 I was considered for pro­ Tenure Review Committee. The October review. I got it, and I'm satisfied. I motion to tenure at the University of 15, 1993 issue also contains an indepen­ could have won or lost, and losing California, Berkeley, Mathematics De­ dent review of my research, conducted meant not only failing to get tenure but partment and was turned down. I dis­ by Science. A summary of my research giving up my day in court-had the TRC puted the outcome, for it seemed I had is available at math. berkeley. edu recommended against my appointment, been held to a different standard from by gopher or anonymous ftp.) I was prohibited by the settlement from men who had been granted tenure. FF­ The university insisted on confiden­ going to court. TAV places great store in the negative tiality of the entire settlement agreement. Berkeley has quite a few famous findings of the Academic Senate's Com­ We can now argue about whether this mathematicians, including Fields medal­ mittee on Privilege and Tenure, which or that portion should have been made ists Smale, Jones, and Thurston. Readers conducted a hearing on my case in 1989. public, but in retrospect it is clear they might ask how I could claim to be their FFTAV fails to point out, however, that made the correct decision to keep the equal. In fact, I make no such claim, this committee was prohibited from con­ names of the reviewers strictly confi­ only that I rank well among the math­ sidering my mathematical merits, much dential. This custom in academia was ematicians Berkeley hired as assistant less the merits of the male assistant pro­ even more important in this case. since professors and promoted to tenure. fessors at Berkeley, all of whom had mathematicians on both sides have been Ultimately the university and I re­ been granted tenure easily and enthusi­ criticized for their opinions about my lied on judgments of people who are astically for nearly two decades.' research. experts in my field, who are world-class The case was settled over a year ago. My case has generated strong feel­ mathematicians, and who were able to It was settled using a process modeled on ings, pro and con. The authors of FFTAV look at my work in a detached way. the one designed by the same architects portray one side of this. (For carefully They recommended I be awarded tenure of positive and constructive change that researched articles following high jour­ FFfAV suggests we look to for guidance nalistic standards see the Science articles Letters to the Editor in matters of sex discrimination-the Letters submitted for publication in the Notices cited here. For other views see the Con­ Association for Women in Mathematics. are reviewed by the Editorial Committee. gressional Record, Case summary, June In their May/June 1992 newsletter the The Notices does not ordinarily publish com­ 1992, Serial No. 102-117, pp. 29-31, plaints about reviews of books or articles. al­ AWM suggested setting up a new tenure 215-264.) A problem with their argu­ though rebuttals and correspondence concerning review rather than going to court. 2 reviews in Bulletin ofthe American Mathematical ment is that it is based only on a small Hundreds of members of the AWM Society will be considered for publication. fraction of the information in the case, Letters should be typed and in legible form or and AMS signed a petition to the re- because that's all that can be revealed to they will be returned to the sender, possibly re­ people who had no role in it, and, with sulting in a delay of publication. All published let­ 1Disparate treatment for comparable worth forms ters must include the name of the author. Letters the basis for most discrimination lawsuits and was all due respect, the authors of FFTAV which have been, or may be, published elsewhere the basis for ours. The Committee on Privilege and had no role in it. The people who had will be considered, but the Managing Editor of the Tenure could not even consider this basic issue. the facts about my mathematical qualifi­ Notices should be informed of this fact when the letter is submitted. 'The AWM is not the first to think of this. cations were the members of the Tenure and it is now fast becoming the norm. Not surpris­ The committee reserves the right to edit let­ ingly. there is disagreement in most of the cases Review Committee, and I reiterate that ters. as to whether discrimination occurred. Academics, they decided I should be awarded tenure. Letters should be mailed to the Editor of the American Mathematical Society. P. 0. lawyers. administrators, judges, and the parties in­ Furthermore, neither the authors of FF­ Notices. volved look for a reasonable way to settle the issue. Box 6248. Providence. RI 02940. or sent by e­ Often this means finding a fair process to review TAV nor the editors of the Notices are mail to notices@math. ams. org. and will be tenure qualifications. privy to the thousands of pages of depo- acknowledged on receipt.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 739 ·-·-·-·-·-·-·-·-·-·-...... -...... _...... _...... _...... ______...... - .. -...... -.. -...... _., ...... ,,,,_,, ...... ,,,,, .. ,_,,,...... Letters to the Editor as a full professor at Berkeley, and I'm their first tenured women research pro­ much his remarks-they are an attempt glad they did. I also realize that some fessors. (However, Cal Tech, Chicago, to state one strain of a current philosophy people can legitimately disagree with Columbia, Harvard, MIT, and Yale have of mathematics, written within the con­ the result, but in many cases across the not yet progressed.) straints set by his magazine to address country, promotions are not unanimous The Support Committee for Jenny a pop near-scientific culture-but rather decisions. I was offered the position, I Harrison has evolved into a statewide his chatty quotations of a spectrum of accepted it, and now I'm off to do what group, We Advocate Gender Equity interesting mathematicians. (Alas, if his I'm paid to do: mathematics. (WAGE), which is helping women aca­ quotation of Krantz's slur against mathe­ For me, the personal losses certainly demics achieve equality throughout the maticians is flawed, then can we trust his outweigh any personal gains from win­ University of California. quotations of others?) Those quotations, ning tenure, but I knew the risks and ac­ Coinciding with the settlement of and their context, suggest that the com­ cepted them from the beginning. There the case, UC Berkeley took the first puter revolution is sweeping all of us up is now a divided department that has steps to establish an affirmative action and that some fields of mathematics are suffered additional tension and division coordinator for the physical sciences enjoying the ride. from a backlash started by a vocal mi­ and mathematics to improve recruitment It is difficult to view without skepti­ nority not prepared to shake hands and and retention of graduate students from cism Krantz's expressed anxiety over a move on. Some members of the depart­ underrepresented groups. projected demise of proof. Proof is the ment appear to have conflicting feelings, Other women have credited my case mathematician's gravity-without it, we welcoming me as a colleague but not al­ as a factor in winning their own discrim­ drift through the Looking Glass. Where together happy with the secrecy of the ination cases. Krantz entertains the possibility that he settlement. Others seem downright de­ My great-grandmother marched for is flogging a dead horse, we agree­ lighted with my appointment. civil rights on the streets of Atlanta at the indeed it seems that the carcass has been Some good things have come out of turn of the century. She had been a so­ shredded into fragments satisfying the this case and all the publicity surround­ ciety woman, and this act, as you might Banach-Tarski theorem and reassembled ing it which the authors of FFTAV may imagine, destroyed the life she knew. into something paradoxically twice the not know. First of all, it has made math­ Never again was she accepted by white size of the original. The main points of ematicians more aware of the general society. However, she did it because she the original may have been these: issue of gender bias. Furthermore: knew racism was wrong. Compared to 1) use of the computer to perform al­ The University of California now her, I took a relatively easy stand. Just as gebra, to check for counterexamples, to allows all candidates for tenure to see civil rights advanced only when African­ produce graphics (images of objects oth­ their confidential files and has cited my Americans organized their resistance to erwise too difficult to visualize)-these case as an influence. discrimination, women mathematicians are all acceptable as part of mathematics; I was the first plaintiff in the State should put aside personal vendettas and 2) use of the computer to "prove" of California to be given comparable, unite in their efforts to gain equal treat­ theorems by assembling statistical ev­ confidential personnel files under court ment. idence of the absence of a counter­ order. This legal precedent has already The senior author ofFFTAV does not example is not acceptable; been important to other women aca­ need to try to justify to the world why 3) there are theorems which have demics with discrimination cases~ she opposed my struggle. Her important proofs for which "computer experi­ Science magazine has promised one work supporting women in mathematics ments" would have been useless; issue a year devoted to women in sci­ stands; it complements rather than con­ 4) there is something called "com­ ence. This was partly inspired by the tradicts my efforts and I suggest to her puter proof' (whatever that is); results of Paul Selvin's research for that it is time we get on with it. 5) the quality of the modern mathe­ his March 13, 1992 Science article on Jenny Harrison matics teacher/student amalgam is dis­ women in mathematics which itself was University of California, maying. an outgrowth of his June 28, 1991 Sci­ Berkeley Clearly (1)-(3) constitute, more or ence article on my case. (Received July 19, 1994) less, yet another fragment of a philoso­ Many see the recent increased hir­ phy of mathematics. There is no reason ing of women mathematicians as, at Response to "The Immortality to reject (1) and (2). As for (3), if the least partially, a result of the public­ of Proof" "computer experiments" are searches for ity surrounding my case. For exam­ The eulogy on the death of the death of counterexamples, it may be valid for the ple, the track record for hiring women proof, "The Immortality of Proof', by theorems cited, but (in a suitable sense) it in ten prestigious mathematics depart­ S. G. Krantz (Notices, January 1994), is invalid for the proof of the Four-Color ments first came to the attention of the is entertaining reading. But so is John Theorem. public in Selvin's June 28, 1991 Science Horgan's "The Death of Proof' (Scien­ As for (4), since Krantz is computer­ article. Since this data became public, tific American, October 1993) against knowledgeable enough to use computer­ Berkeley hired a woman assistant pro­ which Krantz rails. The source of en­ algebra, he likely knows that the term fessor, and Princeton and Stanford hired tertainment in Horgan's piece is not so is an alias for the theory of mechan-

740 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______Letters to the Editor ical theorem-proving (as in Symbolic I stopped subscribing to Mathematical countered when he ventured into an alien Logic and Mechanical Theorem Prov­ Reviews was that the back issues were and rather xenophobic culture known as ing by Chang and Lee, or Introduction taking over all of the bookshelves in my mathematics. to Logic Programming by Hogger), the office; on CD ROM, I would be able to My article's main theme was simple: applications of which include devising fit the entire collection from 1940 to the Mathematics is what mathematicians do, and using languages such as PROLOG, present on about one inch of shelf space and for various reasons-including the PARLOG, and Trilogy-but he seems in my study at home. increasing complexity of mathematics, to find the subject irritating. Unfortunately, when I read the foot­ the advent of computers as mathemat­ As for (5), isn't the situation so notes in the announcement, I found that ical tools, and the decreasing willing­ bad that any current fad regarding the the separation of the cost of producing ness of the government to support pure viability of "proof' could hardly make the database of reviews and the cost research-mathematicians will proba­ things worse? of delivering the product did not com­ bly spend less time in the future doing The interesting question is one which pletely apply to the CD ROM version: I traditional proofs. perhaps Horgan and Krantz will argue am told the disks are ''[a]vailable only to Krantz calls this "a bizarre tapestry about sometime in the future: it is, individuals at sites that subscribe to the with no basis in reality." But his over­ in a sense, related to (4), and it has corresponding current or backfile Math­ heated reaction proves-yes, proves!­ to do with the need for a theory for Sci Disc." I do not know the terms of that he is well aware of the trends I dealing with how computers might be the agreement with SilverPlatter, who describe and in fact is horrified by them. used to establish important theorems licenses the search software used for the In trying to shoot the messenger, Krantz whose minimal-length proof happens MathSci disks, but I wonder whether merely blows off his own toe. to be very long. Granted, Krantz might some of the mental bias which in the Mathematicians like Krantz often view that subject with distaste-it would past forced individual subscribers to sign complain that their field is underappre­ suggest that his current "golden age of agreements not to leave their personal ciated by the press. Yet when a journalist mathematics" is sliding toward a silicon copies of Mathematical Reviews in the tries to write something other than con­ age of mathematics. department coffee room has re-emerged. ventional gee-whiz pap-something that In any case, Krantz should celebrate Since my university library does not takes up serious philosophical and social his (self-ascribed) status of "dinosaur"; subscribe to Mathematical Reviews on issues that are troubling people in the after all, we're living in the Jurassic Park CD ROM, this condition has moved the field-they sneer, "How dare you!" age. CD ROM version of Mathematical Re­ I sought to present the issues in Robert M. Baer views from the category "expensive but a lively and, yes, provocative way. Parallel Logic Corporation affordable" to "unaffordable". My task was to get readers-most of (Received March 10, 1994) I fully understand the difficulty of whom are not mathematicians-to care pricing something whose production about what is happening in mathematics. Pricing Structure for cost is several million dollars for the first That's not easy. Given the response to Mathematical Reviews copy, and perhaps ten dollars for each my article, I think I succeeded rather I was very pleased last fall when the subsequent copy (that is my estimate well. American Mathematical Society an­ for the CD ROM version; probably the A final point: Krantz accuses me nounced a new pricing structure for paper version is substantially higher). of having misquoted him saying that Mathematical Reviews, in which the However, I am very disappointed to see mathematicians are ''spineless slobs". cost of producing and maintaining the Mathematical Reviews missing an op­ I did not. I sometimes eschew such database of reviews (which was to be portunity (as more mathematicians get intemperate remarks to protect sources paid by institutions employing mathe­ CD ROM drives) to become a mass­ from themselves. maticians in the form of a "data ac­ circulation publication. John Horgan cess fee") would be separated from the Richard G. Larson Scientific American cost of actually producing the copies of University of Illinois at Chicago (Received March 18, 1994) Mathematical Reviews (paid for by sites (Received March 17, 1994) and individuals in the form of a "prod­ Math semantics uct delivery fee"). This seemed like a Author of "Death of Proof" I enjoyed reading (Notices, April 1994) very reasonable solution to the prob­ Responds to Krantz about the mathematical importance of lems discussed by the AMS Committee I am flattered that Steven G. Krantz con­ the 1893 World's Columbian Exposition. to Monitor Problems in Communica­ siders me to be an evil pied piper, lead­ Please Note, however, two troubles in tions in the late 1980s, when I was a ing innocent multitudes into the abyss the sentence bridging pages 278-279: member of that committee. I was espe­ of epistemological relativism with my ''The fair drew 27 million people, close cially delighted by the fact that some article "The Death of Proof'. Alas, I to half the U.S. population at the time.'' new formats for Mathematical Reviews must confess I am just a humble re­ The first trouble is statistical. Uni­ seemed to be included in this program, porter, trying to describe as best he versity of Chicago historian William H. such as CD ROM: one of the reasons can some of the interesting things he en- McNeill states on page 1 of Hutchins'

SEPTEMBER 1994, VOLUME 41, NUMBER 7 741 Letters to the Editor

University that the exposition "attracted and symbolic points oj'view by Ostebee calculus is, as Professor Chapman notes, more than 21 million paid admissions." and Zorn. a serious subject and not a joke. The Historical Statistics supplement to I understand that as professional Among our perfectly serious pur­ the Statistical Abstract estimates U.S. mathematicians, many ofus have strong poses is to write a book that students can 1893 resident population at 66,970,000. positive or negative feelings about "Cal­ and will read successfully. One means I don't think we usually consider 27 (let culus Reform". No matter how you feel to that end, we believe, is an exposi­ alone 21) as close to half of 67. about this subject, I believe that the tory style that's both informal enough The second trouble is mathseman­ book in question oversteps the bounds to be inviting and sophisticated enough tic. An admission (paid or unpaid) is of professionalism in calculus texts. Let to convey the subtleties of a deep and no more a "person" than an oscillation me quote two passages from the text, sometimes difficult subject. That's a dif­ is a pendulum. Regardless of the im­ taken from pages 6 and 71: ficult balance to strike, and Professor plications of ordinary speech, relating Chapman is certainly entitled to his Monkey Functions: new functions attendance (unless clearly unduplicated) opinion as to whether we've succeeded. from old. New functions concocted to population makes no sense. Although We invite readers who want to gauge by "monkeying" with other func­ politicians and advertisers often mis­ for themselves-in context-the funda­ tions are so common and so impor­ takenly treat repetitive actions as peo­ mental seriousness of our project (or tant in calculus that we dignify them ple ("415 million Americans flew last anything else about our approach to cal­ with the title Monkey Functions. year"), we shouldn't. We should honor culus) to request an examination copy our mathematical tradition of concern of the current preliminary edition from Any given function can be ·'mon­ for clarity and accuracy by extending it Saunders College Publishing. keyed" with in various ways to to matters of mathsematics. (Received May 31,1994) produce new functions. Among all In any event, given 1893 incomes the species of monkey functions in and transportation, there's no way the An Appeal for Help calculus one reigns supreme-the exposition, which ran only six months, This is an appeal for help for the mathe­ derivative or rate function. could have drawn close to half the matics department at Gadjah Mada Uni­ population of the U.S. Excluding repeat No matter what happens with cal­ versity in Yogyakarta, Indonesia. I vis­ admissions, who knows what share of culus in the future, I hope that I can ited there this spring and found that a fire Americans attended? 15%, 10%, 5%? always instill in my students the idea had destroyed most oftheir books. They I enclose a complimentary copy of that calculus is a serious subject and not would appreciate any used math books Mathsemantics, released by Viking on a joke. I question whether this book, or that you can send them. They would February 24, 1994. The mistaken treat­ any calculus book which uses such ju­ like books especially in discrete mathe­ ment of actions as people is addressed venile satire, is appropriate for a serious matics, but any area that is of interest, on pages 21-27. The better way is given university calculus course. including functional analysis, topology, by the little girl behind the lemonade Scott Chapman algebra, number theory, computer sci­ stand in the "Family Circus" cartoon Trinity University ence, whatever you can spare. Books are who said, "We've had five customers, (Received April 11, 1994) hard to get in Indonesia. and three of them were Daddy." If you have many, you can use an Edward MacNeal M-bag, containing between 15 and 66 Edward MacNeal Associates Response from Ostebee and Zorn pounds. The M-bag BOOK RATE is (Received April 11. 1994) First, the usual response to being quoted $.72 (72 cents) per pound by surface out of context: We were quoted out of mail. It will take 1-2 months to get Questions About Calculus Reform context. Read in isolation, the sentences there. Has "Calculus Reform" gone too far? In Professor Chapman cites may appear SEND TO: the usual manner, my department is in flippant; indeed, reasonable people can Jurusan Matematika the process of selecting a new textbook (and do!) differ as to whether the phrase FMIPA UGMSekip Unit III for our introductory calculus sequence. "monkey functions" deserves to survive Yogakarta, JATENG I have been skeptical of the "Calculus the next editorial cut. Be that as it INDONESIA Reform" movement for several years; may, the fundamental seriousness of our Jack Tull but since one of the texts under consid­ approach to calculus should be clear to Seattle, Washington eration is a "Reform" book, I decided to anyone who reads the full text-or even (Received May 23, 1994) look at it seriously. The book in question a few surrounding pages. It certainly is is Calculus from graphical, llumerical, clear to students who use our book that

742 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY of the American Mathematical Society

To Notices Readers:

Starting with the January 1995 issue, the Notices will have a new look, a new style, a new and more interesting menu of articles. Some of the high­ lights will be:

• Top-quality mathematical exposition of advances in a broad range of areas, aimed at a mathematically literate audience

• A color cover, plus graphics, photos, and illustrations designed to heighten readers' visual enjoyment of the magazine

• Thought-provoking opinion pieces presenting diverse views on math­ ematics and the mathematics profession

• Timely news and information about the profession, its people, and their activities

The January 1995 issue of the ''new" Notices will be mailed in late November. Don't miss it!

WATCH FOR THE PROGRAM FOR THE SAN FRANCISCO JOINT MEETINGS IN THE JANUARY 1995 ISSUE ADDTHISCOVERSHEETTOALLYOUR ACADEMIC JOB APPLICATIONS

The Joint Committee on Employment Opportunities has adopted the cover sheet on the facing page as an aid to job applicants and prospective employers. The AMS Committee on the Profession also endorses its use. The current imbalanced job market has left employers overwhelmed with large numbers of applications to be processed, and job candidates who are justifiably frustrated with the lack of timely responses to their applications. Both sides should benefit from the increased efficiency that a standardized cover sheet will bring to application processing in Mathematical Sciences departments. How to use this form: 1. Using the facing page or a photocopy, (or a TEX version which can be downloaded from the e-MATH gopher on the "Professional Information for Mathematicians"/"Career Development Resources" menu), fill in the answers which apply to ALL of your academic applications. Make photocopies. 2. As you mail each application, fill in the remaining questions neatly on one cover sheet and include it ON TOP OF your application materials.

Mathematics Departments in Bachelor's, Master's and Doctorate granting institutions have been contacted and are expecting to receive the form from each applicant, along with any other application materials they require. Obviously, not all departments will utilize the cover form information in the same manner. It is hoped that this process will become a standard in the mathematical community and that in time further enhancements may lead to real improvement in the process of obtaining employment in the mathematical sciences. Please direct all general questions and comments about the form to [email protected] or call the Professional Programs and Services Department, AMS, at 800-421-4267 extension 4105.

JCEO Recommendations for Professional Standards in Hiring Practices The JCEO believes that every applicant is entitled to the courtesy of a prompt and accurate response that provides timely information about his/her status. Specifi­ cally, the JCEO urges all institutions to do the following after receiving an application: (1) Acknowledge receipt of the application-immediately; and (2) Provide information as to the current status of the application, as soon as possible. The JCEO recommends a triage-based response, informing the applicant that he/she (a) is not being considered further; (b) is not among the top candidates; or (c) is a strong match for the position. Academic Employment in Mathematics APPLICATION COVER SHEET

This cover sheet is provided as an aid to departments in processing job applications. It should be included with your other application material. Please print or type. Do not send this form to the AMS.

Last(Family)Name: ______Social Security Number:----;;-;:---;---­ optional FirstNameor Initial: ______SecondNameor Initial: ______

Address through June 1995______WorkPhone: C. ______

HomePhone: (______

E-mail: ______

CurrentinstitutionalMfiliation: ______If not U.S. Citizen, type of visa: Country of Citizenship: ______0 Permanent Resident 0 Temporary Resident Ph.D. received/expected: ____ ---,--- Ph.D. Advisor: ______Month Year SourceofPh.D.: ------Department Insitiution

Indicate the mathematical subject area(s) in which you have done research using the 1991 Mathematics Subject Classification printed on the back of this form. Iflisting more than one number, list first the one number which best describes your current primary interest. Primary Secondary

Give a very brief synopsis of your current research interests in the box below (e.g. finite group actions on four­ manifolds.) Avoid special mathematical symbols and please do not write outside of the boxed area.

Indicatethepositionforwhichyouareapplying: ______

If unsuccessful for this position, would you like to be considered for a temporary position? DYes DNo If yes, please check the appropriate boxes. D Postdoctoral Position D 2+-Year Position D 1-Year Position

List the names and affiliations of up to four individuals who will provide letters of recommendation if asked. Mark the box provided for each individual whom you have already asked to send a letter.

D 1.

D 2.

D 3.

D 4.

This form is provided courtesy of the American Mathematical Society. 1991 Mathematics Subject Classification

00 General 44 Integral transforms, operational calculus 01 History and biography 45 Integral equations 03 Logic and foundations 46 Functional analysis 04 Set theory 47 Operator theory 05 Combinatorics 49 Calculus of variations, optimal control 06 Order, lattices, ordered algebraic structures 51 Geometry 08 General mathematical systems 52 Convex and discrete geometry 11 Number theory 53 Differential geometry 12 Field theory and polynomials 54 General topology 13 Commutative rings and algebras 55 Algebraic topology 14 Algebraic geometry 57 Manifolds and cell complexes 15 Linear and multilinear algebra, matrix theory 58 Global analysis, analysis on manifolds 16 Associative rings and algebras 60 Probability theory and stochastic processes 17 Nonassociative rings and algebras 62 Statistics 18 Category theory, homological algebra 65 Numerical analysis 19 K-theory 68 Computer science 20 Group theory and generalizations 70 Mechanics of particles and systems 22 Topological groups, Lie groups 73 Mechanics of solids 26 Real functions 76 Fluid mechanics 28 Measure and integration 78 Optics, electromagnetic theory 30 Functions of a complex variable 80 Classical thermodynamics, heat transfer 31 Potential theory 81 Quantum theory 32 Several complex variables and analytic spaces 82 Statistical mechanics, structure of matter 33 Special functions 83 Relativity and gravitational theory 34 Ordinary differential equations 85 Astronomy and astrophysics 35 Partial differential equations 86 Geophysics 39 Finite differences and functional equations 90 Economics, operations research, programming, games 40 Sequences, series, summability 92 Biology and other natural sciences, behavioral sciences 41 Approximations and expansions 93 Systems theory, control 42 Fourier analysis 94 Information and communication, circuits 43 Abstract harmonic analysis

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MathSci Tapes • MathSci Disc • MathSci Online • TEX Software • e-MAm 1994 AMS Election Special Section

In the past few elections, only one of every seven members has The positions to be filled in contested elections this year voted in the annual elections. This year, in order to stimulate are: One vice-president, five members-at-large of the Council, participation in the election process (and to save some money), one trustee, two members of the Editorial Boards Committee the election process is being simplified. In this issue of the and three members of the Nominating Committee. There is Notices you will find all pertinent election material, including an amendment to the Bylaws recommended by the Council the ballot and return envelope. (This material will be separated which members are requested to ratify. into a special election booklet that will be mailed, together I urge you to study the material printed in this section, to with a ballot and return envelope, to foreign members of the find the ballot and return envelope, and to vote. Society.) [You should also note the request from the Society's The Society has tried to make the election process as Nominating Committee, Editorial Boards Committee, and simple as possible. You are asked to complete your voting on Committee on Committees for names of potential candidates, the ballot that accompanies this election material, insert it in editors, and committee members for the corning year. These the envelope provided, sign and seal the envelope, and mail suggestions are most useful if a short note of support it to the election teller. Ballots returned in envelopes that are accompanies the recommendations. Members are urged to not signed will not be counted. The Teller, Dallas Thomason communicate nominations to these committees through the Co., is an independent election service that counts the ballots Secretary.] under contract with the Society. When a signed envelope is received by Thomason, the ballot is extracted and added Robert M. Fossum to the pile of ballots received on that day. The envelope is Secretary discarded. Keyboarders enter the information from the ballot Urbana, Illinois into a computer. (This is the reason for the letters that are assigned to each candidate.)

SEPTEMBER 1994, VOLUME 41, NUMBER 7 749 1994 AMS Election

Candidates To help alleviate this problem, the following replacement proce­ OFFICERS dure has been devised: A member who has not received a ballot by Vice-President (one to be elected) October 10, 1994, or who has received a ballot but has accidentally C. Herbert Clemens Joseph B. Keller spoiled it, may write after that date to the Secretary of the AMS, Post Gian-Carlo Rota (by petition) Office Box 6248, Providence, RI 02940, asking for a second ballot. The request should include the individual's member code and the address to which the replacement ballot should be sent. Immediately Member-at-Large of the Council (five to be elected) upon receipt of the request in the Providence office, a second ballot, Georgia M. Benkart Benjamin A. Lotto (by which will be indistinguishable from the original, will be sent by first Carlos Castillo-Chavez petition) class or air mail. It must be returned in an inner envelope, which will David B. A. Epstein Jerrold E. Marsden be supplied, on the outside of which is the following statement to be Cameron M. Gordon Cora Sadosky signed by the member: James M. Hyman Alice Silverberg The ballot in this envelope is the only ballot that I am submitting Mark W. Winstead in this election. I understand that if this statement is not correct then no ballot of mine will be counted. Board of Trustees (one to be elected) Frank C. Hoppensteadt Donald E. McClure

signature NOMINATING COMMITTEE FOR 1995 (Three to be elected) Although a second ballot will be supplied on request and will be sent Jerry L. Bona Rogers J. Newman by first class or air mail, the deadline for receipt of ballots will not be Ingrid Daubechies Stephen D. Smith extended to accommodate these special cases. William James Lewis Susan G. Williams

EDITORIAL BOARDS COMMITTEE FOR 1995 (Two to be elected) SUGGESTIONS FOR 1995 NOMINATIONS Robert J. Blattner Harold M. Stark Each year the members of the Society are given the opportunity to Rhonda J. Hughes Herbert S. Wilf 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 Election Information Council to fill positions on the Council and Board of Trustees to The ballot for election of officers, members of the Council, and a replace those whose terms expire January 31, 1996. See the AMS trustee and ratification of an amendment to the bylaws is included Reports and Communications section of this issue for the list of in this issue of the Notices (and for members residing outside of current members of the Council and Board of Trustees. Members North America in the election booklet). The deadline for receipt of a are requested to write their suggestions for such candidates in the completed ballot is 10 November 1994. Members are urged to consult appropriate spaces below. the following articles and sections of the Bylaws of the Society: Article I, Section 1; Article II, Sections 1,2; Article III, Section 1; Article IV, Sections 1, 2, 4; Article VII, Sections 1, 2, 5. The complete text of the Bylaws appears on pages 1266-1270 of November 1993, SUGGESTIONS FOR 1995 NOMINATIONS Volume 40, Number 9, issue of the Notices. A list of members of the Council and Board of Trustees Council and Board of Trustees serving terms during 1994 appears in the AMS Reports and Communications section of this issue of the Vice-President (1) Notices (and on a separate page in the special election booklet).

REPLACEMENT BALLOTS Members-at-large of the Council (5) There has been a small but recurring and distressing problem con­ cerning members who state that they have not received ballots in the annual election. It occurs for several reasons, including failure of local delivery systems on university or corporate properties, fail­ ure of members to give timely notice of changes of address to the Providence office, failures of postal services, and other human errors.

Member of the Board of Trustees ( 1)

The completed form should be addressed to AMS Nominating Com­ mittee, Post Office Box 6248, Providence, Rl 02940, to arrive no later than November 10, 1994.

750 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Biographies of Candidates 1994

AMS Committees: Committee on the curity reasons. National security was Human Rights of Mathematicians. 1985- understood in military terms. During Biographical information about the candi­ dates has been verified by the candidates, 1987. recent years. the public's rationale for although in a few instances prior travel ar­ Selected Addresses: International Con­ supporting mathematics has become in­ rangements of the candidate at the time of gresses of Mathematicians, Vancouver, creasingly based on the economic value assembly of the information made commu­ 1974, and Berkeley, 1986; CIME Lec­ of a mathematically literate public. nication difficult or impossible. A candidate tures, Varena, Italy, 1981; AMS Summer Are we moving toward the pre­ had the opportunity to make a statement of Research Institute on Algebraic Geom­ World War II situation in which basic not more than 200 words on any subject matter without restriction and to list up to etry, Brunswick, July 1985. mathematical research, like art, is pur­ five of her or his research papers. Additional Information: Fulbright Fel­ sued for its own sake while one supports Abbreviations: American Association low, 1970; Sloan Fellow, 1973-1975; oneself doing other things? Can we re­ for the Advancement of Science (AAAS); Distinguished Research Award, Univer­ spond more effectively to the perceived American Mathematical Society (AMS); sity of Utah, 1983; Editor, Pacific Jour­ national needs and thereby strengthen American Statistical Association (ASA); nal of Mathematics, 1985-; Commit­ our case with the public? Association for Computing Machinery (ACM); Association for Symbolic Logic tee on Mathematics, National Research The American Mathematical Soci­ (ASL); Association for Women in Mathe­ Council, 1985-1987; Board on Math­ ety is called upon to protect and support matics (AWM); Canadian Mathematical So­ ematical Sciences Education, National our discipline, while at the same time re­ ciety, Societe Mathematique du Canada Research Council, 1985-1987. sponding creatively to the agenda urged (CMS); Conference Board of the Mathemat­ Selected Publications: 1. with Phillip upon us by the public at large and, in ical Sciences (CBMS); Institute of Mathe­ Griffiths, The intermediate Jacobian of particular, by the funding agencies of matical Statistics (IMS); International Math­ ematical Union (IMU); London Mathemat­ the cubic threefold, Ann. of Math. 95 the federal government. I wish to par­ ical Society (LMS); Mathematical Associa­ (1972), 281-356. MR 46 #1796; 2. De­ ticipate in the Society's deliberations on tion of America (MAA); National generation of Kahler manifolds, Duke these issues, and I wish to help develop Academy of Sciences (NAS); National Math. J. 44 (1977), 215-290. MR 56 and implement new policies to meet this Academy of Sciences/National Research #3012; 3. A Scrapbook of Complex challenge. Council (NAS/NRC); National Aeronautics Curve Theory, The University Series and Space Administration (NASA); Nation­ al Council of Teachers of Mathematics in Mathematics, Plenum Press, New Joseph B. Keller (NCTM); National Science Foundation York-London, 1980. MR 82i:14001; 4. Professor, Stanford University. (NSF); Operations Research Society of Homological equivalence, modulo alge­ Born: July 31. 1923, Paterson, New America (ORSA); Society for Industrial braic equivalence, is not finitely gener­ Jersey. and Applied Mathematics (SIAM); The ated, Publ. Math. Inst. Hautes Etudes Ph.D.: New York University, 1948. Institute of Management Sciences (TIMS). An(*) indicates the individual was nom­ Sci. Publ. Math. 58 (1983), 19-38. MR Selected Addresses: Gibbs Lecturer, inated in response to a petition. 86d:14043; 5. Curves on generic hyper­ AMS, 1977; von Neumann Lecturer, swfaces, Ann. Sci. Ecole Norm. Sup. 19 SIAM, 1983; Rouse Ball Lecturer, Uni­ (1986), 629-636. MR 84c:14037. versity of Cambridge, 1993. Vice-President Statement: A sea change has occurred Additional Information: von Karman C. Herbert Clemens in the last decade or so in the pro­ Prize, SIAM, 1979; National Medal of ProfessOJ~ University of Utah. fessional opportunities and challenges Science, 1988; Member: Royal Society. Born: August 15, 1939, Dayton, Ohio. facing mathematicians. During the pre­ National Academy of Sciences, Ameri­ Ph.D.: University of California, Berke­ vious forty years public and federal can Academy of Arts and Sciences. ley, 1966. government support for basic mathemat­ Selected Publications: 1. A geometri­ Offices: Member-at-Large of the Coun­ ical research derived from the perceived cal the01y of diffraction, Calculus of cil, 1990-1992. value of basic science for national se- variations and its applications, Proceed-

SEPTEMBER 1994, VOLUME 41. NUMBER 7 751 ...... _------_ .. Biographies of Candidates

ings of Symposia in Applied Mathe­ L'Aquila, 1990; Member, NAS Com­ AMS Committees: Committee on matics, vol. 8, pp. 27-52. McGraw-Hill, mittee on Women in Science and En­ Mathematical Surveys and Monographs, New York-Toronto-London, 1958. MR gineering, 1991-1993; Medal for Dis­ 1994- . 20 #840; 2. Corrected Bohr-Somn1elfeld tinguished Service, National Security Selected Addresses: MAA Invited Ad­ quantum conditions for nonseparable Agency, 1992; Member of the Husserl dress, Minneapolis, 1988; Canadian systenzs, Ann. Physics 4 (1958) 180­ Circle and the Heidegger Circle. Mathematical Society Seminar on Lie 188. MR 20 #5650; 3. The shape of SelectedPublications: 1. An "alternier­ Theory and Differential Equations, Mon­ the strongest colun1l1, Arch. Rational ende Velfahren'" for general positive treal, 1989; SIAM Meeting on Discrete Mech. Anal. 5 (1960), 275-285. MR operators, Bull. Amer. Math. Soc. 68 Mathematics, Vancouver, 1992; Princi­ 23 #B1204; 4. Rays, vvaves and asymp­ (1962), 95-102. MR 24 #A3671; 2. pal Lecturer, Holiday Symposium, New totics, Bull. Amer. Math. Soc. 84 (1978), On the foundations of combinatorial Mexico State University, 1992; AMS­ 727-750. MR 80g:35002; 5. with theory. I. Theory of Mobius functions, MAA Invited Address, Cincinnati, Jan­ J. K. Hunter, Weakly nonlinear high z. Wahrscheinlichkeitstheorie und Verw. uary 1994. frequency vvaves, Comm. Pure Appl. Gebiete 2 (1964), 340-368. MR 30 Additional Information: Visiting Pro­ Math. 36 (1983), 547-569. MR 85h: #4688; 3. with P. Doubilet and J. A. fessor, Aspen Center for Physics, 1979; 35143. Stein, On the foundations ofcombinato­ University of Wisconsin Distinguished Statement: I will try to encourage the rial theory. IX. Combinatorial methods Teaching Award, 1987; Organizer, Work­ Society's activities in applied mathemat­ in invariant theoly, Stud. Appl. Math. shop and Conference on Lie Alge­ ics with the goals ofincreasing financial 53 (1974), 185-216. MR 58 #16736; 4. bras and Related Topics, 1987-1988; support for research and of improving The pernicious influence ofmathematics NSF Committee on CBMS Conferences, the opportunities for jobs. upon philosophy, New directions in the 1990-1992; NSF U.S.-fSU Cooperative philosophy of mathematics, Synthese Project, 1991; Journal of Algebra Ed­ Gian-Carlo Rota* 88 (1991), 165-178. MR 93a:00007; 5. itorial Board, 1991- ; NSF Panel on Professor of Applied Mathematics and with D. A. Buchsbaum, Projective reso­ Minority Research Initiatives and Re­ Philosophy, Massachusetts Institute oj' lution ofWeyl modules, Proc. Nat. Acad. search Opportunities for Women, 1993; Technology. Sci., U.S.A. 90 (1993), 2448-2450. MR Member: AMS, AWM. Born: April 27, 1932, Italy. 94a:20074. Selected Publications: 1. with J. M. Ph.D.: Yale University, 1956. Statement: I believe the Society should Osborn, Rank one Lie algebras, Ann. Offices: Member-at-Large ofthe Coun­ initiate a wide-ranging and prestigious of Math. 119 (1984), 437-463. MR cil, 1967-1969. system of rewards for expository work 86g:17006; 2. with D. J. Britten and AMS Committees: Interim Editorial at all levels, from grade school to ad­ F. W. Lemire, Stability in modules for Committee for Research Announce­ vanced research. All levels should be classical Lie algebras--a constructive ments, 1978; Bulletin (New Series) Edi­ treated evenly and equally, with equal approach, Mem. Amer. Math. Soc. 85 torial Committee (Associate Editor, Re­ cash prizes awarded simultaneously in (1990), no. 430. MR 90m: 17012; 3. with search Announcements, 1979-1981; As­ a solemn ceremony. Some two dozen S. Kang and K. C. Misra, Graded Lie al­ sociate Editor, Research-Expository Ar­ evenly spread prizes should be awarded gebras ofKac-Moody type, Adv. Math. ticles, 1982-1984); Committee on Steele yearly, and the fact should be stressed 97 (1993), 154-190. MR 94b:17039; 4. Prizes, 1979-1982; Committee on AMS that a grade school teacher may con­ with J. M. Osborn and H. Strade, Con­ Prizes and Awards, 1992- . tribute to the well being of mathematics tributions to the classification of sim­ Selected Addresses: Hedrick Lectures, as much as a Fields Medal winner. The ple modular Lie algebras, Trans. Amer. Mathematical Association of America, next several years are going to be very Math. Soc. 341 (1994), 227-252. MR 1967; International Congresses ofMath­ difficult. Every effort should be made 94c:17035; 5. Tensor product represen­ ematicians, Nice, 1970, and Helsinki, to keep mathematics in the center of tations of general linear groups and 1978; Hardy Lectures, London Mathe­ the public's attention, and the Society's their connections vvith Brauer algebras, matical Society, 1973; Lezioni Lincee, public relations programs should be en­ J. Algebra 165 (1994), to appear. Scuola Normale Superiore, Pisa, 1986. hanced, in line with what other profes­ AdditionalInformation: Sloan Fellow, sional societies are presently doing or Carlos Castillo-Chavez 1962-1964; Fellow, American Academy planning. Associate Professor, Cornell University. of Arts and Sciences, 1963- ; Fellow Born: March 29, 1952, Mexico City. and then Senior Fellow, Los Alamos Member-at-Large of the Council Ph.D.: University of Wisconsin-Madi­ National Laboratory, 1971- ; Corre­ son, 1984. sponding Member, Academia Argentina Georgia M. Benkart Selected Addresses: Fifth IMA Con­ de Ciencias, 1975- ; Member, National Professol~ University of Wisconsin, ference on the Mathematical Theory Academy of Sciences, 1982- ; Doc­ Madison. of the Dynamics of Biological Sys­ tor Honoris Causa, University of Stras­ Born: December 30, 1949, Youngstown, tems, Oxford University, England, 1989; bourg, 1984; Steele Prize, AMS, 1988; Ohio. Hollistier-Stier Distinguished Lecture Doctor Honoris Causa, University of Ph.D.: Yale University, 1974. Series, Washington State University,

752 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ·················--:,.~!11)111!11£------····-··-········-··-········-··-···-·········-· ··········-·············-········-··-··············- ...... Biographies of Candidates

1990; Conference for Ford Foundation vances in theoretical and computational and W. P. Thurston, Word Processing in Fellows, National Academy of Sciences, biology have reenergized the romance Groups, Jones and Bartlett Publishers, Irvine, California, 1990; Gordon Con­ between mathematics and applications. Boston, MA, 1992. MR 93i:20036. ference, 1992; 3rd International Confer­ New mathematical challenges are posed Statement: As a resident of the UK, I ence on Mathematical Population Dy­ every day as we attempt to increase our welcome the joint AMS meetings with namics, Pau, France, 1992; Harry S. understanding of epidemics, genomics, European societies and would encour­ Kieval Distinguished Lecture Series­ ecology, cell biology, and biodiversity. age further international activities and Speaker, Humboldt State University, We must bring the excitement created by research programs. 1993. the interface between mathematics and Two years ago, encouraged by Mum­ Additional Information: Special Rec­ biology to the classroom. ford and Thurston, I founded the journal ognition by the Honorable Mexico City Experimental Mathematics with pub­ Council, 1992; Fellow, Department of David B. A. Epstein lisher Klaus Peters and with coeditor Ecology and Evolutionary Biology, Professm~ Mathematics Institute. Uni­ Silvio Levy to enable researchers to ex­ Princeton University. 1993-1994; Presi­ versity ofWmwick, Coventry, England. plain how their rigorous theories arise dential Faculty Fellowship Award, 1992- Born: May 16, 1937, Pretoria, South from experiments. I was one of Al Mar­ 1997; Editorial Board, SIAM Journal of Africa. den's main assistants in founding the Applied Mathematics; President, North­ Ph.D.: University of Cambridge, 1960. Geometry Center in Minneapolis, and eastern Chapter of the Society for the Selected Addresses: Computers, I regard visualization and experiment Advancement of Chicanos and Native Groups and Hyperbolic Geometry, 4 as important aids to rigorous mathe­ Americans in Science; Member: AMS, lectures, Rome, summer 1984; Auto­ matics. I am interested in experimental SIAM, the Society for Mathematical Bi­ matic Groups, Arbeitstagung 1986; Infi­ (currently not computer-aided) teach­ ology, and the Ecological Society of nite Sets of Rules and Finite Machines, ing methods at the post-calculus level, America. Princeton, February 1989; Growth of where I believe I have been adventurous Selected Publications: 1. Nonlinear Groups, Kyoto, January 1992; Low­ and successful. I would encourage the character-dependent models with con­ Dimensional Topology, 2 addresses, AMS to pay attention to outreach, which stant time delay in population dynamics, Knoxville, May 1992. can be very rewarding in its own right, J. Math. Anal. Appl. 128 (1987), 1-29. Additional Information: Executive though it also indirectly improves the MR 89a:92036; 2. with S. A. Levin Committee, NSF Geometry Center, Min­ public's readiness to fund research. Jus­ and F. Gould, Physiological and be­ neapolis; Founder and Chief Editor, Ex­ tification for research finance depends havioral adaptation to vmying environ­ perimental Mathematics, a new journal; on the intellectual significance of our ments: a mathematical model, Evolution Council of the London Mathematical So­ subject, as well as on its utility, and 42(5) (1988), 986-994; 3. Editor, Math­ ciety (LMS), 1972-1975; Science and we could be doing more to enthuse and ematical and statistical approaches to Engineering Research Council (SERC): inform by communicating mathematical AIDS epidemiology, Lecture Notes in Mathematics Committee, 1983-1986, ideas to a wider audience. My major Biomath .. vol. 83, Springer-Verlag, Ber­ Computational Science Initiative Com­ interest continues to be research in pure lin, 1989; 4. with S. P. Blythe, Scal­ mittee, 1986-1989, and Science Board mathematics. ing law of sexual activity, Nature 344 Computing Committee, 1989-1992; (1990), 202; 5. with H. Thieme. How LMS Senior Berwick Prize, June 1988; Cameron M. Gordon may infection-age-dependent infectiv­ Advisor to the Danish National Research Professor, University of Texas at Austin ity affect the dynamics of HIV/AIDS?, Council on the establishment of a math­ Born: March 2, 1945, Rhynie, Scotland SIAM J. Appl. Math. 53 (1993), 1447- ematical research institute in Denmark, Ph.D.: University of Cambridge, 1971 1479. February 1993. Selected Addresses: Invited Address, Statement: A female former Cornell Selected Publications: 1. Projective British Mathematical Colloquium, New­ graduate student told me recently: "I planes in 3-manifolds, Proc. London castle, 1975; Invited Address, Austin, remember taking a civil engineering Math. Soc. 11 (1961), 469-484. MR November 1981; London Mathematical course at Cornell and thinking that it 27 #2968; 2. The simplicity of certain Society. Spitalfields Lecturer, University was all about bridges and other 'boy groups of homeomorphisms, Composi­ of Sussex, 1987; International Congress stuff'. Mind you, I was not a kid. But tio Math. 22 (1970), 165-173. MR 42 of Mathematicians, Kyoto, 1990; In­ I thought that if engineering had been #2491; 3. Periodic flows on 3-manifolds, vited Address, Australian Mathematical about biological phenomena, rather than Ann. of Math. 95 (1972), 68-82. MR Society, Melbourne. 1991. erector sets, I would have been inter­ 44 #5981; 4. Commutators of 0 00 - Additional Information: Sloan Fellow, ested at a young age. Once I discov­ diffeomorphisms, Appendix to "A cu­ 1979-1981; Member, NSF-CBMS Re­ ered biomechanics in grad school. I rious remark concerning the geomet­ gional Conference Panel, 1989; NSF was hooked. You can't tear me from ric transfer map", by John N. Mather, Postdoctoral Fellowship Evaluation it. There's no reason that introduc­ Comm. Math. Helv. 59 (1984), 111-122. Panel, 1991-1993. tory mechanics courses can't talk about MR 86c:58018; 5. with J. W. Cannon, Selected Publications: 1. Knots in the trees instead of skyscrapers ... " Ad- D. F. Holt, S. V. F. Levy. M.S. Paterson, 4-sphere, Comment. Math. Helv. 51

SEPTEMBER 1994. VOLUME 41, NUMBER 7 753 Biographies of Candidates

(1976), 585-596. MR55 #13435; 2. with Workshop on Modeling of Nonlinear prepare students for real-world appli­ A. J. Casson, On slice knots in dimen­ Stellar Pulsations; Associate Editor, In­ cations and the available jobs. As a sion three, Proc. Sympos. Pure Math. ~2 ternationalJournal on High-SpeedCom­ member of the Council, my goal will (1978), 39-53. MR 81g:57003; 3. Some puting, 1989- ; Vice-Chair, SIAM Spe­ be for the AMS to continue playing an aspects ofclassical knot theoly, Lecture cial Interest Group on Supercomput­ important role in leading high-quality Notes in Math. 685 (1978), 1-60. MR ing, 1989-1991; Committee on the Un­ education, research, and applications of 80f:57002; 4. with M. Culler, J. Luecke dergraduate Program in Mathematics mathematics. I am greatly concerned and P. B. Shalen, Dehn surgery on knots, (CUPM) Subcommittee on the Major about increased pressures to shift basic Ann. of Math. 125 (1987), 237-300. in the Mathematical Sciences, 1989­ research funds toward proposals with MR 88a:57026; 5. with J. Luecke, Knots 1991; Associate Editor, International short-term applications. I would work to are detern1.ined by their complenlents, J. Journal ofSuperconlputer Applications, protect the existing funds for individ­ Amer. Math. Soc. 2 (1989), 371-415. 1989-1992; Co-chair, 1991 DOE Con­ ual mathematicians and to increase the MR 90a:57006a. ference on Experimental Mathematics: funding for long-range research. Computational Issues in Nonlinear Sci­ James M. Hyman ence; Board ofGovernors, NSF Institute Benjamin A. Lotto* Group Leadel~, Mathenlatical Modeling for Mathematics and its Applications, Assistant Professol~, Vassar College. and Analysis Grolll), Los Alanl0s Na­ 1991- ; Chair, 1992 Annual SIAM Born: April 30, 1961, Pittsburgh, Penn­ tional LaboratolY; Adjunct Professol~ meeting; AMS Task Force on Educa­ sylvania. University ofAri:ona. tion, Industry, and Government, 1992­ Ph.D.: University of California, Berke­ Born: March 20, 1950, Lakeland, 1993; Chair, 1993 DOE Conference on ley, 1988. Florida. Modeling the Forces of Nature; SIAM Selected Addresses: Wabash Extramu­ Ph.D.: New York University, Courant Board ofTrustees, 1993- ;Associate Ed­ ral Modem Analysis Miniconference, Institute ofMathematical Sciences, 1976. itor, Computers and Mathenlatics l1Jith Indianapolis, September 1992; Special AMS Committees: AMS-SIAM Com­ Applications, 1993- ; Treasurer, SIAM Session on Operator Theory and Op­ mittee on Applied Mathematics, 1985­ Special Interest Group on Dynamical erator Algebras, Dayton, October 1992; 1993 (Chair, 1992-1993); Organizing Systems; Chief Editor, SIAM Journal on Special Session on Holomorphic Spaces, Committee, 1984 AMS-SIAM Summer Scientific Computing. San Antonio, January 1993; Southeast­ Seminar on Nonlinear Systems. Selected Publications: 1. with ern Analysis Meeting (SEAM), Mem­ Selected Addresses: Invited Colloqui­ R. Knapp and J. C. Scovel, High or­ phis, March 1993; Special Session on ums at University of Arizona, Uni­ der finite volunle approximations of Composition Operators on Spaces of versity of Minnesota, University of differential operators on nonuniform Analytic Functions, College Station, Oc­ New Mexico, University of California, grids, Phys. D 60 (1992), 112-138. MR tober 1993. Los Angeles, and the Rensselaer Poly­ 93i:65110; 2. with P. Rosenau, Conl­ Selected Publications: 1. with D. technic Institute Conference on Adap­ pactons: Solitons l1Jith finite wavelength, Sarasoll, Militiplicative structure of tive Mesh Methods, 1992-1994; In­ PRL 70 (1993), 564-567; 3. with R. de Branges's spaces, Rev. Mat. Iber­ vited Lecture, SIAM Meeting on the Camassa and D. Holm, A nevv inte­ oamericana 7 (1991), 183-220. MR Numerical and Mathematical Analy­ grable shallow water equation, Adv. 92k:46035; 2. with J. McCarthy, Com­ sis of Nonlinear PDEs, 1993; Invited Appl. Mech. 30 (1994), 1-33; 4. with R. position preserves rigidity, Bull. London Lecture, IMA Conference on Adaptive Dougherty, A divide-and- conquer algo­ Math. Soc. 25 (1993), 573-576; 3. with Mesh Methods, 1993; Invited Collo­ rithmfor grid generation, Appl. Numer. D. Sarason, Multipliers of de Branges­ quium Lecture, Army High Performance Math. 14 (1994), 2-11; 5. with J. Li Rovnyak spaces, Indiana Univ. Math. J. Computing Center on Blending Mathe­ and A..Stanley, Threshold conditions 42 (1993), 907-920; 4. Von Nelllnanll's matical and Numerical Approximations for the spread of HIV infection in age­ inequality for conlm.uting, diagonaliz­ to Solve PDEs, 1993; Invited Address, structured populations of homosexual able contractions. I., Proc. Amer. Math. Cincinnati, January 1994. men, J. Theoret. Biology 166 (1994), Soc. 120 (1994),889-895; 5. with T. Ste­ Additional Information: NRC Com­ 9-31. ger, Von Neumann's inequality for com­ mittee on Applications of Mathemat­ Statement: I strongly support the AMS muting, diagonali:able contractions. II., ics, 1982-1985; Co-chair, 1983 Los increasing its role to foster interactions Proc. Amer. Math. Soc. 120 (1994), Alamos Conference on Implicit Meth­ among mathematicians in academia, in­ 897-901. ods for PDEs; Co-chair, 1987 CNLS dustry, and the national laboratories by Statement: The major problems fac­ Workshop on Nonlinear Systems of soliciting more applied mathematicians ing mathematics and mathematicians PDEs; Co-organizer, OSTP Workshop to participate in our conferences through right now-the horrible job market, di­ coordinating a National Scientific Ef­ minisymposia and as invited speakers. minished research funding, smaller de­ fort on AIDS Modeling and Epidemi­ We should aggressively pursue new ini­ partmental budgets, increased teaching ology, 1988; Member, NSFINRC Panel tiatives to help lead the graduate and loads, and so on-have had a particu­ for Computing and Applied Mathemat­ undergraduate educational programs in larly harsh effect on young mathemati­ ics, 1988-1992; Co-chair, 1989 NATO both pure and applied mathematics to cians. (By "young" I mean young in

754 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··················-··-···-·······-...... ______...... Tllll•.BIIBIIBIIBII------··················-·······-···········-··-··- ·····························-········-······· Biographies of Candidates career, so ''young mathematicians" in­ Wiener Prize in Applied Mathemat­ Offices: Member-at-Large of the Coun­ cludes recent Ph.D.s, graduate students, ics, AMS-SIAM, 1990; Humboldt Prize, cil. 1986-1987. nontenured faculty, faculty in nontenure 1991; Fairchild Scholar, California Insti­ AMS Committees: Committee on the track lines, etc.) Many have had to live tute of Technology, 1992; Fellow, Royal Human Rights of Mathematicians, year to year, unemployed or in tempo­ Society of Canada, 1993. 1990- ; Ad Hoc Committee on Co­ rary positions with low salaries and/or SelectedPublications: 1. withR.Mont­ operation with Latin American Mathe­ high teaching loads. Some have quit gomery and T. S. Ratiu, Reduction, sym­ maticians, 1990-1992. mathematics entirely. As a result, much metry, and phases in mechanics, Mem. Selected Addresses: Special Session of the energy that would have been de­ Amer. Math. Soc. 88 (1990), 1-110. MR on Classical Analysis, Joint Meeting of voted to research and teaching has been 91b:58074; 2. with J. C. Simo and D. the American and London Mathemati­ spent worrying about finding employ­ R. Lewis, Stability of relative equilib­ cal Societies, Cambridge, England. June ment for one more year. I believe that ria. I., The reduced energy-momentum 1992 (Organizer); Invited Lecture. Inter­ our profession will feel this loss for method, Arch. Rational Mech. Anal. 115 national Conference in Honor of B. Sz.­ many years. (1991), 15-59. MR 92f:70014; 3. Lec­ Nagy, Szeged, Hungary, August 1993; Action taken on the problems men­ tures on Mechanics, London Mathemat­ Special Session on Harmonic Analysis, tioned above can only have a signifi­ ical Society Lecture Note Series, vol. Syracuse, September 1993; Special Ses­ cant and lasting effect if the situation 174, Cambridge University Press, Cam­ sion on Operator Theory. Manhattan, of young mathematicians is specifically bridge, 1992. MR 93f:58078; 4. with Kansas, March 1994; Invited Address, taken into account. One simple way to A. M. Bloch, P. S. Krishnaprasad, and Richmond, November 1994. do this is to include more young mathe­ G. Sanchez de Alvarez, Stabilization of Additional Information: Member, In­ maticians in the process. If I am elected rigid body dynamics by internal and ex­ stitute for Advanced Study, 1978-1979 to the Council, I will seek to encourage ternal torques, Automatica J. IFAC 28 and 1983-1984; NSF Visiting Profes­ the AMS to nominate more young math­ (1992), 745-756; 5. with J. Scheurle, sorship for Women. 1983-1984; NSF Member, ematicians for elected positions and ask Lagrangian reduction and the double Career Award, 1987-1988; MSRI. 1987-1988; Association for more young mathematicians to serve on spherical pendulum, Z. Angew. Math. I will also try to en­ Women in Mathematics: President-Elect. major committees. Phys. 44 (1993), 17-43. courage more young mathematicians to 1992-1993; President, 1993-1995. Statement: While maintaining the high­ run for office and to serve on commit­ Selected Publications: 1. with M. Cot­ est standards, the mathematics commu­ tees. Finally. I will do my best to bring lar, On the Helson-Szego theorem and a nity needs to work to make interdis­ my perspective as a young mathemati­ related class of modified Toeplitz ker­ ciplinary activities ever more effective. cian to the Council. nels, Proc. Sympos. Pure Math. 35 part of our subject and is This is a vital (1979). 383-407. MR 81j:42022; 2. ultimately motivated by the high level Jerrold E. Marsden lnte1polation of Operators and Singu­ of research mathematics that is used in Professor of Mathematics and Electri­ lar Integrals, Marcel Dekker Inc., New many exciting applications. Both mathe­ cal Engineering and Computer Science, York and Basel, 1979. MR 81d:42001; of mathematics need University of California, Berkeley maticians and users 3. with R. L. Wheeden, Some weighted about how to make Born: August 17, 1942, Ocean Falls, ongoing information norm inequalities for the Fourier trans­ British Columbia, Canada this process more effective while, at the form of functions with ranis/zing mo­ Ph.D.: Princeton University, 1968 same time, the educational infrastruc­ ments, Trans. Amer. Math. Soc. 300 AMS Committees: Committee on Sum­ ture in the University setting needs to (1987), 521-533. MR 88c: 47027; 4. mer Research Conferences, 1983, and learn how to better respond to interdis­ with M. Cotlar, Transference of metrics Committee on AMS-IMS-SIAM Joint ciplinary challenges. This is one of the induced by unitary couplings. J. Func. Summer Research Conferences in the many variables that can be improved in Anal. 111 (1993), 473-488; 5. with M. Mathematical Sciences, 1984-1986 the case mathematics as a whole can Cotlar, Abstract, vveiglzted and multidi­ (Chair, 1986); Science Policy Commit­ make for better scientific and funding mensional AAK theorems and the sin­ tee, 1989-1991; Program Committee for opportunities. Besides working for the gular numbers of Sarason commutants, National Meetings, 1993-. general health of mathematics I would Integral Equations Operator Theory 17 Selected Addresses: Redman Lectures, continue to search for ways to improve (1993), 169-201. McMaster University, January 1993; our subjects' contacts, both scientific Statement: Our profession is facing a Opening Address, ENOC Conference, and educational, with other sciences and double crisis with the shortage of jobs August 1993; Plenary Lecture, Lanc­ engineering. and the shortage of federal funds for zos Symposium, November 1993; Orga­ individual research. The Society has a nizer, National Academy Symposium on Cora Sadosky duty to face these matters in the in­ Locomotion, April 1994; Plenary Lec­ ProfessOl~ Howard University. terest of ALL its membership. At the ture, International Congress on Applied Born: May 23, 1940, Buenos Aires, same time, it must recognize the right to Mathematics, Hamburg. July 1995. Argentina. mathematics of women and other under­ Additional Information: Norbert Ph.D.: University of Chicago, 1965. represented groups. As president of the

SEPTEMBER 1994, VOLUME 41, NUMBER 7 755 ...... --...... _...... _._ ...... _..... _...... _...... _...... ______...... _._ ...... -...... -...... - ...... _. Biographies of Candidates

AWM, and having been at Howard Uni­ toral Fellowship, 1984-1987; ffiM Post­ 1993-; Editor, Concerns ofYoung Math­ versity for fourteen years, I am highly doctoral and Junior Faculty Research ematicians, YMN's electronic newslet­ aware of the urgent need to pass from Fellowship, 1988-1989; Sloan Fellow­ ter, July 1993, vol. 1, nos. 1-4; Post­ declarations to results. Federal funding ship, 1990-1992; MSRI Research Pro­ doctoral Fellow, Institut Mittag-Leffler, shapes research policies in mathematics, fessorship, 1992-1993. fall1993; AWM Panelist, "Are Women which affects all of us, whether we are Selected Publications: 1. M ordell-Wei! Getting All the Jobs?", Joint Mathemat­ individually funded by NSF or not. Cuts groups of generic abelian varieties, In­ ics Meetings, Cincinnati, January 1994; in budgets can warp entire research ar­ vent. Math. 81 (1985), 71-106. MR Member: AMS, AWM, MAA. eas. It is important that the AMS reflects 87b:11046; 2. Cohomology offiber sys­ Selected Publications: 1. with J. Du­ the interest of the whole community in tems and M ordell-Wei/ groups ofabelian fiot and N. Kuhn, A classification of preserving research not only at the top varieties, Duke Math. J. 56 (1988), 41- polynomial algebras as modules over institutions, but everywhere it is demon­ 46. MR 89c: 11098; 3. Canonical models the Steenrod algebra, Comment. Math. strably excellent. For achieving this, and adelic representations, American Helv. 68 (1993), 622-632; 2. The action the involvement of all the mathemat­ J. Math. 114 (1992), 1221-1241. MR of Milnor Bocksteins on Tv M, to ap­ ical community-including its young 94a:14023; 4. Fields of definition for pear; 3. with N. Kuhn, On torsion in the people-is crucial. A persistent problem homommphisms of abelian varieties, J. cohomology of certain mapping spaces, in the AMS has been the alienation of al­ Pure Appl. Algebra 77 (1992), 253-262. to appear. most all its members from planning and MR 93f:14022; 5. with Y. G. Zarhin, Statement: Many junior mathemati­ running the Society's activities. During Isogenies of abelian varieties, J. Pure cians currently find themselves in situa­ the last twenty years some of the power Appl. Algebra 90 (1993), 23-37. tions which do not provide the necessary was wrested from the insiders, and more Statement: The Council should be resources to develop into productive re­ openness was achieved. Currently, con­ guided by the AMS's stated mission searchers, or even effective teachers. At trol is slipping away into a few powerful of furthering mathematical research and the same time, growing pressure to re­ committees selected without the partici­ scholarship. I see this as a time of duce public spending will mean that the pation of the membership. In defending great opportunity and challenge for the mathematical community will at best members' role in the Society, the Coun­ mathematical community. This is a per­ not see any increases in public money cil may be a key point: it is elected by fect time for us to raise the quality of for research. I believe that the math­ the vote of the whole membership, and mathematical communication (includ­ ematical community's response should it has authority over many (not all!) of ing communication with our colleagues, be threefold. First, we should review the Society's organs. I am dedicated to our students, and the public), make bet­ our funding wish lists and consider how keeping the lines of power open. ter use of new technologies (in our we can best nurture mathematical re­ journals, libraries, departments, offices, search in the face of current crises. I Alice Silverberg homes, etc.), view more broadly the job believe that more funding must be found Associate Professor of Mathematics, possibilities for people with mathemat­ to encourage the development of ju­ Ohio State University. ics degrees, and increase fairness and nior mathematicians-the future of our Born: October 6, 1958, New York, openness in our profession. In these and community. This means not only fund­ New York. many other ways we can further the best ing for more postdoctoral fellowships, Ph.D.: Princeton University, 1984. mathematics. but also increasing funds for confer­ AMS Committees: Centennial Fellow­ ences, summer workshops, and travel. ships Committee, 1993- (Chair, 1994- Mark W. Winstead Second, we should learn how to better 1995). Visiting Lecturer, University of Califor­ present our case for continued invest­ Selected Addresses: Conference on nia, San Diego (1994 ). ment in the mathematical sciences. For Arithmetic of Complex Manifolds, Uni­ Born: April24, 1964, Minden, Louisiana. example, think of the impact a public re­ versitiit Erlangen-Ntirnberg, Germany, Ph.D.: University of Virginia, 1993. lations blitz centered on the applications May 1988; Plenary Address, Australian Selected Addresses: Special Session of the mathematics involved in proving Mathematical Society 33rd Annual Meet­ on Homotopy Theory, Bethlehem, April Fermat's Last Theorem could have had ing, Macquarie University, Sydney, Aus­ 1992; Cech Centennial Homotopy Con­ in 1993. Finally, we need to be honest tralia, July 1989; Special Session on ference, Boston, June 1993; Matem­ with prospective mathematicians about Arithmetical Algebraic Geometry, San atikdagar Hostterminen 1993 (a series of the present job situation as well as our Francisco, January 1991; Conference on talks by mathematicians to mathemati­ individual predictions of the future. Number Theory and Arithmetical Al­ cally talented Swedish high school stu­ gebraic Geometry, Institute for Exper­ dents), Institut Mittag-Leffler, Novem­ Trustee imental Mathematics of the University ber 1993; InstitutMittag-Leffler, Septem­ of Essen, Germany, March 1991; MAA ber 1993. Frank C. Hoppensteadt Ohio Section Spring Meeting, Invited Additional Information: A founder of Professor and Dean, College of Natural Address, April1994. the Young Mathematicians' Network Science, Michigan State University Additional Information: NSF Postdoc- (YMN); YMN Editorial Board, July Born: April29, 1938, OakPark, lllinois

756 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Biographies of Candidates

Ph.D.: University of Wisconsin, Jan­ and some applications, to appear. and Robotics, IMS. Philadelphia, 1991; uary 1965 Statement: The AMS should continue Invited Paper Session on Research and AMS Committees: Organizing Com­ to make the mathematical sciences ac­ Applications in Advanced Technology, mittee, AMS-SIAM Summer Seminar cessible to all components of our society International Statistical Institute, Flo­ on Nonlinear Oscillations in Biology, and to enhance its services to mathemat­ rence, 1993. 1978 (Chair); AMS-SIAM Joint Com­ ical scientists. It should be a leader in ad­ Additional Information: Trustee, Con­ mittee on Applied Mathematics, 1978- dressing basic existential questions that sortium for Scientific Computing (John 1980 (Chair); AMS-SIAM Joint Com­ challenge the mathematical sciences to­ von Neumann Center), 1986-1991 (Sec­ mittee on Mathematics in the Life Sci­ day, and it should continue to forge new retary of the Corporation, 1989-1991); ences, 1979-1982; Organizing Commit­ working relationships with other pro­ Member: AAAS. ASA, IMS, MAA, tee, AMS-SIAM Summer Seminar on fessional societies including the AAAS, SIAM. Mathematical Aspects of Physiology, ACS, APS, IEEE, MAA, NCTM, SIAM Selected Publications: 1. Image mod­ 1980 (Chair); Task Force on AMS Con­ and the Canadian and Mexican societies. els in pattern theory, Computer Graph­ ferences, 1994 (Chair). It must enhance external fund raising for ics Image Processing 12 (1980), 309- Selected Addresses: Principal Lecturer, its important activities (meetings, recog­ 325. Republished in Image Modeling, CBMS Regional Conference, University nition of accomplishments, conferences, (A. Rosenfeld, ed.), Academic Press, of West Florida, 1975; CIME Lecturer, and publications) from governments, in­ New York-London (1981). 259-275. Cortona, Italy, 1980; Special Session on dustries, and private sources. The AMS MR 83c:68003; 2. with S. Geman, Sta­ Mathematical Biology, Monterey, 1982; should continue its work in such a way tistical methods for tomographic im­ DMV Seminar Lecturer, Bayreuth, Ger­ that it represents the mathematical inter­ age reconstruction, Bull. Inst. InternaL many, 1984; Akad. Nauk Neurocomput­ ests of all its constituents, and it should Statist. 52 (1987). MR 90g:62005d; 3. ers and Attention Workshop, Moscow, continue to be a primary source for an­ Reports on the Surveys of New Doc­ 1989; Universitat Heidelberg Workshop swers to questions about the mathemat­ torates, Annual AMS-MAA Surveys, on Reaction-Diffusion Systems in Biol­ ical sciences. I would like to contribute First Reports: Notices Amer. Math. Soc. ogy, 1992. to this important work and to the agenda November 1990, 1217-1222; Novem­ Additional Information: Senior Visit­ for the AMS as a member of its Board ber 1991, 1086-1094; November 1992, ing Fellow, Mathematical Institute, Ox­ of Trustees. 1026-1033; November 1993, 1164-1171; ford University, 1974; Editor: SIAM 4. with D. Geman and S. Geman, A Journal on Applied Mathematics, 1975- Donald E. McClure nonlinear filter for film restoration and 1984, Journal on Mathematical Biol­ Professor ofApplied Mathematics, Brown other problems in image processing, ogy, 1983- ; Managing Editor, Cam­ University; Associate Directm~ Center CVGIP: Graphical Models and Image bridge Studies in Mathematical Biology, for Intelligent Control Systems, Brown­ Processing 54 (1992), 281-289; 5. with Cambridge University Press, 1977- ; Harvard-MIT S. Geman and K. Manbeck. A com­ Christensen Fellow, St. Catherine's Col­ Born: October 22, 1944, Portland, Ore­ prehensive statistical model for single lege, Oxford University, 1994; Listed in gon photon emission computed tomography, Who's Who in America. Ph.D.: Brown University, 1970 in Markov Random Fields: Theory and Selected Publications: 1. An Introduc­ AMS Committees: Data Subcommit­ Application (R. Chellappa and A. Jain, tion to the Mathematics of Neurons, tee of the Committee on Employment eds.), Academic Press (Harcourt Brace Cambridge Studies in Mathematical and Educational Policy, 1985-1989; Jovanovich), 1993. 93-130. Biology, Cambridge University Press, AMS-SIAM Committee on Applied Statement: The primary responsibility Cambridge-New York, 1986. MR 88g: Mathematics, 1986-1988; AMS-MAA of the Trustees is to exercise sound 92016; 2. Intermittent chaos, self­ Data Committee, 1990-1992 (Chair, judgment in management of fiscal af­ organization and learning from syn­ 1990-1992) and AMS-IMS-MAA Data fairs and issues that potentially have a chronous synaptic activity in model Committee, 1993 (Chair); AMS Em­ far-reaching impact on the financial con­ neuron networks, Proc. Nat. Acad. ployment Task Force, 1992; Committee dition of the Society. I shall approach the Sci. U.S.A. 86 (1989), 2991-2995. on Resource Needs for Excellence in responsibilities of the position with the MR 90m:92021; 3. with Charles S. Mathematics Instruction, 1993- ; Com­ objective of maximizing the ability of Peskin, Mathematics in Medicine and mittee on the Profession, 1994- . the Society to fulfill its primary mission the Life Sciences, Texts in Applied Selected Addresses: Special Session in support of mathematical scholarship Mathematics, vol. 10, Springer-Verlag, on Radon Transforms and Computed To­ and research, as reflected in policies New York, 1992. MR 92K:92001; mography, New Orleans, January 1986; adopted by the Council and the Policy 4. Analysis and Simulation of Chaotic Symposium on Medical Imaging, An­ Committees. I believe that achieving this Systems, Applied Mathematical Sci­ nual Meeting of the AAAS, Chicago, objective requires prudence and a long­ ences, vol. 94, Springer-Verlag, New 1987; Mathematical Methods in To­ range view towards financial planning. York, 1993. MR 94a:34003; 5. with H. mography, Oberwolfach, 1990; Invited There are uncertainties in the financial Salehi and A. V. Skorokhod, Randomly Paper Session on Statistical Methods future of the Society linked to its ma­ perturbed Volterra integral equations in Image Processing, Remote Sensing, jor role in mathematics publications and

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to the evolution of modes of scholarly 1992; Representative, AAAS Commit­ ership. If elected, I intend to help with communication. The Trustees will re­ tee on Education, 1988-1991; SIAM all these aspects. main cognizant of these uncertainties. I Committee on Committees and Appoint­ shall remain active, as I have been, in ments' 1988-;W. M. KeckAward, 1989; Ingrid Daubechies efforts of the Society concerned with the CUPM Subcommittee on the Major in Membel~ Technical Staff, AT&T Bell status of professions in the mathemati­ the Mathematical Sciences, 1989-1990; Laboratories (untilDecember31 ,1994); cal sciences, even though these personal CUPM Subcommittee on the Calcu­ Professol~, Princeton University (after interests are not part of the main job lus Reform and the First Two Years, January 1,1995). of Trustee. In particular, I shall work 1989-1991; Advisory Committee to the Born: August 17, 1954, Houthalen, Bel­ to improve and broaden employment NSF Division ofMathematical Sciences, gium. opportunities for mathematicians, to in­ 1990-1993 (Chair, 1990-1992); SIAM Ph.D.: Free University, Brussels, 1980. crease the awareness among mathemati­ Visiting Lecturer, 1992- ; Co-director, AMS Committees: Short Course Sub­ cians of areas in technology and science Mathematicians and Education Reform committee, 1993- ; Committee on Com­ where mathematics is needed, to in­ Network, 1993- ; Chair-elect, Mathe­ mittees, 1993- . crease awareness in kindred disciplines matics Section of the AAAS, 1994- ; Selected Addresses: Invited Address, of the important role of mathematics, MAA Program of Consultants, 1994- ; MAA, Baltimore, 1992; Invited Ad­ to encourage and enable participation in Member: AAAS, AMS, AWM, MAA, dress, AMS, Bethlehem, April 1992; mathematics by young people truly re­ SIAM, American Academy of Mechan­ Organizer and Speaker, AMS Short flective ofthe spectrum ofour society, to ics, American Physical Society, Society Course on Wavelets and Applications, improve the public regard and support of for Natural Philosophy. San Antonio, January 1993; Interna­ higher education, and to foster support Selected Publications: 1. with M. S. tional Congress of Mathematicians, Zu­ for research in mathematics. Santos, On the structure of the equilib­ rich, 1994. rium price set of overlapping-genera­ Additional Information: MacArthur Nominating Committee tions economies, J. Math. Econom. 18 Fellow, 1992-1997; Member, American (1989), 209-230. MR 90k:90032; 2. Academy of Arts and Sciences, 1993. with T. B. Benjamin and D. K. Bose, Jerry L. Bona Selected Publications: 1. An uncer­ Solitary-wave solutions of nonlinear Raymond Shibley Professor and ChaiJ~, tainty principleforfermions with gener­ problerns, Phil. Trans. Royal Soc. Lon­ Mathematics Department, Pennsylvania alized kinetic energy operator, Comm. don A 331 (1990), 195-244. MR 91h: State University. Math. Phys. 90 (1983), 511-520. MR 35309; 3. with B. Boczar-Karakiewicz Born: February 5, 1945, Little Rock, 85j:81008; 2. with J. Klauder, Quantum and B. Pelchat, Interaction of internal Arkansas. mechanical path integrals with Wiener waves l1dth the sea bed on continen­ Ph.D.: Harvard University, 1972. measures for all polynomial Hamilto­ AMS Committees: Committee on tal shelves, Continental Shelf Res. 11 nians. II., J. Math. Phys. 26 (1985), Steele Prizes, 1985-1987; AMS-MAA (1991), 1181-1197; 4. with F. Abergel, 2239-2256. MR 86m:81063; 3. Or­ Ad Hoc Advisory Committee on a A mathernatical theory for viscous, free­ thonormal bases ofcompactly supported Newsletter on Collegiate Mathematics sillface flows over a perturbed plane, wavelets, Comm. Pure Appl. Math. 41 Education~ 1988; Chair, Liaison Com­ Arch. Rational Mech. Anal. 118 (1992), (1988), 909-996. MR 90m:42039; 4. mittee with the AAAS, 1990-1992; 71-93. MR 92k:35213; 5. with J.-C. Chair, Ad Hoc Committee on Appli­ Saut, Dispersive blow-up of solutions Tin1e-frequency localization operators: cations of Mathematics, 1989-1992; ofgeneralized Korteweg-de V;·ies equa­ A geometric phase space approach, Committee on Education, 1993- ; Chair, tions, J. Diff. Equations 103 (1993), IEEE Trans. Inform. Theory 34 (1988), Subcommittee on Graduate and Postdoc­ 3-57. 605-612; 5. Ten lectures on wavelets, toral Education, 1994-; University Lec­ Statement: In addition to pursuing its CBMS-NSF Regional Conference Se­ ture Series Editorial Committee, 1994- . primary goal of fostering and dissem­ ries in Applied Mathematics, Society Selected Addresses: International Con­ inating research in mathematics, the for Industrial and Applied Mathematics gress of Mathematicians, Helsinki, American Mathematical Society should (SIAM), Philadelphia, PA, 1992. MR 1978; Invited Speaker, American Phys­ take a leadership role in a number of 93e:42045. ical Society Annual Meeting, Notre other activities. These include mathe­ Statement: In this time of crisis in Dame, 1979; Invited Speaker, SIAM matics education, the organization of the job market as well as in funding Annual Meeting, San Diego, 1989; In­ further training of our recent Ph.D.s, for mathematicians, I believe that the vited Addresses, Minneapolis, Novem­ and closer collaboration with other pro­ AMS should continue to emphasize the ber 1984, and San Francisco, January fessional organizations, especially those importance of good mathematical re­ 1995. representing the mathematical sciences. search, whether basic or linked with Additional Information: Committee The Nominating Committee is espe­ applications. The AMS should also play on the Undergraduate Program in Math­ cially well placed to ensure the devel­ a role in showing to the outside world ematics (CUPM), 1987-1991; SIAM opment of these prospects, as well as that mathematics is not only important Committee of Managing Editors, 1987- abetting the move to diversify our lead- but also fun and exciting.

758 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ·!11_%:__...... ·....·· .... Biographies of Candidates

William James Lewis and education; (2) providing leadership Stephen D. Smith Professor and Chai1~, Department of for mathematics faculties in our col­ Professor, University of Illinois at Mathenzatics and Statistics, University leges and universities as mathematics Chicago. ofNebraska-Lincoln. departments are challenged to accept a Born: June 11, 1948, Houston, Texas. Born: February 11, 1945, Tallahassee, broader mission of research, education, Ph.D.: Oxford University, 1973. Florida. and outreach; and (3) supporting higher­ Selected Addresses: Hour Address, Ph.D.: Louisiana State University, 1971. quality mathematics education for U.S. South Bend, March 1991; Co-organizer AMS Committees: Committee on Sci­ students at all levels from kindergarten (with Mark Ronan), Special Session ence Policy, 1992- ; Committee on through college, with special attention on Groups and Geometries, Chicago, Resource Needs for Excellence to providing opportunities for women March 1985; Co-organizer (with Jon in Mathematics Instruction, 1993- ; and minority students. Alperin), Special Session on Simplicial AMS-MAA Committee on Teaching Complexes Associated to Finite Groups Assistants and Part-time Instructors, Rogers J. Newman and Their Representations, South Bend, 1994- . Professor, Southern Unh'ersity, Baton March 1991; Co-organizer (with Michael Selected Addresses: Invited Speaker, Rouge. Aschbacher), Special Session on Simple National Meeting of AAAS, Chicago, Born: December 22, 1926, Ramar, Al­ Group Classification: Second Genera­ 1992; Invited Speaker, AAUP National abama. tion Proof and Applications, San Fran­ Meeting, Washington, D.C., 1992; Math­ Ph.D.: University of Michigan, 1961. cisco, January 1995. ematicians and Education Reform Net­ AMS Committees: AMS-AAAS­ Additional Information: Rhodes work Workshop, Berkeley, 1993; Spe­ MAA Committee on Opportunities Scholar, 1970-1973; Bateman Instruc­ cial Session on Mathematicians and in Mathematics for Disadvantaged tor, California Institute of Technology, Education Reform, Cincinnati, January Groups, 1987; AMS-AAAS-MAA 1973-1975; Presented talks at 15 AMS 1994. Committee on Opportunities in Math­ special sessions, 1973-1994; NSF Pan­ Additional Information: Principal In­ ematics for Underrepresented Minori­ els: SCREMS, 1987, Calculus Reform, vestigator, Nebraska Statewide Sys­ ties, 1988-1989; Liaison Committee 1990, and NSF Postdocs, 1993; Kenna temic Initiative; Member: AMS, MAA, on Education in Mathematics, 1989- . Lecturer, University of Notre Dame, NCTM. Selected Addresses: First Invited Ad­ 1988; Chair, ICM Travel Awards Panel, Selected Publications: 1. The spec­ dress, National Association of Math­ 1990, 1994; Member: AWM, London trum of a ring as a partially ordered ematicians, 1972; Special Session on Mathematical Society. set, J. Algebra 25 (1973), 419-434. MR Meetings of Mathematicians, Cincin­ Selected Publications: 1. The classifi­ 47 #3361; 2. with J. Ohm, The ordering nati, January 1994. cation of finite groups with large ex­ of Spec R, Canad. J. Math. 28 (1976), 820-835. MR 53 #13183; 3. Invited Additional Information: President traspecial 2-s11bgrollps, The Santa Cruz critique, NRC Report on "Educating Emeritus, National Association of Conference on Finite Groups (Univ. Cal­ Mathematical Scientists: Doctoral Study Mathematicians; Reviewer, Mathen1ati­ ifornia, Santa Cruz, California, 1979), and the Postdoctoral Experience in the cal Rel'iel1Js, 1966-1970; Member, Proc. Sympos. Pure Math., vol. 37, United States", Notices Amer. Math. MAA Board of Governors, 1986-1989. Amer. Math. Soc., Providence, RI, 1980, Soc. 39 (1992), 396-397; 4. Teach­ Statement: The AMS Council plays a pp. 111-120. MR 82c:20034; 2. with ing Mathematics in a State University, crucial role in mathematics research and Mark A. Ronan, 2-local geonzetries for Handbook of College Teaching: The­ education in this country and abroad. some sporadic groups, The Santa Cruz ory and Applications, Greenwood Pub­ As a member of the council, I would Conference on Finite Groups (Univ. Cal­ lishing Group, Inc., Chicago, IL, 1994. assist the AMS in continuing its research ifornia, Santa Cruz, California, 1979), Statement: The primary purpose ofthe focus. I would also be a strong voice Proc. Sympos. Pure Math., vol. 37, Society is to support mathematical re­ for opening wider the doors of opportu­ Amer. Math. Soc., Providence, RI, 1980, search. Traditionally, the Society has nity for the participation of underrepre­ pp. 283-289. MR 82c:20033; 3. Ir­ supported research through its support sented groups, especially minorities and reducible modules and parabolic sub­ for publications, meetings, and confer­ women. groups, J. Algebra 75 (1982), 286­ ences; and these activities should con­ In this regard, I believe that the 289. MR 83g:20043; 4. with M.A. Ro­ tinue to receive a substantial share ofthe AMS can use its influence and resources nan, Sheaves Oil buildings and modu­ Society's time, energy, and resources. to (1) encourage individuals in these lar representations ofChevalley groups, This support can best be provided if groups to get involved in AMS ac­ J. Algebra 96 (1986), 319-346. MR we can assure the overall health of the tivities, including research, and to (2) 87h:20087; 5. with M. G. Aschbacher, mathematical enterprise. This broader suggest strongly to funding agencies, On QuilleJr's conjecturefor the p-groups responsibility obligates substantial at­ both public and private, to give more cOl1zplex, Ann. of Math. 137 (1993), tention to three areas: (1) influencing consideration to the needs of individuals 473-529. federal science policy, especially the fi­ and subgroups as they strive for greater Statement: I would try to nominate nancial support of mathematics research participation. candidates of sound judgement.

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Susan G. Williams schools. This segment of the member­ 95 (1985), 153-172. MR 87h:16016; 5. Associate Professor of Mathematics. ship is seriously underrepresented in Some remarks on quantization, Progress University of South Alabama. AMS leadership. As a member of the in Mathematics, vol. 99, Birkhauser Born: May 26, 1953, Orange, New Jer­ Nominating Committee I would work Boston, Boston, MA, 1991, pp. 37--47. sey. to remedy this imbalance. I would also MR 93a:58070. Ph.D.: Yale University, 1981. seek nominees who reflect the diversity Statement: The Editorial Boards Com­ Offices: Member-at-Large of the Coun­ of the Society in other respects such mittee (EBC) is charged with monitoring cil, 1993-. as age, race, gender, and geographical the work of the editorial committees of AMS Committees: Committee on Sci­ distribution. Recruiting from a wider the Society's journals and with nomi­ ence Policy, 1993- . range of schools will make this easier to nating people to serve on those com­ Selected Addresses: Special Session achieve. mittees. By Council action, the EBC is on Texas Topology and Geometry, Den­ The most healthy and productive de­ required to increase the representation ton, November 1990; Conference on bate comes from a diversity of perspec­ of women on the editorial committees. Symbolic Dynamics and its Applica­ tives. Most mathematicians are willing I strongly support this stand and believe tions, New Haven, August 1991; Col­ to respond to the needs of other members the same must be done for minority loque Arithmetique et Dynamique Sym­ of the mathematical community when representation. I also strongly believe bolique, Marseille, September 1991; these needs are clearly represented to that members of the editorial commit­ Special Session on Ergodic Theory and them. The most difficult arguments are tees must be knowledgeable, thorough, Dynamical Systems, Tuscaloosa, March often among members with substantially dependable, and willing to work hard. 1992. the same backgrounds and interests but Finally, I firmly believe that we can Additional Information: Organizer, conflicting opinions; sometimes a fresh obtain broader representation on the ed­ Southeast Dynamical Systems Confer­ viewpoint helps to bring a resolution. itorial committees without sacrificing ence, Mobile, February 1990; Program quality or standards in any way. Committee, Mathematical Sciences Re­ Editorial Boards Committee search Institute Special Half-Year Pro­ Rhonda]. Hughes gram in Symbolic Dynamics, fall1992; Robert]. Blattner ProfessOI~ Bryn Mawr College. Member: Alabama Mathematics Infras­ Professor Emeritus ofMathematics, Uni­ Born: September 28, 1947, Chicago, tructure Committee, AMS, AWM. versity of California, Los Angeles. Illinois. Selected Publications: 1. Toeplitz min­ Born: August6, 1931,Milwaukee, Wis­ Ph.D.: University of Illinois at Chicago, imal flows which are not uniquely er­ consin. 1975. godic, Z. Wahrsch. Verw. Gebiete 67 Ph.D.: University of Chicago, 1957. Offices: Member-at-Large of the Coun­ (1984), 95-107. MR 86k:54062; 2. with AMS Committees: Notices Editorial cil, 1988-1990. B. Marcus and K. Petersen, Transmis­ Committee, 1987-1990. AMS Committees: Committee on Com­ sion rates and factors ofMarkov chains, Selected Addresses: Invited Address, mittees, 1989-1990; Science Policy Com­ Conference in Modern Analysis and Corvallis, June 1971; AMS Summer Re­ mittee, 1991-1993; Committee on Aca­ Probability (New Haven, Connecticut, search Institute on Harmonic Analysis demic Freedom, Tenure, and Employ­ 1982), Contemp. Math., vol. 26, Amer. on Homogeneous Spaces, 1972; Spe­ ment Security, 1993-. Math. Soc., Providence, RI, 1984, pp. cial Session on Differential Geometry Selected Addresses: Special Session 279-293. MR 85j:28020; 3. Covers of and Mathematical Physics, San Diego, on Functional Analysis, Bryn Mawr, non-almost finite type sofic systems, November 1984; Special Session on 1982; Special Session on Partial Dif­ Proc. Amer. Math. Soc. 104 (1988), Hopf Algebras, San Francisco, January ferential Equations, Louisville, 1984; 245-252. MR 90c:28028; 4. Lattice in­ 1991. SigmaXiNationalLecturer, 1993-1994. variants for sofic shifts, Ergodic Theory Additional Information: Member, Additional Information: National Re­ Dynamical Systems 11 (1991), 787-802. AAAS, 1986-. search Council Doctoral and Postdoc­ MR 92k:58076; 5. with P. Trow, Core Selected Publications: 1. Induced and toral Mathematics Study Committee, dimension group constraints for factors produced representations of Lie alge­ 1990-1991; Sears-Roebuck Foundation of sofic shifts, Ergodic Theory Dynam­ bras, Trans. Amer. Math. Soc. 144 Award for Teaching Excellence and ical Systems 13 (1993), 213-224. MR (1969), 457--474. MR 46 #7338a; 2. Campus Leadership, 1991; Co-director, 94c:58061. The metalinear geometry of non-real Bryn Mawr-Spelman Summer Mathe­ Statement: A substantial proportion of polarizations, Lecture Notes in Mathe­ matics Program. AMS members are faculty at small col­ matics, vol. 570, Springer, Berlin, 1977, Selected Publications: 1. with I. Segal, leges and universities that have few pp. 11--45. MR 56 #9583; 3. with J. Singular perturbations in the interac­ resources to support research. This pro­ H. Rawnsley, Quantization of the action tion representation, J. Func. Anal. 38 portion is growing as the bleak job mar­ of U(k, l) on lR 2(k+ll, J. Funct. Anal. (1980), 71-98. MR 81m:47065; 2. A ket causes more talented young math­ 50 (1983), 188-214. MR 85c:58044; 4. partial integration formula for product ematicians with a strong dedication to with S. Montgomery, A duality theorem integrals of unbounded operator-valued research to take jobs at less prestigious for Hopf module algebras, J. Algebra functions, Proc. Amer. Math. Soc. 96

760 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... llRIJII.. llllllllllllllllllllllllllllllll--lillillillllillillllillilllliiiMil!IIBIMiilll···-···-··················-·····················-·········-·················-··-··················-·····-···-·············· Biographies of Candidates

(1986), 455--461. MR 88g:47084; 3. on Number Theory, Houston, January potential candidates for editorial posi­ with S. Kantorovitz, Spectral represen­ 1967; International Congress of Math­ tions. Although recommendations from tations for unbounded operators with ematicians, Nice, 1970; Invited Ad­ well-functioning editorial boards will real spectrum, Math. Ann. 282 (1988), dress, MAA Annual Meeting, Las Ve­ frequently be passed on to the AMS 535-544. MR 90a:47009; 4. with M. gas, 1972; Invited Address, Missoula, Council, the Committee is not meant to Kon, Norm group convergence for sin­ August 1973; Special Session on the be a rubber stamp; and I believe this is gular Sclzrodinger operators, Ann. Inst. History of Contemporary Mathematics, proper. H. Poincare Phys. Theor. 54 (1991), San Francisco, 1981. 179-198. MR 92m:35057; 5. with P. Additional Information: Editorial Chernoff, A new class of point interac­ Committees: Journal ofNumber TheOI)', Herbert S. Wilf tions in one dimension, J. Func. Anal. 1977- ; Illinois Journal of Mathemat­ Professor, University of Pennsylvania. 111 (1993), 97-117. MR 94a:47080. ics, 1978-1984; American Academy of Born: June 13, 1931. Statement: The publication program of Arts and Sciences, 1983; William Low­ Ph.D.: Columbia University, 1958. the AMS provides the Society with its ell Putnam Problem Committee, 1984- AMS Committees: Committee on Ap­ most effective means of communicating 1987 (Chair, 1987); Editorial Commit­ plied Mathematics, 1965-1966 and and disseminating mathematics to the tee, Pacific Journal of Mathematics, AMS-SIAM Committee on Applied community worldwide. It is important 1985-1994; Board of Trustees, MSRI, Mathematics. 1967-1968 (Chair, 1968); that editorial boards of AMS journals 1990-1994; Chair, Department of Math­ Invitations Committee. Symposium on reflect the standards of excellence to ematics, University of California, San Mathematical Aspects of Computer Sci­ which the AMS is committed, and at the Diego, 1990-1994. ence, April 1966; Committee for a same time provide broad representation Selected Publications: 1. A complete Symposium on Mathematical Aspects ofthe mathematics community. I believe determination of the complex quadratic of Electrical Network Analysis, April it is the responsibility of the Editorial fields of class-number one, Michigan 1969. Boards Committee to widely solicit sug­ Math.J.14(1967), 1-27.MR36#5102; Selected Addresses: Invited Address, gestions and to nominate candidates for 2. An Introduction to Number The01y, Hanover, August 1972; MIT Conference editorial boards to the Council with both Markam Publishing Co., Chicago, IL, on Computers and Mathematics, MIT, these criteria in mind. 1970. MR 40 #7186 (reprinted by MIT June 1989; SIAM International Con­ Press, Cambridge, MA-London, 1978); ference on Optimization and Combina­ 3. Some effective cases of the Brauer­ torics, University of British Columbia, Harold M. Stark Siegel theorem, Invent. Math. 23 (1974), Vancouver, Canada, June 1992; 25th ProfessOI~ Department of Mathematics, 135-152. MR 49 #7218; 4. £-functions Southeastern Conference on Combi­ University of California, San Diego. at s = 1. (IV), First derivatives at s = 0, natorics, Algorithms and Probability. Born: August 6, 1939, Los Angeles, Adv. in Math. 35 (1980), 197-235. MR Boca Raton, FL, March 1994; Inter­ California. 81f:10054; 5. Galois themy, algebraic national Conference on Random Se­ Ph.D.: University of California at Berke­ number the my and :::eta functions, From lection of Combinatorial Objects, Bor­ ley, 1964. Number Theory to Physics, Springer­ deaux, France, January 1994. Offices: N aminating Committee, 1984- Verlag, Berlin, 1992, pp. 313-393. Selected Publications: 1. Generating­ 1985 (Chair, 1985); Member-at-Large of Statement: A 1986 review of the Nom­ fimctionology, Academic Press, Boston, the Council, 1988-1991. inating Committee recommended that MA, 1990. MR 91g:05008; 2. with AMS Committees: Program Commit­ the Committee take a much more ac­ D. Zeilberger, Towards computeri:::ed tee, 1976-1977 and Program Commit­ tive role in the nominating of people proofs of combinatorial identities, Bull. tee for National Meetings, 1978; Com­ for editorial boards. Because of the feel­ Amer. Math. Soc. 23 (1990), 77-83. mittee on Summer Institutes, 1976- ing that this would cause too heavy MR 91a:33003; 3. with A.M. Odlyzko, 1978 (Chair, 1978); Bulletin Editorial a load for the committee, the Edito­ Functional iteration and the Josephus Committee (Associate Editor, Research rial Boards Committee was split off problem, Glasgow Math. J. 33 (1991), Announcements), 1982-1987; Search from the Nominating Committee in the 235-240. MR 92g:05006; 4. with D. Committee for the Position of Secre­ election of 1988. Certainly the Edito­ Zeilberger, An algorithmic proof tlze­ tary, 1986; Chair, Committee to Select rial Boards Committee should consult Ol)' for hypergeometric (ordinary and the Winner of the Cole Prize for 1991 the various editorial boards for sugges­ "q") multisum!integral identities, In­ and 1992. tions, but the EBC should also consult vent. Math. 108 (1992), 575-633. MR Selected Addresses: Special Session widely elsewhere and actively seek out 93k:33010.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 761 Proposed Amendment to the Bylaws of the American Mathematical Society

---·----·------The Council recommends the amendment to the Bylaws the general administration of the affairs of the Society in below. It is intended to replace language concerning the accordance with the policies that are set by the Board of Executive Director so as to conform to current practices. Trustees and by the Council. In the statement of the amendment, deleted words are Section 2. The Executive Director shall be appointed by tiitea ea~; and insertions are in bold face. the Board of Trustees with the consent of the Council. The The ballot on the amendment is on the same sheet as that terms and conditions of employment shall be fixed by the for officers and Council members. Board of Trustees and the performance of the Executive Director shall be reviewed regularly by the Board of Trustees. Section 3. The Executive Director shall ~ tHttlef 4;he iHHBeaiate ait=eeaea ei a be responsible to and shall consult Article VI regularly with a liaison committee consisting of the president as chair, the secretary, &B6 the treasurer, and the presiding Executive Director officer of the Board of Trustees ef wftieft 4;he )"fesiaeftt sftaH Section 1. There shall be an Executive Director who shall 9e ekainH9ft ~ effieie. be a paid employee of the Society. The Executive Director Section 4. The Executive Director shall attend meetings shall have charge of the eeHtTal offices of the Society, except of the Board of Trustees, the Council, and the Executive for the office of the secretary, and shall be responsible for Committee, but shall not be a member of any of these bodies.

Analysis of and on Uniformly Rectifiable Sets Guy David and Stephen Semmes Volume38

This book is about understanding uniform rectifiability of a given set in terms of the approximate behavior of the set at most locations and scales. In addition to being the only general reference available on uniform rectifiability, this book also poses many open problems. some of which are quite basic.

1991 Mathematics Subject Classification: 28; 42, 30, 49 ISBN 0-8218-1537-7, 356 pages (hardcover), December 1993 Individual member $67, List price $111, Institutional member $89 To order. please specify SURV38/NA

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762 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ICM-94 in Zurich

Bourgain, Lions, Yoccoz, and Zelmanov Receive Fields Medals and Wigderson Receives Nevanlinna Prize

Rumors piled up like so many feet of Alpine snow, but few The medalists were mostly honored for a body of work could be really sure who would get Fields Medals until the rather than a single result, though Zelmanov is perhaps names were announced at the International Congress of Math­ an exception in this regard. His major contribution was ematicians (ICM) in ZUrich last month. Sitting unobtrusively the solution of the Restricted Burnside Problem. There are in the front row of the hall where the opening ceremonies actually three Burnside problems, the first two of which were were held, waiting patiently through all the honorific speeches posed by Burnside in 1902 and were solved by Novikov and and musical interludes, were the four medalists-Jean Bour­ Adian. These problems ask whether every finitely generated gain, Pierre-Louis Lions, Jean-Christophe Yoccoz, and Efim torsion group is finite or is of bounded exponent (the exponent Zelmanov-and the Nevanlinna Prize winner Avi Wigderson. of a group is the smallest n such that .r" = 1 for all .r in the The awardees were a composed group: the only detectable group). The Restricted Burnside Problem. which dates back fidgeting was on the part of Wigderson's young daughter, to the 1930s, asks whether there is a bound on the order who had a ringside seat on her father's lap throughout the of a group with a finite number of generators and a given proceedings. exponent. Zelmanov settled this question in the affirmative. ICM-94, held August 3-11, drew about 2.500 participants, A major technical tool in the solution is earlier joint work somewhat fewer than the last couple of Congresses, perhaps of Zelmanov and McCrimmon on quadratic Jordan algebras. due to the worldwide recession and Switzerland's prices, Zelmanov, born in 1955, is at the University of Wisconsin at which tend toward Matterhorn proportions. Congressgoers Madison. were treated not to the bracing air that one tends to associate with a country boasting some of the most spectacular moun­ tains in the world, but rather to a European heat wave that sent temperatures into the ninety degree range on several days of the Congress. The Eidegenossische Technische Hochschule (ETH) and the University of ZUrich, whose adjacent buildings served as the site for most of the Congress sessions, have no air conditioning to speak of, and some of the lecture rooms sweltered. But the outdoor cafes and the sparkle of Lake ZUrich, not to mention the mathematics, provided some distraction from the heat.

The Awardees' Work This year's crop of Fields Medalists represents two or three very classical areas of mathematical research. It includes two French analysts (Lions and Yoccoz) and a Belgian analyst (Bourgain) who has worked in France; Zelmanov, a Russian, works in algebra. With more geometric work Pictured left to right are: Fields Medalist Jean Bourgain. Nevanlinna Prize dominating the three previous rounds of Fields Medals given winner Avi Wigderson. Fields Medalist Jean-Christophe Yoccoz. Fields Medalist in Warsaw, Berkeley, and Kyoto, some speculated that this Pierre-Louis Lions. and Fields Medalist Efim Zelmanov. year's emphasis on analysis was an attempt to balance the different branches of mathematics. In addition. the choice Pierre-Louis Lions received the Fields Medal for contri­ of Lions as a Fields Medalist turns the spotlight on applied butions over the last fifteen years to several areas of partial mathematics, an area that many say has been neglected at differential equations. Lions' work is important because vari­ previous Congresses. ations of methods he has developed have applications to broad

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classes of equations. The so-called "viscosity method" has, possible ratio of faulty to nonfaulty agents. He has also made due in large part to the work of Lions, grown into an elegant contributions to the theory of pseudorandom generators.* and comprehensive theory useful for many equations arising from different applications. Lions has also made important Computers and Ethics in Mathematics contributions to the understanding of the Boltzmann and Onstage throughout the opening ceremonies were Jacques­ other transport equations arising in kinetic theory and other Louis Lions of the College de France, president of the Inter­ areas of physics. Prior to Lions's work, no general theory national Mathematical Union (IMU) (and father of Medalist existed for understanding these equations. He also developed Lions); David Mumford of Harvard University, IMU vice­ the concept of "concentration compactness" for variational president (and recently named president for the coming four problems. Lions was born in 1956 and is at Universite de years); and Henri Carnal of the University of Berne, chair Paris-Dauphine. of the ICM Organizing Committee and president of the Jean-Christophe Yoccoz is one of the leading theorists in Congress. Beno Eckmann, founder of the Mathematical Re­ dynamical systems. The field originated in Poincare's study of search Institute at the ETH and former IMU secretary, was the movement of the planets in the solar system. The attraction named honorary president of the ICM; and, after presenting of the planets to each other causes them to deviate from the a speech, he joined the others onstage and later presented the elliptical orbits predicted by Kepler's laws, raising the question Fields Medals to the recipients. The proceedings took place in of whether or not the solar system is stable. In this generality, English, although most of the speakers greeted the audience in the question is still open today, although about fifty years ago French and German. Eckmann threw in an Italian introduction Carl-Ludwig Siegel formulated a criterion for stability. One of as well, but conceded that he did not speak Switzerland's Yoccoz's major achievements was to establish precise limits fourth language, Romansh. on when such stability theorems hold. He did this through Eckmann, like some of the other speakers, pointed to a combination of ideas from analysis and geometry and the computer as having a major influence on mathematical by using techniques reminiscent of renormalization methods research. "But," he said, "we should not forget that the most from mathematical physics. He also developed combinatorial important tool of a mathematician is the fellow mathematician. methods, called "Yoccoz puzzles", for the study of fractal sets And that is why we are all here today-to exchange ideas, arising in complex dynamics. Yoccoz was born in 1957 and is views, and results, and to listen to each other." Reformulating at the Universite de Paris-Sud (Orsay). the aphorism, "whether mathematicians like it or not, the com­ Jean Bourgain, born in 1954, has held positions at the puter is here to stay," he declared that "whether the computer Institut des Hautes Etudes Scientifiques in BOres-sur-Yvette likes it or not, mathematicians are here to stay." "Mathematics and at the University of lllinois at Urbana-Champaign; he is and remains an abstract intellectual enterprise, despite the will move this year to the Institute for Advanced Study in fact that the natural sciences and technology bear witness Princeton. Bourgain received the Fields Medal for outstand­ to its practical usefulness." He issued a stern warning about ing contributions to several areas of analysis, including the the danger of "worldwide trends trying to completely replace geometry of Banach spaces, convexity in high dimensions, rigorous reasoning and proof by computer visualization and harmonic analysis, ergodic theory, and nonlinear evolution experimentation." equations. For example, he proved well-posedness for the By popular acclaim, the speech of Ruth Dreifuss, a nonlinear Schrodinger equation and the Korteweg-de Vries Swiss federal minister whose portfolio includes science and equation with singular boundary conditions. Bourgain has education, was the hit of the opening ceremonies. To prepare tackled analytical problems using ideas from outside analysis for her speech, Dreifuss sent three questions to more than in unexpected ways; his work on nonlinear partial differential a dozen of the world's leading mathematicians, including Eckmann, Raoul Batt, Rene Thorn, Armand Borel, Phillip equations combined concepts from harmonic analysis and Griffiths, Jiirgen Moser, Friedrich Hirzebruch, Gerd Faltings, number theory. Bourgain has also made important contribu­ and Sir Michael Atiyah. Her first question concerned the tions to Fourier analysis, where he used ideas from geometry difficulty of communicating mathematical results to the public. in his work. "In contrast to a harpist who delights others by her music, I Avi Wigderson, the Nevanlinna Prize winner, was born fear the pure mathematician cannot make his art accessible to in 1956 and is at the Hebrew University in Jerusalem. a wider public," Dreifuss said. "How can pure mathematics Working on the mathematical foundations of computer sci­ justify its art to the state which finances it?'' The second ence, he achieved important insights into the concept of question was, Has mathematics avoided discussion of the zero-knowledge interactive proofs. Using this technique, a ethical implications of what it does? The third struck a lighter "prover" can convince a "verifier", within certain probabilis­ tone: If ten new professorships were to be created in Swiss tic bounds, of the truth of a statement without revealing any universities, how many should go to mathematics? of the details of the proof of the statement. Interactive proofs Perhaps the most interesting answers came in response to find application in distributed systems, where the problem the second question. Although Thorn wrote that "mathematics arises of how to insure that a network is able to perform its task even when some of the computing agents in the network *An upcoming issue of the Notices will carry a longer article about the work are faulty. Wigderson's work established the exact maximal of the Fields Medalists and the Nevanlinna Prize winner.

764 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ICM-94 itself is ethically neutral" and Eckmann that such discussions sessions had finished was a special lecture by Olga Ladyzhen­ are ''not relevant" to mathematics, Dreifuss seemed uncon­ skaya of the St. Petersburg Branch of the Steklov Institute of vinced. "I do not think that making a distinction between the Russian Academy of Sciences. The lecture was sponsored abstract theory and practical application can altogether elim­ by the Association for Women in Mathematics, European inate the problem," she said. "We owe much of our progress Women in Mathematics, and the Committee on Women of in society to mathematicians, and we have to recognize their the Canadian Mathematical Society. This was an unusual merits, while at the same time they have to assume their opportunity to hear the seventy-two-year-old Ladyzhenskaya, responsibilities.'' She seemed to be closest in spirit to Batt, who since the 1950s has been a leader in the theory of partial who responded that "the age of innocence has come to an end differential equations, discuss some of her recent work. The for us all." lecture was centered on two principles which have oriented In response to her third question, most replied, rather her work in this area: first, that uniqueness implies existence, modestly, that only four or five of the ten new professorships and second, that the solvability of a problem follows from should go to mathematicians. "In fact," said Dreifuss. "in boundedness of all possible solutions of the problem (or a Switzerland today only one chair out of twenty is for family of problems connected with it). The quality of her mathematics." A few other respondents were more ambitious. lecture led some to wonder afterward why she had never been Griffiths said that they should all go to mathematics. Faltings invited to give an ICM plenary lecture. Following the lecture was similarly generous in his response, Dreifuss noted: ''Nine was a panel discussion about women in mathematics. chairs for mathematics, but, as he likes music, he leaves the Throughout the Congress, everyone was wondering what tenth chair to the harpist." Andrew Wiles of Princeton University would say in his talk, which was scheduled to be the very last plenary lecture. Wiles, Making History who has been working for the past year to fill a gap in his proof ICM-94 made history in the number of women plenary of Fermat's Last Theorem, has made a tremendous advance speakers. The number was not large, but there were as many at toward proving the Taniyama-Shimura Conjecture, prompting this Congress as in all previous ICMs together, namely, two: some to speculate before the Congress that he might receive Marina Ratner of Stanford University and the University of a Fields Medal. The large room used for plenary lectures California at Berkeley, and Ingrid Daubechies of AT&T Bell was jammed for Wiles's lecture, and a few people had to sit Laboratories and Princeton University. Mter Ratner boycotted in the aisle. There were no earth-shattering announcements ICM-86 because of the lack of women speakers, and after her about Fermat, just an excellent expository presentation of his work was described in lectures by other people at ICM-90, results. At the end of his lecture, Wiles remarked that eight her appearance as a plenary speaker held special significance. years ago, he had been thinking of working on something She described her ground-breaking work that solved some else, an extension of his work on the Iwasawa Conjecture. "I conjectures of Raghunathan and of Margulis, who received thought that problem would not be too taxing, but I thought it a Fields Medal in 1978, and the applications of this work to lacked enough interest, and I should try something new and ergodic theory and to number theory. more challenging," he remarked. "Six years later I found that Plenary speaker Clifford H. Taubes of Harvard University I had reduced the Taniyama-Shimura Conjecture to precisely presented an accessible lecture about "anti-self dual geom­ the problem I thought had insufficient interest." Whether or etry". Under this heading he discussed three topics in the not he was correct in his assessment of the difficulty of that geometry of four-dimensional smooth manifolds: the theory problem, only time will tell. of conformal structures with anti-self-dual Weyl tensor, the theory of anti-self-dual Yang-Mills connections, and sym­ Next ICM in Berlin plectic geometry. Of these, the first is a young subject, and The Closing Ceremonies were held immediately following Taubes described some significant theorems he has proved in Wiles's lecture. There it was announced that, at its meeting it. According to Taubes, the second subject is a mature one, prior to ICM-94, the IMU General Assembly voted its approval due to the work of Donaldson and others that was reported of Berlin as the site for ICM-98. It was also announced that on at previous ICMs. Symplectic geometry is not yet part of Friedrich Hirzebruch, director of the Max-Planck Institute for (anti-)self-dual geometry, but, because a symplectic form on Mathematics in Bonn, will chair the Organizing Committee a four-manifold is self-dual, Taubes speculated that it would for ICM-98. It is unusual to have back-to-back ICMs in sites one day be incorporated. Throughout his lecture, given at the so close geographically and linguistically. But for Berlin, beginning of the Congress, Taubes made references to lectures which lost out on hosting the Olympics, having an ICM was that others would later deliver in the geometry and topology perhaps the next best thing. sessions. Drawing a crowd despite its being held after the regular Allyn Jackson

SEPTEMBER 1994, VOLUME 41. NUMBER 7 765 The Tyranny of the Mean: Gender and Expectations Marcia C. Linn Graduate School of Education University of California, Berkeley

·------·-----·------·----..·-·-·------·------tendency explains what is often called the "gambler's fallacy". For example, in roulette games where red and black are equally An earlier version of this paper was given as the commencement ad­ dress to the Berkeley Statistics Department. May 21, 1993. The author likely, gamblers often argue, "The last of three spins have would like to thank Cathy Kessel, Terry Speed. and Alan Schoenfeld been red, the next one is sure to be black." Here gamblers for helpful comments on these issues. Thanks also to Dawn David­ confuse expectations for the next individual spin of the wheel son and Anna Chang for preparation of the manuscript. This material with expectations for the population distribution of spins. The is based upon research supported by the National Science Founda­ tyranny of the mean constrains expectations about individuals. tion under grants MDR-8954753 and RED-9155744. Any opinions, The tyranny of the mean, confusing population expecta­ findings, and conclusions or recommendations expressed in this pub­ tions with competence expectations, has serious consequences lication are those of the author and do not necessarily reflect the views of the National Science Foundation. for females in the field of mathematics. Women make up 45 percent of the U.S. work force but account for only 21 percent Edward provided exemplary care; he nurtured his patients, of employed scientists and engineers and only 11 percent of listened to their concerns, and helped them prepare for employed mathematicians [11]. Women make up less than 5 conversations with Susan. Susan performed meticulous bypass percent of tenured faculty at the top math departments [8]. surgery. Her success rate was the best in the hospital, yet Reasoners basing expectations on these population statistics Mark was in greater demand. Edward said he understood; would not expect women to be mathematicians. most people expect surgeons to be men-and, for that matter, In the next sections I analyze the impact of the tyranny nurses to be women. of the mean on choosing a mathematics-related major, on People act on their expectations. They draw in relevant, participation in classroom d~scussion, on interpreting math­ circumstantial, and even inaccurate evidence to form their ematics grades and scores, and on composing letters of expectations. Patients who choose Mark instead of Susan may recommendation. base their decision on expectations about female surgeons. People who choose Susan over Mark may base their decision Choosing a Mathematics-related Major on expectations about the role of past performance. As Edward When I chose to major in a mathematics-related field (statis­ remarked, the health consequences of going with expectations tics) at Stanford, many advised against this decision, arguing about gender rather than expectations about past performance that few women went into statistics. Those who advised me could be substantial. based their argument on population data, not on my potential. Yet, many people rely on expectations based on group Of course, they meant well, often pointing out that I would membership rather than expectations based on past perfor­ need to compete with men who would have more time to mance, especially when one group is far more common than work since they would not be raising families (at that time the other. The argument goes something like this: Since more few men participated in child rearing). Yet, the tyranny of the men are surgeons, male surgeons must be better than female mean empowered people to apply population expectations to surgeons. I refer to this phenomenon as the tyranny of the an individual. mean. All members of the group with a larger membership As we know, things turned out differently. Many men are expected to be more competent than all members of the went against these population statistics and found satisfaction group with a smaller membership. in child rearing and family activities. Many of my male col­ In most fields, if anything, the reverse is true: on average, leagues told me they were empowered by female professionals the group with fewer members is more competent, since, to be to take time to chaperone school field trips or volunteer at accepted into the field, its members were often more carefully nursery school. And more and more women found success in scrutinized. careers in mathematics and statistics. Even in situations where groups are equally distributed, For example, a recent New Yorker cartoon showed a boy reasoners confuse group expectations with expectations for and girl playing "hospital". The boy, following the stereotype, individuals, succumbing to the tyranny of the mean. This says, "I will be the doctor and ...", at which point he is

766 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The Tyranny of the Mean: Gender and Expectations interrupted by the girl, who says, "And I will be the Secretary Scores and Grades of Health and Human Services." Interpreting statistical population data elicits reliance on the But expectations for males and females choosing math­ tyranny of the mean. Consider grades in precollege and ematics and statistics remain narrower than they should be. college courses in mathematics and science and multiple­ And nontraditional participants are generally more scrutinized choice test data such as SAT scores. Men score better than their traditional colleagues. than women on mathematics college entrance examinations, while women earn higher grades in mathematics and science Participating in Classroom Discussions courses [5]. Based on the tyranny of the mean, we would When they are asked to defend their ideas in seminars and expect mathematics faculty to defend test scores and to dismiss colloquia, women are often caught between the expectation grades, since scores are consistent with population statistics that females are supposed to be "conciliatory and pleasing to on participation. others" and the expectation that scientists are supposed to be In spite of the consistency with population expectations, ''aggressive and even antagonistic" to their peers [12]. the gap between male and female scores on the SAT is In interactions between instructors and students. males closing [6]. Why? This narrowing of the gap accompanies get more attention and are asked more difficult questions some changes in school requirements and some refinements than females [10]. Ruth Bader Ginsburg, in her Senate of testing practices. confirmation hearing for the Supreme Court, described a Explaining why females earn consistently higher grades less subtle approach from her law school experience: on than males in all subjects, including mathematics, requires ''women's days" women and men were asked questions; more analysis. Data on male and female mathematics grades otherwise women remained silent. This has changed recently appear in Table 1. This result goes against population data on [2, 7]. participation. As such, it surprises many faculty. Some faculty,

Table I : Grades in College Mathematics Courses

% Course Number Female 1.5 2.0 2.5 3.0 3.5

Calculus (several universities) 1 561 29

3.38"s Honors Calculus2 173 26

Courses beyond Calculus3 503 23

Calculus3 4,647 35

Pre-Calculus3 3,530 41

Regular Math3 900 60

Remedial Math3 2.391 48

Algebra and Trigonometry~ 358 39

~ Average Grade - Females College Algebra~ 336 52 • Average Grade - Males

(ns) Difference tested and found not significant ( *) Difference tested and found significant (1) Hughes. 1988. p. 126: at Harvard University, University of Ohio. Tufts University. Temple University. Villanova University (2) Frazier-Kouassi eta!.. 1992. p. 71: at University of Michigan (3) Wainer & Steinberg. 1991. p. 4: data from many universities (4) Struik & Flexer. 1984. p. 338

SEPTEMBER 1994, VOLUME 41, NUMBER 7 767 ...... ______,,_,_, ___ ,,_,______,_,_...... The Tyranny of the Mean: Gender and Expectations

confronted with evidence that they award higher grades to always turned in her homework on time and wrote neatly. females, go so far as to disparage their own grading practices, Wendy says Mike makes quick decisions and rarely reflects. arguing that students who memorize and tum in homework This worked for the SAT, where he scored higher, and it was a on time can succeed. good idea for homework-he always finished first. Evidently Most faculty, however, view the grades they award as it did not work for the doors. good indicators of future success. They describe course If we assume, based on population expectations, that males requirements as appropriate professional activities. They are better at mathematics, we might conclude that Wendy is believe that success in their courses requires sustained, just conscientious while Mike is "smart". Although Wendy cumulative problem solving, deep understanding, and creative was more successful at winning quiz show prizes, Mike won mathematical thinking about novel problems. the big prize, the job at Prestigious University, perhaps based Indeed, faculty often define their grading practices and on expectations that mathematicians should be males, perhaps criticize multiple-choice college entrance examination scores. not. What is the moral of this story? Play TV games, not These tests fail to tap sustained problem solving or creativity. career games, if you want to beat the tyranny of the mean. Although algebra and geometry are sufficient to answer all the questions in the mathematics section of the SAT, skill in rapid estimation, informed guessing among response choices, College Admissions and judicious allocation of energy in answering about thirty Overcoming the tyranny of the mean has also challenged questions in thirty minutes are also essential for a high score. admissions officers at colleges. More women than men Research shows that on average, males need to score 24 to would be admitted to colleges and awarded scholarships if 40 points higher than females on the SAT to end up with the grades were emphasized. The reverse is usually true, because same grade in college mathematics courses [9]. college entrance examination scores are emphasized. This is particularly problematic at institutions that emphasize science A Parable about Grades and Scores and mathematics, fields where males predominate in the work To illustrate how the tyranny of the mean might influence force. interpretation of male and female performance in mathematics, At MIT a few years ago, the Admissions Department consider a parable based on the quiz show "Let's Make a found that they were admitting more males but that females Deal" and the Monty Hall doors problem. On this show, were earning higher grades. So they changed the way they do contestants try to guess which of three doors, when opened, admissions, relaxing the requirement that students score 750 will reveal a prize. First, the contestant selects a door. Next, or higher on the SAT-M [4]. This resulted in an increase in the host, Monty Hall, tells the contestant that the prize is NOT female students and a narrowing of the gap between male and behind one of the unselected doors. He opens the door and female grades. shows that no prize is there. Then, the contestant has a choice: Many commented, "What happened to standards?" But STAY with the selected door or SWITCH to the remaining an unanticipated consequence of the greater balance between unopened door. male and female students at MIT was a general increase in the To make this clearer, we compare two contestants, Macho overall talent in the class. Mike and Wishy Washy Wendy. For example, one trial features Interpreting data about scores and grades for males and a blue, a red, and a green door. Macho Mike picks red because females requires serious attention to the tyranny of the it is his favorite color: reminds him of blood. Wishy Washy mean. Test score data supports expectations about success Wendy also picks red, maybe because it was on the left, who in mathematics based on group membership. Mathematics knows? grades data supports expectations based on past performance. Here is where the twist comes in. Mter the choice is made, the contestants learn something about the doors they did not pick. Monty Hall tells them that the prize is not behind the Letters of Recommendation blue door. They then have the opportunity to stay with their Subtle effects of the tyranny of the mean can also influence first choice or switch to the remaining unopened door. another source of information used in selection decisions for As you would expect, Macho Mike stays with blood red, males and females: letters of recommendation. It seems that while Wishy Washy Wendy switches to green. She says that both males and females, when writing letters about women, Hall seems to be telling her something. The contest continues are more likely to mention information about personal life, with doors of many different colors, but Mike always picks a such as, "She was a great mentor to our undergraduate color and stays with it while Wendy always switches. In the students, helping Sally choose a career in statistics," or "She end, Wendy wins far more prize money that Mike. Is this due went out of her way to establish a career day for high school to female intuition or a smart strategy? students," or "She was our best student while also caring It turns out that Wendy has a smart strategy. For a for her aging father" [1]. I think this generally reflects a discussion of the problem, see Gillman [3]. willingness on the part of some students and often women Following the tyranny of the mean, Macho Mike dispar­ to volunteer information about their personal lives. I have ages Wishy Washy Wendy's success, complaining that this is here exemplified this tendency by describing my experience the same way she earned higher grades in mathematics. She in choosing a statistics major.

768 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···· · ··· · · ···················-···-··-······-···········-· ····················-··········l~~~ • ·• · ]liliiiiBIIr········-··-······-····· ····-··-··-·-···-···--·········-·-··-········-··-··- ···············-·-·-·······-···-··-·····-··-·-··-·-···-········-·······--·-·-···-········-··-······-···· The Tyranny of the Mean: Gender and Expectations

However, perhaps based on population expectations, References letters of recommendation for women that include 1. Association for Women in Science, Not getting the award. grant information about personal lives are often discounted by or job? Check those references! AWlS Magazine 21 (1992), 7-12. readers. Why? Readers argue that the letter writer is certainly a 2. K. Connor and E. Vargyas, The legal implications of gender bias in standardi::ed testing, Berkeley Women's Law Joumal7 (1992). friend of the student they are recommending. Otherwise, how 3. L. Gillman, The car and the goats. American Mathematics Monthly would the writer know that the student is taking care of an 99 (1992), 3-7. aging relative? As a result the writer is unlikely to be 4. E. S. Johnson, College women's pelformance in math-science "objective". So the letter is probably more laudatory than it curriculum: A case study, College and University 68 ( 1993). 74-78. should be. 5. M. C. Linn, Gender differences in educational achie\'ement. Sex Equity in Educational Opportunity, Achievement, and Testing (Proceed­ ings of 1991 Educational Testing Service Invitational Conference) J. Pfleiderer. ed.) Educational Testing Service, Princeton. NJ. 1992. pp. Conclusions 11-50. Expectations have considerable power. The gambler's fallacy 6. M. C. Linn and J. S. Hyde. Gender. mathematics. and science. has enriched casinos and impoverished individuals. Basing Educational Researcher 18 (1989), 17-19.22-27. expectations on group membership rather than on past per­ 7. L. Schwartz and S. Homer, Stumbling blocks and stepping stones: Newcomers' guide to perilous terrain in law school, Vermont Law Re­ formance has narrowed the opportunities for both males and view 15 (1990), 165-195. females. As Edward remarked, the implications for both 8. P. Selvin, Profile of a field: Mathematics-Hemism is still tlze personal and societal well-being deserve scrutiny. norm, Science J. Benditt, AAAS (1992), 1382-1383. Fortunately this is changing. Expectations that both males 9. H. Wainer and L. S. Steinburg, Sex differences in pe7formance on and females will have more balance in their lives between the mathematics section of the Scholastic Aptitude Test: A bidirectional career and family are growing. The expectation that everyone mlidity study, Educational Testing Service, Princeton, NJ, 1991. needs a career is now widely established. The realization I 0. Wellesley College Center for Research on Women. How schools shortchange girls, American Association of University Women Educa­ that diversity in our society is a benefit is more and more tional Foundation. Washington, DC. 1992. widespread. And the belief that talented individuals are a 11. P. E. White, Women and minorities in science and engineering: scarce and valuable resource and must be nurtured and An update, National Science Foundation. Washington. DC. 1992. rewarded independent of their group membership is gaining 12. S. Widnall, Voices from the pipeline, Science 241 (1988). 1740- acceptance. 1745.

GRADUATE STUDIES IN MATHEMATICS The Integrals of Lebesgue, Denjoy, Perron, and Henstock Russell A Gordon

This book provides an elementary. self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. One of the book's unique features is that the Denjoy. Perron. and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which F is approximately differentiable. This part of the book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for first year graduate students who have background in real analysis. 1991 Mathematics Subject Classification: 26. 28 ISBN 0-8218-3805-9. 395 pages (hardcover). August 1994 Individual member $35. List price $59. Institutional member $47. To order, please specify GSM/4NA

to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: tthematicalSociety, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321·4AMS (321-4267) in the U.S. and with VISA or MasterCard. Residents of Canada, please include 7% GST.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 769 Forum

"First and foremost, this is a matrix -oriented course, which deals with Rn and not with abstract vector spaces. The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between 1,000 and Those difficult concepts of subspace, span, and linear 2,500 words long. Readers are invited to submit articles for possible independence appear for n-tuples, not for elements" of inclusion in Forum to: an abstract vector space. Notices Forum Editor In his justification for such a syllabus, he adds: American Mathematical Society " ... consultants from client disciplines told us that ab­ P.O. Box 6248 stract first courses in linear algebra has 'turned them off' Providence, R1 02940 as students." or electronically to [email protected]. ams. org Many mathematicians believe, as I do, that the essence of linear algebra is the study of linear maps and its representation This is Linear Algebra? by means of matrices, not matrices themselves. Assigning Seymour Lipschutz linear maps to be a supplementary topic almost seems (to me) to be a contradiction in terms. My views on this trend Temple University in teaching linear algebra are similar to the views expressed This note is a response to the articles by Carlson, by Steven Krantz (January 1994 Notices) on the teaching of et al., "The Linear Algebra Curriculum Study Group geometry in high school. Specifically, while discussing an Recommendations for a First Course in Linear Algebra", article in the October 1993 issue of Scientific American, he and Carlson, 'Teaching Linear Algebra: Must the Fog wrote: Always Roll In?", which appear in the January 1993 "As the Scientific American article reported, high school issue of the College Mathematics Journal, and to the note teachers in Berkeley are now minimizing proofs in Euclidean by Steven G. Krantz, "The Immortality of Proof", which geometry.... Well-meaning though these changes may be ... , appears in the Forum section in the January 1994 Notices they fly in the face of fundamental mathematical values. The oftheAMS. article itself claims that students no longer appreciate the The suggested syllabus by the Linear Algebra Cur­ value of proofs. So we have to find another way to teach them. riculum Study Group (LACS G) consists of the following "Students do not appreciate the value of reading unless six topics: they are taught. They do not appreciate the value of good music unless they are taught. ... And students will not appreciate the Matrix operations value and importance of mathematical thinking unless they Systems of linear equations are taught. It is our job to teach them, not to bend like reeds Determinants in the breeze." Properties of Rn Let us be clear about one thing, learning procedures Eigenvalues and eigenvectors is not necessarily knowing mathematics. Many people in Orthogonality. the social sciences use SPSS (Statistical Package for Social The following supplementary topics are mentioned: Scientists) in their research. This does not mean they know a) Computational experience statistics. Similarly, knowing how to row reduce a matrix, b) Additional topics, including abstract vector spaces, with or without a computer, does not mean knowing any linear linear transformations, positive definite matrices, and algebra. diagonalization of symmetric matrices The purpose of this article is not to offer an alternative c) Applications, such as Markov chains, input-output syllabus or to discuss the merits of such a syllabus. This I do models, Leslie matrices, difference equations, differential in an article I have submitted elsewhere. The purpose of this equations, and linear programming article is to discuss the role that the AMS might play in this Discussing this syllabus, David Carlson (p. 31) ~tates: conflict.

770 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... illliiiiiOOIIiii&IIOO;II!IIIOOillll-lliilll!lllillOOi lliiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiPII- .... -...... Forum

My feeling (which may be incorrect) is that most members edge, especially in calculus and linear algebra, is through of the AMS agree with my views on the teaching of linear "applications". Also, some mathematics teachers believe that algebra, but that many members of the MAA do not. Although they have to ')ustify" the teaching of mathematics, and they the AMS is basically a research organization and the MAA is think they do this by showing its "applications" in other mainly responsible for mathematical education, the teaching fields. There is no reason in the world to spend time in a of an important mathematical course like linear algebra should course in linear algebra listed by the LACSG: Markov chains, not be left to people, although well-meaning, who may not (in input-output models, Leslie matrices, difference equations, my opinion) know what they are doing. I believe that leaders linear programming. These topics require, at the minimum, of the AMS should somehow speak out, one way or another, additional terminology which, in itself, will require a great on this subject. We all now recognize that the teaching of the deal of time to learn. "new math" in our high schools was a total disaster. We do Summarizing, about thirty years ago the mathematical not want that to happen here. community generally agreed that colleges should offer courses Today (unfortunately?) a great deal of time, energy, money, in linear algebra rather than matrix theory. The current trend and funding has been spent on the use of computers and the seems to reverse this important step. I do not believe there is emphasis of procedures in linear algebra. In other words, there a consensus in the mathematical community at large on these already is a great deal of vested interest in the teaching of new trends. Also, I do not know if there is any mechanism the ''new linear algebra". Many of the most popular texts do for the AMS to make itself felt in this area. Perhaps the not treat linear maps as germane to the subject. In fact, in AMS, either alone or with the MAA, should form a Special order to conform with most current texts, my new (second) Committee (SC) on the teaching of linear algebra. (This edition of my widely read Schaum Outline on Linear Algebra question should not be left to self-appointed committees like treats linear maps after determinants and eigenvectors and the LACSG.) At the least, the SC should present to the eigenvalues, that is, near the end of the text. Changing the mathematical community a minimum list of objectives for trend in the teaching of linear algebra may not be a simple any course in linear algebra. This list of objectives could be task, and it will require, at the least, that established leaders in stated, say, by means of a sample test or list of questions the mathematical community make their opinions known. which we expect our students to be able to answer after There is a secondary issue I would like to raise in this arti­ completing such a course. One can then have a basis to test cle. There seems to be a "virus" spreading in the mathematical whether the new trends, with or without computers, do meet community that says that the way to mathematical knowl- these minimum objectives.

The Emergence of the American Mathematical Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore Karen Hunger Parshall and David E. Rowe This volume traces the transformation of the United States from a mathematical backwater to a major presence during the quatter-century from 1876 to 1900. It presents a detailed study of the major figures involved in this transformation and the principal institutions with which they were associated. This is the first work ever written on the history of American mathematics during this period and one of the few books that examines the historical development of American mathematics from a wide perspective. By placing the development of American mathematics within the context of broader external factors affecting historical events, the authors show how the character of American research was decisively affected by the surrounding scientific. educational, and social contexts of the period. Aimed at a general mathematical audience and at historians of science. this book contains an abundance of unpublished archival material, numerous rare photographs. and an extensive bibliography.

1991 Mathematics Subject Classification: 01 ISBN 0-8218-9004-2, 500 pages (hardcover), August 1994 Individual member $60, List price $100. Institutional member $80, To order, olease specify HMATH/SNA

All prices subject to change. Free shipment by surface: for air delivery. please add $6.50 per title. Prepayment required. Order from: American Mathematical Society. P.O. Box 5904, Boston, MA 02206-5904. or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 771 Computers and Mathematics

Edited by Keith Devlin

This month's column this in AMS-Jb.T:EX, so the running heads were actually done George Gratzer leads off this month's column with the fourth in his in a printing shop and "pasted" to the pages. series of articles on 1E;X. Then, reminding us that you can do some In this article, I would like to introduce you to a software pretty sophisticated mathematics on a pocket calculator. Eugene package, fancyheadings, by Piet van Oostrum which provides Lehman describes a method for solving quartic equations in the all the facilities you would likely need to design your own palm of your hand. headers and footers. Three software reviews complete the column. Edward Spitz­ nagel looks at the group theory packageGAP; Eric Schweitzer reports on jspell, a 'lEX-compatible spell checker for DOS sys­ tems; and Maurino Bautista reviews HiQ 2.02, described as an Off on a Tangent integrated software environment for solving real world problems About twenty-five years ago, I gave a lecture at the University in engineering, mathematics, and the applied sciences. of Montreal in which I claimed, partly in jest, that everything Editor's address: has already been discovered in mathematics, we just don't know it. I illustrated my thesis with two examples; two Professor Keith Devlin well-known problems in my field have been solved in two School of Science completely unrelated fields-and nobody knew this, in my Saint Mary's College of California field or the others. P.O. Box 3517 The situation seems to be similar in 'lEX and Jb.T:EX. Maybe Moraga, California 94575 not all the problems have been solved, but certainly very many Correspondence by electronic mail is preferred, to: tools are available, but not readily accessible. Most all noncommercial tools are available in the Compre­ [email protected]. hensive 1}3X Archive Network (CTAN) sites (see Section 4). For instance, the macro package fancyheadings is in the con­ trib subdirectory of the directory macros/latex. There are 21 megabytes of macros in contrib, which is only one of many directories containing macros. For instance, the mul­ tilingual macro package (babel) is in the language/babel Advances in lEX· subdirectory. IV. Header and footer control in Jb.TEX David M. Jones compiled in 1992 a catalogue of macros [4] which can be found at the CTAN sites as /tex­ George Gratzer* archive/help/tex-styles-and-macros. txt. This cat­ alogue contains a brief description of the macros. And there is now a hacker's guide to the Ib.T:EX universe, namely, the Jb.T:EX Companion [1] by Michel Goossens, Frank Mittelbach, and Alexander Samarin. This book describes over 150 macro Introduction packages. By the nature of this book, some of these de­ When I submitted my AMS-Jb.T:EX book [3] to the publisher, scriptions are more detailed and some are less detailed. And naturally it was all typeset except for the front pages. 150 is a small number; by my count the contrib directory However, the visual designer for the volume decided that the alone contains more than 450 macro packages-some well running head should be ALL UPPERCASE IN 9 POINT BOLD documented and some not documented at all. HELVETICA with a decorative line underneath. I could not do So there would appear to be a real need for a guide informing us what is available with detailed instructions for *George Gratzer is in the Department of Mathematics at the Univer­ sity of Manitoba, Winnipeg. Canada MB R3T 2N2. His e-mail address is: the use of these packages. Please regard this article as a tiny [email protected]. contribution to this project.

772 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·······················-·· -~-·····-····-·····-·······-··········-·········-·····-······-···-·······-··-···············-··-····-····· ... ·····-·····························-···--······-·-··-······-··-·········-·········· Computers and Mathematics

In Part III of this article [2], we discussed how L\JBX 2c If you cannot find the file fancyheadings. sty, issue unifies IbTpc and AMS-IbTpc. By the time you read this the command article-one hopes-L\JEX 2c will have been released along ftp> quote site indexfancyheadings.sty with Version 1.2 of AMS-IbTpc (which is UJEX 2c with the and you will be given a list of directories where the file is amsart document class from the American Mathematical available. Society). The macro package we discuss in this article works with L\'lfX2c, and in particular with AMS-IbTpc. Use of fancyheadings To use this package in a L\JBX 2c document, place the file fancyheadings. sty in a directory/folder where 1EX can What is fancyheadings? find it (normally in the input directory/folder), and include in The fancyheadings macro package by Piet van Oostrum the preamble of your document after allows you to customize in IbT]jX your page headers and \documentclass{ ... } footers in an easy way. You can define: the commands • three-part headers and footers \usepackage{fancyheadings} • decorative lines in headers and footers \pagestyle{fancy} • headers and footers wider than the width of the text We can visualize the page layout we can create with • multiline headers and footers fancyheadings as follows: • separate headers and footers for even and odd pages • different headers and footers for chapter pages LeftHeader CenteredHeader RightHeader Of course, you also have complete control over fonts, uppercase, and lowercase displays, etc. page body LeftFooter CenteredFooter RightFooter Where to Get It LeftFooter are left justified; the You only need the file fancyheadings. sty, which you can The LeftHeader and are centered; the Right­ find at the CTAN sites ftp. shsu. edu (U.S.), ftp. tex. ac. CenteredHeader and CenteredFooter uk (U.K.), and ftp. dante. de (Germany). Header and RightFooter are right justified. Here is how you get it with "anonymous ftp": We define each of the six "fields" and the two decorative ccu%ftp ftp.shsu.edu lines separately. Connected to PIP.SHSU.EDU. 220 pip.shsu.edu FTP server (Version 2 .1aWU(1) A Simple Example Fri Aug 20 14:31:05 CDT 1993) ready. K. Grant is writing a report to Dean A. Smith, on "The Name (ftp. shsu. edu: gratzer) : anonymous performance of new graduates" with the following page 331 Guest login ok, send your complete e-mail layout: address as password. The performance of new graduates Password: 230 Guest login ok, access restrictions apply. page body ftp> cd/tex-archivelmacros/latex/contrib/fancyheadings ftp> get fancyheadings.sty From: K. Grant To: Dean A. Smith 3 (Of course, you should type your e-mail address as password­ this will not be visible on your screen.) This will get you the where "3" is the page number. The title "The performance of file fancyheadings. sty, which you can then download to new graduates" is bold. your personal computer. This is accomplished by the following commands You may also want to get the file fancyheadings. doc, \pagestyle{fancy}: the documentation file, on which this article is in part based. \lhead{} The CTAN sites are undergoing some reorganization. \chead{} When L\'lfX 2c becomes the official IbTpc, the directory \rhead{\bfseries The performance of new latex will be renamed latex209, and the directory latex2e graduates} will be renamed latex. \lfoot{From: K. Grant} The new latex directory will have (at least) three subdi­ \cfoot{To: Dean A. Smith} rectories: base containing UJEX2c; contrib/supported \rfoot{\thepage} containing the IbTpc macros rewritten to work with L\JBX 2c \setlength{\headrulewidth}{0.4pt} and which satisfy some basic guidelines in terms of presen­ \setlength{\footrulewidth}{0.4pt} tation, documentation, and support (moderated by Joachim (The \ thepage macro displays the current page number. Schrod); and contrib/ other for other macros. \bfseries is L\'lfX2c's way of selecting bold face.)

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This is now fine, except that the first page does not need the first page of a chapter in the book class), or you have to all these headers and footers. To eliminate all but the centered do it explicitly with the page number, issue the command \thispagestyle{plain} \thispagestyle{plain} command. after the The redefinition of the plain style is done with the \begin{document} command and the \fancyplain{plain_value}{normal_value} \maketitle inserted into all the appropriate arguments. As an example, commands. let us redefine the plain style for the report in Section 7 by Alternatively, issue making the page number bold. \thispagestyle{empty} The leftheader definition if you do not want any headers or footers. \lhead[]{\bf series The performance of new graduates} changes to An Example of Two-sided Printing \lhead[\fancyplain{}{}]{\fancyplain{} Some document classes, such as book. cls, print two-sided: {\bfseries The}} the even pages and the odd pages have different layouts; other performance of new graduates document classes use the two side option to print two-sided. Note that the first argument of both \fancyplain com­ Now let us print the report two-sided. Let the above page mands is empty, since the redefined plain style has an empty layout be used for the odd (right-side) pages, and the following leftheader. for the even (left-side) pages: The left- and rightfooter definitions change more. For instance, the leftfooter definition changes from The performance of new graduates \lfoot[\thepage]{From: K. Grant} to page body \lfoot[\fancyplain{}{\bfseries \thepage}]{\fancyplain{}{From: K. Grant}} 4 From: K. Grant To: Dean A. Smith Carrying out these changes for all six fields, we get the where ''4" is the page number. code Here are the commands: \lhead[\fancyplain{}{}]{\fancyplain{} \lhead[]{\bfseries The performance of new {\bfseries The graduates} performance of new graduates}} \chead{} \chead{\fancyplain{}{}} \rhead[\bfseries The performance of new \rhead[\fancyplain{}{\bfseries The graduates]{} performance of new \lfoot[\thepage]{From: K. Grant} graduates}]{\fancyplain{}{}} \cfoot[From: K. Grant]{To: Dean A. Smith} \lfoot[\fancyplain{}{\thepage}]{\fancyplain{} \rfoot[To: Dean A. Smith]{\thepage} {From: K. Grant}} \setlength{\headrulewidth}{0.4pt} \cfoot[\fancyplain{\bfseries \thepage} \setlength{\footrulewidth}{0.4pt} {From: K. As you see, the values of the fields for the even (left Grant}]{\fancyplain{\bfseries \thepage} side) pages are given in the square brackets. Again, you may {To: Dean A. Smith}} use \thispagestyle{plain} for a simple page layout for \rfoot[\fancyplain{}{To: Dean A. Smith}] page 1. {\fancyplain{}% {\bfseries \thepage}} \setlength{\headrulewidth}{0.4pt} Redefining Plain Style \setlength{\footrulewidth}{0.4pt} \ thispagestyle{plain} may not be your choice for the For the "fancy plain" pagestyle, the thickness of the lines pagestyle of the first page. For instance, if all the page numbers is defined by are bold, you may want this on the first page also. \plainheadrulewidth and \plainf ootrulewidth fancyheadings also allows you to redefine the plain (both default to Opt). Observe that you may have different pagestyle with the command "fancy plain" pagestyles for even and odd pages. \pagestyle{fancyplain} To use the "fancy plain" pagestyle, define these macros; This command performs the function of in the preamble, include \pagestyle{fancy} \usepackage{fancyheadings} and redefines the plain pagestyle. Note that this does not is­ \pagestyle{fancyplain} sue a \pagestyle{plain} or\thispagestyle{plain} and invoke the pagestyle "fancy plain" with command. This is either done by :u:IEX 210 (for instance, for \ thispagestyle{plain} where desired.

774 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------~- : .,.,.,~------­ Computers and Mathematics

The Default Layout You can influence how chapter, section, and subsection Let us use the book. cls documentclass and the default information (only two!) are displayed by redefining the settings for fancyheadings; so we only issue the commands \chaptermark, \sectionmark, and \subsectionmark \usepackage{fancyheadings} commands. \pagestyle{fancy} Let us illustrate this with chapter info. It is made up of and let fancyheadings take care of everything. On the pages three parts: where new chapters start, we get a centered page number in • the number (say, 2), displayed by the macro\ thechapt er the footer; there is no header, and there are no decorative • the name (in English, Chapter), displayed by the macro lines. \chaptername On an even page, we get the following layout: • the title, contained in the first argument of \markboth Table 1 (see next page) shows some variants for ''Chapter I.2 EVALUATION CHAPTER I. INTRODUCTION 2. Do it now'' (the last example is appropriate in some page body non-English languages). For the lower-level sectioning information, do the same 4 with \markright. So if "Section 2.2. First steps'' is the current section, then On an odd page, we get this layout: \renewcommand{\sectionmark}[1]{ CHAPTER I. INTRODUCTION I .2 EVALUATION \markright{\thesection.\ #1}} will give ''2.2. First steps". page body It should be noted that the IbTpc marking mechanism works fine with chapters (which always start on a new page) 3 and sections (which are reasonably long). It does not work where the header text is slanted uppercase. quite as well with short sections and subsections. This is a This default layout is produced by the following com­ problem with IbTpc. not with fancyheadings. mands: \lhead[\fancyplain{}{\slshape \rightmark}] \fancyplain{}% {\slshape \leftmark}} Fancy Layouts \chead{} You can make a multiline field with the \\ command. It is \rhead[\fancyplain{}{\slshape \leftmark}] also possible to put extra space in a field with the \ vspace \fancyplain{}% command. Note that if you do this you will probably have to {\slshape \rightmark}} increase the height of the header (\headheight) or of the \lfoot{} footer (\footskip). See Section 4.1 of the IbTpc Companion \cfoot{\rmfamily \thepage} for detail. \rfoot{} For instance, the following code will place the section title The following settings are used for the decorative lines: and the subsection title of an article in two lines in the lower \headrulewidth 0.4pt right-hand comer: \footrulewidth 0 pt \documentstyle{article} \plainheadrulewidth 0 pt \usepackage{fancyheadings} \plainfootrulewidth 0 pt \pagestyle{fancy} The header text is turned into all uppercase in book. cls. \renewcommand{\sectionmark}[1]{\markboth{#1} {}} \renewcommand{\subsectionmark}[1]{\markright Custom Layouts {#1}} Usually, for documents of class book and report, you may \rfoot{\leftmark\\\rightmark} want to use chapter and section information in the headings You can customize the decorative lines. You can make the (chapter only for one-sided printing), while for documents of decorative line in the header quite thick with class article, section and subsection information (section \setlength{\headrulewidth}{0.6pt} only for one-sided printing). IbTpc uses a marker mechanism or you can make the decorative line in the footer disappear to remember the chapter and section (section and subsection) with information for a page; this is discussed in detail in the IbTpc \setlength{\footrulewidth}{Opt} Companion, Section 4.3.2. The decorative lines themselves are defined in the two There are two ways you can utilize and change the higher­ macros \headrule and \footrule. For instance. if you and lower-level sectioning information available to you. The want a dotted line rather than a solid line in the header, macros \leftmark (higher level) and \rightmark (lower­ redefine the command \headrule: level) contain the information processed by IbTpc, and you \renewcommand{\headrule}{\vbox to Opt{\hbox can use them directly as shown in Section 9. to\headwidth{\dotfill}\vss}}

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Code: Prints:

\renewcommand{\chaptermark}[1]{ Chapter 2. Do it now \markboth{\chaptername\ \thechapter.\ #1}{}}

\renewcommand{\chaptermark}[1]{ CHAPTER 2. Do it now \markboth{\uppercase{ \chaptername}\ \thechapter. \ #1}{}}

\renewcommand{\chaptermark}[1]{ CHAPTER 2. DO IT NOW \uppercase{\markboth{ \uppercase{\chaptername}\ \thechapter.\ #1}}{}}

\renewcommand{\chaptermark}[1]{ Do it now. \markboth{#1}{}}

\renewcommand{\chaptermark}[1]{ 2. Do it now. \markboth{\thechapter.\ #1}{}}

\renewcommand{\chaptermark}[1]{ 2. Chapter. Do it now. \markboth{\thechapter.\ \chaptername.\ #1}{}} Table 1: Marker variants

Two Book Examples For the second example, we take the AMS-IbT:EX book The following definitions give an approximation of the style [3]. used in L. Lamport's IbT:EX book [5]. Chapter pages have no headers or footers. So we declare Lamport's header overhangs the outside margin. This is \thispagestyle{empty} done as follows. for every chapter page, and we do not need fancyplain. The width of headers and footers is \headwidth, which Chapter and section titles appear in the form 2. DO IT by default equals the width of the text: \textwidth. You can NOW, so we have to redefine \chaptermark and \sec­ make the width wider (or narrower) by redefining \head­ tionmark as follows (see Section 10): width with the \setlength and \addtolength com­ \renewcommand{\chaptermark}[1]% mands. To overhang the outside margin where the marginal {\markboth{\uppercase{\thechapter.\ #1}}{}} notes are printed, add both \marginparsep and \margin­ \renewcommand{\sectionmark}[1]% parwidth to \headwidth with the commands {\markright{\uppercase{\thesection.\ #1}}} \addtolength{\headwidth}{\marginparsep} In an even-header, the page number is printed as the \addtolength{\headwidth}{\marginparwidth} LeftHeader and the chapter info as the RightHeader; in an And now a complete definition of Lamport's book style: odd-header, the section info is printed as the LeftHeader and \documentclass{book} the page number as the RightHeader. The CenteredHeaders \usepackage{fancyheadings} are empty. There are no footers. \pagestyle{fancyplain} There is a decorative line in the header. It is 0.5pt wide, so \addtolength{\headwidth}{\marginparsep} we need the commands \addtolength{\headwidth}{\marginparwidth} \setlength{\headrulewidth}{0.5pt} \renewcommand{\chaptermark}[1]{\markboth \setlength{\footrulewidth}{Opt} {#1}{}} The font used in the headers is 9 pt bold Helvetica. The \renewcommand{\sectionmark}[1]{\markright PSNFSS system by Sebastian Rahtz uses the short (Karl {\thesection\ #1}} Berry) name phv for Helvetica, so this font is selected with \lhead[\fancyplain{}{\bfseries\thepage}] the commands {\fancyplain{}{\bfseries\rightmark}} \fontfamily{phv}\fontseries{b}\fontsize{9} \rhead[\fancyplain{}{\bfseries\leftmark}] {11}\selectfont {\fancyplain{}{\bfseries\thepage}} (See Sections 7.6.1 and 11.9.1 of the IbT:EX Companion.) \cfoot{}

776 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Let us define a shorthand for this: the general solution to the cubic. Instead of publishing the \newcommand{\helv}{% result, they very unprofessionally "classified" the document. \fontfamily{phv}\fontseries{b}\fontsize{9} Eventually they revealed it under oath of secrecy to Del {11}\selectfont} Ferro's pupil Geronimo Cardano (1506-1571), who promptly Now we are ready for the page layout: betrayed their trust by placing it in his Ars Magna in 1545. \lhead[\helv \thepage]{\helv \rightmark} That is why we unjustly call it "Cardano's Method". Still, \rhead[\helv \leftmark]{\helv \thepage} his mentors, Del Ferro and Tartaglia, should be published for \cfoot{} their attempted power grab, and so I use Geronimo's name in Putting this all together: this article. So does everyone else. \documentclass{book} Anyway, using Cardano's Method, the latter's student, \usepackage{fancyheadings} Lodovico Ferrari (1522-1565), produced the solution to the \pagestyle{fancy} general quartic. In my Yale undergraduate days (1929-1933) \renewcommand{\chaptermark}[1]% our profs told us about cubics and quartics but warned us {\markboth{\uppercase{\thechapter.\ #1}}{}} never to attempt exact solutions. "Just too much work," they \renewcommand{\sectionmark}[1]% said. "Be happy with Newton's Approximation. No one will {\markright{\uppercase{\thesection.\ #1}}} ever use those exact solutions." \setlength{\headrulewidth}{0.5pt} My profs (Yale profs!) were wrong. In 1993 I found the \setlength{\footrulewidth}{Opt} cubic and quartic formulas in several texts, notably the (even \newcommand{\helv}{% then) late J. V. Uspensky's, Theory of Equations, McGraw­ \fontfamily{phv}\fontseries{b}\fontsize{9} Hill, 1948, Chapter V, "Cubic and Biquadratic Equations", {11}\selectfont} pages 82-98. Uspensky, pre-Casio handicappee that he was, \lhead[\helv \thepage]{\helv \rightmark} painfully solved quartics using hand adding machine and log \rhead[\helv \leftmark]{\helv \thepage} tables. Excruciating! But in a week of concentrated effort I \cfoot{} programmed it! Now my grade IV-VI students can do it in five minutes. First, instructions on how to execute the program. I References refer you to Uspensky [op cit] for rigorous proof. [1] Michel Goossens. Frank Mittelbach. and Alexander Samarin. The general quartic is The Je.Tpi: Companion. Addison-Wesley. Reading. MA, 1994. [2] George Gratzer, Admnces in 1FX implementations. III. A new Y4 = ax4 + bx3 + cx2 + dx + e version ofJe.Tpi:,fmally, Notices Amer. Math. Soc. 41 (6) (1994). [3] __ , Math into 'IFX- A simple introduction using AvtS­ Je.Tpi:. Birkhliuser Boston, Boston, MA, 1993. but since a, the leading coefficient, isn't 0, we divide the [4] David M. Jones, A catalogue of 1FX macros. CTAN /tex­ whole equation by it to get archive/help/tex-styles-and-macros.txt, 1992. [5] Leslie Lamport. Je.Tpi:: A document preparation system, Addison-Wesley. Reading. MA, 1985.

which is easier; here the uppercase letters are the locations I use. Thus b e Pocket Calculating the Quartic F=-, ... ,J=-. a· a Eugene Lehman* Now any self-respecting quartic who seeks a solution must employ a younger manservant called her "resolvent" cubic A program created for interested and alert subteen students at Hebrew Academy, Solomon Schechter Academy, Willingdon 3 2 and Royal Vale elementary schools in Montreal. y3 = .r + B x + C x + D where B = -G, C = FH- 4J and D = 4GJ- F 2J- H 2 , Evariste Galois (1811-1832) grouply proved to us in his as Ferrari taught us. extreme youth (he never had anything else) that the general solution of polynomials of degree more than 4 is impossible Next we use Cardano 's Method to find a root of this cubic. using only addition, subtraction, multiplication, division, and Any of the three roots will do, but since we are guaranteed extraction of roots (square, cube, fourth, ... ). one real root, let's use that, calling it Z. This is what we do: But long before Galois's time, in Bologna about 1515, Sci­ pione Del Ferro (1465-1526) and Niccolo Fontana "Tartaglia" Let P = 9~:2 - 3St and Q = - 2 f~3 + :.3 - fr D2A. (1499-1559; so nicknamed because he stuttered) worked out These definitions are by Cardano and refer to the general cubic; use them for most cubics. In resolvent cubics, however, *Eugene Lehman is in the Department of Mathematics. Dawson College. the leading coefficient A is always 1 and may therefore be Canada. omitted when solving quartics. Now I call l¥ = Q 2 - P 3 the

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"cubic discriminant". Unlike a quadratic discriminant or

W < 0 => 3 real distinct roots Z, Y, X; Yz(LN) = x2 + Lx + n and Yz(EM) = x 2 + Ex+ M, W = 0 => 3 real roots Z, Y, X, of which at least 2 are in which Ferrari (if he has access to my Casio) defines duplicates; and W > 0 = > 1 real root Z and a pair of complex z L= -+F VF2- -G+Z fZ2-: E=F-L, conjugates, R ± li. 2 4 ' M= 2+V4-J,

If W < 0, let () be an angle whose cosine is _g_ N=Z-M. PVP' Now one of the following two expressions will equal H, 0 ~ () ~ 180°. the coefficient of the linear term of the quartic ~ : (Your calculator must be in degree mode.) ME+NL or NE+ML. Then Z = 2VPcos ~- ~. Y = -2v'Pcos(~ + 60°)- ~. 3 3 If ME + N L turns out to be H, then hire the first pair of X= -2v'Pcos(~- 60°)- 3~. quadratic pageboys; if N E+ M L = H, employ the second pair. The four solutions thus obtained will be the four solutions If W = 0, use either the previous or following method; of the original quartic y4, be they reals (with or without since U = V (below), I= 0; so we are guaranteed three real duplicates), two reals and a pair of complex conjugates, or roots, two of which are duplicates. two pairs (perhaps duplicates) of complex conjugates. It is well to install a simple program which evaluates If W > 0, let U = 1Q + JW and V = 1Q - JW, then ~ immediately. Test all real roots this way. In the case of complex roots, we must check the coefficients which those Z - U + V- .fl._ R- - U+V - _!l_ and I- v'3

Table 1

PRESS SEE ON SCREEN EXPLANATION AC Turns on Casio SHIFf PRGM F3 Prog aKEXE Prog K? aFEXE F? aGEXE G? aHEXE H? aJEXE J? We have entered coefficient F G H J of 11i. aAEXE A? aBEXE B? aCEXE C? aDEXE D? We have entered coefficients A B C D of Y3. The screen will show ME + N L, then N E + M L. If the former is H , then EXE ? aKEXE K? aLEXE L? aMEXE M? We have entered the coefficients of the first quadratic yz (LM) of the first pair. The screen shows the discriminant. If this is nonnegative press EXE twice for 2 real roots T1 and S 1 (which could be the same) of the quaratic. If the discriminant is negative press EXE twice for the real part R 1 andtheimaginarypart I 1 of two complex conjugate roots of the quartic. Now press

778 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

PRESS SEE ON SCREEN EXPLANATION EXE ? aKEXE K? aEEXE E? aNEXE N We have entered the coefficients of the second quadratic y2(EN) of the first pair. The discriminant of this quadratic will appear. Repeat previous paragraph to obtain the other 2 roots, either Tz and Sz or Rz and [z, or the quartic. But if ME+ NL wasn't H then NE + ML was, so push EXE ? aKEXE K? aLEXE L? aNEXE N We have entered the coefficients of the first quadratic Y2 (LN) of the second pair; screen shows its discriminant. Proceed as before to obtain the first two roots of the quartic. Then EXE ? aKEXE K? aEEXE E? aMEXE M We have entered the coefficients of the second quadratic y2 (EM) of the second pair. Its discriminant is visible. Proceed as before to obtain the other 2 roots.

Now here is the program, which I call Prog K, QUARTIC: ? -+ F:?-+ G:?-+ H:?-+ J:?-+ 1-+ A: G-+ B: FH- 4J-+ C: -FF J + 4GJ- HH-+ D:PROG7: 1 -+ K: f + JF[ - G + z-+ L: F - L -+ E : t + {¥-- J -+ M : Z - M -+ N : ME + N L display N E + M L display:PROG G

In this program I refer to Prog 7 which solves a cubic and Prog G which solves a quadratic. First the CUBIC: ? -+A:?-+ B:?-+ C:?- D -+: 9~~- 3~-+ P: 2fffA + 6~~- 2~-+ Q: QQ- PPP-+ W: W::; 0 =? GOTO 1:\jQ+M-+U: \jQ + JW-+ U: \1,-Q---JW-W--+ V: U + V- :& -+ Z: u;v- 3~-+ R: v'3(~-V)-+ I: GOTO 2: LBL 1: ARCCOS P~-+ e: 2VP COS~- 3~-+ Z: -2-../P COS(~+ 60°)- :& -+ Y: -2-../PCOS (~- 60°)-+ X: LBL 2

And finally the QUADRATIC: ? -+ A:? -+ B :? -+ C : BB - 4AC -+ D :display D < 0 =? GOTO 1: -~~v'2 -+ T display -~A.v'2 -+ S display GOTO 4 : LBL 1 : 2: -+ R display 'fl -+ I Charles Hermite ( 1822-1901) gave a method "of spectacu­ which isn't H, but N E + M L = 121 which is. lar brilliance" (the phrase used by Eric Temple Bell in his Men So the correct pair of quadratic pageboys is of Mathematics, Simon and Schuster, 1937, 6th paperback printing, page 461) for solving the general quintic, but he Yz(LN) = x2 + 4x + 3 = (x + 3)(x + 1), and needed elliptic modular equations, too much even for my 2 Talented And Gifted Power Graphic. yz(EM) = x - 13x + 40 = (x- 5)(x - 8). It is interesting to graph on my Power Graphic not only the original quartic but its coterie of three servants: the resolvent Try fitting these four on the screen simultaneously! At least cubic and the correct pair of quadratic pageboys. But watch note their relationship. your limits carefully. The curve may be so distant as to make This program is quite safe and may be used by my it impossible to place them all on the same screen at the same sophisticated preteen students as a parlor game to mystify time. For example, try colleagues. But occasionally it may not work if there are jumps in which a cubic discriminant (W in my program), supposedly zero, reads -10-11 , a little-known and rarely used y4 = x4 - 9x3 - 9x2 + 121x + 120, which factors as negative, very powerful in a denominator. This occurs if we roots, i, in (x + 3)(x + l)(x - 5)(x - 8) have two identical pairs of pure imaginary ±I which case the quartic was y4 = x 4 + 2I2x2 + I 4 ; but then the Her resolvent cubic manservant is y3 = x 3 + 9x2 - 1569x - quadratic formula will do, so why drive a Ferrari? Thus we 28681, which factors as (x - 43)(x + 23)(x + 29). We use the see this program is not 100 percent foolproof, but it ought to first factor as Z = 43; from this we obtain ME+ N L = -508 handle all the ordinary quartics most of us need to solve in our daily lives.

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... ,_, Rubik's cube, of order 43,252,003,274,489,856,000. Clearly, ··-·-.. ·-·--·--·-·-.. ··-...... _,_, __ ,,_------· ... -...... _ __ ,_,_,_,_ GAP is capable of handling problems of very large sizes. Reviews of Mathematical Software In this review, we will use a much smaller example, 84 , the symmetric group on four objects. This is the largest GAP: Groups, Algorithms, symmetric group that is solvable and, of course, is of considerable historical interest in connection with solvability and Programming of polynomial equations. Reviewed by Edward L. Spitznagel* In what follows, the reviewer has modified some of the longer output from its actual format, which uses nearly the full width of the output window, into an aligned one that is Twelve years ago Herbert Wilf wrote a charming article titled more easily read. "The Disk with the College Education". In it he described the Any symmetric group can be generated by just two first symbolic mathematics package available for a personal elements: a transposition, say, (1,2), and a cycle, say, (1,2,3,4). computer. The package was muMATH. At the end of the article, Here is how we can generate the group 84 in GAP: Wilf predicted that in a "few years", one could expect such gap> s4 := Group((1,2),(1,2,3,4)); software to run on calculator-sized machines. That prediction As the above suggests, GAP follows a Pascal-like syntax. has indeed come true; DERIVE, the successor to muMATH, is A single semicolon terminates each command. The result is available on a card that slips inside Hewlett-Packard palmtop echoed back to the screen: computers. Group( (1,2), (1,2,3,4) ) At the same time that college-educated software has To suppress the echo, the command can be terminated reached the ultimate in portability, symbolic mathematical with two semicolons. software has generally become much more sophisticated. One of GAP's idiosyncrasies is that the name of the object Today there are several software systems that might be we have just created, s4, is available for us to use in giving claimed to hold a Ph.D. rather than just a bachelor's degree. commands to GAP, but GAP does not use it in communicating One such software system is the package GAP, whose degree results back to the user. Therefore, it is a good idea to tell is in group theory. GAP how to refer to the object just created: GAP is shareware from the University of Aachen, Ger­ gap> s4.name := 11 G11 ; many. It was originally conceived by Joachim Neubtiser and Now, what does everyone know about the symmetric four of his students, of whom Martin Schoenert has become group on four objects? Well, it has 24 elements, it is not the main architect of GAP. Over approximately nine years abelian, but it is solvable. Let's see how GAP can be made to it has grown to a package of phenomenal capabilities (and give us this information: about 1,000 pages of 'lEX-formatted documentation). It is gap> Size(s4); written in C and runs on a wide variety of hardware, including 24 UNIX workstations, PCs with at least a 386 processor, and gap> IsAbelian(s4); Macintoshes. false Larger than what would fit on a disk, GAP is a "zoo" gap> IsSolvable(s4); file of about 6 megabytes. The primary ftp server for GAP true is samson. math. rwth-aachen. de (137 .226.152.6), direc­ One can "see" the solvability of 84 by asking for its tory /pub/gap/. However, users in North America will prob­ derived series: ably find archives .math. utk. edu (128.169.202.163), di­ gap> DerivedSeries(s4); rectory /multi-platform/group.theory/gap/ the most conve­ [ G, Subgroup( G, [ (1,2,3), (2,3,4) ] ) , nient. Macintosh users will find a ported copy on ftp. cc. Subgroup( G, [ (1,4)(2,3), (1,3)(2,4) ] ) , umanitoba. ca (130.179.16.24) in the directory /pub/mac/. Subgroup( G, [ ] ) ] The usual caveat about the Internet applies: addresses and This tells us that the first object below 84 in the series directories tend to change over time. is the alternating group A4 (generated by the cycles (1,2,3) At last count there are 230 users subscribed to the GAP and (2,3,4)), the second is the Klein four-group (generated by forum listserver, which one might consider a rough estimate (1,4)(2,3) and (1,3)(2,4)), and the final is the identity group. of those currently using GAP professionally. (One-third are These subgroups within the series can be extracted and from the United States.) This review is intended for the much investigated on their own. For example: larger group of potential users and demonstrates the relative gap> d1 := DerivedSubgroup(s4); ease with which GAP can be obtained and used. Subgroup( G, [ (1,2,3), (2,3,4)] ) A README file that comes with GAP contains a tour de gap> Size(d1); force demonstration of analysis of the transformation group of 12 gap> d2 := DerivedSubgroup(d1); Subgroup( G, [ (1,4)(2,3), (1,3)(2,4) ] ) *Edward L. Spitznagel, Washington University, Department of Mathematics, gap> Size(d2); St. Louis, Missouri 63130-4899; e-mail: ed@mathwustl. edu. 4

780 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·················-··········-·-······ ··········-···-···········-··············-··- ···········-··-····-··········-············-· ··········-··········~•·•••••••••n••r••~tmlil!lllf.illil ... :····· Computers and Mathematics

In a similar vein, we can investigate the conjugacy class This is heady stuff for a beginning graduate course, but GAP structure of 84 , finding that there are five conjugacy classes, makes it accessible: the identity, the set of two-cycles, the set of three-cycles, gap> CharTable(s4); products of disjoint two-cycles, and the set of four-cycles: rec( order := 24, gap> ConjugacyClasses(s4); centralizers ·= [ 24, 4, 3, 8, 4], [ ConjugacyClass( G, () ), orders := [ 1' 2, 3, 2, 4], ConjugacyClass( G, (3,4) ), classes := [ 1, 6, 8, 3, 6], ConjugacyClass( G, (2,3,4) ), irreducibles := [ [ 1, 1, 1, 1, 1 ], ConjugacyClass( G, (1,2)(3,4) ), [ 1' -1, 1, 1, -1 ], ConjugacyClass( G, (1,2,3,4) ) ] [ 2, 0, -1, 2, 0], If we want more detail, we can find out the size of a [ 3, -1, 0, -1, 1], conjugacy class and even obtain a listing of its elements: [ 3, 1, 0, -1, -1 ] ] , gap> c1 := ConjugacyClass(s4, (3,4)); operations := CharTableOps, ConjugacyClass( G, (3,4) ) name := "G", gap> Size(c1); powermap := [ ' [ 1, 1, 3, 1, 4 ] ' 6 [ 1, 2, 1, 4, 5 ] ] ' gap> Elements(c1); automorphisms :=Group( () ), [ (3,4), (2,3), (2,4), (1,2), (1,3), (1,4)] text :="origin: Dixon's Algorithm", One of the high points in a first course in group theory group := G ) is the Sylow theory. With 8 being the highest power of 2 The first three vectors describe the five conjugacy classes dividing the order of 84 , we expect to find several subgroups of 84 , which are in the same order as listed earlier: identity, of order 8 embedded within S.~: two-cycles, three-cycles, products of two-cycles, and four­ gap> sy2 := SylowSubgroup(s4, 2); cycles. The identity is centralized by everything, has order Subgroup( G, [ (2,3), (1,4)(2,3),_ 1, and belongs to a class by itself. Each two-cycle has a (1,2)(3,4) ] ) centralizer of order 4, is of order 2. and belongs to a conjugacy gap> Size(sy2); class of 6 elements. And so on. 8 Each of the five vectors called "irreducibles" is one of gap> Elements(sy2); the irreducible characters. By looking at the first position [ (), (2,3), (1,2)(3,4), (1,2,4,3), (1,3,4,2), of each vector, which is the character value for the identity (1,3)(2,4), (1,4), (1,4)(2,3)] element, we see that the irreducible representations are made We see that GAP has produced one such subgroup for us. up of matrices of orders 1, 1, 2, 3, and 3. The first of the We can obtain the full set by using the fact that all Sylow representations is the trivial one; the second is the even-odd subgroups for a given prime are conjugates of each other: permutation map, with A4 as kernel. The third has the Klein gap> C := ConjugacyClassSubgroups(s4,sy2); four-group as kernel, and the fourth and fifth are faithful ConjugacyClassSubgroups( G, representations. Subgroup( G, [ (2,3), (1,4) (2,3), A very instructive exercise can be built around the (1,2)(3,4) ] ) ) character table of a Sylow 2-subgroup of 84 , illustrating gap> Size(C); among other things, the tables of groups that GAP contains in 3 its libraries. The first step is to obtain the character table: gap> Elements(C); gap> CharTable(sy2); [ Subgroup( G, [ (3,4), (1,2) (3,4), The next step is to obtain a list of non-abelian groups of (1, 3)(2,4) ] ) ' order 8 from the GAP library: Subgroup( G, [ (2,3), (1,4) (2,3), gap> nab8 := AllTwoGroups(Size,8, IsAbelian, (1,2)(3,4) ] ) ' false); Subgroup( G, [ (2,4), (1,3) (2,4), [Group( a1, a2, a3 ), Group( a1, a2, a3)] (1,2)(3,4) ] ) ] The AllTwoGroups library contains all distinct 2-groups A quick look at this list reveals that all three subgroups of order less than or equal to 256. There are two non-abelian have the Klein four-group in common and are generated by groups of order 8. In the response above, GAP confirms combining a two-cycle with that subgroup. this. Now print the character tables of these two non-abelian One of the most powerful tools in modem group theory groups: is the character table. Characters are the traces of matrix gap> CharTable(nab8[1]); representations of groups. Over the field of real numbers, gap> CharTable(nab8[2]); matrix representations can be decomposed into ''irreducible" The first group is the dihedral group, and the second representations. There are as many irreducible representations is the quaternion group. Surprisingly, both groups have the of a finite group as there are conjugacy classes. Furthermore, same character table. This can lead to lively discussions as since traces are invariant under similarity transformation, all to how much information the character table really contains. elements of a given conjugacy class have the same characters. The groups can be distinguished based on the orders of their

SEPTEMBER 1994, VOLUME 41, NUMBER 7 781 Computers and Mathematics

elements, which is part of the information GAP provides in (compressed). Currently it can be found in the subdirectory the CharTable output. Thus, by the end of the exercise, the /multi-platform/group.theory/gap/split/. It is formatted to print Sylow subgroup can be identified with the dihedral group. on 8.5 x 11 inch paper and produces about 1,000 pages of The GAP libraries contain tables of the 58,760 2-groups beautifully written material. of order up to 256, the 594 3-groups of order up to 729, Anyone becoming a user of GAP should certainly sub­ the 406 primitive permutation groups of degree up to 50, scribe to the GAP forum. The forum is a standard listserver and the 1,045 solvable groups of order up to 100. There are which averages about thirty messages per month, including functions in GAP to generate basic types of groups, such replies to questions. Details on subscribing are given at the as cyclic, elementary abelian, symmetric, alternating, general end of the README file. There is a wonderful camaraderie linear, special linear, and so on. There are six "third-party" in the forum, with conversation being very courteous and software packages distributed with GAP. supportive. Quarterly logs of the GAP forum are available. Two of those third-party packages are written in what is They appear in the /etc subdirectory when the zoo archive is called the "GAP language" and thereby illustrate an important received and expanded. feature of GAP's architecture. Adopting the philosophy of To summarize, the authors of GAP have produced a most Maple, the authors of GAP constructed a small kernel of impressive and useful package. They deserve heartfelt thanks compiled C code, which serves as an interpreter for an for having devoted so much time and care to its development. intermediate language called the GAP language. The functions May they continue to progress at the phenomenal rate they that implement the group theory are written in this language. have in the past. The GAP library currently contains about 120,000 lines ofthis interpreted code, which is easier to read and write than C. This References structure allows users to playa much more active part in the [1] H.S. Wilf, The disk with the college education, Amer. Math. development ofGAP, helping to find bugs, adapting functions Monthly 89 (1982),4-8. to their own needs, and even providing entire packages of [2] M. Schoenert et aI., GAP-Grollps, algoritll1ns, and progranz­ new functions to the user community. rning, 3rd ed., Lehrstuhl D fuer Mathematik, Rheinisch Westfaelische Having covered approximately 1 percent of the GAP Technische Hochschule, Aachen. Germany, 1993. package in the examples above, let us now turn to the me­ chanics of obtaining GAP. With ftp or gopher, connect to the "l1IIR~IRJiI~""_" __""""""""""""""""""""'" .. mathematics archives at University ofTennessee at Knoxville (archives.math.utk.edu, or 128.169.202.163). Change jspell to the directory /multi-platform/group.theory/gap/. (Macin­ Version 2.0 tosh users shouldinstead connect to ftp. cc . umanitoba. ca, as mentioned earlier.) This directory contains a file called Reviewed by Eric Schweitzer* README, which will give a description of the most recent version of GAP. Get this file first and read it. It contains full instructions for obtaining and installing GAP. Since GAP is likely to have been updated before this review Introduction appears, there is some risk in giving installation instructions Computers have long been used for document preparation, here. However, for those concerned about the resources GAP and have been supplying spell-checking facilities for such will require, here is a brief summary ofthe installation process: documents for almost as long. Over the past ten years, The entire GAP package is compressed into a single "zoo" there has been an increasing number of people using lEX archive, somewhat greater than 6 megabytes in size. This to do their document preparation. And yet, lEX-compatible will expand into approximately 30 megabytes of C source spellcheckers are not (at least in the DOS world) common. code, libraries, and documents. There are "make" files for Whether it's a stand alone ASCII file spellchecker or one built all popular computers, which automate compilation of the into a word processor, chances are good it will have trouble program. It took approximately half an hour to get GAP with names like Godel (G\"odel) and Erdos (Erd\H{o}s), up and running on the reviewer's NeXT computer. (Before words like gar<;on (gar\c{c}on) and sefior (se\-{n}or) compiling, however, users should check the subdirectory and sequences in math mode like fgh(x) ($fgh(x) $). /multi-platform/group.theory/gaplbin/ to see if executable jspell is a spell checker designed to work with lEX code is already available for their particular machine.) documents in a DOS environment. It is reasonably small, While many tasks can be accomplished with a fraction fast, and does its job quite well. It is capable of working in of the full package, it is best to start with a machine large a local area network, though I did not evaluate that aspect enough to hold everything. In the beginning, when one is of the software. jspell requires an IBM compatible machine getting accustomed to the software, it is simpler not to worry about whether a particular ability has been installed. *Eric Schweitzer is at the CUNY Graduate School, Department of Mathe­ Except for the README file, all GAP documentation is matics, and Hunter College. CUNY, Department of Computer Science. He uses 1}jX, embodied as em1}jX, and L\1EX to write everything from exams to (ShOli) in lEX. For convenience of the user, this has been compiled papers and warns that he will confuse these names whenever convenient. He can into a single DVI file approximately 1 megabyte in size be reached at ershc@cunyvm. cuny. edu.

782 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics running DOS 3.3 or later and a graphics video system (VGA, dictionary. Words can be case sensitive, so it knows, for ex­ CGA, EGA, or Hercules). It has color options allowing use ample, that \aa is not the same as \AA. It also knows to ignore with monochrome and LCD screens. A mouse and hard drive in \cite{ } and to ignore and are recommended. I ran }spell on an ffiM clone with a 386 in \newcommand{ }{ }. These processor running at 33 MHz, 4MB RAM, running DOS 5.0. last 1FX commands and their arity are stored in the text file }spell is a shareware product. Shareware products are jsptex.cfg. distributed freely, with the proviso that if one uses the product, The other configuration file, j spell. cfg, is also a text one is expected to pay a fee. In exchange for this the author file. This file stores various default settings, for example, the generally sends the latest version of the software (frequently locations of dictionaries, type of video card, minimum wor--i with features not in the unregistered version) and a printed length, and whether to ignore words in math mode or not. manual. The shareware product is available via anonymous ftp Most of these defaults can be overridden when invokingjspell from oak. oakland. edu in the pub/msdos/tex directory. via command line options. These options are not too arcane, Get j spel202. zip. One can register by sending $27, e.g., the option -ud d: some \path \mywords. die would plus $4 shipping, to the author: Joohee Jeong, Nemosoft load the user dictionary specified rather than the default user Technologies, P.O. Box 1619, El Cerrito, CA 94530; or with a dictionary. One must note that j spell. cfg is line sensitive; credit card by calling 800-2424-PSL; or by sending e-mail to for example, the sixth line must start with either Mathignore 71355. 470@compuserve. com. The author's e-mail address or with MathNoignore. This is made quite clear both in the [email protected]. file itself and in the documentation. As a review package, I received both a registered and an One of the advantages ofjspell is its flexibility in dictionary unregistered version of }spell. The registered version comes handling. It allows you to have many main dictionaries, for with a printed manual and without the "don't forget to register" example, separate French, American English, and British message when one exits the program. Although the two ver­ English dictionaries (though only one may be used at a time). sions seemed otherwise identical, most of my reviewing was It allows you to have at least three dictionaries active when done with the registered version 2.03. The package consists of checking a document: the base dictionary, a user dictionary, two main parts: the spell checker software (j spell . exe) and and a file dictionary. (In a networked setting, the user and a dictionary maintenance program (di ctman. exe). The spell file dictionaries are "local", while the base dictionary could checker also requires a dictionary (a 39,049-word dictionary reside on the server.) The base dictionary is generally the is supplied) and two configuration files. largest of the dictionaries. It is compressed, fast to load, and (using dictman) is easy to modify. The other dictionaries The Spell Checker are plain text files. They need not be alphabetically ordered, The spell checker is the heart of this package. Like most and they need not have one word per line (though if you spell checkers, once started, this program reads a text file add words one at a time with }spell, they will be). As their and compares the words contained therein to words found in names imply, the user dictionary is associated to the user, one or more word lists (dictionaries). If the word is not in a while the file dictionary is associated to the file being checked. dictionary, the spell checker uses some algorithm to determine One can append dictionaries to a text dictionary by starting which words in the dictionary are possible matches for the it with a reference to another dictionary. For example, to read word. One must achieve a balance between the dictionary include math. die and logic. die in the file dictionary contents and this algorithm. For example, if one types manger mypaper. die (the dictionary associated to mypaper. tex), when one means to type manager, no error will be spotted just start mypaper. die as follows: if "manger" is in the dictionary. If "manger" is not in the +math.dic dictionary, one would hopefully be faced with a short list of +logic.dic alternatives including "manager". Unlike most spell checkers, word1 }spell keeps track of its last 400 actions, allowing the user to word2 undo them. The output screen is clearly laid out and easy to read. The various actions displayed include a suggested alternate word }spell can be fooled. If it is ignoring spelling in math mode list, single and global ignore, mark and replace, and adding and you \begin{eqnarray*} ... \end{eqnarray},jspell the word to either the user or the document dictionary. They will think everything from the \begin{eqnarray*} on are accessible by point-and-clicking with a mouse, by using (until it finds an \end{eqnarray*}) is in math mode, so to the cursor control keys to highlight the option and hitting be ignored. For this reason it is suggested you run 'lEX on a , or by using +initial to invoke the option file before you run }spell. Similarly, if }spell is not ignoring (for example, +i to Ignore that non-dictionary word, comments (another option) but is ignoring math mode, $s +G to Ignore it globally). in comments can confuse it. Other 1FX legal but unnatural This spell checker is happy dealing with 1FX source code. constructions can bother }spell, for example, with: When in 1FX mode, it ignores words that start with \. It can, if . .. some text.$%Is this any way to start dis­ you like, ignore text in math mode. It knows about legitimate play mode? subwords, so does not accept Godel when G\ "odel is in the $a-n+ b-n e-n$$ It is known ...

------SEPTEMBER 19g4, VOLUME 41, NUMBER 7 783 ...... _.. ______._ ... ,...... Computers and Mathematics

jspell Wordperfect ShareSpell T:EXwords 1 (em in em\TeX) 11 10 words misspelled 26 28 27 correct alternative 2 1 2 not offered

jspell will think "is this ... " is in math mode and "It is dictionary, add a word, delete one or a file of words, or known . . . " is in displayed math mode. optimize (compress the added entries) or expand (make an A preliminary version of this review was run through ASCII file of the words in) the dictionary. One can also jspell and two other spell checkers. One was ShareSpell, load a user dictionary (or other ASCII file) and merge it to another shareware spell checker with no 'lEX ability. This a base dictionary. All of this is achieved via menus which spell checker ignores \. and over the years I have added are accessible either by mouse or by cursor control arrows. many 'lEX commands to the (single) user dictionary it allows. The screen is easy to read, and the system's responses are I did not use that user dictionary in the following test. The tastefully color-coded. other spell checker was the one supplied in WordPerfect 5.1. By loading a text file as a user dictionary and merging I kept track of how many 'lEX entries were identified as it into an empty base dictionary, one can create one's own misspellings, how many misspelled words were identified, dictionary. One can also get an alphabetized list of words in a and for how many of these the correct alternative was offered. file (one word per line) by loading the file as a user dictionary The results are summarized in the table above. and then saving it as a user dictionary. Most of these operations There was only one aspect of this program that a bad are reasonably fast. The longest operation, making a text word speller like me would like to have changed. When a word is list into a base dictionary, took about 2 minutes on a 40,000 misspelled so badly that the correct alternative is not found, word file; 50 seconds to read the file as a user dictionary one has no choice but to resort to a paper or on-line dictionary and move it to an empty base dictionary; and another 1 to find the correct spelling. WordPerfect 5.1, for example, will minute 10 seconds to optimize it. The same operations done take my second guess at the spelling and attempt to find the to the 9,000-word Chaucer dictionary took a total of about word again, but jspell only informs me that the word is still 10 seconds. Adding the Chaucer dictionary to the large base not found and prompts me to mark it, ignore it, or put it in dictionary was also fast (less than 1 second) and optimizing a dictionary. E-mail to the author has resulted in a promise the resulting dictionary took another 15 seconds. Of course, all that this feature will be available in version 2.04, expected in these times depend on the sizes of the dictionaries involved, August 1994. as well as your processor's speed.

Dictionary Maintenance Register Now! A base dictionary is a compressed file. These dictionaries can jspell does what it claims to do, and does it quite well. Its be modified using dictman, jspell's dictionary maintenance usage was easy to master, and it works immediately upon program. These compressed dictionaries not only take up unziping. It is easily customized using a straightforward set less disk space, but they are faster to load. This ability to of text files. It costs nothing to "try before you buy"; and if modify the base dictionary is apparently not common. Neither you are as pleased as I with the way it works, you will send ShareSpell nor WordPerfect 5.1 allow this (though they each your $27. allow you to add words to a user dictionary). jspell comes with a dictionary, base. die, of over 39,000 ...... words. As a text file, this would take some 392 KB of ______space. Compressed it is only 172 KB, a compression to HiQ 2.02 44% of its original size. Languages other than English get less compression, as the compression algorithm relies on Reviewed by Maurino P. Bautista* various standard English constructions. Hence, a dictionary made from Chaucer's Canterbury Tales 1 (in Middle English) Program Description 9,155 words. The compressed version was about 67 showed HiQ claimed to be the first completely integrated software KB, the expanded version some 79 KB, compression to only environment for solving real-world problems in engineering, 85 percent. Once dictman is started, the user can load a base *Maurino P. Bautista is an associate professor of mathematics at Rochester Institute of Technology, Rochester, NY 14623. He received his Ph.D. in mathematics from Purdue University (1984). He has interests in inverse prob­ 1A public domain file edited and digitized by Ted and Florence Daniel, New lems. partial differential equations, and computer algebra systems and he is Wave Publishers, Portland. Oregon, and available from the Invention Factory a beta-tester for a number of software companies. He can be reached at: BBS. [email protected].

784 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics mathematics, and the applied sciences. Its principal developer, pear in your document. Double-clicking a SymRep activates David Russel, wrote Math View Professional, one of the first one of five linked editors (Data, HiQ-Script, Graph, Text, or math programs for the Macintosh. He has paid particular atten­ Problem Solvers) for easy access to any component of your tion to computational efficiency and the graphical interface in solution. Here is the hierarchy of the component tools in HiQ: HiQ. The program uses a desktop metaphor to provide access to mathematical, simulation, and graphing tools necessary to produce practical solutions and present them in a highly Project Worksheet professional manner. HiQ is a large, extremely complex program. It is impossi­ ble in a short review to do justice to its vast capabilities, so we will concentrate on the more interesting and unique features of the program.

Hardware Requirements The program runs on any Macintosh with a 68020 or higher CPU equipped with a floating-point unit (numeric coprocessor) and at least 5 Mbytes of RAM. The package comes in two high-density diskettes (which can be exchanged Built-In Functions for 800 KB diskettes if your machine does not have a high­ density drive, as with the original Mac II), each containing a compressed file. Installation is extremely easy and requires HiQ contains all the tools you need in one place to solve ten 8 Mbytes of storage on the hard drive, although the main classes of problems. A powerful graphical user interface pro­ program and its accompanying files occupy only about 5.4 vides complete access to these tools through intelligent menus Mbytes after installation. The second disk contains several and icon-driven screen displays. It has a fully documented very well-written tutorials and example projects; it is not function library of over 600 functions/algorithms organized required to run the program but is extremely useful to into three levels encompassing simple to complex mathemati­ the beginner and occupies about 3.6 Mbytes. If disk space cal operations such as orthogonal functions, Fourier analysis, is at a premium, these files can be off-loaded to floppies specialized matrix operations, etc. This library is the main after installation to recover space. Since the program is analytical engine that serves as the "computational kernel", computationally intensive, it will run better on faster machines; while the remainder of the program provides a simple way of and because the interface requires working with several communicating with this kernel. windows, a big screen is essential in my view. I found it difficult and frustrating working on small screens such as the SE/30 or the Powerbook. I had several sessions with the program, starting with the The Project Worksheet Quick Start tutorial in the User Manual. Initially, I found it The basic framework that connects the powerful components almost impossible to do anything without first looking at the of HiQ into an integrated whole is the project worksheet which manual. I tested the program just as I have done with other functions as a "virtual desktop" environment upon which all programs. Some of these are Matlab, Maple 4.2 and Maple V, phases of a project can be addressed and integrated. The Models 1.03, TEMATH, and Calculus TIL. project worksheet provides a graphical and intuitive means of managing the wide range of HiQ's functionality as well as organizing and presenting the input data, structure and Basic Operation solution, and output data of a technical problem. Following HiQ is an object-based mathematics program that can dynam­ is a sample worksheet containing an icon view of an input ically organize and manipulate numerical data, solve standard matrix A, an icon view of a script, and an expanded view problems, create specialized routines, graph data, and present of the output matrix b, which is really the inverse of A. reports with the ease of a graphical user interface. The basic Icons can be placed anywhere in the worksheet and can be document is called a Project Worksheet and is a standard expanded to show all or just portions of their contents (using a Macintosh document file. AHiQ session can begin either with scrolling window). Using the String Editor to enter text in any a new project worksheet or with a previously saved project available font, size, and style is as easy as using an ordinary worksheet. You can open a maximum of eight worksheets in word processor; however, it does not have the capability to one HiQ session. With a click of the mouse, you can create enter complex mathematical symbols or expressions. This icons (called SymRep for Symbolic Representation in HiQ) prevents the use of HiQ to write publication-quality papers for each component of your solution. Hence, for example, you containing mathematical formulas, although output from HiQ can have an icon for each input data to a problem, an icon for can be exported to other programs such as 1FX in several each output data, an icon for each graph, as well as an icon for formats-Text (tabbed, comma, space) or standard Macintosh the solution script. You select which symbols of interest ap- PICT. The (floating) Tools Palette to the left offers an easy

SEPTEMBER 1994, VOLUME 41, NUMBER 7 785 ...... _.__..... ______...... Computers and Mathematics

the solution to this problem. The next step is to select the Data Fitting tool to help set up the problem. You will be presented with the preceding window which is typical of all Problem Solvers in HiQ. Double-clicking the data icons activates the Data Editor, allowing you to enter the input data to the problem. After selecting the appropriate options and entering the correct parameters (if any are required) for the data fitting algorithm, clicking the Run button (the big arrow between the Inputs box and the Outputs box) will produce a window summarizing the results of the calculation. This window contains a list of all the new symbols and/or data created by the Data Fitter. It is similar to the output of a Fortran compile and is run on a mainframe. What makes HiQ unique is that all these symbols can be viewed and edited in their own editor and you can select which symbol will appear in the worksheet. The way to create other objects and place them on the worksheet. completed project is shown below. Tools with an arrow in the upper right corner expand to reveal other tools. For example. the Problem Solver tool in the lower left corner of the palette expands to reveal the following additional tools:

An Example To illustrate how the various components of HiQ work. we consider briefly the problem presented in the Quick Start Ave.-.p Annuet ReJnfall section of the User Manual: fitting a curve through eleven years of average rainfall data, plot the result. and perform some what-if analysis. The first step is to create a new project worksheet on which we shall organize all the components of

First Problem:Datafltl _.,..., ~-OutP

Problem Solvers rOo•- HiQ has ten classes of Problem Solvers that significantly Method:! linear reduce the effort required to set up and solve standard problems 1 btwNt*" T~Cit- 0 line fit ~~~~ in applied mathematics. Each Problem Solver functions as a ® Polynomial Fit IL!J ... ?:10 I preprogrammed set of instructions designed to help you set 0 General Fit :01t1 F"tt P\ot P•~mtttrt up the solution to a problem, the data/parameters defining I® smooth Curve r·"-=·~_1 the problem, and the mathematical functions necessary for 0 Use Input Del a the solution. A graphical user interface enables you to pose these problems, select algorithms, and execute them without any programming, eliminating the need to learn a command language. HiQ automatically produces the script required to

1816raph 181 EMe~ute 0 saue Strfpt 0 IJ"'bllse solve the problem and run it repeatedly with different sets of ~~ input data. The scripts could also be combined to solve larger

786 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics and more complex applications with very little effort. (See The answers I obtained are at least as accurate as those printed below) in most books on numerical analysis. HiQ 2.02 contains the following problem solvers: • Expression Evaluator • Fourier Analyzer ; File Plot Moules • Integral Equation Solver • Integrator • Nonlinear Systems Solver • ODE - Initial Value Problem Solver • ODE - Boundary Value Problem Solver • Optimize • Root Solver • Statistical Analyzer Each solver is represented by a button in the expanding Tool Palette shown earlier. Here is the script generated automatically by the Data Fitter tool for the Rainfall Analysis project:

First Problem:DIIInFill scriptl 01

Problems? As with any new program, especially those as complex as HiQ, there are always a few minor problems and design flaws. Although HiQ makes it easy to solve standard problems in any of the ten areas stated earlier, it oftentimes makes solving simple problems in other areas unnecessarily complicated by requiring you to write a script and compile it before running. Opening a long file can take forever. After a little experimentation, the Symbols List could be so long that it may be difficult to locate a particular SymRef. In fact, simply Good Features highlighting problem solvers or data icons creates unnecessary One of the best features of this program is the ease with symbols that clutter the Symbols List. You cannot experiment which one can plot three-dimensional curves or surfaces without saving changes. It is not possible to edit data right in defined explicitly or parametrically, in cartesian, cylindrical, their cell; it can be done only in the edit area in the top part or spherical coordinates, and display them in various views, of the Data Editor window. In order to change the name of a styles, and lighting sources with projections on coordinate SymRep, one must first select its icon with the mouse, then planes, location of points, and other options and enhancements. press the Return key before keying the new name. One should Various labels and annotations can be included. A similar be able to change the name by clicking on the icon's name statement can be said about plotting plane curves. In my and typing over. To input a data matrix, one needs to use the opinion, HiQ has one of the best interfaces for plotting curves Get Info command to declare the dimensions of the matrix. A and surfaces, and the figures that come out are excellent. In more efficient way would simply be to use the Tab, Return, the following graph, the three numbers at the bottom represent and Enter keys to create the matrix dynamically. Finally, in the x, y, and z coordinates of the small dotted circle on top the Numerical Integrator window, pressing the Tab key allows of the surface. By selecting the Point Locator tool (black you to cycle through all the input data except the function background) in the tool palette, this circle can be moved f(x) to be integrated. To enter it, you cannot just click in the around the surface by dragging the mouse. The graph also f(x) window. One must click on the first line in the window! shows contours projected onto the x-y plane. It would be nicer if the options were presented via drop-down Another good feature is the large collection of files menus instead of Previous and Next buttons. (sample documents, tutorials, and scripts) such as simple The indispensable User Manual is rather skimpy, while calculus problems, a heart pump model, an airfoil design, the heftier Reference Manual is reminiscent of the IMSL user statistical applications, and others that come with the package. manuals. These can be used as templates to create other models, making I am sure there are other quirks that can lead to frustration, it much easier to use the program. The mathematics behind but I can happily say that the mathematics seem to be correct. the program is solid and the algorithms are state of the art. (I have yet to obtain a wrong answer!)

SEPTEMBER 1994, VOLUME 41, NUMBER 7 787 ...... ··········...,.11•.; m.·.'·__.•.w'·.;II.:...·..·..·. Computers and Mathematics

The Competition comment is that Macsynza is available from other sources in HiQ is in a class by itself on the Macintosh-although the addition to Macsyma, Inc., and this should have been stated latest version of Matlah 4.0 offers a comparable interface in in the review. The versions produced and maintained by these graphics and, with some object-oriented programming, even sources are not all the same. This should be taken into account allows you to create customized graphical user interfaces in any forthcoming review of the new version ofMacsyma. (containing push buttons, check boxes, menus, sliders, radio Macsyma was developed at MIT from the late 1950s buttons, editable text, etc.) for building any application. to about 1983. At that time support by the government Matlah has more functionality and its Toolboxes are more terminated, and work at MIT on Macsyn'za ceased. Symbolics, versatile, but much of the interaction is still done with a Inc., then took over and sold versions of Macsynla. I do not command line interface. When it comes to standard problem­ know the fate of the program under that company. It seems solving in the ten classes mentioned above, HiQ blows away that the MIT Macsynla is public domain property, and anyone the competition in every respect. can use the MIT Macsynla and enhance the product and sell the result. One of those who did so was Leo Harten at The Bottom Line Paradigm, Inc. His present version is called ParaMacs. In spite of the difficulties and design flaws, HiQ is Mac ParaMacs is a commercial follow-on to DOE-Macsynza, software at its best. The program is easy to learn, flexible, and contains enhancements, speed-ups.. and bug-fixes not and powerful enough to solve industrial problems. I would present in the older software. It is available for VAXNMS, recommend it to anyone who needs to solve real-world SUN-3, and SUN-4 machines and can be ported to other sys­ problems in any of the software's ten problem-solving areas. tems with a common-lisp that meets stringent acceptance tests. It is also an excellent tool for classroom engineering and Copies for single machines and site-licenses are available. scientific problem solving where the emphasis is on solutions Contact: Leo Harten Paradigm Associates, Inc., 29 Putnam rather than computer programming. Avenue, Suite 6, Cambridge, MA 02139, USA; tel. 617-492­ 6079; e-maillph@paradigm. com for more information. Harten has improved the product considerably and ex­ Obtaining the Program cellent maintenance and support are provided. Harten also The commercial list price of the program is $995, but the provides advice at most hours of the week, even late at academic price is only $195. A student version is available for night. So in addition to the version reviewed by Crow as $125-a real bargain! It can be obtained from Bimillenium sold by Macsyma, Inc ... I recommend the version produced by Corporation, 16795 Lark Avenue, Suite 200, Los Gatos, CA Paradigm, Inc. 95030. The package comes with two high-density diskettes I have had the opportunity to compare Macsynza and and two manuals-a User Manual and a Reference Manual. Ma/J!e. My opinion is that one needs the union of the two. To order or for additional information, you can call 800-488­ Each has virtues that are missing in the other. 8662.

...... ij.. 'fi!B ., : k&~ . Commentary on Macsyma Review The column in the May/June issue included a review of w. A. Beyer* Mathematica Help Stack for Math.ernatica version 1.2. The updated versions (2.2) of Mathernatica Help Stack and Mathenzatica Hel]J .for Windovvs are already on the market This comment concerns the review of Macsynla by John and will be reviewed in a future column. A. Crow that appears in the Notices, April 1994. My main

*w. A. Beyer is at the Los Alamos National Laboratory. His e-mail address isbeyer©beta.lanl.gov.

788 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY CONTEMPORARY MATHEMATICS

------CONTEMPORARY MATHEMATICS ------Recent Advances in Real Algebraic Geometry Recent Advances in Real Algebraic Geometry and Quadratic Forms and Quadratic Forms William B. Jacob TsU-Yuen Lam Robert 0. Robson William B. Jacob, Tsit-Yuen Lam, Editors and Robert 0. Robson, Editors Volume 755 ------­" "'"'..,.,.~,~-"""" s,~.,,

The papers in this volume grew out of a year-long program in "Real Algebraic Geometry and Quadratic Forms", held at the University of California at Berkeley during the 1990-1991 academic year. This valuable collection of research articles by top workers serves as a record of current developments in these areas and as a tribute to the fruitful interaction between them. Students and researchers alike will find this book a useful reference, with articles ranging from the technical to the expository. Also included are summaries of the current developments in several subdisciplines and indications of new research directions.

1991 Mathematics Subject Classification: 00, 11, 14 ISBN 0-8218-5154-3, 405 pages (softcover), January 1994 Individual member $34, List price $57, Institutional member $46 To order, please specify CONM155/NA ------CONTEMPORARY MATHEMATICS ------The Structure

The Structure of Relation Algebras of Relation Algebras Generated by Relativizations Generated by Relativizations steven It Glvant Steven R. Givant

------­hmor.

This book aims to analyze the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures. This book is well written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses on algebras of binary relations or algebraic logic.

1991 Mathematics Subject Classification: 03; 08 ISBN 0-8218-5177-2, 134 pages (softcover), January 1994 Individual member $20, List price $34, Institutional member $27 To order, please specify CONM/156NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. Inside the AMS

Committee on Science Policy Congress, and to the executive branch. Right now Congress John W Morgan, Chair is the main focus. It is time now for the Washington office to swing into action, so that mathematicians are routinely Columbia University talking to Congressional representatives and their staff. As At its April 1994 meeting, there were three major areas of mathematicians come to Washington for whatever reason, emphasis for the Committee on Science Policy: new funding they could be in coordination with the AMS Washington modes at the National Science Foundation (NSF), developing office, picking up materials and getting a briefing. This will connections in Washington, and the recently completed Na­ help prepare mathematicians for these meetings and also give tional Policy Statement. In addition, the committee discussed a certain level of coordination to the messages emanating questions posed to it by the Division of Mathematical Sci­ from the community. At the other end of the spectrum, when ences (DMS) at the NSF: how to define "adequate" funding there is some specific issue before Congress, such as the for mathematical sciences research and how to determine how bill containing the budget for the NSF, there are special many investigators should receive federal support. key legislators who serve on these committees; and the Washington office can bring mathematicians in to talk to those New Funding Modes at NSF legislators and their staff. Some of this kind of activity has There are some new funding mechanisms at the NSF that gone on in the past year or so already. the committee discussed. The DMS has started group grants, This year AMS President Ronald Graham presented which would provide an alternate funding mechanism for testimony before the committee considering the bill that those investigators without salary support needs who would contains the budget for the NSF. The Committee on Science benefit by participation in a research group. Three or more Policy discussed a preliminary version of his testimony. The researchers can apply for a group grant which could support Committee believes such testimony must touch on research, computing, travel, students, or any special needs the group education, and applications. However, there is always a might have to carry out its research. The group must have question of balance, and the committee's interest is to make some sort of scientific connection, but its members need sure the research part is well represented and not downplayed. not be all at the same institution. The budgets can be up to There is always pressure to downplay research because, of $250,000 a year. This kind of support for groups of researchers the three activities, research is the hardest one to sell in is one of the things that the Committee on Science Policy Washington. However, that is all the more reason for the recommended to the DMS. I think this is a very good method committee to see to it that the case for research is made well. of support for mathematics. Another new program at the NSF provides for university­ industry research opportunities in the mathematical and phys­ Building on the National Policy Statement ical sciences. The DMS already has an industrial postdoctoral The third area of focus has to do with the National Policy program, and this new program expands that type of support Statement, which was completed this spring and which to the physical sciences as well. There is another part of the appeared in the May/June issue of the Notices. This broadly program, new in mathematics as well as in the physical sci­ based statement tries to cover the entire waterfront of national ences, called university-industry senior research scholarships. issues of interest to the Society. In order to build on it, the This component is aimed at senior scientists. It provides half committee intends to develop more focused documents that a salary to faculty who want to broaden their experience elaborate on specific topics in the National Policy Statement; by working in an industrial environment and also allows for example, postdoctoral programs, the plight of young industrial researchers to do research at a university. mathematicians, or education. Frank Warner, who chaired the subcommittee that produced the National Policy Statement, The AMS Message in Washington is working on a plan to set up an operational mechanism to A second area of focus for the committee is getting the generate such documents, and the committee will discuss this AMS message out in Washington to federal agencies, to the at its next meeting in September.

790 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

What is Adequate Research Support? to a number. This is a good question to throw out to the The committee also discussed two questions about which the community: How would you establish such a number and go OMS had asked for some advice. The first question was, What about justifying it? constitutes adequate support for mathematics? The committee came up with a number of responses to this question. although Goals for the Committee there were various interpretations of what this question means. One of the main roles of the Committee on Science Policy is to After some discussion. we formulated and sent to the OMS educate the members of the AMS about national governmental a single response which outlines various items (computing, policy issues: what the mood in Washington is. how the travel, students. postdocs. salary) that are part of adequate government is viewing mathematics. what the prospects in funding for mathematics research. funding are. what is happening at the NSF. The committee also The second question was, What is a reasonable num­ is involved in the effort to move information in the opposite ber of mathematicians to be supported? The committee had direction. by getting the message of the AMS distributed much more trouble coming to terms with this question. so in Washington to the people we think need to hear it. As we have not yet proposed a response, though we have a is clear from the National Policy Statement the committee subcommittee working on this. The difficulty is that most has considered a broad range of issues. such as education. answers to this question start with something about today's underrepresented groups. applications. and public awareness funding environment and then derive a number. For example. of mathematics. Ideas generated within the committee on one might start with the number of currently supported peo­ Science Policy are often passed along for action by other ple in mathematics, the number of mathematics departments committees. Because of the wide range of issues it considers. where research is done, or the number of graduate students in the Committee on Science Policy serves a pivotal role in the mathematics. None of them is very satisfactory. and all can Society. be challenged. For example, if one starts with the number The Committee on Science Policy welcomes input and of departments doing research. one might ask if the nation suggestions .fi"om the community. The e-mail address for the needs that many departments doing research, or why that Committee is comsp@math. ams. org. Comments may also he number could not be half of what it is today. In other words. sent to: Committee on Science Policy, American Mathematical it is difficult to start from initial principles and work forward Society, P.O. Box 6248. Proridence. RI 02940-6248.

PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Algebraic Groups and Their Generalizations Proceedings of Symposia in PURE MATHEMATICS William J. Haboush and Brian J. Parshall, Editors Volume 56

Algebraic Groups and These volumes contain papers based on lectures presented at the conference. ""Algebraic Groups and Their Generalizations Their Generalizations"'. held at Pennsylvania State University in July 1991. This conference reflected WIIIlam J. Haboush Brian J. Parshall both the diversification of technique in the classical theory and the beginnings of the study of new Editors objects. These new objects include quantum groups and vertex operator algebras, as well as various kinds of infinite-dimensional groups and algebras inspired by new work in mathematical physics and quantum field theory. The first volume focuses on classical methods. while the second centers on quantum and infinite-dimensional methods. Each section begins with expositions and then turns to new results. This collection provides readers with an excellent introduction to these astonishing new mathematical worlds.

1991 Mathematics Sul>ject Classification: 14, 20. 55. 17. 16 ISBN (Set) 0-8218-1-197--1. !Part I) (qCJ8-1540-7. (Par1 2) 0-8218-15-11-5. 798 pages (Set). 383 pages (Par1 I). -115 pages (Part 2). Apri I 1994 Set: Individual member $80. List price $133. Institutional member $10o. Part I: Individual member $-11. List price $68. Institutional member $54. Part 2: lndiYidual member $-13. List pri.:e $72. Institutional member $58 To order, please specify PSPUM/56NA (Set), PSPUM/56.1NA (Part I), PSPUM/56.2NA (Part 2)

All prices subject to change. Free shipment by surface: for air deliYery. please acid $o.50 per title. Prepayment l"l'ljllirl'd. Order from: American Mathematical Society. P.O. Box 5904. Boston. MA 0220o-590-l. or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada. please include 7'7r GST.

SEPTEMBER 1994. VOLUME 41. NUMBER 7 791 News and Announcements

Stephen Cole Kleene friend and fellow student, J. Barkley of the College of Letters and Science. 1909-1994 Rosser (who joined him in Wisconsin Kleene was president of the Associa­ Stephen Cole Kleene, the main devel­ in 1963), Kleene created recursive func­ tion for Symbolic Logic in 1956-1958 oper of recursive function theory and tion theory, his major lifelong research and editor of the .Journal of Symbolic one of the most important mathematical interest. Logic for twelve years. He served as logicians of the twentieth century, died Kleene's greatest impact was as the president of the International Union of in Madison, Wisconsin, on January 26, principal developer of this theory, which the History and the Philosophy of Sci­ 1994, after a long illness. He was 85 investigates computability and undecid­ ence in 1961 and of the union's Division years old. ability in mathematics. A major branch of Logic, Methodology, and Philosophy Kleene was born in Hartford, Con­ of comtemporary mathematical logic, of Science in 1960-1962 and was a necticut, on January 5, 1909, to Gus­ recursive function theory is of central founder of both. He was elected to the tav Adolph Kleene, a professor of eco­ importance in computer science. Kleene National Academy of Sciences in 1969. nomics, and Alice Cole Kleene, a pub­ is responsible for many of the funda­ At a symposium held at the University lished poet. He received a bachelor's mental results in the area, including the of Wisconsin in honor of his seventieth degree from Amherst College in 1930 Kleene normal form theorem (1936), the birthday in 1978, he presented an im­ and a Ph.D. from Princeton University, Kleene recursive theorem ( 1938), the de­ portant paper on higher-type recursion under the direction of Alonzo Church, velopment of the arithmetical and hyper­ theory. In 1983 he won the American in 1934. For most of his career, Kleene arithmetical hierarchies in the 1940s and Mathematical Society's Steele Prize for was a member of the mathematics fac­ 1950s, the Kleene-Posttheory of degrees his seminal 1955 papers on recursion ulty at the University of Wisconsin at of unsolvability (1954), and higher-type theory and descriptive set theory, and Madison, first as an instructor and assis­ recursion theory. which he began in the in 1990 he was awarded the National tant professor from 1935 to 1941, and late 1950s and returned to in the late Medal of Science, the nation's highest then as full professor from 1946 until his 1970s. His 1952 book Introduction to scientific honor. retirement in 1979. He was appointed Metamathematics laid the foundations Kleene had a strong interest in na­ Cyrus C. MacDuffee Professor in 1964. of the subject and inspired several gen­ ture and the environment and visited In 1941 he returned to Amherst for a erations of logicians. Beginning in the his family farm in Maine almost ev­ brief period as an associate professor. late 1940s, Kleene also worked in a sec­ ery summer. He discovered a variety of From 1942 to 1945 he served in the U.S. ond area, Brouwer's intuitionism. Using butterfly, Beloria todde ammiralis ab. Navy as a navigation instructor at the tools from recursion theory, he intro­ kleenei. He was an avid climber and, Naval Reserve's Midshipmen's School duced recursive realizability, an impor­ until well into his seventies, led the and later as a project director at the tant technique for interpreting intuition­ biannual logic picnic at Wisconsin (now Naval Research Laboratory in Wash­ istic statements. In the summer of 1951 the Kleene Memorial Logic Picnic) on ington, D.C. He achieved the rank of at the Rand Corporation, he produced a hikes up the cliffs at Devil's Lake. Steve lieutenant commander. major breakthrough in a third area when Kleene's knowledge of mushrooms was The exciting period in mathemati­ he gave an important characterization of legendary. One of my family's fondest cal logic that followed the appearance events accepted by a finite automaton. memories is of the time in the mid-1970s of Kurt Godel's completeness and in­ In addition to supervising the work when he took me and my three sons completeness theorems coincided with of thirteen Ph.D. students at Wiscon­ on an outing through our own wooded Kleene's graduate years at Princeton, sin, Kleene served two terms as chair land, collecting an impressively large where he attended GOdel's lectures at of the mathematics department and one and varied supply of tasty mushrooms. the Institute for Advanced Study. During term as chair of the numerical analy­ Although a private man, he was a skillful this period, along with Church, Godel, sis (now computer science) department. and enthusiastic teller of anecdotes. He Emil L. Post, Alan Turing, and Kleene's From 1969 to 1974 he was also dean possessed a powerful voice that always

792 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements made it possible for others to know with­ of Calabi-Yau manifolds has attracted greatly to the development of science, out seeing him whether he was in the considerable interest in quantum field as well as the deepening and uplifting of math building. In 1942 Kleene married theory. the human spirit." Nancy Elliot, who died in 1970. In 1978 One of Weil's major achievements he married Jeanne Steinmetz, who sur­ was his proof of the Riemann hypothesis vives him. He is also survived by three for the congruence zeta functions of Biographical Sketch sons and a daughter from his first mar­ algebraic function fields of one variable Andre Weil was born May 6. 1906, in riage, three stepchildren from his second over finite fields. In 1949 he raised Paris. He received his D.Sc. from the marriage, and ten grandchildren. certain conjectures about the congruence Universite de Paris in 1928. He was a H. Jerome Keisler zeta functions of algebraic varieties over professor at Aligarh Muslim University University of Wisconsin at Madison finite fields. These "Weil conjectures", in India (1930-1932) and Universite de Strasbourg (1933-1940). He was alec­ as they came to be called. grew out of turer at Haverford College and Swarth­ his deep insight into the topology of Weil Receives more College (1941-1942) and was a algebraic varieties and provided guiding Kyoto Prize professor at Universidade de Sao Paulo principles for subsequent developments ANDRE WElL of the Institute for Ad­ in Brazil (1945-1947) and atthe Univer­ in the field. The Weil conjectures were vanced Study in Princeton has received sity of Chicago (1947-1958). He became proved about twenty years ago by Pierre the 1994 Kyoto Prize in Basic Sci­ a professor at the Insitute for Advanced Deligne, who received a Fields Medal in ences. The Kyoto Prizes are interna­ Study in 1958 and assumed his present 1978. tional awards presented each year by the position of Professor Emeritus in 1976. Weil also contributed a great deal Inamori Foundation of Japan and carry Weil presented invited addresses at to the development of number theory a prize fund of 45,000,000 Japanese yen AMS meetings in New York (April through his efforts to combine that field (approximately $430.000). The prize 1944) and Chicago (February 1948). with algebraic geometry. For example, presentation ceremony will be held in He was an invited speaker at the In­ he established the number theory of al­ Kyoto in November. ternational Congress of Mathematicians gebraic groups, laying the foundation for in 1950 and in 1954. In 1979 Weil re­ the theory of modular forms. automor­ ceived the Wolf Prize, and in 1980 the phic functions. and automorphic repre­ AMS Steele Prize. He is a member of sentations. He also carried out global the Academie des Sciences (Paris) and investigations of certain functions of a foreign member of the Royal Society algebraic varieties over number fields, (London) and of the National Academy known as the Hasse-Weil zeta functions. of Sciences (U.S.). A pioneer in the development of topology, differential geometry, and com­ plex analytic geometry. Weil linked About the Kyoto Prizes these areas through his foundational The Kyoto Prizes are awarded each year work on harmonic analysis on topologi­ by the Inarnori Foundation. The founda­ cal groups. characteristic classes, Kahler tion's mission is to recognize individuals geometry, and the geometric theory of and groups worldwide who demonstrate theta functions. significant contributions to the better­ Weil was also one of the founders of ment of mankind. To further these aims, Bourbaki, formed by half a dozen French the Foundation has established the Ky­ mathematicians in the mid-1930s. To oto Prizes as an incentive for outstanding counter what they felt was a lack of achievement and creativity. To date, the Andre Wei! rigor in the mathematics of the day, the foundation has presented twenty-eight group wrote books under the pseudonym Kyoto Prizes, including one special com­ On the Work of Andre Weil of Nicolas Bourbaki. The Bourbaki tra­ memorative award to the Nobel Foun­ Beginning in the 1940s, Weil started dition of abstraction and rigor had a dation of Sweden in 1985. The fields for the rapid advance of algebraic geometry great influence over the years, though the Kyoto Prizes for 1994 are advanced and number theory by laying the founda­ today its impact has lessened. technology: biotechnologies (including tions for abstract algebraic geometry and A statement from the Inamori Foun­ medical technologies); basic sciences: the modern theory of abelian varieties. dation says: "The results achieved and mathematical sciences; and creative arts His work on algebraic curves has influ­ problems raised by Dr. Weil through and moral sciences: theater, cinema. In enced a wide variety of areas, including his deep understanding of and sharp addition to the award to Weil, the Ky­ some outside of mathematics, such as insight into mathematical sciences in oto Prize in advanced technology was elementary particle physics and string general will continue to have immea­ awarded to Paul Christian Lauterbur. a theory. Recently, the mirror symmetry surable influence on the development of chemist at the University of Illinois, and in three-dimensional algebraic geometry mathematical sciences. and to contribute the prize in creative arts and moral sci-

SEPTEMBER 1994. VOLUME 41. NUMBER 7 793 ...... ------·························································································-·······························-···········································... •·····•··•·· News and Announcements

ences went to the Japanese film director or institutions. The Crafoord Prize is lying compact smooth four-dimensional Akira Kurosawa. awarded to mathematicians every six manifold. The intersection form of a 4- The Inamori Foundation was estab­ years. Previous winners in mathemat­ manifold is an integral unimodular bilin­ lished in 1984 through a personal do­ ics are: Vladimir I. Arnold and Louis ear symmetric form which algebraically nation by Kazuo Inamori, the founder Nirenberg in 1982, and Pierre Deligne reflects how pairs of two-dimensional of the Kyocera Corporation, the world's and Alexandre Grothendick in 1988. submanifolds intersect. Two years ear­ leading producer of advanced ceram­ This year the Crafoord Prize amounts lier Michael Freedman had showed that ics. Kyocera employs 26,000 people in to approximately $300,000 and is di­ any integral unimodular bilinear sym­ thirty-five nations and recorded fiscal vided equally between the prizewinners. metric form can be realized as the inter­ 1994 sales of $4.2 billion. The prizes will be awarded at a ceremony section form of a compact topological 4- -from Inamori Foundation nel-l'S release at the Swedish Academy on September manifold. In 1982, while a second-year 28, 1994. Oxford graduate student, Simon Don­ aldson showed that if a compact simply Donaldson and Yau connected smooth 4-manifold Af has a Receive Crafoord Prize On the work of Simon Donaldson positive definite intersection form, then The 1994 Crafoord Prize has been Ronald Stem of the University of Cal­ the associated moduli of anti-self-dual awarded to SIMON K. DONALDSON of the ifornia, Irvine, prepared for the Notices connections dictates that this form be University of Oxford "for his fundamen­ the following piece on the work of Si­ diagonalizable over the integers. Thus tal investigations in four-dimensional mon Donaldson: no simply connected, compact topologi­ geometry through applications of in­ The study of manifolds is at the cal4-manifold with a nondiagonalizable stantons, in particular his discovery core of geometry and topology. The positive definite intersection form has of new differential invariants"; and to goal is to understand and classify metric a smooth structure. As a spectacular SHING-TuNG YAU of Harvard Univer­ spaces which are locally homeomorphic corollary, this result verified the exis­ sity "for his development of non-linear to Euclidean n-space. On a smooth n­ tence of an exotic smooth structure on techniques in differential geometry lead­ dimensional manifold lvfn one has the Euclidean 4-space; it is only in dimen­ ing to the solution of several outstanding further ability to differentiate continuous sion four that such perverse behavior problems." functions. These natural objects perme­ ate mathematics and science. During the can occur. Donaldson has extended this 1960s and through the 1970s the field result concerning definite forms to ar­ of topology was devoted to the study bitrary smooth 4-manifolds through a of n-manifolds for n =I 4. During that difficult and detailed study of the ori­ time their intrinsic structure and the re­ entations of these moduli spaces. In an­ lationship between smooth, topological, other direction Donaldson and Sullivan and piecewise linear (a combinatorial have extended these results for definite intermediary) manifolds became better forms to Lipschitz and quasi-conformal understood. four-dimensional manifolds. In 1982 Simon Donaldson pioneered Subsequently, through a study of the application of Yang-Mills theory to the compactification of these anti-self­ 4-manifold topology, and since then his dual moduli spaces, Simon Donaldson ideas have grown to occupy an im­ extended his results for definite inter­ portant place in current mathematical section forms to indefinite forms. In research. As a result of Simon Donald­ particular he showed that if the inter­ son's work over the past twelve years, section form of a smooth manifold is smooth 4-manifolds have become better an even form with nontrivial negative understood; unexpected and mysterious signature, then the number of nontrivial phenomena about the geometry of four­ positive eigenvalues of this form (b+) is Simon Donaldson dimensions have been discovered. These at least three. The Anna-Greta and Holger Cra­ ideas have revolutionized the study of Mathematicians had earlier been foord Fund was established in 1980 by a manifolds and have fixed the direction working on the problem of explicitly donation to the Royal Swedish Academy of research in geometry and topology. finding all the anti-self-dual connections of Sciences from Anna-Greta and Hol­ Donaldson's first major work in­ on Euclidean 4-space. In a very elegant ger Crafoord. The purpose of the fund troduced the metric-dependent moduli and decisive piece of work Simon Don­ is to promote basic scientific research in space of anti-self-dual connections as a aldson related this problem to algebraic Sweden and in other parts of the world. topological tool to study smooth four­ vector bundles on the complex projec­ The fund supports research through the dimensional manifolds. He showed that tive plane (which can be viewed as a international Crafoord Prize, awarded the existence of these particular solu­ compactification of Euclidean 4-space). annually to outstanding scientists, and tions to the Yang-Mills equations con­ Donaldson then used related ideas to through research grants to individuals strains the intersection form of the under- study magnetic monopoles. In particular

794 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements he provided solutions to Nahm's equa­ one smooth structure. and geometry of smooth 4-manifolds. tions and an explicit parameterization of Donaldson then introduced new met­ Simon K. Donaldson was born in the solutions to the Bogomolny equa­ ric independent invariants for smooth Cambridge, UK, in 1957. He was Junior tions over Euclidean 3-space. He proved four-dimensional manifolds with odd Research Fellow at All Soul's College in the remarkable result that the parameter b+ > 1 which have proven immensely Oxford (1983-1985) and visiting mem­ space of monopoles of magnetic charge useful in distinguishing smooth 4-mani­ ber at the Institute for Advanced Study in k can be identified with the space of folds which are topologically equivalent. Princeton (1983-1985). Since 1985 he rational functions of a complex variable These invariants serve as the focal point has been Wallis Professor of Mathemat­ of degree k. for much current activity in differential ics at Oxford University. He received Then, in a very influential and pre­ and algebraic geometry as well as topol­ the Fields Medal in 1986 and is a Fellow scient piece of work, Donaldson showed ogy. Roughly, these invariants encode of the Royal Society (of London). that for arbitrary algebraic surfaces these the differentiable structure of a smooth moduli of anti-self-dual connections four-dimensional manifold in the alge­ have a purely algebraic description. In braic topology of the moduli spaces particular, he showed that there is a of anti-self-dual connections. Donald­ one-to-one correspondence between sta­ son first proved a vanishing theorem for ble vector bundles and irreducible anti­ these invariants which stated that if a self-dual connections on an algebraic smooth four-dimensional manifold was surface. This built upon Donaldson's the connected sum of two smooth man­ earlier analytical proof of a theorem of ifolds, each with b+ > 0, then these in­ Narasimhan and Seshadri. These results variants vanished. Then, using his earlier place the study of anti-self-dual connec­ work relating anti-self-dual connections tions within the framework of algebraic with stable vector bundles, he showed geometry and are a key computational that these invariants were nontrivial for tool for the invariants that Donaldson complex surfaces. This immediately im­ will later define. plies that a complex surface with even Since this early work, Donaldson intersection forms doesn't decompose has continued to demonstrate how these as a connected sum and provides rich moduli spaces of anti-self-dual connec­ families of manifolds with many smooth tions can be used in a large variety structures. Shing-Tung Yau of settings to further understand the During this period it was becom­ topology and geometry of smooth four­ ing clearer to Donaldson that the study dimensional manifolds. of symplectic 4-manifolds would play On the Work of Shing-Tung Yau Donaldson has shown that the h­ a role central to the understanding of Gang Tian of the Courant Institute of cobordism theorem, a tool fundamen­ smooth 4-manifolds. This area also con­ Mathematical Sciences at New York tal to the successful study of higher­ tains many fascinating questions about University prepared for the Notices the dimensional manifolds, is false for sim­ which little is known. For example, it following piece about the work of S.-T. ply connected smooth four-dimensional was not known if there are obstructions Yau: manifolds. In dimension four this h­ to the existence of a symplectic structure Differential geometry is a new branch cobordism conjecture implies that two on an almost-complex 4-manifold. Most of geometry which was developed in simply connected smooth 4-manifolds recently, Simon Donaldson has devel­ the last century. In the beginning, one with the same intersection form are dif­ oped new obstructions to the existence worked mainly with curves, and, when feomorphic. In this fundamental work of symplectic structures on manifolds formulating their properties, one used Donaldson ingeniously conceived the of arbitrary dimension. In particular, ordinary differential equations. Modern idea of using these anti-self-dual mod­ he proves that if (V, w) is a compact differential geometry studies manifolds, uli spaces as a topological invariant of symplectic manifold with w integral or which include surfaces, and their global the underlying smooth four-dimensional rational, then the class kw is dual to a structure. Nonlinear partial differential manifold. His first invariant was defined symplectic submanifold w,, c V, for all equations emerge when one studies these for manifolds with b+ = 1. This invariant large enough k. global properties in terms of curvatures. is metric dependent; however through In 1982 Simon Donaldson began a Examples of such equations are mini­ a detailed analysis of this dependency, rich geometrical journey that is leading mal surfaces equations and Yang-Mills Donaldson was able to show that these us to an exciting conclusion to this cen­ equations. invariants smoothly distinguished the tury. He has created an entirely new and As a result of Yau's work over the Doglachev surface from the rational sur­ exciting area of research through which past twenty years. the role and un­ face with the same intersection form. much of mathematics passes and which derstanding of basic partial differential This provided the first examples of sim­ continues to yield mysterious and unex­ equations in geometry has changed and ply connected manifolds with more than pected phenomena about the topology expanded enormously within the field of

SEPTEMBER 1994. VOLUME 41, NUMBER 7 795 News and Announcements mathematics. His work has had, and will solved by Yau and R. Schoen. The proof that there is a one-to-one correspondence continue to have. a great impact on areas required a deep analysis of how mini­ between stable vector bundles and irre­ of mathematics and physics as diverse as mal surfaces behave in space-time, and ducible Yang-Mills-Hermitian metrics topology. algebraic geometry, represen­ also has consequences for our under­ on a compact Kahler manifold. Yau and tation theory, and general relativity as standing of how black holes form. The Uhlenbeck solved this conjecture by de­ well as differential geometry and partial proof of the Positive Mass Conjecture riving powerful estimates for perturbed differential equations. and the higher-dimensional generaliza­ Yang-Mills-Hermitian equations. They One of Yau's most important works tion leads to demonstration of the sta­ used their solution to give a characteri­ is his solution for the Calabi conjec­ bility of Minkowski space-time. Later, zation for flat bundles in terms of Chern ture. In 1954, E. Calabi conjectured that, Yau and Schoen generalized their proof numbers. given a compact Kahler manifold and a to study manifolds of positive scalar I will discuss briefly three other im­ fixed Kahler class on it, any (L 1)-form curvature in higher dimensions. portant works. Along with S. Y. Cheng, representing the first Chern class is the The Plateau problem asks if a Jor­ Yau solved the Minkowski problem on Ricci curvature form of a Kahler metric dan curve in a Riemannian manifold whether a positive function on sn can be within the fixed Kahler class. In 1976 bounds an area-minimizing surface. A the Gauss curvature of an n-dimensional Yau used his estimates for certain com­ generalized solution to this problem was convex hypersurface. The case of n = 2 plex Monge-Ampere equations to solve obtained by Douglas and Rado indepen­ was solved by Nirenberg in 1950. P. this conjecture. He also proved existence dently for Euclidean spaces in the 1930s, Li and Yau derived sharp estimates on of Kahler-Einstein metrics on Kahler and by C. Morrey for general manifolds eigenvalues and heat kernels on a mani­ manifolds with negative first Chern in 1948. Osserman, Hildebrandt, Gul­ fold with Ricci curvature bounded from class. These results represent a major liver, etc., had shown by 1970 that Dou­ below. More recently, Yau and Jost ap­ step forward in the Uniformization Prob­ glas's solution is a smooth immersed plied harmonic maps and a nonlinear lem for complex manifolds. A striking surface if the boundary curve lies in a version of the Matsushima vanishing consequence of these results is that any convex surface in a three-dimensional theorem to rigidity problem for locally compact Kahler manifold with vanish­ manifold. The question was left open symmetric spaces. The same result was ing first Chern class admits a Ricci-flat as to whether Douglas's surface was independently obtained by Mok, Siu, Kahler metric; for example, a so-called actually embedded. Around 1980 Yau and Yeung. K3 surface has a Ricci-flat Kahler met­ and Meeks solved this problem. They Shing-Tung Yau was born in Guan­ ric. Ricci-flat Kahler manifolds with applied their solution to the topology dong in southern China in 1949. He finite fundamental group, now called of three-dimensional manifolds. They studied with Shiing-Shen Chern at the Calabi-Yau spaces, are widely studied by proved an equivariant version of Dehn's University of California at Berkeley and mathematical physicists in connection lemma for 3-manifolds, which is part of received his Ph.D. there in 1971. He with string theory. Other applications the solution for the Smith conjecture on received his D.Sc. from the Chinese include the Miyaoka-Yau inequality be­ group action on 8 3• Meeks, Simon, and University of Hong Kong in 1980. Dur­ tween Chern numbers, uniqueness of the Yau also generalized the work to em­ ing 1971-1972 and 1979-1980 he was Kahler structure on a complex projec­ bedded spheres and surfaces of higher a member of the Institute for Advanced tive space, numerical characterization of genus. In particular, they solved the fa­ Study in Princeton and was a professor quotient of complex balls by discrete mous problem that the universal cover there from 1980 to 1984. He was an as­ groups, characterization of locally sym­ of an irreducible 3-manifold is still ir­ sistant professor at the State University metric spaces, and surjectivity of the reducible. The techniques of minimal of New York at Stony Brook from 1972 period map for K3 surfaces. With his surfaces have since become a major tool to 1973. He was an associate professor collaborators, Yau also generalized Cal­ in 3-manifold theory. and then a professor at Stanford Univer­ abi's conjecture to noncompact Kahler The Yang-Mills equation, which ex­ sity (1974-1979) and a professor at the manifolds. plains the behavior of elementary parti­ University of California at San Diego Traditionally. minimal surfaces were cles, was introduced by Yang and Mills (1984-1987). He has been a professor studied by geometers for their own in­ in the 1950s. In four dimensions, anti­ at Harvard University since 1988. Yau trinsic beauty. Yau was the first to pio­ self-dual connections are special solu­ received the Fields Medal in 1982. He neer the application of minimal surfaces tions of the Yang-Mills equation. These was elected to the National Academy of to questions in geometry, mathematical special solutions were used in S. Don­ Sciences in 1993. physics, and topology. aldson's fundamental theory of the dif­ -R. Stern. G. Tian, and Royal Swedish Einstein's theory of general relativity ferential topology of 4-manifolds. In Academy news release includes the Positive Mass Conjecture. 1985 Donaldson proved that there is which says that the total energy, in­ a one-to-one correspondence between Manin Receives cluding contributions from gravity and stable vector bundles and irreducible Nemmers Prize matter, is positive in an isolated phys­ anti-self-dual connections on an alge­ Northwestern University has announced ical system. This fundamental question braic surface. In higher dimensions, the that YuRI MANIN of the Max Planck in classical general relativity was re- Hitchin-Kobayashi conjecture predicted Institute for Mathematics has been se-

796 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements lected as the first recipient of the Fred­ ern algebraic geometry. In 1971 Manin, Academy of Sciences. and a member of eric Esser Nemmers' Prize for distin­ jointly with Iskovskih, found counterex­ the Academia Europaea. guished achievement in mathematics. amples to the longstanding conjecture of -.from North\\'estern Vnirersity Manin will receive the $100,000 prize Luroth concerning rational uniformiza­ (/ /1/1(}/1/l('£'111£'/lf and deliver the inaugural Nemmers' lec­ tion of algebraic loci. ture at Northwestern in the spring of Manin's work in number theory, es­ 1995. pecially in p-adic analysis and the theory Gelfand Receives The Frederic Nemmers' Prize in of modular forms, drew intuition from MacArthur Fellowship mathematics and the Erwin Plein Nem­ geometry and used "continuous" tech­ I. M. GELFAND of Rutgers University mers· Prize in economics were made niques to attack fundamental arithmetic has been awarded a MacArthur Fel­ possible through bequests to Northwest­ problems. His study of the arithmetic of lowship from the John T. and Cather­ ern University from the late Erwin E. cubic hypersurfaces set the standard in ine D. MacArthur Foundation. Com­ Nemmers, a former member of the the field for two decades. monly known as ""genius awards''. the Northwestern faculty, and his brother. Among the many contributions of MacArthur Fellowships are no-strings­ the late Frederic E. Nemmers. The math­ Manin to mathematical physics is the attached awards that are intended to ematics prize will be awarded every two classification of instantons. the solu­ foster creativity in a wide range of hu­ years. Nominations for the prize were tions of field equations describing mi­ man endeavors. The award to Gelfand is widely solicited and were reviewed by croscopic quantum fluctuations of the $375,000. to be paid over five years. a selection committee. which recom­ vacuum. Done jointly with Drinfel' d. mended the recipient to the provost of Manin 's 1978 work on this problem, be­ Northwestern. The selection committee sides being of fundamental importance consisted of Martin Kruskal of Rutgers in physics. laid the foundations for the University. Mark Mahowald of North­ recent progress in the purely mathe­ western University, and John Milnor of matical study of 4-manifolds. He has the State University of New York at also done important work on Hamilto­ Stony Brook. nian structure of completely integrable wave equations, construction of algebra­ geometric solutions ofYang-Mills-Dirac equations, and string theory.

Biographical Sketch Yuri Manin was born in Simferopol, Russia, in 1937. He received his bach­ elor's degree in 1958 and his doctorate in 1960 from Moscow State University. From 1960 to 1991 he was a member of the Steklov Mathematics Institute in Moscow, and from 1965 to 1991 he held I.M. Gelfand the chair in algebra at Moscow State University. During 1991-1993, he held Gelfand is a professor in the de­ visiting positions at Harvard University, partments of mathematics and biology Massachusetts Institute of Technology, at the Center for Mathematics. Science. and Columbia University. In 1993 he and Computer Education and the In­ became a member of the Max Planck In­ stitute for Discrete Mathematics and stitute for Mathematics in Bonn. Manin Computer Science at Rutgers Univer­ YuriManin is the author or coauthor of ten mono­ sity. A renowned mathematician. he has graphs and more than 150 papers. He also made important contributions to bi­ delivered invited addresses at the Inter­ ology. He has written more than 500 Oil the Work ofYuri Mallill national Congresses of Mathematicians papers in mathematics. applied mathe­ Manin's work spans such diverse in 1966, 1970, 1978 (when he gave a ple­ matics, and biology. In 1992 he founded branches of mathematics as algebraic nary address), 1986, and 1990. He was the Gelfand Outreach Program. which geometry, number theory. and mathe­ awarded the Brouwer Gold Medal for fosters mathematical excellence in high matical physics. His 1963 proof of the work in number theory and the Lenin school students. Gelfand emigrated to Mordell conjecture for function fields Prize for work in algebraic geometry. the U.S. from Russia in 1990. While in introduced what is now known as the He is a corresponding member of the Russia, in addition to his foundational Gauss-Manin connection, which has in Russian Academy of Sciences, a for­ contributions to mathematics research, turn become an important tool in mod- eign member of the Netherlands Royal he also conducted a correspondence

SEPTEMBER 1994, VOLUME 41. NUMBER 7 797 ...... News and Announcements school in mathematics, which helped scott High School, Swampscott, Mas­ Army Research Office, the Office of to bring rich mathematical experiences sachusetts; STEPHENS. WANG, Illinois Naval Research, Microsoft Corporation, to students all over the Soviet Union. Mathematics and Science Academy, Au­ and the Matilda R. Wilson Fund. The correspondence school is the model rora, Illinois; and JoNATHAN WEIN­ -From IMO News Release for the Gelfand Outreach Program. STEIN, Lexington High School, Lex­ Born September 2, 1913, in Rus­ ington, Massachusetts. sia, Gelfand received his Ph.D. in 1935 Here is a representative question NSF Awards and his D.Sc. in 1940 from Moscow appearing on this year's IMO: Show Mathematical Sciences State University. He was a professor at that there exists a set A of positive Postdoctoral Research the Academy of Sciences of the USSR integers with the following property: Fellowships (1935-1941) and at Moscow State Uni­ For any infinite set S of primes there The Division of Mathematical Sciences versity (1941-1990). He taught at Har­ exist two positive integers m in A and (DMS) of the National Science Founda­ vard University (1989-1990) and at the n not in A each of which is a product tion (NSF) has awarded Mathematical Massachusetts Institute of Technology of k distinct elements of S for some k Sciences Postdoctoral Research Fellow­ (1990), and has been a Distinguished greater than 1. ships to thirty-nine recent recipients of Visiting Professor at Rutgers since 1990. Prior to the competition, the U.S. stu­ doctoral degrees. -from MacArthur Foundation dents participated in a month-long sum­ Awards are made to U.S. citizens, news release mer program at the U.S. Naval Academy nationals, or permanent residents based under the direction of professors Anne on their demonstrated ability and on the National Academy Hudson, Titu Andreescu, and Paul Zeitz. significance of career improvement the of Sciences Elections The U.S. team was chosen on the basis of fellowship would potentially provide. In April the National Academy of Sci­ performance in the Twenty-third Annual The program is designed to allow recip­ ences announced the election of sixty United States of America Mathematical ients to choose research environments new members and fifteen foreign asso­ Olympiad (USAMO) held earlier this at fellowship institutions that will have ciates. A number of mathematical scien­ year. The winners of the 1994 USAMO maximal impact on their future scientific tists were among those elected: SPENCER were honored on June 6 at the National development. J. BLOCH, University of Chicago; ROGER Academy of Sciences in Washington, A panel of mathematical scientists, E. HOWE, Yale University; RUDOLF E. DC. chosen by the AMS, the Institute of KALMAN, University of Florida; and The Mathematical Olympiad is a Mathematical Statistics, and the Society ANDREW J. MAmA, Princeton Univer­ program of the Mathematical Associa­ for Industrial and Applied Mathemat­ sity. Elected as a foreign associate was tion of America. It is co-sponsored by ics, evaluated 226 applications. Final SERGEI P. NOVIKOV, L. D. Landau In­ nine national organizations in the math­ selections were made by NSF. stitute of Theoretical Physics in Russia. ematical sciences, including the AMS. The stipend of $66,000 provides sup­ -from NAS news release Financial support is provided by the port for two 9-month academic years and

U.S. Team Places First in International Olympiad The U.S. team for the International Mathematical Olympiad (IMO) placed first in the competition, held in July in Hong Kong. To top it off, the U.S. team achieved the first perfect score in the thirty-five year history of the IMO. Each of the six U.S. team members scored the maximum number of points on the nine­ hour competition, and each received a gold medal. Sixty-nine countries sent teams to this year's IMO. The top five teams are, in order: the U.S., China, Russia, Bulgaria, and Hungary. The members of the U.S. team are: JEREMY BEM, Ithaca High School, Ithaca, New York; ALEKSANDR L. KHAZ­ ANOV, Stuyvesant High School, New York, New York; JACOB A. LuRIE, Mont­ The USAMO winners. with AMS President Ronald L. Graham. at the National Academy of Sciences. From left to right are: Christopher Chang, Jonathan Weinstein, Jacob Rasmussen, gomery Blair High School, Silver Spring, Noam Shazeer, Graham. Aleksandr Khazanov, Stephen Wang, Jeremy Bern, and Jacob Lurie. Maryland; NOAM M. SHAZEER, Swamp- Weinstein, Shazeer, Khazanov, Wang. Bern, and Lurie fmmed the team that competed in the IMO.

798 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements three 2-month summers. Each awardee nia, spectral and scattering theory for stitute for Mathematics and its Appli­ may choose between two options for re­ the Laplacian on manifolds with cylin­ cations at University of Minnesota, an ceiving the academic year support: full­ drical ends; DAVID EDWARDS (Califor­ inverse problem in diffuse tomography; time support for any eighteen academic­ nia Institute of Technology), North­ DANIEL POLLACK (Massachusetts Insti­ year months in a three-year period, in western University, in extensions of tute of Technology). Massachusetts In­ intervals not shorter than three consec­ Cohen's general model for nonlinear stitute of Technology, constant scalar utive months (the Research Fellowship diffusion; SAMUEL ELDERSVELD (Stan­ curvature metrics with isolated singu­ Option); or a combination of full-time ford University), University of Califor­ larities; BJORN PooNEN (University of and half-time support over a period of nia at San Diego, on numerical methods California at Berkeley). Mathematical three academic years, usually one aca­ for very large-scale nonlinearly con­ Sciences Research Institute and Prince­ demic year full-time and two academic strained optimization; PAVEL ETINGOF ton University; Galois representations years half-time (the Research Instructor­ (Yale University). Harvard University, associated with Tate modules of Drin­ ship Option). Partial support for some of representation theory of affine Lie al­ feld modules over global function fields; the awards was provided by the Division gebras and quantum groups and re­ ENPING QIAN (Florida State University), of Computer and Computation Research lated problems of quantum field the­ Massachusetts Institute of Technology. and the Division of Astronomy at the ory and statistical mechanics; BENSON models of galaxies and potential den­ NSF. FARB (Princeton University), University sity sets of three-dimensional systems; For each fellowship recipient, the of California at Berkeley and the Uni­ JIE QING (University of California at following lists the doctoral institution versity of Maryland, pure mathematics; Los Angeles). Columbia University, an­ (in parentheses). the institution at which MARK HovEY (Massachusetts Institute alytical aspects of harmonic maps in the recipient will use the fellowship, and of Technology), Massachusetts Insti­ the study of geometric structure of his or her area of research. tute of Technology, algebraic topology, manifolds; TAL RABIN (Hebrew Univer­ JAMES AKAO (University of Cali­ specifically chromatic filtration in stable sity), Massachusetts Institute of Tech­ fornia at Berkeley). Institute for Ad­ homotopy theory; LIZHEN JI (North­ nology, practical distributed algorithms vanced Study. fast computational meth­ western University), Institute for Ad­ and protocols for resilient and secure ods for fluid dynamics and for statistical vanced Study and Princeton University, computations; RACHEL ROBERTS (Cor­ mechanics; DAVID AucKLY (University spectral degeneration of hyperbolic Rie­ nell University), University of Texas at of Michigan), University of Califor­ mann surfaces; DAVID KARGER (Stan­ Austin. pure mathematics; LoUis Rossi nia at Berkeley. low-dimensional ge­ ford University), Princeton University, (University of Arizona). Northwestern ometry; ERIC BABSON (Massachusetts analysis of algorithms and combinato­ University, vortex monopole and dipole Institute of Technology), Cornell Uni­ rial optimization; NADINE KoWALSKY interactions; MARK SHIMOZONO (Uni­ versity, combinatorial exterior vector (University of Chicago), Institute for versity of California at San Diego), spaces; SEAN BATES (University of Cal­ Advanced Study and Stanford Univer­ Massachusetts Institute of Technology, ifornia at Berkeley). Stanford Univer­ sity, actions of noncompact simple al­ Specht modules for arbitrary diagrams; sity, symplectic end invariants and C­ gebraic groups on noncompact Lorentz RICHARD STONG (Harvard University). symplectic topology; JONATHAN BECK manifolds; YuAN MA (Massachusetts In­ University of California at San Diego, (Massachusetts Institute ofTechnology). stitute of Technology), Rutgers Uni­ geometric topology of topological four­ Harvard University. structure and rep­ versity. fault-tolerant circuit design and manifolds; YOULANG TIAN (University resentation theory of quantum affine hypercubic sorting networks; RICHARD of New Mexico), Harvard University algebras; MARTIN BETZ (Stanford Uni­ McLAUGHLIN (Princeton University), and Courant Institute of Mathemat­ versity). University of California at University of Utah, turbulent transport, ical Sciences. topological aspects of Berkeley, Floer cohomology operations specifically effects of randomness in the moduli spaces of instantons-the and Donaldson invariants which arise passive and active scalars; CHRISTO­ Atiyah-Jones conjecture; SusAN ToL­ via the topology of stratified infinite­ PHER MILLER (University of Illinois MAN (Harvard University), Massachu­ dimensional manifolds; SARA BILLEY at Urbana-Champaign), University of setts Institute of Technology, pure math­ (University of California at San Diego), Illinois at Chicago. pure mathemat­ ematics; TATIANA ToRo (Stanford Uni­ Massachusetts Institute of Technology, ics; PETER OzsvATH (Princeton Uni­ versity), University of Chicago. the re­ Schubert polynomials and other bases versity). California Institute of Tech­ lationship between geometric measure related to diagonal harmonic spaces; nology, pure mathematics; JAMES NAGY theory and partial differential equa­ JARED BRONSKI (Princeton University), (North Carolina State University), Uni­ tions; ORLI WAARTS (Stanford Univer­ Institute for Mathematics and its Ap­ versity of Maryland. fast numerical sity), University of California at Berke­ plications at the University of Min­ solution of structured ill-posed prob­ ley, development of mathematical tools nesota, phenomenon of localization in lems in engineering; JoHN PALMIERI for online algorithms and distributed the presence of nonlinearity; TANYA (Massachusetts Institute ofTechnology), computation, with applications in ap­ CHRISTIANSEN (Massachusetts Institute Massachusetts Institute of Technology, plied mathematics and statistics; WAYNE of Technology). Johns Hopkins Univer­ algebraic topology; SARAH PATCH (Uni­ WHEELER (University of Chicago), Uni­ sity and the University of Pennsylva- versity of California at Berkeley), In- versity of Georgia. varieties and local-

SEPTEMBER 1994, VOLUME 41, NUMBER 7 799 ... -...... -...... _...... -...... - ... -...... -...... -...... -...... News and Announcements

ization in the cohomology of groups; and program director at the National Science tics, and the history of mathematics. JIAN ZHANG (Massachusetts Institute of Foundation (NSF). While at the AMS, -from Tidbits electronic newsletter Technology), University of Washing­ Bradley served as managing editor of ton, noncommutative projective geome­ the Notices and as director of the AMS Ferran Sunyer i Balaguer try and graded regular algebras. Washington Office. Prize -from DMS announcement Bradley has joined the staff of the Each year the Institut d'Estudis Cata­ Division of Elementary, Secondary, and lans awards an international mathemat­ Wan Leaving NSF Informal Education in the NSF's Educa­ ical research prize. The prize honors for UC Irvine tion and Human Resources directorate, the memory of Ferran Sunyer i Bala­ Frederic Y.-M. Wan has accepted an ap­ where he will be involved with cur­ guer (1912-1967), a self-taught Catalan pointment as vice chancellor of research ricular issues and teacher enhancement mathematician who, in spite of a serious and dean of graduate studies at the Uni­ projects. These projects focus on im­ physical disability, was very active in re­ versity of California at Irvine. Currently, proving the background of teachers in search in classical analysis and acquired Wan is director of the Division of Mathe­ a particular subject area-mathematics, international recognition. matical Sciences at the National Science in this case-while trying to bring in The competition is open to all math­ Foundation and professor of mathemat­ pedagogical issues, such as those raised ematicians. The prize is awarded for a ics at the University of Washington in in the Standards of the National Council mathematical monograph of an exposi­ Seattle. of Teachers of Mathematics. tory nature presenting the latest devel­ In his new position, Wan will be re­ "I think that helping the teachers is opments in an active area of research sponsible for research policy, allocation clearly one of the most important factors in mathematics in which the applicant of campus research and graduate fel­ in improving mathematics education," has made important contributions. The lowship funds, and contracts and grants Bradley notes. He says he also plans prize of 12,000 ECU is provided by the development at U.C. Irvine, which re­ to work on ways to increase the in­ Ferran Sunyer i Balaguer Foundation. ceives more that $100 million annually volvement of mathematicians in K-12 The winning monograph will be pub­ in outside research support. education. lished in Birkhauser's series, ''Progress Born in Shanghai, China, Wan grew From 1989 until he joined the AMS in Mathematics", subject to the usual up in Saigon (now Ho Chi Minh City), staff in 1991, Bradley served a tour regulations concerning copyright and Los Angeles, and Seattle. He received of duty at the NSF as program director author's rights. his bachelor's, master's, and doctoral for the calculus curriculum development On the committee choosing the win­ degrees in mathematics at the Mas­ program. Before that, he was the head ner of the prize are Gerhard Frey (Uni­ sachusetts Institute of Technology. In of the mathematics department at the versitat Essen), Joan Girbau (Universitat addition to his tenure as director of the University of Tennessee, Knoxville. Autonoma de Barcelona), Paul Malli­ DMS, Wan served as a program officer Bradley can be reached at: Division avin (Universite de Paris VI), Joseph for the Division's Applied Mathematics of Elementary, Secondary, and Informal Oesterle (Universite de Paris VI), and Program during 1986-1987. Education, Room 855, National Sci­ Alan Weinstein (University of California Wan is an expert in the theory of ence Foundation, 4201 Wilson Boule­ at Berkeley). plates and shells, an area of struc­ vard, Arlington, VA 22230; telephone Monographs, preferably typeset in tural mechanics. Among the many ap­ 703-306-1620. l.EX. should be sent to: Insitut d'Estudis plications of the theory is his design Catalans, Carme, 47, 08001 Barcelona, analysis of the corrugated Tupperware Tucker Appointed Spain; e-mail icrmO@cc. uab. es. The Astroflex Seal. His other research in­ BMS Director monographs must arrive before Jan­ terests include mathematical problems John Tucker has been appointed direc­ uary 15, 1995. The submission of a in resources management, urban land tor of the Board on Mathematical Sci­ monograph implies the acceptance of economics, and neurons under random ences of the National Research Council the conditions explained above. excitations. (NRC). Tucker joined the NRC staff in The prizewinner will be announced The author of over one hundred 1989 as a program officer. Since 1993 he in Barcelona in April1995. research papers, Wan has also written has been a senior program officer, pri­ -from call for nominations two graduate textbooks. He is a founding marily responsible for the programs of for Ferran Sunyer i Balaguer Prize member and former president of the the Committee on Applied and Theoreti­ Canadian Applied Mathematics Society, cal Statistics. Tuckerreceivedhis doctor­ New MAA Report which awarded Wan the first Arthur ate in mathematics from George Wash­ on Preparation Beaumont Distinguished Service Award ington University in 1980 and taught at of College Teachers in 1991. -from U .. C. bTine news release Mary Washington College and Virginia The Mathematical Association of Amer­ Commonwealth University before join­ ica (MAA) has released a new report Bradley Joins NSF ing the BMS staff. His research interests called You're the Profe sso1~ What Next?. John S. Bradley, formerly associate ex­ include nonlinear dynamics, complex­ The report is a compendium of infor­ ecutive director of the AMS, is now a ity, functional analysis, applied statis- mation about the ins and outs, the trials

800 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... - ...... ,.,._§,.~..,•• Ill!_II"" ... ;l' ...."il""-m.·-. _....,;;;;; R 7iljii-.Bilt&••· ;;.,..,.:;::...,..,...,.,.~,,.....,;;;._.r.=.··n=~···WiJ'"ililililil!lilllli IUIM ...... News and Announcements and tribulations, and the responsibilities state of the profession more generally. over the last few years. The articles are and obligations of teaching mathematics You're the Professor contains practical broken into three sections, on graduate at the collegiate level. New doctorates information as well as theoretical per­ preparation and career issues, underrep­ will find a great deal of useful infor­ spectives. For example, Ed Dubinsky of resented groups, and education reform. mation here, as will mathematics de­ Purdue University contributed a paper The amount of material may border partments concerned about adequately on pedagogical change. After all the on the overwhelming. Nevertheless, the preparing their new doctorates for ca­ hoopla over calculus, Dubinsky argues, committee has provided a valuable ser­ reers in teaching. The report is fairly little in the content of the course has vice by collecting together articles by bulging with information, data, and ref­ changed, and most people have come some of the leaders in the community erences;. suggestions, tips, and advice; around to the view that what's needed is who have thought carefully about a wide philosophies, viewpoints, and perspec­ change in pedagogy. However, the peda­ range of educational issues. tives. Covering the gamut from algebra gogical changes, while often carried out You're the Professor, What Next?, to xenophobia, the volume may at first with the best intentions, are haphazard. Volume 35 in the "MAA Notes" se­ look daunting, but stick with it-there's "[l]n the face of all this experience, ries, is available for $24 prepaid (this a gold mine of ideas here. sincerity, dedication, and hard, creative includes shipping and handling; orders The group producing the report is the thinking about specific innovative teach­ billed with an invoice will include an ad­ Joint Committee on Preparation for Col­ ing methods ... , we are still having the ditional shipping and handling charge). lege Teaching, sponsored by the AMS, same results," Dubinsky writes. "Our Contact: Mathematical Association of the MAA, and the Society for Indus­ students are not learning mathematics America, 1529 Eighteenth Street, NW, trial and Applied Mathematics. Bettye as well as we would like them to-as Washington, DC 20036; telephone 1- Anne Case of Florida State University well as we believe it is possible for them 800-331-1MAA (331-1622); fax 202- chaired the committee and also served to do." Dubinsky makes a case for the 265-2384. as editor of the report. Through a grant way in which theoretical analysis of how -Allyn Jackson from the Department of Education, the people learn mathematics can provide a committee conducted two surveys of sound basis for pedagogical change. News from the mathematics doctoral-granting depart­ You're the Professor takes the view Mathematical Sciences Institute ments to find out, among many other that mathematics faculty should be at Cornell University, things, what kinds of programs exist for least aware of the issues confronting University of Puerto Rico, helping graduate students prepare for school mathematics. For example, the and SUNY Stony Brook future teaching responsibilities. In ad­ report includes an essay by Eleanor MSI Center for Stochastic Analysis, dition, the grant supported programs in Palais of Belmont High School. As a Cornell University, will hold a meeting eight mathematics departments around teacher "who desperately wants this re­ at the Mathematical Sciences Institute on the country that carried out activities to form movement to succeed", Palais takes January 15-17, 1995, on "Random Par­ help ease the transition from being a a critical look at some of the ideas being tial Differential Equations". The very graduate student to being a junior fac­ proposed for reforming school math­ general subject will be partial differen­ ulty member. The eight departments are ematics. She is especially concerned tial equations in which something is ran­ from University of Cincinnati, Clemson about the passivity of the current gener­ dom. Different methods of introducing University, Dartmouth College, Univer­ ation of high schoolers, who have grown the randomness lead to quite different sity of Delaware, Harvard University, up on a steady diet of TV. While enthusi­ problems. The goal of this meeting is a Oregon State University, University of astically endorsing the use of computers useful exchange of information between Tennessee, and Washington University. in the classroom, Palais cautions, "we people familiar with different ends of The report provides descriptions of must be wary that as we encourage this "elephant". these programs, written by the program greater interaction with the computer, Initial planning is underway for a directors, which could be valuable in which is clearly less passive than a two-and-a-half day workshop on "Logic providing models and ideas that are use­ student's watching a TV screen, we are and Optimization", to be held at MSI at ful to other institutions. Also provided nevertheless teaching by having students Cornell University, August 1-3, 1995. are descriptions of other programs, not watch a TV screen ... Please, educators, Suggested topics should be sent to supported by the DoEd grant, which are keep the pencil, the paper, and the mind Anil Nerode at anil@msiadmin. cit. designed to help prepare new doctorates still active. Mathematics is learned only cornell . edu. to become productive faculty members. by doing, not by watching!" -From MSI Announcemellf These include the teaching postdoctoral About half the report consists of program at St. Olaf College and a pro­ previously published articles from such News from the fessional development program for new publications as Notices, Focus, SIAM Institute for Mathematics faculty at the University of Michigan. News, UME Trends, AMATYC Review, and its Applications The report also presents a number and so on. These articles give an ex­ University of Minnesota of invited papers giving views on fac­ cellent sampling of discussion within The 1994-1995 program at the IMA will ulty development issues and about the the mathematical sciences community be Waves and Scattering. This topic

SEPTEMBER 1994, VOLUME 41, NUMBER 7 801 ...... ,------_ .. News and Announcements has acquired especially high interest in Other Fast Algorithms (Multipole, propagation in the earth. recent years, due in part to the numerous FFT) and their Use in Wave Propaga­ The winter 1995 program will focus areas ofscience in which wave propaga­ tion. The workshop will be organized by on Inverse Problems in Wave Prop­ tion and scattering theory play a central G. Beylkin, I. Daubechies, and G. Pa­ agation and will include two tutorials role: geophysics, acoustics, electromag­ panicolaou. During the last few years during January and a two-week work­ netic theory, surface waves, waves in the numerical techniques for the solu­ shop in March. Concentration during nonlinear materials, etc. Certain prob­ tion of elliptic problems, in potential spring 1995 will be on Singularities, lems which arise in these areas of ap­ theory for example, have been drasti­ Oscillations, Quasiclassical and Mul­ plication are ripe for close examination cally improved. Several fast methods tiparticle Problems, with three tutori­ by mathematicians; at the same time, have been developed which reduce the als, each paired with a workshop. the insights which have been achieved required computing time by many or­ For more information about IMA by natural scientists hold promise for ders of magnitude. The new methods activities, see the Meetings and Con­ approaching challenging mathematical include multigrid, fast Fourier trans­ ferences section of this issue of the problems. The organizing committee­ forms, multi-pole methods, and wavelet Notices or contact the IMA, (ima­ consisting of George Papanicolaou, In­ techniques. Wavelets, in particular, have staff@ima. umn. edu). Also, weekly grid Daubechies, William Symes, Jef­ recently been developed into a very use­ IMA seminar schedules with titles and frey Rauch, Bjorn Engquist, and Barry ful tool in signal processing, the solution abstracts are available on Usenet (umn. Simon-expects that "through a well­ of integral equations, etc. Wavelet tech­ math. dept and by fingering semi­ planned program of workshops and tu­ niques should be quite useful in many [email protected]). lEX files for the torials, mathematicians will come in wave propagation problems, especially Newsletter and the quarterly Update contact with a variety of problems in in inhomogeneous and nonlinear media are available via anonymous ftp (at applied science and engineering that can where special features of the solution, i.ma. umn . edu). benefit from more efficient mathemati­ such as singularities, must be tracked - IMA GJlIlOllllcernenf cal methods and a deeper mathematical efficiently. understanding." The tutorial November 9-10 and BMS Study on The fall 1994 program will in­ the workshop November 14-18 will Computational Chemistry clude three week-long workshops, each cover the subject of Waves in Random The National Research Council (NRC) preceded by a three-day tutorial. The and Other Complex Media. Organiz­ has launched a new study on mathemat­ tutorial September 7-9 and workshop ers for the workshop are R. Burridge ical research related to computational September 19-23 will be on Computa­ and G. Papanicolaou. The effects of chemistry. The NRC's Board on Mathe­ tional Wave Propagation. B. Engquist inhomogeneities on wave propagation matical Sciences and Board on Chemi­ and G. Kriegsmann will be the workshop will be studied, both theoretically and cal Sciences and Technology are jointly organizers. The topics will include many computationally. Topics include long conducting the study. The two fields general methods used for wave prob­ wave propagation in periodic and ran­ are interrelated in that many impor­ lems, such as finite differences, finite dom media; effective media theory and tant and interesting mathematical ques­ elements, spectral methods, and bound­ homogenization; nonlinear wave prop­ tions arise in computational chemistry, ary element methods. Special techniques agation; waves in strongly inhomoge­ and many crucial questions in computa­ based on asymptotic theory, such as ray­ neous media and localization; localiza­ tional chemistry need new mathematical tracing techniques and modal methods, tion-transmission transition and the approaches. The study will document will be addressed as well. Topics of in­ spectra of random operators; geomet­ progress in the collaboration between terest in connection with computational rical optics (short waves) in randomly these two areas and describe the math­ algorithms range from convergence the­ inhomogeneous media; multiple scat­ ematical challenges that could lead to ory to parallel implementation. Physical tering by discrete scatterers; transport important advances in computational boundary conditions (diffraction phe­ theory for waves in random media, chemistry. nomena) and computational boundaries including the derivation of transport The committee established to carry are of basic importance. Computational equations and the connection with ra­ out the study is chaired by Frank H. techniques for linear waves in non­ diative transport theory; nonlinearity, Stillinger of AT&T Bell Laboratories. smooth media are of particular inter­ dispersion, and randomness in long­ The charge of the committee is to "in­ est. Related areas include acoustic dis­ wave transmission; applications to opti­ vestigate and report on opportunities for cretization techniques, electromagnetic cal fibers; reflection and transmission collaborative and synergistic research asymptotics, parallel techniques for sur­ of waves by nonlinear random me­ in the mathematical sciences that can face waves, computational geometrical dia, including the competition between accelerate progress in theoretical and optics for flow acoustics, and controlled nonlinearity (focusing-defocusing) and computational chemistry and their ap­ damping of waves. randomness (localization-transport); plications, and make recommendations The tutorial October 11-13 and the and applications to radio-wave propa­ for promoting this research." In addi­ workshop October 17-21 will be on gation in the atmosphere, sound propa­ tion to writing the report, the committee the topic Wavelets, Multigrid and gation in the ocean, and seismic-wave intends to carry out activities designed

802 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______·················-·······-·············-·······················-···········-···········-····-·-·················-·········-··························································-·-···-········· News and Announcements to increase communication and collab­ and sampling of higher-dimensional ob­ University of Utah, will serve as Edi­ oration between the mathematical and jects like kinetic pathways and hyper­ tor. The Editorial Board will consist of: chemistry communities. To this end, the surfaces; practical and accurate ways of Robert Fossum, University of Illinois at committee has organized sessions for coupling electronic and conformational Urbana-Champaign; Susan Friedlander, professional society meetings. degrees of freedom; longitudinal or sta­ University of Illinois at Chicago; Steven The study is an outgrowth of an tistical analyses of families of structures, Krantz, Washington University; Susan NRC workshop, held in June 1991, that such as molecular systems; efficient lo­ Landau, University of Massachusetts at brought together chemists, biochemists, cation of points in a 3n-dimensional Amherst; Andy Magid, University of mathematicians, and computational sci­ space that complies with simple con­ Oklahoma; and Mary Beth Ruskai, Uni­ entists to examine prospects for in­ straints (such as that no two atoms versity of Massachusetts at Lowell. creased involvement of mathematical are allowed within a certain distance In order to insure a smooth transition scientists in computational chemistry. of each other); computational crystal­ in production, the November 1994 and Part of the motivation for the study, lography and the phase problem; and the December 1994 issues will be com­ says Stillinger, is "the rapid growth of chemical topology. bined into a single issue. Allyn Jackson, computational chemistry as an identi­ The committee encourages the math­ AMS Staff Writer, will serve as Interim fiable and legitimate area of research, ematical sciences community to con­ Managing Editor for the October 1994 engaging hundreds of professionals and tribute ideas and suggestions that could and the November/December 1994 is­ utilizing substantial computational re­ help the committee identify topics to sues. sources." Because there is no natural explore and insure that the study will For further information on the new boundary between theoretical and com­ be useful in stimulating fruitful col­ vision for the Notices, see the article by putational chemistry, he notes, the com­ laborations between mathematics and Hugo Rossi in the March 1994 issue, mittee will "examine the entire contin­ chemistry. Comments may be sent to: page 307. uum". The contributions of mathematics Frank H. Stillinger, AT&T Bell Labora­ -AMS to computational chemistry could have tories, 600 Mountain Avenue, Box 636, ramifications in chemistry, pharmaceuti­ Murray Hill, NJ 07974-0636; e-mail AMS Meetings cal development, and materials science. [email protected]. and Conferences Survey One of the purposes of the study -Allyn Jackson This fall the AMS Committee on Meet­ and of the discussion that the committee ings and Conferences (COM C) will con­ hopes to engender is the building of duct a survey of a segment of the mem­ bridges between different communities. bership regarding the Society's annual "It has become clear to us that substantial "New" Notices meeting which takes place in January. educational, stylistic, and cultural dis­ to Start in January 1995 The survey is to help COMC determine continuities have existed, and continue Starting with the January 1995 issue, the whether our annual meetings are ful­ to exist, between mathematics and chem­ Notices will have a new look, a new filling our members' professional and istry," Stillinger explains, "and that these style, a new and more interesting menu personal goals, and the results of the constitute barriers to effective research of articles. survey will become part of a review collaboration." There have been some The most important change will be of AMS national meetings being con­ productive collaborations-he cited as in the content, which will emphasize ducted by a subcommittee of COMC an example the recent mathematical high quality expository accounts of cur­ over the next several months. If you contributions to the understanding of rent advances in mathematics. There receive one of these surveys, we urge the buckyball (see "Mathematics and will also be news and articles on other you to complete and return it as soon the Buckyball", Fan R. K. Chung and topics of interest to the mathematical as convenient so that you will be as­ Shlomo Sternberg, American Scientist, science community, such as the profes­ sured of having a voice in how these January/February 1993). The study will sion and education. Thought-provoking important meetings are conducted in the provide a look at several such areas. opinion pieces will provide perspectives future. All ideas, suggestions, or criti­ At its meeting in March of this year, on the mathematical sciences commu­ cisms regarding the national meetings the committee came up with a prelimi­ nity today. In addition, the "new" No­ are welcomed by COMC at any time, nary list of topics. The following topics tices will feature four-color covers and and can be referred to them by send­ taken from the list give some flavor of eyecatching graphics to enhance visual ing e-mail to hhd@math. ams . org, or the kinds of things the committee will enjoyment of the magazine. surface mail to COMC, c/o AMS Meet­ be considering: numerical solution of the The editorial structure of the No­ ings and Conferences Department, Post Schrodinger equation for one atom and tices will also change. Starting with Office Box 6887, Providence, RI 02940. for many atoms; statistical descriptions the January 1995 issue, Hugo Rossi, -AMS

SEPTEMBER 1994, VOLUME 41. NUMBER 7 803 Funding Information for the Mathematical Sciences

Mathematical Sciences of Special Projects, Room 1025, Divi­ careers and provide guidance and en­ Postdoctoral Research sion of Mathematical Sciences, National couragement to young women seeking Fellowships Science Foundation, 4201 Wilson Blvd., research careers. The National Science Foundation's Arlington, VA 22230, 703-306-1870, The research proposed by program (NSF) Mathematical Sciences Postdoc­ e-mail msprf@nsf. gov (Internet) or applicants must be in a field supported toral Research Fellowship program is msprf@nsf (Bitnet); or the American by the NSF. Approximately 70 percent designed to permit recipients to choose Mathematical Society, 401-455-4105, e­ of the award period must be spent on research environments that will have mail nsfpostdocs@math. ams. org. research activities. The remaining time maximal impact on their future scientific The deadline for applications is Sat­ should be spent on teaching and other development. Awards will be made for urday, October 15, 1994. activities designed to increase the visi­ appropriate research in pure mathemat­ -NSF bility of women faculty in the sciences ics, applied mathematics and operations or engineering at either the graduate or research, and statistics at an appropriate undergraduate levels. A portion of these nonprofit United States institution. Target Dates for the NSF activites may also be directed to the The fellowships will be offered only Last year the Division of Mathematical community at large. to persons who (1) are citizens, na­ Sciences (DMS) of the National Sci­ The VPW support period may not be tionals, or lawfully admitted permanent ence Foundation established target dates less than six months or more than fifteen resident aliens of the United States as of for proposals submitted to its programs. months. The maximum award tenure of The target dates for fiscal year 1995 January 1, 1995; (2) will have earned, fifteen months may provide support for are: October 12, 1994, for algebra and by the beginning of their fellowship one academic year and two summers. number theory, classical analysis, mod­ tenure, a doctoral degree in one of the The general eligibility requirements ern analysis, and applied mathematics; mathematical sciences; (3) will have include a doctorate in a field of research and November 9, 1994, for topology held the doctorate for no more than supported by the NSF, employment in and foundations, computational mathe­ an instituion of higher education or re­ five years as of January 1, 1995; and matics, geometric analysis, and statistics (4) will not previously have held any & probability. search or in government or industry, other NSF postdoctoral fellowship. Sub­ Priority will be given to proposals and U.S. citizenship (nationals and per­ ject to the availability of funds, it is arriving on or before the target dates. manent residents are also eligible). In expected that in FY 1995 thirty to forty Proposals that miss the target dates will addition, the applicant must not have a awards will be made. The evaluation be handled as time permits. These target salaried position, or the promise of one, of applicants will be based in part on dates do not apply to the activities of the from the host institution, nor can she be ability as evidenced by past research Office of Special Projects, which already receiving funds through grants to that work and letters of recommendation, have specified target dates or deadlines. institution. likely impact on the future scientific -from DMS announcement For further information about the development of the applicant, and sci­ VPW program, contact: VPW Program entific quality of the research likely to Director, Room 907, National Science emerge. Applicants' qualifications will Visiting Professorships Foundation, 4201 Wilson Boulevard, be evaluated by a panel of mathemati­ for Women Arlington, VA 22230; e-mail vpw@nsf. cal scientists. Women, underrepresented The Visiting Professorships for Women gov; telephone 703-306-1697; fax 703- minorities, and persons with disabili­ (VPW) program of the National Sci­ 306-0468. The program announcement ties are strongly encouraged to submit ence Foundation (NSF) enables women can also be found on STIS, the NSF's applications. doctoral scientists and engineers to un­ online information system. One can log For copies of the application brochure dertake research and teaching at host in­ into STIS by using Telnet and the ad­ or further information, contact the Office stitutions where they can advance their dress st is . nsf . gov. For an informa-

804 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... -- ...... '!i-l!!il!!lllll!l!il!il!!il!~f--l!------·~·~·li--1!1!"""""'"'""""""'""'""""""'"'""""""""'"'-·----...... - ..... --. Funding Information tiona! flyer about STIS, send an e-mail mathematics and computer science pro­ to cover research expenses incurred as a message to stisfly@nsf. gov. fessors can spend a sabbatical year at the result of accepting the fellow. -NSF NSA, learning how mathematics can be For further information on the STA applied to solving problems of national Fellowship Program, contact: Janice M. NSA Grants Program significance. Applicants and their imme­ Cassidy, Japan Programs, Room 935, The Mathematical Sciences Program diate families must be U.S. citizens, and Division of International Programs, Na­ (MSP) at the National Security Agency a full security clearance is required. tional Science Foundation, 4201 Wilson (NSA) continues its efforts to fund high For further information about these Boulevard, Arlington, VA 22230; tele­ quality mathematical research in the ar­ programs, contact: Charles F. Osgood, phone 703-306-1701; fax 703-306-0476 eas of algebra. number theory, discrete NSA Mathematical Sciences Program, (or 0477). mathematics, probability, statistics, and National Security Agency, ATTN: R51A, -from STA W1/IOIIIICement cryptology. The program, which began Ft. George G. Meade, MD 20755-6000; in its present form in 1987. is currently telephone 30 1-688-0400; msp@math13. NRC Twinning Program being vigorously supported by the NSA. math. umbc. edu. For information on with Bulgaria and Romania The program provides for summer sabbaticals for the 1995-1996 year, con­ The Office for Central Europe and Eura­ salary, professional travel, graduate stu­ tact Osgood as soon as possible at the sia of the National Research Council dent support, postdoctoral support, and above address. (NRC) is accepting proposals for re­ conference support. Grant proposals sub­ -NSA search programs which link individual mitted to the program are reviewed by U.S. scientists with Bulgarian or Ro­ the NSA Mathematics Review Panel, Research Fellowships manian counterparts in fields which are which is appointed and administered by in Japan normally supported by the National Sci­ the AMS. Under the guidance of this The Science and Technology Agency ence Foundation. These '·twinning pro­ panel, the program has been particu­ (STA), an administrative organ of the grams" should have the strong support larly interested in supporting promising Japanese government, established the of the scientists' home institutions and young investigators with summer salary STA Fellowship Program in 1988. This should lead to significant publications grants. The program has also directed program offers opportunities for promis­ and long-term sustained linkages. funds to senior investigators for support ing young foreign researchers in sci­ Twinning programs require a two­ of their graduate students and to univer­ ence and technology to conduct research year commitment beginning in 1995. sity departments for support of special in national laboratories and public re­ Funding will be provided to support conferences and workshops. search corporations in Japan (univer­ travel and living expenses for research In an attempt to formalize these ob­ sities and university-affiliated institutes visits by American grantees to Bulgaria jectives, the MSP now offers funding are excluded). or Romania and for visits by their for­ in four distinct categories: the Young The program is managed by the eign counterparts to the U.S. Applicants Investigators Grant, the Standard Grant, Research Development Corporation of may also request modest funding for the Senior Investigators Grant, and the Japan (JRDC), in cooperation with the scientific supplies, computer fees, and Conferences, Workshops, and Special Japan International Science and Tech­ publication costs. Situations Grant. Grant holders and nology Exchange Center. The JRDC Applications are due October 14, graduate students should be U.S. cit­ works with the support and cooperation 1994, and applicants will be notified of i:::ens or permanent residents. of a number of organizations around the selection by mid-December 1994. There is a firm deadline of Octo­ the world, including the U.S. National For further information on the twin­ ber 15, 1994, for all proposals (except Science Foundation. ning programs. contact: Kelly Robbins, those for conferences). Funding will The fellowship tenure is six months Office for Central Europe and Eura­ commence as soon as possible after Oc­ to two years. The JRDC provides travel sia (F02014), National Research Coun­ tober 15, 1995. Conference proposals support to Japan, a monthly living al­ cil, 2101 Constitution Avenue, NW, are accepted at any time. Allow eight lowance, a family allowance, an initial Washington, DC 20418, ATTN: Twin­ months for the review, negotiations, and settling-in allowance, housing, medical ning Program; telephone 202-334-2644; funding. insurance, and support for travel within fax 202-334-2614; e-mail krobbins@ The NSA has another related pro­ Japan during the fellowship. In addition, nas. edu. gram, the Sabbatical Program, whereby funds are paid to the host institution -From NRC Announcemellf

SEPTEMBER 1994. VOLUME 41, NUMBER 7 805 For Your Information

Department of Education As important as these topics may be (and there is a wide Launches Algebra Initiative range of opinion about how important they actually are), most AI Cuoco of what is in precollege algebra courses is clearly preparation for calculus. Very little of the content and almost none of the Education Development Center techniques and approaches can be considered preparation for and what most mathematicians consider algebra. Carole B. Lacampagne As a result, many college students lack the experiential U.S. Department of Education base to make sense out of linear and abstract algebra. Even The U.S. Department of Education's Office of Research has students who do well in such courses often see them as launched an Algebra Initiative in an attempt to establish a abstract intellectual games that have very little connection to coherent approach to algebra education in grades K-16. The the algebra they took in high school, to other mathematics, or framework for the initiative states: to fields outside mathematics. Many linear and abstract algebra courses make little attempt to connect up with students' prior Algebra is central to continued learning in mathemat­ experiences, interests, or learning styles. ics. The position of the National Council of Teachers of But the problem goes beyond the mathematical preparation Mathematics (NCTM) and of the ensuing reform in math­ of students who intend to go to college: Algebraic thinking ematics recognizes the need for restructuring algebra to is becoming an important skill for many people who never make it part of the curriculum for all students. More­ get to linear and abstract algebra. High school graduates over, reform is just under way in college curriculum and who enter the technical workforce, consumers who interact teaching of mathematics, including algebra. However, with electronic media and the Internet, and people who there is no coordinating mechanism to link all the groups work in business all find themselves needing to reason about concerned with the content, teaching and learning, and calculations in abstract symbol systems. Some people are able research in algebra. It is the aim of the proposed Algebra to develop such skills on the fly, but many more cannot. Initiative to provide this coordinating mechanism. As the need to use algebraic reasoning becomes more The purpose of this article is to describe the initiative as widespread, mathematics teachers at all levels need prepara­ well as some current efforts in algebra curriculum reform. tion in how to develop algebraic habits of mind in settings outside formal algebra courses. This is especially true in The Need for the Algebra Initiative precollege education, where there is a growing movement to There are currently two meanings attached to "algebra" in eliminate first-year algebra as a course and to spread early American education. There is the algebra that students are algebraic training over the first eight years of school. But even taught in middle and high school, and there is the algebra in in two- and four-year colleges, students who stop taking math­ courses with titles like "abstract algebra". ematics after one or two semesters need a substantial algebra Algebra before college (and in many remedial courses experience that is missing from the current curriculum. in college) has evolved into a study of polynomial func­ To address these issues, the Algebra Initiative is organized tions (especially linear and quadratic functions) as modeling around four themes: tools. Typical activities have students moving between tables, • creating an appropriate algebra experience for all grade expressions, and graphs of such functions, studying, for ex­ K-12 students; ample, the effect of changes in the leading coefficient of a • educating teachers, including K-8 teachers, to provide these quadratic polynomial on the graph of the associated function. algebra experiences; The paper and pencil manipulation of algebraic expressions • reshaping algebra to serve the evolving needs of the technical has been greatly reduced, and the polynomial manipulation workforce; and that remains is performed in the context and service of the • renewing algebra at the college level to serve the future analysis of the corresponding functions and their graphs. mathematician, scientist, and engineer.

806 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··--·--·-·-·-··-······-·-·-...... - ...... _...... ______.....•..•..•.. _.. _...... -.. - ················-···-····-··-···-········-·-············-·-··-···-·····-·····-··-··-··-·-···-·-·-········ ······-···-··········-·····-·-··-··-···-····-·· For Your Infonnation

There have been prior efforts to improve algebra education are important in the algebra experience of all students, not just in each of these areas (see [1], [2], and [3], for example), but those who are college bound. With college-bound students, it the emphasis of the Algebra Initiative is on algebra reform that might even be possible to introduce some of the actual topics cuts across these boundaries. The framework for the Algebra from advanced algebra (especially from linear algebra). Initiative states: • New ways must be found to connect with and engage students in linear and abstract algebra courses. The algebra experiences . . . [by] taking the broad view of algebra, from the of university students should build on and be informed by teaching and learning of algebra in the elementary school the various reforms and changes that are taking place at through breakthroughs in research, [we] will spur teachers the secondary level. These include mixing deduction with of mathematics, teachers of teachers of mathematics, and experiment, using cooperative teams of learners, developing the mathematics and mathematics education communities project-based activities, and incorporating technology into to coordinate and extend the role of algebra for all learners courses. and users of mathematics. • Part of the dialogue between K-12 and 13-16 educators might be a search for algebraic themes that could run First Steps throughout a student's algebra experience. To launch the Algebra Initiative, the Department of Edu­ 2. Technology in college courses. Educators ought to cation held a three-and-a-half-day invitational conference at consider the use of technology in linear and abstract algebra the Xerox Document Center in Leesburg, Virginia, December courses. 9-12, 1993. The colloquium involved about forty participants, • Faculty need to devise effective uses for technology in their including representatives from the National Center for Re­ courses. There are computational environments that seem search in Mathematics and Science Education, directors of the well suited for use in linear and abstract algebra (MATLAB, National Science Foundation's (NSF) algebra materials de­ ISETL, and systems like Geometer's Sketchpad, Maple, and velopment and research projects, college teachers of algebra, Mathematica, for example). There is also a great deal that is and mathematics and mathematics education researchers, plus known about the uses of technology for learning mathematics additional mathematics experts from federal agencies. The at the precollege level, and some of this can be transported meeting was organized by Carole Lacampagne in coordina­ to the university setting. But there are challenges in teaching tion with William Blair ofNorthem illinois University, James linear and abstract algebra with technology, challenges that Kaput of the University of Massachusetts at Dartmouth, and call for new ideas and solutions. Innovative work is going Richard Lesh of the NSF. on at some colleges and universities, but significant research The colloquium was organized around four working is needed to find effective ways to use technology to help groups (corresponding to the four themes in the initiative's students learn algebra. framework), each of which produced summary reports. In • If technology is used in a course, it ought to be integrated addition, there were plenary speakers, and each participant rather than appended. Integration of technology into algebra submitted a paper. The proceedings of the conference will be requires a significant rethinking of the algebra curriculum. published in both complete and summary forms (details for Different uses of technology will lead to different kinds of obtaining these reports are given at the end of this article). curricula. For example, a linear algebra course that uses Discussions at the conference were, as the publications will MATLAB to explore applications of matrix algebra to topics show, lively and informative. Especially important were the in engineering is likely to be quite different from a course that connections that were forged between participants involved asks students to use, say, Maple to write programs that test with algebra at the college level and those working in K- vectors for linear independence. 12 algebra. Another recurrent discussion was around the 3. The role of applications. It is preferable to integrate identification of the central mathematical ideas that run applications into a course rather than offer separate applied throughout algebra. A third topic that received considerable courses. discussion was the algebra experience for students in grades • Applications in elementary courses should not be so K-9; many participants argued for the elimination of the overpowering as to detract from the mathematics. Applications Algebra 1 course, replacing it with a K-8 algebra experience can be used for motivation or for enhancing understanding. that would emphasize algebraic thinking. The applications can be from practical situations or to other parts of mathematics. Summary of the University Algebra Group 4. Abstraction and proof. For many students there is a In its summary report, the group that considered algebra at the barrier between the courses that stress mechanical skills and university level had four recommendations: the courses than emphasize abstraction and proof. 1. Algebra across the grades. There should be more • Abstractions should come only after concrete examples have dialogue between K-12 educators and 13-16 educators. been introduced. Some of these examples might come from • It might be possible to lay the basis in high school for some previous courses and experiences; others might be developed important ideas from linear and abstract algebra. These ideas, within the linear or abstract algebra course itself. In order for including various uses of proof and explanation, reasoning students to see the utility of abstraction in algebra, they need about binary operations, and working with symbol systems, to have a concrete basis from which abstractions can be made.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 807 ...... ______._ .... ,...... , .. , ...... For Your Information

• Linear algebra is a good course for developing some proof a forum in which projects like these can communicate with techniques. Most proofs of results in elementary linear algebra each other. are transparent and constructive enough so that students can The Algebra Working Group. Organized in 1992 by build several important skills. Jim Kaput, this electronic conference has a distribution list of • Students should use proof as a research technique throughout 140 members. AWG can also be followed as a news group their mathematics experiences. The de-emphasis on two­ on the Swarthmore Forum (where it is known as the Algebra column proof in geometry and the reduced emphasis of proof Forum and shares the same server a<; the Geometry Forum). in calculus and other elementary courses should not signal Over the past two years, the working group has discussed a completely proof-free experience for students before they questions about algebra curriculum, the nature of algebra, get to linear algebra. Activities should be developed in lower­ research issues in algebra education, political and social level courses that illustrate the value of proof as a mechanism dimensions that affect algebra education, and connections for communicating, establishing, and even discovering new between abstract algebra and school algebra. To join the results. conference, contact Jim Kaput at jkaput@umassd. edu. The NCTM Algebra for All Project. In the K-12 arena, Next Steps the NCTM Algebra Working Group (not to be confused A follow-up session to the December meeting was held in with Kaput's electronic conference) is working on a vision February 1994 in Washington. The attendees addressed three statement for ''Algebra for All" and an elaboration of this issues that were raised at the December meeting: vision through examples, practical ideas, and promising • Fostering communication among the diverse groups practices. The group will write a draft this summer and concerned with the reform in algebra. Communication then conduct focus groups at five regional meetings during is needed within the mathematics community (especially the fall. Comments will also be solicited from individuals between those involved in K-12 and 13-16 algebra), between and groups. A final copy will be written in December and the mathematics community and federal agencies (including January. One goal of the group is to get some of the issues those working on the transition from school to work), and on the table; suggestions are welcome, especially about the between the mathematics community and the public. issues of "symbol sense" and algebraic structure in K- • Determining how to promote research on the learning 12 mathematics. Contact Betty Phillips of Michigan State and teaching of algebra and on the actual uses of algebra University at 21144eap@msu. bitnet. in the work force. Several research agendas were discussed, The NSF Initiatives. The National Science Foundation including research about the algebra needed by a mathemat­ is currently funding several precollege curriculum devel­ ically literate public and an investigation into how algebraic opment and teacher enhancement programs that attempt to reasoning is used in the workplace. Jim Kaput announced a infuse elementary school curricula with algebraic thinking new research project to examine ways of introducing algebraic and to reorganize algebra at the secondary school level. Con­ reasoning into the early grades, including an examination of tact Henry Kepner (hkepner@nsf. gov) or Eric Robinson the efforts in countries whose school students do well on inter­ ( erobinso@nsf. gov) for more information. national tests of mathematical achievement. This will involve Teachers, Time, and Transformations. Faye Ruopp a conference and an associated book on Early algebra. directs this NSF-funded teacher enhancement project at Ed­ • Initiating a search for and disseminating promising ucation Development Center in which forty-two elementary, programs and practices in algebra and determining what middle, and high school teachers attend a series of biweekly new programs and pilot projects are needed. The Algebra seminars held during the school day. Designed by project Initiative intends to support projects that develop and dissem­ staff, the seminars enable teachers to redefine and identify inate curricular materials that reflect what is known about algebraic thinking in grades 4-12, examine exemplary cur­ learning, teaching, the effect of technology, and the needs of riculum materials, begin the process of adapting their current the workforce. curricula, and develop a district-based course, Algebra for Future activities of the Algebra Initiative, in addition to Everyone, as a vehicle for reform in their districts. In addition, the publications that will emerge from the colloquium and the project staff support the teachers throughout the project by follow-up meeting, include: classroom coaching and providing opportunities for teachers • a proposed two-year discretionary grant solicitation for a to work with colleagues as they share ideas and support one "Linking Algebra" project; and another. Contact Faye Ruopp at f ayer@edc. org. • the linking of other initiatives, both within the Department Visualization in Abstract Algebra. Doris Schatt­ of Education and across other federal agencies, to what is schneider has been using dynamic geometry software in learned from the Algebra Initiative. her algebra courses at Moravian College. Schattschneider is using visualization tools (including the Geometer's Sketch­ Related Algebra Activities pad software and three-dimensional polyhedral models) to There are several independent projects under way around teach concepts in group theory. Through visualization, stu­ the country that are dealing with aspects of algebra reform. dents investigate generating systems for groups, commuta­ The following paragraphs give only a small sample of the tivity, inverses, composition, orbits, subgroups, and cosets. activities. One goal of the Algebra Initiative is to establish Some theorems that are constructive in nature can even be

808 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY For Your Information carried out step-by-step visually. The materials from the theorems, and finally prove the theorems. Each week one Visual Geometry Project that are distributed by Key Curricu­ group is responsible for leading the class and another group is lum Press are very useful. Contact Doris Schattschneider at responsible for compiling notes for the class. All groups are schattdo©moravian.edu. responsible for writing up the examples they have examined Learning Abstract Algebra: A Research-Based Lab­ and the conjectures they have made based upon these ex­ oratory and Cooperative Learning Approach. This is an amples. Freije believes this method has made students more NSF-funded international project, now in the third year actively involved in the learning process, has allowed them to of a three-year grant. Codirected by Ed Dubinsky (Purdue see the logical structure of the discipline, and has forced them University, USA), Uri Leron (Technion-Israel Institute of to confront the problem of saying precisely what they mean Technology, Israel), and Rina Zazkis (Simon Fraser Univer­ as well as saying it in a useful way. Contact Margaret Freije sity, Canada), it uses the method of students implementing atfreije©hcacad.holycross.edu. mathematical concepts on a computer in the mathematical pro­ gramming language ISETL and reflecting on their activities. More Information The students are in cooperative teams for all aspects of their The short or long document on the Algebra Initiative Col­ work. A course has been designed and is being implemented loquium can be obtained from Carole Lacampagne, Senior in ten to fifteen colleges. This past June a workshop was Research Associate in Mathematics, U.S. Department of held at Purdue University for algebra instructors interested in Education, 555 New Jersey Avenue, NW, Washington,DC learning about this approach. The project also involves a con­ 20208. siderable research component in which qualitative research methodology is used to develop epistemological analyses of References the major topics in abstract algebra. The work has resulted [1] National Council of Teachers of Mathematics, Algebra for the in a textbook published by Springer, an expository paper to twenty-first century, Proceedings of the Algebra for the Twenty-first appear in the Monthly this spring, and several research papers. Century Conference, NCTM Reston, VA, 1992. Contact Ed Dubinsky at bbf©sage . cc .purdue. edu. [2] James R. C. Leitzel (ed.), A call for change: Recommendations for the mathematical preparation of teachers of mathematics, Mathe­ An Algebra Seminar. Margaret Freije of the College matical Association of America, Washington, DC, 1991. of the Holy Cross conducts an alternative to the lecture [3] David Carlson, C. Johnson, D. Lay, and A. Porter, The linear format in second-semester abstract algebra. Students work algebra curriculum study group recommendations for the first course in in groups of three to examine examples, make conjectures, linear algebra, College Mathematics Journal, vol. 24, 1993, 4-46. establish appropriate definitions, give precise statements of

TRANSLATIONS OF MATHEMATICAL MONOGRAPHS Problems and Theorems in Linear Algebra V. V. Prasolov Volume 134 New results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, Prasolov provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It would be a fine supplementary text for an undergraduate or graduate algebra course. 1991 Mathen1atics Subject Classification: 15 ISBN 0-8218-0236-4, 225 pages (hardcover), June 1994 Individual member $48, List price $80, Institutional member $64 To order, please specify MMONO/134NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: Amelican Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 809 Acknowledgment of Contributions

The officers and staff of the Society acknowledge with gratitude gifts and con­ tributions received during the past year. The names listed below include those whose contributions were received during the year ending March 31, 1994. In January 1994 the Society introduced its Program Development Fund, established by the Executive Committee and Board of Trustees, which will direct unrestricted contributions in support of mission-related programmatic initiatives. The Society also benefitted from new and continuing support for its AMS Centennial Fellow­ ship. The thoughtful and generous donors listed in the following pages provide important support in advancing the mission of the American Mathematical Society.

AMSMission

The AMS, founded in 1888 to further the interests of mathematical research and scholarship, serves the national and international community through its publications, meetings, advocacy and other programs, which

• promote mathematical research, its communication and uses, • encourage and promote the transmission of mathematical understanding and skills, • support mathematical education at all levels, • advance the status of the profession of mathematics, encouraging and facilitating full participation of all individuals, • foster an awareness and appreciation of mathematics and its connections to other disciplines and everyday life.

CONTRIBUTING MEMBERS

Al-Droubi, Akram Garnett, John B. Martin, Gary A. Rosenblum, Marvin Whitmore, William F. Amir-Moez, Ali R. Graves, Robert L. Mathsen, Ronald M. Rovnyak, James L. Wilkins, J. Ernest, Jr. Assmus, Edward F., Jr. Greicar, Richard K. Mattson, H. F., Jr. Rushing, T. Benny Woeppel, James J. Babcock, William W. Greif, Stanley J. Mislin, Guido Sally, Paul J., Jr. Xenos, Philippos John Bauer, Frances B. Gromov, Mikhael Morris, Robert A. Samit, Jonathan Yohe, J. Michael Baumslag, Gilbert Haddad, George F. B. Moschovakis, Yiannis N. Sawyer, Stanley A. Yossif, George Beachy, John A. Haddix, George F. Muhly, Paul S. Seligman, George B. Anonymous (I ) Bjorklund, Peter B. Halberstam, Heini Murphy, Donald P. Sexauer, Norman E. Bressoud, David M. Hassinger, Bill, Jr. Murphy, Elizabeth M. Singmaster, David B. Buianouckas, Francis R. Hernstead, Robert J. Nishiura, Togo Skoug, David L. Chafee, Nathaniel Hochster, Melvin Olum, Paul Spencer, Joel H. Cohen, Henry B. Horrigan, Timothy J. Orlik, Peter P. Stakgold, Ivar Cohn, Richard M. Howe, Roger E. Osofsky, Barbara L. Sternberg, David Cootz, Thomas A. Hunt, Richard A. Otermat, Scott C. Strauss, Frederick B. Corrigan, Thomas Carney Hutchinson. George A. Palais. Richard S. Sudler, Culbreth, Jr. Das, Anadi Jiban Jaco, William H. Palmer, Theodore W. Sullivan, Richard W. Daverman, Robert J. Johnson, Albin I. Pearson, Robert W. Taft. Margaret W. DeFacio, Brian Kamp, William P. Perry, William L. Taylor, Laurence R. DeLeon, Morris Jack Kelly, John B. Petro, John W. Uhlenbeck, Karen Demana, Franklin D. Kettner, James E. Polking, John C. de Valpine, Jean E. DeMarr, Ralph E. Krause, Ralph M. Pratt, Vaughan R. Veech, William A. Dickerson, Charles E. Lagarias, JeftTey C. Ratliff, Louis J ., Jr. Warren, William E. Dinneen, Gerald P. Lemay, William H. Rawson, John Elton Weintraub, Steven H. Earle, Clifford J ., Jr. Mamelak, Joseph S. Reedy, Christopher L. White, Edward C., Jr. Ecklund, Earl F., Jr. Mandell, Arnold J. Renfield, Joseph W. White, George N., Jr.

810 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY General Contributions

GENERAL CONTRIBUTIONS

Edwards, C. M. Kita, Hiroo Overholt, Marius Spielberg, Stephen E. A'Campo, Norbert Edwards, Elwood Gene Kobayashi, Yukio Paciorek, Joseph W. Stackelberg, Olaf P. Aeppli, Alfred Eisman, Sylvan H. Kolodner, Ignace I. Paisner, Helen L. Starr, Norton Aissen, Michael I. Ellis, Wade, Jr. Krause, Ralph M. Palmieri, John H. Stegeman, Jan D. Allen, J. Thomas, III Emerson, Thomas J. Krumpholz, Gary R. Park, Sang Ro Steinberg, Maria W. Allen, William C., III Engle, Jessie Ann Kurtzke, John F., Jr. Parker, Francis D. Steinberg, Robert Al-Shakhs, Adnan A. Erbe, Lynn H. Kyrouz, Thomas J. Passell, Nicholas Sterba-Boatwright, Blair D. van Alstyne, John P. Fass, Arnold L. Lampe, William A. Peck, N. Tenney Sterk, Henri J. Antman, Stuart S. Fenley, John C. Larson, Suzanne Lynne Perrine, Serge St Pierre, Charles Gregory Arisaka, Nakaaki Ferreira Rosa, Jose Humberto Leavitt, William G. Pesotan, Hoshang Sugita, Kimio Athavale, Ameer Field, Michael J. Leger, George F. Petersen, Johannes A. Sullivan, Francis J. Auslander, Bernice L. Figiel, Tadeusz Lemay, William H. Philip, Davaraj Sullivan, Richard W. Auslander, Maurice Follmer, Hans Levinson, Henry W. Phillips, Ralph S. Swanson, Irena Babcock, William W. Freeman, James H. Levit, Robert J. Pittie, Harsh V. Taft, Margaret W. Bachman, George Friedberg, Solomon Lewis, Hugh L. Poorman, Alan G. Takenaka, Shigeo Ballard, William R. Friedman, Eugene M. Libby, Richard Allan Poston, Tim Tan, Henry K. Balser, Arienne S. Fuchs, Wolfgang H. Lichnerowicz, Andre Prakash, Nirmala Tatevossian, Leon H. Bartick, Philip R. Fujii, Nobuhiko Lickorish, W. B. Raymond Pratt, Vaughan R. Thiele, Ernst-Jochen Baruch, Herbert M., Jr. Fukuda, Komei Lindstrom, Wendell D. Quinn, Frank S. Thomas, P. Emery Baruch, Herbert Mark, III Furutani, Kenro Lombardo, Charles J. Ratliff, Louis J., Jr. Thron, Wolfgang J. Baur, Lynne A. Gantos, Richard L. Long, John M. Rawson, John Elton Toll, Kathryn B. Bayo, Enrique Glass, Michael S. Longbotham, Harold G. Reade, Maxwell 0. Torre, Nicolo Goodrich Beck, William A. Goldberg, Donald Y. Lorentz, George G. Reese, Sylvester Traina, Charles R. Beesley, E. Maurice Goldberg, Samuel Lu, Tsu-Ming Regan, Francis Tsukui, Yasuyuki Bender, John Goldberg, Seymour Luecking, Daniel H. Reissner, Eric Tugue, Tosiyuki Bengtson, Thomas E. Goss, Robert N. Luther, Chester F. Renno, James G., Jr. Umeda, Tomio Bennett, William R. Grabiel, Federico Maeda, Hironobu Restrepo, Guillermo Unai, Yasushi Unai Birkhoff, Garrett Graves, Robert L. Maehara, Kazuhisa Rickart, Charles E. Upatisringa, Visutdhi Bohn, S. Elwood Greville, Thomas N. E. Marchand, Margaret 0. Riffelmacher, David A. de Valpine, Jean E. Booth, George W. Griess, Robert Louis, Jr. Margerum, Eugene A. Roberts, Richard C. Van Casteren, Johannes A. Bourion, Georges Gurney, Margaret Margulies, William Robinson, Paul Lee Vasconcelos, Wolmer V. Bradley, John S. Hagis, Peter, Jr. Marshall, David Imler Robinson, Raphael M. Vetjovsky, Alberto S. Brothers, John E. Hagler, James N. Massey, David B. Rochon, Donna F. Vilcius, AI R. Brown, Ron Hain, Richard Martin Matchett, Andrew J. Rodriguez-Exposito, Jose Vincze, Istvan Bryn, Milo F. Harden, Milton W. Maule, Robert G. Rose, N.J. Wagner, Daniel H. Buianouckas, Francis R. Harris, Theodore E. Maxwell, Charles N. Rosen, William G. Walter, John H. Busemann, Herbert Hassinger, Bill, Jr. Maynadier-Averous, Genevieve Royer, James Samuel Wathan, Herbert Harold Butts, Thomas R. Belson, Henry Mayor, John R. Rudakov, Alexey N. Weibel, John L. Cantrell, James C. Henkin, Leon A. McAdam, Stephen J. Rudnick, Karl Weidner, Anthony A. Carlson, Bengt G. Henriques, Anna S. McArthur, C. W. Rutledge, Dorothy S. Wendel, James G. Whitt, Lee B. Carmichael, Richard D. Herrera, Robert B. McCarty, George S. Saliani, Costanza Chafee, Nathaniel Hildebrandt, Theodore W. McConnell, Thomas Sally, Paul J., Jr. Wiegand, Roger A. Wiegand, Sylvia Margaret Cho, Choong Yun Hodgson, Jonathan P. E. McDonald, Janet Samelson, Hans Willcox, Alfred B. Choksi, Jal R. Honda, Kin-Ya McNaughton, Robert F., Jr. Sarafyan, Diran Chumack, Mikhail L. Hoye, Laurence G. Meacham, Robert C. Sarason, Donald E. Willis, Paul A. Winograd, Shmuel Clapp, Michael H. Huerta, Carlos Cuevas Meisner, Morris J. Schauer, Richard L. Wright, David J. Cobb, Philip A. Hughes, Cephas D. Mellender, James W. Schechtman, Gideon Yagi, Fumio Cohen, Daniel I. A. Humphreys, James E. Michael, Ernest A. Schlesinger, Ernest C. Yamada, Naoki Cohen, Michael P. Ishimoto, Hiroyasu Moller, Raymond W. Schneider, Hans Yamada, Toshihiko Cole, Paul Dana Ito, Kiyosi Moore, Richard A. Schuster, Seymour Yamaguchi, Hiroshi Comenetz, Daniel Ito, Ryuichi Morris, Chester Ray Scollo, Giuseppe Yamasaki, Masayuki Cooper, Michael J. P. Izumino, Saichi Morris, Robert A. See, Richard Yang, Chung-Tao Copeland, Arthur H., Jr. Jacob, Niels Mortland, Richard L. Selby, Alan M. Yanowitch, Michael Cordes, Heinz 0. Jara Martinez, Pascual Mrowka, Stanislaw G. Shabazz, Abdulalim A. Yasuhara, Ann Cornelis, Eric Jockusch, Carl G., Jr. Mundt, Marvin G. Shanahan, Patrick Yasuhara, Mitsuru Craft, George A. Johnson, Donald G. Nagase, Michihiro Sharp, Henry, Jr. Yoshino, Takashi Curtis, Philip C., Jr. Jonsson, Bjarni Nevai, Paul Shelly, Eugene P. Zaharopol, Radu Cusick, David A. Kahn, Jeremy Adam Newman, Morris Shiraiwa, Kenichi Zara, Francois Dade, Everett C. Kakihara, Yuichiro Nikolai, Paul J. Siegel, Paul H. Ziebur, Allen D. Dahlin, Rolf B. Kamishima, Yoshinobu Nishiura, Togo Silberger, Allan J. Anonymous ( 100 ) Damyanov, Blagovest Petrov Kamowitz, Herbert M. Niven, Ivan Skora, Richard Kevin DeFacio, Brian Kanda, Mamoru Oguchi, Kunio Slater, John B. DeMarr, Ralph E. Kaplan, Wilfred Ohm, Jack E. Sledd, William T. Deshouillers, Jean-Marc Karle, Jerome Ohta, Haruto Slook, Thomas H. Desoer, Charles A. Kamo, Zbigniew O'Neill, Barrett Smith, Richard A. Devaney, Robert L. Keet, Arnold Peter Onishi, Hironori Smith, Spurgeon E. Dou, Alberto M. Keisler, James E. Orlik, Peter P. Smith, William K. Douche!, Jacques Kennedy, Edward S. Orr, Martin Snyder, Andrew K. Dutton, Charles Everett Kent, George A. Ortiz Fernandez, Alejandro Solski, Jeffrey Elliott Eachus, J. J. Kipps, Thomas C. Osner, H. J. Somach, Ira Harwyn Ecklund, Earl F., Jr. Kishi, Masanori Otermat, Scott C. Sommese, Andrew John

SEPTEMBER 1994, VOLUME 41, NUMBER 7 811 AMS Centennial Fellowship Fund

AMS CENTENNIAL FELLOWSHIP FUND IMU SPECIAL DEVELOPMENT FUND

The following list consists of contributors to the AMS Centennial Fellowship Fund and/or the IMU Special Development Fund. The e indicates a contribution to the AMS Centennial Fellowship Fund. The * indicates a contlibution to the IMU Special Development Fund. A listing with neither symbol indicates a contribution to both.

Aarts, Johannes M. Albugues, Alain Vincent Anderson, Donald W. Artola, Michel Baker, Blanche J. Abate, Marco *Alcorn, David P. Anderson, Douglas R. Arveson, William B. Baker, Charles R. Ahhott, H. L. Alder, H. L. Anderson, Greg W. *Arzarello, Ferdinando Baker, Edward G. Abbott. Stephen D. Alderton, Ian W. Anderson, Joel H. *Asano, Kouhei Baker, George A.. Sr. *Ahe, Terutake AI-Droubi. Akram Anderson. John Patrick Asano, Shigemoto Baker, Irvine Noel Abellanas, Pedro Alegria, Carlos A. *Anderson, John T. Aschbacher. Michael Baker, Kirby A. Abello, James Aleman, Alexandru Anderson, Marlow E. Asensio Mayor, Jose Baker, Peter Fritz *Ahels, Herbert Alexander, Daniel S. Anderson, Michael T. *Ashhacher. Charles D. Bakker. Lennard Frank Aberhach, Ian M. Alexander, John R., Jr. Anderson, Richard D. *Ashbaugh, Mark S. Baksa, Dennis John *Ahikoff, William Alexander, Kenneth S. Andersson, Lars Askey, Richard A. Baladi, Viviane Ahramovich, Dan Alexander, Roger K. *Andima, Susan e Asprey, Winifred A. *Balder, Erik Jan *Ahramovich, Yuri A. Alexander, Stephanie B. Ando, Matthew Assmus. Edward E, Jr. Baldi. Paolo Abramovici, Flavian Alexanderson, Gerald L. Ando, Shiro Athavale, Ameer Baldwin, John T. *Abrams, Gene D. *Alexcevski, Andrei Ando, Tsuyoshi *Atiyah, Michael F. Bales, John W. A'Campo, Norbert Alford, Neill H., III Andre, Peter P. *Atkin, Christopher Balibrea, Francisco *Acar, Robert AI-Ghabban, Ahmed M. Andreadakis, Stylianos Atkinson, H. R. *Balkema. A. A. *Accascina, Giuseppe Ali, Hydar *Andrew, Paul Anthony eAu, Kwok-Keung *Ball. John M. Accola, Robert D. M. Ali, M. Kursheed *Andruskiewitsch. Nicolas AulL Charles E. BalL Joseph A. Achilleas, Sinefakopoulos *AI-Jarrah, Abdulla M. Angad-Gaur, Hendrik W. K. Ault, J. C. eBall, Keith Adams, Barry G. Alkhaldi. Ali T. Anger, Frank D. Auslander, Bernice L. Ball. Richard Neal Adams, Colin C. Allan, Graham R. Anselone, Philip M. *Auslander. Joseph *Balla, Katalin Adams, Jeffrey Allday, Christopher J. Anshel, Michael Auslander, Louis Ballard, William R. Adams, William W. Allen, David L. *Ansorge, Rainer Auslander, Maurice Ballieu, Michel A. *Addington, Susan L. Allen, Harry P. Antoniadis. Anestis A. Aust. Catherine C. e Ballou. Donald H. Adelani. Lateef A. Allen, Howard Antoniadis. Jannis A. Au-Yeung. Yik-Hoi Balmerth, Rudolf Georg Adelberg, Arnold M. Allen, J. Thomas, III Appel, Kenneth I. Avelsgaard, Roger A. Baloglou. George *Adeyeye, John O. Allen, William C., III Appling, William D. L. Aversa, Vincenzo L. eBalser. Arienne S. Adkins, William A. Allouba, Hassan Ashraf *Arad, Zvi *Avgerinos. Evgenios P. Banaszak. Zbigniew Antoni Adler, Irving Alltop, William O. Arai. Hitoshi * Avramov. Luchezar L. Banchoff. Thomas F. Adler, Robert J. *Almgren, Robert Frederick *Araki. Huzihiro Avrin, Joel D. Bandle, Catherine Adler, Roy L. Almkvist. Gert Arapostathis. Aristotle * Avrunin, George S. Bandler, Wy11is Adolphson, Alan C. Alonso, Agustin *Arason, Jon Kr Axler, Sheldon *Bandt. Christoph Aeppli, Alfred Alonso, James Araujo, Jesus *Ayers. Kathleen L. Banerjee, Utpal Afenya, Evans K. Alonso, Juan M. Arazy. Jonathan Ayoub. Christine W. Bang, Chang Mo *Agard, Egbert Alpay, Daniel A. *Archbold. Robert J. *Azarnia, Nazanin eBang, Hyunsoo Aharonov, D. Alpern, Steven *Arena, Orazio Azevedo, Jose V. Banks, David L. Ahmad, Hamid K. *AL;;eda i Soler, Lluis Arens, Richard F. Azoff, Edward A. Bankston, Paul J. *Ahmed, N. U. *Alshaniafi, Yousef Saleh e Arenstorf. Richard F. Ba, Boubakar Bannai, Eiichi Ahn, Sun Shin Alsholm, Preben Arguedas. Vernor Baba, Kiyoshi Baouendi. M. Salah *Ahsanullah, T. M. G. Alsina, Claudi Arias, Arturo Fernandez Babbitt. Albert E., Jr. *Baragar, F. Alvin Ahuja, Desh B. *Alspach, Brian R. *Arias-de-Reyna. Juan Babcock, William W. eBarber, S. F. Aidoo, Emmanuel B. Alspach, Dale E. Aribaud. F. Babich, Amy Juliet Barbieri. Francesco Aihara, Shin !chi van Alstyne, John P. Arima. Satoshi Bacciotti, Andrea Barbosa, J. Lucas M. Aikawa, Hiroaki Althoen, Steven C. Arkin, Joseph *Bacher, Roland Barcelo, Bartolome Aissen, Michael I. *Altomare, Francesco Arkowitz. Martin A. Bachman, George Bardaro, Carlo *Aitsahlia, Farid Aluffi, Paolo Arlinghaus, Sandra L. Bachmuth. Seymour Barety, Julio Edgardo Aizawa, Sachiko Alvarado, Juan M. Arlinghaus, William C. *Back, Allen H. Barge, Marcy Aizenman, Michael *Alvarez, Josefina Armbrust. Manfred K. Bade, William G. *Barger, Samuel F. Ajala, Samuel Omoloye *Amann, Herbert Armentrout. Steve *Badiozzaman, Abdul Jabbar Bari. Ruth A. Akcoglu, Mustafa A. Ambrose, Richard D. Armitage, John V. Bae, Soon-Sook *Baribeau, Line *Akdenizci. Inane Amburgey, Jay K. Arms, Judith M. Baer. Robert M. Barja, Jose M. Akin, Ethan J. e Ames, Karen A. e Armstrong, Mark Anthony *Baez, John C. Barker, William Henry Akiyama, Yoshio eAmillo, J. Armstrong. Thomas E. Bagby, Richard J. Barnard, Roger W. *Akyildiz, Ersan Amir-Moez, Ali R. Arnberg, Robert L. *Baica. Malvina Florica Barner, Klaus Alama, Stanley A. Anantharaman. Rajan Arnold, David M. *Baider, Alberto Barnes, Anthony M. Alhano, Alberto Ancel, Fredric Davis Arnold, Douglas N. Bailey, Evelyn C. Barnes, David C. AI-Bassam, Mohammed Ali A. Andersen, Janet Lynn Aron, Richard M. Bailey, Rohert E. Barnet. Frank Albert, John P. *Andersen, Kurt Munk Aronson. Donald G. *Bailey. Toby N. Baron. John 1. Albertson, Michael O. Andersen, Lars Dovling *Artal-Bartolo. Enrique BaillieuL John B. Baron, Simson Albrecht. Ernst Anderson, A. Wayne *Artemiadis, Nicolas Bailyn. Paul M. Barrar, Richard B. Alhrecht. Felix R. Anderson, Allan G. Arthur, James G. Baker. Alan *Barreca. J. R. Albright. Hugh N. • Anderson, Charles A. Artin, Michael *Baker, Andrew James *Barrera-Rosillo. Domingo

812 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... _. I!WIIIIf!'P!?W&t~~1------····---·---·----...... _.. _ .. _.. ______AMS Centennial Fellowship Fund

Barros-Neto, Jose Bell, Wolfgang Bilaniuk, Stefan Booth, George W. *Brinkmann, Hans-Berndt Barsky, Daniel Bellamy, David P. Biles, Charles M. Booth, Raymond S. Brisse, Edward M. Bart, H. Bellissard, Jean V. *Bilge, Ayse Humeyra Boothby, William M. *Brito, Margarida A. Barth, Karl F. Belzunce Torregrosa, Felix Luis Billera, Louis J. Boratynski, M. Brlek, Srecko Bartick, Philip R. Benac, Theodore J. eBillik, Martin Borchers, Brian T. Brodkey, Jerald S. *Bartle, Robert G. Bencsath, Katalin A. Bilopolska, Ya I. Borden, Robert S. Broise, Michel Jean *Bartnik, Robert A. Benda!, Julius S. eBindschadler, David E. Borel, Armand *Brokate, Martin de Bartolomeis, Paolo Bender, John Birch, Bryan J. Borkowski, Szczepan Broline, Duane M. Barton, Thomas J. Bendersky, Martin Bircher, John J. Borucki, Leonard John Bromberg, Eleazer •Baruch, Herbert M., Jr. Benedicks, Michael •Bird, Elliott H. Borwein, Jonathan M. Brommundt, Eberhard W. •Baruch, Herbert Mark, III Benes, Vaclav E. Birkhoff, Garrett *Bosch, Carlos Brons, Morten Barvinok, Alexander I. Benham, James W. Biroli, Marco Bosch, William W. Brooks, Robert Barwise, Kenneth J. Ben-Israel, Adi Bishop, Alan A. *Bosma, Wieb Brothers, John E. Basor, Estelle Ben ttez, Carlos Bishop, Richard L. *Botelho, Fernanda Broue, Michel •Bass, Hyman Benkart, Georgia M. *Bishop, Wayne *Bottazzini, Umberto *Broughan, Kevin A. Bastian, Gregory A. Benke, George Bisson, Terrence Paul Bottcher, Albrecht *Broughton, S. Allen Batie Nicolau, Nadal *Bennett, John Makepeace Bisztriczky, Tibor *Bottema, Murk J. Browder, William Batt, Jurgen 0. Bennett, William R. Bjorklund, Peter B. Bottoms, Charles L. Brown, Arthur B. Batterson, Steven L. *Benson, Dave Black, Robert Eugene Botvinnik, Boris I. Brown, Edgar H., Jr. Batty, Charles J. K. Benson, David Bernard Blackall, Clair J. *Bouchard, Pierre Brown, George B. Bauer, Frances B. Benson, Donald C. Blackmore, Denis L. Bourion, Georges Brown, Gerald D. *Bauldry, William C. Benson, F. Chal Blair, Charles E. Bousfield, Aldridge K. Brown, Gerald L. Baum, Paul F. Benyamini, Yoav •Blair, William D. *Boutot, Jean Francois •Brown, Howard H. Bauman, Patricia E. Bercovici, Hari Blais, J. A. R. Bouwsma, Ward D. *Brown, Jack B. *Baumeister, Johann Berend, Daniel Blakemore, Carroll F. *Bouzar, Nadjib *Brown, Kenneth S. Baumgartner, James E. Berenstein, Carlos A. *Blanc, David Bowie, Harold E. Brown, Lawrence G. Baumslag, Gilbert Berezansky, Yurij M. Blanch, Gerttude Bowron, Paul J. *Brown, Richard C. Baur, Lynne A. *Berg, Christian Blanche, Ernest E. Boyce, Donald J. Brown, Richard G. * B a vinck, Herman Berg, Gene A. Blanton, John D. Boyce, William E. *Brown, Richard K. Baxendale, Peter H. Bergelson, Vitaly *Blatter, Christian *Boyd, David W. Brown, Richard L. W. Bayer, David Berger, Alan E. Blatter, Jorg Boyd, Stephen H. Brown, Robert Dillon *Bayer, Margaret M. *Bergeron, Francois Blattner, Robert J. Boyle, Mike Brown, Robert F. Bayer-Fluckiger, Eva Bergman, George M. Bleiler, Steven A. Bozonis, Petros Brown, Ronald Bayo, Enrique Bergmann, Peter G. Blessinger, Todd David *Braaksma, B. L. J. Brown, Sharan Inez Bazinet, Jacques • Bergstrom, Roy C. Blij, Frederik Van Der *Braam, Peter J. Brown, Thomas A. Beachy, John A. Bergum, Gerald E. Blitch, Patricia M. Brachman, Malcolm K. Brown, William G. •Beadle, Allen Jay Bergweiler, Walter Bloch, Ethan D. Brackx, Fred F. Brownawell, W. Dale Beale, J. Thomas *Beringer, Alfred Bloch, Stephen A. Bradford, David B. Browne, Patrick J. Beals, R. Michael Berkovitz, Leonard D. Block, Richard E. Bradie, Brian D. Brualdi, Richard A. Beals, Richard W. *Berkowitz, Jerome Blohm, David A. Bradley, John S. Bruck, Ronald E. Beard, Helen P. Berlekamp, Elwyn R. Bloom, David S. Bradley, Richard C. Bruckner, Andrew M. Beattie, Margaret Berman, Stephen eBJum, Dorothee Jane *Bradley, Robert E. Bruckstein, Alfred M. Beaudet, Fernand Bermudez, Alfredo Blum, Joseph Bradlow, Steven B. Brueggemann, Wolfgang *Beaulieu, Liliane Bernardi, Salvatore D. Blum, Lenore Brady, Wray G. Bruggeman, Roelof W. Beaulieu, Patricia Wright Bernau, Simon J. Blundell, Solon F. Brakke, Kenneth A. Brunat, Josep M. *Beauzamy, Bernard M. Bernfeld, Stephen R. Boardman, John M. Bralver, Peter Jeffrey Brungs, Hans H. Beaver, Philip F. Bernhardt, Chris Bobisud, Larry E. Bramsen, John D. Bruni, Anthony J. *Beavers, Merwin Gordon, Jr. Bemis, Francisco Bodnar, Istvan •Brandli, Emil R. *Brunk, Hugh D. •Bechtell, Homer F. Bernstein, Allen R. Bodnarescu, M. V. Brandt, Dennis E. •Brunner, Hermann Beck, William A. Bernstein, Barry M. Boeckle, Gebhard Brandt, Keith A. Bruns, Winfried Beckenstein, Edward Berresford, Geoffrey C. • Bogar, Gary A. Branner, Bodil Brunson, Barry W. Becker, Eberhard *Herrick, A. J. Bogart, Kenneth P. *Branson, Thomas Patrick Brunswick, Natascha A. Becker, Howard S. Berriozabal, Manuel P. Bogorad, Valery B. Brant, Larry J. *Brussee, Rogier Becker, James C. *Berrizbeitia, Pedro J. Boguslavskii, L. B. Brauer, Fred Bryant, Billy F. *Becker, Ronald I. Berti, Patrizia Bohn, S. Elwood Brauer, George U. Bryant, John G. Becker, Thomas Bertin, Emile M. Bohnke, G. C. •Bravo, Raul Bryant, Robert L. Beckman, Frank S. Bertran, Jean-Denis Stephane Boillat, Jacques E. Brechner, Beverly L. Brydges, David C. *Beckmann, Sybilla Beschler, Edwin F. *Boivin, Andre Breckenridge, John C. • Brylinski, Jean-Luc Beckner, William Beseda, Vladimir A. Bojars, Juris A. *Breen, Lawrence Brylinski, Ranee Kathryn *Beder, Jay H. *Bessenrodt, Christine Bolger, Robert Edwin *Bremigan, Ralph J. Bryn, Milo F. Bedford, Eric D. Betancourt, Carlos M. Bolker, Ethan D. Brennan, Joseph P. Brzezinski, Juliusz *Bedford, Tim Betsch, Gerhard *Bolli, Pierre *Brenneis, James M. Bshouty, Daoud Beebee, John C. Betz, Ebon E. Bollinger, Robert A. Brenner, Philip Buchsbaum, David A. *Beekman, John A. Beylkin, Gregory *Bollman, D. A. *Brenner, Sheila Buck, R. Creighton *Beekmann, Wolfgang Bhaskaran, Meempat *Boman, Jan *Brent, Richard P. Buckley, Joseph T. *Beery, Janet L. Bhathena, Dinyar Barjor •Bonavero, Laurent *Brenti, Francesco Bucy, RichardS. Beeson, Michael J. Bhattacharya, Rabi N. Bonet, Jose Bressler, David W. eBuddrus, Lee Edward Beghi, Luigi *Bhaya, Amit Bonin, Joseph E. Bressoud, David M. Budney, Paul Edward *Beidleman, James C. *Bianchi, Gabriele Bonk, Mario Breves Filho, J. A. Budnik, Paul, Jr. Beig, Robert •Bibisi, Keith Bonnesar, David • Brickell, Ernest F. Buehler, Royce E. *Belair, Luc Bickel, Thomas F. Bonnington, Craig Paul *Bridges, Douglas S. Buekenhout, F. Bell, Allen D. Bidwell, Leonard N. Booker, T. Hoy Briem, E. Bugajska, Krystyna M. Bell, Janie L. Bierstedt, Klaus D. Boos, Johann Brierley, William L. Buianouckas, Francis R. Bell, Steven R. Bierstone, Edward Boos, William Brin, Matthew G. Bulens, Pierre Victor

SEPTEMBER 1994, VOLUME 41, NUMBER 7 813 ...... -...... -...... _._ ... _._,., ...... _._.,_.,_, .... _.. _._._._, ...... _._._._._._ ...... _._._, ...... ______.. _.. _._._._._._._ .. _._._ .. _.. _,_ .. _._ .. _._ .. _._ ...... _...... _.. _... -.. -...... _._._ ...... ,...... _._._ .. AMS Centennial Fellowship Fund

Bulirsch. Roland Zdenek Campos, L. M. B. C. Chanillo. Sagun *Chung. Sang K. *Comfort. W. Wistar Bullen, P. S. *Candiotti, Alan Chao. Faith Y. Church. Philip T. *Comiskey. Daniel C. Bullivant. David P. *Cannon, James W. Chapin. Steven Arthur Churchill. Edmund Conlon, Joseph G. Bumby. Richard T. Cantor, David G. Chapman, Robin John Churchill. Richard C. Conlon. Lawrence W. Bump. Daniel Willis Cantor. Robert M. Charney. Ruth M. Ciarlet. Philippe G. Connell. Ian • Bunch, Henry Forrest Cantrell, James C. Chattergy, Rahul Cieslik. Thomas P. *Connelly, Robert Bungart. Lutz Cantwell. John C. *Chauveheid. Paul G. *Cifuentes, Patricio *Connor, Frank F. Buraczewski. Adam Cap. Clemens Heinrich Chauvin. Andre •Cima, Joseph A. Connor, Jeffery S. Burchard. Hermann G. Caplan. Harry *ChaYey. Darrah P. Cinlar. Erhan •connors. Edward A. Burckel. Robert B. Capozzi. Alberto Chawla. La! M. *Citrin, Stuart Conrad. Bruce P. Burda. Pavel Cappell. Sylvain E. *Chee. Pak Soong •Civin. Paul Conrey, J. Brian B urdzy, Krzysztof Capriotti, Anthony D. Cheeger, Jeff *Claasen, H. L. Constantin, Peter S. Burger. Marc R. Caranti, A. E. Chein. Orin N. Clancey. Kevin Constantinescu. Corneliu Burgess, C. Edmund *Carbery, Anthony Chen. Concordia C. *Clark. David M. *Cook. Joseph M. Burgess. Richard Dennis *Cardoso, Domingos M. Chen. Fen Clark. Jeffrey W. *Cooke. Kenneth L. *Burgess, Walter D. Carfora. Mauro Chen. Louis H. Y. *Clark. John Coolsaet, Arnold A. Burghduff, John Brian Carleson, Lennart A. E. *Chen, Pei-Li Clark. Robert A. •Coombes. Kevin R. *Burkard. Rainer E. Carlson. Bengt G. Chen. W. W. L. Clarke. Bob W. Cooper. Jeffery M. *Burkert. Daniel A. Carlson, Jon F. *Chen. Xu-Ming *Clarke. Francis *Cooper. Mark A. *Burkhart, Richard H. *Carlson. Philip R. Chen, Y. W. Clarke. Graham Thomas Cooper. Michael J. P. Burkholder, Donald L. Carlson. Robert C. Cheng. Horace B urk •Clarkson. Helen E. Coornaert, Michel Burns. Daniel M .. Jr. Carlson, Timothy J. Cheng. Jih-Hsin Clary, Stuart ecootz, Thomas A. Burns, Keith H. *Carlsson, Renate Cheng, Kuo-Shung Claus-McGahan. Elly Cope, Davis K. Burr, Stefan A. do Carmo. Manfredo P. Cherlin. Gregory L. Clee. William A. Copeland. Arthur H., Jr. B urstall. Francis E. *Carr, Jack Cherlin. Mokurai Clemence, Dominic Pharaoh *Coppens. Marc Busemann, Herbert Carrie, Dennis Chern, Shiing S. Clemens, Charles Herbert Coram, Donald S. Buser, Peter J. Carrillo-Escobar. Julio Cesar *Cherniavsky, John C. *Clement. Philippe P. Corbett, John V. Bushnell. Colin J. •Carroll, Ron M. Chernikova. Olga Sergeevna *Clements. George F. Cordero, Luis A. Busque, Claudi Carruth. James H. Chernoff. Herman Cliborn. James H. •Cordes. Craig M. Buss, Samuel R. Carstens. Allan M. Chernoff. Paul R. Cline, Edward T. Cordes, Heinz 0. Butchart, John H. Cartan, Henri Cheni. Mona Y. Closs. Joseph N. eCordovil. Raul Butcher, Ralph Stevens Carter. David W. Cheslack-Postava, Kevin A. Clover, William J.. Jr. Corduneanu. Constantin *Butkovic, D. *Carter, J. Scott Cheung. B. K. S. Cobb, Philip A. Corlette, Kevin David Butler. James William Carter, Thomas J. •Cheung. Chi-Keung Cobham, Ian P. Comelis. Eric Butts. Thomas R. Cartier. Pierre Chiang, Peter H. S. Cochran. James A. Corsi Tani, Gabriella Byerly. Robert E. Casati. Paolo Chicco, Maurizio Cock, John C. Corson, Jon M. Byers. Stephen Paul Case. Bettye Anne Chichilnisky. Graciela Cockburn. Bernardo Corwin, Thomas L. Byrd, Kenneth A. Casey, Stephen D. *Chicone, Carmen C. Cockcroft, Wilfred H. Cosner, George C. *Byrne. Angelina H. J. Casimir, John F. R. Chihara. Theodore S. *Coffee. Terence *Cossio. Jorge *Byrne. Catriona M. *Cassels, J. W. S. Chikuse. Yasuko Coffey, John Costabel, Martin Byrne. Charles L. Cassidy. Phyllis J. Chikwendu. Sunday C. *Cogburn. Robert F. Costenoble. Steven R. Byrom. Robert Lawrence •Cassity. C. Ronald Chillag, David Cogdell. James Wesley Cote. Louis J. Cable, Charles A. Castillo. Jose E. *Chillingworth. David R. J. Cohen, Amy ecotlar. Mischa Caboz. Regis Castore, Glen M. *Chinburg, Ted C. *Cohen, Aijeh M. Cotton. Robert M. Caccianotti, Luciano *Catanese. Fabrizio M. E. Ching. Wai-Sin Cohen. Daniel I. A. •couch, W. Eugene *Cadogan. Charles C. Cateforis, Vasily C. Chiswell. Ian M. •Cohen. Frederick R. Coulibaly. Akry Caenepeel, Stefaan Cato, Benjamin R., Jr. Cho. Choong Yun Cohen. Henry B. Coulter. Malcolm A. Caflisch. Russel Cavallini. Fabio Cho. Han-Hyuk Cohen. Herbert E. Countryman, William Mark *Cagnac, Francis Cavaretta. Alfred S. Cho. Jung R .. Cohen. Marshall M. Coutant, Basil W. Cahen. Paul-Jean Cavender, James A. Cho, Yeo! Je *Cohen, Martin J. Coutts. Julian Thomas Cahill. Rotraut G. Cavicchioli. Alberto Choe, Geon Ho Cohen. Michael P. Couty. R. Cain, Bryan E. Caviness. B. F. Choe, Young Han *Cohen, Moses E. Covachev. Valery •Cain, George L., Jr. Cayford. Afton H. •Choi. Kwok-Pui Cohen, Steve M. Cowen. Carl C. Caines. Peter E. Cazzaniga. Franco •Choi, Suhyoung Cohn. Donald L. Cowens. J. Wayne Cairoli, R. Cegielski. Patrick Choi. Sung Kyu •Colbourn. Charles J. *Cowling, Michael G. Calderbank. Robert *Cerda. Joan Choi, U. J. Colby. Robert R. *Cox, David A. Calderer. M. Carme Cerruti, Umberto Choksi. Jal R. Cole. Charles A. Cox. Raymond H. Calderon, Alberto P. Cervone. Davide P. *Cholewinski. Frank M. Cole. Chris Crabtree, J. B*dup of crjmba •caldwell. William V. deCesare, Kenneth M. Chong. Chi Tat Cole. George Craft. George A. *Calhoun, William C. Chabert, J. L. Choo. Koo-Guan Cole, Herman D. Craggs, Robert F. Calica, Arnold B. Chacon. Paul R. Choquet, Gustave Cole. Paul Dana Craig. Jessica Marguerite Callahan. James J. •Chae, Soo Bong Chouteau. Charles C. Coleman. A. John Craig, Walter L. *Callahan, Michael J. Chafee. Nathaniel •Chow, Pao-Liu Coleman, Courtney S. Crandall, Stephen H. *Calvi. Jean-Paul Chakerian. Gulbank D. Chow. Tseng Yeh Coleman. Robert Cranston, Michael Craig Camacho, James, Jr. Chan. Jack-Kang Choy. Marguerite E. Coleman, William Crapo, Henry H. Camarena Badia. Vicente Chan, Jor-Ting Christensen, Chris Colley. Susan Jane Crauder. Bruce C. •camera. Gerardo A. Chandra. J agdish *Christensen. Helen Collier. Jarrell D. Craven, Bruce D. Cameron. Douglas E. Chang. Chao P. Christian, Floyd L., Jr. Collins. Heron S. Crawford, James P. Camina, A. R. Chang. Gerard J. *Christianson. D. Bruce *Collins. Michael D. Creede, Geoffrey D. Campbell. Duff G. Chang. Jen-Tseh Christofides. Tasos C. *Colonius. Fritz Creese. Franklyn G. Campbell, Harold E. A. Chang. Kun Soo Chu. Chinku Colson. Henry D. Creese, Thoma.~ M. Campbell. L. Andrew Chang. Shao-Chien Chuang. Pi-Chun Comar, Timothy D. ecriscenti, Jacqueline P. Campbell. Paul J. Chang. Sun-Yung Alice Chumack, Mikhail L. Comenetz. Daniel Critchlow. Florence G. Campiti, Michele Chang. Yu Chung, Dong Myung *Comerford. Leo P.. Jr. Crone. Lawrence J.

814 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ·...... ·...... ·..·12& BHIJ[lllf. .:2.i••lIl..... AMS Centennial Fellowship Fund

Cronheim, Arno Dean, Richard A. Diener, Karl-Heinz Driver, Bruce K. EI Hatri, Mohamed Cross, James 1. *Dearden, Bruce Gary Dieter, Ulrich Drouilhet, S. 1., II *EI-Hodiri, Mohamed Cross, Ronald W. *Debnath, Lokenath Dietmair, Thomas Drucker, Thomas L. Elia, Michele Crothers, Derrick S. F. * De Canniere, Jean Dijkhuizen, Mathijs S. Druet, Robert L. Elias, Juan Crouzeix, Jean-Pierre *De Castro, Rodrigo Dijksma, Aalt Drumm, Todd A. Elias, Uri Crow, Edwin L. Deck, Karin M. Di1cher, Karl H. Dubisch, Roy .Eliashberg, Yakov Cude, Joe E. De Clerck, Frank Di Maio, Giuseppe .Dubson, Alberto S. *Eliasson, Halldor I. Cuer, Michel DeFacio, Brian Dimiev, Stancho Duchamp, Thomas E. EI Kacimi Alaoui, Aziz Cullen, Helen F. Defrancesco, Henry F. *Dimitric, Radoslav Dudley, Richard M. Elkjaer, Sigurd Cunkle, Charles H. DeGray, Ronald W. • Dimsdale, Bernard Dudziak, James J. Elko, Constance B. *Cuntz, Joachim Deguenon, Charles Dincbas, Mehmet Duer, John L. L. Elliger, Sigurd Curbera, Guillermo Phelan *Dehesa, Jesus Sanchez Dipper, Richard T. *Dunbar, William Dart, Jr. Ellingham, Mark N. Curran, Mark C. De longh, Johan J. Dippolito, Paul R. *Duncan, Andrew M. Ellingsrud, Geir Currier, Albert W. Dekker, Jacob C. E. *Di Prisco, Carlos A. Duncan, Cecil E. Elliott, Brady A. Curtis, Charles W. Dekleine, Herbert A. Divis-Poracka, Zita M. Duncan, Richard D. Elliott, George A. Curtis, Herbert J. DeKoninck, Jean Marie Dixit, G. D. *Duncan, T. E. Elliott, Joanne Curtis, Philip C., Jr. Dekster, B. V. *Dixon, John D. Dunham, Douglas J. Elliott, John Curto, Raul E. Delahunty. Michael D. .Dlab, Vlastimil Dunwoody, Martin John Elliott, Sheldon E. Cushing, Jim M. Delange, Hubert Dodia, Bharat T. Dupre, Maurice J. Ellis, James W. Cusick, Larry William Deleanu, Aristide Dodziuk, Jozef Durand, Loyal Ellis, Nancy F. Cuthill, Elizabeth H. DeLeon, Morris Jack Doering, Boro Duren, Peter L. Ellis, Robert Cutler, Colleen D. Delgado, William Dolan, James M. Durfee, Alan H. Ellis, Wade, Jr. *Cuttle, Yvonne H. *Delgado-Gomez, Jorge Joaquin Dolbeault, Pierre E. Durfee, William H. Elman, Richard S. Cwikel, Michael Dell'Antonio, Gianfausto Dold, Albrecht E. • Durst, Lincoln K. *Elmendorf, Anthony D. Dacorso Netto, Cesar Delporte, Jean Dold, John William Duskin, John W., Jr. Eloe, Paul W. Dade, Everett C. Del Riego de Del Castillo, L. Dolgachev, Igor Duszynski, Martin, Jr. *Elsdon, Rod *Dadok, Jiri Del Val, Pablo Dollard, John D. Dutton, Charles Everett Emch, Gerard G. Daepp, Ulrich Delvos, Franz J. Dolph, Charles L. Duvall, Andrea V. Emerson, Thomas J. Dafermos, Constantine M. DeMarr, Ralph E. Dombrowski, Joanne M. * Dwork, Bernard M. Emmanuele, Giovanni Dahl, Erlend *Demetriou, Ioannes C. Dominici, Paolo Dydak, Jerzy .Emmer, Michele Dahlin, Rolf B. DeMeyer, Frank R. * Domokos, Gabor Dyer, Matthew J. *Enayat, Ali Dai, Xianzhe • Demko, Stephen *Donaldson, James A. Dynin, Alexander Endsley, Neil H. *Dajczer, Marcos Demmel, James W. *Donaldson, Simon K. Eachus, J. J. • Engber, Michael *Dalang, Robert C. De Moor, Bart L. R. Donaly, James P. Eames, William P. *England, Julie A. Daly, John T. *Dencker, Nils Donnay, Victor J. Earle, Clifford J., Jr. Engle, Jessie Ann D'Ambrosio, Ubiratan *Deninger, C. Donovan, John E., II Easley, David H. Engler, Hans P. Damiani, Ernesto *Dennin, Joseph B. Doob, Joseph L. Easton, Richard J. *Engquist, Bjorn Damiano, David B. Dennis, Nichola Jane *Doolen, Gary Dean Eberlein, Patrick Barry Engstrom, Philip G. Dana, Martin P. Dent, Elliod *van Doorn, Erik A. Echenique, Marcial Luis Enneking, Marjorie Danes, Stephen Deodhar, Vinay Vithal *Doplicher, Sergio Echeverria, Javier Enomoto, Kazuyuki Daney, Charles G. DePagter, Bernardus Doppel, Karl Ecklund, Earl F., Jr. Enomoto, Masatoshi * Danforth, Katrine *De Pascale, Espedito Doran, Robert S. Eckmann, Beno Enqvist, Arne Dangello, Frank Ralph Depperschmidt, Thomas Dean Dordal, Peter L. Edelson, Allan L. Ensign, Elaine Cook D'Angelo, John P. Deruaz, Marcel A. F. Dorfmeister, Josef F. Edelstein, Michael *Epelbaum, Jennifer *Daniels, Karen M. .Derwent, John E. Dorlas, Tony C. Edelstein-Keshet, Leah Epkenhans, Martin Danov, Stanislav N. DeShalit, Ehud Dorroh, James R. Edixhoven, Sebastian Johan Epp, Susanna S. *D'Aprile, Margherita Deshouillers, Jean-Marc Dorwart, Harold L. Edjvet, Martin Epstein, Benjamin Daras, Nicholas J. Deshpande, Janardan V. *Dos Santos, Antonio F. *Edmonds, Allan L. Epstein, Bernard Dariescu, Ciprian De Snoo, Hendrik S. V. Dossey, John A. .Edmundson, H. P. Epstein, Charles L. D'Aristotile, Anthony J. Desoer, Charles A. Doty, Charles F. Edrei, Albert *Erban, Daniel Dark, R. S. Desquith, Etienne Dou, Alberto M. Edwards, C. M. Erbe, Lynn H. Darko, Patrick W. • Detlefsen, Michael E. Douchet, Jacques Edwards, Charles H., Jr. Erdahl, Robert M. Darling, Donald A. *Detrez, Eric Louis Dougherty, Michael M. Edwards, David Albert *Erdem, S. Darmon, Henri Rene Deumens, Erik *Dougherty, Randall Edwards, Elwood Gene Erdman, John M. .Darnel, Michael R. *Deutsch, Daniel H. Dougherty, Steven T. Edwards, Harold M. *Erdos, John Das, Anadi Jiban Devaney, Robert L. Douglas, Jim, Jr. Edwards, Robert D. Ericksen, Wilhelm S. Dashiell, Fred K., Jr. *Deveney, James K. Douglas, Ronald G. Edwards, Roderick Erickson, Roger P. Da Silva, Amaro Rica *Devinatz, Ethan S. *Douglass, J. Matthew Eells, James * Erkama, Timo *Da Silva Azenhas, Olga Devitt, John S. *Doust, Ian R. Eenigenburg, Paul J. *Erle, Dieter H. D'Attorre, Leonardo Dewallens, Jean H. Dovermann, Karl Heinz • Efrat, Isaac Y. Ern, Alexandre Daubechies, Ingrid Dhillon, Hardev K. Dovidio, Catherine Slanta Eggers, William I. *Ernst, Claus Daverman, Robert J. Dhooghe, Paul F. J, Dow, Keith Ehrlich, Paul Ewing Errico, Thomas G. Davidov, Johann Todorov Diamantaras, Dimitrios I. Dowling, Diane M. Eigel, Edwin G., Jr. Escassut, Alain *Davies, E. Brian Diamond, Beverly E. J. * Downey, Rodney G. Eigen, Stanley 1. Escobales, Richard H., Jr. Davis, Chandler Diamond, Fred I. Doyle, Brian J. Eilenberg, Samuel Eskin, Gregory Davis, Martin D. Diamond, Jack *Doyle, Peter G. *Eilers, Soren Eslinger, Robert C. Davis, Paul L. Dias, Frederic Drager, Lance D. Einthoven, Isabella H. Esquivel, Manuel Leote Davis, William J. Dias Da Silva, J. A. Drake, Ronald Lewis Eirola, Timo J. *van den Essen, Arno R. *Dawson, Donald A. Diaz Gomez, Jose Luis *Drazin, Michael P. • Eisenberg, Murray Essen, Matts R. *Dawson, John W., Jr. Diaz-Miranda, Antonio .Dressel, Francis G. Eisenbud, David *Esteban, Maria J. Day, Jane M. Dibner, Steve Drew, Gerald C. Eisner, Elmer Estep, Donald J. Daybell, Dorothy A. *Dickenstein, Alicia M. Dreyer, Thomas P. *Ekeland, Ivar *Estrada, Luis Dayton, Barry H. Dickerson, Charles E. van den Dries, Lou P. • Eldridge, Klaus E. • Etgen, Garret J. *Dean, Anthony K. Diederich, Klas Dritschel, Michael A. Elhadad, Jimmy *Eudave-Munoz, Mario

SEPTEMBER 1994, VOLUME 41, NUMBER 7 815 ...... · ··········..···..· 15••••••••••••••••••·..· . AMS Centennial Fellowship Fund

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*Evens, Leonard Figueres. Maurice C. Frawley. Timothy 1. *Gadea, Pedro M. Gerver, Joseph L. *Evens, Samuel R. *Fillmore. Peter A. Frazier, Michael W. Gadella, Manuel Gessel, Ira M. Evers, Joseph J. M. Finch, David V. Frederickson. PaulO. Gage. Michael E. *Gesztesy, Fritz Ewy, Daniel J. Finch. Steven Richard Fredricks. Andrew J. Gaier, Dieter Gevirtz. lulian *Ezin, Jean-Pierre O. *Finkelstein. Elizabeth Free, Norman S. Galaz-Fontes, Fernando Gewirtz. Stephen J. *Faber, Carel F. Finkelstein, Leib Freeland, Mark S. Galbiati, Margherita eGhaffari, Abolghassem Fabes, Eugene B. Finn. David L. Freeman. James H. Gale, G. Brook Ghent. K. S. Faierman, Melvin Fischer, Addison M. Freeman. Robert S. *Gale. Jose E. Ghisa. D. *Fainsilher, Laura Fischer, H. Freese, Ralph S. Gallardo, Luis eGhosh, Parimal K. eFaith, Carl Fischer. Klaus G. *Freiman, Gregory A. Gallego, Eduardo *Ghoudi. Kilani Falbo, Clement E. Fishhack, William T. *Freire, Alexandre S. Gallier, lean H. Giaquinta, Mariano *Falcone. Maurizio Fisher. Benji N. Freire NistaL J. L. Galliher, Herbert P. *Gidon. Esin Kaneti Falkner, Neil F. Fisher, Stephen D. Freitag, Herta T. Gallo, Daniel M. Giga. Yoshikazu Faltings, Kai Fishman. Louis Freundlich. Marianne Smith *Galperin, Eflm A. *Gigena. Salvador D. R. Fan, Ky Fisk, Steve e Freyd, Peter J. Gamba, Irene Martinez Gilat. David Faran, James 1. * Fitzgerald. Eugenia E. Frias, Simon *Gamble, A. Bruce Gilbarg. David *Farbrother, Ian FitzGerald, G. C. Frick, Hans Ganelius, Tord H. Gilbert, Michael D. *Farenick, Douglas R. Fitz-Gerald. Gary F. Fricker, Francois Gangolli, Ramesh A. Gildenhuys. Dion FUlTis, Frank A. • Fitzgihbon. William E. Fridman. Burna L. Gani. Joseph M. *Giles, lohn R. Fass, Arnold L. Fitzsimmons, Patrick 1. eFridy. John A. Ganser, Carl C. Gilewicz.lacek Fauntleroy, Amassa C. *Fjelstad, Paul T. Fried, David *Ganster, Maximilian Gillard, Roland D. Faurre. Pierre L. Flahive. Mary Elizabeth *Friedberg. Solomon Gantner. Thomas E. Gillette. Richard M. Fava, Norherto *Flajolet, Philippe Friedberg. Stephen H. Gantos, Richard L. Gillilan, lames H. Feehan, Paul M. N. Flanigan. Francis J. Friedlander, Leonid Gao. Qi Ren Gillis. James T. Feeman. George F. *Fleck. Margaret M. Friedman. Eugene M. Gao, Zhanhai Gillman, David S. *Feeman, Timothy G. Fleissner, William G. Friedman, lane E. Gapaillard, Jacques *Gillman, David W. Feferman, Solomon Fleming, Daniel J. Friedman, Merwyn M. Garahan, James C. Gilman. Jane P. Fegan. H. D. Fleming, Richard 1. Friedman. Robert David *Garay. Oscar J. Gilmore, Maurice E. Feigenbaum, Joan Flensted-lensen. Mogens Friedman. Sy D. eGarb. Regina H. Gilsdorf, Thomas E. Feighn, Mark E. Flesner, Harold E. Friese, John L. Garcia. Domingo *Gimigliano. Alessandro Fein, Burton I. * Fletcher, Peter Fritsch, Rudolf Garcia, Jose Luis eGingrich, Ross B. Feingold, Alex 1. * Fleury, Patrick 1. Fritsche, Richard T. Garcia-Archilia, Bosco Ginzburg, Viktor L. Feinsilver, Philip Flexner. William W. Frizzoni. Piero F. G. *Garding. Lars Gioia. Anthony A. Feit, Paul Florence. John B. Frohardt, Daniel E. Gardner, Merritt P. Girela. Daniel Feit. Walter Floret, Klaus Frohlich. lurg M. Garfunkel, Solomon A. Gider, Samuel *Fejer, Peter Andrew Florides, Petros Serghiou Frohliger, John A. eGarland, Howard Giuli. Eraldo Feldman, Arnold D. *Floyd. William J. From. Steve G. *Garling, David J. H. Glass. Michael S. Feldman, Chester Flucher. Martin G. *Frosali, Giovanni Garrido. Isabel Glassey, Robert T. Feldman, Norman Fogelberg, Gunnar *Frosini. Patrizio Garrison, Betty B. Glauherman. George e Feldman, Raisa Epstein de Foglio. Susana F. L. Fry, Cleota G. Garvan, Frank G. GIaz, Sarah Feldman, William Alan Folland, Gerald B. Fu. Yen-Tzu Gasper, George, lr. Glazebrook. lames F. Feliciano-Dodonoff, Manuel Follmer. Hans Fuchs, Peter Rudolf Gatterdam. Ronald W. Gleason. Andrew M. Feliu. Sagols Troncoso *Fomin. Sergey Fuchs, Wolfgang H. Gauchman, Hillel Glenn, Paul G. *Fellman. Jahan Fong, Che-Kao Fuchssteiner. Benno Gauthier, Paul M. *Gloor, James Alan *Fender, Timothy N. Fong. Paul Fuglede. Bent Gautschi, Walter Glover, Henry H. e Fendrich, lohn W. Fonseca, Irene Fuji-Hara. Ryoh Gaviano, Marco Glowinski. Roland Feng, Shui Fontenot, Robert A. Fujii. Nobuhiko *Gavrilik, Alexandre M. Gluck. Herman R. *Feng. Xiaohing Fontrier, Gabriel Fujisaki. Rieko Gechter, Jerry Glueck, Brian W. e Fenley, Sergio Roberto e Foote, S. Ashby Fujiwara, Daisuke Geddes. Keith O. Glynn. John J. Fenske. Christian • Forhes. Stephen H. Fujiwara. Hidenori Gehring. Frederick W. *Gneiting. Tilmann J. Fenstad. Jens E. * Ford. David Fujiwara, Masahiko Geissinger. Ladnor D. Goblirsch. Richard P. Ferber. Thomas Ford. David A. Fukuda, Komei eGeller. Daryl Neil Goddard. J. D. Ferebee. Ann S. *Forman. Susan L. Fukushima. Masatoshi Geller, Susan C. *Goddard. Wayne D. Ferenstein, Elzbieta Z. Fornaess. lohn Erik Fuller, F. Brock Geman. Stuart Alan Godfrey. Colin Ferguson, David R. Forster, Klaus-lurgen *Fuller. Kent R. eGenensky, Samuel M. Godin. Paul J. Ferguson, Helaman eForsythe, Keith W. *Fuller, Mark E. Genet, lean Raymond Goebel, K. *Fernandez. Roberto Fossum, Robert M. Fuller, William R. Gentili. Graziano Goettfert, Rainer Fernandez-Rodriguez, Marisa *Foster. Andrew Fuller, William R. Geoghegan. Ross *Goggin. Eimear M. *Fernando. T. Sarath *Foster, James H. Fulton, Curtis M. Georgakis. Peter eGolan, Jonathan S. Ferrari. Andrew B. Foulis, David 1. Fulton. John D. Geraldo C.. Pedro 1. eGoldberg, Charles H. Ferrari. Carlo Fox. Jeffrey Stephen Fulton. William Geramita, Anthony V. Goldberg, David *Ferreira, Fernando 1. Fox. John Michael Funabashi. Shoichi *Gerardo, Mora Alpizar Goldberg, David M. Ferreira. Maria loao Fox. Ralph Fuqua. leffry B. *Gerards, Bert Goldberg. Seth 1. Ferreira Rosa. Jose Humberto Foxby, Hans-Bjorn Fursikov. Andrei Vladimirovich Gerber. Marlies Goldberg. Seymour *Ferreirim. Isabel M. Fragoso, Marcelo D. Furutani. Kenro Gerhardt, C. *Goldblatt, Robert I. Ferrer, lesus Frame, J. Sutherland Fwu, Chihchy eGerig, Stephen R. Goldfeld, Dorian Ferrero, Miguel Frame, Michael Lee Fyfe. Andrew Gerisch, Wolfgang Goldman, Jerry *Ferreyra, Guillermo Segundo *Franchi, Bruno Gaal, Lisl Novak Gerlach, Eberhard G. P. Goldman, William Mark Ferri. Massimo Frangos. Nicholas Efstr Gahardo. lean-Pierre Germain, Paul Goldsmith. Judy Ferris, Ian M. * Frank. Michael Gabay, lacques Germay, Noel Goldstine, Herman H. Ferro, Ruggero Frankel. Theodore T. Gabriel, Richard F. Geronazzo. Lucio *Goldston, Daniel A. Feser, Victor G. Franks, John M. *GabrieI, Steven Allen *Geronimo. leffrey S. Golland. Louise A. *Field, Michael 1. Fransen, Arne Gabrielov, Andrei Gershenson. Hillel H. Golland, Ronald W. Figiel, Tadeusz Frappier. Clement Gaes, Peter Gerstenhaber. Murray Golomb. Michael

816 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------_. n 1111'1\Wii AMS Centennial Fellowship Fund

•Golubitsky. Martin *Green. William L. Gustafson, Sven-Ake Harborth. Heiko *Heinicke, Allan G. Gomes, M. Gabriela Miranda •Greenbaun, Nicholas N. *Gustafsson, Bjorn Sture Lennart Harbourne. Brian Heinig. Georg •Gomez. Luis Arbey Green berg. Ralph *Gusted!. Jens Hardarson. Askell *Heinonen. Juha M. Gomez, Luis Enrique W. Greenblatt, George E. Gutenmakker. Victor Harden. Milton W. Heins. Maurice H. Gomez Pardo, Jose Luis Greene. Curtis Guterman. Martin M. Hardt. Robert M. *Heinze. Joachim Gomez-Ruiz. Francisco Greene. John Robert Gutknecht. Martin H. *Harmand. Peter Hejtmanek. Johann Hans *Gomez Tato, Antonio Greengard. Leslie F. Guy. Richard K. Harmelin. Reuven *Helfer. Adam D. Gomi. Kunio Greenhall. Charles A. Guy. Wynne Alexander Harms. Eerik Thomas Helgason. Sigurdur *Gompf. Robert E. Greenleaf. Frederick P. *Guzman. Miguel de Hamad. John P. Hellberg. H. Stefan *Gonzalez. Faustino *Greenlees. John P. C. Ha. Ki Sik *Harness. Richard S. Heller. Alex *Gonzalez. Fulton Beltran *Gregory. David A. Ha. Kwang Chul *Harnett. Gerald P. Heller. Daniel J. Gonzalez. Joe Fred. Jr. Gregory. Thomas B. Haack. W. Harrell, Andrew William Heller. Dorothy M. *Gonzalez. Raul Ernesto Greicar. Richard K. *Haaland. Inger J. *Harrell. Ronald E. Hellerman. Leo Gonzalez-Barrios. Jose M. Greif. Stanley J. Haas. Andrew H. Harrington. Paul J. Hellerstein. Nathaniel Shawn *Gonzalez-Diez. Gahino Greiner. Peter C. Habetha. Klaus Harrington. Walter J. Hcllerstein. Simon Goodearl. Kenneth R. Greville. Thomas N. E. Habre. Samer S. *Harris. Desmond J. Helton. J. William Goodman. Roe W. Grey. Louis D. Hack, Melvin N. Harris. Gary A. *Helwig. Karl-Heinz Goodman. Sue E. Griess. Robert Louis. Jr. Hackenbroch. Wolfgang Harris . .Joe Hemasinha. Rohan •Goodrich. Suzanne Dinga Grigni, Michelangelo Hackett. Hal Harris. John C. *van Hemmen. J. Leo •Goodrick. Richard E. Grilliot, Thomas J. Haddix, George F. Harris. Melanie J. *Hemminger. Robert L. Goodwillie. Thomas G. Grinshpan. Arcadii Z. *Hadjidimos. Apostolos *Harris. Michael H. Hemmingsen, Erik Gopal. Mangalam R. Gritzmann, Peter *Haebich. William Han·is, Theodore E. Hempel, J. A. Gopalsamy. Kondalsamy Groberg. Lowell A. Haemmerlin. Guenther Harrison. Carol Nicoline Hempel. John P. *Goranko. Valentin F. Grobler, Jacobus J. Hag. Per Harrop. Fred F. Hemstead, Robert J. Gorbounov. Vassili *Grochenig. Karlheinz U. Hagglund. Lee 0. Hart. Evelyn L. Henderson. David W. Gordon. B. Brent Gn)enenbnom. A. Hagis. Peter, Jr. Hart. Neal Henderson. Francis Me Vey Gordon. C. M. *Van Groesen, E. Hagler. James N. Hartig. Donald *Henderson. Gregory P. Gordon. Carolyn S. Grognard. Rene J. M. *Hagood. John W. *Hartl. Johann Henderson, James P. *Gonion. Hugh *Groisser. David Hahn. Gena Hartman. James L. Henkin. Leon A. Gordon. Robert *Gromoll. Detlef •Hahn. Kyong T. Hartmanis. Juris Henniger. J. P. Gorecki. Henryk Gromov, Mikhael •Hahn. Susan G. Hartshorne. Robin Henning. Michael A. Gorenflo. Rudolf *Gronau. Hans-Dietrich 0. F. Hahne. Gerhard E. Haruki. Shigeru Henrich. Christopher J. *Goresky. R. Mark Grondin, Francois Haight. John A. •Hasegawa. Minoru Henriques. Anna S. Gorkin. Pamela B. •Gross. Benedict H. Haiman. Mark Hashimoto. Ki-ichiro Hensley. Douglas A. Goss. David M. Gross. Daniel Joseph Hain, Richard Martin *Haske II. Cymra Henstock. Ralph Goss. Robert N. Gross. Leonard Haken. Wolfgang Haskell. Deirdre *Herfort. Wolfgang Norbert Gosselin, John A. Gross. Paul W. Hakim. Jeffrey L *Haslinger. Friedrich Hering. Roger H. Gosselin. Richard P. *Grasse-Erdmann. Karl-Goswin Halberstam. Heini Hasselblatt. Boris Herman. Richard H. Goth. John A. Grossman. Edward H. Hales. Alfred W. Hassinger. Bill, Jr. Hermann, Margaret A. Goto, Hideo Grossman, Marvin W. • Hales. R. Stanton. Jr. *Hastad, Johan Hermann. Robert Goto. Midori S. *Grotowski. Joseph Francis Hall. Brian C. Hastings. Harold M. Hernandez. Fernandez Teresa Goto. Shiro Grove. Edward A. Hall. Mark Edwin Hasumi. Morisuke Hernandez. Jesus Gottlieb. Daniel H. Grove. John W. Haller. Thomas Hatori. Osamu Hernandez. Rafael Gottlieb. David Grove. Larry C. •Hamadani. Davar A. Hattori. Akin *Hernandez. Sah·ador Goutier. Claude *Groves. J. R. J. *Hamaya. Yoshihiro *Haughton. Dominique M. A. *Hernandez G .. Carlos Gouvea. Fernando Quadros Grubb, Gerd *Hamedinger. Wolfgang Hausknecht. Adam O'Neill *Hernandez-Guerra. Juan M. *Goyo. J. 0. Gruber, Peter M. Hamenstadt. Ursula Hausmann. Jean-Claude Hernandez Ruiperez. Daniel Goze. Michel Grudin. Arnold Hamilton. David 0. Hautau. Ralph H. Herrera. Robert B. Graber. James S. *Grundhofer. Then Hammack. William D. Hayashi. Mikihiro Herreshot'f. James B. •Grabiner. Sandy Gryllakis. Constantinos Hammer, Carl Hayashi. Nakao Herriot. John G. *Grace. Edward E. Gualtierotti. A. F. Hammett, Michael E. Hayashi. Takao Herrmann. Joseph M. *Gradel, Erich Guaraldo. Rosalind J. Hammond. William F. Hayashida. Tsuyoshi Hertzlinger. Joseph *Graf. Siegfried Gudder. Stanley P. Hamrick. Gary C. Hayden. John L. Herwitz. Paul S. *Gragert, Peter K. H. Guenard, Francois Han. Chong-Kyu Haydn, Nicolai T. A. *Herzberger. J uergen P. Graham. Ian Guenette. Robert Hanche-Olsen. Harald Haydon. Richard G. Herzog. Emil R. Graham. Sidney W. Guerin. Esther E. Handel. David Hayek. Nacere Herzog. Ivo *Gramain, Andre •Guerrieri, Bruno Handley. George Donald Hayes. David R. Hethcotc, Herbert W. Gramsch. Bernhard *Guest. Martin A. Hanes, Kit Hayne, Roger M. Hettling. Karl F. Grande. Patrick A. eGuetti, Joan F. Hanges. Nicholas He. Xiao Liang Hetzer. Georg Grannell. Michael John Guglielmi, Josephine P. •Hanisch, Herman Headley, Velmer B. Heuer. Gerald A. Graver. Jack E. Guilbault, Craig R. Hank. John L. Hearne. Leonard B. Heuver. John G. Graves, Larry K. Guillemin. Victor W. Hanlon. Philip J. Hearst. Will Hewitt, Edwin •Graves, William H. Guillot, Jean-Claude C. Hann. Kathleen Marie Heath-Brown. Roger Hewitt. Gloria C. Gravesen, Jens Guimier, Alain Hanna. J. Ray *Hebda. James J. Heyer, Herbert K. *Gray, Alfred Gulden, S. L. Hano. Jun-ichi *Hebert, Michel *Hiai. Fumio Gray, Jeremy John Gulliver, Robert D .. II *Hansell. Roger W. Hechler. Stephen H. *Hibbard. Allen C. Gray, John W. Gundersen, Gary G. *Hansen. Carsten Heckman. G. J. •Hickling. Fred *Gray, Mary W. Gunduzalp, Yavuz *Hansen. Mary E. *Hedberg. Lars I. Hicks. Robert L. Gray, Robert E. Gundy, Richard F. Hansen, R. 0. Hedlund. James H. • Hida. Haruzo Greaves, George Gunnarsdottir Bodvarsson. Hansen. Vagn Lundsgaard *Hegland. Markus Hida. Takeyuki Greear, Delbert P. T. Gudrun M. Hanson. Stanley C. *Heigho, George W. Higgins. James Logan Green. David J. Gunnarsson. Thomas E. W. Harada. Shigeharu Heijmans. Johannes G. Higgins. John R. Green. James A. *Guo. Li Haralampidou, M. Marina *Heine. George W.. IJI Higuchi. Yasunari *Green. Leon W. Gurney. Margaret Harbater. David Heineken. Hermann Hijab. Omar

SEPTEMBER 1994, VOLUME 41, NUMBER 7 817 """'"'"""'"'""""""'"""""'"'"'"""""""'""'"'"""""""'"'"'"'"'"'"'"'"'"'"""""'"'""""'"'"'"'"'"'""'""'""'"""'"'"'"'"'"'"'"'"'"'"'"'"'"""'"'"------·-.. -··-··-""'"'"'"'"'"'''"'"'"'"'"'"""""""""'"'"""""""'""'"""'"'"'"'"'"'"'"'"""'"""""'"'"'"""''""""'"'"'"'""'""'"'"'"""""'"'"'"'"'"'"'"'"'' AMS Centennial Fellowship Fund

*Hijazi. Oussama Holland, Samuel S .. Jr. Hughes, Michael Scott Ingram. Nancy Jane J ameyson. Stephen Hilbert, Stephen R. Holland, W. Charles • Hughes. Rhonda J. Innami. Nobuhiro Jami, C. Adrien Hildebrand, Adolf J. Holman. Wayne James. III Hughes, Richard P.. Jr. Inoue, Hiroshi Jamjoom. Fatmah B. Hildebrandt, Theodore W. *Holmann. Harald R. A. Hughes. Ruth L. lnsel, Arnold J. Janicki, Ryszard Hilden, Hugh M. Holmes. Charles S. Huh, Won Invernizzi. Sergio *Jannsen, U. •Hilgers, John W. •Holmes, John P., III Huibregtse. Mark E. *Ion. Patrick D. F. *Janowsky, Steven A. Hill. David G. B. Holmes, Philip John Huige. Gustavus E. lpina, Lynne Kamstra Jans, James P. *Hill. Donald M. •Holmes. Randall Reed Huilgol, Raja R. Irving, Ronald S. Janse van Rensburg, Esaias J. Hill, E. Stamford. II Holmes, Richard B. *Huisken, Gerhard Isaac. Richard E. Janson. Richard W. Hill, James Holten, Robert P. Hukle. George W. Isaacs. I. Martin *Janson, Svante Hill. Ralph Norman Homer. Roger H. Hulkower, Neal D. Isaacson. Eli Jantosciak. James S. Hill. Shirley A. *Homma. Masaaki Hull, Thomas E. Isaacson, Eugene *Jantzen. Chris S. Hiller, David Halsey Honda. Kin-Ya Hulsbergen, Wilfred W. J. *Isard, Stephen D. Jantzen, J ens Carsten *Hillman, Jonathan Arthur Honold. Thomas Hume, Leigh R. *Isbell. John R. Janusz, Gerald J. Hilt. Sandra N. Hoobler, Raymond T. Hummel, James A. Iseki, Kiyoshi Jara Martinez. Pascual Hilton. Peter J. Hood, Rodney T. Humphreys, James E. Ishihara. Hajime *Jarchow, Hans Himonas, Alexandrou A. Hopkins. Laurie B. Huneke, Brian H. *Ishihara. Tadashige Jardine, John Frederick Hinchey, Michael G. Hopkins. Neil E. Huneke, Craig L. Ishihara. Toru *Jarvi, Pentti K. *Hind. Hugh Robert * Hormander. Lars V. Hung. Henry Hin-Lai Ishii. Hitoshi Jarvis, Peter M. Hinder, Rainer Horn, Jean MacGregor Hunt, Bruce Ishii, Jyun J ategaonkar, Arun V. *Hindley. James Roger *Horn, Werner *Hunt, FernY. Ishii, Noburo *Jefferies, Nigel P. Hindman, Neil B. *Horna. Luis Hunt, Louis Roberts Ishii, Shihoko *Jeffrey, Lisa Claire Hingston, Nancy Horner. Mary Lynn Hunt, Richard A. Ishimoto, Hiroyasu Jeltsch-Fricker. Rita Hinman. Peter G. Horowicz. Paul Hunt. Walker E. Islamov, Galimzian G. •Jenck, Mike P. Hinson. Edward K. Horrigan. Timothy J. Hunter, Norma Gerkens •Ismail. Mourad E. H. Jennings. George A. Hintzman, William R. Horrocks. Geoffrey Hunter, Thomas J. ltai. Masanori Jennings, Leslie Stephen Hirano. Norimichi Horsfield, Christopher H. Hunzeker. Hubert L. Itatsu, Seiichi Jensen, Bjarne S. Hirsch, Michael D. Horvath. Charles Daniel Huotari, Robert Heikki Ito, Kiyosi Jensen, Christian Ulrik Hirschfeld, James W. P. Horvath. John M. Hupperich, Marcel Ito, Noboru Jensen, Robert R. Hirschfelder, Elizabeth S. Horvath, Jozsef Hurley. Donal J. Ito. Ryuichi Jepsen, Charles H. Hirschfelder, John J. *Horwitz. Alan L. Hurley, James F. Ito, Yoshifumi Jerison, David Hirschfelder, Rosemary Hosack. John M. •Hurley, Michael G. •Ito, Yuji Jerome, Joseph W. Hirshfeld. Joram Hosoi, Tsutomu *Hurrelbrink. Jurgen Itoh, Tatsuo *Jessup, B. J. Hirzebruch, F. E. P. Haste, Jim E. Hurtubise, Jacques C. ltoh, Yoshiaki Jha, Vikram Hislop. Peter David *Hostettler, Maria Hurwitz. Carol M. ltokawa, Yoe *Ji. Ronghui Hitchin, Nigel J. Hotta, Ryoshi Hurwitz, Solomon *Ivanov. A. F. *Jiang, Renfang Hitotsuyanagi, Nobuo Householder, James E. Husain, Taqdir Ivanov, Alexandre Jimenez, Jose Alfredo Ho, Yue-Chan P. Houston. Evan G. *Hosler, Jurg R. I ves, Robert T. *Jin, Gyo Taek Hobart. Sylvia A. * Housworth, Elizabeth Ann Hosseini. Sufian Y. Ivochkina. N. M. Jockusch, Carl G .. Jr. *Hobbs. Arthur M. Howard, Edgar J. Hustin. Deborah L. lwamiya. Toshiyuki •Jofre. Alejandro Hobbs. Stephen Howard, Fredric T. Hutchinson. George A. Iwanaga. Yasuo *Johannson, Klaus Hochman. Daryl W. Howard. Paul E. Hutchinson. Joan P. Iwaniec. Henryk Johansen. Torben Bygballe Hochschild, Gerhard P. Howard, William A. Hutton. Edward L. Iwasaki, F. Shigeo Johanson, Paul J. Hochstadt, Harry Howe. Roger E. Hveberg. Steinar Magne !washita, Hirokazu *Johansson, Kurt Hochster, Melvin Howell. Joseph 0. Hwang. Jang C. *Izadi. Elham John, David J. Hochwald, Scott H. Howell. Seth Andrew Hwang. John Jew-Chen lze. Jorge A. Johnsen, Eugene C. *Hodel, Richard E. *Howie, James Hyllengren. Anders R. •Izumino. Saichi Johnsen, Ronald L. Hodges, Lucille M. Hoye. Laurence G. Iannelli, Mimmo lzumiya, Shyuichi Johnsen, Trygve Hodges, Wilfrid A. Hoyt, W. L. Iarrobino. Anthony A .. Jr. Jablow. Eric Robert *Johnson. Aimee S. A. Hodgson. Jonathan P. E. Hsia. J. S. Ibrahim, A. Shawky Jackins. Harvey Johnson, Barry E. Hoefer. Edwin T. Hsiang, Wu-Chung lei, Yutaka *Jackowski, Stefan Johnson. Bradford W. Hofer. Helmut H. W. Hu, Bei Igarashi, Akira Jackson. Lloyd K. *Johnson. Brenda L. *Hofer, Robert D. Hu, Kai-Yuan Igarashi, Masao Jaco, William H. Johnson. Charles N. Hoffman. Jerome William *Hua. Yang lgari, Satoru Jacob, Henry G. Johnson, D. Randolph Hoffman, Michael E. Huang, Huaxiong lgnaczak. J ozef Jacob, Kurt S. Johnson, David Copeland Hoffman, Michael J. Huang, Zhi Yuan lgodt, Paul G. Jacob, Niels Johnson, David L. Hoffman. William C. Hubbard, Darryl F. Iha, Franklin T. Jacob, William Burkley Johnson, David Lewis Hoffmann, Detlev W. Hubbard, John Hamal lhara, Yasutaka Jacobs, Felix J. Johnson, Donald G. Hoffmann-Jorgensen, Jorgen Hubbart, Wayland M. !ina, Riichi Jacobs, Harold *Johnson, Gene Douglas Hofmann, Karl H. Huber. Alfred 0. Iio, Tutomu Jacobsen. Martin Johnson, Gerald W. Hogan. Daniel A. Huber. Heinz Ikeda, Kazuoki Jacobson, Clas A. Johnson, Guy. Jr. *Hogan, Guy T. Huber, Klaus Il'ichev, Vitaly Grigorevich Jacobson, David W. Johnson, Harold H. Hogan. Peter A. Huber-Dyson. Verena *Illman, Soren A. Jacquet. Herve M. Johnson. Jon L. *Hogbe-Nlend, Henri Hudgins, Archibald Perrin Ilmanen. Tom Jaffa. Robert E. Johnson. Kenneth Walter Hogesteeger, F. W. *Hudson, Robin L. Ilyashenko, Yulij Sergeevich *Jaffard. Stephane P. *Johnson, Michael A. *Hognas, Goran Huebschmann, Johannes Im. Geun Bin *Jaffe. David B. *Johnson, Peter M. •Hogreve, H. J. *Huerta, Carlos Cuevas lmai. Hideo Jaffe. Martha A. Johnson, Robert Shepard Hoholdt. Tom Huet, Denise *Imam, Ali Jaffe, William J. Johnson. Rodney W. Hoke, Harry F., III •Huff, Charles W. *Imamoglu. Ozlem Erverdi Jager. H. Johnson. Theodore D. •Holberton, John V. •Huff. W. N. Imayoshi. Yoichi *Jakobsen. Arne *Johnston, Elizabeth A. Holder. L. I. Hufford, George A. lm Hof, Hans Christoph Jambois. Thomas F. *Johnstone, P. T. Holland. Barbara A. Hughes. Anne *Immerman, Neil *James, David M. *Jolson. Sheldon B. Holland, Finbarr Hughes, Cephas D. Imrich. Wilfried James, Gordon D. Jones, F. Burton *Holland, Martin P. Hughes, Joseph A. Infante. Ettore James, Robert C. Jones, Harold T.

818 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ----·------·····""···------·------·------·--...... ______,...... , ______...... ______, .. , .... ______, ______,,.,...... - ...... _.. ______,,.,...... AMS Centennial Fellowship Fund

Jones, James P. Kanold, Hans-Joachim Kelly, John B. Kirwan. Frances C. Kojima, Sadayoshi Jones, Marsha Finkel *Kantor. Michael J. *Kelly, Theresa D. Kirwan, William E., II Kolhig. Kurt Siegfried Jones, Phillip S. Kaplan, Alexander J. Kemp, Daniel C. *Kiselman, Christer 0. Kolesar. R. J. Jones, Ray L., II Kaplan, Samuel R. *Kemp. Yvonne A. Kishi. Masanori Kolibal. Joseph G. Jones. Vaughan F. R. Kaplan, Stanley Kenison, Jeanne H. Kister, Jane • Kolitsch. Louis Worthy Jongen, Hubertus Th Kaplan. Wilfred Kennedy, Edward S. Kisynski, Jan *Kolk. Johan A. C. Jonker, Leo B. Karade, Tryambak Mahadeorao Kennedy, Gary P. Kita, Hiroo *Koller. Herbert Jonsdottir, Kristin Halla Karailiev. Lubomir Alexandrov Kennedy. Judy Anita eKitada. Hitoshi Kolmus, Peter A. Jonsson, Bjarni Karamatsu, Yoshikazu •Kennedy, Robert E. Kitada. Yasuhiko Kolodner, Ignace I. Jonsson, Thordur *Karamzadeh, 0. A. S. *Kennedy. Stephen F. Kitano, Koh-Ichi *Kolsrud. Torhjorn Sigurd Jorba, Angel Karcher, Hermann Kennison, John F. *Kittel, Phyllis M. Komatsu, Hikosaburo *Jordan, Byron D. Karel. Martin Lewis *Kenschaft. Patricia Clark Kivenko. Ken Komatu. Yusaku Jordan. Kirk E. *Karisch, Stefan E. Kent, George A. Kiyek. K. Komiya. Yurin Jordan. Steven L. Karle, Jerome Kernast, John C. Kiyohara. Mineo eKomm. Horace Josephson, William Allen Karlsson, Johan Kerr, Sandria N. *Kiaasen. Gene A. Komura. Takako *Josephy. R. Michael Karno, Zbigniew Kerzman. Norberta L. Klainerman. Sergio Kon, Mark Andrew Jouanolou, Jean-Pierre Karnowski, Eric E. Keshishyan. Joseph •Kiamkin. Murray S. Konig, Heinz J. *Ju. Hyeong-Kwan • Karpishpan, Yakov Kesten. Harry *Klassen. Eric P. Konno. Yasuko del Junco, Andres Karrass, Abraham *Keum. Jong Hae Klatman. David S. *Koppelberg. Sabine Jurca, Dan Karydas, Nicholas G. Keyfitz, Barbara L. Klauder. John R. Kopperman. Ralph D. Just, Winfried Kashihara. Kenji Kezdy, Andre E. Klay, Matthias P. Koranyi. Adam *Justice. James H. *Kashiwagi, Yoshimi Khajah, H. G. Kleban. Peter H. Korchmaros, Gabor Jyoo, Yeong-Heum Kasriel. Robert H. Khalimsky, Efim Kleiner. Alexander F.. Jr. Korenblum. Boris Kaashoek. Marinos A. *Kass. Steven Neil Khasminskii. Rafail Z. Kleisli. H. Korevaar. Nicholas Jacob Kadlecek, David *Katavolos, Aristides Khuri, Soumaya Makdissi Kleiter, Gernot D. Koriyama. Akira Kagstrom, Bo T. Kates, Louis K. *Kichenassamy, Satyanad Kleppner, Adam •Korman. Philip L. Kahan, William M. Kato, Takao Kido, Kazuo Kletzing, Dennis R. Koschorke, Ulrich M. Kahaner. David Kenneth Kato, Tosio *Kidwaii. Hariss Kliemann. Wolfgang H. Kose, Tairoku Kahn, Daniel S. Katsuda, Atsushi Kientzle, Timothy Brian Koonce Klimenko, Stanislav V. Kosinski. Antoni A. Kahn. Donald W. Katsura, Toshiyuki Kierlanczyk. Marek Klotz. Eugene A. *Koskela, Pekka J. Kahn, Jeffry N. Katz, Victor J. Kiesel, Harry A. *Kiyatskin, Valery I. Koski, Timo J. Kahn, Peter J. Katzen, Dahn Kikuchi, Koji *Knapp. Wolfgang D. * Kosmann-Schwarzbach. Yvette *Kaidi. El-Amin Katznelson, Y. Killeen. John *Knaust, Helmut Kosmodemyanskii, A. A. Kaijser, Sten Kauffman, Louis H. Killgrove, Raymond B. *Knieper. Gerhard • Kossack, Carl E *Kaijser, Thomas Olof Kauffman, Robert M. *Kim, Ann Chi Knight, Frank B. Kostclich, Eric J. *Kailath. Thomas Kaufman, Arthur Kim, Hayon Knight. Julia *Kotiuga, P. Robert *Kaiser, Paul J. Kaufman. William E. Kim, Hong Jong Knill, Ronald J. Kotler, Reed S. *Kaishev. Vladimir Krumov Kaufmann, Karl Jorg Kim, Hyuk •Knio. Omar M. Kotlow. Daniel B. Kajiwara, Joji * Kaup. Burchard Kim, Hyung Kook Knoerr, Alan P. *Kourouniotis, Christ

----·--·------~-----.. ---~---- ... ------SEPTEMBER 1994, VOLUME 41, NUMBER 7 819 ------·-·-·-···-·------·------AMS Centennial Fellowship Fund .. -·-·-.. ··----

• Kubo, Fujio Lamoureux. Claude Lebel. Jean E. Lever, Edward L. Livorni, Elvira Laura *Kubo, Fumio Lampe, William A. Leborgne, Daniel Levin, Jacob J. Livshits, Leonya Kudla, Stephen S. Lampert, David S. Lebow, Arnold Levin, Richard G. Llarull. Marcelo Kudo, Tatsuji Lampone, Leo W. Lebowitz, Joel L. Levine, Eugene Llave, Rafael de Ia Kuenzi, Norbert J. Lancaster, Kirk E. *LeBrun, Claude R. Levine, Harold I. Llosa, Joseph Kugler, Lawrence D. *Lancaster, Peter LeCam, L. M. Levine, Jack Lloyd. Stuart P. Kuhn, William W. *Landau, Susan Lecomte. Pierre C. Levine, Jerome P. La, Tzee-Nan Kuo Kuhne!, Wolfgang Lander, Felix I. Lee, Carl W. *Levy. Azriel Lo, William Kuiken, Kathryn Landin, Joseph •Lee, Cheng-Ming Levy, Gene Lobo-Pereira, Fernando M. F. *Kuiper. Nicolaa.~ H. Landrock. Peter Lee. Cho-Seng Levy, Joshua B. Lochak. Pierre Kulisch, Ulrich *Landsman, Nicolaas P. Lee, Chun-Nip Levy, Lawrence S. Lockhart, Deborah Frank *Kulkarni, Ravi S. *Landstad, Magnus B. Lee, Dong Hoon Lewan. Douglas Lockhart, Jody Meyer Kumagai, Donna J. *Landucci, Mario Lee, Do-Won Lewis, Adrian S. *Loday, Jean-Louis Kumahara, Keisaku Landweber, Peter S. Lee. Jack Yu Lewis, David W. Loeb, Peter A. Kuma.~awa, Nin Lanford, Oscar E., III Lee, John M. Lewis. Hugh L. *Loewe, Stefan Kumazawa, Toshihisa •Lang, William E. *Lee, Jong-Hyeon Lewis. John B. Lofaro, Thomas P. Kumjian, Alexander *Lange, Ridgley E. Lee, Jyh-Hao Lewis. L. Gaunce, Jr. Loh, Gunter Kumlin, Peter Langebartel, Ray G. Lee. Ke-Seung Lewis. Roger T. Lok, Walter L. *Kummer, Martin P. Langenhop, Carl E. Lee, Myrna Pike Lewis. William James Lolli, Gabriele Kunimura, Dennis E. *Langer, Heinz Lee. Ronnie *Leyton, Rigoberto Medina Lombardo, Charles J. *Kunisch. Karl K. Langsam, Joseph A. Lee, WillY. Li, Bingxi *Londen, Stig Olof •Kunkle, Thomas Laning, J. Halcombe Lee. Young Whan Li. Li Long, Dong Yang Kunle, Heinz Lanza de Cristoforis. M. Leemans, H. W. *Li. Ming-Sun Long, John M. *Kunoff, Sharon Lapidus, Arnold Leep, David B. *Li. Yingchen Longbotham, Harold G. Kunze, Ray A. Lapidus, Michel L. Letkovitch, Leonard P. *Lial. Margaret L. *Longley. James Wildon *Kunzle, Hans Peter Lappan, Peter A .. Jr. *Lefton, Lew E. Libby, Richard Allan Longobardi. Patrizia Kuroda, S. T. Lara, Francisco Leger, George F. Liberman, Zvie Loo, Joseph C. Kurshan, Robert P. Lardy, Lawrence J. Leggett, Robert N .. Jr. Lichnerowicz, Andre Looijenga. Eduard J. N. Kurss, Herbert Larrazabal, J. M. *Lehman, R. Sherman Lichtenbaum, Stephen Loone, Leiki *Kurtz. David C. Larsen, Mogens Esrom Lehmann, Robert E. *Lick, Dale W. Lopez, Amparo Kurtz, Stuart A. Larson, David R. Lehner, Joseph Lieb, Elliott H. Lopez. Antonio Fernandez *Kurtz. Thomas G. Larson, Edward H. Leibnitz, Edward A. Lieberman, David I. Lopez-Carmona, Antonio Kurtzke, John F., Jr. Larson, Jean Leibowitz, Gerald M. •Lieberman, Gary M. Lopez-Escobar. Edgar G. K. Kushner, Harvey Larson, Loren C. *Leichtweiss, Kurt *Liebers, Annegret C. Lorch, Lee *Kustak. Jamie E. Larson, Richard G. Leinbach, L. Carl •Lien, Magnhild *Lorentz. George G. * Kusuda, Masaharu Larson, Suzanne Lynne Leipnik. Roy B. Lightbourne. James H .. III *Lorentz. Rudolph A. Kusunoki. Yukio LaSalle, Margaret M. Leites, Dimitry A. Ligozat. Gerard Yvon *Lorenz. Dan H. *Kuttler, Kenneth Latimer Lashof, Richard K. Leith, Cecil E .. Jr. *Lih, Ko-Wei Lorenz, Martin *Kuusalo, Tapani J. Laska, Michael Leitzel, James R. C. *Lim. Jong In *Lorica, Benjamin G. Kuwahara, Ruisbi Lasker, Mohammed G. *Leitzel, Joan P. Lima, Asvald *Loring. Terry A. Kuzennyi, N. F. * Lasserre, Jean Bernard Lejeune-Jalabert, Monique *Lima-Filho, Paulo Loss, Michael P. Kwak, Hyo Chul La.~settre, Edwin R. *Leland. Kenneth 0. *Lin, Chin-Cheng Lotito, Pablo Andres Kwak, Nosup Latch, Dana May Lelong. P. J. Lin, Jindra Loud, WarrenS. Kwembe, Tor A. Laubenbacher, Reinhard *Lemaire, Jean-Michel Lin, Shen Louton, Tom *Kwon, Kil H. Lauchli, Hans *Lemaire, Luc *Lin, Wen-Hsiung Low, Emmet F.. Jr. *Kwon, 0-Hun Lauer, Mark D. *Lemay, William H. *Lin, Yizhong Low, Erik Kwon, Yonghoon Laufer, Henry B. Lemei, Han Lind. Douglas A. Lozowicki, Adam Kwon, Young-In *Laugesen, Richard Snyder *LeMesurier. Brenton John Lindberg. John A., Jr. Lu. Hongwen eKyrouz, Thomas J. *Lauman, Gerard Lemmer, Anna Aletta Lindemann, Ina •Lu, Kau-Un Kyuno, Shoji Laurence. Peter Michael Lempert, Laszlo Lindenstrauss, Joram Lu, Qi-Keng *Labarca. Rafael *Lauria, Francesco E. *Lempken. Wolfgang *Linder, David W. Lu. Tsu-Ming Labbe, Marcel Adrien Laurie, Cecelia •Lengyel, Bela A. Lindgren, Georg Lubarsky. Robert S. *Labesse. J. P. Laush, George *Lenis, Victor R. Lindgren. John E. Lucas, Billy Joe *Labouriau. Isabel Salgado LaValle, Irving H. Lenstra, Jan Karel Lindstrom. Mikael *Lucas. Carolyn D. Labrousse, Jean-Philippe *Law, Peter R. Lentz, William D. Lindstrom. Tom L. *Lucas, William F. LaBudde. Christian D. *Lawler, Gregory F. Lenz Peckham, Kathryn E. Lindstrom, Wendell D. Luce, R. Duncan Lacampagne, Carole B. Lawlor, Gary R. Leonard, Henry S .. Jr. Line, John P. Lucier, Bradley J. Lacey. Michael T. Lawniczak, AnnaT. *Leong. Yu Kiang *Ling. William Halstead Ludden, Gerald D. Lachance, Michael Anthony *Lawrence, John W. Lepowsky, James I. Lingefjard, Thomas Lue, Huei-Shyong *Lachlan, Alistair H. Lawson, David F. *Leroy. Andre G. Linnell. Peter A. *Luecking. Daniel H. Lackey, Jackson B. Lawson, H. Blaine, Jr. Leschen, John G. Lions. J. L. Luehr. Charles P. Laderman. Julian David •Lawson, Linda Graynel Lescot. Paul *Lipschutz-Yevick, Miriam A. Lueneburg, E. LaDuke, Jeanne Lawson, Walter R. Lesieur, Leonce Lipshutz, Robert J. Luk, Ring-Sun • Laffey, Thomas J. Lawvere. F. William Leslie, Joshua A. Lipton, R. J. Luke, Jonathan H. C. Lafontaine. Jacques Lax, Anneli Lesmes, Jaime Litchfield, Kay P. *Lukes. Jaroslav Lagarias, Jeffrey C. Lax, Peter D. Leth, Steven C. Little, Charles H. C. *Lumiste, Ulo Lagnese, John E. Lax, Robert F. Letzter, EdwardS. Little, John B. Luna, Eduardo A. Lahdelma. Risto Lazarov, Connor *Leu, Ming-Guang Little, Robert D. *Luna-Torres, Joaquin P. *Laine, Ilpo Lazarov, R. D. Leung, Dominic S. P. Littman, Walter Lund, Eric E. Laing, Alan J. Lazarsfeld, Robert K. Leung, Ka Hin Liu, Shih-Chao Lundell, Albert T. * Laksov, Dan Lazzari, Claudio Leung, Tat-Wing *Liu. Yung-Way *Lupton, Gregory M. Lambert, Howard W. Le, Anbo Leutscher, Trevor J. • Li verance, Eric E. Luther. Norman Y. Lambert, John Patrick Leach, P. G. L. Levaro, Richard A. Liverani, Carlangelo Lutterodt. Clement Henry *Lami Dozo. Enrique Jose Leavitt. William G. LeVeque, William J. Livingston. Albert E. Lutz, Julie H.

820 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund

Lutzer, David J. Manders, Kenneth L. Mather, John Norman McCracken, Marjorie Frost •Melrose, Richard B. Luxemburg, Wilhelmus A. J. Manderscheid, David C. Matheson, John D. McCray, Patrick D. •Mendenha11, Robert V. Lynch, Robert E. *Manfredi, Juan J. Mathis, Darren L. McCrea, Michael M. *Mendia, Pedro Lynch, William C. Manis, Merle E. Mathis, Frank H. *McCree, Paul W., Jr. Meng, Dao Ji •Lyons, Carter G. Manjarrez, Victor M. Mathsen, Ronald M. McCroan, Keith D. *Menini, Chantal Lyons, Jeremiah J. Mann, Patrick J. Matijevic, Jacob R. McCu11oh, Leon R. *Mercer, Richard Lyons, Richard N. *Manning, Anthony K. Matiyasevich, Yuri McCu11ough, Darryl *Mercourakis, Sophocles Lyons, Russe11 D. Mannion, Conal Liam Matovsky, John-Anton Charles McDonald, Janet Merikoski, Jorma K. Lyscas, Margie L. Mannix, C. E., Jr. *Matravers, David R. McDonald, John N. Merkes, Edward P. Lysko, Janusz M. *Mann-Nachbar, Pauline *Matsko, Vincent J. McDonald, Judith M. Merrie11, David M. •Lytle, Raymond A. Mans, Lothltr G. •Matsuda, Shigeo McDonough, J. M. *Merri11, Kathy Donovan Lyubeznik, Gennady M. Mansfield, Ralph Matsumoto, Yukio McDonough, Joseph Michael Merritt, John E. *Ma, Wen Xiu Mantel, Heinrich Matsumura, George McDougal, James A. Merzbach, Uta C. Mac an Airchinnigh, Micheal Mapa, Felina G. Matsumura, Hideyuki McDuff, Dusa Metas, Nick Macbeath, A. M. Marathe, Kishore B. Matsuoka, Yasushi McEliece, Robert J. •Metzen, Gerhard MacCamy, Richard C. Marce11an, Francisco Matsushita, Yasuo McE11igott, John Metzler, Richard C. MacCarthy, Justin G. *March, Jonathan D. Matsuyama, Hiroshi *McFarland, Robert L. Meurman, Arne MacCluer, Barbara D. Marchand, Margaret 0. Matsuzawa, Tadato *McGarry, Dorothy *Meuse!, Steffen G. Macdonald, I. G. Marchi, Ezio Mattei, Jean-Francois McGavran, Dennis R. *Meuser, Diane MacDonne11, John J. Marchiafava, Stefano Matti, Joseph T. McGehee, 0. Carruth Meush, Anatol A. Macfarlane, Andrew Ian Marcus, Brian Harry *Mattila, Pertti *McGettrick, Michael Meyer, Burnett C. *Machado, Armando Marcus, Leo G. *Mattner, Lutz McGibbon, Charles A. Meyer, Donald V. Mack, John E. *Marcus, Morel Moshe *Mattson, H. F., Jr. McGraw, Michael J. Meyer, Helmut Mack, John Michael Margerum, Eugene A. Mattson, Leroy T. McGuinness, Francis Oisin Meyer, Herman *Mackenzie, Kirill C. H. Margosian, Zaven Mattuck, Arthur P. *Mcintosh, Alan G. R. Meyer, Jean-Pierre G. Mackey, Michael C. Margulies, William *Matumoto, Hisayosi Mcintosh, William D. Meyer, Michael J. *Mac Lane, Saunders Margulis, Grigorii A. Matumoto, Takao *Mcintyre, Eldon A., Jr. Meyer, Paul R. MacLaren, M. Donald Marhuenda, Francisco Maugin, Gerard A. McKay, James H. Meyer, W. Weston MacNaughton, John S. Marichal, Gilles *Mauldin, R. Daniel McKay, Thomas G. Meyer, Wolfgang T. Macphail, Moray S. Markel, Scott A. Maule, Robert G. McKee, Earlena F. *Meyerhoff. Robert MacPherson, Robert D. Marker, David E. Maurer, Stephen B. McKee, Thomas Glenn, Jr. Mez, Hans-Christian MacQueen, David B. Markowitch, Walter, Jr. Mawata, Christopher P. *McKelvey, Robert W. *Miate11o, Roberto J. Maculan, Nelson F. Markvorsen, Steen Mawyer, Farley •McKemie, M. Jean Michael, Ernest A. *Madan, Manohar L. Marie, Charles Michel Maxfield, John E. McKenzie, Gary W. Michael, T. S. Madden, James Joseph Marlowe, Thomas J., Jr. •Maxson, Carlton J. McKenzie, Lionel W. Michaux, Christian Maddux, Roger D. Marotto, Frederick R. •Maxwe11, Charles N. McKibben, William P. Michel, Alexis Mader, Adolf *Marsden, Edwin L., Jr. Maxwe11, James W. McKinney, Richard L. Michiaki, Watanabe Madison, Bernard L. Marsden, Jerrold E. May, J. Peter *McLarnan, Timothy J. Michler, G. Madsen, Ib Marsha11, David Imler *Mayer, Daniel C. McLaughlin, Joyce R. *Michor, Peter Maeda, Hironobu Marsha11, Murray Angus Mayer, Laura Louise McLean, Richard James Mickens, Ronald E. Maeda, Michie Marte11i, Mario Umberto Mayer, Raymond A., Jr. McLennan, Andrew M. Mielke, Marvin V. Maeder, Roman E. Martens, Henrik H. *Mayer-Wolf, Eddy McLeod, Edward B., Jr. Mielke, Paul T. Maehara, Kazuhisa Marti, Jurg T. *Maynadier-Averous, Genevieve McMillan, Brockway Mihalas, Stelian *Maennel, Hartmut Martin, Daniel Maynard, James W. McMinn, Trevor J. Mihalik, Michael L. Magenes, Enrico Martin, Donald A. Mayor, John R. *McMullen, John R. Mihnea, Tatiana Magnuson, Alan William Martin, E. Dale *Mayorga, Jose B. *McMu11en, Peter Mikami, Kentaro Magri, Franco Martin, Gary A. Mazorow, Moya Miche11e McMurtrie, Kenneth A. Mikami, Toshio Magruder, Richard B. Martin, George E. Mazur, Barry *McNeal, Jeffery D. Mikolic-Torreira, Igor Magyar, Peter M. Martin, George W. Mazza, Christian McNeary, S. S. *Mikulska, Margaret Mahoney, Anne Martin, John R. Mazzeo, Rafe R. McNerney, Gerald M. *Milcetich, John G. Mahowald, Mark Martin, Nathaniel F. G. Mazzilli, Emmanuel McNulty, George F. Miles, Thomas J. Maier, Robert S. *Martin, Nigel Mazzocca, Francesco McOwen, Robert C. Milgram, R. James Maj. Mercede Martin, Norman M. Mbuyi-Kalala, Alafuele •McPhail, Joseph G. Milicic, Dragan Majda, Andrew J. Martin, William J. McAdam, Stephen J. McReynolds, Samuel E., Jr. Millar, Robert F. *Majewski, Wladyslaw Adam Martin Cabrera, Francisco McArthur, C. W. Meacham, Robert C. Miller, Charles F., III Makar-Limanov, L. G. Martindale, Wallace S., III McAsey, Michael J. Meade, Douglas B. Miller, Curtis P. Makepeace, Coline M. Martinez-Villa, Roberto McBrien, Vincent 0. Meakin, John C. •Miller, D. D. Makkai, Michael Martino, James R. *McCanna, Joseph E. *Meaney, Christopher Miller, Dale A. Makovoz, Yuly Martinon, Antonio *McCarter, Merdis J. Mears, Florence M. Miller, Donald S. *Makowsky, Johann Andreas Martin-Reyes, Francisco Javier *McCarthy, Charles A. Meda, Stefano Miller, Edward Makrides, Gregoris A. Maruyama, Toru McCarthy, Donald J. Meeker, Loren David Miller, E11en Rammelkamp Malafronte, Thomas A. Marvin, John W. McCarthy, Randolph, III Megginson, Robert Eugene Miller, Jack M. *Maleki, Amir Mascioni, Vania D. McCaughan, Dennis J. Mehrrnann, Volker Miller, John Boris Ma11et-Paret, John J. Maserumule, Motodi S. *McCleary, John H. Meier, David Miller, John G. Malliavin, Marie-Paule Maskit, Bernard McCleary, Stephen H. Meier, John E. •Miller, Kenneth S. Maim, Dennis R. *Mas Mari, Jose McClenahan, Maurice D. Meilan, Gerard *Miller, Matthew Malon, David M. Mason, Robert M. *McColm, Gregory Loren Meisner, Morris J. *Miller, Michael J. *Malonek, Helmuth R. Massey, David B. McConne11, John C. Meister, Erhard V. Miller, Nicholas S. Maloof, Giles W. Masson, David R. *McConne11, Mark W. Melancon, Guy *Miller, Richard Alan Maloshevskii, S. G. Masumoto, Makoto McConne11, Robert K. Melendez, Enrique Asensio Miller, Richard R. Maltese, George J. •Masur, Howard A. McConne11, Thomas Melikhov, A. N. Miller, Thomas Len •Mamelak, Joseph S. Matchett, Andrew J. McCormick, Ferris E. Melin, Anders Miller, Wi11ard, Jr. *Mampitiya, Upali Mate, Attila McCoy, Robert A. Me11ender, James W. Miller, William David *Manca, Vincenzo *Mathas, Andrew Patrick McCoy, Thomas L. *Me11o, Maria Herminia P. L. *Miller, William V.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 821 ...... _------_ . AMS Centennial Fellowship Fund

Miller, Zevi Moore, Richard A. *Munoz Masque, Jaime Neidinger, Richard Dean Noll, Landon Curt eMillett, Kenneth C. Moore, Robert H. Munoz-Porras. Jose M. Neittaanmaki. Pekka Noot, Rutger Mills, Janet E. Moore, Robert Laurens eMunsey, Kyle Malone, Jr. *Nel, Louis D. Norden, Jeffrey S. Mills, William H. Moore, William E. Murase, Nobuyuki Nelligan, John D. Nordgren, Eric A. Milman, Mario *Moori. Jamshid Murata, Hiroshi Nelson, Edward Norman, Francis Alexander *Milman, Mark H. Mora, Leonardo E. eMurdoch, David C. Nelson, Edward O. *Norman, R. Daniel Milner, Eric C. Morain. Francois Murphy. Donald P. Nelson, Gail S. Norman, Robert Z. Milnor, John W. Morales-Luna, Guillermo *Murphy, Grattan P. *Nelson. Gary S. Norris, John W. *Mimar, Arman Moran, Charles W. Murphy, Paul F. Nelson, Larry D. Norris, Nancy E. Minac, Jan Moran, William Murphy, R. B. Nelson, Robert R. Northcutt, Robert A. Minagawa, Takizo Morawetz, Cathleen S. Murray, G. Graham Nelson, Roger B. Northrup, James I. *Minc, Piotr *Morchalo. Jaroslaw *Murray, William O. Nemethi, Csaba Norton, Alec Minda, C. David Mordeson, John N. *Murre, Jacob P. eNeri, Umberto *Norton, Graham H. Minemura, Katsuhiro Morduchow. Morris Musson, Ian M. Nerode, Anil Notarnicola, Filippo *Mines, Ray Morel. Benoit F. Muthiah, Muthu Nesbitt, Cecil J. *Nottrot, Roel Miniere, Michael A. Moreno, Guillermo Muto, Hideo Nesin, Ali H. Novella, Joseph D. Min-00, Maung Morewood, Robert Paul *Myers, Dale W. *Neubauer, Gerhard J. Novick, Beth A. Minsker, Steven Morgan, Frank Myerson, Gerald *Neuberger, John W. *Nowak, Werner Georg *MirabaL Ramon A. *Mori, Andrea Myrvold, Wendy J. Neugebauer, Christoph J. N owosad, Pedro Miranda, Rick eMoriah. Yoav Nachman, Louis J. Neumann, Bernhard H. Nucci, Maria-Clara *Mirchandaney, Arjan Sobhraj Morimoto. Akihiko *Nachtergaele, Bruno L. Neuwirth, Erich Nugari, Rita Mirollo, Rennie Morin, Ghislain Nacinovich, Mauro eNevai, Paul Nulton, James D. Mirsky, Norman D. Morley, Larry 1. *Naevdal. Geir Nevard, John A. Nunez-Doval, Ramon M. Misiurewicz, Michal Moron, Manuel Alonso Nagahara, Takasi Neveu, Jacques Nuss, Philippe Mislin, Guido *Morris, Alun O. Nagai. Osamu Neville, Charles W. Nussbaum, Roger D. Mitchell, A. Richard Morris, L. E. Nagano, Tadashi Newberger, Stuart M. N usse, Helena E. Mitchell, Josephine M. Morris, Robert A. Nagao, Hirosi Newlander, August, Jr. Nutt, Michael D. Mitchell, Stephen Ames Morrison, David R. Nagasaka, Kenji Newman, Morris *Nymann, James E. Mitchell, Theodore Morrison, Ian L. Nagase, Michihiro *Newsam, G. N. Oakland, David O. Mitchell, William J. Morrison, John A. Nagata. Masatsugu *Newstead, Peter E. *Oates-Williams, Sheila Mitchem, John A. Morrison. Kent E. Nagel, Alexander J. Ney, Peter E. Oba, Roger M. Mitskevich, Nikolai V. Morrison, Sally D. Nagel, Bengt C. H. Ng, Ho Kuen Obaid, Samih A. Mityagin, Boris Morrow. James R. Nagel, Rainer Ng, Max C. Obata, Morio Miura, Robert M. Morse, Burt 1. Nakagawa, Kiyokazu Ng, Tsz Yin Neville Oberguggenberger, Michael B. Miura, Takashi Mortensen. Karen Pinney Nakagawa, Yoko Nguyen, Bao Gia Oberschelp, Walter Miyadera, Isao Mortland. Richard L. Nakajima, Haruhisa Nguyen, Dung X. de las Obras, Carmen Miyahara, Yoshio Morton. Keith W. Nakajima, Shoichi *Nguyen-Huu-Bong Ochanine, Serge Miyakawa, Tetsuro *Morton, Patrick Nakamitsu, Kuniaki Niblo, Graham A. Ochiai. Mitsuyuki Miyazaki, Ken-Ichi Moschovakis, Joan Rand Nakamura, Hiroaki Nichols, Edward *Ochoa Castillo, Carlos Orlando Miyoshi. Shigeaki Moschovakis, Yiannis N. Nakamura, Masahiro Nichols, Eugene D. Ocone, Daniel L. Miyoshi. Takeo Mosco, Umberto Nakamura, Yoshimasa Nichols, Janet Ellen Greenhouse O'Connor, M. Lesley *MizeI, Victor J. Moser, Joseph G. Nakanishi. Yasutaka Nicholson, Victor A. Octavia, Alfredo *Mizumoto, Hisao Moser, Jurgen K. Nakano, Kazumi *NiChuiv, Nora eOda, Tadao Mizuno, Hirobumi Mosher, Lee D. Nakata, Masaomi Nickel, James A. Odenthal. Charles J. Mizutani. Tadayoshi Mosier, Ronald G. Nakata, Mie Nicol, Charles A. Odlyzko, Andrew M. *Mlitz, Rainer eMoskowitz, Samuel E. Naldi, Giovanni Nicolaenko, Basil *Odom, Earl T., Jr. *Mockenhaupt, Gerd Moss, Carl J. Namba, Kanji *Nicolas, Jean-Louis Oehmke, Robert H. Modica, Luciano Moss, Kenneth N. Namba, Toshiyuki Niedzwecki, G. P. *Oehrlein, Christopher D. Modugno, Marco Moss, Lawrence Stuart Nambooripad, K. S. S. Niefield, Susan B. Oeljeklaus, E. Moerdyk. Ieke *Motamedi, Mansoor *Namikawa, Yukihiko *Niemenmaa, Markku Ogawa, Hajimu Mohamed, I. J. Motoyama, Tetsuro Namioka, Isaac *Niessner, Herbert Ogawa, Hidemitsu Mohapeloa, Khomo T. S. *Mott, Orville B. eNamkoong, Kyu-Oh Nievergelt, Yves Ogg, Andrew P. *Moller, Jesper M. Mount. Kenneth R. Nance, Anthony C. Niino, Kiyoshi Oguchi, Kunio *Moller, Manfred H. Moussa, Pierre *Nandakumar, N. R. Niknam, Assad Oh, Sei-Qwon Moller, Raymond W. *Moy, Allen eNanyes, Ollie *Nillsen, Rodney V. *Oh, Yong-Geun Moller, Rognvaldur G. Moyls, Benjamin N. *Narang, Kamal Nirenberg, Louis Oh, Yoon Yong Molzon, Robert E. Mozzochi. C. J. *Narasimhan, Carolyn C. Nishida, Takaaki Ohm, Jack E. Monier, Jean-Marie Mrowka, Stanislaw G. Narayanaswami, P. P. *Nishikawa, Seiki Ohriska, Jan *Monk, J. Donald Mueller, Bruno J. W. Narushima, Hiroshi Nishimura, Yasuichiro Ohshika, Ken'ichi *Monsky, Paul H. Muhly. Paul S. *Nataf, Frederic Nishiura, Togo Ohta, Haruto Montes De Oca, Francisco Rafael *Mulder, Henry Martyn Natarajan, Ponnammal Nissim, Leonard 1. *Ohwaki, Shin-Ichi *Montgomery, Aaron G. Muldoon, Martin E. Nation, James B. Nita, Valerian M. eOka, Shinpei Montgomery, Hugh L. Muldowney, James S. *Naumann, David A. Nitchiporenko, Alexandre I. Okada, Ikutaro eMontgomery, M. Susan Muller, Gert H. eNavarro, Francisco J. Nitecki, Zbigniew H. Okada, Masami Montgomery, Peter L. Mullin, Albert A. Navarro Sandalinas, Joaquim Nitsche, Johannes C. C. Okamoto, Kiyosato Monticone, Leone C. Mullin. Ronald C. Nayar. Brij M. Niven, Ivan Okayasu, Takateru Moody, Robert V. Mulvey. Irene Nduka, A. Njastad, Olav Oksendal. Bernt K. Moon, Kyung-Ho *Mumbru Rodriguez, Pere Nebres, Bienvenido F. Nkashama, Mubenga Ngandu *Oktem, Ozan Moore, Edward F. *Mumey, Brendan M. *Neeb, Karl-Hermann *Noble, Christopher Okubo, Tanjiro Moore, James Andrew *Mundt, Marvin G. Neggers, Joseph Nobusawa, Nobuo Okumura, Haruhiko *Moore, John Garber *Munemasa, Akihiro Negrepontis, Stylianos Noel, Guy G. 1. Okuyama, Akihiro Moore, Lawrence C., Jr. Munkholm, Hans J. Nehaniv, Chrystopher Lev Noguchi, Mitsunori *Olafsson, Gestur Moore, Marvin G. Munkres, James R. Nehs, Robert M. Nogura, Tsugunori Oldham, Frank Ernest eMoore, Omar K. Munoz, Miguel-C Neidhardt Arnold L. *Nolan, John P. *Oldham, Janis M.

822 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ..... _...... _.,._ .... _.. _...... _ ...... -...... _.,. ... _...... _ """""·-·-·-·-·--·-·-·-... -..... ______,., ...... ,.• ,.• ,,,, .. ,...•. -...... _,_,,_ ...... •.•... _.,_.,,_,,_,,_, __ ,,_,,,.,,,,,•. , .. ,...... _,_,_,_,,_,_,_,,,,,,,.,,,.,,,...... AMS Centennial Fellowship Fund

O'Leary, Robbin Lerch Owings. James C., Jr. *Patterson. Paul L., III Petree. Vance W. Pommerening, Klaus Oler, Norman Owre. Sam Patton. Charles M. *Petrie, Emily R. *Ponce, Gustavo Alberto Olesen, Dorte Marianne Oyabu, Takashi *Patula, William T. Petrie. Pamela I. Pons, Montserrat Olesen. Mogens Norgaard Ozeki. Michio *Paul. Pedro J. Petro. John W. *Pontecorvo, Massimiliano Olevskii, Alexander M. Ozimkoski, Raymond E. Paur, Sandra 0. *Petryshyn, W. V. Poorman. Alan G. Olivares. Rene Ozsvath, Istvan *Paveri-Fontana, Stefano L. Petty. James Alan Port, Sidney C. *Olive. Victor M. *Pacella. Filomena Pawalowski, Krzysztof Peyerimhoff; Alexander Porta. Horacia A. Oliveira. Roberto F. Pacheco-Castelao, Jose M. Pawelke, Siegfried H. R. Peyre. Emmanuel R. Porte, Jean *Oliver, Dale R. Paciorek. Joseph W. Pawlaczyk, Thomas J. Peyriere, Jacques *Porter, Gerald J. Oliver, Kenneth S. Packer. Judith A. Paya. Rafael Pfau. Matthias Porter. Willis B. *Oliver. Robert A. *de Paepe. Peter J. Payoe. Lawrence E. Pflug. Peter *Poschel. Jurgen Olivier. Jean-Pierre •Page. Stanley S. Payne. Thomas H. *Pflugfelder. Hala 0. Posey, Eldon E. *Olivier, Reinhard M. Paige, Lowell J. Pazy, Amnon J. Phan. Quoc Khanh Post, Karel A. Olmsted, John M. H. Paisner. Helen L. Pears. Alan R. Pheidas. Athanasios C. Poston, Tim Olsen, Lars 0. R. Pak, Jingyal Pearson. Robert W. Phelps, Robert R. *Pott, Alexander *Olsen, Martin Palais. Richard S. Pearson, Ronald K. Phili. Christine Melle *Potthoff, Jurgen K. Olshen. A. C. Palais. Robert A. *Peart. Paul B. *Philip, Davaraj Potts, Donald H. *Olson, David A. Palanques-Mestre, August Peccati. Lorenzo Phillips. Ralph S. ePouzet, Maurice Olson, Loren D. Pales. Z. Peck. Emily Mann Phillips. Richard E. Powell, C. Spencer Olson, Tamara Pallai. David F. *Peck, N. Tenney *Piacentini Cattaneo, Giulia Maria *Power. Anthony John Olum. Paul Pallara. Diego M. Peckham. Bruce B. Piatetski-Shapiro. I. *Power, Stephen C. Olver. Peter J. Pallares, Antonio Jose Pecuch Herrero, Marta B. Picard. Rainer H. •Powers. Morris Walton Oman. John Arthur Pallaschke, Diethard Pedersen. Edward A. Picavet. Gabriel Powers, Robert T. O'Meara. Kevin C. Palmer, Edgar M. Pedersen, Erik Kjaer Piccinini, Renzo A. Powls, Keith W. O'Meara, 0. Timothy Palmer. Theodore W. Pedersen. Henrik Piccinni. Paolo Prabhu. Narahari Umanath Omori. Hideki Palmieri, John H. Pego. Robert L. * Pichet, Claude Prakash. Nirmala O'Nan, Michael E. Panangaden. Prakash Peiffer, Barry L. Pickel. Paul Frederick Prasad, Gopal *Onder, Turgut M. Pandolfi, Luciano *Peil, Timothy S. Pickering, Douglas Arthur Pratt, Vaughan R. O'Neill. Anne F. *Pankin, Mark D. Peixoto, Mauricio M. *Piene. Ragni Preiser. Stanley *O'Neill. Edward J. *Papadakis, Manos Peleg. Bezalel Pigozzi, Don L. *Preissendorfer. Manfred W. Onishi, Hironori Papageorgiou, Nikolaos S. Peletier. Lambertus A. Pihko. Jukka A. Prendergast, Bruce Thomas Ono. Takashi Papangelou, Fredos • Peligrad, Coste! Piirila. Olli-Pekka Prenowitz, Walter Ono. Yoshie Papanikolas. Andrew M. *Pelletier. Donald H. Pila. Jonathan S. *Prest, Michael Y. Onose. Hiroshi Papantonopoulou. Aigli Helen Peltier, Charles F. Pillay, Anand *Prevatt, Truman W. Onstott, Edward D. Pappas. Peter C. *Peltola. Veli-Pirkka *Pilz, Gunter ePribitkin. Wladimir de Azevedo Oodaira. Hiroshi Pardee. Otway O'M Pence, Dennis D. Pimbley. George H .• Jr. Price, G. Baley *Ooms. Alfons I. * Pardis. Cyrus J. *Pengelley, David John Pinch, Richard G. E. *Price, Jack Oono. Yoshitsugu Pareja-Heredia. Diego Pennell. Stephen A. Pinero. Alfredo Price. Justin J. Oppenheimer, Seth F. Paris. Luis *Pennings, Timothy James Pinkham. Henry C. Price, Roderick A. Orellana, Chacin Mauricio *Paris, Matteo J. Pennisten. John W. Pinkus, Allan M. *Prieto, Carlos Orban, Cihan *Park. Chin-Hong *Pensavalle, Carlo A. Pinney. Edmund Prince. Geoffrey Eamonn Orlik, Peter P. •Park. Chull Pepper. Paul M. Pinsky. Mark A. Proctor, C. Wayne *Orponen. Pekka Park. Eunsoon Perelli. Alberto Pinsky, Ross George Propp. James Orr, Kent Park, Hyungbin *Peres, Yuval Piranian, George Protas, David S. •orr. Martin Park, J ae Keol *Perez-Munuzuri. V. *Pischettola. Cos D. eProtter. Murray H. Orr. Richard J. Park. Jong An *Perez Romero, Jose J. Pisier. Gilles Protter. Philip E. Orsted, Bent Park, Jun S. *Perkel, Manley Pistone, Giovanni Proulx. Ronald J. Ortega, Joaquin Park, Kwang S. *Perkins. Peter Pitt, Loren D. Pruss. Jan Ortiz Fernandez, Alejandro •Park. Samuel Perkins. Wesley T. Pittie, Harsh V. *Prus-Wisniowski, Franciszek Osbo, Bruce T. •Park, Sang Ro Perko. Lawrence M. * Pittnauer. Franz ePrzebinda, Tomasz Osborn. J. Marshall Park. Young Soo Perlis. Robert V. Pitts, Andrew M. *Przytycka. Teresa M. *Osborn, James M. *Parker, Ellen Maycock •Perlman, Sanford Pixley, Carl P. *Przytycki, Jozef H. Osborne, Mason S. Parker. Elwood G. Permpoon, Pimpa Pizer, Arnold K. Pszczel, Mark B. Osgood, Brad G. Parker, Francis D. *Perozzi. Vince J. Piziak. Robert Pukanszky. Lajos *Osgood, Charles F. Parker. George D. Perrine. Serge Pla-Carrera, Josep Pullman. Norman J. Oslon, Steve G. *Parker, John R. Perry. Charles R., Jr. *Piachky, Detlef Pursell, Lyle E. *Osner. H. J. Parker. Thomas H. Perry. Peter Anton Plambeck, Thane Earl *Pustilnik. Seymour W. Osofsky, Barbara L. Parr, James T. Perry. William L. Plank. Donald L. Putnam, Alfred L. Osondu. Kevin E. Parrott, David Persek, Stephen C. Plesken, Wilhelm Puyau. Hermes Augusto Osserman, Robert •Parry, Walter R. *Persson, Ulf Pless. Vera S. *Pym, John S. *Ostapenko. Peter Parry. William Pertica, Horacia N. Pogorzaly, Zygmunt *Quach-Hongler, Cam Van Osterburg. James •Parshall, Brian J. *Pervin, Edward C. Pogu, Marc Quarles, D. A., Jr. *Osterwalder. Konrad Paschke. William L. • Peskin. Charles Samuel * Poguntke, Detlev Que!, John L. Ostrom, T. G. *Pascual-Gainza. Pere •Pesotan, Hoshang *Pobst, Michael E. Query. Kim A. S. Oswald, Urs *Pascual-Garda, Joaquin *Pestov, Vladimir G. Polachek, Harry Quigley, Frank D. Otermat, Scott C. Pasik-Duncan. Bozenna J. Petermann. G. E. *Poliquin, Rene A. Quinn. FrankS. Otero, Maria Carmen Pasini. Antonio Peters, John E. •Polk, Sam W. Quinn. John M. *Otsu. Yukio Passell, Nicholas *Peters, Meinhard H. Polking, John C. Quint, Richard A. Otsuki, Nobukazu Passerini, Henry J. Petersen, Bent E. * Pollara. Victor J. *Quint, Thomas Oty. Karla J. Passman. Donald S. Petersen. Troels *Pollatsek. Harriet S. *Quintero. Antonio *Oubina. Jose Antonio *Passty. Gregory B. Peterson, Gary L. Poluikis. John A. Quinto. Eric Todd Overbeck, Julius W. Pastur, Leonid Peterson, John C. *Pomerance, Carl Rabinowitz, Paul H. Overholt. Marius *Paternain, Gabriel P. *Peterson, Tod J. Pomeranz, Shirley B. Rabinowitz, Stanley Owa. Shigeyoshi •Patil, Dattatraya J. Petersson. H. P. Pommelet. Alain Nash Radcliffe. Andrew J.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 823 ...... _,_,,_ .. ,, ...... _, ______,, ...... -._ .... ,...... _,_,_, ___ ,_, ______AMS Centennial Fellowship Fund

Rade. Johan Reingold. Haim Roberts, Joel L. Rosenthal. Haskell P. Rykken. Charles John *Rademacher, Hans-Bert •Reinoehl. John H. Roberts. Joseph B. *Rosenthal. Joachim *Sabbagh. Gabriel Rader. Cary Baker Reinschke. K. J. Roberts, Lawrence Gordon Rosenthal, Steven M. Sablatash. Mike Radford, David E. *Reisewitz, Tammo M. Roberts, Lois J. • Ross. Bertram Saccoman. John J. *Radjavi. Heydar Reissner, Eric *Roberts, Mark Ross. Kenneth A. •sachs. Jeffrey R. Raukowski. Alfred F. Rehberger, Heinrich Roberts. Richard C. •Rossa. Robert F. Sacks. Paul E. Radulescu. Nicholas Andrew Reiter, Stanley Robert~. Stephen G. *Rossello. Francese A. *Sadofsky. Hal Rafels i Pallarola. Carles Reller. Austin F. Robertson. James B. Rossi, Guido A. Sadosky. Cora S. *Rahman, Ali Abdul Rempel, Richard S. Robertson, Malcolm S. •Rossi. Hugo Sadovski. Alexey L. *Rahula. Maido Ren. Yanxia Robertson. Neil •Rossi, Leonardo L. *Sadun. Lorenzo A. Rakosnik. Jiri Renardy. Michael Robinson, Daniel A. Rost. Markus Saeki, Sadahiro Rail, Louis B. Renault, Jean N. Robinson, Derek J. S. Rostand. John S. Saff. Edward B. Ralston, James V. *Render, Hermann *Robinson, Helen Drummond Rota, Gian-Carlo Sagan, Bruce E. Ramaley, James F. Renegar. James M. Robinson. Mark Preuss Roth, James W. Sah. Chih-Han *Ramalho, Margarita Renner. Lex E. Robinson, Paul Lee Roth, Richard L. Sahoo, Prasanna Ramamurtie, Buddhavarapu S. Renno, James G .. Jr. Robinson, Raphael M. Roth, Rodney J. Saigo, Megumi Ramanujan, Melapalayam S. * Renz. Peter L. Robkin, Eugene E. Rothaus, Oscar S. Saigusa, Youichi Ramirez. Arturo Flores Repka, Joe *Rocco, Norai R. Rothschild. Bruce L. Saito. Kazuyuki Ramsay, Arlan B. Ress, Richard R. •Rod. David L. Rothschild, Linda Preiss Saito, Kichi-Suke Ramsay, Keith Andrew Restrepo. Guillermo *Roddy. Michael S. Rothstein, Mitchell J. Saitoh, Saburou Ramsey. Helen Mary Revill, James A. Rodin, Yury L. Rotthaus. Christel Sakaguchi. Shigeru Ranck. James B. Reyes. Miguel *Rodrigues. Paulo R. Rouche. Nicolas *Sakai, Katsuro Range. R. Michael Reynolds, Donald F. Rodriguez, Gerardo Roush, !'red Sakai. Ryozi *Rankin. Robert A. Reynolds, Robert J. Rodriguez. Sanjmjo Jose Rousseau, Cecil C. *Sakamoto, Kunimochi Rankin. Stuart A. *Reza. Faz!ollah Rodriguez-Exposito, Jose Rousseau, Christiane *Sakamoto, Kunio *Ransford, Thomas J. *Reznick. Bruce A. *Roe, John Rouxel, Bernard Sakmann. Pascal Rao, M. M. • Rhee. Choon J ai *Roe, Robert P. Rouys, Robert L. *Saksman. Eero *Rao, Vidhyanath Kajana Rhee, Jong-Han *Roelants, Herman Rovnyak, James L. Sakuma, Motoyoshi Rapp, P. E. Riaza. Roman *Rofman. Edmundo *Rovnyak, Virginia G. *Sa!amanca-Riba, Susana Alicia Ras. Antoni *Ribes, Luis Rogawski. Jonathan David Rowe. Niles W. Salamin. Eugene Raskind, Wayne Mark Ricca. Renzo L. Rogers, Jack W.. Jr. Roxin, Emilio 0. Salas, Hector N. * Rassias. George Michae I *Ricci, Fulvio Roggenkamp. Klaus W. Royle. John C. *Sa!avessa, Isabel M. Da Costa •Ratcliff. Gail D. L. Ricci, Stephen J. Rohrlich. David E. Royster. Wimberly C. Salazar-Leyva. Enrique Ratiu, Tudor Stefan *Rice, John William eRoitman, Judith Rozenblyum. Gregory V. Salehi. Hahib Ratliff. Louis J .. Jr. *Rich, Andrew Roitman. Moshe Ruben, Flores Espinoza Suleski. Alan J. Ratz. Jurg J. • Richard, Philip Henry. Jr. Rojas, Raul Ruherman, Daniel Salinas, Luis C. Rauch. Lawrence L. Richards, Franklin B. Rolf, Howard L. Rubin, Herman Salisbury, Thomas S. Raussen, Martin Richards, John F. Rolfsen, Dale P. 0. •Rubin, Jonathan E. Salkind, William Ravenel. Douglas C. Richards, Pamela C. Romaguera, Salvador Rubin, Robert J. Sallee. G. Thomas Rawlings. Don Paul Richardson. Charles Alden Romanyuk. Leonid Rubinstein. Joachim H. Salles, Maurice Rawnsley. John H. Richardson, Kenneth S. Romero, Neptali Ruch. David Karl Sally. Paul J .. Jr. Rawson. John Elton Richardson, Rickey W. Romero Chesa, Carles Rudin, Bernard D. esa!off-Coste, Laurent *Rawsthorne, Daniel A. •Richardson. Thomas M. *Rondoni, Lamberto *Rudolph, Daniel Jay *Saludes. Jordi Ray-Chaudhuri. Dwijcndra K. Richert, Hans-Egon *Ronga. Felice L. L. Ruelle, David P. Samelson, Christopher L. *Raymond. Frank A. Richert, Norman J. *Ronsse, Gregory S. Ruess, W. Samelson, Hans *Rayner, Francis J. Richmond. Glayvera Ronveaux, Andre Rufeger, Waltraud Sampson, Gary Reade. Maxwell 0. Richmond. Lawrence B. Rooney. Paul G. Ruh. Ernst A. Samuel. Pierre Reardon. Philip C. •Richter, Horst P. *Roos. Guy Ruijsenaars. Simon Norbert •Sanchez. David A. Reher, Douglas C. Richter, Michael M. Root, William L. * Ruiz, Alberto Sanchez. Jose Alberto Recaman. Bernardo •Richter, Stefan *Roozemond. Leen Ruiz, Ceferino *Sanchez. Juan Miguel Redmond, Don *Richter. Wayne H. Rope, Crispin M. *Rukimbira, Philippe Sanchez. Rafael J. *Redner, Richard A. Richtmyer, Robert D. Rosa, Domenico *Rumbas, Adolfo J. Sanders, Robert W. Reed, Coke Stevenson Rickan. Charles E. Rosales. Rodolfo R. Rumelhart, David E. Sanderson, Brian J. Reed. Robert E. Rickert. John H. Rosay, Jean-Pierre Rumely. Robert S. Sandler, HannaM. Reedy. Christopher L. Rickey. V. Frederick Rose, N.J. Rushing. T. Benny Sands. Jonathan Winslow *Rees. Elmer Riddle. Malcolm Lee Roselle, David P. *Ruskai. M. Beth Sangwine-Yager. Jane Rosamund Rees, Paul K. Rieffel, Marc A. Roseman. Joseph J. •Rusodimos. Jason *Sanje Mpacko. Guillaume D. Reese, Richard H. Rieger, Georg J. Rosen, Kenneth H. Russo, Bernard *Sankey, Alyssa D. Reese, Sylvester Riehemann, Robert M. Rosen, Michael I. Russo. Paula A. San Miguel. Angel *Reeves-Hicks. Ernestine Riesel. Hans I. Rosen. Ned Ira * Rusu, Petre Sano, Shigeru Regan, Francis Rigdon. Robert D. Rosen. William G. Rutland, Leon W .. Jr. Sant. Lino *Regan, Kenneth W. Rigo. Pietro Rosenbaum, Robert A. Rutledge, Dorothy S. Santalo, L. A. Regazzini. Eugenio Rijavec. Nenad *Rosenberg, David Rutter, Marianne C. P. Santos, Fernando *Regli. William C. *Rijnks, H. Rosenberg, Ivo G. Ruttimann, Gottfried T. Sanz. Miguel Angel * Rego. Eduardo F. Rinne, Dan C. Rosenberg, Jonathan M. Ruzsa, lmre Z. Sanz-Serna, J. M. *Rehmann. lllf Rio, Jose Rosenblatt, Joseph Max Ryabov. Gernady Saphar, Pierre David Reichel. Hans Christian Rishel. Thomas W. •Rosenbloom. J. H. Ryan. Anthony John Sarafyan. Diran *Reichel. Lothar Risnes, Martin Rosenfeld, Gerald Ryan. Frank B. *Sarantopoulos. Joannis C. *Reid, K. Brooks Rivet, Roger Rosenfeld, Ronald L. Ryan, Patrick J. Sarason. Donald E. Reid, Les Roach, Michael D. Rosenmann. Amnon Ryan, Peter M. • Sarkar. Asis K. Reid, William H. Robbins, David P. Rosenstein. George M .. Jr. Ryan, Robert D. Sarrat. Charles F. Reilly. Norman Raymond Robert, Alain Rosenthal, Arthur J. Ryan. Robert M. Sasaki, Hiraki Reineck. James F. Roberts, David Peter Rosenthal. Eric S. *Rybowicz. Marc Sasaki, Takeshi *Reiner, Victor S. Roberts, Jean E. Rosenthal. Erik J. Ryehurn. David Sasano, Kazuhiro

824 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Sastri, Chelluri C. A. Schn~id~r. Hans s~id~I. J. J. *Sherman, Gary J. esing~r. David All~n Satake, lchiro Schneid~r. Joel E. Seid~n. Esther *Sheu. Alb~rt Jeu-Liang Singer, Micha~l F. Sato. Hidco •Schneider. Manfred F. *Seiler, Wolfgang K. *Sh~u. Sh~y-Shiung Sing~r. William M. Sato, Hiroki Schn~ider, Rolf Sein, Hla Hla Shi. Yixun *Singerman. David Sato, Hiroshi Schneider. Todd J. *Seip. Kristian Shiba, Masakazu Singh, Kumud *Sato. K~n-iti Schneiders, J~an-Pierre Seitoh. Akira Shibata. Masanori K. Singh. Smjeet Satn. Masako Schnitzer, Franz J. Seitz. Gary M. *Shibata. Yukio Singmaster. David B. Sauerb~rg. Jam~s J. *Schoch~!. Steven H. Sekigawa, Hisao *Shibuya. Yuji Sinkala. Zachariah Saund~rs. Munro R. Schoen. Richard M. Sekino. Kaoru Shiffman, Bernard Sinkov. Abraham Sauvigny, Fri~drich Schoenfeld, Lowell Selby. Alan M. Shiffman. Max Sira-Ramirez, Hebert! J. Savina. Christopher L. *Schoenwaelder. Ulrich F. *Selby. Michael J. P. Shifrin. Theodore Siu. Man-K~ung *Samye. Philip *Scholz. E. Seligman. Georg~ B. *Shiga, Hiroshige Siu. Yum Tong Sawada, Hideki Schonbek. Maria El~na Seligman. Mark L. Shiga. Koji *Sivakumar, N. *Sawin. Stephen F. *Schoof, Rene *Seligson. Stuart A. Shimada. Nobuo Sizer. WalterS. Sawyer, Eric T. *Schori. Richard M. Sell. George R. Shimamoto. Don H. *Sjamaar. Reyer Sawyer. Patrice Schraegle. Horst Sempi, Carlo E. Shimizuike. Yuzi *Skaff. Michael S. Sawyer, Stanley A. Schrauf. Geza H. Semyonov, Alexey Shimura. Goro *Skau. Christian F. *Sayratiezad~h. Mahmoud Schraut. K. C. Senechal. Marjorie Shin. Dong Sun Skidmore. Alexandra S. Scalzo, Richard C. Schreiber. Bert M. Senger, Steven 0. Shin, Kee-Young Skiffington. John Jns~ph. Ill Scaramuzzi. Roberto Schreiner, Walter J. *Sengupta, Ambar Niel Shinohara. Yaichi Sklar. David Scarborough, Steve Douglas Schrijver, Alexander *Seppala-Holtzman, David Shiohara. Hiroshi Sknf. Fulvia Scarpellini. Bruno J. Schroder. M. *Sepulveda, Eric *Shira. Jack L. Sknug. David L. Scarpi. Giambattista Schriieder, Johann Serapioni, Raul Shiraiwa. Kenichi Skowronski. Andrzej Schaal. Werner G. H. *Schroeder. Viktor M. H. *Serre. Denis A. Shiratani. Katsumi Skubachevskii, Alexander Schacher, Murray M. Schryer. Norman L. *Serre. Jean-Pierre *Shirley. Kevin L. Leonidovich Schaefer, Edward Frank *Schub~rt. Cedric F. •s~rr~ll. Robert •Sholander, Marlow C. Slack. Micha~l D. Schafer, Alice T. Schuett. Werner Sesay. Mohamed W. I. Shorter. William Ivan Slack. Stephen Schafer. Richard D. *Schultz, Phillip *Sessa, Salvatore *Shpilrain. Vladimir *Slade. Gordon D. Schaffer. Juan Jorge *Schulze-Pillot, R. Sevenster. Arjen Shreve. David C. Slater. John B. Schafke, R. •Schumacher, Georg B. Sever, Michael Shreve, Steven E. *Slattery. Michael Schapiro, Philip J. Schumaker. John A. Sexauer. Norman E. Shubin. Carol Ann Sleeman. Brian D. *Schaps. Maika Elisheva Schumitzky. Alan Shabazz. Abdulalim A. *Shubin. Mikhail A. *Slodowy. Pet~r J. Scharlau. Rudolf M. E. Schuster, Seymour Shackell, John R. Shubsda. Stanley R .. Jr. Slook, Thomas H. *Schattschneider, Doris W. Schutt, Carsten *Shaffer, Eric Gene Shuchat. Alan H. Sloss. Bruce G. Schatzman, Michelle Schutt. Ingo Shahabi. M. A. Siapas. Athanassios G. Sloss, James M. Schauer. Richard L. Schwabik. Stefan *Shahriari. Shahriar *Sibley. Thomas Q. *Siuchin. Benny Schaumberger, Norman *Schwaller, Thomas E. Shakunle. Lere Sibner. Lesley M. Slud. Eric V. *Schechtman. Gideon Schwartz, Alan L. Shallit. Jeffrey Outlaw Sibner, Robert J. Slye. John M. *Schechtman, Vadim V. Schwartz. Charles Freund Shanahan. Patrick Sichler, J. *Small. Anthony James Schecter. Stephen Schwartz. Jacob T. Shannon, Gerald Peter Siddiqi, Rafat N. Small. Lance W. Schet1ler, Hans-Peter Schwartz, Lionel eshao. Sai Lai Sidney. Stuart J. Small. Lynne Barnes Schell. Emil D. Schwarz. Binyamin Shapiro. Daniel B. esieburg, Hans B. Smart. John R. Schellhorn. Jean-Pierre Schwarz. G~rald W. Shapiro, Dawn M. Si~gcl. Alan Smiley. Leonard Schellwat, Holgcr Schweiger, Fritz Shapiro, Harold N. Siegel. Martha J. Smillie, John Sch~mbari, Nunzio Paul Schweitzer. Eric *Shapiro, Jay A. Siegel. Paul H. *Smith. Bruce T. Schempp. Walter *Schweitzer, Paul A. Shapiro. Joel H. Siemon, Helmut *Smith. Bryan A. *Scheurle. Jurgen K. Schweizer, Berthold Shapiro, Louis W. Siemons, Johannes Smith. David A. Schichl. Hermann R. Schwietzer, Michael J. Shapiro. Michael D. *Siersma. Dirk Smith. Edgar C .. Jr. Schiffmann. Gerard M. Sclove, Stanley L. *Shapley. Lloyd S. Sigrist, Francois *Smith. Elizabeth A. Schiller. John J. Scollo. Giuseppe •Sharp. David H. Sigurdsson, Ragnar Smith. Frank D .. Jr. Schillo. Paul J. *Scoppola. Carlo M. Sharp. Henry, Jr. Sikorav, Jean-Claude *Smith. James R. Schindler, Christian Scott. Damon Sharpe. Michael J. Silberger, Allan J. *Smith. John Howard Schlesinger. Ernest C. *Scott, David R. Sharpe. Richard W. Silberger. Donald Morison Smith, John M. *Schlichenmaier, Martin Scott, Leonard L., Jr. Shatz. Stephen S. *Silva. Cesar E. Smith. Karen E. *Schlick, Tamar Scott. Peter Shaw, Guy B. Silva, Jorge-Nuno Oliveira *Smith. Kay E. Schmerl. James H. *Scott, Richard A. *Shaw, Mei-Chi Silver. Daniel S. Smith, Lisa Wydawski Schmets, J. Scntt. Ridgway Shaw. Rnnald Silver. Jeffrey *Smith. Martha K. Schmetterer, Leopold K. Scott, Warner Henry Harvey. III *Shaw. Sen-Yen Silverman, Herb Smith, Michael F. Schmid, Josef Scott-Thomas. John F. Sheil-Smail. Terence Brian Silverman. Joseph H. Smith. Paul R. Schmid. Jurg Scourfield. Eira J. Shelly. Eugene P. *Silverman. Judith H. Smith. Perry B. Schmid, Wilfried *Scriba, Christoph J. Shelly. Maynard W. *Silvia, Evelyn Marie Smith, Richard A. Schmidlin, Dean J. Seal. Charles Edwin •Shemanske. Thomas R. *Simanca, Santiago R. Smith. Robert Colman Schmidt, Harvey J .. Jr. Seen, Luis A. *Shemesh. Meir Sime. Patrick J. Smith. Roger R. Schmidt. Henry J .. Jr. *Sedaghat, Hassan Shen. Yuan-Yuan *Simion. Rodica E. Smith. S. Paul *Schmidt, Klaus D. Sedory. Stephen A. *Shen. Zhong-Wei Simmons. Dayllln C .. III esmith. Spurg~on E. *Schmidt. Robert C. Sedwick. Jackson L. Shene, Ching-Kuang Simmnns. Harold Smith. Stephen B. *Schmidt. Roland Seebach. J. Arthur Shenitz. Charles Simo, Carles Smith, Tara L. Schmidt, Thomas A. Seebeck, Charles L .. III Shenitzer. Abe Simon. Anne-Marie Smith. Wayne Stewart Schmidt. Wolfgang M. *Seeger, Andreas *Shepard. Allen D. Simon, lmre Smith, Wilbur L. *Schmitt, Peter Seeley. Rob~rt T. Shepherd. J. C. Simonis. Juriaan Smithies. Frank *Schmudgen, Konrad Alfred *Seelinger, Georg~ F. Shepherdson, John C. Simons, Lloyd D. Smoke. William H. Schmuland. Byron A. Seger!, Jan Sherk. F. A. Simos. Theodore Elias Smolarski, Dennis C. Schneebeli. H. R. Sei, Alain Sherlock. Philip Thomas Sims. Charles C. Smolinsky. Lawr~nce J. *Schneider. Cynthia Louise Seid, Howard A. Sherman, Bernard *Sinclair. Rodney F. Smoller. Joel A.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 825 ...... ______, __ ,_,., ...... AMS Centennial Fellowship Fund

Smyth, William P. Staley, Russell L. Stokes, Russell A. Summers, John W. Talmadge. Andrew V. Sneddon, ian N. Stallmann, Friedemann W. Stokes, William G. *Summers, Stephen J. *Talvila. Erik 0. Snyder. Andrew K. Stamey, William L. Stolarsky, Kenneth B. Summerville, Richard M. Tam, Bit-Shun Snyder. John L. Stammbach, Urs Stolberg, Harold J. Sun. Cun-Jin Tan. He Liang esoare, Robert I. *Stamp, Mark Stoll. Wilhelm P. Sun. Tien-Yu Tan, Henry K. Sobral. Manuela Stanley, Lee James Stoltenberg-Hansen. Viggo Sundar, P. Tanabe, Michimasa Soffer, Avraham Stanley, Richard P. Stoltzfus, Neal W. Sundararaman. D. Tanaka, Hisao Sohmer, Bernard Stanley, Walter C. Stolz. Stephan A. Sundaresan, Kondagunta Tanaka, Jun-lchi Sohrab, Siavash H. Stanton, Charles S. Stone, Alexander P. *Sunderland, Andrew Michael Tanaka, Katsumi del Solar-Petit, Emilio Stanton, Robert J. Stone, Arthur H. Sunderland, Benjamin B., Jr. Tang, Alfred S. Soldate, Albert M .. Jr. Staples, Edmund Beauclerc, III Stone, Arthur L. Sunouchi, Haruo Tang, Betty M. *Solian, Alexandru Staples, John C. Stone, David R. Sunseri. Mary V. Tang, Hwa Tsang *Solna, Knut Starbird, Thomas W. •stone, John David Susanka, Lawrence A. Tankou, Victoire Tyntynou Sologuren, Santiago Stark, Christopher W. Stone, Lawrence D. Sussman, Myron M. *Tannenbaum, Peter Solomon, Bruce Stark, Matthias J. Stong, Richard A. *Sussmann, Hector J. Tanno. Shukichi Solomon, David R. Stark. Richard K. *Stonier, Russel J. *Suter, Ueli Tapia, Joseph A. Solomon, Ronald M. Stark, Sheldon H., Jr. Storey, Albert J. Sutton, Charles S. *Targonski, Jolan M. Solomon, Stephen J. Stasheff. James D. Stormer, Erling *Sutton, Michael D. Tarres, Joan Solomonides, Anthony E. •Stavrakakis, Nickolas M. *Storrer, Hans H. Suzuki. Haruo Tartakoff. David S. *Solovej, Jan Philip Stavroudis, Orestes N. Stortz, Clarence B. Suzuki. Humio Tasche, Manfred Solski. Jeffrey Elliott Steele, Alfred T. *SI Pierre. Charles Gregory Suzuki, Michio Tashiro, Yoshihiro •somach, Ira Harwyn Steele, William P. *Straffin, Philip D.. Jr. Suzuki, Naoyoshi Tatevossian, Leon H. *Somer, Lawrence E. Steenbrink, J. •Straley, Tina H. Suzuki, Shinichi Tatsuo, Fuji 'I' E Soner, H. Mete Stegeman, Jan D. Stralka, Albert R. *Svensson, Erik Taussky, Olga Soni, Raj Pal Steger. Arthur Strang. Gilbert Sverdlove. Ronald Tavantzis, John *Sonin. Isaac M. Steger, Tim J. Strassberg, Helen A. Swamy. Srikanta M. N. Taylor. Angus E. Sonneborn, Lee M. Stegun. Irene A. Straubing, Howard Swan. Richard G. Taylor, B. A. Sonner. Johann Stein, Alan H. Strauss, Frederick B. Swanek, James J. Taylor, Donald E. Sons, Linda R. Stein, Elias M. Strauss, Leon Swardson, Mary Anne Taylor, Jean E. •sopka. John J. Stein, Marvin L. Strauss, Walter A. Swart, Johan Taylor. Laurence R. Sorbi, Andrea Stein. Sherman K. Strebel, Kurt Swartz, Bill *Taylor, M. A. Sorenson. John R. •Steinhart, Enid M. Strebel. Ralph Swearingen, Daniel B. Taylor, Michael D. Sorel, Mark Steinberg. Leon *Street. Ross H. Sweeney. William J. Taylor, Michael E. *Soria, Fernando Steinberg. Maria W. Strehl, Volker *Swiatek, Grzegorz Taylor, Peter G. Sormani. Michael J. Steinberg, Paraskevi Stretch, Christopher T. Swick, Kenneth E. Taylor, S. James •Soules. George W. Steinberg, Robert Strickland, Susan R. Swickard, Joe S. Taylor, Thomas J. esoundalgekar, Vyenkatesh M. Steinby. Magnus Strikwerda, John C. *Swiech. Andrzej Janusz Taylor, William W. Sousa Ramos, Jose *Steiner, Anne K. Stroeker, R. J. Swierczkowski, Stanislaw S. Teicher, Mina Southgate, Theodore J. Steinert, Leon A. Strohl, G. Ralph. Jr. •Swimmer, Alvin *Teirlinck. Luc M. •southworth, Raymond W. Steinborn, Charles I. Strohmer, Gerhard 0. *Sylve•'ter, Donna L. G. *Teissier, Bernard Spaltenstein, Nicolas Steketee, Jakob A. Strom. Arne Symes, William W. *Teixidor i Bigas. Montserrat Sparr. Gunnar Stell, George R. Stromberg. J. 0. *Szabo, Zoltan I. Teleman, Constantin Spatz, Ian N. Stell, John G. *Stromme, Stein A. Szarek, Stanislaw J. Teleman, Silviu Spatzier, Ralf J. Stella, Sergio Stromquist. Walter R. Szczarba, Robert H. Temam, Roger Specht, Edward J. Stembridge, John R. *Stroth, Gernot H. W. Szekeres, George Temesvari, Agota H. *Spector, Rene Stenger. Frank *Strouse, Elizabeth J. Szenthe, Janos Tenenbaum. Gerald Speh, Birgit Stenlund, Mikael Lennart Stroyan, K. D. Szepessy, Anders *Tenenblat, Keti Spellman, Dennis Stenson. Ellen M. Strube, Richard P. E. Szeto. Mabel Tengstrand, Sven Anders *Spencer, Joel H. •Stenzel, Matthew B. *Struwe, Michael Szigethy, Stephen M. Tennant, Raymond Frederick Spencer, Philip H. Stephens. James H. *Stuart, David M. Sznitman. Alain-Sol Teolis, Antonio G. B. Spencer, Thomas Crawford *Stephenson, Kenneth *Stuck, Garrett James Szokefalvi-Nagy, Bela Tepedino A., Gaetano Spielberg, Stephen E. Sterba-Boatwright. Blair D. Stuckwisch. Stephen E. *Szucs, Joseph M. Terao, Hiroaki *Spiro. Andrea Sterk. Henri J. Stuhler, Ulrich *Szulkin, Andrzej Temg, Chuu-Lian *Spivack, Mark Sterling. Theodor D. Stummel, Friedrich Tabachnikov. Serge *Terrell, Maria S. Spolter, Pari D. Stem, Alan Spector Sturley. Eric A. Tabak, Barbara L. *Terrell, Robert E. Spratt, John A. Stem, Ronald J. Sturm. Teo Tabib, Claudette Thrzakis. Dimitris Sprecher, David A. Sternberg, David *Sturmfels, Bernd Tadic, Marko Terzuoli, Andrew J. *Spring, David H. *Sternberg, Peter J. *Styer, Robert A. *Tadmor. Eitan Testerman, Donna M. Spruck, Joel *Stetkaer, Henrik *Suarez, Rodolfo Taft, Earl J. *Textorius. Bjorn 0. B. Srinivasan, Aravamuthan Stevens, Glenn H. •Sucheston, Louis Taft, Margaret W. *Theohari-Apostolidi, Theodora Srinivasan, Bhama *Stevens, John G. Sudler, Culbreth. Jr. Tagawa, Masa-Yoshi *Thera. Michel A. Sritharan, Sivaguru S. •stevens, T. Christine Sueyoshi, Yutaka *Tahvildar-Zadeh, A. Shadi Thibon, Jean-Yves Srivastav, Anand •Stevenson, John C. Sugimoto, Mitsuru Taiani, Geraldine Thiele, Emst-Jochen •Srivastav, Ram P. *Stewart, Cameron L. Sugita. Kimio Taibleson. Mitchell H. Thieme, Horst R. Stacey, Peter John Stewart, James W. Sugiura, Mitsuo Takacs, Lajos P. •Thieroff, Kirk J. Stachel. Hellmuth *SI George, Greg Suita, Nobuyuki Takahashi, Masako Thistlethwaite, Morwen B. Stackelberg, Olaf P. Stiadle. Thomas A.. Jr. Sullins, Kenneth W. Takahashi, Shuichi •Thoele, Edward C. *Staffeldt, Ross E. Stich. Werner J. A. Sullivan, Dennis P. Takano, Kyoichi *Tholen. Walter P. Stafford, J. T. *Stifer, Sabine *Sullivan, Michael C. Takayama, Nobuki Thoma, Elmar H. Stafney, James D. Stigter, Jurgen Olivier Sullivan. Richard W. Takeda, Ziro Thomas. Alan T. Stahl, Herbert R. Stock, John R. *Suman, Kelly John Takenaka, Shigeo Thomas, Erik G. P. Stahl. Saul Stocker, Harold Edward *Sumin, Mikhail I. Takesaki, Masamichi *Thomas, Jean-Claude Stakgold, Ivar Stockmeyer, Paul K. Summer, Debra Takeuchi, Kisao Thomas, Lawrence E. Staknis, Victor R. Stokes, H. Christine B. *Summers, Arthur R. Takeuchi, Masaru Thomas, Marc Phillip

826 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund

Thomas, P. Emery Trager. Hans • Vafeades. Peter Verma, Ghasi R. •Walsh, John J. Thomas, Pascal J. Trone!. Gerard *Vaillancourt, Pierre Vermes. Robert Walsh, John Thomas *Thomas, Richard M. Tronzo, Mark D. Vainberg, Boris R. Verona. Andrei Walter, Gilbert G. *Thomas, RobertS. D. Trotter. Hale F. * Vainikko, Gennadi Vesentini, Edoardo Walter, John H. *Thomason, Steven K. Troubetzkoy, Serge Vainio, Reina Johan Vetter, Udo *Walter, Martin E. Thomee, Vidar Troyanov, Marc Valdivia-Gutierrez, Oscar Viader, Pelegri Walters. Samuel G. Thompson, Abigail A. eTrucano, Timothy Guy Valle, Antonio Viano Rey, Juan M. Walther, Hans-Otto Thompson, Jon H. Trytten, George N. *Vallejo, Ernesto *Vide! a, Carlos Rodolfo Walton, Jay R. Thompson, Layton 0. Tsai, Tian-Yue Valluri, Sreeram Vilcius, AI R. Walus, Herwig Thompson. Mary E. Tsai. Yen-Shung de Valpine, Jean E. Villalongue, Pierre Wan, Tom Yau-Heng Thomsen. D. L.. Jr. *Tsau, Chichen Michael *Van Arkel, Nicolaas A. Vilonen, Kari Wang. Frank Y. H. Thrall. Robert M. Tsuchikura, Tamotsu Van Assche, Walter * Vinacua, Alvaro Wang. Hsiao-Lan Thrash, Joe B. Tsuchiya, Takuya Van Bendegem, Jean Paul Vincze, Istvan *Wang. Jenn-Nan Thron, Wolfgang J. eTsui, Sze-Kai Jack Van Casteren, Johannes A. Vine!. Gerard F. Wang, Jian-pan Throop, T. Tsuji, Kazo Vance, Elbridge P. * Vinsonhaler, Charles I. Wang. Paul K. C. Thunberg. Hans Tsukiyama, Kouzou Vance. Richard J. Viola, Carlo Wang. Shuzhou *Thybo, Christian Tsukui. Yasuyuki Van Den Ban, Erik P. Viramontes, Jorge Rosalia *Wang, Stuart Sui-Sheng *Tice. Allen P. Tucci, Ralph P. Van den Bergh. Michel Viro. Oleg Wantland. Evelyn K. *Tichy, Robert F. Tucker, Albert W. Vanderbauwhede, A. L. * Virsik, George Wanzong, Robert C. Tierney, John A. Tucker, Howard G. Van der Geer, Gerard Vitale, Joseph N. *Ward. Andrew James Tignol, Jean-Pierre Tuckerman, Bryant Van Der Kallen, Wilberd *Vitale, Michael A. Ward, Harold N. *Tilidetzke, Robert James *Tudor, David W. Van Der Mee, Camelis V. Vitale, Richard A. *Ward. Josephine A. Tillmann, Heinz G. Tugue, Tosiyuki Vandevelde, J. Richard *Viviente, Jose L. *Ward, Lesley A. Timm. Mathew T. Tung, On-Ki A. Van de Wetering, R. Lee Vo, Quoc Dinh Ware. Buck Timoney, Richard M. Tunnell, Jerrold B. Van Duijn, Camelis J. Vodola. Paul A. Warne, Ronson J. *Timotin, Dan Turesson, Bengt Ove Van Eck, H. N. Vogan, David A .. Jr. *Warner, C. Robert Timourian, James G. *Turett, J. Barry Van Geemen, Bert *Vogel. Andrew L. Warner, Frank W .. III *Tirrnizi, Syed lkram Turgeon, Jean M. Van Gils, Stephan A. Vogelius, Michael Steenstrup Warrinnier, Alfred E. Tirta Seputro. Theresia M. H. Turiel, F. J. *Van Lint, Jacobus H. Vogt, Dietmar Washington. Lawrence C. Tischler, David C. Turisco. Joann Stephanie •Van Osdol, Donovan H. Vogt, Elmar Watanabe. Nobuya Titani, Satoko Turner, Edward C. Van Rootselaar, Bob Vogtmann, Karen Watanabe, Shoji Titi, Edriss Saleh Turquette, Atwell R. evan Rossum, Herman Voichick, Michael *Watanabe, Toshihiro Tits, Jacques L. *Turyn, Lawrence Van Scheepen, Frans Voiculescu, Dan Watatani, Yasuo Tjiok, Mouw-Ching Tutte, W. T. Vanstone, James R. •Voit, Michael P. •Waterhouse, William C. *Toby, Ellen H. Twersky, Victor Van Strien, Sebastian J. Volkmann, Bodo Wathan, Herbert Harold Toda. Nobushige *Twomey, J. Brian *Van Trung, Tran Volkmer, Hans W. Watkins, David S. Todd, John eTyl, Mary Ann Van Tuyl. A. H. * Voloch. Jose Felipe Watkins. Mark E. Todor, Fabian •Tylli, Hans-Olav Van Veldhuizen, M. Vanessen, Nikolaus Watson, David K. *Toh, Kim-Chuan Tysk, Johan • Van Vleck. Fred S. *Vanta, Filia Watson, Martha F. Tokat, Gulsen Tzavaras, Athanassios E. Vaquie, Michel Voreadou, Rodiani *Watson, Stephen Toll, Kathryn B. Tzeng, Chun-Hung Varadhan, Srinivasa S. R. *Voss, Heinrich Wayne, Alan Tollefson, Jeffrey L. Ubriaco, Marcelo R. Varadi, Ferenc * Vrabec. Franz Weaver. John C. *Tolosa, Juan * Udina, Frederic Varberg. Dale E. Vrbik. Jan Webb. David L. Tomari, Masataka Ueno, Kazushige Varea, Vicente R. Waadeland, Haakon *Webb, Peter J. Tomita, Yoshihito Ueno, Kenji *Varga, Richard S. Wachter, William John. Jr. •Weber. Frank P. Tomiyama, Jun Ueno, Yoshiaki Vargas-Calvo, Jorge A. Wacker, Paul F. *Webster, Jeffrey Scott Tong, Mary Powderly Uglanov, Alexei Vladimirovich *Varilly, Joseph C. Wada, Hidekazu Webster, Sidney M. Tonne, Philip C. Uhl, J. Jerry, Jr. Varina, Francis H. Wada. Junzo Wechsler. Martin T. Torgerson, Norman Wesley Uhlenbeck, Karen *Varona, Juan L. Wada. Toshimasa Week, Norbert Torre, Nicolo Goodrich Ukegawa, Takasaburo Vasak. Janet Trzcinski Wagener, Raymond *Wee, ln-Suk Torrecillas, Bias Ullery. William D. Vasconcelos, Walmer V. Wagner. Daniel H. Wefelmeyer, Wolfgang *Torres, Luz G. Ullman, Daniel *Vassiliou, Peter John Wagner, Gretchen B. Wefelscheid, Heinrich Torres, M. Ulmer, Douglas L. Vaz Pinto, Maria Rasquilha Wagner, William M. *Wegert, Elias *Torres de Squire, Maria L. Ulrich, Bernd *Vazquez, Juan L. Wagoner, John B. Wehausen, John V. *Tovar S .. Luis Manuel Umeda, Takata Vazquez Polo, Francisco Jose Wagreich, Philip D. *Weibel, Charles A. Traina, Charles R. Umeda, Tomio eveech, William A. Wahba, Grace Weibel. John L. *Traldi, Lorenzo Ummel. Brian R. *Vega, Luis Wainger, Stephen *Weidmann. Joachim *Transue, William R. Umminger, Frederick William *Vein, Howard B. Wainwright, John Weidner, Anthony A. Trautman, Andrzej Unai, Yasushi Unai Velasco-Hernandez, Jorge X. *Wajda. Louis W. Weidner, Jens Trautman, David A. Ungar, Abraham A. Velazquez. Robert Wakae, Masami Wei!. Clifford E. eTrebels. Walter Unger, Ernst R. Veldman, Willem H. Wakana, Kaoru Weill, Lawrence R. Treibergs, Andrejs E. *Unger, Luise Velez-Rodriguez, Argelia L. Wakayama, Masato Weiner, Jerome H. Tremmel. John J. Uno, Katsuhiro •Vella. David C. Walcher, Sebastian Weiner, Joel L. Trench, William F. Upatisringa, Visutdhi *Venema, Gerard A. Waldhauer, Amy R. Weinkam, James J. Tresser, Charles Upmeier, Harald Venkateswaran, S. Waldinger, Hermann V. •Weinstein, Alan D. Treuden, Michael L. Upton. John A. W. *Ventriglia. Francesco Wales, David B. *Weinstein. Michael I. Treves, Francois *Urbina, Wilfreda 0. *Ventura, Belisario A. *Walker, Michael F. Weinstein, Stephen T. Treybig, L. Bruce *Urias, Jesus Venzi, P. Walker, Wayne James *Weintraub, Steven H. Trias Capella, Rosa M. Uribe, Alejandro Vera, Gabriel *Wall, Charles T. C. *Weiss, Alan A. *Trias Pairo, Joan Ursini. Aldo *Vera, Jorge R. Wall, Curtiss E. Weiss, Guido L. Tricerri, Franco van der Vaart. H. Robert Verchota, Gregory C. Wallace. Dorothy W. Weiss, Norman J. Trimble, Selden Y. *Vaccaro, Ugo Verde Star, Luis Wallace, William Weiss, Richard M. •Trione, Susana Elena * Vachuska. Colleen A. Verduyn Lunel, Sjoerd M. Wallen, C. J. *Weissler. Frederic B. *Trivieri, Lawrence A. Vachuska, Peter L. Verjovsky, Alberto S. Wallen, Lawrence J. Welch, Lloyd R.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 827 ...... _------_ .. AMS Centennial Fellowship Fund

WeIIe. Mark A. Wihstutz. Volker Wollman. Stephen Yandl, Andre Louis Zaharopol, Radu eWellinger. David Wiid. Frans G. Wolpert. Scott A. Yang, Chung-Chun Zaikov. Raiko WeIIner, Jon A. Wijsmuller. Marijke Wong, Henri S. F. Yang. Chung-Tao *Zakalyukin. Vladimir WeIIs, Charles F. Wik, Anders Wong. James S. W. Yang, Deane Mickailovich Wells. David M. Wik. Ingemar L. *Wong. Ngai-ching *Yang, Jae-Hyun Zalik. R. A. *Welters. Gerald E. Wildenhain. Kenneth R. Wong, Raymond Y. Yang. Jeong Sheng Zama. Nobuo Wend. David V. V. Wilf, Herbert S. *Wong. Sherman K. Yang. Kung-Wei Zambrini, Jean-Claude Wendel, James G. Wilker. John B. Wong. Yung-Chow Yang, Paul C. Zamorano. Nelson Arturo Wene. Gregory P. Wilkie. Alec J. Woo. Sung-Sik Yang. Seung Kab Zanolin. Fabio Wenger. Ronald H. Wilkinson, John F. Wood. Alastair D. *Yanik, Elizabeth G. Zapf, Hermann Wente. Henry C. Willcox. Alfred B. Wood. Geoffrey V. .Yanowitch. Michael Zara. Francois Wentworth, Richard Alan Williams, Bennie B. Wood, Jay A. Yao, Bi Yun *Zarach. Andrzej M. Wermer, John WiIIiams. Clinton Curtis Wood. John C. *Yap. Weng-Yin Zaslavsky. Thomas Werner. Dirk Williams. David A. Woodrow. Rohert Edward Yaqub, Jill S. *Zeeman, Mary Lou Werner, Elisabeth *Williams. David E. eWoodruff. Edythe P. Yasuda. Yutaka Zehnder. Eduard J. Werner, Peter eWiIIiams. Lawrence R. Woods. Alan C. Yasue, Kunio Zeidan, Vera M. *Werner. Wend eWilliams, Mark Woods. Jerry D. Yasuhara. Ann Zeidler, Eberhard Wernick. Robert J. Williams. Michael S. *Woods. R. Grant Yasuhara. Mitsuru Zeidler, Michael Edward West. Dennis E. *Williams. Neil H. *Woodward. Gordon S. Yebra, Jose Luis Andres Zelinsky. David S. West. Donald C. Williams, Peter David *Woodward, Scott Yen, David H. Y. Zeller, Karl West, James E. Williams. Susan Gayle Wooley. Trevor D. Yeung. Chi Shing Zemmer, Joseph L., Jr. Westbrook. Edwin P. Williams. Wm A. *Wortman, Dennis H. *Yeyios. Apostolos K. Zero. Jose R. Western. D. W. Williamson. Charles K. Woyczynski. Wojbor A. Yhap. Ernesto Franklin Zerzan, John M. Westheimer, Ellen Williamson. Susan Wright. Charles R. B. Yin. Weiping Zhang, Guang-Lu Weston, Jeffrey D. eWiIIis. Barton L. Wright, David G. *Yiu. Paul Y. H. Zhang. Jin Hao Westphal-Schmidt. U. *WiIIis. George A. Wright. David J. *Yoder. Margaret A. *Zhevandrov, Peter N. *Wette, E. W. eWillis, Paul A. eWright. Marcus W. Yohe. J. Michael Zia, Lee L. Wetzel, John E. Willson. Stephen J. eWright, Margaret H. Yokoi. Hideo Ziegler. Zvi *Whang, In-Hong Wilson. Alan Wright. Mary H. *Yokonuma. Takeo Ziemer, William P. Wheeler, Robert F. Wilson, Leslie Charles *Wright, Ron Yokota, Hisashi Zierau, Roger Craig Whelan, E. A. Wilson. Raj Wright, Thomas Perrin, Jr. Yokura, Shoji Zierler. Neal White. Alvin M. Wilson. Raymond B. *Wschebor, Mario Yoo. Ki-Jo Zimmer. J. W. White. Arthur T. Wilson, Richard Wu, Ching-mu Yood. Bertram *Zimmerman, Grenith J. White. Benjamin S. Wilson. Richard G. *Wu, Hung-Hsi *Yoshida, Julie K. Zimmerman. Marlene G. White, Denis A. Wilson, Robert Lee Wu, T. C. Yoshida, Masaaki Zimmermann-Huisgen. Birge K. White. Edward C.. Jr. Winbish, Glenn Joseph eWulf, Leo M. Yoshida, Zensho *Zink, Ernst-Wilhelm White. George N.• Jr. *Winfree. Erik Wylie, Clarence R.. Jr. Yoshino. Ken-ichi Zink. Thomas F. White. Gregory B. Wingate, John W. Wyman, Bostwick F. Yoshino, Masafumi Zinn. Joel White. Neil L. Winograd. Shmuel Xenos. Philippos John Yoshino. Takashi Zinterhof. Peter Whitehead, George W. Winter. Eva P. Xiao, Ti Jun *Yoshinobu, Stan T. ZippeL Richard E. Whitehead. Kathleen B. Wirszup. Izaak *Xiong. Zhen Xiang *Yoshizawa. Taro Zipse, Philip W. Whitehead. Sarah Tamsen Wiskott, Bettina Xu. Jia Gu Yossif, George Zirbel, Craig L. eWhiteman. Albert L. Wismath. Shelly *Yackel, James W. You, Hong Zirilli, Francesco Whitfield. John H. M. Wissner. Heinz-Wolfgang Yajima, Kenji Young. Lael M. Zitarelli. David E. Whitman, Andrew P. Witsch. K. J. *Yale. I. Keith Young, Paul M. Zitko. Jan Whitmore. William F. Witsenhausen. Hans S. Yamada. Hirofumi Young. Robin Zizler, Vaclav Whitney. D. Ransom Witten, Edward Yamada, Hiromichi Young. Sam Wayne Zo. Felipe J. Whittaker. James V. Witten, Louis Yamada, Miyuki Younis, Rahman Mahmoud Zoch, Richmond T. Whyburn. Kenneth G. *Woerdeman. Hugo J. Yamada. Naoki Yovanovich, M. Michael *Zoreda-Lozano. Juan J. eWhyburn. Lucille E. Woerner. Edwin L. Yamada, Osanobu *Yu. Jing Zorn, Paul Wickerhauser, Mladen Victor *Wogen, Warren R. Yamada. Shinichi YueChiming. Roger Y. S. *Zou, Qisu *Wickless. William J. eWoldar. Andrew J. Yamada, Toshihiko Yuen, David S. Zsido, Laszlo *Wicklin. Frederick J. Wolf. Edwin M. Yamagata. Shuji Yuhasz, Wayne D. Zucker. Steven M. Widom. Harold Wolf. Thomas R. Yamaguchi, Kohhei Yui. Noriko Zuckerman. Gregg J. Wiedemann. Douglas H. Wolfe. Dorothy W. Yamaguchi. Seiichi Yung, Tin-Gun Zumoff. Nancy E. Wiegand, Roger A. Wolfenden. Peter John Yamaki. Hiroyoshi Yurinsky. Vadim Zwaan. Marcel Wiegand. Sylvia Margaret Wolfmann. Jacques *Yamamoto. Masahiro * Yushkevich, A. A. ZweibeL John A. Wiegmann, Klaus Werner Wolfram. Stephen *Yamanoshita. Tsuneyo Zaballa. Ion Anonymous (202 ) Wiegold. James Wolfson, Kenneth G. Yamasaki. Masayuki Zabric, Eva *Wieschenberg. Agnes Arvai Wolk. Elliot S. Yan, Shi-Jian *Zacher. Giovanni G. Wightman. Arthur S. Wolkowicz. Gail S. K. Yanagawa, Minoru

AMS fSU AID FUND CONTRIBUTIONS

Anderson. Richard D. Hano. Jun-ichi McCarthy, Charles A. Rieffel, Marc A. NonindividuaI Blanc, M. L. Helson, Henry McCarthy, John Samelson. Hans University of Illinois. Browder. William Hendirman. Dadang Meister, Erhard V. Sansigre. Gabriela Association for CantreII. James C. Huneke. Craig L. Morrison, David R. Seitz, Gary M. Symholic Logic Chinn, William G. Kennedy, Edward S. Nakajima, Haruhisa Stembridge, John R. Members of Groups Drasin. David Krigman, Steven Slava Peck. N. Tenney Vojta. Paul A. of Mathematics Fisher, Benji N. Lehner. Joseph Pfeiffer, Paul E. Yorke. James A. and Computer Services Freundlich. Marianne Smith Massey. David B. Phillips, Ralph Anonymous (5 ) of FIMRT

828 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS PDF Fund Contributions

AMS Program Development Fund

In recognition of the vmied and substantial challenges confronting the Society's mission. and the need to set aside General Fund monies to specifically address these challenges. the Executive Committee and Board of Trustees voted to establish a Program Development Fund. The Fund was initiated in January 1994. It will permit the Society to invest its unrestticted member support in mission-related programmatic initiatives, providing a greater degree of flexibility and responsiveness to engage in critical issues facing the community.

Baker, Edward D. Edris, G. M. Hosack, John M. Morawetz, Cathleen S. Sakai, Makoto Ballard, William R. Folland, Gerald B. Igarashi, Masao Newman, Morris Schneider. Joel E. Botts, Truman A. Frame, J. Sutherland Karle, Jerome Nijenhuis, Albert Solomon. Louis Brown, Robert E. Gantos, Richard L. Kawahigashi. Yasuyuki Ono, Takashi Sturley. Eric A. Burkholder. Donald L. Goggins, Timothy Kawamoto, Shunji Osserman. Robert Sullivan. Richard W. Chinn, William G. Gordon, Hugh Kelly. John B. Piranian. George Todd, Michael J. Cohen, Daniel I. A. Gurney, Margaret Lenstra, H. W .. Jr. Richards. John F. Warner. Frank W .. Ill Duren, William L .. Jr. Hastad, Johan Maule. Robert G. Rothherger. Fritz Willcox. Allred B. Eachus, J. J. Herreshoff, James B. Mayor, John R. Sachs, Jeffrey R. Zink. Ernst-Wilhelm

Corporate Members and Institutional Associates

The Society also acknowledges with gratitude the support rendered by the following corporations, as Corporate Members or Institutional Associates of the Society during the past year.

Corporate Members Institutional Associates AT&T Bell Laboratories Birkhauser Boston General Motors Corporation Daniel H. Wagner Associates International Business Machines Fields Institute for Research Corporation in the Mathematical Sciences National Security Agency Institute for Defense Analyses Princeton University Press Kluwer Academic Publishers Springer-Verlag New York Incorporated Supercomputer Research Center

Memorial and Commemorative Gift Listing Memorial and commemorative gifts are a distinctive and thoughtful way to memorialize or honor a colleague, friend, or family member and to support the Society's work to promote mathematical scholarship and research. The Society acknowledges these gifts upon receipt of the gift and through the listing below. The list designates gifts made through March 1994. In addition, notification of the gift is sent to persons designated by the donor.

Memorial Gift In Memory of Elmer Tolsted. Pomona College In Memory of Irving Reiner Robert B. Herrera (To Centennial Fellowship Fund) In Memory of my parents (Abraham and Rebecca Weinstein) Irma M. Reiner Mordechai M. Weinstein Anonymous (1)

Peabody Bequest The Society received a bequest from the estate of Mary K. Peabody in memory of Professor Einar Hille. In recognition of this gift. and in accordance with the terms of her bequest, the ECBT has instructed that the executive conference room at its Providence office be known as the "Einar Hille Conference Room, made possible by a gift from the estate of Mary K. Peabody."

SEPTEMBER 1994, VOLUME 41, NUMBER 7 829 Oklahoma State University, Stillwater, Oklahoma October 28-29, 1994 Second Announcement

The eight hundred and ninety-fifth meeting of the American Accommodations Mathematical Society will be held at Oklahoma State Uni­ Rooms have been blocked for participants at the Best Western, versity in Stillwater, Oklahoma, on Friday, October 28, and Holiday Inn, and Student Union hotels. Participants should Saturday, October 29, 1994. All sessions will be held in the make their own arrangements directly with the hotel of their OSU Student Union. choice and state that they will be attending the AMS meeting. All rooms will be on a space-available basis after October Invited Addresses 1,1994. V. Lakshmibai, Northeastern University, Combinatorics, ge­ Holiday Inn (2 miles to OSU Student Union): West 6th ometly, and representation themy -an inte1play. Avenue, Stillwater, OK 74074. Telephone: 405-372-0800. David E. Marker, University of illinois at Chicago, Single, double, and triple rooms are $45.00 (plus tax). Model themy and exponentiation. David J. Wright, Oklahoma State University, Counting Best Western (0.5 miles to OSU Student Union): 600 East numberfields as orbits of representations. McElroy, Stillwater, OK 74074. Telephone: 405-377-7010. Joel Zinn, Texas A&M University, On the Gaussian Single $41.00 (plus tax); double, triple, and quadruple rooms measure of the intersection of symmetric, convex sets. are $46.00 (plus tax). Transportation between these hotels and the OSU campus Special Sessions will be available. New doctoral work in mathematics, Efraim Armendariz, University of Texas at Austin; D. J. Lewis, University of Student Union Hotel (located on campus): Student Union Michigan; Andy R. Magid, University of Oklahoma; and Building, Stillwater, OK. Telephone: 405-744-6835. Single, Robert J. Zimmer, University of Chicago. double, and triple rooms are $42.00 (plus tax). Complex hyperbolic geometly and discrete groups, Ara S. Registration Basmajian and Robert R. Miner, University of Oklahoma. The registration desk will be located inside the Student Union Representations of algebraic groups, Edward T. Cline, in the east wing and will be open from 7:00 a.m. to 7:00 University of Oklahoma. p.m. on Friday, October 28, and Saturday, October 29. The Number themy, Brian Conrey, Oklahoma State Univer­ registration fees are $30 for members of the AMS; $45 for sity, Stillwater, and William D. Duke, Rutgers University. nonmembers; and $10 for emeritus members, students, or Algebraic geomet1y, Bruce C. Crauder and Zhenbo Qin, unemployed mathematicians. Oklahoma State University, Stillwater. Geometly and representations of Lie groups, Edward G. Social Events Dunne and Roger C. Zierau, Oklahoma State University, There will be a Cowboy Barbecue Dinner on Friday evening, Stillwater. October 28, 1994. The price will be $15 per person. Fluid dynamics, Alan R. Elcrat, Wichita State University. This is a ticketed event. Those interested in participating The evolving undergraduate mathematics curriculum, should contact Caroline Morris at 405-744-5688 or e-mail Benny D. Evans, Oklahoma State University, Stillwater. mcaroli@math. okstate. edu by October 1. Several complex variables, Vladimir Ezhov and Alan V. Noell, Oklahoma State University, Stillwater. Travel Technology in the classroom, Jerry A. Johnson, Univer­ Delta has been selected as the official airline for this meeting. sity of Nevada. The following benefits are available exclusively to mathe­ Arithmetic groups and topology, Mark W. McConnell, maticians and their families attending the meeting: a savings Oklahoma State University, Stillwater. of up to 10% off any published domestic fare (includes U.S., Geomet1y and geodesics, Phillip E. Parker, Wichita State Canada, Bermuda, the Bahamas, Puerto Rico, and the U.S. University. Virgin Islands), subject to applicable fare restrictions. Call There also will be sessions of· contributed ten-minute 800-241-6760 between 8:00a.m. and 11:00 p.m. EST to con­ papers. tact Delta directly or call any licensed travel agent. Instruct The deadline for submission of abstracts for all sessions has the ticket agent to refer to file M0456 in order to qualify for expired. Unfortunately, late papers cannot be accommodated. the applicable discount.

830 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY University of Richmond, Richmond, Virginia November 11-13, 1994 Second Announcement

The eight hundred and ninety-sixth meeting of the American Accommodations Mathematical Society will be held at the University of Rooms have been blocked for participants at the following Richmond, in Richmond, Virginia, on Friday, November 11; hotels. Participants should make their own arrangements Saturday, November 12; and Sunday, November 13, 1994. directly with the hotel of their choice and request the AMS meeting rate to obtain the rate listed. All rooms will be on a space-available basis. The AMS is not responsible for rate changes or the quality of the accommodations offered by Invited Addresses these hotels/motels. The hotels are not close to campus, so Loren D. Pitt, University of Virginia, Probabilistic studies of private transportation to and from campus will be necessary. nondifferential functions. Cora S. Sadosky, Howard University, Lifting weights for Comfort Inn: 7201 West Broad Street, Richmond, VA 23294. fun and profit. Telephone: 804-672-1108. Single or double is $45. Deadline Doron Zeilberger, Temple University, '='. for reservations is October 27, 1994. Comfort Inn West: Parham and Quioccasin Roads, Rich­ mond, VA 23229. Telephone: 804-285-9061. Rooms are $44 Special Sessions for single and $48 for double. Deadline for reservations is Interpolation and dilation theory, Joseph A. Ball, Virginia September 10, 1994. Polytechnic University, and Cora S. Sadosky. Set theoretic topology and set theory, Amer Beslagic, George Mason University. Registration Operators on Banach spaces of analytic functions, Paul The registration fees are $30 for members of the AMS; $45 S. Bourdon, Washington and Lee University, and William T. for nonmembers; and $10 for emeritus members, students, or Ross, University of Richmond. unemployed mathematicians. Groups, rings, and forms, Douglas L. Costa and Gordon E. Keller, University of Virginia. Social Events Codes and designs, James A. Davis, University of Rich­ The mathematics department will host a reception on cam­ mond, and Harold N. Ward, University of Virginia. pus, Saturday, November 12, at 8:00 p.m. Look for further Quantum mechanics, Ira W. Herbst, University of Vir­ information about this at registration. ginia. Nonassociative algebras, Teresa Magnus, St. Mary's Travel College. USAir is the official airline for this meeting. The following Stochastic processes, John P. Nolan, American Univer­ benefits are available exclusively to mathematicians and sity. their families attending the meeting: 10% discount off any Identities and enumeration, Rodica E. Simion, George published domestic fare with a seven-day advance purchase. Washington University, and Doron Zeilberger. Call USAir's Meetings and Convention Reservation Office at The deadline for submission of abstracts to be considered 800-334-8644 between 8:00a.m. and 9:00p.m. EST or call for any of these sessions has expired. any licensed travel agent. Instruct the agent to refer to gold There will also be sessions for contributed ten-minute file #16950015 in order to qualify for the applicable discount. papers. This deadline has also expired.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 831 Joint Mathematics Meetings in San Francisco AMS Special Sessions and Contributed Papers MAA Contributed Papers

The Joint Mathematics Meetings in San Francisco will learning of advanced undergraduate mathematical topics, and be held January 4-7 (Wednesday-Saturday), 1995. The first the preparation of teachers. full announcement of the meetings will appear in the October 1994 issues of the Notices and FOCUS. This preliminary AMS Special Sessions announcement is made to encourage participation and to A list of Special Sessions for this meeting can be found in the provide lead time for submission of abstracts for consideration Invited Addresses, Special Sessions, and Contributed Papers for presentation in AMS Special Sessions and for submission section of this issue. of abstracts for AMS and MAA Contributed Paper Sessions. Most of the papers to be presented at these Special Sessions will be by invitation; however, anyone contributing Registration Deadlines an abstract for the meeting who feels that his or her paper In order for us to accommodate all participants in a timely would be particularly appropriate for one of these sessions fashion, especially everyone who would like their programs should indicate this clearly on the abstract and should submit and badges mailed, you are encouraged to send in your it by September 9, 1994, three weeks earlier than the normal registration and housing requests as quickly as possible. The deadline for contributed papers, in order that it be considered following deadlines will be strictly enforced: for inclusion. If the paper cannot be accommodated in the EARLY advance registration special session requested, it will be automatically considered a (housing and room lottery eligibility) November 9 ten-minute contributed paper unless proper notation has been ORDINARY advance registration made on the abstract form. (housing, tickets, Employment Register) November 16 AMS Contributed Paper Sessions FINAL advance registration There will be sessions of ten-minute contributed papers. (no housing, no Employment Register, Contributed papers will be grouped by related Mathemati­ no receipt of program/badge by mail) December 7 cal Reviews subject classifications into sessions insofar as The full meeting announcements and registration forms possible. The title of each paper accepted and the time of will appear in the October issue. The Mathematics Meetings presentation will be listed in the program of the meeting. Service Bureau will be happy to answer questions and assist in any way possible. We are just a phone call away (800-321- 4267, Ext. 4143). Submission Procedures for AMS Abstracts Abstracts should be prepared on the standard AMS form available from the AMS office in Providence or in departments AMS-MAA Special Contributed Paper Session of mathematics, or submitted electronically. See the Invited Papers are being solicited for the following session cospon­ Speakers, Special Sessions, and Contributed Papers section sored by the AMS and MAA. Potential contributors should of this issue. follow the instructions for MAA contributed papers and make Unfortunately, late papers cannot be accommodated. their submissions to the organizer indicated by the asterisk (*). Note that days and times are tentative. Research in undergraduate mathematics education, Friday evening and Saturday afternoon. DanielL. GorofT *,Depart­ MAA Contributed Paper Sessions ment of Mathematics, Harvard University, Cambridge, MA Contributed papers are being accepted on several topics in 02138; phone: 617-495-4869; fax: 617-495-3739; e-mail: collegiate mathematics for presentation in contributed paper goroff@math. harvard. edu; and Joan Ferrini-Mundy, sessions at the meeting. The organizers listed below solicit University of New Hampshire. contributed papers pertinent to their sessions' interests and We solicit research papers which address questions about concerns; material should be sent to the organizer whose the teaching and learning of undergraduate mathematics. We name is followed by an asterisk(*). Please note that the days are especially interested in including reports from completed scheduled for any session are tentative. The topics, organizers, research studies. Areas of particular interest are: visualization, and their affiliations are: the role of technology in learning undergraduate mathemat­ Experiences with modeling in elementa1y differential ics, student learning in reformed curricular settings, student equations, Saturday morning and Saturday afternoon. Robert

832 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

L. Borrelli*, Department of Mathematics, Harvey Mudd NM 88003-0001; phone: 505-646-3901; fax: 505-646-6218; College, Claremont, CA 91711-5990; phone: 909-621-8896; e-mail: davidp©nmsu. edu; and Reinhard Laubenbacher, fax: 909-621-8366; e-mail: bob_borrelli©hmc. edu; and New Mexico State University. Courtney S. Coleman, Harvey Mudd College. Teaching with original sources is becoming increasingly Modeling is playing an increasingly important role in widespread. This session is a forum for exchanging experi­ elementary differential equations courses mostly because of ences with using original sources from all time periods in the ready availability of inexpensive ordinary differential teaching at any level. Papers are invited which address the equations solver platforms. These platforms open the door for incorporation of specific sources in a particular instructional students to consider an incredibly rich variety of applications setting. and models which more closely fit the needs of client Dynamic geometry, Thursday morning and Saturday disciplines. Papers are invited on how modeling has been morning. James R. King*, Department of Mathematics integrated into the teaching of differential equations, whether GN-50, University of Washington, Seattle, WA 98195; phone: by case studies, cooperative projects with industry, or a 206-543-1915; e-mail: king©math. washington. edu; fax: laboratory experience. 206-543-0397; and Doris J. Schattschneider, Moravian Col­ Making statistics come alive, Thursday morning and lege. Friday evening. Robert W. Hayden*, Plymouth State College, The availability of "dynamic" geometry software such 20 River Street, Ashland, NH 03217-9702; phone: 603-968- as CABRI Geometre and Geometer's Sketchpad has opened 9914; e-mail: hayden©oz. plymouth. edu; and Mary R. the door to many changes in the teaching of geometry. This Parker, Austin (Texas) Community College. session invites papers that present instructive examples of the The MAA has a joint committee with the American Statis­ use of dynamic geometry software in the classroom or for tical Association. One of its goals is to support mathematicians research, and also invites papers that discuss the implications teaching statistics, and this session is part of that effort. We of dynamic geometry software for what mathematics we invite papers related to statistics in any undergraduate course. teach and how we teach it. Note: If you will need computer Possible areas include specific curriculum topics and exam­ equipment for your presentation, please include with your ples, the use of real data, student projects, writing, computers, submission a clear statement of your needs. innovative approaches to grading, using student feedback to Laboratory approaches to teaching mathematics, Wednes­ improve teaching, and curriculum organization issues. day morning and Thursday evening. Jon Wilkin*, Northern The first two years, Thursday morning and Saturday Virginia Community College, 6725 North 27th Street, Alexan­ morning. William J. Davis*, Department of Mathematics, dria, VA 22213-1204; phone: 703-536-5290; fax: 703-450- The Ohio State University, Columbus, OH 43210-1328; 2536; e-mail: nvwilkj©vccscent. bitnet; and Marilyn e-mail: davis©math. ohio-state. edu; phone: 614-292- E. Mays, North Lake College. 0365; fax: 614-436-7919; and Donald B. Small, U.S. Military The use of laboratory techniques and approaches in teach­ Academy. ing mathematics is gradually permeating all undergraduate As various reform efforts are implemented, the character mathematics courses. This session will present papers that of courses in the first two years of college mathematics deal with laboratory approaches to teaching mathematics is changed. Certain aspects of differential equations, linear courses other than the calculus. We are interested in papers algebra, and discrete mathematics have been incorporated which present courses which have laboratory experimentation into most of the calculus courses, and the several variables and/or exercises as their primary mode of teaching and learn­ offerings thus look quite different from what they used to. ing. Presentations may include methodology, equipment used, This session will look at various efforts toward building a and sample laboratory exercises, as well as a discussion of the coherent mathematical sciences program for the first two years merits of the particular approach. of college. Innovations in teaching linear algebra, Wednesday after­ Chaotic dynamics and fractal geometry, Wednesday af­ noon, Thursday evening, and Friday afternoon. Donald R. La­ ternoon and Friday afternoon. Denny Gulick*, Department Torre*, Department of Mathematical Sciences, Clemson Uni­ of Mathematics, University of Maryland, College Park, MD versity, Clemson, SC 29634-1907; phone: 803-656-3437; fax: 20742-0001; phone: 301-405-5157; fax: 301-314-0827; e­ 803-656-5230; e-mail: latorrd©clemson. clemson. edu; mail: dng©math. umd. edu; and Jon W. Scott, Montgomery Steven J. Leon (ATLAST), University of Massachusetts College. at Dartmouth; and David C. Lay (LACSG), University of To commemorate the twentieth anniversary of the sci­ Maryland. entific terms "chaos" and "fractals", a session on chaotic The teaching of linear algebra is undergoing substantial dynamics and dynamic geometry is being offered. The session change. This session invites papers on personal experiences invites papers on topics related to either chaotic dynamics with innovations in teaching linear algebra, including: (1) the or fractal geometry. The papers need to have an expository creative use of computer algebra systems, supercalculators, flavor. or computer software; (2) experiences with the NSF-funded Teaching with original sources, Wednesday morning and project to Augment the Teaching of Linear Algebra through Thursday afternoon. David J. Pengelley*, Mathematical Sci­ the use of Software Tools (ATLAST) summer workshops; ences Department, New Mexico State University, Las Cruces, (3) experiences with the core curriculum recommended by

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the Linear Algebra Curriculum Study Group (LACSG); (4) A 1991 National Research Council report, Mathematical "gems" of exposition in linear algebra; and (5) otherinnovative Sciences, Technology, and Economic Competitiveness, em­ teaching or curriculum initiatives in undergraduate linear phasized the central importance of mathematics to modem algebra. industry. This session invites papers that describe case studies Recruitment and retention of women faculty, Thursday of mathematics in use in industry. A case study should explain afternoon and Friday morning. Marcelle Bessman*, Frost­ what mathematical problems were involved, what solutions burg State University, 644 Geneva Place, Tampa, FL 33606; were generated, and how the solutions were implemented. It e-mail: jtaylor@madonna. coedu. usf. edu; phone: 813- should also describe project sponsorship-how the company 253-6584; Gerald J. Porter, University of Pennsylvania; and defined, approved, and managed the project; the working Sr. Miriam P. Cooney, University of Notre Dame. relations between the members of the project team; and the Women are obtaining doctoral degrees in mathematics reasons for success or failure. in increasing numbers. Mathematics departments are seeking qualified women faculty. This session, sponsored by the Submission Procedures for MAA Abstracts MAA Committee on Participation of Women, seeks papers Presentations are normally limited to ten minutes, although on strategies that are being used, or could be used, to recruit selected contributors may be given up to twenty minutes. and retain female faculty. Papers should take approximately Individuals wishing to submit a paper for any of these sessions twenty minutes to present. should note the following: The name(s) and address(es) of New directions in student assessment, Wednesday morn­ the author(s) and a one-page summary of the paper should ing and Thursday evening. Rose C. Hamm*, Honors be sent directly to the organizer whose address is given. Program, College of Charleston, Charleston, SC 29424- The purpose of this summary is to enable the organizer(s) to 0001; phone: 803-953-7154; fax: 803-953-7135; e-mail: evaluate the appropriateness of your paper for the session, so hammr@ashley. cofc. ed; andRichardVandervelde,Hope you should include as much detailed information as possible College. within the one-page limitation. Your summary must reach Assessing students' performance with respect to critical the designated organizer by Friday, September 2, 1994. thinking, mathematical communications skill, and the use The organizer will acknowledge receipt of all summaries. of technology demands assessment techniques dramatically If the organizer accepts your paper, you will receive a different from those many institutions and instructors have standardized abstract form to be used to prepare a brief traditionally relied upon. We invite contributed talks from abstract which will be published in the journal Abstracts persons regarding new (and old) evaluation techniques which (copies of which will be available in the registration area at are effective in this new environment. the meeting). Please return the completed form to the organizer Preparing teachers to implement change (three mod­ by Friday, September 16, 1994. Abstracts not received by els), Wednesday afternoon and Friday morning. Bettye M. that date cannot be published. If desired, an abstract form Clark*, Department of Mathematics, Box 171, Clark Atlanta may be obtained in advance from either the AMS office University, Atlanta, GA 30314; phone: 404-880-8188; fax: or the MAA office. Do not forward completed abstracts 404-880-8250; Robert A. Bix, University of Michigan-Flint; directly to the MAA or to the AMS unless instructed by and M. Kathleen Heid, Pennsylvania State University. the organizer. Sponsored by the Committee on the Mathematical Prepa­ ration of Teachers (COMET), this session solicits papers Audio-Visual Equipment describing model programs, creative partnerships, research, Rooms where Special Sessions and Contributed Paper Ses­ and position papers on how colleges and universities are sions will be held are equipped with one overhead projector changing attitudes and curricula in the mathematics and and screen. Blackboards are not available. Speakers requiring mathematics education departments to implement change additional equipment should contact the audio-visual coordi­ in teaching mathematics in all collegiate mathematics and nator for the meetings at the AMS office in Providence at mathematics education courses. 401-455-4140 or by e-mail wsd@math. ams. org prior to Mathematical sciences, technology, and economic com­ November 1, 1994. petitiveness, Thursday afternoon and Friday evening. S. Brent Requests for equipment made at the meeting most likely Morris*, 5088 Lake Circle West, National Security Agency, will not be satisfied because of budgetary restrictions. Columbia, MD 21044-1442; phone: 301-688-0332; fax: 301- 688-0289 (but call voice phone before sending fax); e-mail: sbmorri@sirius. alpha.ncsc .mil; and Patrick D. Mc­ Cray, G. D. Searle & Co.

834 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Addresses, Special Sessions, and Contributed Papers

Invited Addresses at AMS Meetings Organizers and Topics of Special Sessions The individuals listed below have accepted invitations to The list below contains all the information about Special address the Society at the times and places indicated. For Sessions at meetings of the Society available at the time this some meetings the list of speakers is incomplete. For full issue of the Notices went to the printer. announcements or programs of meetings occurring prior to the first meeting listed below, see the table of contents in this issue. Members wishing to nominate candidates for invited January 1995 Meeting in San Francisco, California addresses should send relevant information to the associate Associate Secretary: Andy R. Magid secretary for the section, who will forward it to the Section Deadline ji>r organi=<•rs: E.\pired Program Committee. Deadline ji,- consideration: Septemha 9, 199-1 Alex Adem and Jon F. Carlson, Cohomology and representa­ tions offinite groups San Francisco, CA, January 1995 Walter Allegretto, Alfonso Castro, and Ratnasingham Shivaji, Jerry L. Bona Leila Schneps Nonlinear elliptic boundary value problems and applica­ Alexander B. Givental Doris J. Schattschneider tions Jeff Kahn (AMS-MAA) Thomas Archibald and Victor J. Katz, History of mathematics John William Lott John Smillie Michael Aschbacher and Stephen D. Smith, The simple group Andrew J. Majda classification: Second generation proof and applications (Gibbs Lecture) Eric D. Bedford and John Smillie, Complex dynamics David C. Carothers, Undergraduate research Gary Chartrand and MichaelS. Jacobson. Graph theory Hartford, CT, March 1995 Saber N. Elaydi and John R. Graef, Difference equations: Ben F. Logan Kari Vilonen Themy and applications Nina N. Uraltseva Shouwu Zhang NaomiFisher, Harvey B. Keynes, Kenneth C. Millett, Hugo Rossi, and Christine Stevens, Mathematics and education reform (AMS-MAA-MER) Orlando, FL, March 1995 Ben A. Fusaro and Suzanne M. Lenhart. Enrironmental Dave Benson Krystyna M. Kuperberg modeling Bjorn Jawerth De Witt L. Sumners Jacob E. Goodman and Janos Pach, Discrete geometT)' Daniel L. Goroff, Research in undergraduate mathematics Chicago, IL, March 1995 education (AMS-MAA) Ian Graham and David Minda, Geometric jimction theory in Rodrigo Banuelos Jeremy T. Teitelbaum one and sereral complex variables Berit Stensones Efim Zelmanov Shouchuan Hu and Nikolaos S. Papageorgiuo, Multivalued dynamical systems and applications Kent, OH, November 1995 Jeff Kahn and Robin A. Pemantle. Probability and combina­ Luchezar L. Avramov Peter J. Sternberg torics Alice Silverberg Rodolfo H. Torres A. G. Karstatos. The my and applications of nonlinear opera­ tors of accretive and monotone type Ellen E. Kirkman and James J. Kuzmanovich, Noncomnwta­ Greensboro, NC, November 1995 tire algebra H. Thomas Banks Bodil Branner Yanping Lin, Numerical solution for integra-differential equa­ Mladen Bestvina Curtis Greene tions Terry A. Loring. Almost multiplicative maps. C*-algebras, and deformations Orlando, FL, January 1996 John William Lott and Rafe R. Mazzeo. Index themy and Irving Kaplansky elliptic operators on manifolds (Retiring Presidential Address) Benjamin A. Lotto. Holommphic spaces

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Daniel Madden, Effective approaches to the training of De Witt L. Sumners, Scientific applications of geometry and teaching assistants topology David E. Marker and Charles I. Steinborn, Model theory Wim F. Sweldens, Wavelets for PDEs and integral equations John L. Orr and David R. Pitts, Non-self-adjoint operator Ahmed I. Zayed, Sampling the01y, wavelets, and signal algebras processing Jack R. Quine and Peter Sarnak, Extremal Riemann swfaces Douglas C. Ravenel, Homotopy theory March 1995 Meeting in Chicago, Illinois Sivapragasam Sathananthan, Stochastic systems and applica- Central Section tions Associate Secretary: Andy R. Magid Seenith Sivasundaram, Nonlinear dynamics Deadline for organizers: Expired Deadline for consideration: December 19, 1994 Curtis D. Tuckey, Applied logic Nigel Boston and Jeremy T. Teitelbaum, Arithmetic geomet1y Bernd Ulrich and Walmer V. Vasconcelos, Commutative Richard A. Brualdi, Cary Huffman, and Vera S. Pless, Codes algebra: Rees algebras and related topics and their applications Roger A. Wiegand and Sylvia M. Wiegand, Commutative Theodore A. Burton, Periodic and almost periodic solutions Noetherian rings and modules of differential and functional equations William Chin and Ian M. Musson, Hopf algebras and quantum March 1995 Meeting in Hartford, Connecticut groups Eastern Section Jonathan Cohen and Eduardo Gatto, Extensions and applica­ Associate Secretary: Lesley M. Sibner Deadline for organi=ers: Expired tions of harmonic analysis: Spaces of homogeneous type Deadline for consideration: November 9. 1994 and wavelet analysis William Abikoff, Aras S. Basmajian, and Andrew H. Haas, Carl C. Cowen, Research in mathematics by undergraduates Geometric function theory Stephen R. Doty, Daniel K. Nakano, and Karl M. Peters, Lie David A. Cox, Enumerative geometry. toric varieties, and the my mirror symmetry Richard J. Maher, Mathematics education reform Sarah Glaz and Evan G. Houston, Commutative algebra Eric F. Rieders and Gang Wang, Probability and harmonic Joe McKenna and Alan C. Lazer, Nonlinear boundmy value analysis problems Jacob Towber, Three manifolds, six j symbols, and coherent Michael D. Rice, Cayley graphs and computation tensor operators Steven Rosenberg, Geometric methods in mathematical Mary H. Wright, Rings and modules physics Alexander A. Voronov, Moduli spaces, operads, and repre­ May 1995 Meeting in Givat Ram, Jerusalem, Israel sentation themy (Joint Meeting with the Israel Mathematical Union) Associate Secretary: Lance W. Small March 1995 Meeting in Orlando, Florida Deadline for mxani=ers: Expired Southeastern Section Deadline for consideration: JanUGI)' 19. 1995 Associate Secretary: Robert J. Daverman Deadline for organi=ers: Expired Deadline for consideration: November 9. 1994 August 1995 Mathfest in Burlington, Vermont Marcy Barge, The geomet1y of dynamical systems Associate Secretary: Robert J. Daverman Dave Benson and Clarence W. Wilkerson, Classifying spaces Deadline for organi=ers: November 4, 1994 Deadline for consideration: April 27, 1995 and cohomology of groups Philip L. Bowers, Discrete conformal geomet1y Robert C. Brigham and Richard P. Vitray, Combinatorics and October 1995 Meeting in Boston, Massachusetts Eastern Section graph themy Associate Secretary: Lesley M. Sibner John R. Cannon, Inverse and ill-posed problems Deadline for organi=ers: January 6, 1995 Bettye Anne Case, Jean Larson, and Joe L. Mott, Future Deadline for consideration: July 3, 1995 directions for the mathematics doctorate S. Roy Choudhury, Nonlinear dynamical systems, chaos, and November 1995 Meeting in Kent, Ohio turbulence Central Section S. Roy Choudhury and Lokenath Debnath, Solitons and Associate Secretary: Andy R. Magid nonlinear waves Deadline for mxani=ers: Februal)" 4. 1995 Deadline for consideration: July 25, 1995 Chat Yin Ho, Alexandre Turull, and Helmut Voelkein, Finite groups and related topics Sam Huckaba and Bernard L. Johnston, Commutative algebra November 1995 Meeting in Greensboro, North Carolina Southeastern Section Xin Li and Ram N. Mohapatra, Approximation themy and Associate Secretary: Robert J. Daverman special functions Deadline for organizers: Febmary 17. 1995 Piotr Mikusinski, New trends in generalized functions Deadline for consideration: July 25, 1995

836 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Alexandra Kurepa and Stephen B. Robinson, Nonlinear January 1998 Meeting in Baltimore, Maryland boundary value problems Associate Secretary: Robert J. Daverman Jerry E. Vaughan, Set-theoretic topology Deadline for organizers: April 10, 1997 Deadline for consideration: To be announced Jie Wang, Complexity theory March 1998 Meeting in Manhattan, Kansas January 1996 Meeting in Orlando, Florida Central Section Associate Secretary: Lance W. Small Associate Secretary: Andy R. Magid Deadline for organizers: April 12, 1995 Deadline for organizers: June 26, 1997 Deadline for consideration: To be announced Deadline for consideration: To be announced

March 1996 Meeting in Iowa City, Iowa Information for Organizers Central Section Associate Secretary: Andy R. Magid Potential organizers should refer to the January issue of the Deadline for organizers: June 22, 1995 Notices for guidelines on organizing a session. Proposals for Deadline for consideration: To be announced any of the meetings mentioned in the preceding section should Daniel D. Anderson, Commutative ring theory be sent to the cognizant associate secretary by the deadline Tuong Ton-That, Group representations and mathematical indicated. No Special Sessions can be approved too late to physics provide adequate advance notice to members who wish to participate. April1996 Meeting in New York, New York Western Section Eastern Section Lance W. Small, Associate Secretary Associate Secretary: Lesley M. Sibner Department of Mathematics Deadline for organizers: July 13, 1995 University of California, San Diego Deadline for consideration: To be announced La Jolla, CA 92093 E-mail: g_small@math. ams . org April1996 Meeting in Baton Rouge, Louisiana Telephone: 619-534-3590 Southeastern Section Central Section Associate Secretary: Robert J. Daverman Andy R. Magid, Associate Secretary Deadline for organizers: July 19, 1995 Department of Mathematics Deadline for consideration: To be announced University of Oklahoma 601 Elm PHSC 423 November 1996 Meeting in Columbia, Missouri Norman, OK 73019 Central Section E-mail: g..magid@math. ams . org Associate Secretary: Andy R. Magid Telephone: 405-325-6711 Deadline for organizers: February I, 1996 Eastern Section Deadline for consideration: To be announced Lesley M. Sibner, Associate Secretary MarkS. Ashbaugh, Partial differential equations and mathe­ Department of Mathematics matical physics Polytechnic University Nakhle Habib Asmar and Stephen J. Montgomery-Smith, Brooklyn, NY 11201-2990 Harmonic analysis and probability E-mail: g_sibner@math. ams. org Telephone: 718-260-3505 John K. Beem and Adam D. Helfer, Differential geometry Z. Q. Chen and Zhongxin Zhao, Stochastic analysis Southeastern Section Carmen C. Chicane and Yuri Latushkin, Differential equations Robert J. Daverman, Associate Secretary Department of Mathematics and dynamical systems University of Tennessee Steven Dale Cutkosky and Hema Srinivasan, Commutative Knoxville, TN 37996-1300 algebra E-mail: g_daverman@math. ams . org Fritz Gesztesy, Spectral theory and completely integrable Telephone: 615-974-6577 systems Jan Segert and Shuguang Wang, Gauge theory and its Other Information interaction with holomorphic and symplectic geometry General information for speakers as well as information on site selection for Sectional Meetings can be found in the January January 1997 Meeting in San Diego, California issue of the Notices. Electronic submission of abstracts is Associate Secretary: Lesley M. Sibner available to those who use the 1EX typesetting system. To Deadline for organizers: April 8, 1996 Deadline for consideration: To be announced obtain the envelopes for electronic abstracts from e-MATH via e-mail, follow these instructions: 1. Type telnet e-math. ams. org. May 1997 in Detroit, Michigan 2. Login and password are both e-math. Associate Secretary: Andy R. Magid Deadline for organizers: August 2, 1996 3. Type Q to bypass welcome information and go directly Deadline for consideration: To be announced to the Main Menu.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 837 ·····..·····.. i.ii.l£L..• w t ' ,. ,.. ,..JL JiJJL.,.",JL£lJ..L£I.,., .. .., ,,,J , ,.,., . Meetings

4. In the Main Menu, select Gopher. idence, RI 02940. When requesting the abstracts package, 5. In Gopher, select Meetings and Conferences. be sure to specify either the plain lEX, AMS-ltX, or the 6. In Meetings and Conferences, select Abstracts, then the UltX package. Requests for general information concern­ type of lEX macro package needed. ing abstracts may be sent to abs-misc©math. ams. org. Users may also obtain the package on IBM or Macintosh Completed electronic abstracts should be submitted to diskettes, available free of charge by writing to Electronic abs-submit©math.ams.org. Abstracts, AMS Meetings Department, P.O. Box 6887, Prov-

In Search of Symmetry, William Browder

William Browder served as President of the American Mathematical Society during 1990-1991. This videotape contains his Retiring Presidential Address-preceded by an informal interview in which he discusses a range of topics, including public awareness of mathematics. The lecture discusses the action of finite groups on manifolds, exploring the question of how large a finite group can effectively act on a given manifold. Browder concentrates on familiar examples such as the sphere, the n-sphere, or a product of spheres of different dimensions. The lecture is accessible to mathematics majors with background in algebraic topology.

1991 Mathematics Subject Classification: 55 ISBN 0-8218-8091-8, NTSC format on 1/2" VHS videotape; approx. 90 minutes, July 1994 Individual member $34.95, List price $54.95, Institutional member $44.95 To order, please specify VIDEO/93NA

The Current Interface of Geometry and Elementary Particle Physics, 1. M. Singer

This lecture covers three intriguing examples of interactions between physics and geometry: (i) the use of mirror symmetry in a conformal field theory to enumerate rational curves on a quintic, (ii) the Kontsevich matrix model that led to a solution of a conjecture of Witten, and (iii) the Jones-Witten knot invariant and Chern-Simons quantum field theory. The lecture is preceded by an interview with Singer. Providing insight on one of the hottest topics in mathematics, as well as a personal look at one of the leaders in the field, this videotape will interest students and researchers in mathematics, physics, and the history of science.

1991 Mathematics Subject Classification: 14, 58, 81 ISBN 0-8218-8092-6, NTSC format on 1/2" VHS videotape; approx. 90 minutes, July 1994 Individual member $34.95, List price $54.95, Institutional member $44.95 To order, please specify VIDEO/94NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

838 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1 AMS-SIAM Summer Seminar in Applied Mathematics

Mathematics of Numerical Analysis: Real Number Algorithms Park City, Utah, July 17 -August 11, 1995

The twenty-fifth AMS-SIAM Summer Seminar in Applied Ronald A. DeVore, University of South Carolina, Columbia; Mathematics will be held July 17-August 11, 1995 at the Gene H. Golub, Stanford University; Prospector Square Inn and Conference Center, Park City, Utah. Arieh Iserles, University of Cambridge, UK; The seminar will be sponsored by the American Mathematical Hubertus Th. Jongen, Reinisch-Westf Tech Hochschule, Society, the Society for Industrial and Applied Mathematics, Aachen, Germany; and the International Mathematical Union. It is anticipated Herb Keller, California Institute of Technology; that the seminar will be partially supported by grants from Jacques Louis Lions, College de France; federal agencies. The proceedings will be published by the James M. Renegar, Cornell University; AMS in the Lectures in Applied Mathematics series. Steve Smale (chair), University of California, Berkeley; The mathematical theory of real number algorithms is to Michael Shub, IDM; be the subject of this proposed conference. Thus numerical Gilbert Strang, MIT; analysis will be central with emphasis on geometrical, alge­ ShmuelWinograd,IDM;and braic, analytic, and foundational perspectives. Investigations Henryk Wozniakowski, University of Warsaw and Columbia of efficiency will play a special role. Practical algorithms will University. be the subject of theoretical analysis, but immediate useful To date the following have accepted invitations to speak: results will not be demanded. all members of the organizing committee; It is hoped that the conference will give the subject of Roger Brockett, Harvard University; numerical analysis a greater coherence through a focus on John Canny, University of California, Berkeley; the mathematical side, in particular, to aim to strengthen the W. Dahmen, Reinisch-WestfTech Hochschule, Aachen, Ger­ unity of mathematics and numerical analysis and to narrow many; the gap between pure and applied mathematics. That goal is David Donoho, University of California, Berkeley; appropriate, since many of the heroes of pure and applied James G. Glimm, SUNY at Stony Brook; mathematics-Newton, Euler, Lagrange, and Gauss among N. Karmarker, AT & T Bell Laboratories; them-established the basic real number algorithms. With the T. Y. Li, Michigan State University; revolution of the computer and the great achievements of Arkadi Nemirovski, Israel Institute of Technology; scientific computation, it does service to both the pure and Victor Pan, Herbert H. Lehman College, CUNY; applied communities to support the mathematical development Vladimir Rokhlin, Yale University; of numerical analysis. Marie-Fram;oise Roy, Universite de Rennes; This is an appropriate time to schedule such a meeting in Roger Temam, Indiana University; view of the rapid development of heuristic work, a good base RichardS. Varga, Kent State University; of theoretical work, and a widespread desire for mathematical Victor A. V. Vassiliev, Institute for System Studies, Moscow; deepening of the subject. Margaret H. Wright, AT & T Bell Laboratories; and The conference will be international in character with Yosef Yomdin, Weizmann Institute of Science, Israel. strong representation from the most mathematically devel­ Park City is a popular summer vacation destination with oped parts of numerical analysis. Besides tutorials and short a comfortable, temperate climate in the mountains of Utah. courses, seminars in the following areas are contemplated: Housing for participants has been arranged at the Inn at linear algebra, nonlinear systems-path following, differential Prospector Square and Conference Center. Reasonably-priced equations, linear programming problems, algebraic questions, restaurants, food shops, and other attractions are within walk­ foundations, information-based complexity, lower bounds, ing distance of the Inn. The Inn at Prospector Square includes and approximation theory. nine buildings with newly remodeled accommodations in The organizing committee includes: addition to a large lecture hall and meeting rooms. A sports Eugene L. Allgower, Colorado State University; center including pool, exercise machines, racquetball courts, Lenore Blum, MSRI; etc. (all available for a nominal fee), is located on the prop­ Alexandre J. Chorin, University of California, Berkeley; erty. All rooms being held for participants contain one or Philippe G. Ciarlet, Universite Pierre et Marie Curie, Paris; two queen-sized beds, television, telephone, coffee maker mi­ Felipe Cocker, Universitat Pampeu Fabra, Spain; crowave oven, and refrigerator. Some units have full kitchens. James W. Demmel, University of California, Berkeley; The daily cost is $45 single or double occupancy ($50 triple

------·------·-·------·-·----·------·-··--·-····--·--··------·-·---·-····· SEPTEMBER 1994, VOLUME 41, NUMBER 7 839 ------_ . Meetings and $55 quad) plus 10.13% lodging tax. Note that these prices 4. Anticipated arrival and departure dates; are per room, not per person. For those attending the full 5. Your scientific background relevant to the topic of the four weeks of the seminar, a very limited number of one-, seminar; please indicate if you are a student or if you two-, and three-bedroom condominium units is available on a received your Ph.D. on or after 7/1/89; monthly basis. Those interested should contact the conference 6. Financial assistance requested (please estimate cost of coordinator. More detailed information, including how to travel); indicate if support is not required and if interested make reservations, will be included with the official invitation in attending even if support is not offered. to the seminar. 7. Indicate if you would like to be included on a list of There is a registration fee of $40. Everyone interested those desiring a roommate for the seminar. If yes, please receiving an invitation to attend should send the following indicate if you are male or female, and list any other information before February 15, 1995, to AMS-Summer pertinent information (i.e., smoking/nonsmoking). Seminar Conference Coordinator, AMS Meetings and Con­ Special encouragement is extended to junior scientists to ferences Department, P.O. Box 6887, Providence, RI 02940; apply. A special pool offunds expected from federal agencies e-mail dls@math. ams . argo Please type or print the follow­ has been earmarkedfor this group. Otherparticipants who wish ing: to apply for a grant-in-aid should so indicate; however, funds 1. Full name and mailing address; available for the seminar are very limited, and individuals 2. Telephone number and area code for office and home; who can obtain support from other sources should do so. 3. E-mail address if available; Advanced graduate students are encouraged to participate.

The Journal of Geometric Analysis Volume 5, 1995 The Journal of Geometric Analysis is a forum for the best work in the field of geometric analysis. This journal publishes work which most clearly exhibits the symbiotic relationship among techniques of analysis, geometry, and partial differential equations. The Journal of Geometric Analysis is committed to being the journal of record for important new results that develop the interaction between analysis and geometry. It has established and will maintain the highest standards of innovation and quality in the field. Topic Coverage Analysis on manifolds. Non-linear partial differential equations. Geometric complex analysis • Geometric aspects of the study of partial differential equations • Minimal surface theory • Differential. geometry • Dynamical systems theory • Mathematical physics Editorial Board Managing Editor, Steven G. Krantz; Executive Editors, Eric Bedford, Luis Caffarelli, John Erik Fornress, Robert E. Greene, Gennadi M. Henkin, Nessim Sibony, and Guido Weiss. Formerly published by CRC Press, Inc., the Journal of Geometric Analysis is now published by Mathematica Josephina, Inc. and is printed and distributed by the American Mathematical Society. Starting with the 1994 volume (volume 4), the journal will be published quarterly. ISSN 1050-6926 Volume 5, 1995 subscription prices: Individuals $105, List price $255 To order, please specify 95JGANNA

All prices subject to change. Free shipment by surface to destinations in the United States. Postal surcharge: India $15, other foreign $10. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-32l--4AMS (321··4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

840 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematical Sciences 1994 Meetings and Conferences 1994-1995. Mittag-Leffier Institute's Aca­ demic Program for 1994-1995: Statistical Mechanics and Stochastic Analysis, Mittag­ Leffler Institute, Djursholm, Sweden. (Dec. 1993, p. 1444) THIS SECTION contains announcements of meetings and conferences of interest to some segment of the mathematical public, including ad hoc, local, or regional meetings, and meetings or symposia devoted to specialized topics, as well as announcements of regularly scheduled meetings of national or international mathematical organizations. A complete listing September 1994 of meetings of the Society, and of meetings sponsored by the Society, will be found inside the front cover. Suslin Jubilee International Conferences, AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers Suslin Foundation, Russia. (Oct. 1993, p. 1088) and specifies the place, date, subject (when applicable), and the speakers; a second published only if there are changes or necessary additional information. Fall 1994. Workshop on Exterior Differ­ announcement will be Once an announcement has appeared, the event will be briefly noted in each issue until it has ential Systems and Applications, Centre been held and a reference will be given in parentheses to the month, year, and page of the de Recherches Mathematiques, Universite de issue in which the complete information appeared. Asterisks (*) mark those announcements Montreal. (Jan. 1994, p. 57) containing new or revised information. Fall1994. Workshop on Geometry of Non­ IN GENERAL, announcements of meetings and conferences held in North America carry compact Manifolds, Centre de Recherches only date, title of meeting, place of meeting, names of speakers (or sometimes a general Mathematiques, Universite de Montreal. (Jan. statement on the program), deadlines for abstracts or contributed papers, and source of Meetings held outside the North American area may carry more detailed 1994,p.57) further information. information. In any case, if there is any application deadline with respect to participation in 4-10. Topologie, Oberwolfach, Federal Re­ the meeting, this fact should be noted. All communications on meetings and conferences in public of Germany. (Apr. 1993, p. 416) the mathematical sciences should be sent to the Editor of the Notices, care of the American 5-7. 6th IMA Conference on the Mathemat­ Mathematical Society in Providence, or electronically to not i ces@math. ams. org. ics of Surfaces, Brune1 University, London, 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 UK. (May/June 1994, p. 509) to submit information for these listings early enough to allow them to appear in more than 5-8. 4th European Workshop on Logics in one issue of the Notices prior to the meeting in question. To achieve this, listings should be AI (JELIA '94), York, UK. (Apr. 1994, p. 382) received in Providence SIX MONTHS prior to the scheduled date of the meeting. 5-8. ECCOMAS-Second European Com­ EFFECTIVE with the 1990 volume of the Notices, the complete list of Mathematical Sciences putational Fluid Dynamics Conference, Stutt­ Meetings and Conferences will be published only in the September issue. In all other issues, only meetings and conferences for the twelve-month period following the month of that issue p. 1452) gart, Germany. (Dec. 1993, will appear. As new information is received for meetings and conferences that will occur later 5-9. Meeting on Quaternionic Structures than the twelve-month period, it will be announced at the end of the listing in the next possible in Mathematics and Physics, Trieste, Italy. issue. That information will not be repeated until the date of the meeting or conference falls (May/June 1994, p. 509) within the twelve-month period. 5-9. IX Brazilian Meeting of Topology, Universidade Federal Fluminense, Instituto de Matematica, Niteroi, Rio de Janeiro, Brazil. 11-17. Homotopietheorie, Oberwolfach, Fed­ [email protected]@ere. (Jan. 1994, p. 57) eral Republic of Germany. (Apr. 1993, p. 416) umontreal. ca. 5-10. Analyse Numerique des Polynomes 12-16. Geometrie Algebrique et Analyse 13-17. II International Symposium on Ha­ Orthogonaux, CIRM, Marseille, France. (Feb. Reelle, CIRM, Marseille, France. (Feb. 1994, miltonian Systems and Celestial Mechanics, 1994, p. 144) p. 144) Cocoyoc, Mexico. (May/June 1994, p. 509) 6-8. International Conference on Parallel 12-17. Workshop on Non Compact Mani­ * 14-16. Fourth International Conference on Processing: CONPAR 94-VAPP VI, Linz, folds and Asymptotic Invariants, Centre Algebraic and Logic Programming, Sixth Austria. (Oct. 1993, p.1088) de Recherches Mathematiques, Universite de International Symposium on Programming 6-10. 8th International Conference of the Montreal, Montreal, Canada. Language Implementation and Logic Pro­ European Consortium for Mathematics in PROGRAM: The following topics are cur­ gramming (ALP '94, PLILP '94), Madrid, Industry, University of Kaiserslautem, Ger­ rently the subject of intense activity and Spain. (Feb. 1994, p. 144) many. (Apr. 1994, p. 382) will be discussed in the workshop: scalar 14-18. Sixteenth Linz Seminar on Fuzzy 7-9. 1st International Conference on Con­ curvature, quasi-regular mappings, convex Set Theory, Topology, and Related Topics, straints in Computational Logics (CCL), metric spaces and CAT(O) spaces, func­ Linz, Austria. (May/June 1994, p. 510) Munich, Germany. (May/June 1994, p. 509) tion theory on open manifolds, buildings, 15-19. Fifteenth International Symposium 7-9. IEEE European Workshop on Computer­ dynamical and probabilistic methods. on Mathematical Programming, University Intensive Methods in Control and Signal ORGANIZERS: M. Troyanov and M. Min­ of Michigan, Ann Arbor, MI. (Apr. 1993, Processing: Can We Beat the Curse of Di­ Oo. p. 416) mensionality?, Prague, Czech Republic. (Jan. CoNFIRMED SPEAKERS: U. Abresh, N. Be­ for Indus­ 1994,p.57) nakli, M. Bourdon, M. Bridson, T. Coulhon, 18-20. Teaching of Mathematics try, Prague. (Jul./Aug. 1993, p. 715) 7-9. IMA Thtorial on Computational Wave P. Delanoe, A. Haefliger, I. Holopainen, G. Propagation, Institute for Mathematics and its Knieper, P. Li, J. Lott, I. Nikolaev, P. Pansu, 18-24. Risk Theory, Oberwolfach, Federal Applications, University of Minnesota, Minne­ S. Rickman, R. Schoen, and V. Schroeder. Republic of Germany. (Apr. 1993, p. 416) apolis, MN. (Feb. 1994, p. 144) INFORMATION: L. Pelletier; electronic mail: 18-24. DMV-Jahrestagung 1994 (Annual

·---~-~-·------·------·-----····------SEPTEMBER 1994, VOLUME 41, NUMBER 7 841 ,_,.. ,...... ,_,.. , .. ,_,_,_,_,_,.. ,,, .. ,_,_,_,_,_,_,_, __ ,_,_,.. ,...... ,.. ,_,.. ,...... ,_,.. ,...... ,.... _,_,_.,._, .... ______...... ,_,_,_,...... -...... _.... ,...... ,_ ... , __ , ____ ,_, __ ,_ .. Meetings and Conferences

Meeting of the German Mathematical Soci­ mail:Friedhelm.Schieweck@Mathematik. implicit discretizations and multiple time­ ety), Duisburg, Federal Republic of Germany. Uni-Magdeburg.d400.de. stepping, constrained dynamics, energy (Nov. 1993, p. 1258) minimization techniques (including global 26-28. Image Processing: Mathematical 19-23. IMA Workshop on Computational * methods), locally enhanced sampling tech­ Methods and Applications, Cranfield Uni­ Wave Propagation, Institute for Mathematics niques, parallel computing schemes for versity, UK. and its Applications, University of Minnesota, biomolecules, building quantum mechan­ Minneapolis, MN. (Feb. 1994, p. 144) INFORMATION: P. Irving, Conference Offi­ ical effects into molecular dynamics, and 19-23. 3eme Atelier International de Theo­ cer, The Institute of Mathematics and its continuum solvation models in molecu­ rie des Ensembles, CIRM, Marseille, France. Applications, 16 Nelson St., Southend-on­ lar dynamics simulations. The format will (Apr. 1993, p. 416) Sea, Essex, SS 1 lEF, UK. include a mix of 25- and 40-minute talks. PARTIAL LIST OF SPEAKERS: P. Bash (Ar­ 21-22. International Symposium on Object­ 26-29. Second International Conference on gonne), J. Board (Duke), D. Chandler Oriented Methodologies and Systems, Pa­ Theorem Provers in Circuit Design: The­ (Columbia), R. Elber CUI-Chicago/Hebrew lermo, Italy. (Nov. 1993, p. 1258) ory, Practice, and Experience, Bad Herrenalb Univ.), B. Honig (Columbia), P. Koll­ 21-23. Meeting on Matrix Analysis and (Blackforest), Germany. (Feb. 1994, p. 144) man (UCSF), Z. Luthey-Schulten CUI­ Its Applications, Vitoria-Gasteiz, Spain. (Oct. 26-30. Journees de Probabilites, Marseille, Urbana-Champaign), M. Pettitt (Houston), 1993, p. 1088) France. (Jan. 1994, p. 58) C. Post (Purdue), T. Schlick (NYU), K. 23-26. EUROPROJ 94, Barcelona Annual Schulten CUI-Urbana-Champaign), R. Scott 26-30. International Workshop on Total Meeting, Sant Feliu de Guixols, Spain. (Apr. (Houston), and P. Wolynes CUI-Urbana­ Positivity and its Applications, J aca, Spain. 1994,p.382) Champaign). (Jul./Aug. 1994, p. 673) 25-30. International Conference/Workshop ATTENDANCE: Space is limited. There will * 26-30. Aunual Conference of the European on Computers and Mathematics (Special be a registration fee of $100. Some funds Association for Computer Science Logic SAMSA Conference), University of Zim­ are available to assist with expenses. The (CSL '94), Kazirnierz, Poland. (Feb. 1994, babwe, Harare, Zimbabwe. workshop will receive support from the p. 144) National Science Foundation, the DOE AIM OF CONFERENCE: To inform about 26-0ctober 1. 4th International Conference Office of Scientific Computing, and the existing software and methods, and en­ on Evolution Equations and Semigroups, Kansas Institute for Theoretical and Com­ courage the use of computers for teaching Scuola Normale Superiore, Pisa, Italy. (Apr. putational Science (KITCS), an interdisci­ and researching in mathematics. 1994, p. 382) plinary NSF-funded research institute. Re­ ToPICS: Using computers in the teaching 26-0ctober 1. First International Workshop cent Ph.D.s, women, and members of un­ of undergraduate mathematics; numerical on Functional Analysis, Trier University, near derrepresented minorities are particularly analysis, computational mathematics; us­ Luxembourg, Germany. (Oct. 1993, p. 1088) encouraged to apply. ing computers in research; laboratory and INFORMATION: Address inquiries to the 28-30. Thirty-second Annual Allerton Con· campus networking; and computers and organizers or to KITCS, 651 Snow Hall, ference on Communication, Control, and the general transmission of information, The Univ. of Kansas, Lawrence, KS 66045; Computing, University of Illinois, Urbana­ e-mail, journal, summaries, etc. tel: 913-864-3913; fax: 913-864-5255; e­ Champaign. (May/June 1994, p. 510) INFORMATION: The Secretary, Conference/ mail:[email protected]. Workshop on Computers and Mathematics, 28-30. Third International Conference on Dept. of Mathematics, University of Zim­ Parallel and Distributed Information Sys­ babwe, P.O. Box MP 167, Mount Pleasant, tems, Austin, Texas. (Jan. 1994, p. 58) Harare, Zimbabwe; tel: (263)(4) 303211 30-0ctober 1. 22nd Aunual Mathematics October 1994 Ext. 1177; fax: (263)(4) 33407/335249; and Statistics Conference on Classical Anal· electronic mail: uzmaths@mango. ape. org. ysis and General Topology in the Undergrad­ 1-2. lOth Anniversary Symposium, Ottawa­ uate Curriculum, Miami University, Oxford, Carleton Institute of Mathematics and Statis­ 25-0ctober 1. Mathematical Methods in Ohio. (Apr. 1994, p. 383) tics, Ottawa, Canada. (May/June 1994, p. 510) Tomography, Oberwolfach, Federal Republic 2-6. International Conference/Workshop of Germany. (Apr. 1993, p. 416) * 30-0ctober 2. Algorithms for Macromolec­ ular Modeling (an interdisciplinary work· on Applications of Operator Theory, Win­ 26. The Mathematics of Impact: The dy­ shop), Kansas Institute for Theoretical and nipeg, Manitoba, Canada. (May/June 1994, namics of discontinuous systems, University p. 510) of Bristol, U.K. (Jul./Aug. 1994, p. 673) Computational Science, University of Kansas at Lawrence. 2-8. Randelementmethoden: Anwendungen 26-27. National Research Council Sympo­ und Fehleranalysis, Oberwolfach, Federal Re­ sium on Large-Scale Structures in Acoustics ORGANIZERS: J. Hermans (UNC), K. Kucz­ public of Germany. (Apr. 1993, p. 416) era (KU), B. Leimkuhler (KU), and R. and Electromagnetics, National Academy of 3-7. Groupes Finis, CIRM, Marseille, France. Sciences, Washington, D.C. (Jul./Aug. 1994, Skeel (UIUC). (Feb. 1994, p. 145) p. 673) PROGRAM: This is a special workshop on al­ gorithms and parallel implementations for 6-7. Combustion, Environment, and Heat­ 26-27. WOGDA'94 Ill Workshop de Oto­ ing Technology-The Role of High-Perfor­ no: Geometria Diferencial y Sus Aplica­ macromolecular dynamics, protein fold­ ing, and structure refinement, including the mance Simulation, Columbus, Ohio. (Jul./Aug. ciones (Ill Autumn Workshop: Differential 1994,p.673) Geometry and its Applications), Granada, treatment of quantum effects. The emphasis 6-9. Combinatorial Methods for DNA Map· Spain. (Jul./Aug. 1994, p. 673) is on the numerical and algorithmic chal­ lenges to achieving dramatic gains in the ping and Sequencing (DIMACS Workshop), 26-28. GAMM • Workshop on Multilevel * performance of software for the simulation Rutgers University, Piscataway, NJ. (May/June Methods, Meisdorf, Germany. of proteins, nucleic acids and other poly­ 1994, p. 510) - --- INFORMATION: F. Schieweck, Dept. of mers. Topics appropriate to the workshop 7-8. The 23rd Annual Midwestern Differ­ Mathematics, University Magdeburg, PSF include (but are not limited to) the fast ential Equations Conference, Univ. of Okla­ 4120, D-39016 Magdeburg, Germany; e- multipole method for theN-body problem, homa, Norman, OK. (May/June 1994, p. 511)

842 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

9-15. Arbeitsgemeinschaft mit Aktuellem 17-21. Visualization '94 Conference, Shera­ and Distributed Processing, Dallas, Texas. Thema (Wird in den Mitteilungen der DMV ton Premiere at Tysons Corner, VA (Washing­ (Mar. 1994, p. 251) Heft 3/1994 Bekanntgegeben), Oberwolfach, ton, DC area). (May/June 1994, p. 511) 28-29. 1994 Mathematical Sciences Depart­ Federal Republic of Germany. (Apr. 1993, 17-21. IMA Workshop on Wavelets, Multi­ ment Chairs Colloquium, Arlington, Virginia. p. 416) grid and Other Fast Algorithms (Multipole, (Apr. 1994, p. 383) 10-14. Journees d'Etude en Statistique, FFT), and Their Use in Wave Propagation, 28-29. Central Section, Oklahoma State Uni­ CIRM, Marseille, France. (Feb. 1994, p. 145) Institute for Mathematics and its Applications, versity, Stillwater, Oklahoma. 10-28. School/Workshop on Variational University of Minnesota, Minneapolis, MN. INFORMATION: W. Drady, AMS, P.O. Box and Local Methods in the Study of Ha­ (Feb. 1994, p. 145) 6887, Providence, RI 02940; e-mail: meet@ miltonian Systems, International Centre for 17-21. Atelier MEDICIS-SMF: methodes math. ams . org. Theoretical Physics, Trieste, Italy. (Jul./Aug. algebriques et geometriques pour les sys­ 1993, p. 715) temes differentiels, CIRM, Marseille, France. 28-30. Hybrid Systems and Autonomous 11-13. IMA Thtorial on Wavelets, Multi­ (Feb. 1994, p. 145) Control, Cornell University, Ithaca, NY. (May/ grid and Other Fast Algorithms (Multipole, * 20-22. International Conference on "Sys­ June 1994, p. 511) FFT), and Their Use in Wave Propagation, tems, Control, Information", Methodologies 30-November 5. Finite Volume Methods, Institute for Mathematics and its Applications, and Applications, Wuhan, China. Oberwolfach, Federal Republic of Germany. University of Minnesota, Minneapolis, MN. INFORMATION: M.-Y. Chen, Dept. of Au­ (Apr. 1993, p. 416) (Feb. 1994, p. 145) tomatic Control Engineering, Huazhong 31-November 4. Orthogonality, Moment 12-18. CARl '94: Second African Confer­ Univ. of Science and Technology, Wuhan Problems, and Continued Fractions: An In­ ence on Research in Computer Science, Oua­ 430074, China; or G. Mesnard, President ternational Conference in Honor of T.J. gadougou (Burkina-Faso ). (Nov. 1993, p. 1259) AMSE, 16 Av. Grange Blanche, 69160 Stieltjes, Jr. (1856-1894), Delft, Holland. 13-14. Numerical Analysis Colloquium (to Tassin la-derni-lune, France. (Dec. 1993,p. 1453) honor the 60th birthday of Jean Descloux), 31-November 4. International Conference Ecole Polytechnique Federale, Lausanne, Switz­ 20-24. First Slovenian Congress of Math­ of the Chilean Computer Science Society, erland. (Jul./Aug. 1994, p. 674) ematics, Cankarjev dom, Ljubljana, Slovenia. Concepcion, Chile. (Apr. 1994, p. 383) (May/June 1994, p. 511) 13-16. Semi-annual Regional Workshop in Dynamical Systems and Related Topics, 21. Women in Mathematics and Computer Penn State University, State College, Penn­ Science, Kean College of New Jersey, Union, sylvania. (Jul./Aug. 1994, p. 674) NJ. (May/June 1994, p. 511) November 1994 14-15. Midwest Math History Conference 21-22. Fourteenth Annual Meeting of the V, University of Indianapolis, Indianapolis, Southeastern-Atlantic Regional Conference 2-4. Mathematique lnformatique, CIRM, Indiana. (Jul./Aug. 1994, p. 674) on Differential Equations, University of Ten­ Marseille, France. (Feb. 1994, p. 145) nessee, Knoxville, Tennessee. (Apr. 1994, 14-15. 1994 Sixteenth Midwest Probability 4-5. Ninth Annual Pi Mu Epsilon Re­ p. 383) Colloquium, Northwestern University, Evan­ gional Undergraduate Mathematics Con­ ston, IL. (May/June 1994, p. 511) * 22. Mid-Atlantic Probability and Statistics ference, St. Norbert College, De Pere, WI. Day, American University, Washington, DC (May/June 1994, p. 512) * 15-19. Workshop on Exterior Differential Systems, Centre de Recherches Mathematiques, INVITED SPEAKERS: R. Durrett, Cornell, 7-9. ISCIS IX (International Symposium Universite de Montreal, Montreal, Canada. and E. Parzen, Texas A&M. There will also on Computer and Information Sciences - 9), be contributed sessions. Antalya, Turkey. (May/June 1994, p. 512) PROGRAM: This workshop will focus on ap­ INFORMATION: J. Nolan, Mid-Atlantic Prob­ 7-18. 2nd Workshop on Three-dimensional plications to the calculus of variations, the ability and Statistics Day, Math/Stat Dept., Modelling of Seismic Waves Generation, geometric study of p.d.e's, and Reimannian American Univ., 4400 Mass. Ave. NW, Propagation, and Their Inversion, Trieste, geometry. Washington, DC 20016; e-mail: jpnolan@ Italy. (Feb. 1994, p. 145) ORGANIZER: N. Kamran. american. edu. 9-10. IMA Thtorial on Waves in Random CoNFIRMED SPEAKERS: I. M. Anderson, and Other Complex Media, Institute for R. Bryant (Aisenstadt Chair Holder), J. 22-23. Northeastern Operator Theory Sem­ Mathematics and its Applications, University Conn, D. de Turck, Y. Eliashberg, M. inar, Vassar College, Poughkeepsie, NY. of Minnesota, Minneapolis, MN. (Feb. 1994, Pels, R. B. Gardner, H. Goldschmidt, P. A. (Jul./Aug. 1994, p. 674) p. 145) Griffiths, M. Henneaux, L. Hsu, T. lvey, M. 23-29. WahrscheinlichkeitsmaBe anfGrup­ Kossowski, M. Kuranishi, J. M. Landsberg, 11-13. Southeastern Section, University of pen und Verwandten Strukturen, Oberwol­ Richmond, Richmond, VA. P. J. Olver, J. Pohjanpelto, W. F. Shadwick, fach, Federal Republic of Germany. (Jul./Aug. J. Stasheff, K. Tenenblat, R. Tucker, P. 1993, p. 715) INFORMATION: W. Drady, AMS, P.O. Box Vassiliou, and G. Wilkens. 6887, Providence, RI 02940; e-mail: meet@ 24-26. International Symposium on Com­ INFORMATION: L. Pelletier; electronic mail: math. ams . org. PELLETL@ere. umontreal. ca or elec­ putational Molecular Dynamics, University tronic mail: CRM@ere. umontreal. ca. of Minnesota Supercomputer Institute, Minne­ 12. Southern California Matrix Theory apolis, Minnesota. (Jul./Aug. 1994, p. 674) Conference, University of Utah, Salt Lake 16-18. Women in Probability, Cornell Uni­ 24-November 11. Fourth Autumn Course City, Utah. (Jul./Aug. 1994, p. 675) versity, Ithaca, NY. (Apr. 1994, p. 383) on Mathematical Ecology, Trieste, Italy. (Jan. 13-17. 1994 International Symposium on 16-22. Geometrie, Oberwolfach, Federal Re­ 1994, p. 58) Logic Programming, MSI, Ithaca, NY. (Jul./ public of Germany. (Apr. 1993, p. 416) 25-27. Thirteenth Symposium on Reliable Aug. 1993 p. 715) 17-18. 1994 Symposium on Volume Visual­ Distributed Systems, Near Irvine, California. 13-19. Komplexitatstheorie, Oberwolfach, ization, Sheraton Premiere at Tysons Corner, (Apr. 1994, p. 383) Federal Republic of Germany. (Apr. 1993, VA. (May/June 1994, p. 511) 26-29. Sixth IEEE Symposium on Parallel p. 417)

SEPTEMBER 1994, VOLUME 41, NUMBER 7 843 Meetings and Conferences

14-18. International Conference on Math- 127""16. International Conference on Set­ TN 37235; e-mail: dfisher@vuse. - -ematical-E-cology-;-rrieste;-Italy~tFeb~I-994, theoretic Topology and its Applications, vanderbilt . ed-u. ------p. 145) Ehime University, Matsuyama, Japan. (May/ 6-7. Association for Symbolic Logic, 1994­ 14-18. IMA Workshop on Waves in Ran­ June 1994, p. 513) * 1995 Winter Meeting (in conjunction with dom and Other Complex Media, Institute for ADDITIONAL SPEAKERS: The list of invited the annual meeting of the AMS), San Fran­ Mathematics and its Applications, University speakers published in the May/June issue cisco, California. of Minnesota, Minneapolis, MN. (Feb. 1994, has been enlarged to include the following p. 145) persons: Z. Balogh (USA), A. Bella (Italy), CONFERENCE SCHEDULE: The meeting will 14-18. Nouvelles Tendances et Approxima­ K. Kuperberg (USA), Y. Sternfeld (Israel), begin on the morning ofJanuary 6 and end tion, CIRM, Marseille, France. (Feb. 1994, M. Tkavcenko (Mexico), and V. Tkavcuk at 5 p.m. on January 7. p. 145) (Mexico). PROGRAM CHAIR: A. Blass, Math. Dept., 14-18. Supercomputing '94, the Seventh Univ. of Michigan. Annual High-performance Computing and 12-17. International Conference on Opera­ CONTRIBUTED PAPERS: Abstracts of con­ CommunicationConference, Convention Cen­ tor Theory for Complex and Hypercomplex tributed papers from ASL members should ter, Washington, DC. (Apr. 1994, p. 384) Analysis, Mexico City, Mexico. (May/June be sent by the deadline of October 21, 1994,p.513) 1994, to the program chair, A. Blass, Dept. 16-18. Envirosoft 94 (Development and Ap­ of Math., Univ. of Michigan, Ann Ar­ plication of Computer Techniques to En­ 12-17. Pacific Rim Geometry Conference, National University of Singapore, Republic of bor, MI 48109; e-mail: Andreas .Blass@ vironmental Studies), San Francisco, CA. math.lsa.umich. edu. (May/June 1994, p. 512) Singapore. (Feb. 1994, p. 146) * 18-20. Conference in Probability and Mod­ * 14-16. New Asymptotic Methods in Geo- 8-12. 8th Texas International Symposium ern Analysis, University of California, River­ physical Flows, Cambridge, U.K. on Approximation Theory, College Station, side. INFORMATION: P. Irving, Conference Offi­ TX. (May/June 1994, p. 514) cer, The Institute of Mathematics and its HONOREE: Professor M. M. Rao, on the *9-10. Least Squares Methods: Theory, Al­ occasion of his 65th birthday. Applications, 16 Nelson St., Southend-on­ gorithms and Applications, Linkoping, Swe­ INFORMATION: Please submit abstracts to Sea, Essex, SS 1 lEF, U.K. den. J. A. Goldstein (Louisiana State Univ., 16-19. International Symposium on Meth­ INFORMATION: L. Elden or T. Petersson, Baton Rouge), e-mail: goldstei@math. ods and Applications of Analysis, Hong Dept. of Math., Linkoping Univ., S-581 83 lsu. edu; N. E. Gretsky (Univ. of Califor­ Kong. (Mar. 1994, p. 251) Linkoping, Sweden; e-mail: laeld@math. nia, Riverside), e-mail: neg@math. ucr. 18-23. Asymptotik Hochdimensionaler Sta­ liu. se or thpet@math .liu. se. edu; or 1. J. Uhl, Jr. (Univ. of Illinois, tistischer Modelle, Oberwolfach, Federal Re­ Urbana-Champaign), e-mail: j uhl@math. * 11-13. Symposium to Celebrate Germund public of Germany. (Apr. 1993, p. 417) uiuc. edu. Dahlquist's 70th Birthday, Stockholm, Swe­ 27-31. 21st Holiday Mathematics Sym­ den. 20-26. Mathematical Aspects of Computa­ posium on Grobner Bases and Convex tional Fluid Dynamics, Oberwolfach, Federal Polytopes, New Mexico State University. INFORMATION: G. Soderlind, electronic Republic of Germany. (Apr. 1993, p. 417) (May/June 1994, p. 513) mail: [email protected]. 21-27. Thanksgiving Workshop on Con­ 14-21. The 15th Winter School: Geometry trolled Topology, Geometry and Algebra, and Physics, Srni, Bohemian Forest, Czech IMADA, Odense University, Odense, Den­ 1995 Republic. (Ju1./Aug. 1994, p. 676) mark. (May/June 1994, p. 512) Second International Conference on Nu­ 15-17. Random Partial Differential Equa­ 27-December 3. The Norbert Wiener Cen­ merical Methods for Volterra and Delay tions, MSI, Ithaca, NY. (May/June 1994, tenary Congress, Michigan State University, Equations (A conference to celebrate the p.514) East Lansing, MI (Preliminary Announcement 100th anniversary ofVolterra's birth.), Italy. * 16-18. 1995InternationalWorkshoponNu­ (May/June 1994, p. 512) (Mar. 1992, p. 251) merical Solution ofMarkov Chains, Raleigh, 27-December 3. Mathematical Models for North Carolina. Infectious Diseases, Oberwolfach, Federal Re­ public of Germany. (Ju1./Aug. 1993, p. 715) INFORMATION: W.1. Stewart, Dept. ofCom­ January 1995 puter Science, Box 8206, North Carolina January-June. Financial Mathematics, Isaac State Univ., Raleigh, NC 27695-8206. Newton Institute for Mathematical Sciences, December 1994 16-19. First Asian Computational Fluid Cambridge, UK. (May/June 1994, p. 513) Dynamics Conference, Hong Kong University 4-10. Applied Probability, Oberwolfach, 4-7. Joint Mathematics Meetings, San Fran­ of Science and Technology, Clear Water Bay, Federal Republic ofGermany. (Ju1./Aug. 1993, cisco, CA (including the annual meetings of Hong Kong. (Jan. 1994, p. 58) p.715) the AMS, AWM, MAA, and NAM). 17-20. IMA Tutorial 1 on Inverse Problems 5-9. 20th Australasian Conference on Com­ INFORMATION: H. Daly, AMS, P.O. Box in Wave Propagation, Institute for Mathemat­ binatorial Mathematics and Combinatorial 6887, Providence, RI 02940; electronic ics and its Applications, University of Minne­ Computing, Auckland, New Zealand. (Apr. mail: meet@math. ams .org. sota, Minneapolis, MN. (Feb. 1994, p. 146) 1994,p.384) 22-24. Sixth ACM-SIAM Symposium on 8-9. Workshop on Mobile..Computing Sys­ *4-7. Fifth International Workshop on Arti­ Discrete Algorithms, San Francisco, CA. tems and Applications, Santa Cruz, CA. ficial Intelligence and Statistics, Fort Laud­ (Ju1./Aug. 1994, p. 676) erdale, Florida. (Jul.lAug. 1994, p. 675) 22-25. First International Symposium on 12-14. SIAM Conference on Inverse Prob­ INFORMATION: D. Fisher, Dept. of Com­ High-Performance Computer Architecture, lems, Fish Camp, CA. (Dec. 1993, p. 1453) puter Science, Vanderbilt Univ., Nashville, Raleigh, N.C. (Ju1./Aug. 1994, p. 676)

844 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ••mmm •••••••••••••••••••• m --ZiJUiiiiJ& ·--- MeetingS and Conferences

23-27. 3rd International Symposium on the Workshop on Approximations and Numeri­ 30-April 2. Association for Symbolic Logic Development of Mathematics, Havana, Cuba. cal Methods for the Solution of the Maxwell Annual Meeting, University of California at (May/June 1994, p. 514) Equations, Oxford, UK. Irvine. (Jul./Aug. 1994, p. 677) 3D-February 3. IMA Thtorial 2 on Inverse INFORMATION: P. Irving, Conference Offi­ Problems in Wave Propagation, Inst. for cer, The Institute of Mathematics and its Mathematics and its Applications, Univ. of Applications, 16 Nelson St., Southend-on­ April1995 Minnesota, Minneapolis, MN. (Feb. 1994, Sea, Essex, SS 1 lEF, UK. p. 146) * I -September 30. Special Session and Con­ 26-29. IMS Eastern Regional Meeting and ference on Geometry and Physics, Matema­ Biometric Society/ENAR Spring Meeting, tisk lnstitut, Aarhus Universitet, Aarhus, Den­ February 1995 Birmingham, AL. (May/June 1994, p. 514) mark 24-25. Central Section, DePaul University, PROGRAM: The session, organized by Aar­ * 3-5. 5th Annual Conference of Jammu Chicago, IL. Mathematical Society: A Symposium on hus and Odense Universities, will run from Functional Analysis and Applications, De­ INFORMATION: W. Drady, AMS, P.O. Box April 1 to September 30, 1995, with a partment of Mathematics, Univ. of Jammu, 6887, Providence, RI 02940; e-mail: meet@ conference from July 18 to 27 on Quantum India. math. ams. org. Invariants and Low Dimensional Topology including Special Holonomy and Twistor INFORMATION: D. K. Gupta, Dept. of Math., * 27-29. The Applications of Logic, York, UK. Theory. Univ. of Jammu, Jammu-180004, India. INFORMATION: P. Irving, Conference Offi­ ORGANIZERS: J. Andersen (Aarhus, e­ mail: andersen@mi. aau. dk), J. Dupont 5-8. The Joint Meeting of the Third Carib­ cer, The Institute of Mathematics and its (Aahrus, e-mail: dupont@mi. aau. dk), H. bean Congress on Fluid Dynamics and the Applications, 16 Nelson St., Southend-on­ Pedersen (Odense, e-mail: henrik@imada. Third Latin-American Symposium on Fluid Sea, Essex, SSllEF, UK. ou. dk), and A. Swann (Odense, e-mail: Mechanics, The University of Simon Bolivar, 27-Aprill. Dynamical Systems Conference, swann@imada. ou. dk). Caracas, Venezuela. (Apr. 1994, p. 384) * Montevideo, Uruguay. ADVISORY COMMITTEE: S. K. Donaldson, 8-11. Third SIAM Conference on Math­ N.J. Hitchin, V. G. Turaev, and S.-T. Yau. SuBJECT: Dynamical systems and related ematical and Computational Issues in the INFORMATION: Send name, address, e-mail topics, including subjects such as ergodic Geosciences, San Antonio, TX. (Jul./Aug. address, provisional dates of attendance theory, symplectic geometry, homoclinic 1994,p.676) and accommodation requirements to: Ge­ bifurcations, strange attractors, billiards, * 15-17. Seventh SIAM Conference on Paral­ ometry and Physics, Matematisk Institut, lel Processing for Scientific Computing, San and geodesic flows. Ny Munkegade, DK-8000 Aarhus C, Den­ SCIENTIFIC COMMITTEE: M. Herman, J. Francisco, CA. (Jul./Aug. 1994, p. 676) mark; e-mail: gap@mi. aau. dk. A small Lewowicz, R. Mane, J. Mather, S. New­ 19-25. Applications of Interval Compu­ amount of support may be available for house, J. Palis, and Ya. Sinai. tations (First International Workshop), El financial assistance. Priority will be given SPEAKERS: To be announced. Paso, TX. (May/June 1994, p. 514) to young researchers. DEADLINE: Deadline for application to par­ ticipate: January 31, 1995. 1-4. International Conference on Survey INFORMATION: M. Cerrninara, G. Paternain, Measurement and Process Quality, Bristol, March 1995 A. Rovella, or R. Ures; or IMERL - Fac­ England. (May/June 1994, p. 514) 4-5. Eastern Section, Hartford, Connecticut. ultad de Ingenieria, Julio Herrera y Reissig 2-9. 7th International Conference on Ge­ 565 CC 30, Montevideo, Uruguay; fax: ometry, Nahsholim, Israel. (May/June 1994, INFORMATION: W.S. Drady, AMS, P.O. Box (5982) 715446; e-mail: dynsys@imerl. p. 514) 6887, Providence, RI 02940; e-mail: meet@ edu.uy. math. ams. org. 4-6. IMA Thtorial on Singularities and Os­ * 28-31. Twenty-sixth Annual Iranian Math­ cillations, Institute for Mathematics and its 6-17. IMA Workshop on Inverse Problems ematics Conference, Shahid Bahonar Univ. of Applications, University of Minnesota, Minne­ in Wave Propagation, Institute for Mathemat­ Kerman, Kerman, Iran. apolis, MN. (Mar. 1994, p. 252) ics and its Applications, University of Minne­ 5-7. International Conference on Rewrit­ PROGRAM: Plenary talks and special ses­ sota, Minneapolis, MN. (Apr. 1994, p. 384) ing Techniques and Applications (RTA- sions for contributed papers. 95), Kaiserslautern, Germany. (Jul./Aug. 1994, 17-18. Southeastern Section, Orlando, FL. CALL FOR PAPERS: There will be 20-rninute p. 677) INFORMATION: W.S. Drady, AMS, P.O. Box sessions for contributed papers. Abstracts 6887, Providence, RI 02940; e-mail: meet@ not exceeding 500 words should be re­ * 6-8. Geometric Mechanics, Dynamical Sys­ math. ams. org. ceived no later than October 22, 1994. tems and Control Theory, Fayetteville, INFORMATION: M. Mohseni-Moghadam, Arkansas 19-22. Colloquium Carolus Magnus on Dept. of Math., Shahid Bahonar Univ. PRINCIPAL SPEAKER: J. E. Marsden, Univ. Arithmetic and Geometry (Celebrating 1200 of Kerman, Kerman, Iran; phone and of California, Berkeley. Years of Science in Central Europe), Aachen, fax: +98-341-263244; e-mail: aimc26@ OTHER INVITED SPEAKERS: M. Alber, A. Germany. (May/June 1994, p. 514) irearn. bitnet. Bloch, G. Haller, V. Jurdjevic, P. S. Krish­ 20-21. DIMACS Workshop on Global Min­ naprasad, R. Montgomery, R. Murray, T. 29-31. Environmental Modelling, Lancaster imization of Nonconvex Energy Functions: * Ratiu, J. Scheurle, M. Silber, G. Walsh, and Univ., UK. Molecular Conformation and Protein Fold­ S. Wiggins. ing, DIMACS (Center for Discrete Mathe­ INFORMATION: P. Irving, Conference Offi­ CALL FOR PAPERS: Contributed papers matics and Theoretical Computer Science at cer, The Institute of Mathematics and its should be submitted before February 15, Rutgers Univ.) (Jul./Aug. 1994, p. 676) Applications, 16 Nelson St., Southend-on­ 1995. * 20-24. 3rd International Conference and Sea, Essex, SS 1 lEF, UK. FINANCIAL ASSISTANCE: It is expected that

SEPTEMBER 1994, VOLUME 41, NUMBER 7 845 ...... -._·· ...... - ...... -... -.... -...... ------··························-·-···-··-·-·····-···········-·-···················-·························-···························································-·-·····-··· Meetings and Conferences

funds will be available to enable recent of Southern California, Los Angeles, CA H. L. Montgomery (Univ. of Michigan), Ph.D.s and graduate students to participate. 90089-2562; vox: 213-740-4483; fax: 213- R. Murty (McGill Univ.), A M. Odlyzko, INFORMATION: R. E. Miller or P. Tantalo, 740-4449; Internet: ipps95@halcyon. (AT&T Bell Labs), C. Pomerance (Univ. Dept. of Mathematical Sciences, SCEN usc. edu. Send tutorial submissions by of Georgia), and R. C. Vaughan (Imperial 301, Univ. of Arkansas, Fayetteville, Arkan­ October 31, 1994, to A Khokhar. Dept. College). sas 72701; e-mail: rmiller@mathnext. of Computer Sciences, 1398 CS Bldg., ORGANIZERS: H. G. Diamond, B. C. Berndt, uark. edu orptantalo@comp. uark. edu. Purdue Univ., West Lafayette, IN 47907- and A. J. Hildebrand (Dept. of Math., Univ. 1398; vox: 317-494-6530; fax: 317-494- of lllinois, Urbana). 10-12. International Conference on Typed 0739; Internet: ashfaq@cs. purdue. edu. CALL FOR CONTRIBUTED PAPERS: Persons Lambda Calculi and Applications (TLCA), Send industrial-commercial submissions wishing to give a 15-minute contributed Edinburgh, Scotland. (May/June 1994, p. 514) by October 31, 1994, to J. K. Antonio, talk should submit an abstract (of about ten * 10-12. The Application of Statistical Meth­ School of Electrical Engineering, 1285 lines) by March 1, 1995. ods to Quality Improvement, Cirencester, Electrical Engineering Bldg .. Purdue Univ., FINANCIAL SUPPORT: Partial support will UK. West Lafayette, IN 47907-1285; vox: 317- be available for advanced graduate students 494-6416; fax: 317-494-6440; Internet: and recent Ph.D.s attending the conference. INFORMATION: P. Irving, Conference Offi­ [email protected]. INFORMATION: H. Diamond, UIUC Math. cer, The Institute of Mathematics and its FURTHER INFORMATION: For further in­ Dept., 1409 W. Green St., Urbana, IL Applications, 16 Nelson St., Southend-on­ formation or to submit a research manu­ 61801; fax: 217-333-9576: electronic mail: Sea, Essex, SS 1 lEF, UK. script, contact the program chair, J. Ja'Ja', [email protected]. 10-14. IMA Workshop on Singularities and IPPS '95, Institute for Advanced Computer Studies, Univ. of Maryland, College Park. 16-20. Seventh International Conference Oscillations. Institute for Mathematics and its on Random Structures and Algorithms, Applications, University of Minnesota, Minne­ MD 20742; fax: 301-314-9658: Internet: [email protected]. Emory University, Atlanta, GA. (May/June apolis, MN. (Mar. 1994, p. 252) 1994,p.515) Spring 1995. Workshop on Groups and 27-29. Third SIAM Conference on Con­ 21-24. Third SIAM Conference on Dynam­ Three-Manifolds. Centre de Recherches Mathe­ trol and Its Applications, St. Louis, MO. ical Systems. Snowbird, UT. (Jul./Aug. 1994, matiques, Universite de Montreal. (Jan. 1994, (Jul./Aug. 1994, p. 677) p. 677) p. 59) 22-26. IMA Workshop on Quasiclassical Spring-Summer 1995. Workshop on Gauge Methods, Institute for Mathematics and its Theory and Applications to Low-dimen­ May 1995 Applications, University of Minnesota, Minne­ sional Topology, Centre de Recherches Mathe­ apolis, MN. (Mar. 1994, p. 252) matiques, Universite de Montreal. (Jan. 1994, 11-13. First International Conference on 24-27. Second International Conference on p. 59) Nonlinear Problems in Aviation and Aero­ space 1995, Embry-Riddle Aeronautical Uni­ Dynamic Systems and Applications, Atlanta, Spring-Summer 1995. Workshop on Sym­ versity, Daytona Beach, FL. (Sep. 1993, p. 928) GA. (May/June 1994, p. 515) plectic Geometry and Topology, Centre de 14-20. Mathematical Models in Phase Tran­ 25-June 5. Summer School and Interna­ Recherches Mathematiques, Universite de Mont­ sitions. Oberwolfach. Federal Republic of Ger­ tional Conference on Combinatorics, Hefei, real. (Jan. 1994, p. 59) many. (Apr. 1993, p. 416) China. (May/June 1994, p. 515) 23-25. Conference on Applied Statistics in * 16-18. European Convention on Security 28-31. First International Conference on Agriculture, Manhattan. KS. (May/June 1994, and Detection, Brighton, UK. Neural, Parallel & Scientific Computations, p. 515) Atlanta, GA. (May/June 1994, p. 515) 23-26. KdV '95, Amsterdam, The Nether­ INFORMATION: P. Irving, Conference Offi­ cer, The Institute of Mathematics and its 29-June 1. International Conference on lands. (Dec. 1993, p. 1453) Mathematical Modelling, Universiti Brunei Applications, 16 Nelson St., Southend-on­ 24-28. Third International Conference on Sea. Essex, SS11EF, UK. Darussalam, Brunei Darussalam. (Feb. 1994, Mathematical and Numerical Aspects of p. 146) Wave Propagation, Juan-les-Pins, France. 16-18. IMA Tutorial on Quasiclassical Meth­ 29-June 2. Seventh International Confer­ (Jul./Aug. 1994, p. 677) ods, Institute for Mathematics and its Applica­ ence on Formal Power Series and Alge­ * 25-28. 9th International Parallel Processing tions, University of Minnesota, Minneapolis. braic Combinatorics, Marne-la-Vallee, Paris, Symposium. Fess Parker's Red Lion Resort, MN. (Mar. 1994, p. 252) France. (Jul./Aug. 1994, p. 678) Santa Barbara, California. * 16-20. International Conference on Ana­ * 31-June 3. Tenth Biennial Conference of lytic Number Theory, University of Illinois, SPONSORS: IEEE Computer Society Tech­ the Association of Christians in the Math­ Allerton Park, Monticello, IL nical Committee on Parallel Processing, in ematical Sciences, Taylor Univ., Upland, IN. cooperation with ACM SIGARCH; Dept. PROGRAM: This conference, which honors (Jul.!Aug. 1994, p. 678) of Computer Science, Univ. of California at Heini Halberstam on the occasion of his Santa Barbara; and Institute for Advanced upcoming retirement from the University Computer Studies, Univ. of Maryland at of Illinois. will focus on recent progress in June 1995 College Park. analytic number theory and related topics. CALL FOR PARTICIPATION: The Techni­ There will be both invited and contributed Model Oriented Data Analysis, Spetses, cal Committee on Parallel Processing in­ talks. Greece. (May/June 1994. p. 515) vites engineers and scientists to submit PRINCIPAL SPEAKERS: G. Andrews, (Penn *5-7. 3rd International Applied Statistics in proposals for workshop, tutorial, or in­ State Univ.), J. -M. Deshouillers (Univ. of Industry Conference (Continuing Continu­ dustrial track/commercial exhibit presen­ Bordeaux), R. R. Hall. (Univ. of York), R. ous Improvement), Dallas, Texas tations. Send workshop submissions by Heath-Brown (Oxford Univ.), H. Halber­ September 30. 1994. to V. K. Prasanna, stam (Univ. of Illinois), C. Hooley (Univ. KEYNOTE SPEAKERS: M. Kutner, J. Neter, Dept. of BE-Systems, EBB 244, Univ. of Cardiff), H. lwaniec (Rutgers Univ.), and C. Nachtscheim.

846 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

SPECIAL SPEAKERS: G. Box and D. Mont­ Degrees of Freedom", S'Agar6, Barcelona, Univ.), K. Devlin (St. Mary's College of gomery. Spain. California), I. Grattan-Guinness (Middle­ CALL FOR PAPERS: Papers and workshops sex Univ.), T. Hailperin (Lehigh Univ.), OBJECTIVES: The intention is to make a in areas of interest to industry are so­ D. MacHale (University College, Cork), J. survey on the state of the art concerning licited. Statistical methods with applica­ McCarthy (Stanford Univ.), and R. Penrose Hamiltonian systems with three or more tions in software, aerospace, communi­ (Univ. of Oxford). degrees of freedom. The final goal is to set cations, manufacturing, petroleum, health INFORMATION: UCC 150 Office, Univer­ up a good basis to understand systems with care, business, retail, insurance, banking, sity College, Cork, Ireland; tel: +353- 3D as an essential feature. consulting, real estate, and all other indus­ 21-276871; fax: +353-21-276647; e-mail: INFORMATION: Send an empty e-mail to e­ tries are desired. Spatial statistics, econo­ [email protected]. mail: [email protected] or write to metrics, biometrics, reliability, cluster anal­ NATO ASI 3DHAM95, Dept. Matematica ysis, designed experiments, and other statis­ Aplicada i Anhlisi, Uni versitat de Barcelona, tical methods with applications to industrial Gran Via 585, 08071 Barcelona, Spain. July 1995 situations are especially requested. Special Deadline for applications is January 31, consideration will be given to papers from 1995. 3-7. AMAST'95, Fourth International Con­ international presenters. ference on Algebraic Methodology and Soft­ INFORMATION: S. Angell, Conference Pro­ * 20-24. AMCA-95 International Conference ware Technology, Concordia University, Mon­ gram Director, 1995 Statistics Conference, on Advanced Mathematics, Computations treal, Canada. (Jul./Aug. 1994, p. 678) Analytical Consulting Group, Inc., 2183 S. and Applications, Academtown, Novosibirsk, 3-7. The Third International Congress on Cooper Ct., Wichita, KS 67207-5834; tel: Russia. Industrial and Applied Mathematics, CCH 316-777-4425; fax: 316-689-6889 or 316- Congress Centrum, Hamburg, Germany. (Jan. PRoGRAM: The conference, in honor of G. 744-9829; Internet: susan@acginc. com. 1994,p.59) I. Marchuk, is arranged under the slogan 8-9. Mathematics in Mathematics Research 5-8. International Conference on Optimiza­ "On the threshold of the 21st century: The and Education, UniversityofTasmania. (May/ tion: Techniques and Applications (ICOTA main results and a look into the future". The June 1994, p. 516) '95), Chengdu University of Science and Tech­ scientific program includes plenary invited nology, Chengdu, China. (May/June 1994, lectures, workshops on different science 10-12. Conference on Linear Algebra and p. 515) areas, and poster communications. In par­ its Applications, University of Manchester, allel with sessions will be presentations of England. (Jan. 1994, p. 59) 6-10. Symposium on Inertial Manifolds, software on numerical analysis and appli­ 10-14. 7th Biennial Conference of the Approximate Inertial Manifolds, and Re­ cations. There will also be a roundtable Computational Mathematics Group at Mel­ lated Numerical Algorithms, Xi' an, China. meeting with representatives of industrial bourne (CTAC 95), Melbourne, Australia. (Jul./Aug. 1994, p. 678) circles. (May/June 1994, p. 516) 7-8. IMA Tutorial on Multiparticle Quan­ CALL FOR PAPERS: Abstracts of no more * 17-19. BEM 17-17th International Confer­ tum Scattering with Applications to Nuclear, than 300 words should be submitted to ence on Boundary Element Methods, Madi­ Atomic, and Molecular Physics, Institute for the conference secretariat no later than son, Wisconsin. Mathematics and its Applications, University September 30, 1994, by mail, fax or e­ of Minnesota, Minneapolis, MN. (Apr. 1994, mail (in a lt\l.EX file). Indicate full name, PuRPOSE: The purpose of this conference is p.385) organization, address, phone, fax, and e­ to foster the interchange of ideas at every mail numbers. level on the use of boundary element tech­ 11-14. Second IMACS International Sym­ niques, with a particular emphasis on their posium on Iterative Methods in Linear Alge­ INFORMATION: Conference secretariat, T. Vishnevskaya, Computing Center SD RAS, practical application. The conference will bra, Blagoevgrad, Bulgaria. (Jul./Aug. 1994, also deal with papers of a more theoreti­ p. 678) 6 Lavrentiev Ave., Novosibirsk, 630090, Russia; tel: (3832)-35-27-56; fax: (3832)- cal character, state-of-the-art reviews, and * 12-16. Brazil-USA Conference on Multi­ 32-42-59; e-mail: tanya@comcen. nsk. advanced mathematical and computational dimensional Complex Analysis and Partial su. aspects. Differential Equations, Sao Carlos, SP, Brazil. CALL FOR PAPERS: Submit abstracts by * 27-29. Moving Boundaries 95 (Computa­ October 14, 1994. PROGRAM: Dedicated to the 65th birthday of tional Modelling of Free and Moving Bound­ INFORMATION: L. Ouellette, Computational Francois Treves, the conference will focus ary Problems), Bled, Slovenia. Mechanics, Inc., 25 Bridge St., Billerica, on recent results and future perspectives MA 01821; tel: 508-667-5841; fax: 508- on the theory of CR and complex mani­ INFORMATION: Conference Secretariat, Wes­ 667-7582; e-mail: cmina@netcom. com. folds, hyperfunctions, and overdetermined sex Institute of Technology, Ashurst Lodge, systems of differential equations. Ashurst, Southampton, S040 7AA, UK.; 17-21. International Conference on the INFORMATION: P. D. Cordaro, IME-USP, tel: (44) (703) 293223; fax: (44) (703) Mathematics ofProgram Construction, Klos­ C. Postal 20570, 01452-990, S. Paulo, SP, 282753; e-mail: CMI@ib. rl. ac. uk. ter Irsee, Germany. (Jul./Aug. 1994, p. 679) Brazil; e-mail: mcapdes@ime. usp. br. * 28-30. Conference on the Legacy of George 12-16. IMA Workshop on Multiparticle Boole, University College, Cork, Ireland. August 1995 Quantum Scattering with Applications to PROGRAM: In conjunction with the 150th Nuclear, Atomic, and Molecular Physics, anniversary of its founding, University Col­ * 1-5. 16th RolfNevanlinna Colloquium, Uni- Institute for Mathematics and its Applications, lege, Cork, will hold a conference honoring versity of Joensuu, Joensuu, Finland. University of Minnesota, Minneapolis, MN. George Hoole, who was its first professor PROGRAM: Plenary lectures, invited lec­ (Apr. 1994, p. 385) of mathematics. tures, and poster sessions. * 19-30. NATO Advanced Study Institute on INVITED SPEAKERS: G. K. Batchelor (Univ. PLENARY SPEAKERS: L. Carleson, A. Ere­ "Hamiltonian Systems with Three or More of Cambridge), R. L. Devaney (Boston menko, W. K. Hayman, T. Iwaniec, T.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 847 ...... _------_ .. Meetings and Conferences

Jorgensen, A. Kupiainen, 1. Maly, P. Pansu. CALL FOR PAPERS: Abstracts for contributed H. M. Reimann, and K. Saito. papers should be received by January 1, CALL FOR PAPERS: Titles and abstracts of 1995. The following new announcements will not posters should be received by April 30, INFORMATION: Secretary S. Zlatev. Mathe­ be repeated until the criteria in the last 1995. matical Faculty of the Plovdiv Univ., Tsar paragraph in the box at the beginning ofthis REGISTRATION FEE: The conference fee Assen Str. 24, Plovdiv 4000, Bulgaria. section are met. will be $100 (free ofbank transfer charges) until June 30, 1995, and $120 thereafter. 28-September 1. A.C. Aiken Centenary Conference, incorporating the 3rd Pacific INFORMATION: 16. Rolf Nevanlinna Collo­ October 1995 quium, c/o Dept. of Math., University of Statistical Congress and the annual meeting Joensuu, P.O. Box 111, FIN-80101 Joen­ of the New Zealand Statistical Association, 7-8. 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CRM MONOGRAPH SERIES, Volumes 4 & 5 Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval David Ruelle The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0, 1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of ((z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M, J, g).

1991 Mathematics Subject Classification: 58 ISBN 0-8218-6991-4, 62 pages (hardcover), Aplil 1994 Individual member $23, List plice $38, Institutional member $30 To order, please specify CRMM/4NA

Differentiation of Real Functions Andrew Bruckner

Bruckner addresses in detail the problems that arise when dealing with the class D.' of derivatives. Bruckner studies generalized derivatives and indicates "geometric" conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail. The book unifies many important results from the literature as well as some results not previously published.

1991 Mathematics Subject Classification: 26 ISBN 0-8218-6990-6, 195 pages (hardcover), Ap1il 1994 Individual member $32, List p1ice $53, Institutional member $42 To order, please specify CRMM/SNA

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Spectral Operator Theory and Related Topics Ten Lectures on the V. A. Marchenko, Editor Interface Between Analytic Volume 19 Number Theory and This collection contains papers Harmonic Analysis by participants in the Seminar on Mathematical Physics in Kharkov, Hugh L. Montgomery Ukraine. The papers mainly focus on Volume 84 nontraditional problems of spectral theory, This book contains lectures presented such as new types of inverse problems by Hugh L. Montgomery at the NSF­ for one-dimensional differential operators, CBMS Regional Conference held at new classes of solutions to nonlinear differential equations obtained Kansas State Universityin May 1990. using spectral methods, distribution of eigenvalues of large random The book focuses on important topics in matrices, and related problems of statistical physics of disordered analytic number theory that involve ideas from harmonic analysis. One systems. In addition, the papers explore the spectral aspects of valuable aspect of the book is that it collects material that was either homogenization and of properties of ergodic dynamical systems. All the unpublished or that had appeared only in the research literature. This papers contain original results published for the first time. book would be an excellent resource for harmonic analysts interested Contents in moving into research in analytic number theory. In addition, it is D. S. Lundina and V. A. Marchenko, Limits of the rejlectionless Dirac suitable as a textbook in an advanced graduate topics course in number operator; M. Novitski!, Quasianalytic classes and isospectral Hill's operators; theory. V. A. Tkachenko, Discriminants and generic spectra of nonselfadjoint Hill's Contents operators; V. Ya. Golodets, A. I. Danilenko, and S. I. Bezuglyl, On cocycles Uniform distribution; van der Cmput sets; Exponential sums I: The methods of ergodic dynamical systems and automorphisms compatible with them; ofWeyl and van der Cmput; Exponential sums II: Vinogradov's method; An A. M. Khorunzhy and L. A. Pastor, On the eigenvalue distribution of introduction to Turan's method; Irregularities of distribution; Mean and large the defmmed Wigner ensemble of random matrices; E. Ya. Khruslov and values of Dirichlet polynomials; Distribution of reduced residue classes in short V. P. Kotlyarov, Soliton asymptotics ofnondecreasing solutions of nonlinear intervals; Zeros of Lfunctions; Small polynomials with integral coefficients; completely integrable evolution equations; I. E. Egorova, The Cauchy problem Some unsolved problems; Index. for the KdV equation with almost periodic initial data whose spectrum is 1991 Mathematics Subject Classification: ll-02, 42-02; 11K06, IIK38, IIK70, nowhere dense; D. G. Shepel1sky, The inverse problem of reconstruction of IIL03, IIL07, IIL15, IIM20, IIM26, IIN05, IIN25, IIN30, 11N69, IIR06, the medium's conductivity in a class of discontinuous and increasing functions; 41A30, 42A05, 42AIO E. Khruslov and L. Pankratov, Homogenization of boundary problems for the ISBN 0-8218-0737-4, LC 94-26864, ISSN 0160-7642 Ginzburg-Landau equation in weakly connected domains; B. Khoruzhenko, 220 pages (softcover), September 1994 L. Pastor, and M. Shcherbiua, The infinite component limit of the random List price $44, All individuals $26, anisotropy n-vector model. To order, please specify CBMS/84N 1991 Mathematics Subject Classification: 34L40; 34B20, 34B24, 34B30, 34005, 34Ll5, 34L20, 35B27, 35B40, 35C20 ISBN 0-8218-4122-X, LC 91-640741, ISSN 1051-8037 286 pages (hardcover), September 1994 . Individual member $60, List price $100, Institutional member $80 To order, please specify ADVSOV/19N

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850 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Publications Offered by the AMS ------··-·······"""""""""""""""""""" ... """""

in arithmetic geometry. The volume also contains material on the CONTEMPORARY MATHEMATICS Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including p-adic £-functions and p-adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and computation of torsion groups Geometry of the Spectrum of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.-P. Serre in 1973, concerning Serre's Robert Brooks, Carolyn conjecture on Galois representations. With contributions by some of the Gordon, and Peter Perry, leading experts in the field, this book provides a look at the state of the Geometry of the Spectrum Editors art in arithmetic geometry. Volume 173 Contents M. D. Fried, D. Haran, and H. Vi:ilklein, Real Hilbertianity and the field of Spectral geometry runs through much totally real numbers; D. Harbater, Galois groups with prescribed ramification; of contemporary mathematics, drawing T. Metsiinkylii, Note on the zeros of p-adic L-functions; B. Perrin-Riou, La on and stimulating developments in fonction L p-adique de Kubota-Leopoldt; A. Plater, Supersingular p-adic height such diverse areas as Lie algebras, graph pairings on elliptic curves; K. A. Ribet, Fields of definition of Abelian varieties theory, group representation theory, and with real multiplication; A. Sofer, p-adic interpolation of half-integral weight Riemannian geometry. The aim is to relate modular forms; G. Stevens, A-adic modular forms of half-integral weight and a the spectrum of the Laplace operator or its graph-theoretic analogue, A-adic Shintani lifting; J. Tate, The non-existence of certain Galois extensions of the adjacency matrix, to underlying geometric and topological data. Q unramified outside 2; D. S. Thakur, Iwasawa the01y and cyclotomic function This volume brings together papers presented at the AMS-IMS-SIAM fields; D. L. Ulmer, Slopes of modular forms; F. R. Villegas, On the Taylor Joint Summer Research Conference on Spectral Geometry, held in July coefficients of theta functions ofCM elliptic curves; H. G. Zimmer, Torsion 1993 at the University of Washington in Seattle. With contributions groups of elliptic curves over cubic and certain biquadratic number fields. from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry. 1991 Mathematics Subject Classification: 11-06; 11F33, 11R23, 11R42, 12Fl2 ISBN 0-8218-5174-8, LC 94-22801, ISSN 0271-4132 Contents 220 pages (softcover), September 1994 E. Y. Amiran, An inverse problem and spectral invariants for hi/lards; J. Angel, Individual member $29, List plice $48, Institutional member $38 S. Poulos, A. Terras, C. Trimble, and E. Velasquez, Spherical functions To order, please specify CONM/174N and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces; R. Brooks, LP spectral geometry; R. Brooks and P. Glezen, An LP spectral bootstrap theorem; X. Dai and G. Wei, Finite FIELDS INSTITUTE COMMUNICATIONS part of spectrum and isospectrality; J. Dodziuk, Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator; K. Fujiwara, Convergence of the eigenvalues of Laplacians in a class offinite graphs; C. S. Gordon, Isospectral closed Riemannian manifolds which are not locally isometric, Part II; R. Gornet, The length spectrum and representation Hamiltonian and Gradient the01y on two and three-step nilpotent Lie groups; E. Gutkin, A few remarks Flows, Algorithms, and on the billiard ball problem; L. Ji and S. Zelditch, Hyperbolic cusp forms Control and spectral simplicity on compact hyperbolic swfaces; Ya. Kurylev, Inverse boundmy problems on Riemannian manifolds; L. Malozemov, Spectral theory Hamiltonian and Gradient Anthony Bloch, Editor of the differential Laplacian on the modified Koch curve; Y. Mao, Conjugate Flows, Algorithms. and Control Volume3 curved manifolds; H. Pesce, Varietes isospectrales geodesic flows in negatively This volume brings together ideas of eigenvalues for et representations de groupes; Y. N. Petridis, On differences from several areas of mathematics that swfaces; G. Quenell, Combinatorics offree product flat tori and hyperbolic have traditionally been rather disparate. SchrOdinger graphs; T. Sunada, A discrete analogue of periodic magnetic The conference at the Fields Institute operators. which gave rise to these proceedings was 1991 Mathematics Subject Classification: 58025, 35R30; 05C25, 22E27, 53C20 intended to enourage such connections. ISBN 0-8218-5185-3, LC 94-26306, ISSN 0271-4132 One of the key interactions occurs between dynamical systems and 299 pages (softcover), September 1994 algorithms, one example being the by now classic observation that the Individual member $35, List plice $58, Institutional member $46 as the time-1 To order, please specify CONM/173N QR algorithm for diagonalizing matrices may be viewed map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated Arithmetic Geometry with such programming problems have proved valuable in the analysis of the corresponding discrete problems. More recently, other smooth Nancy Childress and John flows have been introduced which carry out discrete computations W. Jones, Editors (such as sorting sets of numbers) and which solve certain least squares problems. Another interesting facet of the flows described here is that Arithmetic Geometry Volume 174 they often have a dual Hamiltonian and gradient structure, both of NancyChlldrlln from a research JollfiW,Jonos This book resulted which tum out to be useful in analyzing and designing algorithms for ""'" conference in arithmetic geometry held at solving optimization problems. This volume explores many of these Arizona State University in March 1993. interactions, as well as related work in optimal control and partial The papers describe important recent differential equations. advances in arithmetic geometry. Several (continued) articles deal with p-adic modular forms of half-integral weight and their roles

SEPTEMBER 1994, VOLUME 41, NUMBER 7 851 ...... ______...... New Publications Offered by the AMS

Contents V. Isakov, On uniqueness in the inverse conductivity problem with one M. S. Alber and J, E. Marsden. Resonant geometric phases for soliton boundary measurement; A. I. Katsevich and A. G. Ramm, A method for equations; G. S. Ammar and W. B. Gragg, Schur flows for orthogonal finding discontinuities offimctions from the tomographic data; A. Kuruc, Hessenberg matrices; A.M. Bloch, P. E. Crouch, and T. S. Ratiu, Probability measure estimation using "weak" loss functions in positron emission Sub-Riemannian optimal control problems; 0. I. Bogoyavlenskij, Systems of tomography; S. Lissianoi, On stability estimates in the exterior problem for hydrodynamic type, connected with the toda lattice, and the volterra model; the radon transform; S. J, Lvin, Data correction and restoration in emission R. Brockett, The double bracket equation as the solution of a rariational tomography; R. Mukhometov, On problems of integral geomet1y in the problem; J.-P. Brunet, Integration and risuali=ation of matrix orbits on the non-convex domains; F. Natterer, Recent developments in X-ray tomography; connection machine; M. T. Chu, A list of matrix flows with applications; V. P. Palamodov, Some mathematical aspects of 3D X-ray tomography; L. Faybusovich, The Gibbs mriational principle. gradient flows, and S. K. Patch, A note on consistency conditions in three dimensional diffuse interior-point methods; S. T. Smith, Optimi=ation techniques on Riemannian tomography; E. T. Quinto, Radon tramforms on curves in the plane; G. manij(Jlds; B. Sturmfels, On the number of real roots of a sparse polynomial Uhlmann, Inverse boundary value problems for first order perturbations of the system; W. S. Wong. Gradient flows for local minima of combinatorial Laplacian; A. I. Zaslavsky, Multidimensional analogue of the Erdelyi lemma optimi=ation problems. and the radon transform; J, Zhou, On the Willmore deficit of convex swfaces. 1991 Mathematics Subject Classification: 34A34. 70H05. 93CIO, 65F15, 90C05 1991 Mathematics Subject Classification: 92C55, 35R30, 44A12 ISBN 0-8218-0255-0, LC 94-28546, ISSN 1069-5265 ISBN 0-8218-0337-9, LC 94-28800, ISSN 0075-8485 !55 pages (hardcover), September 1994 287 pages (softcover), September 1994 lndhidual member $43, List price $71, Institutional member $57 Individual member $31, List price $51, Institutional member $41 To order, please specify FIC/3N To order, please specify LAM/30N

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A'P·r;l:li:'o Tomography, Impedance ME~t9IRS The Full Set of Unitarizable MATHEMATICS --\m< 0; The unitarizable highest weight modules of of mathematics can be used to solve dramatically different problems in D(m, n); Borderline cases; F(4); G(3); D(2, 1, a); Further developments; pure and applied mathematics. Radon transforms can be used to model Bibliography. impedance imaging problems. These proceedings include exciting 1991 Mathematics Subject Classification: 17 A 70, 46C05; 17B35, 17B 10, 22E47, results in all three fields represented at the conference. 17A60. 81R05 Contents ISBN 0-8218-2593-3, LC 94-16907, ISSN 0065-9266 116 pages (softcover). September 1994 C. A. Berenstein and E. C. Tarabusi, An inversion formula for the horocyclic Individual member $20. List price $33, Institutional member $26 Radon transform on the real hyperbolic space; W. K. Cheung and A. Markoe, To order, please specify MEMO/lll/532N Image reconstruction and dense subspaces in the range of the radon transform; A. Correa, R. Cruz, and P. M. Salzberg, On a spatial limited angle model for X-ray computeri:ed tomography; G. F. Crosta, The backpropagation method in inverse acoustics; L. Ehrenpreis, Some nonlinear aspects of the radon transform; S. Gindikin, J, Reeds, and L. Shepp, Spherical tomography and spherical integral geometly; E. L. Grinberg, That kappa operator: Gelfand-Graev-Shapiro inversion and radon transforms on isotropic planes;

852 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··························-···-······-···········-··········-····-···-···-···························-·········-···················-·-···········-···· ················-·······-··-··-·····------New Publications Offered by the AMS

~ Anticipative Girsanov MEMOIRS Christoffel Functions and MEJY!.9IRS ofth "mcr!cun \!~tl" m~th "t Soo l~t} Transformations and \.o.t

MEJY!.9IRS Molecular Propagation MEJY!.OIRS Orthogonal Decomposi­ \merkm ~fattH m >lie ll S<>cl,t~ --'"'~r!c m Mulhcmutlcul ~ ch!y -- through Electron Energy tions and Functional Limit ~ ' ~ " ( " Level Crossings Theorems for Random Molecular Propagation through Electron Energy George A. Hagedorn Orthogonal Decompostt1ons and Graph Statistics Level Crossings Functional Limit Theorems Volume Ill, Number 536 for Random Graph Statistics Svante Janson This largely self-contained book Volume 111, Number 534 provides a thorough discussion of the This book develops a method to obtain mathematics of molecular dynamics and limit theorems for various functionals fills a gap in the theoretical knowledge of random graphs. The method is based of the subject. Most knowledge of on a certain orthogonal decomposition. molecular propagation is derived from the Janson's results include limit theorems time-dependent Born-Oppenheimer approximation. This approximation for the two standard random graph models, Gn,p and Gn,m• as well breaks down at electron energy level crossings, which are prevalent in as functional limit theorems for the evolution of a random graph and molecular systems. Hagedorn classifies generic, minimal multiplicity results on the maximum of a function during the evolution. Janson level crossings and derives a normal form for the electron Hamiltonian obtains both normal and nonnormallimits, and the method provides an near each type of crossing. He then extends the time-dependent explanation for the appearance of nonnormallimits. Applications to Born-Oppenheimer approximation to accommodate the propagation of sub graph counts and to vertex degrees are presented as examples. nuclei through each type of electron energy level crossing. Contents Contents Foundations; Limit theorems; Examples; References. Introduction; Generic minimal multiplicity quantum eigenvalue crossings; 1991 Mathematics Subject Classification: 05C80; 60F05 Technical preliminaries; Born-Oppenheimer propagation away from crossings; ISBN 0-8218-2595-X, LC 94-17088, ISSN 0065-9266 Codimension1 crossings; Codimension 2 crossings; Codimension 3 crossings; 78 pages (softcover), September 1994 Codimension 5 crossings; References. Individual member $19, List price $31, Institutional member $25 1991 Mathematics Subject Classification: 81 V55; 81 Q05, 92E20, 35B25 To order, please specify MEM0/111/534N ISBN 0-8218-2605-0, LC 94-17086, ISSN 0065-9266 130 pages (softcover), September 1994 Individual member $20, List price $34, Institutional member $27 To order, please specify MEMO/lll/536N

SEPTEMBER 1994, VOLUME 41, NUMBER 7 853 ------·---"-'""'"""""''"'""-'"''"""-·-·-····""'"''"''"''-'"'-·-···············"-"-·-·-·······--·-····"'""""'"'''""-"'"''''"''"''"''-'' New Publications Offered by the AMS

in various research papers. The first half of the book is an expository TRANSLATIONS OF MATHEMATICAL account of the field, explaining the main technical aspects. McDuff MONOGRAPHS and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe Identities of Algebras the Givental-Kim calculation of the quantum cohomology of flag and their Representations manifolds, leading to quantum Chern classes and Witten's calculation Yu. P. Razmyslov for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and Volume 138 curve counting formulas are also discussed. The book closes with an During the past forty years, a new outline of connections to Floer theory. trend in the theory of associative algebras, Contents Lie algebras, and their representations Introduction; Local behaviour; Moduli spaces and transversality; Compactness; has formed under the influence of Compactification of moduli spaces; Evaluation maps and transversality; mathematical logic and universal algebra, Gromov-Witten invariants; Quantum cohomology; Novikov rings and Calabi-Yau namely, the theory of varieties and manifolds; Floer homology; Gluing; Elliptic regularity; Bibliography; Indexes. identities of associative algebras, Lie 1991 Mathematics Subject Classification: 53C15; 58F05, 57R57 algebras, and their representations. The last twenty years have seen the ISBN 0-8218-0332-8, LC 94-25414, ISSN 1047-3998 creation of the method of 2-words and a-functions, which allowed a 207 pages (softcover), August 1994 number of problems in the theory of groups, rings, Lie algebras, and Individual member $25, List price $42, Institutional member $34 their representations to be solved in a unified way. The possibilities of To order, please specify ULECT/6N this method are far from exhausted. This book sums up the applications of the method of 2-words and a-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the OTHER BOOKS AVAILABLE THROUGH AMS theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians. Contents LATE)(: A Document Preliminary results; Characters and a-functions on 2-words and varieties of representations of Lie algebras distinguished by them; a-functions related to Preparation System, the killing form and to irreducible representations of semisimple Lie algebras. Second Edition Central polynomials of irreducible representations of reductive Lie algebras; Leslie Lamport a-functions related to full matrix algebras. Trace identities and central polynomials offull matrix algebras Mn and matrix superalgebras Mn,k; The Fast becoming the lingua franca of a-function related to representations of the simple three-dimensional Lie algebra the scientific world, U1J3X is a software g and its applications to varieties of groups and associative algebras; Varieties system for typesetting technical documents generated by Lie algebras of Cartan type; Algebraic supplements. on almost any kind of computer. U1J3X, 1991 Mathematics Subject Classification: 17B99, 16RIO; 17B30 a special version of the revolutionary ISBN 0-8218-4608-6, LC 94-20766, ISSN 0065-9282 technical typesetting system 1J3X, marries 318 pages (hardcover), September 1994 the power of 1J3X with ease of use. The Individual member $72, List price $120, Institutional member $96 release of U1EX 2,, the new standard version, brings a wider variety To order, please specify MMON0/138N of features to the user. This manual, written by the original architect of U1EX is the definitive user's guide to lb'IEX 2,. New users will benefit from the clear, concise, and practical explanations that earned UNIVERSITY LECTURE SERIES the original U1EX documentation worldwide praise. Experienced users will want to learn about the new features and capabilities ofU'IEX 2,. An appendix is included that describes the changes in the new version. This book is published by Addison-Wesley. ------Contents 1 Jill\ ( l ~''\ J-holomorphic Curves and LECTURE Getting acquainted; Getting started; Carrying on; Moving information around; SclH Quantum Cohomology ------Other document classes; Designing it yourself; Pictures and colors; Errors; Dusa McDuff and Dietmar Using Makelndex; The bibliography database; Reference manual; What's new; J'-holomorphlc Curves Using plain T[$. commands; Bibliography; Index. and Quantum Cohomology Salamon 1991 Mathematics Subject Classification: 00 Volume 6 ISBN 0-201-52983-1, LC 93-39691 J -holomorphic curves revolutionized 235 pages (softcover), August 1994 the study of symplectic geometry when Member $32, List price $35 Gromov first introduced them in 1985. To order, please specify LATEXN 'J'brQJJgh quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered

854 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... _llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll-·-···-··-···-··-··-·-·····-·-··-·-··-··-·-···-·-·-·-·-······-··-··-··-···-··-·········-·-··-········-··-··-··- ... ··-··-······-···-··············-···-···-··········-···-·-········-···-

Publications of Continuing Interest Following are some of our more popular books and videotapes as well as some with similar topics to those appearing in the New Publications section of this issue.

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SEPTEMBER 1994, VOLUME 41, NUMBER 7 855 Officers and Committee Members

Numbers to the left of headings are used as points of reference in a index to Associate AMS committees which follows this listing. Primary and secondary headings Secretaries* Robert J. Daverrnan 1996 are: Andy Roy Magid 1995 Lesley M. Sibner 1996 Officers Lance W. Small 1995 1.1 Liaison Committee Treasurer Franklin P. Peterson 1996 2 Council Associate 2.1 Executive Committee of the Council Treasurer B. A. Taylor 1996 3 Board of Trustees 4 Committees 4.1 Committees of the Council 2.0.2. Representatives of Committees 4.2 Editorial Committees American Journal of 4.3 Committees of the Board of Trustees Mathematics Henri Gillet 1994 4.4 Internal Organization of the AMS Bulletin RichardS. Palais 1995 4.5 Committees of the Executive Committee and Board of Trustees Colloquium Luis A. Caffarelli 1994 4.6 Program and Meetings Executive Committee Joan S. Birman 1995 4. 7 Status of the Profession Executive Committee John M. Franks 1996 4.8 Prizes and Awards Executive Committee Arthur M. Jaffe 1994 4.9 Institutes and Symposia Journal of the AMS H. Blaine Lawson, Jr. 1994 4.10 Joint Committees Mathematical Reviews Philip J. Hanlon 1995 5 Representatives Mathematical Surveys and 6 Index Monographs Marc A. Rieffe1 1994 Terms of members expire on January 31 following the year given unless Mathematics of Computation otherwise specified. Walter Gautschi 1995 Proceedings Irwin Kra 1994 Transactions and Memoirs Peter B. Shalen 1995 1. Officers------2.0.3. Members-at-Large President Ronald L. Graham 1994 President-Elect Cathleen S. Morawetz 1994 Ruth M. Charney 1994 Elliott H. Lieb 1994 Vice-Presidents Linda Keen 1994 Carl C. Cowen, Jr. 1994 Frank Morgan 1996 Ani! Nerode 1995 Rebecca A. Herb 1994 Norberto Salinas 1996 Jean E. Taylor 1996 Svetlana R. Katok 1995 Sylvia M. Wiegand 1996 Secretary Robert M. Fossum 1996 Steven George Krantz 1995 Susan Gayle Williams 1995 Associate Robert K. Lazarsfeld 1996 Robert J. Zimmer 1996 Secretaries Robert J. Daverman 1996 James I. Lepowsky 1995 1994 Andy Roy Magid 1995 Peter W. K. Li 1995 Lesley M. Sibner 1996 Lance W. Small 1995 Treasurer Franklin P. Peterson 1996 Associate Treasurer B. A. Taylor 1996 2.1. Executive Committee of the Council Joan S. Birman 1995 1.1. Liaison Committee Robe1t M. Fossum ex officio John M. Franks All members of this committee serve ex officio. 1996 Chair Ronald L. Graham ex officio Robert M. Fossum Arthur M. Jaffe 1994 Chair Ronald L. Graham Cathleen S. Morawetz ex officio Franklin P. Peterson Marc A. Rieffe1 1997

2. Council------3. Board of Trustees------2.0.1. Officers of the AMS Secretary Roy L. Adler 1997 Ronald L. Graham ex officio President Ronald L. Graham 1994 Maria M. Klawe 1996 President-Elect Cathleen S. Morawetz 1994 D. J. Lewis 1998 Vice-Presidents Linda Keen 1994 Chair M. Susan Montgomery 1995 Ani! Nerode 1995 Jean E. Taylor 1996 * Only one Associate Secretary at a time is a voting member of the Council, Secretary Robert M. Fossum 1996 namely the cognizant Associate Secretary for the scientific sessions.

856 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Franklin P. Peterson ex officio Associate Editors for Research - Expository Papers John C. Polking 1994 B. A. Taylor ex officio John C. Baez 1995 Jerry L. Kazdan 1995 David Donoho 1995 Kenneth A. Ribet 1995 David Eisenbud 1995 1995 4. Committees 4.2.4. Collected Works Richard A. Askey 1995 4.1. Committees of the Council R. Keith Dennis 1995 I. G. Macdonald 1995 Standing Committees Barry Mazur 1995

4.1.1. Editorial Boards 4.2.5. Colloquium Bryan J. Birch 1995 William Browder 1995 Chair Fan R. K. Chung 1995 Chair Luis A. Caffarelli 1994 Martin Golubitsky 1996 1996 Carolyn S. Gordon 1996 Bhama Srinivasan 1994 4.2.6. Contemporary Mathematics Robert J. Zimmer 1994 Chair Craig Huneke 1995 4.1.2. Nominating Committee Clark Robinson 1994 Terms begin on January I Linda Preiss Rothschild 1995 J. T. Stafford 1995 Daniel M. Bums, Jr. 1994 Peter M. Winkler 1994 Chair Jerome A. Goldstein 1995 Morris W. Hirsch 1996 Vaughan F. R. Jones 1995 4.2.7. Graduate Studies in Mathematics Joseph Lipman 1994 James E. Humphreys 1995 Hugh L. Montgomery 1996 Robion C. Kirby 1995 Linda Preiss Rothschild 1996 Chair Lance W. Small 1995 Nancy K. Stanton 1995 Carol S. Wood 1994 4.2.8. Journal of the AMS Special Committee William Fulton 1995 Benedict H. Gross 1996 Chair H. Blaine Lawson, Jr. 1994 4.1.3. Meetings of the Council Andrew M. Odlyzko 1994 Joan S. Birman Elias M. Stein 1995 Chair Robert M. Fossum Franklin P. Peterson Associate Editors Steven H. Weintraub James G. Arthur 1995 Hugh L. Montgomery 1996 4.2. Editorial Committees Luis A. Caffarelli 1995 Marina Ratner 1994 Persi W. Diaconis 1994 Richard Schoen 1994 4.2.1. Abstracts Editorial Committee Michael H. Freedman 1996 Richard P. Stanley 1994 Joe Harris 1996 W. Hugh Woodin 1996 All members of this committee serve ex officio. DusaMcDuff 1994 1994 Robert J. Daverman Chair Robert M. Fossum 4.2.9. Mathematical Reviews Andy Roy Magid Lesley M. Sibner AMS staff contact: Jane E. Kister. Lance W. Small Wendell H. Fleming 1994 4.2.2. American Journal of Mathematics, Chair Philip J. Hanlon 1995 Society's Representatives Jean-Louis Loday 1996 John L. Selfridge 1994 Chair Henri Gillet 1994 Sergio Klainerman 1996 Mathematical Surveys and Monographs 4.2.3. Bulletin (New Series) 4.2.10. Georgia Benkart 1996 Haynes R. Miller 1996 Robert E. Greene 1995 Chair RichardS. Palais 1995 David W. McLaughlin 1994 Murray H. Protter 1994 Chair Marc A. Rieffel 1994 Associate Editors for Research Announcements Gergory L. Cherlin 1995 Zoltan Furedi 1993 4.2.11. Mathematics of Computation William G. Dwyer 1993 Harry Kesten 1993 Chair Walter Gautschi 1995 Charles L. Epstein 1993 Robert Lazarsfeld 1995 Andrew M. Odlyzko 1994 DanielS. Freed 1993 PaulS. Muhly 1993 Frank W. J. Olver 1996 Michael D. Fried 1993 Jeffrey Rauch 1995 Lars B. Wahlbin 1995

SEPTEMBER 1994, VOLUME 41, NUMBER 7 857 ,_,, ,_,_, _.. ,...... _...... _, .... ,, .. ,_,.. ,_ ...... -...... _._,_, ...... ______...... _...... Officers and Committee Members

Associate Editors 4.2.15. Transactions and Memoirs Robert L. Bryant 1995 James Bramble 1994 Rene Schoof 1995 Sun-Yung Alice Chang 1994 Susanne C. Brenner 1995 Ridgway Scott 1995 Gregory L. Cherlin 1996 E. W. Cheney 1994 Daniel Shanks 1996 RichardT. DmTett 1994 James W. Demmel 1994 Chi-Wang Shu 1995 Philip J. Hanlon 1995 Eugene Isaacson 1995 Frank Stenger 1995 David Jerison 1994 James N. Lyness 1996 Hans J. Stetter 1994 Wen-Ching Winnie Li 1995 Harald Niederreiter 1996 G. W. Stewart 1995 Mark Mahowald 1996 Jorge J. Nocedal 1996 Nico M. Temme 1995 John J. Mallet-Paret 1995 Syvert P. N¢rsett 1996 Vidar C. Thomee 1994 Daniel Jay Rudolph 1997 John Osborn 1995 Hugh C. Williams 1994 Chair Peter B. Shalen 1995 Stanley J. Osher 1995 John W. Wrench. Jr. 1996 Robert J. Stanton 1997 Carl Pomerance 1994 E. Zelmanov 1997 4.2.12. Notices 1995 Sheldon Axler 1996 4.2.16. Translation from Chinese John S. Bradley Sun-Yung Alice Chang Amassa C. Fauntleroy 1994 S.-Y. Cheng Chair Robert M. Fossum ex officio Chair Tsit-Yuen Lam Susan J .. Friedlander 1996 Tai-Ping Liu Carolyn S. Gordon 1994 Chung-Chun Yang Carl R. Riehm 1996 Ridgway Scott 1994 4.2.17. Translation from Japanese Associate Editor Shoshichi Kobaya~hi Chair Katsumi Nomizu Special Articles Jeffrey C. Lagarias 4.2.13. Proceedings Standing Committees William W. Adams 1996 Dale Alspach 1995 4.2.18. Electronic Products and Services J. Marshall Ash 1996 Nancy Anderson 1994 Albert Baernstein 1995 R. Keith Dennis 1995 Eric Bedford 1995 Chair John M. Franks 1994 Andreas Blass 1996 Maria M. Klawe 1994 Christopher Croke 1995 Frank S. Quinn 1994 Richard T. Durrett 1996 William B. Woolf ex officio Coordinating Clifford J. Earle, Jr. 1996 Eric M. Friedlander 1995 4.2.19. History of Mathematics Theodore W. Gamelin 1994 Bruce Chandler 1995 Coordinating James G. Glimm 1995 Charles W. Curtis 1994 Kenneth R. Goodearl 1996 Paul R. Halmos 1996 Roe Goodman 1995 Chair Guido L. Weiss 1995 Thomas Goodwillie 1995 Dennis A. Hejhal 1995 4.2.20. Reprinted Books Palle E. T. Jorgensen 1996 Eugenio Calabi 1996 Jeffry Kahn 1997 Charles W. Curtis 1995 Coordinating Linda Keen 1997 Chair Oscar S. Rothaus 1994 Chair Irwin Kra 1994 4.2.21. University Lecture Series Coordinating Peter W. K. Li 1994 Wei Y. Lob 1995 Jerry L. Bona 1996 Joseph S. B. Mitchell 1995 Theodore W. Gamelin 1994 Coordinating M. Susan Montgomery 1995 Donald S. Ornstein 1995 J. Rauch 1997 Chair Leonard L. Scott 1996 Mary Rees 1997 4.2.22. What's Happening, Advisory Board for David Sharp 1995 AMS staff contact: Donald G. Babbitt. Lance W. Small 1997 HalL. Smith 1995 Noga Alon Christopher D. Sogge 1997 Randolph E. Bank Ronald M. Solomon 1994 Robert Osserman Ronald J. Stem 1995 Carl Pomerance Franklin Tall 1997 Herbert S. Wilf John Trangenstein 1995 Wolmer V. Vasconcelos 1995 Special Committee James E. West 1995 4.2.14. Proceedings of Symposia in Applied 4.2.23. Member Publications, Committee to Review Mathematics Sheldon Axler Chair Peter S. Constantin 1995 Consultant H. Hope Daly Robert Krasny 1995 John Ewing Laszl6 Lovasz 1995 Robert M. Fossum ex officio

858 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

John M. Franks 4.3.8. Legal Aid Ronald L. Graham ex officio Todd Dupont Judy Green Chair Murray Gerstenhaber William H. Jaco ex officio B. A. Taylor Haynes R. Miller Richard S. Palais 4.3.9. Membership John C. Polking Consultant Samuel M. Rankin ill AMS staff contact: Carol-Ann Blackwood. Carol S. Wood Roy L. Adler ex officio Consultant William B. Woolf Consultant Carol-Ann Blackwood Susan J. Friedlander 1995 D. J. Lewis 1996 4.3. Committees of the Board of Trustees Edith N. Starr 1996 1994 4.3.1. Agenda and Budget All members of this committee serve ex officio. 4.3.10. The Publication Program AMS staff contact: Donald G. Babbitt. Robert M. Fossum Ronald L. Graham Roy L. Adler ex officio Arthur M. Jaffe Robert M. Fossum ex officio M. Susan Montgomery Eric M. F1iedlander 1996 Franklin P. Peterson William H. Jaco ex officio B. A. Taylor Elliott H. Lieb 1994 M. Susan Montgomery ex officio 4.3.2. Appeals Committee on Discounted David Morrison 1996 Subscriptions John C. Polking ex officio AMS staff contact: Carol-Ann Blackwood. B. A. Taylor 1996 1996 Consultant Carol-Ann Blackwood 1996 Consultant Philip J. Hanlon William H. Jaco ex officio 4.3.11. Salaries Chair Morton Lowengrub M. Susan Montgomery All members of this committee serve ex officio. Franklin P. Peterson Maria M. Klawe 4.3.3. Audit M. Susan Montgomery All members of this committee serve ex officio. Franklin P. Peterson AMS staff contact: Gary G. Brownell. B. A. Taylor M. Susan Montgomery 4.3.12. Staff and Services Franklin P. Peterson All members of this committee serve ex officio. 4.3.4. Computer Operations and Facilities, Roy L. Adler Visiting Committee on Franklin P. Peterson AMS staff contact: William B. Woolf. Chair B. A. Taylor Maria M. Klawe ex officio Douglas A. Lind 1996 Special Committees Chair Jill P. Mesirov 1994 Richard S. Palais 1995 4.3.5. Corporate Relations 4.3.13. Copyright Policy Chair Ramesh A. Gangolli Elliott H. Lieb Maria M. Klawe M. Susan Montgomery Oscar S. Rothaus Chair Andrew M. Odlyzko 4.3.6. Endowment and Planned Giving Samuel M. Rankin III AMS staff contact: Timothy J. Goggins. 4.3.14. Institutional Membership Andrew M. Gleason 1996 Consultant Carol-Ann Blackwood Arthur M. Jaffe 1996 Ramesh A. Gangolli Chair W. Ted Martin 1996 Chair Frederick W. Gehring Cathleen S. Morawetz 1996 William A. Veech T. Benny Rushing 1996 ex officio 4.3.7. Investment 4.3.15. Search Committee for Executive Director All members of this committee serve ex officio. Robert M. Fossum Chair Ramesh A. Gangolli M. Susan Montgomery ex officio Ronald L. Graham Chair Franklin P. Peterson ex officio Maria M. Klawe T. Benny Rushing 1994 M. Susan Montgomery B. A. Taylor ex officio Franklin P. Peterson

SEPTEMBER 1994, VOLUME 41, NUMBER 7 859 ...... ______...... Officers and Committee Members

4.3.16. Search Committee for Executive Editor of 4.5.4. Publications Mathematical Reviews AMS staff contact: Donald G. Babbitt. Philip J. Hanlon William H. J aco Sheldon Axler 1994 Franklin P. Peterson Fan R. K. Chung 1994 B. A. Taylor Robert M. Fossum ex officio John M. Franks 1994 John R. Garrett 1995 4.4. Committees of the Executive Committee and Ronald L. Graham ex officio Board of Trustees William H. Jaco ex officio Robert K. Lazarsfeld 1996 Haynes R. Miller 1994 4.4.1. Long Range Planning M. Susan Montgomery ex officio All members of this committee serve ex officio. Andrew M. Odlyzko 1996 AMS staff contact: Raquel E. Storti. Chair Richard S. Palais 1995 FrankS. Quinn 1995 Chair Joan S. Birman Norbetto Salinas 1996 Robert M. Fossum John M. Franks Ronald L. Gral!am William H. Jaco 4.6. Program and Meetings M. Susan Montgomery Franklin P. Peterson 4.4.2. Nominating Standing Committees All members of this committee serve ex officio. John M. Franks 4.6.1. Meetings and Conferences Jerome A. Goldstein AMS staff contact: H. Hope Daly. William H. J aco Arthur M. Jaffe Bettye Anne Case 1994 Chair John C. Polking Robert M. Fossum ex officio Ronald L. Gral!am ex officio William H. Jaco ex officio 4.5. Internal Organization of the Linda Keen 1994 American Mathematical Society D. J. Lewis 1996 Peter W. K. Li 1995 Frank Morgan 1996 Standing Committees Hugo Rossi 1994 David R. Scott 1995 4.5.1. Archives Nancy K. Stanton 1996 D. L. Su1sky 1996 Gert Almkvist (AMS) 1996 William Ys1as Velez 1994 R. Keith Dennis (AMS) 1996 Chair Sylvia Wiegand 1996 Chair Everett Pitcher 1994 Ruth Williams 1996 4.5.2. Committee on Committees M. Salal! Baouendi 1994 4.6.2. Program Committee for National Meetings Hyman Bass 1994 Hermann Flaschka 1994 Lenore Blum 1994 Robert M. Fossum ex officio Ingrid Daubechies 1994 Jeffrey C. Lagarias 1996 Persi W. Diaconis 1994 Chair H. W. Lenstra 1994 James A. Donaldson 1994 Jen·old E. Marsden 1995 Robett M. Fossum ex officio Joel H. Spencer 1996 Ronald L. Gral!am ex officio Mary F. Wheeler 1994 Rebecca A. Herb 1994 Chair D. J. Lewis 1994 4.6.3. Short Course Subcommittee Peter W. K. Li 1994 Stefan Burr 1995 Cathleen S. Morawetz ex officio Ingrid Daubechies 1995 RichardS. Palais 1994 Robert L. Devaney 1995 Carl Pomerance 1994 Lis! Novak Gaa1 1995 William Y slas Velez 1994 Jeffrey C. Lagarias 1994 4.5.3. Library Committee Patrick D. McCray 1994 Co-chair Nancy Anderson 1994 Chair James J. Tatters all 1996 George E. Andrews 1996 Felix E. Browder 1996 4.6.4. Central Section Program Committee R. Keith Dennis 1994 John Erik Fornaess 1995 Dorothy MeGan')' 1994 Andy Roy Magid ex officio Co-chair James Rovnyak 1994 Christel Rotthaus 1994 Mary Ann Southern 1994 Chair Karl Rubin 1994 John W. Weigel III 1996 Mary Ellen Rudin 1995

860 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

4.6.5. Eastern Section Program Committee 4.6.16. Task Force on AMS Conferences Stephen S. Kudla 1995 Consultant H. Hope Daly Lesley M. Sibner ex officio Robert M. Fossum ex officio Chair Birgit Speh 1994 Consultant Timothy J. Goggins Bernd Stu!Tnfels 1995 Chair Frank C. Hoppensteadt 1994 Steven George Krantz Consultant James W. Maxwell 4.6.6. Southeastern Section Program Committee Brian J. Parshall Chair Steven L. Batterson 1994 Consultant Samuel M. Rankin III Jon F. Carlson 1995 B. A. Taylor Robert J. Daverman ex officio Philip D. Wagreich Matthew Miller 1994 Sylvia Wiegand ex officio Michelle L. Wachs 1995 Carla Wofsy 4.6.7. Western Section Program Committee Josefina Alvarez 1994 William G. McCallum 1995 4.7. Status of the Profession Lance W. Small ex officio John Sylvester 1995 Chair Ruth J. Williams 1994 Standing Committees 4.6.8. Agenda for Business Meetings Carl C. Cowen, Jr. 1994 4.7.1. Academic Freedom, Tenure, and Chair Robert M. Fossum Employment Security Rebecca A. Herb 1994 Chair Josefina Alvarez 1994 Leon Brown 1994 4.6.9. Arnold Ross Lecture Series Committee Mary Elizabeth Flahive 1996 Harvey B. Keynes 1994 Mu!Tay Gerstenhaber 1995 Chair Paul J. Sally, Jr. 1995 Simon Hellerstein 1995 Jean E. Taylor 1996 Rhonda J. Hughes 1995 4.6.10. Gibbs Lecturer for 1995 and 1996, Donald E. Myers 1996 Committee to Select 4.7.2. Education Joseph B. Keller AMS staff contact: Ivar Stakgold. Andrew M. Odlyzko Chair Edward Witten Hyman Bass 1996 J eny L. Bona 1995 4.6.11. Progress in Mathematics Carl C. Cowen 1996 Michael G. Crandall 1995 Chair Ronald G. Douglas 1996 John B. Friedlander 1994 Robert M. Fossum ex officio Mary Ellen Rudin 1996 Ramesh A. Gangolli 1994 Chair James B. Serrin 1994 Ronald L. Graham ex officio 1996 Rebecca A. Herb 1996 Deborah Hughes Hallett 1995 Special Committees William H. Jaco ex officio Harvey B. Keynes 1995 4.6.12. Meetings Coordinating Committee for the Maria M. Klawe 1994 John W. Morgan ex officio Minneapolis Mathfest August 1994 Judith Roitman 1995 Hermann Flaschka Alan H. Schoenfeld 1995 H. W. Lenstra Alan C. Tucker 1996 Donna L. Salter Lesley M. Sibner 4.7.3. Subcommittee on Graduate and Postdoctoral Affairs 4.6.13. Meetings Coordinating Committee for the San Francisco Meeting January 1995 Jeny L. Bona Carl C. Cowen Hermann Flaschka Rebecca A. Herb H. W. Lenstra Roger Howe Andy Roy Magid Deborah Hughes Hallett Donna L. Salter Donald J. Lewis 4.6.14. Meetings Coordinating Committee for the Burlington Meeting August 1995 4.7.4. Subcommittee on Undergraduate Affairs Donna L. Salter David A. Cox Joseph A. Galli an Harvey B. Keynes 4.6.15. Meetings Coordinating Committee for the Kenneth C. Millett Orlando Meeting January 1996 Judith Roitman Donna L. Salter Alan H. Schoenfeld Lance W. Small Abdulalim A. Shabazz Je!Told E. Marsden Alan C. Tucker

SEPTEMBER 1994, VOLUME 41, NUMBER 7 861 _, .... _...... _...... -.. _···"·-············-...... _._ ...... ______...... _...... _...... Officers and Committee Members

4.7.5. Education in Mathematics, Liaison 4.7.11. Science Policy Committee on AMS staff contact: William H. Jaco. John A. Dossey Ronald G. Douglas ex officio Melvin Hochster Richard Ewing 1995 Rogers J. Newman Robert M. Fossum ex officio Louise A. Raphael Eric M. Friedlander 1994 Chair Paul J. Sally, Jr. Ronald L. Graham ex officio James D. Stasheff William H. Jaco ex officio Lynn Arthur Steen Raymond L. Johnson 1994 James I. Lepowsk.')' 1996 4.7.6. Human Rights of Mathematicians William James Lewis 1994 Raymundo Bautista 1994 Cathleen S. Morawetz ex officio Alfred Gray 1995 Chair John W. Morgan 1995 Sufian Y. Husseini 1994 Melvyn Nathanson 1995 Chair Neal I. Koblitz 1996 Ani! Nerode 1996 Joel L. Lebowitz 1996 Linda Preiss Rothschild 1994 Gordana Matic 1996 Jean E. Taylor 1995 Murray H. Protter 1995 Susan Gayle Williams 1996 Cora S. Sadosky 1995 Subcommittee Jonathan M. Wahl 1994 4.7.12. Federal Policy Agenda Hyman Bass 4.7.7. International Affairs Ivar Stakgold ex officio Arthur M. Jaffe Chair Raymond G. Ayoub 1995 Linda Keen Lenore Blum 1995 John W. Morgan Alice Fialowski 1995 John C. Polking Robin Hartshorne 1994 Chair Frank W. Warner III A. 0. Kuk.'ll 1996 Margaret H. Wright Motohico Mulase 1994 Robert J. Zimmer V. Kumar Murty 1995 Harold J. Stolberg 1994 4.7.13. World Mathematical Year 2000, Blue Ribbon Hung-Hsi Wu 1994 Committee for Chair Felix E. Browder 4.7.8. Pi Mu Epsilon Liaison Committee Charles L. Fefferrnan Joseph P. Brennan 1995 Robert M. Fossum Dennis DeTurck 1996 Ronald L. Graham Aparna W. Higgins 1996 Peter D. Lax Mary B. Martin 1994 William P. Thurston Robert Sefton Smith 1997 Chair De Witt Sumners 1994 Elliot A. Tanis 1996 Special Committees

4.7.9. Profession 4.7.14. Employment Task Force AMS staff contact: James W. Maxwell. S.-Y. Cheng Roy L. Adler 1995 Ronald M. Davis Chair M. Salah Baouendi 1994 Helen G. Grundman Ruth M. Charney 1994 Chair D. J. Lewis Annalisa Crannell 1996 Bernard L. Madison Robert M. Fossum ex officio James W. Maxwell ex officio Frank L. Gilfeather 1995 Donald E. McClure Ronald L. Graham ex officio Calvin C. Moore Richard J. Griego 1995 Carol S. Wood William H. Jaco ex officio Joseph Lipman 1996 4.7.15. Former Soviet Union Mathematics, Advisory William A. Massey 1994 Committee on Donald E. McClure 1996 AMS staff contact: Timothy J. Goggins. M. Beth Ruskai 1994 Michael Artin Ronald J. Stern 1995 Felix Browder Steven H. Weintraub 1994 Susan J. Friedlander Robert J. Zimmer 1996 Ronald L. Graham William H. Jaco 4.7.10. Professional Ethics David Kazhdan David Eisenbud 1996 Chair Robert D. MacPherson Simon Hellerstein 1995 Cathleen S. Morawetz Donald J. Lewis 1994 John C. Polking Chair Albert Marden 1994 Linda Preiss Rothschild Claude L. Schochet 1996 Daniel Stroock

862 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... _... _...... ______...... Officers and Committee Members

4.7.16. Handicapped, Accessibility for the 4.8.5. Satter Prize for 1995, Committee to Select the Carlos E. Kenig 1996 Winner of the Chair Peter W. K. Li 1996 Chair Cathleen S. Morawetz 1994 Horacia A. Porta 1996 William P. Thurston 1995 Lai-Sang Young 1995 4.7.17. Professional Ethics, Advisory Committee on Murray Gerstenhaber 4.8.6. Steele Prizes Frank L. Gilfeather Terms expire on June 30 Judy Green Chair Linda Keen Chair Eugenio Calabi 1995 Elliott H. Lieb Eugene B. Dynkin 1997 Robert P. Langlands 1995 4.7.18. Resource Needs for Excellence in Barry Mazur 1996 Mathematics Instruction Paul Rabinowitz 1995 AMS staff contact: Raquel E. Storti. Marina Ratner 1996 Gary M. Seitz 1994 Richard W. Beals William P. Thurston 1996 Project Director Thomas R. Berger 1997 John B. Garnett Ettore Infante Raymond L. Johnson Special Committees Barbara Lee Keyfitz Joan P. Leitzel 4.8.7. AMS Prizes and Awards William James Lewis Joan S. Birman Chair Morton Lowengrub Frederick W. Gehring Donald E. McClure Ronald L. Graham Alan Newell Joseph J. Kohn Alan C. Tucker Gian Carlo Rota David A. Vogan, Jr. Chair Joseph L. Taylor 4.8.8. Automatic Theorem Proving, Committee to 4.8. Prizes and Awards Recommend Winners of Prizes for Chair David Mumford Standing Committees Jacob T. Schwartz John L. Selfridge 4.8.1. Award for Public Service, Committee to 4.8.9. Cole Prize for 1995, Committee to Select the Select the Winner of the Winner of the Chair William Browder 1995 Barry Mazur Kenneth M. Hoffman 1996 Shigefumi Mori Harvey B. Keynes 1997 Chair Jean-Pierre Serre John C. Polking 1994 Isadore M. Singer 1998 4.8.10. Veblen Prize for 1996, Committee to Select the Winner of the 4.8.2. Centennial Fellowships Jeff Cheeger Terms expire on June 30 Peter W. K. Li Chair Clifford Taubes Roger C. Alperin 1996 Robert Calderbank 1997 Robin A. Pemantle 1995 Chair Alice Silverberg 1995 4.9. Institutes and Symposia Daniel W. Stroock 1997 Kari Vilonen 1995 1997 Standing Committees 1997 4.8.3. National Awards and Public Representation 4.9.1. Liaison Committee with AAAS Efraim P. Annendariz ex officio Robert M. Fossum ex officio Jerry L. Bona ex officio Frederick W. Gehring 1995 Margaret Cheney 1995 Chair Ronald L. Graham ex officio Ronald L. Graham ex officio Cathleen S. Morawetz ex officio Deborah Tepper Raimo ex officio Gian-Carlo Rota 1995 Raymond L. Johnson ex officio 4.8.4. Subcommittee on Appointments of the Wanen Page ex officio Committee on National Awards and Public Chair Charles Radin 1995 Representation V. Frederick Rickey ex officio Chih-Han Sah ex officio Robert M. Fossum ex officio Joel H. Spencer 1995 Chair Irwin Kra Melvin Thornton ex officio John C. Polking 1995

SEPTEMBER 1994, VOLUME 41, NUMBER 7 863 .. _...... -...... _... _...... _._._,_._._,_,_,_._._. __ ,_,_._,. __ , ...... _._._ ...... _...... ______._ .. _._._ ...... _._._ ...... _.. _._ ...... _._,,_,, Officers and Committee Members

4.9.2. Summer Institutes and Special Symposia lMS Subcommittee Members Terms expire on February 28 Chair M. I. Freidlin Jonathan L. Alperin 1996 B. Pittel Chair Donald L. Burkholder 1995 A. Rukhin Jonathan B. Goodman 1997 W. J. Studden Melvin Hochster 1995 4.10.4. AMS-IMS-MAA Data Committee Antoni A. Kosinski 1997 AMS staff contact: James W. Maxwell. Lai-Sang Young 1996 Paul W. Davis (AMS) 1996 LmTaine Denby (AMS) 1996 Consultant Lincoln K. Durst 4.10. Joint Committees Chair John D. Fulton (MAA) 1994 James F. Hurley (AMS) 1994 Don 0. Loftsgaarden (MAA) 1996 4.10.1. AMS-AAAS-MAA Committee James W. Maxwell (AMS) ex officio on Opportunities in Mathematics Donald B. Rubin (IMS) 1995 for Underrepresented Minorities Donald C. Rung (AMS) 1995 Joaquin Bustoz 1995 Ann K. Stehney (AMS) 1995 Chair Gloria F. Gilmer 1995 Ann E. Watkins (MAA) 1996 Leon A. Henkin 1995 Shirley Malcom ex officio 4.10.5. AMS-IMS-SIAM Committee on Joint James C. Turner 1995 Summer Research Conferences in the Consultant Argelia Velez-Rodriguez Mathematical Sciences Terms expire on June 30 4.10.2. AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Katalin A. Bencsath (AMS) 1997 Committee on Women in the Alan F. KruT (AMS) 1996 Mathematical Sciences Barbara L. Keyfitz (AMS) 1998 NCTM members' terms expire April I of the year given. Andrzej Manitius (SIAM) 1994 BartS. Ng (SIAM) 1994 Lynne Billard (IMS) 1994 Chair David Ruppert (IMS) 1995 Lynne M. Butler (SIAM) 1995 John R. Stembridge (AMS) 1997 Kathryn M. Chaloner (ASA) 1995 Clifford Taubes (AMS) 1997 Margaret B. Cozzens (SIAM) 1995 Sue Whitesides (AMS) 1996 Susan Groshen (IMS) 1995 ___,(AMS) 1998 Joan Hutchinson (AWM) 1994 Patricia C. Kenschaft (MAA) 1994 4.10.6. AMS-IMU Joint Program Committee Don J. Lewis (MAA) 1994 Joan S. Birman (AMS) J. Peter May (AMS) 1994 Miriam Cohen (IMU) Anita McDonald (MAA) 1994 Robert M. Fossum (AMS) ex officio Frances Rosamond (MAA) 1995 Stephen S. Gelbart (IMU) Chair M. Beth Ruskai (AMS) 1995 E. Christopher Lance (AMS) Tamar Schlick (SIAM) 1996 Andy R. Magid (AMS) L. Alayne Parson (AWM) 1996 Menachem Magidor (IMU) Berit Stensones (AMS) 1995 Marie-Paule Malliavin (AMS) Sandra Stinnett (ASA) 1994 Lance W. Small (AMS) ex officio Tilla Weinstein (AMS) 1995 Uri Srebro (IMU) Patricia S. Wilson (NCTM) 1996 4.10.7. AMS-MAA Committee on Research in Undergraduate Mathematics Education 4.10.3. AMS-ASL-IMS-SIAM Committee on Translations from Russian and Other Slavic (CRUME) Languages Amy Cohen (AMS) 1996 Chair James D. Stasheff (AMS) 1995 Chair Ed Dubinsky (MAA) 1995 Joan Ferrini-Mundy (NCTM) 1995 Daniel L. Goroff (AMS) 1996 AMS Subcommittee Members James J. Kaput (MAA) 1996 Consultant V.I. Amol'd GeorgeS. Monk (MAA) 1994 Luchezar Avramov 1994 Warren Page (AMATYC) 1995 Igor Dolgachev 1994 Alan H. Schoenfeld (AMS) 1995 Consultant S. G. Gindikin John Selden (AMS) 1994 Consultant Askol'd Georgievic Khovanskil RobertS. Smith (MAA) 1994 Robert D. MacPherson 1996 4.10.8. AMS-MAA Committee on Teaching Grigorii A. Margulis 1996 Assistants and Part-time Instructors Consultant N. K. Nikol'sJ...ir (TAIPTI) Chair James D. Stasheff (AMS) 1995 Reuben C. Drake (MAA) 1994 ASL Subcommittee Members Timothy L. Lance (AMS) 1994 Suzanne Lenhart (AMS) 1995 George Boolos 1995 William James Lewis (AMS) 1996 Boris I. Zi11ber 1994 Chair Daniel J. Madden (AMS) 1994

864 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Shelba J. Morman (MAA) 1995 4.10.15. AMS-MAA Arrangements Committee for the Stephen B. Rodi (MAA) 1994 San Francisco Meeting Raymond 0. Wells (MAA) 1995 January 4-7, 1995 Yousef Alavi 4.10.9. AMS-MAA Joint Archives Committee Joe Buckley Gert Almkvist (AMS) 1996 Jean B. Chan R. Keith Dennis (AMS) 1996 Chair William G. Chinn Albert C. Lewis (MAA) 1996 Allan B. Cruse Karen Parshall (MAA) 1995 Newman Fisher Everett Pitcher (AMS) 1994 William H. Jaco ex officio Chair Sanford L. Segal (MAA) 1994 Millianne Lehman Don Lick 4.10.10. AMS-MAA Joint Meetings Committee Andy Roy Magid ex officio Tristan Needham All members of this committee serve ex officio. Peter Pacheco Consultant H. Hope Daly Franklin Sheehan Chair Robert M. Fossum Marcia P. Sward ex officio William H. Jaco Hwa Tsang Tang Marcia P. Sward S. Y. Tang Donovan H. Van Osdol Donovan H. Van Osdol ex officio Maurice D. Weir 4.10.11. AMS-MAA Exhibits Advisory Subcommittee Eileen T. Ling-Erl Wu Donald J. Albers 4.10.16. AMS-MAA Joint Program Committee for the H. Hope Daly San Francisco Meeting Robert M. Fossum Thomas F. Banchoff (MAA) Rudiger Gebauer Jeffrey C. Lagarias (AMS) Joyce Glynn Barbara L. Osofsky (MAA) Rhoda Goldstein Chair Marian B. Pour-El (AMS) Debbie Hamar Michael C. Reed (AMS) Fred Osborne Penny Pina 4.10.17. AMS-MAA-SIAM Joint Administrative Kenneth A Ross Committee Elaine Sullivan All members of this committee serve ex officio. Gerald L. Alexanderson (MAA) I. Edward Block (SIAM) Chair Robert M. Fossum (AMS) Avner Friedman (SIAM) Samuel Gubins (SIAM) 4.10.12. Subcommittee on Summer Meetings William H. Jaco (AMS) David W. Ballew Donald L. Kreider (MAA) Robert M. Fossum Franklin P. Peterson (AMS) Chair H. W. Lenstra Marcia P. Sward (MAA) Donovan H. Van Osdo1 4.10.18. AMS-MAA-SIAM Joint Committee on Employment Opportunities 4.10.13. AMS-MAA Local Arrangements Committee for AMS staff contact: James W. Maxwell. the Minneapolis Mathfest August 15-17, 1994 Consultant Duane E. Anderson Stanley Benkoski (MAA) 1996 Eugene Fabes James W. Bond (AMS) 1996 Paul Humke Consultant Annalisa Crannell William H. Jaco ex officio Frank R. Demeyer (AMS) 1994 Walter Littman James W. Maxwell ex officio Willard Miller Chair S. Brent Morris (MAA) 1994 Chair Marian B. Pour-El Leon H. Seitelrnan (SIAM) 1997 Kenneth A Ross ex officio lvar Stakgold (SIAM) 1995 Karen Saxe Lesley M. Sibner ex officio 4.10.19. AMS-MAA-SIAM Joint Policy Board Monika Stumpf for Mathematics (see 1994 Mathematical Sciences Marcia P. Sward ex officio Professional Directory, page 28) 4.10.20. AMS-SIAM Committee 4.10.14. AMS-MAA Joint Program Committee for the on Applied Mathematics Minneapolis Mathfest Marsha J. Berger 1994 Laura M. Chihara (AMS) Shui-Nee Chow 1996 Chair James W. Daniel (MAA) James W. Demmel 1995 Lisl Novak Gaal (MAA) Paul C. Fife 1994 Robert Gilmer (AMS) Tai-Ping Liu 1995

SEPTEMBER 1994, VOLUME 41, NUMBER 7 865 ...... ,_,_,_,_,_,.. ,...... ,_,_,_,_,,...... -...... -...... -...... ______...... _,_, ...... -...... ,_,.. ,...... -...... ,.. , __ , ___ , ___ ,_, __ , __ ,_,_,___ ,_, _____ ,,__ , Officers and Committee Members

Dianne O'Leary 1996 5.0.3. Commission on Professionals in Science and Technology 4.10.21. AMS-SIAM Committee to Select the Winner of the Birkhoff Prize for 1994 Ann K. Stehney 1996 Michael Aizenman 5.0.4. Committee on the American Mathematics Chair Thomas G. Kurtz Competition Mary Fanett Wheeler Term expires on June 30 4.10.22. AMS-SIAM Committee to Select the Winner Richard P. Stanley 1997 of the Wiener Prize for 1995 Chair Thomas Kailath 5.0.5. Conference Board of the Mathematical Peter D. Lax Sciences Jerrold E. Marsden Ronald L. Graham 1994 4.10.23. AMS-SIAM-SMB Committee on 5.0.6. Fulkerson Prize Committee Mathematics in the Life Sciences Alan J. Hoffman Chair Jack D. Cowan 1994 5.0.7. MAA Committee on Undergraduate Program Leah Edelstein-Keshet 1994 in Mathematics Michael C. Mackey 1996 John M. Rinzel 1996 Theodore Shifrin 1996 Michael S. Waterman 1995 Dorothy Wallace 1996 Carla Wofsy 1995 5.0.8. MAA-NCTM Task Force on Mathematical Competitions Special Committees Peter W. Shor 4.10.24. AMS-MAA Committee on Cooperation 5.0.9. U.S. National Committee on Theoretical and Applied Mechanics Don Albers (MAA) Gerald L. Alexanderson (MAA) Term expires on October 31 Michael G. Crandall (AMS) Constantine M. Dafermos 1996 Robert M. Fossum (AMS) Ramesh A. Gangolli (AMS) Co-chair Ronald L. Graham (AMS) ex officio 6. Index------Staff William H. Jaco (AMS) ABC Committee ...... 4.3.1 Co-chair Donald L. Kreider (MAA) ex officio AMS Prizes and Awards ...... 4.8.7 M. Susan Montgomery (AMS) AMS-AAAS-MAA Committee on Opportunities in Mathematics for Ken Ross (MAA) ex officio Underrepresented Minorities ...... 4.1 0.1 Mary Ellen Rudin (AMS) AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Committee on Women in David A. Sanchez (AMS) the Mathematical Sciences ...... 4.10.2 Doris Schattschneider (MAA) AMS-ASL-IMS-SIAM Committee on Translations from Russian and Staff Marcia P. Sward (MAA) Other Slavic Languages ...... 4.10.3 Alan C. Tucker (MAA) AMS-IMS-MAA Data Committee ...... 4.10.4 4.10.25. AMS-MAA-SIAM Committee on Preparation AMS-IMS-SIAM Committee on Joint Summer Research Conferences for College Teaching in the Mathematical Sciences ...... 4.10.5 AMS-IMU Joint Program Committee ...... 4.10.6 Donald W. Bushaw Chair Bettye Anne Case AMS-MAA Arrangements Committee for the San Francisco Meeting January 4-7, 1995 ...... 4.10.15 Robert H. McDowell RichardS. Millman AMS-MAA Committee on Cooperation ...... 4.10.24 Robert R. Phelps AMS-MAA Committee on Research in Undergraduate Mathematics Richard D. Ringeisen Education (CRUME) ...... 4.10.7 Stephen B. Rodi AMS-MAA Committee on Teaching Assistants and Part-time James G. Simmonds Instructors (TAIPTI) ...... 4.1 0.8 Guido L. Weiss AMS-MAA Exhibits Advisory Subcommittee ...... 4.10.11 AMS-MAAJointArchives Committee...... 4.10.9 AMS-MAAJointMeetings Committee ...... 4.10.10 s. Representatives------AMS-MAA Joint Program Committee for the Minneapolis Mathfest . 4.10.14 AMS-MAA Joint Program Committee for the San Francisco Meeting 4.10.16 5.0.1. Advisory Board of the National Translations AMS-MAA Local Arrangements Committee for the Minneapolis Mathfest August 15-17, 1994 ...... 4.10.13 Center of the John Crerar Library AMS-MAA-SIAM Committee on Preparation for College Teaching . 4.10.25 AMS-MAA-SIAM Joint Administrative Committee ...... 4.10.17 5.0.2. American Association for the Advancement of AMS-MAA-SIAM Joint Committee on Employment Opportunities .. 4.10.18 Science AMS-MAA-SIAM Joint Policy Board for Mathematics (see 1994 Mathematical Sciences Professional Directory, page 28) . . . . 4.10.19 Terms expire on February 21 AMS-SIAM Committee on Applied Mathematics ...... 4.10.20 Section A Raymond L. Johnson 1995 AMS-SIAM Committee to Select the Winner of the Birkhoff Prize for Section B Chih-Han Sah 1995 1994 ...... 4.10.21 Section L V. Frederick Rickey 1995 AMS-SIAM Committee to Select the Winner of the Wiener Prize for Section Q Efraim P. Armendariz 1995 1995 ...... 4.10.22 Section T Melvin Thornton 1995 AMS-SIAM-SMB Committee on Mathematics in the Life Sciences .. 4.10.23

866 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Abstracts Editorial Committee ...... 4.2.1 Institutional Membership ...... 4.3.14 Academic Freedom, Tenure, and Employment Security . 4.7.1 Internal Organization of the American Mathematical Society . 4.5 Administrative Committee ...... 4.10.17 International Affairs . . 4.7.7 Advisory Board of the National Translations Center of the John Crerar Investment . . 4.3.7 Library...... 5.0.1 JCEO ...... 4.10.18 Agenda and Budget ...... 4.3.1 JPBM ...... 4.10.19 Agenda for Business Meetings ...... 4.6.8 Japanese, Translation from . 4.2.17 American Association for the Advancement of Science . 5.0.2 Joint Administrative Committee . 4.10.17 American Journal of Mathematics, Society's Representatives . 4.2.2 Joint Archives Committee. . 4.10.9 American Mathematics Competition, Committee on . . 5.0.4 Joint Committees ...... 4.10 Appeals Committee on Discounted Subscriptions . . 4.3.2 Joint Meetings Committee . 4.10.10 Applied Mathematics, AMS-SIAM Committee on . . 4.10.20 Joint Policy Board...... 4.10.19 Archives ...... 4.5.1 Joint Summer Research Conferences 4.10.5 Arnold Ross Lecture Series Committee ...... 4.6.9 Journal of the AMS 4.2.8 Arrangements Committee for the Minneapolis Mathfest . . 4.10.13 LRP ...... 4.4.1 Arrangements Committee for the San Francisco Meeting . 4.10.15 Legal Aid . . . . . 4.3.8 Audit ...... 4.3.3 Liaison Committee 1.1 Automatic Theorem Proving, Committee to Recommend Winners of Liaison Committee with AAAS. 4.9.1 Prizes for ...... 4.8.8 Library Committee . . 4.5.3 Award for Public Service, Committee to Select the Winner of the . 4.8.1 Life Sciences ...... 4.10.23 Birkhoff Prize .... . 4.10.21 Long Range Planning ...... 4.4.1 Board of Trustees . . . 3 MAA Committee on Undergraduate Program in Mathematics . . 5.0.7 Bulletin (New Series) . 4.2.3 MAA-NCTM Task Force on Mathematical Competitions . 5.0.8 CAFTES. . 4.7.1 Mathematical Reviews ...... 4.2.9 CBMS .. . 5.0.5 Mathematical Surveys and Monographs . 4.2.10 COB ... . 4.7.2 Mathematics in the Life Sciences . . . . . 4.10.23 CRUME. . 4.10.7 Mathematics of Computation ...... 4.2.11 CSP ... . 4.7.11 Meetings Coordinating Committee for the Burlington Meeting August Centennial Fellowships . 4.8.2 1995 ...... 4.6.14 Central Section Program Committee . 4.6.4 Meetings Coordinating Committee for the Minneapolis Mathfest Chinese, Translation from ...... 4.2.16 August 1994 ...... 4.6.12 Cole Prize for 1995, Committee to Select the Winner of the 4.8.9 Meetings Coordinating Committee for the Orlando Meeting January Collected Works ...... 4.2.4 1996 ...... 4.6.15 Colloquium ...... 4.2.5 Meetings Coordinating Committee for the San Francisco Meeting Commission on Professionals in Science and Technology 5.0.3 January 1995 ... . 4.6.13 Committee on Committees ...... 4.5.2 Meetings and Conferences ...... 4.6.1 Committee on the American Mathematics Competition 5.0.4 Meetings of the Council ...... 4.1.3 Committees ...... 4 Member Publications, Committee to Review . . 4.2.23 Committees of the Board of Trustees ...... 4.3 Members-at-Large . . 2.0.3 Committees of the Council ...... 4.1 Membership . . 4.3.9 Committees of the Executive Committee and Board of Trustees . 4.4 Memoirs ...... 4.2.15 Computer Operations and Facilities, Visiting Committee on . 4.3.4 Monographs . . . . . 4.2.10 Conference Board of the Mathematical Sciences . 5.0.5 National Awards and Public Representation 4.8.3 Contemporary Mathematics . 4.2.6 National Meetings ...... 4.6.2 Copyright Policy . . 4.3.13 National Translations Center of the John Crerar Library, Advisory Corporate Relations . 4.3.5 Board of the . . 5.0.1 Council ...... 2 Nominating ...... 4.4.2 Data Committee . . . 4.10.4 Nominating Committee ...... 4.1.2 Discounted Subscriptions, Appeals Committee on 4.3.2 Nominating Committee of the ECBT . 4.4.2 EC ...... 2.1 Notices ...... 4.2.12 Eastern Section Program Committee 4.6.5 Officers ...... 1 Editorial Boards . . . 4.1.1 Officers of the AMS ...... 2.0.1 Editorial Committees ...... 4.2 Opportunities in Mathematics for Underrepresented Minorities . 4.10.1 Education ...... 4.7.2 PSAM ...... 4.2.14 Education in Mathematics, Liaison Committee on 4.7.5 Pi Mu Epsilon Liaison Committee 4.7.8 Electronic Products and Services 4.2.18 Prizes and Awards ...... 4.8 Employment Opportunities . . . 4.10.18 Proceedings ...... 4.2.13 Employment Task Force . . . . . 4.7.14 Proceedings of Symposia in Applied Mathematics . . 4.2.14 Endowment and Planned Giving 4.3.6 Profession ...... 4.7.9 Ethics ...... 4.7.10 Professional Ethics ...... 4.7.10 Executive Committee of the Council 2.1 Professional Ethics, Advisory Committee on . . . . . 4.7.17 Federal Policy Agenda Subcommittee 4.7.12 Professionals in Science and Technology, Commission on . . 5.0.3 Former Soviet Union Mathematics, Advisory Committee on 4.7.15 Program Committees Fulkerson Prize Committee ...... 5.0.6 Central...... 4.6.4 Gibbs Lecturer for 1995 and 1996, Committee to Select . 4.6.10 Eastern ...... 4.6.5 Graduate Studies in Mathematics . . 4.2.7 National Meetings . . 4.6.2 Handicapped, Accessability for the . 4.7.16 Southeastern . . . 4.6.6 History of Mathematics ...... 4.2.19 Western ...... 4.6.7 Human Rights of Mathematicians . 4.7.6 Program and Meetings . . 4.6 Institutes and Symposia ...... 4.9 Progress in Mathematics . 4.6.11

------·--·------SEPTEMBER 1994, VOLUME 41, NUMBER 7 867 ···········-·-·············-··-···························-...... ______,_____ ,,, ...... Officers and Committee Members

Publication Program. . 4.3.10 Subcommittee on Undergraduate Affairs . . 4.7.4 Publications ...... 4.5.4 Subscriptions ...... 4.3.2 Representatives . . . . 5 Summer Institutes and Special Symposia . . 4.9.2 Representatives of Committees . 2.0.2 Summer Research Conferences . . . 4.10.5 Reprinted Books ...... 4.2.20 TAIPTI ...... 4.10.8 Resource Needs for Excellence in Mathematics Instruction . 4. 7.18 Task Force on AMS Conferences . . 4.6.16 Russian and Other Slavic Languages, Translations from . . . 4.1 0.3 The Publication Program ...... 4.3.10 Salaries ...... 4.3.11 Theoretical and Applied Mechanics . 5.0.9 Satter Prize for 1995, Committee to Select the Winner of the . 4.8.5 Transactions and Memoirs . 4.2.15 Science Policy ...... 4.7 .11 Translations: Search Committee for Executive Director ...... 4.3.15 Chinese ...... 4.2.16 Search Committee for Executive Editor of Mathematical Reviews . 4.3.16 Japanese ...... 4.2.17 Short Course Subcommittee ...... 4.6.3 Russian and Other Slavic Languages . 4.10.3 Southeastern Section Program Committee . 4.6.6 Trustees ...... 3 Special Symposia . 4.9.2 U.S. National Committee on Theoretical and Applied Mechanics . 5.0.9 Staff Salaries ...... 4.3.11 Undergraduate Program in Mathematics, MAA Committee on . 5.0.7 Staff and Services . . . . 4.3.12 Underrepresented Minorities ...... 4.10.1 Status of the Profession . 4.7 University Lecture Series ...... 4.2.21 Steele Prizes ...... 4.8.6 Veblen Prize for 1996, Committee to Select the Winner of the . . 4.8.10 Subcommittee on Appointments ofthe Committee on National Awards Western Section Program Committee . . . 4.6.7 and Public Representation ...... 4.8.4 What's Happening, Advisory Board for ...... 4.2.22 Subcommittee on Graduate and Postdoctoral Affairs . . 4.7.3 Women in the Mathematical Sciences ...... 4.10.2 Subcommittee on Summer Meetings ...... 4.10.12 World Mathematical Year 2000, Blue Ribbon Committee for . 4.7.13

.....,A..J ...... ,.....,INGS OF SYMPOSIA IN PURE MATHEMATICS Motives Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre, Editors Volume 55 Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas-Hodge theory, algebraic K -theory, polylogarithms, automorphic forms, L-functions, £-adic representations, trigonometric sums, and algebraic cycles-have discovered that an enlarged (and in part conjectural) theory of "mixed" motives indicates and explains phenomena appearing in each area. These volumes contain the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.

1991 Mathematics Subject Classification: 14; 11, 19 ISBN (Set) 0-8218-1635-7, (Part I) 0-8218-1636-5, (Part 2) 0-8218-1637-3 1423 pages (Set), 747 pages (Part 1), 676 pages (Part 2), (hardcover), February 1994 Set: List price $250, Individual member $150, Institutional member $200 Part 1: List price $140, Individual member $84, Institutional member $112 Part 2: List price $129, Individual member $77, Institutional member $103 To order, please specify PSPUM/55NA (Set), PSPUM/55.1NA (Part !), PSPUM/55.2NA (Part 2)

to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and with VISA or MasterCard. Residents of Canada, please include 7% GST.

---·---·-·---·------·------868 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Miscellaneous

Personals Zhihong Xia, formerly of the Geor­ versity, died in January 1994. She was Theodore W. Anderson, of Stanford gia Institute of Technology, has been born on October 8, 1927, and was a University, has been elected a Foreign appointed a professor of mathematics at member of the Society for 31 years. Member of the Norwegian Academy of Northwestern University. Robert L. Pexton, of Lawrence Liv­ Science and Letters. ermore National Laboratories, died on Qui-Qiang Chen, formerly of the Deaths January 3, 1994. He was born on August University of Chicago, has been ap­ Masahisa Adachi, of Kyoto University, 12, 1922, and was a member of the pointed associate professor of Mathe­ died on March 24, 1993. He was born Society for 35 years. matics at Northwestern University. on February 7, 1932, and was a member William E. Pruitt, of the University Jozef lgnaczak, of the Rochester of the Society for 23 years. of Minnesota, died on July 25, 1993. He Institute of Technology, has been elected Harry L. Krall, Professor Emeritus was born on May 11, 1934, and was a a member of the New York Academy of at Pennsylvania State College, died on member of the Society for 37 years. Sciences and the Acoustical Society of June 9, 1994. He was born on June 13, Guo Zhong-heng, of Peking Uni­ America. 1907, and was a member of the Society versity, died in September 1993. He Andrei Suslin, formerly of the Stek­ for 61 years. was born on March 2, 1933, and was a lov Institute, has been appointed profes­ Rosalyn S. Lee, of Duquesne Uni- member of the Society for 6 years. sor and holder of a Trustee's Chair at Northwestern University.

CONTEMPORARY MATHEMATICS ------CONTEMPORARY MATHEMATICS Lie Algebras, Cohomology, and ------New Applications to Quantum Mechanics Lie Algebras, Cohomology, and New AppllcaHons to Quantum Mechanics Niky Kamran and Peter J. Olver, Editors

NlkylCQmaran ,....,J.Oiver...... Volume 760 This volume is devoted to a range of important new ideas arising in the applications of Lie groups ------and Lie algebras to SchrOdinger operators and associated quantum mechanical systems. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents a look at some of the current developments in this extraordinarily rich and vibrant area.

1991 Mathematics Subject Classification: 17, 81, 33 ISBN 0-8218-5169-1,310 pages (softcover), March 1994 Individual member $31, List price $51, Institutional member $41 To order, please specify CONM/160NA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 869 Visiting Mathematicians (Supplementary List)

Listed below are foreign mathematicians visiting in the United States.

Visiting Foreign Mathematicians Name and Home Counl!:Y Host Institution Field of Special Interest Period of Visit Bayarri, M. J. (Spain) Purdue University Bayesian Analysis 8/94-12/94 Biebel, Martin (Germany) Purdue University Decision Theory, Probability 8/94- 5/95 Camilli, Fabio (Italy) Brown University Stochastic Control 9/94- 8/95 Czelakowski, Janusz (Poland) Iowa State University Algebraic Logic and Universal 8/94- 5/95 Algebra Denzler. Jochen (Germany) Brown University Dynamical Systems 9/94- 7/95 Dobrushkin, Vladimir (Russia) Brown University Partial Differential Equations 6194- 6195 Eckhoff, Knut (Norway) Brown University Scientific Computation 10/94 Ghosh, Jayanta (India) Purdue University Statistics, Bayesian Inference 6/94-12/94 Hernandez-Hernandez, Daniel Brown University Stochastic Control 8/94- 8/95 (Mexico) Insua. David Rios (Spain) Purdue University Bayesian Analysis 8/94-12/94 Iwaki, Katsuaki (Japan) Purdue University Statistical Inference, Bayesian 8/94- 7/95 Analysis Liseo, Brunero (Italy) Purdue University Bayesian Analysis 1195- 5195 Lu, Zhidong (People's Republic Brown University Computed Tomography 6/94- 5195 of China) Lyashenko, Andrei (Russia) Iowa State University Partial Differential Equations 8/94- 5/95 Ma, Henping (People's Brown University Scientific Computation 8/94- 7/95 Republic of China) Spies, Ruben (Argentina) Iowa State University Control of Smart Materials 8/94- 5/95

...... _.. _...... __ ...... ------870 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

ORDINARY MEMBERS Jan Franciszek Bochenek, Krakow, Abdol Ali Coochak Poor, Ahvaz Edilio Escalona-Fernandez, Maracay, Ugur Gjulhussein Oglu Abdullaev, Poland Univ, Iran Venezuela Baku State Univ, Azerbaijan Borislav Bojanov, Univ of Sofia, Paulo Manuel Barros Correia, Univ Benny Dan Evans, Oklahoma State Alisher S Abdullayev, National Univ, Bulgaria de Evora, Portugal Univ, Stillwater Sacramento, CA James William Bond, San Diego, CA Severino C Coutinho, Rio de Janeiro, Jie Fang, Zhongshan Univ, Roberto Acosta-Abrue, Mexico Iouri E Boreicha, National Univ of Brazil Guangzhou, People's Republic of David I Adu, Univ of Botswana, Lesotho, Republic of South Giang Vu Dang, Bolyai Institute, China Gaborone Africa Szeged, Hungary Farid Omar Farid, Vernon, British Girdbar G Agarwal, Lucknow Univ, Sujit K Bose, National Center for Igor Karlovich Daugavet, Saint Columbia Canada India Basic Sciences, Calcutta, India Petersburg State Univ, Russia Giovanni Felder, Univ of North K G Aggarwal, Maharshi Franc Bresar, Univ of Maribor, F J Craveiro De Carvalho, Univ of Carolina, Chapel Hill International Univ, Rohtak, Slovenia Coimbra, Portugal Anargyros G Fellouris, National India David C Brooks, Seattle Pacific Dorothy Louise Dean, Salisbury, MD Technical Univ, Athens, Greece Mostafa K Mahmoud Ahmed, Cairo Univ, WA Mohhamad Ali Dehghan, Univ of Minfu Feng, Sichuan Univ, People's Univ, Egypt Teri Nicole Brooks, Tennessee Kennan, Iran Republic of China Hyungsok Ahn, West Lafayette, IN Ridge, TN James W Del Valle, Chattanooga, Javier Fernandez-Navas, Purdue Maks Aizikovich Akivis, Moscow, John Christopher Brown, Pomona TN Univ, West Lafayette, IN Russia College, Claremont, CA Gennadii Vladimirovich Demidenko, Frederick Charles Ferneyhough, Fatima M Al-Oboudi, Girls College Kama Lynn Bryan, Lincoln, NE Russian Academy of Sciences, Al-Ain, United Arab Emirates of Education, Riyadh, Saudi Tomasz Brzezinski, Univ of Novosibirsk Judith H Fethe, Pellissippi State Arabia Cambridge, England Tristan Mark Denley, Univ of Umea, Technical Community College, Bilandar P Alakhverdiev, Azerbaijan Vassil Bugadze, Tbilisi State Univ, Sweden Knoxville, TN Academy of Sciences, Baku Republic of Georgia Vishwanath Laxman Deshpande, Andrey Matveevich Filimonov, MilT, Mohammed T Alam, Brussels, Meghan Anne Burke, Pittsburgh Maharashtra, India Moscow, Russia Belgium Cancer Institute, PA Gilberta Diaz, Havana, Cuba Sergei Borisovich Filippov, St John W Alexander, Laurel, MD Alexander P Buslaev, Moscow William Dilworth, Beloit, Wl Petersburg, Russia Daniel J Allcock, Berkeley, CA Automobile Road Institute, Dung Dinh, Institute of Information V V Filippov, Moscow State Univ, Janet Lea Amburn, Columbus, OH Russia Technology, Hanoi, Vietnam Russia Gabil M Amiraliyeu, Baku, Dennis Callas, State Univ of New Ruwel Ya Doktorskii, Kara Susan Finley, Marietta, GA Azerbaijan York, Delhi Rostov-on-Don, Russia Gregory Dean Foley, Conroe, TX Titu Andreescu, North Aurora, IL Vasile Campian, Technical Univ of Rodman E Doll, Schoolcraft College, Vasiliy Ilyich Fomin, Tambov, Ataollah Askari Hemmat, Vali Asr Cluj, Cluj-Napoca, Romania Livonia, MI Russia Univ, Rfsanjan, Iran Alin-Andrei Carsteanu, Univ of Karen E Donnelly, Saint Joseph's Maria Fragoulopou!ou, Univ of Ismail Asian, Ohio Univ, Athens Minnesota, Minneapolis College, Rensselaer, IN Athens, Greece P Avtar, Delhi, India Frank Peter Cass, Univ of Western Julian M Dontchev, Jarvenpaa, Robert Isaac Freidson, St Petersburg, David Howard Bachman, Orrville, Ontario, London, Ontario Finland Russia OH Canada Sandor Fridli, Eotvos Lorand Univ, Kamoliddin Khamroevich Baimatou, Hilda Draskovicova, Comenius Budapest, Hungary Dushanbe, Tajikistan Fred W Cerkan, Houston, TX Univ, Bratislava, Slovak Federal Bogdan Baishanski, Ohio State Univ, Gurmeet K Chadha, Panjab Univ, Republic Leonid M Fridman, Samara Columbus Chandigash, India Ana Lia Duran, Tres Ries, Costa Architecture & Building Jacov Baris, Cornel State Univ, Hongsen Chen, Texas A & M Univ, Rica Institute, Russia Belarus College Station Ismail H Durn, ICPAM, Edirne, Stanislav Dmitrievich Furta, Moscow Svetlana Michailovna Bauer, St Victor Grigor Cherednichenko, Turkey Aviation Institute, Russia Peters burg, Russia Novosibirsk, Russia Paul M Elizarov, Tver State Univ, Vladimir Fedorovich Gaposhkin, Haluk Beker, Bogazici Univ, Mi-Gyung Cho, Pusan National Russia MilT, Moscow, Russia Istanbul, Turkey Univ, Korea Etienne Emmrich, Magdeburg, Catherine Garcia-Reimbert, Tlalpan, Maxim Gennadyevich Bekishev, Stefanka Stefanova Chukova, GMI Germany Mexico Siberian Trade Bank, Engineering & Management, Horia Ion Ene, Romanian Academy Bradley E Garner, Beltsville, MD Novosibirsk, Russia Flint, MI of Science, Bucharest Leszek Piotr Gawarecki, Michigan Eugeniy Ivanovich Berezhnoi, Zbigniew J Ciesielski, Polish Boris A Ershov, Saint Petersburg State Univ, East Lansing Yaroslavl State Univ, Russia Academy of Sciences, Sopot, State Univ, Russia Haik Gegham Ghazarian, Erevan Balazs Biro, Hungarian Academy of Poland Eugene Konstantynovich Ershov, State Univ, Armenia Science, Budapest Carlos Agra Coelho, Almada, Civil Engineering Institute, St Alexander L Gladkov, Vitebsk State James E Blevins, Kent, OH Portugal Petersburg, Russia Pedagogical Institute, Belarus

SEPTEMBER 1994, VOLUME 41, NUMBER 7 871 """""""""'"''"""'"""'"'"""'""""""""""''"'"'"'"'"""'""""'"'""'""'"'"'"''"'"'"'"''"'""'"'"'"''"'"""""'"""'""''""""'''''"'"'"'"'"'"'"""'"""'"''''------"""'"'"'"'"'""'""'"'"""'"'"'"'"""'"'"'"'"'"'"'"'"""'"""""""""""'""""'""'-'"'"'"""'"'"'"""""'"'""""'""'"""'"'"""'"'"'"'"'"'"""'""'""" New Members of the AMS

Mary Glazman. Univ Nac Autonoma Philip C Kenny, San Mateo, CA Yu F Luchko, Belarussian State Tadeusz Nadzieja, Wroclaw Univ. de Mexico, Mexico Alexander Kerimovich Kerimov, Univ, Minsk, Belarus Poland Alexei Oscar Gokhman, Voronezh, Russian Academy of Sciences, S F Lukomskii, Saratov State Alexander Yur'evich Nenashev, St Russia Moscow Pedagogical Institute, Russia Petersburg, Russia Weihang Gong, Qufu Normal Univ. Irshadullah Khan, Newton Centre, Gregory G Luther, Univ of New Charles H Neumann, Clarkston, MI Shandong. People's Republic of MA Mexico, Albuquerque Yury Arkadjevich Nickolayevsky, China Sergey M Khrissanoff. Kiev, Ukraine Olga B Lykova, Academy of the Kharkov, Ukraine Snezhana Gueorguieva Beth A Kilday, Boxeman, MT Ukraine, Kiev Sergei Yakovlevich Novikov, Samara Gotcheva-Ilieva, Plovdiv, Jin-Soo Kim, Seoul National Univ, Deirdre A Lynch, Saunders College State Univ, Russia Bulgaria Korea Publishing, Philadelphia, PA Herminia Ochsenius, Pontifica Univ David J Gries, Cornell Univ, Ithaca, Yonggu Kim. Chonnam National Lev Sergeevich Maergoiz, Catolica, Santiago. Chile NY Univ. Kwangju, Korea Krasnoyarsk Civil Engineering Vladinir Lukich Oleinik, Saint Grezgorz Gromadzki, Pedagogical Kimberly K J Kinateder, Ohio State Institute, Russia Petersberg State Univ, Russia Univ, Bydgoszcz, Poland Univ, Columbus Julie C Mahoney, Frankfort, KY Sharon L Osting, Univ of Findlay, Lyubomir T Gruyitch, Ecole Vladimir V Kisil, CINVESTAV del Aleksandr Leonidovich Maiboroda, OH St Petersburg, Russia Nationale D'Ingenieurs, Belfort, lPN, Mexico Baburao Govindrao Pachpatte, Oleg Ivanovich Klesov. Kiev, A P Makhmudov, Baku. Azerbaijan France Aurangabad. India Vladimir Ilia Gurariy, South Euclid, Ukraine Vera Vladimirovna Malygina, Perm, Padmavathamma, Univ of Mysore, OH Alois Klic. Prague Institute of Russia India Sergey Alekseevich Gusarenko, Chemical Technology, Czech Leonid Isakovitch Manevitch. K Pan, Barry Univ, Miami Shores, Perm, Russia Republic Institute of Energy Problems of FL Evgeniy Gulamovich Guseinov, Janet Kondo, Portland, OR Chemical Physics, Moscow, Sotirios Nick Papakostas, Athens, Odessa State Univ. Ukraine Sergei Vladimir Konyagin, Moscow Russia Greece Istvan Gyori. Univ of Veszprem, State Univ, Russia Milan Mares, Prague. Czech Hungary Yuri A Kordyukov, Ufa State Republic Ernest R Paquet, North Canton. OH Duan Haibao, Peking Univ, Beijing, Aircraft Technical Univ, Ufa David Clark Marshall, Anaheim, CA Narahari Parhi. Berhampur Univ, People's Republic of China Marek Kosiek, Jagiellonian Univ. Andrei Martinez Finkelshtein, India Rosa Hale-Tamayo, La Paz, Mexico Krakow, Poland Havana Univ, Cuba Jayaram Parida, Regional Deguang Han, Qufu Normal Univ, Michail Kovalev. Minsk, Belarus Osamu Maruo, Hiroshima Univ, Engineering College, Rourkela, Shandong, People's Republic of Karen Michelle Kramer, North Japan India China Olmsted, OH Matjan S Matvejchuk, Kazan, Russia Kalyanpuram R Parthasarathy, Indian Kevin Lewis Hartshorn. Thousand Richard J Krantz, Denver, CO Andrew J Mauer. LaGrange. IL Statistical Institute, New Delhi Oaks. CA Myroslav Ivan Kratko, Kiev, Ukraine Sean D McKee, Kaysville, UT Rajagopalan Parvatham, Univ of Alan P Harvey, Cambridge Univ Ivan Krivy. Univ of Ostrava, Czech Alko R Meijer. Univ of Natal, Madras, India Press, Stanford, CA Republic Durban, Republic of South Rizz-an Teymur Oglu Pashayev, Lisa Lea Hastings. Wooster, OH Tomasz Krzyzynski, Polish Academy Africa Baku State Univ, Azerbaijan Warren John Hawley, Brookfield, IL of Sciences. Warsaw Margarida Pinheiro Mello, Vyacheslav N Pavlenko, Chelyabinsk Daichuan He, Beijing Educational Jaromir Kuben, Brno. Czech IMECC-UNICAMP, Campinas. State Univ, Russia Institute, People's Republic of Republic Brazil Matej Pavsic, Univ of Ljubljana, China Jozef Kubik, Polish Academy of Yuri A Melnikov, Middle Tennessee Slovenia Patricia Lynn Hersh, Cambridge, MA Sciences, Poznan State Univ, Murfreesboro Delene Perley, Wooster, OH David G Hild. Yellow Springs, OH Vladimir I Kukulin, Moscow State Miguel Carvalho Melo, Lisbon. Michael Victor Pimsner, Univ of Albertus Hof, McMaster Univ, Univ, Russia Portugal Pennsylvania, Philadelphia Hamilton, Ontario Canada Ashok Kumar, Rohtak, India Luis E Merchan, Maracaibo. Slawomir Plaskacz, Nicolaus Irene Rueter, Univ of California Vitodrag Kumperscak, Univ of Venezuela Copernicus Univ, Torun, Poland Berkeley Maribor, Slovenia Robert Lee Mertens, Columbus, OH Michael Nickolaevich Podoksyonov, Vasile Iftode, Technological Univ, Nand La!, Banaras Hindu Univ, Igor Mezic, California Institute of Pedagogicheskii Institute, Bucharest, Romania Varanah, India Technology, Pasadena Vitebsk, Belarus Alejandro lllanes, Circuito Exterior, Vicky L Lante, Savage, MD A B M A Sobhan Mian, Dmitrii A Popov, Moscow, Russia Mexico Tracy Lynn Lawrence, Atlanta. GA Jahangirnagar Univ, Dhaka, Balaji S Prabhakar, Los Angeles, CA Yury J Ionin, Central Michigan Univ, S G Leiko, Odessa, Ukraine Bangladesh Juraj Prochazka, Comenius Univ, Mount Pleasant Eduardo B T Leite, Sao Paulo. Gigel Militaru, Univ of Bucharest, Bratislava, Slovenia Romania Rebecca Ann Isaac, Lexington, KY Brazil Anatolii P Prudnikov, Computing Ruisheng Li, Shandong Univ, Elaine I Miller, Toledo, OH M Ataharul Islam, Dhaka Univ, Center, Moscow, Russia Bangladesh Weihai, People's Republic of J Lyn Miller, Univ of Maryland, Paul Stephen Prveitt, South Hill, VA Alexander P Ivanov, Moscow, Russia China College Park Douglas A Quinney, Univ of Keele. Sergei V Ivanov, Univ of Illinois, Jin Liang, Kunming Institute of Ronald J Milne, Goshen College, IN Staffordshire, England Urbana Technology, People's Republic Angela Michelle Minnick, Adbeel N Quinones, Queens Village, Vladislav Aleksandrovic Ivanov, St of China Centerville, OH Petersburg, Russia Jason R Lieberman, Valley Stream, Joannis Mittas, Thessaloniki, Greece NY Tonya Monique Jenkins, Austin, TX NY Takunari Miyazaki, Univ of Oregon, Robert J Radin. West Hartford, CT Vicki S Jennings, Univ of Chicago Paul L S Lin, Simi Valley, CA Eugene Ravinder Krishna Raina, College Press, IL Romulo Campos Lins. Univ of Sao Cyr E Mlan, Univ Laval. Ste-Foy, of Technology & Agricultural Christopher David Jeris, Naperville, Paulo, Brazil Quebec Canada Engineering, Ragasthon, India IL Nicholas W Locantore Jr. Yardville, Felicia I Mocanu. Bucharest, Madhu Raka, Panjab Univ, Celeste M Jordan, Morgantown, WV NJ Romania Chandigarh, India Margaret A Kalter, Allentown, PA A A Lodkin, Saint Petersburg State Leticia J Monsivais, El Paso, TX Thomas G Railey, Ohio State Univ, Eunju Kang, Seoul National Univ, Univ. Russia Jaime Edilberto Munoz Rivera, Columbus Korea Anthony Wai Keung Loh, Imperial National Laboratory of Computer Nagaraj S Rao. Mohegan Lake, NY Lev Kapitanski, Kansas State Univ, College of Science, Technology Sciences, Rio de Janeiro, Brazil G L Reddy, Univ of Hyderabad, Manhattan & Medicine, London, England Teri Jo Murphy, Champaign, IL India Om Parkash Kapoor, Indian Institute Guoqi Lu, Univ of South Florida, Mursaleen, Aligarh Muslim Univ, Emilio A Reyes Hernandez. of Technology. Kanpur Tampa India Matanzas, Cuba

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

Mahmut Reyhanoglu, King Fahd Vasil K Skenderi, Univ of Tirana, Valerii Vladimirovich Trofimov, Niancai Yu, Peking Univ, Beijing, Univ of Petroleum & Minerals, Albania Moscow State Univ, Russia People's Republic of China Dhahran, Saudi Arabia Sergei Yuryevich Slavyanov, Saint Carlos Alberto Trujillo Solarte, P P Zabreiko, Minsk, Belarus Nelson G Rich, Nazareth College of Petersburg State Univ, Russia Madrid, Spain Vladimir Grigoryevich Zadorozhnii, Rochester, NY Lech Andrzej Slawik, Cracow, David C Trunnell, Xavier Univ, Univ PMM, Voronezh, Russia A Perez Blackaller Rod!igo, Poland Cincinnati, OH Filareti Zafiropoulos, Univ of Patras, Xochimilco, Mexico Andrei Leonidovich Smirnov, St Martha A Tucker, Univ of Greece Jiri Rohn, Charles Univ, Prague, Petersburg, Russia Washington, Seattle Afaf A Zagrout, Cairo, Egypt Czech Republic Alexei Alexeevich Solyanik, Odessa, James Clarence Turner, Ohio State Albert D Zain, Livonia, MI Yak:ov A Roitberg, Chernigov Ukraine Univ, Columbia Edward Juan Zaldivar, Houston, TX Pedagogical Institute, Ukraine Gregory Scott Spradlin, Univ of Daniel Turzik, VSCHT, Prague, Ignacio Zalduendo, Univ de Natalia B Romalis Reyiblatt, Wisconsin, Madison Czech Republic San Andres, Buenos Aires, Chicago, IL V K Srivastava, Lucknow Univ, Fidelis Ifeanyi Ugwuowo, Univ of Argentina Edward R Rozema, Univ of India Nigeria, Enugu State Aleksandar Zatezalo, Univ of Tennessee at Chattanooga Richard J Stanley, Berkeley, CA Nina N Uraltseva, Saint Petersburg Minnesota, Minneapolis Konstantin Gr Rubinstein, Moscow, Gheorghe Gh Stefanescu, Institute of Univ, Russia Hao Zhang, Michigan State Univ, Russia Mathematics of the Romanian Alexander Victorovich Vakulenko, East Lansing Karen Rudie, Queen's Univ, Academy, Bucharest Rostov-on-Don, Russia Zhenxiang Zhang, Anhui Normal Kingston, Ontario Canada Neelacanta Sthanumoorthy, Univ of Jeffrey Mark VanDerkam, Durham, Univ, Wuhu, People's Republic Galo Ruiz-Soto, Mexico, Mexico Madras, India NC of China Deborah K Rummel, Spearfish, SD Aleksander Strasburger, Univ of Jennifer Vanden Eynden, Champaign, Andrej A Zolotykh, Moscow State Eugenii M Russakovskii, Kharkov, Warsaw, Poland IL Univ, Russia Ukraine Ivan Straskraba, Czech Academy Vladimir Vasilevich Vasin, Institute Zhong Zhu Zou, Huaihua Teachers Lev V Sabinin, Moscow, Russia of Sciences, Prague, Czech of Mathematics & Mechanics, College, Hunan, People's Marcelo Jose Saia, UNESP, Rio Republic Ekaterinburg, Russia Republic of China Claro, Brazil Robe1t K Stump, Muhlenberg Dmitri Vladislavovich Vassilevich, Yuri A Zuev, Russian Academy of Viacheslav N Salii, Saratov, Russia College, Allentown, PA Saint Petersburg Univ, Russia Sciences, Moscow M V Samokhin, Moscow, Russia Kenneth W Sublett, Lexington, KY Monica J Vazirani, Berkeley, CA Jovisa D Zunic, Univ of Novi Sad, A A Sapozhenko, Moscow State P V Subrahmanyam, Madras, India Jacob Johan Casper Vermeulen, Univ Serbia Fda Silva, State Univ Univ, Russia Tamara G Sukacheva, Novgorod, of Cape Town, Rondebosch, Pantaleao A of New York at Stony Brook Rodney EITic Saulsberry, Austin Russia Republic of South Africa Clarksville, Victor H de Ia Pena, Columbia Univ, Peay State Univ, Sergei K Suslov, Kurchatov Institute Mathukumalli Vidyasaqar, Center New York, NY TN of Atomic Energy, Moscow, for Artificial Intelligence & Matthias Scherzer, Chemnitz, Russia Robotics, Bangalore, India Germany Laura R C Suzuki, Fairborn, OH A K Vijayarajan, Indian Statistical Lynn Schmitt, Chaswick, PA Ramdorai Svjatha, Ohio State Univ, Institute, Bangalore Vasiliy Igorewitch Sedenko, MEMBERS Columbus, OH Luc Vinet, Univ of Montreal, RECIPROCITY Rostov-on-Don, Russia Robert E Swihart, Worthington, OH Quebec, Canada Croatian Mathematical Society Nick Grigorevich Semeiko, Kiev, S A Tersenov, Institute of Boikov I Vladimirovich, Penza, Ukraine Davor Kondenar Mathematics, Novosibirsk, Russia Tanya Ann Seph, Norwalk, CA Deutsche Mathematiker-Vereinigung Russia Eva F Wailes, Northampton, MA Julie Ann Sety, Chewelah, WA e. V. Ithaca, Yan Ming Wang, Zhongshan Univ, Richard J Sgroi, New Windsor, NY Rekha R Thomas, NY Prairie View A Guangzhou, People's Republic of Jurgen Buser Romyar Thomas Sharifi, Berkeley, Evelyn E Thornton, &MUniv, TX China Joachim Hilgert CA James Oran Warren, Friona, TX Som Datt Sharma, Univ of Jammu, Tiffany J Thornton, Orlando, FL Korean Mathematical Society Michael S Waters, New Richmond, India Venugopal Thothathri, Madurai Tae-Geun Cho Vishnu Dutt Sharma, Indian Institute Kamaraj Univ, India OH Chang Han Kim Hollins College, of Technology, Bombay Karen R Thrash, Hattiesburg, MS David G Weinman, Yong Soon Shin Chris P Tlu:on, Univ of Kentucky, Roanoke, VA Galina A Sharshanova Hodareva, of Japan Lexington Matthew George Weiss, Mahwah, NJ Mathematical Society Kharkov, Ukraine Yasuhiro Asoo Nabil T Shawagfeh, Univ of Jordan, Alexander S Tikhomirov, Yaroslav Volkmar Welker, Institute for Shuichi Jimbo Amman State Pedagogical Univ, Russia Experimental Mathematics, Zinovi Sheftel, Pedagogical Univ, Edward Timsans, Ontario, CA Esseu, Ge1many Tak:uya Sobukawa Chernigov, Ukraine Vladimir Vladimirovich Lisa M Werner, Baldwin-Wallace Tetsuya Takahashi Berea, OH Myroslav Mykolayovych Sheremeta, Tkachuk, Univ Autonoma College, Norsk Matematisk Foreningros Kim Renee White, Frankfort, KY Lviv, Ukraine Metropolitana-lztapalapa, Berner Larsen Michael Andrew Sherry, Cincinnati, Mexico Darlene Whitkanack, Sycamore, IL Societe Mathematique de France OH Valentin N Tkhai, Khimki, Russia Elaine Virginia Williams, Dallas, TX Ilia A Shishmarev, Moscow State Vadim A Tolokonnikov, Rheinweiler, Nikki L Williams, Atlanta, GA Daniel Barlet Univ, Russia Germany Ronald Dee Winn, Nacogdoches, TX Christian Blanchet Gendelman Oleg Shlomo, Institute Alexander Tovbis, West Virginia Tady H Woods, Albuquerque, NM ThieiTy Delbecque of Energy Problems of Chemical Univ, Morgantown Heather J Woolf, Pickerington, OH J P Demailly Physics, Moscow, Russia Nelson C E Townsend, Lawrence, Jie Xiao, Beijing Normal Univ, Gerard Duchamp Veniarnin Boris Shteinbuk, Riga KS People's Republic of China Jean-PieiTe Duport Technical Univ, Latvia Dong Dao Tran, Hue Univ of Askhab Ya Yakubov, State Univ of Henri Gaudier Pedagogy, Vietnam Chechen Republic, Grosnyi, B G Sidharth, B M Birla Science Andre Goldman Center, Hyderabad, India Dielu Cong Trinh, Pedagogical Russia Denis Hemard Grigory Sindalovsky, Moscow, Institute, Ho Chi Minh-City, Dmitry V Yak:ubovich, Univ Russia Vietnam Autonoma de Madrid, Spain Alan HucklebeiTy Anand Prakash Singh, Univ of Mukut Mani Tripathi, Lucknow Zikun Yan, Fujian, People's Republic Patrice Le Calvez Jammu, India Univ, India of China Jean-Claude Mitteau Rani Siromoney, Madras, India L Trlifaj, Prague, Czech Republic Hong Yang, Princeton, NJ Jean Pascal Ollivry

SEPTEMBER 1994, VOLUME 41, NUMBER 7 873 , , ...... _,_,_,_, __ ,_,_, __ ,.,, ...... ______.. _,_,_,_,_,_,_,_,_,_, ...... New Members of the AMS

Richard Perez Marco Dalhousie University Reed College Yuka 0 Hughes Bruno Seznec Mohammad S Chowdhury J Bruce Fields Kathleen Michelle McGarvey Jean-Louis Verger-Gaugry Florida State University George Wilfred Wright Barry Joseph Monk Societe de Mathematiques Appliquees Laurent Auriault SUNY, College at BIVckport Yaodong Wang et Industrielles Brian Harvey Felkel Michael J Acton University of Ari::ona Christian Lecot Chitra Jain Richard M Hollenbeck Michael Edward Shea Southeast Asian Mathematical Society Srinivas Narasimhamurthy Yao Li University of California, Berkeley Pak-Hong Cheung Michelle Anne Ragle Marcy L Plummer Arthur A Drisko Fengping Wen Dora Lea Ras Unione Matematica Italiana University of Chicago Giorgio Faina Georgetown University San Francisco State University Jordan A Samuels Joseph E Shashaty Charles S Rambo Giovanni Giachetta University of Hartford Carlo Petronio Louisiana Tech University Simon Fraser University Lynda L Ledder Sathiamngalam Aijunan Aruliah Francesco Serra Cassano Seshadri S Dhavide Unh·ersity of Missouri-Kansas City Tamara Dakic Wiskundig Genootschap Jzan Yu Judit Kardos State Unh·ersity Heidi Elizabeth Grunwald Peter de Jong Michigan University of Southern California Chen YLu Jun lljin Park Serna Salur Guohua Min Yusheng Qin University of Texas at El Paso Millersville University of Pa NOMINEE MEMBERS Hongjian Shi Jiazheng He Richard E Yensev Boston College Daniel Lvovich Tchertok Ju Li Naval Postgraduate School Jacqueline T H Tran Hongchang Tian Yan-Wen Wang Thomas Thaddeus Koesters Guo Wei California State University, Chico Xianfu Wang New Jersey Inst of Tech Qiang Zuo Dennis I Goslin Texas A & M Univ-Kingsville Yanping Wang University of We stem Ontario Cleveland State University George Steele Boatright Nicholls State University Zhuo Li James Allen Halamek Union College Louise Anne Faucheux David J Medd College of Staten Island, CUNY Devra A Eskin Northeastern University VPI & SU Koohye Chung Wendy T Liebeck Arkady Dmitrievich Berenstein Giles S Levy Andrew M Comba Holly J McCall Leaderson Brutus John Paul Crowdell United States Naral Academy Western Illinois University Shannon Rebecca Leckey Oakland University Daniel P Moloney Mohammad Ali Al-Shehri Spellman Ibrahim Bin Jusoh John M Panettiere Amy E University of Alabama-Tuscaloosa Sharareh Tabrizi Balasu Saravanabavan Pennsylvania State University, Brett Anthony Bagwell Nicodemo Schipano Uni1•ersity Park Jason Scott Briley Wichita State University Daemen College Michael Geoffrey Herstine Yuhong Feng Ilia Vitalyevich Bouchouer Andrew Paul Dansereau Randolph Macon Woman's College Jeffrey Wayne Hanvey Steven M Kautz Timothy H Hodge

Topological Invariants of Plane Curves and Caustics V.I. Arnold

This book describes recent progress in the topological study of plane curves. Arnold describes applications to the geometr of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theoren of elementary plane geometry to estimates on the minimal numbe:· >JE ,,.,."P"" =-"'-'-v"""'axy· ,fu-..tlv-•"--v

1991 Mathematics Subject Classification: 53, 57, 58 ISBN 0-8218-0308-5, 60 pages (softcover), July 1994 Individual member $18, List price $30, Institutional member $24. To order, please specify ULECT/SNA

All prices subject to change. Free shipment by surface: for air delivery. please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston. MA 02206-5904. or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

874 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

SUGGESTED USES for classified advertising are positions available, books or lecture notes for Applicants should have an earned doctorate sale, books being sought, exchange or rental of houses, and typing services. or equivalent, strong administrative skills, an THE 1994 RATE IS $70 per inch on a single column (one-inch minimum), calculated from the established record in research, and a commit­ top of the type; $40 for each additional 1h inch or fraction thereof. No discounts for multiple ads or ment to excellence in teaching, research, and the same ad in consecutive issues. For an additional $10 charge, announcements can be placed other scholarly activities. Candidates in all ar­ anonymously. Correspondence will be forwarded. eas of applied mathematics will be considered. 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There are no member discounts are National Merit Scholars. The curriculum for classified ads. Dictation over the telephone will not be accepted for classified advertising. emphasizes breadth in science and engineering DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising with a commitment to studies in the humanities Department. and social sciences. The program is rigorous U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, and designed to prepared students for industry religion or national origin. "Positions Available" advertisements from institutions outside the U. S. as well as graduate study. Change magazine cannot be published unless they are accompanied by a statement that the institution does not reports that HMC was the first in the country in discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific the percentage of its alumni who earn Ph.D.s. wording may be found near the Classified Advertisements in the January and July/August issues The college has an enrollment of 630 and is as­ of the Notices. sociated with four other undergraduate colleges SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians and a graduate school in Claremont, forming an are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) academic community of about 5,000 students. in the U.S. and Canada, or 401-455-4084 worldwide, for further information. Faculty at HMC may also have an appointment SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, to the graduate school faculty and can advise Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street, doctoral students in research. HMC has eleven Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not mathematics and five computer science faculty required to do so. AMS FAX 401-455-4004. and the Claremont Colleges combined have a total of forty-eight mathematics and computer science faculty. The department has an ex­ POSITIONS AVAILABLE among students, faculty, staff, administrators, cellent network of both office and laboratory alumni, and industry. Required qualifications: computer workstations. possess an earned doctorate; a record of re­ Harvey Mudd College is an affirmative ac­ search, teaching, and scholarship to support a tion, equal opportunity employer. Minority and ===,,,::~:-:~£AriFoBFJE:~== senior faculty appointment; and three or more women candidates are especially encouraged to apply. Preference will be given to applica­ CALIFORNIA STATE years of successful administrative experience tions received by December 1 , 1994. Applicants POLYTECHNIC UNIVERSITY requiring academic leadership and stewardship. Candidates will be judged on demonstrated should be prepared to have three letters of refer­ Pomona, California leadership ability within a decentralized mode ence sent upon request and send a curriculum Dean, College of Science of administration, and developing good working vitae, a description of their research, teaching, and administrative experience, to: California State Polytechnic University, Pomona, relations with people from diverse specialties. Professor Robert Borrelli Calif. is seeking applications and nominations Date of appointment: July 1, 1995, but willing to Search Committee Chair for dean of the College of Science. Req. negotiate a later date. Salary: Commensurate Department of Mathematics qualifications: earned doctorate; record of re­ with qualifications and experience; attractive Harvey Mudd College search, teaching and scholarship to support benefits package included. Committee consid­ Claremont, CA 91711 a sr. faculty appt.; three or more yrs. of ad­ eration of completed applications will begin min. experience requiring academic leadership November 1, 1994, and will continue until po­ and stewardship. Application/job description call sition is filled. Address nominations or requests 909-869-3409; FAX: 909-869-4395 or e-mail to: to: Dr. Sidney A. Ribeau, vice president for UNIVERSITY OF CALIFORNIA, LOS [email protected]. AAiEOE. academic affairs, California State Polytechnic ANGELES University, Pomona, CA 91768-4016; or e-mail Department of Mathematics to: [email protected]. AAiEOE Regular Positions in Pure and Applied Mathematics CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA HARVEY MUDD COLLEGE The UCLA Department of Mathematics invites Dean of the College of Science Department of Mathematics applications for three or more tenure-track Senior Position in Applied Mathematics positions in pure or applied mathematics. Ex­ Applications and nominations for the position ceptional promise in research and teaching is of Dean of the College of Science are invited. The department invites qualified candidates who required. Positions are initially budgeted at the The position reports to the vice president for can provide leadership in applied mathematics assistant professor level, but sufficiently out­ Academic Affairs. Duties and responsibilities: to apply for a senior position, which will begin standing candidates will be considered at higher highly responsive to student and faculty aca­ July 1, 1995. levels. Specific search areas are: statistics; ap­ demic needs; must be able to communicate The successful candidate will be eligible plied and computational mathematics; logic; ge­ the strengths and accomplishments of college for appointment to the rank of associate or ometry, topology and dynamical systems; anal­ departments to external forums; responsible full professor, and is expected to assume a ysis and differential equations; algebra, number for fiscal and personnel management, strategic term as department chair in the near future. theory and combinatorics; mathematical devel­ planning, development and advancement, pro­ The anticipated hiring of several new faculty opments arising from physics. Teaching load is moting excellence in teaching and research and members over the next five years will give the an average of 4.5 quarter courses per year. educational equity efforts; and play a critical role successful candidate a unique opportunity to Positions are subject to availability of resources in building productive long-term relationships have a strong hand in shaping the department. and administrative approval. To apply, send

SEPTEMBER 1994, VOLUME 41, NUMBER 7 875 ------·-.. ·------·------·------···-·---- Classified Advertisements

electronic mail to search@math. ucla. edu year 1995-1996, contingent upon availability of Mathematics and Computer Science has nine or write to John Garnett, chair, Department funds. full-time and two part-time faculty members who of Mathematics, University of California, Los Applications should be sent to the Empha­ are active researchers and teach courses in Angeles, CA 90024-1555. Attn: Staff Search. sis Year secretary, Department of Mathematics, mathematics, computer science, and statistics. UCLA is an equal opportunity/affirmative action Northwestern University, Evanston, IL 60208- Normal annual teaching load is five courses, one employer. 2730, and include a curriculum vitae and three of which may be during the January Program. letters of recommendation. In order to ensure full Colby is an AA/EO employer and encourages consideration, an application should be received applications from women and minorities. by January 15, 1995. Northwestern University The campus of 700 acres is on the outskirts GEORGIA is an affirmative action, equal opportunity em­ of Waterville, a city of 20,000. Waterville is ployer committed to fostering a diverse faculty; located on the Kennebec River in an area of GEORGIA INSTITUTE OF TECHNOLOGY women and minority candidates are especially lakes, forests, and farms. Mountains (includ­ encouraged to apply. ing Saddleback and Sugarloaf ski areas) and The School of Mathematics expects to have seacoast (including Acadia National Park) are some visiting and tenure-track positions in sev­ within a two-hour drive. Boston is approximately eral areas of applied mathematics at various a three-hour drive. levels beginning in fall 1995. Candidates with NORTHWESTERN UNIVERSITY Send nominations or applications in hard strong research and teaching records or poten­ Department of Mathematics copy to Dale Skrien, chair, Department of Math­ tial should send a resume, at least three letters 2033 Sheridan Road, ematics and Computer Science (dj skrien@ of reference, and a summary of future research Evanston, Illinois 60208-2730 colby. edu.) Review of applications will begin plan to The Hiring Committee, School of Mathe­ on October 15, 1 994, and will continue until the matics, Georgia Institute of Technology, Atlanta, Applications are invited for an anticipated position is filled. Georgia 30332-0160 U.S.A. Applications will be tenure-track assistant professor position start­ reviewed beginning November 30, 1994. Geor­ ing September 1995. Priority will be given to gia Tech, a member of the University System exceptional research mathematicians. Fields of of Georgia, is an Equal Opportunity/Affirmative interest within the department include algebra, action Employer. analysis, dynamical systems, probability, partial differential equations, and topology. Northwest­ ern is an affirmative action, equal opportunity employer committed to fostering a diverse COLBY COLLEGE ILLINOIS faculty; women and minority candidates are Department of Mathematics especially encouraged to apply. Candidates and Computer Science NORTHWESTERN UNIVERSITY should arrange that at least three letters of Department of Mathematics recommendation be sent to Prof. J. Sally, chair, We have two tenure-track openings at the assis­ 2033 Sheridan Road, Personnel Committee, Department of Mathe­ tant professor level, commencing September 1, Evanston, Illinois 60208-2730 matics, Northwestern University, Evanston, Illi­ 1995. Ph.D. required. The salary is competitive, nois 60208-2730. Initial inquiries may be sent and based on experience. Applications are invited for a newly created via e-mail to hiring@math. nwu. edu. In order Colby is a small, private, highly selective position of lecturer in mathematics starting in to receive full consideration, applications should liberal arts college located in central Maine. September, 1995. This position carries a two be received by December 15, 1994. Hiring is The student body numbers some 1, 700, the course teaching responsibility in each of the contingent upon eligibility to work in the United faculty 165. The Department of Mathematics three quarters of the academic year. The term States. and Computer Science currently numbers nine of appointment will be for one year and will full-time and two part-time, all of whom have the be renewable twice upon evidence of excel­ Ph.D. We have major and minor programs in lence in teaching. Candidates must present mathematics and computer science. solid evidence of effective teaching and quality We are a young, active department, which research. Teaching experience of at least two MAINE places a high value on both teaching and courses is expected, and teaching performance research. The annual teaching load is five COLBY COLLEGE should be substantiated, if possible, by tab­ courses. The largest class size is thirty. ulated student evaluations. Send applications Department of Mathematics For one of the openings, we prefer some­ and three letters of reference to chairperson, and Computer Science one with a pure mathematics background. For Personnel Committee, Department of Mathe­ Waterville, Maine 04901 the other position we prefer someone with matics, Northwestern University, Evanston, IL a strong computer science and mathemat­ Carter Professor of Mathematics and 60208-2730. Initial inquiries may be sent to: ics background. Candidates who are able to Computer Science [email protected]. In order to receive full demonstrate excellence in teaching are likely to Colby invites nominations and applications for consideration, applications should be received be ranked higher in our selection process. Carter Professor of Mathematics and Computer by December 15, 1994. Northwestern Univer­ Colby actively encourages applications from Science, effective September 1, 1995. Neces­ sity is an Equal Opportunity/Affirmative Action women and minority candidates. We are an sary qualifications include: a Ph.D. in math­ employer and encourages applications from EO/AA employer. ematics or computer science; a distinguished minority and women candidates. Review of applications will begin on De­ career as scholar and teacher; commitment to cember 10, 1994, and will continue until the liberal arts, undergraduate mathematics, and positions are filled. computer science education. Send a letter of application and a current cur­ NORTHWESTERN UNIVERSITY The Carter Professorship is an endowed riculum vita in hard copy to: Dale Skrien, chair, position for a nationally recognized scholar Department of Mathematics Department of Mathematics and Computer and teacher. The Carter Professor is expected 2033 Sheridan Road, Science, Colby College, Waterville, Maine to maintain a distinguished research program Evanston, Illinois 60208-2730 04901 ([email protected]). Also, arrange for and teach undergraduate mathematics, sta­ three letters of reference to be sent to the same The mathematics department will sponsor an tistics, and/or computer science classes and address. These letters should deal with both Emphasis Year in analysis/applied analysis. participate in the departmental programs. The your research and your teaching abilities. This program will include two two-year assis­ Professorship includes funds for research and tant professorship positions starting September travel. 1995, and possible visiting positions for more Colby is a highly selective college of 1,700 senior mathematicians for part of the academic students and 165 faculty. Its Department of

876 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______Classified Advertisements

220 Maryland Hall RUTGERS UNIVERSITY-NEWARK MARYLAND Baltimore, Maryland 21218-2689. Assistant Professor of Mathematics Applications are requested by January 15, INSTITUTE FOR DEFENSE ANALYSES 1995. The Department of Mathematics and Computer SUPERCOMPUTING RESEARCH CENTER Science invites applications for an anticipated t~nure-track assistant professor position begin­ Applications are invited from Ph. D. level math­ mng September 1995. Candidates must have ematicians, statisticians, computer scientists, a Ph.D., have a strong research record, and and electrical engineers for research positions be able to demonstrate outstanding promise, on our technical staff. Initial appointment would MASSACHUSETTS as well as a commitment to effective teaching. be for one or two years, possibly leading to Research interests of the department include a permanent position. Wide interests, and the WILLIAMS COLLEGE th~ following: representation theory, automor­ ability to motivate one's own work are more phic Department of Mathematics forms, number theory, low dimensional important than knowledge of specific technical topology, Riemann surfaces, and algebraic ge­ Williamstown, Massachusetts areas. 01267 ometry. Additionally, we also organize each year a Anticipated tenure-eligible position in mathemat­ Applicants should arrange for a curriculum summer program for which places are available ics or applied mathematics, beginning fall 1995, vitae and at least four letters of recommen­ in 1995. proba~ly at the rank of assistant professor; in dation, including one which addresses teach­ Salaries will be competitive and commensu­ exceptional cases, however, more advanced ing •. to be sent to William Keigher, associate rate with experience and qualification. appointments may be considered. Excellence cha1r, Department of Mathematics and Com­ IDA/SRC is an equal opportunity/affirmative in both teaching and research is essential; a puter Science, Rutgers University, Newark, NJ, action employer, and encourages application doctorate is required. 07102. Responses may also be a-mailed to from women and members of minority groups. Please have a vita and three letters of mathl1landromeda. rutgers . edu. Processing Send resume and publication list to: recommendation on teaching and research sent of applications will begin in December 1994. Dr. D.B. Heifetz to Hiring Committee. Evaluation of applications Rutgers University is an equal opportu­ Deputy Director will begin November 15 and continue until nity/affirmative action employer. IDA/SRC th~ position is filled. As an EEO/AA employer, 17100 Science Drive W1lhams especially welcomes applications from Bowie, MD 20715-4300 women and minority candidates. U.S. citizenship required.

STATE UNIVERSITY OF NEW YORK AT BUFFALO THE JOHNS HOPKINS UNIVERSITY Department of Mathematical Sciences WILLIAMS COLLEGE The Department of Mathematics anticipates the appointment of tenured or tenure-track fac­ The Department Department of Mathematics of Mathematical Sciences at ulty members beginning September 1, 1995. t~e Johns Hopkins University invites applica­ Williamstown, Massachusetts 01267 Salary will be competitive. We see applicants tions for an anticipated faculty position to begin in all areas with excellent research accomplish­ in fall The core areas Anticipated visiting position for the 1995-96 1995. of the department ments/potential and a strong commitment to are discrete mathematics, year, probably full-time, probably at the rank matrix and numerical teaching. analysis, operations research and optimization, of assistant professor, in exceptional cases, Applicants should send supporting informa­ and probability and statistics. Candidates with however•. more advanced appointments may tion, including a c.v. with a list of research a strong background in one of these areas be considered. Excellence in teaching and interests, and have four letters of recommenda­ or in the area of numerical research, and doctorate expected. Please have mathematics are tion sent to: encouraged vita and three letters of recommendation on to apply. We especially welcome Search Committee Chairman applicants who can interact effectively teachi~g and research sent to Visitor Hiring with fac­ Department of Mathematics ulty .and stu~ents in the Committee. Evaulation of applications will begin School of Engineering, SUNY/Buffalo particularly 1n such thrust areas as information ~o~ember 15 and continue until the position 106 Diefendorf Hall biomedical, environmental, and materials IS f1lled. As an EEO/AA employer, Williams sci~ 3435 Main Street ences. A broad and outstanding mathematical especailly welcomes applications from women Buffalo, New York 14214-3093 background is essential. Applicants at all levels and minority candidates The deadline for applications is November 1, will be considered. Selection will reflect demon­ 1994. Late applications will be considered until stration (for senior applicants) and promise positions are filled. (for junor applicants) of excellence in research, SUNY/Buffalo is an Equal Opportunity/Affir­ teaching and innovative applications. A Ph.D. mative Action Employer. We are interested degree is required. Applications in the areas in identifying prospective minority and women of algebra, analysis, geometry, number theory, candidates. No person, in whatever relationship and topology will not be accepted by the Math­ with the State University of New York at Buffalo ematical Sciences Department, which is distinct RUTGERS UNIVERSITY shall be subject to discrimination on the basis from the Mathematics Department. ~ubject to budget constraints, Rutgers Univer­ of age, creed, color, handicap, national origin, Minority and women candidates are encour­ Sit¥ - .camden expects to hire three computer race, religion, sex, marital or veteran status. aged to apply. The Johns Hopkins University sc1ent1sts (at least one senior level) and one is an Affirmative Action/Equal Opportunity Em­ f!!athematician, to start fall 1995, rank nego­ ployer. tiable. Those who can teach both math. and Applicants are requested to send initially comp. sci. are expecially encouraged to submit only a curriculum vita with a cover letter de­ letters of interest. Send a vita and arrange for scribing professional interests and aspirations. three or four letters of recommendation to be UNIVERSITY OF OKLAHOMA Recommendation letters, transcripts, preprints sent directly to J. Garver, Dept. of Mathemat­ Department of Mathematics and reprints are to be furnished only upon ical Sciences, Rutgers University, Camden, NJ request. Please address applications to: 08102. Nominations and applications are invited for the Faculty Search Committee position of chair of the Department of Mathe­ Department of Mathematical Sciences matics. The appointment is to be effective by The Johns Hopkins University the start of the fall 1995 semester or earlier.

SEPTEMBER 1994, VOLUME 41, NUMBER 7 877 ··--···------·------··------·-·------· ------Classified Advertisements

Candidates must possess an earned doctorate, PUBLICATIONS FOR SALE ] a substantial record of research achievement, PUERTO RICO a commitment to excellence in teaching, and leadership and administrative abilities appro­ UNIVERSITY OF PUERTO RICO MATH SCI PRESS, 53 Jordan Rd., Brook­ priate to a department that is dedicated to AT MAYAGUEZ line, MA 02146; 617-738-0307. Lie-Theoretic a balanced program of quality research and Department of Mathematics ODE Numerical Analysis, Mechanics and teaching. The Mathematics Department has Differential Systems by Robert Hermann, $95. over thirty faculty and approximately seventy The Department of Mathematics has a tenure­ In Preparation: C-0-R Generalized Function graduate students. There are active research track opening for an assistant professor in the Algebras and Current Algebras. programs in a wide range of topics. The scientific area of applied mathematics, with emphasis activity of the department is further enhanced in numerical methods and inverse problems by a substantial endowment for discretionary in nonhomogeneous bodies. The salary is funds. The department offers programs for the $27,420 per year. Fluency in spoken and written I PUBLICATIONS WANTED bachelor's, master's, and Ph.D. degrees. Can­ Spanish or English, a Ph.D., and at least one didates should send a cover letter, vita, selected year of academic or industrial experience are reprints, and names and addresses of four required. The appointee will be expected to Wanted: Mathematical books, journals, reprints, references (at least one of whom could address teach graduate and undergraduate courses and ephemera. Contact R. K. Dennis, Math. Dept., the candidate's administrative abilities) to: to do research. White Hall, Cornell U., Ithaca, NY 14853-7901. Dr. Paul Goodey, Chair Search Send resume and three letters of recom- Tel: 607-255-4027, FAX: 607-255-7149. e-mail: Committee mendation to: [email protected] Department of Mathematics Dr. Darrell W. Hajek University of Oklahoma Acting Director Norman, Oklahoma 73019-0315 Department of Mathematics- UPR Screening will begin on November 1, 1994, P. 0. Box 5000 Mayaguez, PR 00681-5000 r: :: I and continue until the position is filled. The University of Oklahoma is an Equal Op­ Mathematics Professor, Ph.D. 1989. Specialty: portunity/Affirmative Action Employer. Women Algebra. Two published articles. Five years and minorities are encouraged to apply. OU has teaching experience. Willing to retrain for indus­ a policy of being responsive to the needs of UNIVERSITY OF PUERTO RICO try. South or Midwest U.S. preferred. References dual-career couples. ATMAYAGUEZ and resume available upon request. Available Department of Mathematics immediately. Timothy P. Keller, 2718 Luce, Cape Girardeau, MO 63701. The Department of Mathematics has a tenure­ track opening for an assistant professor in the PENNSYLVANIA area of algebra and logic. Background in numer­ ical linear algebra and computer science would also be desirable. The salary is $27,420 per APPLIED MATHEMATICIAN, RESEARCH AND UNIVERSITY OF PITTSBURGH DEVELOPMENT OR TEACHING AND RE­ Department of Mathematics year. Fluency in spoken and written Spanish or English, a Ph.D., and at least one year of aca­ SEARCH. Ph.D. Speciality: Analysis. Experi­ enced in solving industrial and management The Department of Mathematics of the Uni­ demic or industrial experience are required. The problems as well as teaching and academic versity of Pittsburgh invites applications for the appointee will be expected to teach graduate research. Excellent communication skills. Inter­ position of department chairperson, beginning and undergraduate courses and to do research. nal reports, published articles and book. Any fall1995. Send resume and three letters of recom- location. Available August 1994. Robert Jolly, Located in urban Pittsburgh, the Univer­ mendation to: POB 2175, Kihei, HI 96753-2175. sity of Pittsburgh is a research university with Dr. Darrell W. Hajek approximately 10,000 graduate and 18,000 un­ Acting Director dergraduate students. The department currently Department of Mathematics - UPR has thirty-five faculty members with research P. 0. Box 5000 specialties including algebra, analysis, differ­ Mayagiiez, PR 00681-5000 Ph.D. 1980 India. Specialty: Numerical Analysis. ential equations, differential geometry, discrete Twenty-one years teaching experience. Desires mathematics, foundations, mathematical biol­ appointment immediately anywhere in the U.S.; ogy, numerical analysis, scientific computing, in the field of teaching, research, education, or relevant position; in two- or four-year colleges or and topology. Candidates should have research and teach­ GERMANY universities. Contact: Dr. M. Shakil, 3 South Pine ing credentials consistent with a tenured ap­ Island Road, Apt. 116, Plantation, FL 33324; pointment at the rank of full professor, as UNIVERSITY OF GOTTINGEN phone: 305-472-2082. well as a commitment to aggressive promo­ Institute of Mathematics tion of excellence in research and teaching The Institute of Mathematics of Gottingen in­ at all levels. Administrative experience is also vites applications for the position of professor DISTINGUISHED MATHEMATICS PROFES­ desirable. Interested parties should contact (C4, successor of Grauer!) for complex analysis Professor Charles Hall, chairperson Search SOR AND RESEARCHER (ALGEBRA, GE­ (complex geometry, algebraic geometry, com­ OMETRY). Ph.D. 1959, Dr. Sci. 1972. Ninety Committee, Department of Mathematics, Uni­ plex diff. geometry) beginning October, 1995. versity of Pittsburgh, Pittsburgh, PA 15260 publications. Founder of "Nonlinear Geometric (For the conditions of employment see §51 Algebra". Thirty-five years research and teach­ (hall@vms. cis . pitt . edu, 412-624-8379). of Nieders. Hochschulgestz.) Applications by Complete applications should include a cur­ ing experience in Russia and abroad. Super­ women and minorities are especially encour­ visor of sixteen mathematicians earned Ph.D. riculum vitae and the names and addresses aged. Applications with vita, including teaching of three references. For full consideration, in­ and Dr. Sci. Lev Sabinin, Varga Street 8, Apt. 12, experience should be sent to: Dekan des Moscow, 117133, Russia. Fax:+7(095)9540336. quiries should be received by October 15, 1994. Fachbereichs Mathematik der Georg-August­ Women and minorities are especially encour­ Universitat Gottingen, Bunsenstr, 3/5, 37073 aged to apply. The University of Pittsburgh is an Gottingen, Germany. The application deadline EO/AA employer. is October 15, 1984.

878 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Interactive TEX It WYSIWYGTEX It User-friendly TEX It

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'~ ,, ------Nonlinear World

EDITORS: V. Lakshmikantham, Melbourne, FL, USA T.G. Hallam, Knoxville, TN, USA

ASSISTANT EDITORS: L. Krishnamurthy, Melbourne, FL, USA N.S. Papageorgiou, Melbourne, FL, USA

HONORARY EDITORS: J.L. Lions, Paris, France • G.l. Marchuk, Moscow, Russia Yu.S. Osipov, Moscow, Russia • I. Prigogine, Austin, TX, USA

This journal is published in cooperation with the International Federation of Nonlinear Analysts (IFNA), which was founded in August 1991 to promote collaboration in the world community of nonlinear analysts from various disciplines. Nonli11ear World welcomes all experimental, computational and/ or theoretical advances in nonlinear phenomena, in any discipline-especially those that further our ability to analyze and solve the nonlinear problems that confront our real world. The goal is to bring together such diverse disciplines as • Aerospace Sciences • Atmospheric Sciences • Biological Sciences • Chemical Sciences • Cosmological Sciences • Economics • Engineering and Technological Sciences • Environmental Sciences • Geophysical Sciences • Mathematical Sciences • Medical and Health Sciences • Numerical and Computational Sciences • Oceanographic Sciences • Physical Sciences • Social Sciences Nonlinear World will feature papers which demonstrate multidisciplinary interaction, preferably those presented in such a way that other nonlinear analysts can at least grasp the main results, techniques, and their potential applications. In addition to survey papers of an expository nature, the contributions will be original research papers demonstrating the relevance of nonlinear techniques.

Subscription information: Nonlinear World. ISSN 0942-5608 1994. Volume 1 (4 issues): $195.00. Single issue price: $59.00 1995. Volume 2 (4 issues): $195.00. Single issue price: $59.00

Sample copy available upo11 request.

For North America: Walter de Gruyter Walter de Gruyter, Inc. 200 Saw Mill River Road Berlin • New York Hawthorne, NY 10532 Two Lectureships

Department of Mathematics, School of Mathematical & Information Sciences Volumes 13 & 14 Vacancy UAC.458

The Department of Mathematics. one of the three departments (along with Computer Science and Statistics) in the School of Mathematical & Information Idempotent Analysis Sciences. teaches a full range of under­ V. P. Maslov and S. N. Samborskii, Editors graduate and postgraduate courses. Within the Department there are two The articles in this collection show how idempotent analy­ units, the Applied and Computational sis is playing a unifying role in many branches of mathemat­ Mathematics Unit and the Mathematics ics related to external phenomena and structures-a role Education Unit, each of which operates with a certain degree of autonomy. similar to that played by functional analysis in mathematical physics, or numerical methods in partial differential equa­ The Department has particular research strength in combinatorics, group theory, tions. Such a unification necessitates study of the algebraic functional analysis and operator theory, and analytic structures appearing in spaces of functions with complex analysis, topology and numerical values in idempotent semirings. The papers collected here analysis. constitute an advance in this direction. Applicants must have a Doctorate or Mathematics Subject Classijkation: equivalent and ~hould have a proven 1991 16, 20, 35, 47. 49, 90; 81 ISBN 0-8218-4114-9, 210 pages (hardcover), December 1992 record in research and teaching in any Individual member $65, List price $108, Institutional member $86 branch of Mathematics, but preference To order, please specify ADVSOV /13NA may be given to applicants whose field of interest is allied to those of existing staff. One of the lectureships is reserved for Pure Mathematics. Commencing salary will be established within the range NZ$39,500- NZ$50,000 Nonlinear Stokes Phenomena per annum. Yu. S. Il'yashenko, Editor Further information, Conditions of Appointment and Method of Application, The nonlinear Stokes phenomenon occurs in the local should be obtained from the Academic theory of differential equations and finds application in Appointments Office, The University of Auckland. Private Bag 92019, Auckland. singularity theory. This book contains a number of papers New Zealand. telephone 64-9-373 7999 on this subject, including a survey that begins with Stokes' ext 5097. fax 64-9-373 7454. Three copies pioneering works on linear theory, and discusses the work of of applications should be forwarded to Voronin. reach the Registrar by 26 September 1994. Please quote Vacancy Number 1991 Mathematics Subject Classijkation: 32, 34, 35, 58; 43 ISBN 0-8218-4112-2, 287 pages (hardcover), February 1993 UAC.458 in all correspondence. Individual member $70, List price $116, Institutional member $93 W B NICOLL, REGISTRAR To order, please specify ADVSOV /14NA

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All prices subject to change. Free shipment by surface: for air delivery, The University has an please add $6.50 per title. Prepayment required. Order from: American equal opportunities Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll policy and welcomes free 800-321-4AMS in the U.S. and Canada to charge with VISA or applications from all MasterCard. Residents of Canada, please include 7% GST. qualified persons New from de Gruyter Motion by Mean Curvature and Related Topics

Proceedings CONTENTS of the A Phase-Field Model with a Double Obstacle Potential, ].F. Blowey and C.M. Elliott • Cahn and Hilliard Fluid on an Oscillating Boundary, G. Bouchitte and International P. Seppecher • Mathematical Models of Phase Boundaries in Alloys: Phase Conference Field and Sharp Interface, G. Caginalp and W. Xie • New Ideas in Calculus of Variations and Geometric Measure Theory, E. De Giorgi • The Minimum Time held in Trento, Problem and Its Applications to Front Propagation, M. Falcone • Planar Motion of an Anisotropic Interface, M.E. Curtin • Singular Limit for an Allen-Cahn July 20-24, 1992 Equation with a Nonlocal Term, D. Hilhorst, E. Logak, and Y. Nishiura • Axiomatization of Shape Analysis and Application to Texture Hyperdiscrimination, C. Lopez andj.M. Morel• Variational Approximation of Giuseppe Buttazzo and the Geometric Motion of Fronts, R.H. Nochetto, M. Paolini, S. Rovida, and C. Augusto Visintin, editors Verdi • On Radial Growth in Crystallization Theories of Hyperbolic Nature, P. Podio-Guidugli and G. Vergm·a Ca.ffarelli • Physics and Geometry of Flow Under Curvature: Singularity Formation, Minimal Surfaces, Geodesics, and 1994. viii + 219 pages. With 64 figures. Surface Tension, ].A. Sethian and D.L. Chopp • Computing Hypersurfaces 3-11-013881-6. Cloth $98.95 Which Minimize Surface Energy Plus Bulk Energy, j.M. Sullivan • Boundary Regularity for Flows of Nonparametric Surfaces Driven By Mean Curvature, N.N. Uraltseva • Some Questions of De Giorgi about Mean Curvature Flow of Triply-Periodic Surfaces, B. White Algebra and Number Theory

Proceedings CONTENTS of a Conference Strict Factorisability and Shadows, A. Frohlich • Frobenius Order­ Sequences of Curves, A. Garcia and M. Homma • Discriminants of held at the Institute Hermitian R[G]-Modules and Brauer's Class Number Relation, E. Kani • On for Experimental Coverings of Elliptic Curves, G. Martens • On Artin-L-Series of Irreducible Mathematics, University Characters of the Symmetric Group Sn> G.O. Michler • Higher Bmhat-Tits Buildings and Vector Bundles on an Algebraic Surface, A.N. Parshin • 1/2 ofEssen (Germany), Riemann Existence Theorem with Galois Action, F. Pop • On a Variation December 2-4, 1992 of Hilbert's 17th Problem, A. Prestel • On the Local Galois Stmcture of S-Units, ]. Ritter and A. Weiss • Abelian Varieties, p-Adic Heights and Derivatives, K. Rubin • The Tate Conjecture for Non-Simple Abelian Gerhard Frey and Varieties over Finite Fields, Yu. G. Zarhin Jiirgen Ritter, editors

1994. x + 296 pages. 3-11-014250-3. Cloth $119.95 Prices subject to change.

For North America: Walter de Gruyter Walter de Gruyter, Inc. 200 Saw Mill River Road Berlin • New York Hawthorne, NY 10532 Program Officer "f 0 SCIENCE AND ENGINEERING z I'll The Board on Mathematical Sciences of the National Research FELLOWSHIPS IN JAPAN Council (NRC) seeks a dynamic individual as a full.time Program :.- + Officer to cany out strategic studies in disciplinary areas of the liNDA~' mathematical sciences, in interdisciplinary areas, and in education. Responsible for organizing and managing projects, assisting in The National Science Foundation (NSF) offers opportunities for identifying prospective committee members, establishing and research• in Japanese universities, national research institutes, and maintaining liaison with researchers, policy makers, sponsors, etc., corporate research facilities. Applicants must be U.S. citizens or writing background papers, technical summaries, and permanent residents. interim/final reports, contributing to deliberations, preparing and revising report drafts, and developing proposals for future proj~. fellowship programs are conducted in cooperation with the Activities will include, among others, the Committee on Applied These and Theoretical Statistics, and projects on Statistics Research for Center for Global Partnership (CGP) and other Japanese organizations. Massive Data Sets and Statistics in the 21st Century. Awards are available for graduate students, postdoctoral fellows, and senior investigators for 3-24 month research visits in Japan for The successful candidate will be an innovative, entrepreneurial (deadlines are indicated in parentheses): individual with a PhD in Statistics (preferred), or in Probability, Applied Mathematics, Operations Research, Scientific Computing, • Long and Medium Term Research (November 1, Aprill) or Pure Mathematics, and at least two years of relevant experience. • Short Term Visits for Cooperative Research (May 15) Must possess strong background and interests in statistics and in • Dissertation Enhancement (November 1, Aprill) the entire spectrum of the mathematical sciences community, and • Summer Institute for Graduate Students in Science and have demonstrated effectiveness in written and oral communication, Engineering (December 1) especially in preparing scientific and technical reports, research writing, briefing technical experts, and coordination with research sponsors. Prior experience in relevant administrative Awards are also available for Bilateral Seminars in Japan or the United areas desirable, as is experience in or with federal agencies. States (May 15). Application review will begin immediately. Please send applications to: NRC/CPSMA/BMS, NAS 315 (JT), 2101 To apply for these programs, you may request the program Constitution Avenue, NW, Washington, DC 20418. TEL: announcement "International Opportumties for Scientists and is available 202;3~4-2421, • .., 202-334-1597,~NAsl Engineers" NSF 93-51 (Revised 11/93). This publication Email: jtuck~as.edu. through STIS (Science and Technology Information System), NSF's online publishing system, described in NSF 94-4~ "SP:S flyer:" To The NRC is an Equal OpportunityI Affirmative NA.E receive a paper copy of the flyer, call the NSF Pubhcatmns SectiOn at Action Employer. Women and minorities are lQM encouraged to apply. (703)-306-H-30. For an electronic copy send an E-mail message to .r [email protected] (Internet) or stisfly@nsf (BITNET). The TDD number is (703) 306-0090.

UNIVERSITY OF OXFORD MAIL ORDER & SAVE II TEXTBOOKS & REFERENCE University Lecturership in Expert Service-Immediate Shipping Worldwide Pure Mathematics 10% Standard Academic Discount* On association with Lincoln College) Applications are invited for the above post, tenable SPECIAL OFFER from 1 October 1995. Stipend according to age, on the scale £14,756- £27,473 per annum. The NEW CUSTOMERS WILL RECEIVE successful candidate may be offered a tutorial 20% DISCOUNT ON FIRST ORDER** fellowship by Lincoln College, for which additional emoluments would be payable. To order, call TOLL FREE 800-621-1220 Further particulars, containing details of the duties and full range of emoluments and allowances Monday to Saturday: 1 Oam-6pm EST attaching to both the University and the College post, Visa/Mastercard accepted may be obtained from the Chairman of Mathematics, Catalog available Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, (telephone: Oxford (0865) 273538; fax: (0865) 273583; e­ FAX orders: (212) 675·4230 maii;[email protected]) to whom To write: 18 East 16th Street applications (1 0 copies or one only from overseas New York, NY 10003 candidates) should be sent by 21 October 1994. New York residents only add sales tax The University is an Equal Opportunity Employer. • Minimum two books ** Order limit: Three books. Offer expires Oct. 30th, 1994 ADVANCED CONCEPTS FROM CAMBRIDGE An Introduction to Twistor Theory Singularities Second Edition Lille 1991 S. A. Huggett and K. P. Tod Edited by Jean-Paul Brasse/et From a review ofthe First Edition ... Singularity theory encompasses many different aspects of geometry " ... a quick introduction to some ofthe deeper problems oftwistor and topology, and an overview of these is represented here by papers theory. .. book is recommended to anyone seeking to get acquainted given at the International Singularity Conference held in 1991 at Lille. with the area." -American Scientist London Mathematical Society Lecture Note Series 201 London Matbemattcal Society Student 'Jexts 4 1994 c. 432 pp. 46631-8 Paperback $39.95 1994 c. 250 pp. 45157-4 Hardback $49.95/45689-4 Paperback $21.95 Group Theory and Physics Introduction to Finite Fields and Sh/omo Sternberg Their Applications An introduction to group theory and its application to physics. The phys­ Second Edition ical applications are considered as the mathematical theory is developed so that the presentation is unusually cohesive and well-motivated. Rudolf Lid/ and Harald Niederreiter 1994 c. 400 pp. 24870-1 Hardback $69.95 An introduction to the theory, and its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of Geometric Differentiation switching circuits. For the Intelligence of Cuntes and Surfaces 1994 c. 400 pp. 46094-8 Hardback $47.95 I. R. Porteous Invariant Potential Theory in the Unit Ball of C" Elementary differential geometry is approached from a new standpoint Manfred Stoll inspired by Thorn's work on singularity theory. The umbilics and ridges An introduction and a survey of recent results in potential theory with of a smooth surface are here considered in detail. respect to the Laplace-Beltrami operator D in several complex varia­ 1993 c. 200 pp. 39063-X Hardback $54.95 bles, with special emphasis on the unit ball in C". London Matbemattcal Society Lecture Note Series 199 1994 183 pp. 46830-2 Paperback $29.95 Available in bookstores or from A Handbook of Categorical Algebra 40 West 20th Street Volume 1: Basic Category Theory CAMBRIDGE NewYork, NY10011-4211 Francis Borceux Call toll-free 800-872-7423 A detailed account of everything a mathematician needs to know about UNIVERSITY PRESS MasterCard/VISA accepted. category theory. Prices subject to change. 1994 c. 380 pp. 44178-1 Hardback $69.95

NEW JOURNAL FROM KLUWER ... ;;;;;;;;;;;;;;;;;; Lifetime Data An a lysis:;;;;;;;;;;;;;;; An International Journal Devoted to the Methods and Applications of Reliability and Survival Analysis Commencing with publication in 1995, Kluwer plans a quarterly journal. Editor-in-Chief Editors Mei-Ling ling Lee - Harvard University Nicholas P. Jewell - University of California, Berkeley and Brigham and Women's Hospital Alan C. Kimber - University of Surrey G. Alex Whitmore - McGill University Scope: The objective of the journal is to advance and promote statistical science in the various applied fields that deal with lifetime data, including: Actuarial Science • Economics • Engineering Sciences • Environmental Sciences • Management Science Medicine • Operations Research • Public Health • Social and Behavioral Sciences The goal of the editorial board is to have fast dissemination of papers. Authors will receive an initial editorial decision within four months of submission.

'-UII lUI rUJJt::l:>. Karen Cullen ~~ Kluwer Academic For Instructions to Authors and Lifetime Data Analysis Where to submit Manuscripts PH: 617-871-6300 '" Publishers for Lifetime Data Anal sis - FX: 617-878-0449 101 Philip Drive ISSN 1380-7870, please contact: EM: [email protected] Norwell, MA 02061 ==~~. MASSEY Translations of \\\\~~} UNIVERSITY

,___ MATHEMATICAl. MONOGRAPHS ---1 Massey University Is an Volume 123 innovative aca,demic institution with a proud history of growth since its foundation In 1927. Today, through its nine faculties and three schools itteaches over Elie Cartan (1869-1951) 12,000 fulltime equivalent students in New Zealand and M. A. Akivis and B. A. Rosenfeld throughoutthe Pacific Basin. The Masser. campus is situated in beauti ully landscaped grounds This book describes the life and achievements of the great in a parklike setting surrounded French mathematician, Elie Cartan. Here readers will find by University farmland. The City of Palmerston North (population detailed descriptions of Cartan's discoveries in Lie groups 70,200) is centrally located in and algebras, associative algebras, differential equations, and the southern half of the North differential geometry, as well as later developments Island, and hosts four tertiary education institutions and stemming from his ideas. The volume includes a biograph­ several major government and ical sketch of Cartan' s life. A monumental tribute to a private research institutions. The lifestyle is cosmopolitan but towering figure in the history of mathematics, this book will relaxed and friendly. appeal to mathematicians and historians alike. POSTDOCTORAL 1991 Mathematics Subject Classification: 01 FELLOWSHIP ISBN 0-8218-4587-X, 317 pages (hardcover), June 1993 Mathematics lndiv. member $92, List $153, Inst. member $122 Department To order, please specify MMON0/123NA This fellowship in Mathematics is designed to contribute to research programmes in the area of algebraic geometry in collaboration with .,.,~"""'0~ All prices subject to change. Free shipment by surface; for air delivery, Professor W Vogel, Professor of Pure /[1],"""""'; <~ please add $6.50 per title. Prepayment required. Order from: American Mathematics. This position, tenable for \ ~ ~ § Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call up to two years from 1 April 1995, is ·"' @: toll free 800-321-4AMS in the U.S. and Canada to charge with VISA or designed to extend the Department's 00 " 0 " 0 ' MasterCard. Residents of Canada, please add 7%GST. activities in the area of Pure Mathematics and Algebraic Geometry especially. The research group, headed by Professor Vogel is working on problems in the area of intersection theory. Enquiries of an academic nature can be directed to Professor Vogel in the Department (email W.Vogel® massey.ac.nz; phone (64) 6 350-5391). Please do not forward your application by email to Professor Vogel. Please refer to the instructions at the bottom of the advertisement. Reference number: NAMS 50/94 must be quoted. ARC RESEARCH FELLOW /SENIOR RESEARCH FELLOW Closing Date: 30 September 1994. An information package including School of Mathematics and Statistics Conditions of Appointment are (Renewable) obtainable by phoning(64) 6 356-9099, Reference No: A25/01 ext 7318. The successful applicant will be part of the ARC funded project 'Group Representation Theory and Cohomology of Algebraic Varieties'. Preference will be given to applicants with expertise in all or some of the following areas: Ue and algebraic groups, geometJy and Applications, including a full curriculum topology of manifolds; group representation on cohomology spaces, Schubert varieties; Heeke algebras, hyperplane complements. vitae and the names, addresses and Applicants should have, or expecl to receive shortly, a PhD or equivalent quaiHication, and should have a strong record of publication of original research in the area. facsimile numbers of three referees The School has a large network of high pe~ormance work stations to support both research and teaching. should be sent to Mrs V B Bretherton, The position Is available for 12 months in~ially, with the possibility of renewal for up to a further 3 years, subject to need and funding. Personnel Section before the closing For further Information contact Professor G Lehrer on (612) 692 2976, fax on (612) 692 4534 . eman on [email protected]. Salary: ARC Research Fellow A$41 ,000- $48,688 p.a. date specified. ARC Senior Research Fellow A$50,225- $57,913 p.a. We are an Equal Opportunity Employer. Method ol.appllcatlon: Three copies of the application, quoting Reference No, including curriculum vitae, list of publications and the names, addresses and fax numbers of at least three and not more than five referees to: The Personnel Officer (Group A), Carslaw Building, (F07), The University of Sydney NSW 2006, Australia, by 6 October 1994. Private Bag 11-222 Equal employment opportumty and no smokmg m the workplace are Un1vers1ty pol•c•es :2 The Un1vers1ty reserves the nght not to proceed w1th any appomtment for fmanc1al or other reasons ~ Palmerston North • New Zealand Telephone (64) 6 356-9099 Fax (64) 6 350-5615 Jo~ of~pp(~l 9WtttihPeWWJ.tics Wl1lJi Sto~ ~sis An International Quarterly Journal

PRINCIPAL EDITOR J.H. Dshalalow, US Celebrates LAJOS TAKAcs• 70th Birthday HONORARY EDITOR A. Skorokhod, S. Asmussen W. Whitt, N. Ahmed R. Dobrushin, D. Daley, V. Kalashnikov, S. D.G. Kendall, UK Ross, R. Liptser, B. Melamed, I. Kovalenko, S. Stidham, and L. Servi are among 20 contributors. Orders for the Jubilee Issue should be sent to North Atlantic Science Publishing Compaey, ADVISORY BOARD JAMSA-OrderDepartment, P.O. Box 1017, Melbourne, FL 32902-1017, U.S.A. Price $29.50 for C. Heyde, Australia individuals, $49.5{) for institutions. Add $8.00 for airmail (outside the US). D. Konig, Germany M. Krasnoselskii, Russia JAMSA publishes significant research papers in NONLINEAR and STOCHASTIC ANALYSIS, V. Lakshmikantham, US VALUE PROBLEMS. R. Liptser, Russia STOCHASTIC MODELS, and BOUNDARY M. Neuts, US Send papers in triplicate by regular mail (or e-mail in TEX format) to: J.H. Dshalalow, Principal A. Skorohod, Ukraine Editor, JAMSA, Department of Applied Mathematics1 Florida Tech, Melbourne, FL 32901, ASSOCIATE BOARD U.S.A. Fax (407) 726-8200,.~ Ph. (407) 951-8306, e-mail: [email protected] Peer review is L. Abolnikov US mandatory. JAMSA (ISSN 1u48-9533) is published four times a year. Vol. ., (1994). Institutional P. Bremaud, France rates: US $125.00 for US/Canada, $ 35.00 elsewhere, $60.00 for developmg countries. H. Dad una, Germany Individual rates: US $50.00 for US/Canada, $60.00 elsewhere. Send mail orders to: North W. Derrick, US Atlantic Science Publishing Co., Subscription Department, P.O. Box 1017, Melbourne, FL K. Farahmand, UK 32902-1017, U.S.A. Z. Karian, US E. Khalimsky, US I. Malyshev, 1JS ASSISTANT EDITORS: J. Becker, Germany, Y. Berezanski, Ukraine, D. Fausett, US, A. Martynyu~ Ukraine C. Fulton, US, B. Fusaro, US, A. Krasnoselskii, Russia V. Matrosov,Kussia ADVISORY CS EDITOR W. Shoaff, US R. Melka, U" ADVISORY TECHNICAL EDITORS: J. Herndon, L. Kiaer, D. Konwinski, G. Russell, US N. Papageorgiou, US A. Rosafsky liS ' © 1994, North Atlantic Science Publishing Company, Inc. A. Vatsala, US

PROCEEDINGS OF SYMPOSIA IN APPLIED MATHEMATICS

Different Perspectives on Wavelets Ingrid Daubechies, Editor Volume 47

The wavelet transform can be seen as a synthesis of ideas that have emerged since the 1960s in mathematics, physics, and electrical engineering. The papers in this book give some theoretical and technical shape to the intuitive picture of wavelets and their uses. The papers collected here were prepared for an AMS Short Course on Wavelets and Applications, held at the Joint Mathematics Meetings in San Antonio in January 1993. Here you will find general background on wavelets as well as more detailed views of specific techniques and applications. With contributions by some of the top experts in the field, this book provides an excellent introduction to this important and growing area of research.

1991 Mathematics Subject Classification: 35, 42, 46, 62, 94 ISBN 0-8218-5503-4, 205 pages (hardcover), December 1993 Individual member $27, List price $45, Institutional member $36 To order, please specify PSAPM/47NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. Elliptic Curves and Related Topics Hershy Kisilevsky and M. Ram Murty, Editors Volume 4

This book represents the proceedings of a workshop on elliptic curves held in St. Adele, Quebec, in February 1992. Containing both expository and research articles on the theory of elliptic curves, this collection covers a range of topics, from Langlands's theory to the algebraic geometry of elliptic curves, from Iwasawa theory to computational aspects of elliptic curves. This book is especially significant in that it covers topics comprising the main ingredients in Andrew Wiles's recent result on Fermat's Last Theorem.

1991 Mathematics Subject Classification: 11 ISBN 0-8218-6994-9, 195 pages (softcover), February 1994 Individual member $33, List price $55, Institutional member $44 To order, please specify CRMP/4NA

Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems

D. A. Dawson, Editor Volume5

Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these processes are described, including branching in catalytic media, branching with change of mass, and multilevel branching. Sample path and spatial clumping properties of superprocesses are also studied. Several papers are also devoted to particle systems studied in statistical physics and to stochastic partial differential equations which arise as hydrodynamic limits of such systems. With overview articles on some of the important new developments in these areas, this book would be an ideal source for an advanced graduate course on superprocesses. 1991 Mathematics Subject Classification: 60 ISBN 0-8218-6992-2, 241 pages (softcover), March 1994 Individual member $35, List price $59, Institutional member $47 To order, please specify CRMP/SNA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. Geometric Topology Cameron Gordon, Yoav Moriah, and Bronislaw Wajnryb, Editors Volume 764

Geometric Topology Geometric topology has undergone tremendous changes in the past decade.

Cclm&ronGat'dcn Many of the big questions facing mathematicians in this area have been answered, YllavMof!Qil BronlslawWc;Jnryb and new directions and problems have arisen. One of the characteristics of the field """" is the diversity of tools researchers bring to it. A Workshop on Geometric Topology was held in June 1992 at Technion-Israel Institute of Technology in Haifa, to bring together researchers from different subfields to share knowledge, ideas, and tools. This volume contains the refereed proceedings of the conference.

1991 Mathematics Subject Classification: 57 ISBN 0-8218-5182-9, 246 pages (softcover), May 1994 Individual member $25, List price $42, Institutional member $34 To order, please specify CONM/164NA

p-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture Barry Mazur and Glenn Stevens, Editors Volume 765

p-Adte Monodromy ond the Birch This book contains papers presented at the Workshop on p-Adic Monodromy and and SWinnerton-Dyer Conjecture the Birch and Swinnerton-Dyer Conjecture, held at Boston University in August 1991. BOIIYMa!ur Glonncstovom: The workshop aimed to deepen understanding of the interdependence between '"'= p-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, p-adic uniformization theory, p-adic differential equations, and deformations of Galois representations. Much of the workshop was devoted to exploring how the special values of (p-adic and "classical") L-functions and their derivatives are relevant to arithmetic issues, as envisioned in "Birch-Swinnerton-Dyer-type conjectures", "Main Conjectures", and "Beilinson-type conjectures" a Ia Greenberg and Coates.

1991 Mathematics Subject Classification: 11; 14 ISBN 0-8218-5180-2, 315 pages (softcover), June 1994 Individual member $30, List price $50, Institutional member $40 To order, please specify CONM/165NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. TRANSLATIONS OF MATHEMATICAL MONOGRAPHS •

Algebraic Geometry Masayoshi Miyanishi Volume 136 This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting the necessary background along the way. Originally published in the Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes and algebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces. 1991 Mathematics Subject Classification: 14; 13 ISBN 0-8218-4615-9, 246 pages (hardcover), July 1994 Individual member $60, List price $100, Institutional member $80 To order, please specify MMON0/136NA

Heavy Traffic Limits for Multi phase Queues F. I. Karpelevich and A. Ya. Kreinin Volume 137 This book analyzes several types of queueing systems arising in network theory and communication theory. Karpelevich and Kreinin use numerous methods and results from the theory of stochastic processes. The main emphasis is on problems of diffusion approximation of stochastic processes in queueing systems and on results based on applications of the hydrodynamic limit method. The book will be useful to researchers working in the theory and applications of queueing theory and stochastic processes. 1991 Mathematics Subject Classification: 60, 90 ISBN 0-8218-4597-7, 143 pages (hardcover), August 1994 Individual member $47, List price $79, Institutional member $63 To order, please specify MMON0/137NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. Application for Membership 1994 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ......

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NOTIONS OF CONVEXITY FOUNDATIONS OF LAWS OF SMALL NUMBERS L. Hormander, University of Lund GAME THEORY Extremes and Rare Events This book discusses notions of convexity Noncooperative Games M. Falk, Katholische Universitaet Eichstaett, that are found in the theory of partial dif­ Translated from the Russian by R.P. Boas Germany; J. Huesler, Universitiit Bern, ferential equations and complex analysis. N.N. Vorob'ev, Russian Academy of Sciences, Switzerland & R.-D. Reiss, Universitiit The applications here are presented in the St. Petersburg Gesamthochschule Siegen, Germany author's well known masterly style with This book contains results on the theory Laws of small numbers concern rare excellent exposition and illuminating of equilibrium points in noncooperative events, it is reasonable to describe such insight and perspective. Both experts games with numerical pay-offs that are events as truncated empirical point and advanced graduate students should considered as the basic class of games. processes, and a point process of rare find the book useful and enjoyable. The work is intended to be studied by events can be approximated by a Poisson CoNTENTs: Convex functions of one variable • mathematicians seeking an introductory process. This approach is applied to: Convexity in a finite-dimensional vector space • textbook on game theory, and by those extremes and rare events of stochastic Subharmonic functions • Plurisubharmonic whose specialities involve operations processes; Poisson point processes and functions • Convexity with respect to a linear statistics in extreme value models. group • Convexity with respect to differential research and mathematical applications operators • Convexity and condition ('¥) • in the fields of economics, ecology and Includes a statistical software system Appendices • Index defense activities. 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S.K. BERBERIAN, University of Texas at M. DO CARMO, lnstituto de Mathematica Fourth Edition Austin, TX Pura e Aplicada, Brazil J.J. ROTMAN, University of Illinois, Urbana, IL DIFFERENTIAL FORMS A FIRST COURSE IN REAL AN INTRODUCTION TO AND APPLICATIONS ANALYSIS THE THEORY OF GROUPS The author, known for his precision This book covers differential forms and care in writing, has composed a and uses them to study some local and Anyone who has studied abstract book primarily intended to support a global aspects of the differential geo­ algebra and linear algebra as an under­ first course in real analysis- normally metry of surfaces. Differential forms graduate can understand this book. taken after a year of elementary calcu­ are introduced in a simple manner which This edition has been completely re­ lus. The result is a leisurely and thorough will make them attractive to "users" of vised and reorganized, without losing developme'lt of the properties of the mathematics. A brief and elementary any of the clarity of presentation that field of real numbers. The topology of introduction to differentiable manifolds was the hallmark of the previous editions. the real line is worked out using con­ is given so that the main theorem, name­ The first six chapters provide ample vergent sequences as the fundamental ly the Stokes' theorem, can be presented material for a first course. Topics concept. The highlight of the book is in its natural setting. The applications covered include: groups and homo­ the Fundamental Theorem of Calculus, consist of developing the method of morphisms, isomorphism theorems, proved for cominuous functions in the moving frames of Elie Cartan to study symmetric groups and G-sets, Sylow context of the Riemann integral. In the local differential geometry of theorems, normal series, finite series, addition, an experimental final chapter immersed surfaces in R', as well as, extentions and cohomology, simple gives an elementary exposition of the the intrinsic geometry of surfaces. linear groups, permutations and the Fundamental Theorem of Calculus for Everything is then put together in the Mathieu groups, abelian groups, free the Lebesgue integral. Each section is last chapter to present Chern's proof groups and free products. and the word fo llowed by a list of exercises, (totalling of the Gauss-Bonnet theorem for problem for finitely presented groups. nearly 400), often supplied with hints compact surfaces. 1994/app. 450 pp., 60 illus.;Hardcover /$59.00 and many of them easy enough to be used ISBN 0-387-94285-8 1994/app. 120 pp./Softcoverj$29.50 GRADUATE TEXTS IN MATHEMATICS, VOLUME 148 on a test. ISBN 0-387-57618-5 1994/237 pp .. 19 illus./Hardcover /$39.95 UNIVERSITEXT ISBN 0-387-94217-3 G. GRIMMETT, University of England, UNDERGRADUATE TEXTS IN MATHEMATICS Bristol, UK Second Edition

H.-D. EBBINGHAUS, J. FLUM, both of PERCOLATION w.s. ANGLIN , Luther College at University Universitat Freiburg, Germany; and of Regina, Canada The importance of Percolation for w. THOMAS, Universitat Kiel, Germany modelling random media is appreciated MATHEMATICS MATHEMATICAL LOGIC by probabilists and mathematical physi­ A Concise History and Philosophy cists. This concise reworking of the This junior/senior level text is devoted mathematical .theory is self-contained This is a concise introductory textbook to a study of first-order logic and its and approachable by the non-specialist. for a one-semester course in the history role in the foundations of mathematics. It makes extensive use of recent proofs and phi losophy of mathematics. The It begins with an introduction to first­ of the uniqueness of the critical point only prerequisite is precalculus, and the order logic, Godel' s theorem, and model and of the infinite cluster, and includes format is shorter than other textbooks, theory. A second part covers extensions an attempt to communicate to the thus more accessible to students who of first-order logic and limitations of mathematician the physical theory of have trouble coping with vast amounts the formal methods. Also covered are scaling and the critical phenomenon. of reading. Furthermore, the many several advanced topics, not commonly The case of two dimensions receives detailed explanations of the important treated in an introductory text, such as, special attention, with a modern proof mathematical procedures actually used Trachtenbrot's undecidability theorem. that the critical probability of bond by famous mathematicians, gives Fraisse's elementary equivalence, and percolation on the square lattice equals mathematically talented students a Lindstrom's theorem on the maximal­ 'h. The emphasis throughout is upon greater opportunity to learn the history ity of first-order logic. providing the most direct proofs. and phi losophy by way of problem solving. Several important philosophi­ 1994/289 pp./Hardcover/$44.50 1989/296 pp., 76 illus.;Hardcoverj$49.80 cal topics are pursued throughout the ISBN 0-387-94258-0 ISBN 0-387-96843-1 UNDERGRADUATE TEXTS IN MATHEMATICS text, giving the student an opportunity to come to a full and consistent know­ Order Today! ledge of their development. These Call Toll-Free 1-800-SPRINGE(R): topics include infinity, the nature of 1-800-777-4643. In NJ call motion, and Platonism. This book offers, 201-348-4033 (8:30 AM-5:30 PM EST). in fewer pages, a deep penetration into Write Send payment plus $2.50 the key mathematical and philosophical postage and handling for first book aspects of the history of mathematics. and $1.00 for each additional book to: Springer Verlag New York Inc., Dept. 1994/app. 275 pp .. 23 illus./Hardcoverj$39.00 #S232, PO Box 2485, Secaucus, ISBN 0-387-94280-7 NJ 07096-2491. (CA, ll, MA, NJ, NY, PA, UNDERGRADUATE TEXTS IN MATHEMATICS TX, VA, and VT residents add sales tax, Canadian residents add 7% GST.) I Visit your local technical bookstore. .Springer-Verlag Instructors: Call or Write for information on textbook examination copies! N 'E W ' Y 0 R K • 9/94 REFERENCE: 5232 . I