OTICES OF THE
AMERICAN MATHEMATICAL SOCIETY
1991 AMS-MAA Survey First Report page 1086
NOVEMBER 1991, VOLUME 38, NUMBER 9
Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences
This calendar lists all meetings approved prior to the date this issue went to press. is possible. Abstracts should be submitted on special forms which are available The summer and annual meetings are joint meetings of the Mathematical Asso in many departments of mathematics and from the headquarters office of the So ciation of America and the American Mathematical Society. The meeting dates ciety. Abstracts of papers to be presented at the meeting must be received at the which fall rather far in the future are subject to change; this is particularly true headquarters of the Society in Providence, Rhode Island, on or before the deadline of meetings to which no numbers have been assigned. Programs of the meet given below for the meeting. The abstract deadlines listed below should be care ings will appear in the issues indicated below. First and supplementary announce fully reviewed since an abstract deadline may expire before publication of a first ments of the meetings will have appeared in earlier issues. Abstracts of papers announcement. Note that the deadline for abstracts for consideration for presenta presented at a meeting of the Society are published in the journal Abstracts of tion at special sessions is usually three weeks earlier than that specified below. For papers presented to the American Mathematical Society in the issue correspond additional information, consult the meeting announcements and the list of special ing to that of the Notices which contains the program of the meeting, insofar as sessions. Meetings
Abstract Program Meeting# Date Place Deadline Issue 871 * January 8-11 , 1992 Baltimore, Maryland October 2 December (98th Annual Meeting) 872 * March 13-14, 1992 Tuscaloosa, Alabama January 2 March 873 * March 20-21, 1992 Springfield, Missouri January 2 March 874 * April11-12, 1992 Bethlehem, Pennsylvania January 30 April 875 * June 29-July 1, 1992 Cambridge, England February 28 May-June (Joint Meeting with the London Mathematical Society) 876 * October 3D-November 1, 1992 Dayton, Ohio August3 October January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) March 26-27, 1993 Knoxville, Tennessee April9-10, 1993 Salt Lake City, Utah May 21-22, 1993 DeKalb, Illinois August15-19, 1993 Vancouver, British Columbia (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) October 22-23, 1993 College Station, Texas January 12-15, 1994 Cincinnati, Ohio (1 OOth Annual Meeting) March 18-19, 1994 Lexington, Kentucky March 25-26, 1994 Manhattan, Kansas January 25-28, 1995 Denver, Colorado (1 01 st Annual Meeting) March 24-25, 1995 Chicago, Illinois January 1Q-13, 1996 Orlando, Florida (1 02nd Annual Meeting) *Please refer to page 1158 for listing of Special Sessions. Conferences
January 6-7, 1992: AMS Short Course on New scientific applications July 6-24, 1992: AMS Summer Research Institute on Quadratic of geometry and topology, Baltimore, Maryland. forms and division algebras: connections with algebraic K-theory June 13-July 24, 1992: Joint Summer Research Conferences in the and algebraic geometry, location to be announced. Mathematical Sciences, Mount Holyoke College, South Hadley, July 26-August 1, 1992: AMS-SIA Summer Seminar in Aoolied Massachusetts. Mathematics, Exploiting symmetry in appliec analysis, Colorado State University, Fort Co Deadlines
January Issue February Issue March Issue April Issue Classified Ads* December 12, 1991 January 9, 1992 January 30, 1992 February 26, 1992 News Items December 4, 1991 December 31, 1991 January 21, 1992 February 20, 1992 Meeting Announcements** December 5, 1991 January 6, 1992 January 23, 1992 February 24, 1992 * Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. ** For material to appear in the Mathematical Sciences Meetings and Conferences section. OTICES OF THE
AMERICAN MATHEMATICAL SOCIETY
DEPARTMENTS ARTICLES 1083 Letters to the Editor 1129 Forum 1086 1991 Annual AMS-MAA Survey First Report 1144 News and Announcements The first report on the 1991 survey includes the 1991 survey of new 1149 Funding Information for the doctorates, starting salaries of new doctorates, faculty salaries, and a list of Mathematical Sciences names and thesis titles for members of the 1990-1991 Ph.D. class. 1150 1992 AMS Elections 1123 Mathematics under Hardship Conditions in the Third World 1153 Meetings and Conferences of Neal Koblitz the AMS Baltimore, MD What is the situation for mathematics in the Third World? In this lively and January 8-11, 1153 controversial article, Koblitz examines such questions as why mathematics 1992 Summer Research Institute, research flourishes in Vietnam, while other countries contend with "brain 1155 drain" to the U.S. and Europe. He also looks at mathematics education in Joint Summer Research some Central American countries, where the "New Math" craze took hold, Conferences in the Mathematical sometimes with disastrous results. Koblitz concludes with a number of Sciences, 1156 suggestions for ways to improve the conditions for mathematical colleagues Invited Speakers, 1158 in the Third World. 1162 Winter Meeting of the Canadian Mathematical Society FEATURE COLUMNS 1164 Mathematical Sciences Meetings and Conferences 1133 Computers and Mathematics Keith Devlin 1173 New AMS Publications Computer-assisted proofs are the theme of this month's feature article, 1177 Bylaws of the AMS by William Farmer and Javier Thayer of the MITRE Corporation. This is followed by two software reviews. Larry Riddle of Agnes Scott College 1192 Miscellaneous reviews Plot and Tevian Dray of Oregon State University describes his Personal Items, 1192 experiences with the two programs Cube and Tess. Deaths, 1192 Visiting Mathematicians, 1192 1142 Inside the AMS 1193 New Members of the AMS Jeremy Soldevilla, the director of marketing, discusses the role of the newly 1195 Classified Advertising formed AMS Marketing Division. 1219 Forms
NOVEMBER 1991, VOLUME 38, NUMBER 9 1081 From the Executive Director ...
VALUES What do we, as mathematicians, value in our profession? Do we adequately AMERICAN MATHEMATICAL SOCIETY encourage our values? How do we recognize merit within our value system? What is the basis for reward? These questions, addressed here to mathematicians, echo a central theme facing the professoriate and higher education. The value and reward system of faculties and the relationship between mission and practice of institutions of higher education are under examination. Although these issues, in the broad sense, EDITORIAL COMMITTEE are independent of discipline, it is necessary that we as mathematicians consider Michael G. Crandall discipline-dependent values and how we recognize and reward merit. Amassa Fauntleroy Responsibilities of the mathematics professoriate have not really changed; re Robert M. Fossum (Chairman) Carolyn S. Gordon (Forum Editor) search, teaching, and service are the generally accepted broad categories. What has D.J. Lewis changed is the clear need to respond in a more pro-active and balanced way to our L. Ridgway Scott full range of responsibilities. Of course, not every faculty member will have the same Robert E. L. Turner (Letters Editor) expectations, but collectively, ours is a challenging range of responsibilities.
MANAGING EDITOR U.S. mathematics research has been preeminent in the world, but there are serious John S. Bradley concerns for the maintenance and renewal of the mathematics research enterprise. We have a responsibility to the quality and vitality of mathematics research. Socio ASSOCIATE EDITORS economic and demographic trends indicate that fewer students will study mathematics Ronald L. Graham, Special Articles and choose mathematically related careers, while other indicators point toward the Jeffrey C. Lag arias, Special Articles increasing need for a mathematically literate workforce. The nation depends on the success of mathematics education, and the college/university mathematics faculty SUBSCRIPTION INFORMATION share the responsibility for mathematics education. Mathematics is identified as a Subscription prices for Volume 38 (1991) are $121 list; $97 institutional member; $73 individual critical and enabling component of science and technology that is vital to economic member. (The subscription price for members is in competitiveness. It is a responsibility of mathematics faculty to connect discovery in cluded in the annual dues.) A late charge of 10% mathematics to discovery, education, and applications in other disciplines. The need of the subscription price will be imposed upon or for mathematics faculty to respond to these responsibilities is more critical than ever ders received from nonmembers after January 1 before; in this context, it is essential that the value and reward system reflect all the of the subscription year. Add for postage: Surface responsibilities borne by the college/university faculty. delivery outside the United States and lndia-$15; to lndia-$27; expedited delivery to destinations in The Joint Policy Board for Mathematics (JPBM), which represents the AMS, North America-$28; elsewhere-$67. Subscrip the Mathematical Association of America, and the Society for Industrial and Applied tions and orders for AMS publications should be Mathematics, has appointed a task force to undertake a study of the values and rewards addressed to the American Mathematical Society, structure within the mathematics professoriate. The task force is to identify those P.O. Box 1571, Annex Station, Providence, Rl characteristics and activities of professional mathematicians that are most valued, 02901-1571. All orders must be prepaid. formulate ways to measure and evaluate merit within this value structure, and review ADVERTISING rewards. The task force is to report its findings, make recommendations based on Notices publishes situations wanted and classified these findings, and lay plans to mobilize the community for action. advertising, and display advertising for publishers The task force activities are intended to set directions for mathematicians to look and academic or scientific organizations. closely at what they value and how these values fit within their broad responsibilities. Copyright @ 1991 by the American Mathematical If we do hold discovery and creativity in highest esteem, then we need to examine their Society. All rights reserved. Printed in the United connections to the traditional roles of teaching and research. Are there nontraditional States of America. ways that discovery and creativity can be brought to bear on the responsibilities for The paper used in this journal is acid-free and falls connecting research mathematics to education and applications? Creativity and schol within the guidelines established to ensure perma arship exist not only in new discoveries but also in the organization of knowledge, nence and durability. (§ Most of this publication was typeset using the TEX typesetting system. the communication of knowledge, and the applications of knowledge. There is little question that we do value good exposition, the lucid lecture, the novel approach to (Notices of the American Mathematical Society is an old question that brings new understanding, and the stimulating connections of published monthly except bimonthly in May, June, July, and August by the American Mathematical So mathematical research to discovery and applications in other disciplines. However, ciety at 201 Charles Street, Providence, Rl 02904- do we encourage and promote this valued scholarship in our reward system? 2213. Second class postage paid at Providence, The task force will receive staff support from the Society. It begins its work this Rl and additional mailing offices. POSTMASTER: fall and expects to have a report to JPBM and the community within a year. There Send address change notices to Notices of the American Mathematical Society, Customer Service may be concurrent studies by other groups that are cross-disciplinary or directed at Department, American Mathematical Society, P. 0. some particular responsibility of the professoriate. The mathematics community is Box 6248, Providence, Rl 02940-6248.] Publication taking a progressive step in addressing, directly and actively, these important issues here of the Society's street address, and the other as they affect our discipline. information in brackets above, is a technical require ment of the U. S. Postal Service. All correspon William Jaco dence should be mailed to the Post Office Box, NOT the street address. Tel: 401-455-4000.
1082 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY as a highly active research field. By working largely on his or her own, and Letters the time I graduated, I knew what I will in general have access to poorer wanted to do with my life, and have library and computational facilities, all to the Editor been actively involved in research and of which may result in a far lower pub teaching in mathematics ever since. lications rate than might be expected of Three years close contact with a small someone at a large research school. group of highly active mathematicians The existence of the RUI program Funding Small College did that for me, and for well over half played a large factor in my own de Researchers my class who went on to pursue Ph.D.s cision to go to such a school (Colby In his letter to Notices (Notices 38, and research careers in mathematics. College) as chairman two years ago. As No. 6, p. 541), Sheldon Kamienny ex (At least three of us are now on college I set about hiring four new faculty over presses the fear that the NSF peer faculty in the U.S.A. and one is a the past two years, I mentioned the pro review system acts against research former program director at NSF!) gram to every candidate I interviewed, proposals that do not fit the preconcep When, a few years ago, government in order to encourage them to come to tions of the reviewers. He may well policies made conditions for teaching Colby. That hiring process led to our have a point. But worrying funding and research so intolerable at my uni acquiring four young mathematicians priorities at NSF are not restricted to versity in Britain that I was forced to who are not only excellent teachers the role played by the independent re consider moving to the United States, viewers. In my own recent case, all with a strong commitment to under I could see the value of accepting the three reviewers were extremely pos graduate, liberal arts education, but are offer of the chairmanship of a good, itive about my proposal, which also also highly successful researchers, with small college that sought to provide its was of the novel, "non-standard" na fairly recent doctorates from Harvard, students with the same kind of research ture Kemienny is concerned about, but Berkeley, Madison, and New Hamp exposure that I had received. The prob despite the reviewers positive remarks shire. In short, Colby now has the kind lem is, how does any mathematician and their rankings of E, VG, VG, and of department that, like my own Alma sustain research at such an institution? despite the program director stating in Mater, should be successful not only his report that the research definitely de For the small British colleges there is served support, the proposal was turned no problem; they are all grouped into Policy on Letters to the Editor down. larger units, in London, Cambridge, Letters submitted for publication in Notices are reviewed by the Editorial Committee, whose task Now, the pages of Notices are not and Oxford. In the U.S.A., most of the good small colleges are geographically is to determine which ones are suitable for pub the appropriate place to discuss one lication. The publication schedule normally re particular research proposal. But they spread out, so the active researcher at quires from one to two months between receipt are, I think, exactly the right forum to such a place has to work hard to keep of the letter in Providence and publication of the in touch with new developments. Email earliest issue of Notices in which it could appear. examine a general issue raised by this Publication decisions are made by a letters proposal, namely the increased empha is a great help in this regard. But the editor who is appointed by the Editorial Com sis that should be given to research at biggest factor is the extended summer mittee from among its members and who is ac research trip to a large research center. countable to the committee for those decisions. small undergraduate colleges such as There is provision for discussion among com my own, something I see as crucial to Indeed, two of the three external re mittee members, by mail or at meetings, before the future growth of our subject. viewers of my recent research proposal decisions are made by the letters editor. Let Let me start by saying that I know stressed in their reports, as I did in the ters requiring collateral correspondence and/or proposal, the crucial importance to my revision may require several months to process. the value of a small college experience, Letters which have been, or may be, published where the students are in close daily work of being able to spend large parts elsewhere will be considered, but the Managing contact with active research faculty. I of each summer at a large research Editor of Notices should be informed of this fact center. when the letter is submitted. was an undergraduate at King's College The committee reserves the right to edit let in London, a highly selective institution Now the NSF has a special pro ters. that admitted at most 25 mathematics gram for people such as myself: The Notices does not ordinarily publish com majors each year. As one of the most RUI program (Research at Undergrad plaints about reviews of books or articles, al though rebuttals and correspondence concerning prestigious colleges in the University uate Institutions). RUI proposals are reviews in Bulletin of the American Mathemat of London system, King's had a faculty evaluated along with all other research ical Society will be considered for publication. of world class calibre, and my fellow proposals, and subject to the same peer All published letters must include the name of review process, the only difference at the author. students and I got to know them very Letters should be typed and in legible form well, both as teachers and on a social the initial evaluation stage being that or they will be returned to the sender, possibly basis. The experience quite literally reviewers are sent a cover sheet ex resulting in a delay of publication. changed my life. I went to college plaining that as a professor at a small Letters should be mailed to the Editor of No tices, American Mathematical Society, P.O. Box knowing I wanted some sort of career college, the proposer will have a con 6248, Providence, RI 02940, or sent by email to involving mathematics; but, at the time, siderably larger teaching load than col [email protected], and will be acknowl I had little conception of mathematics leagues at a research university, will be edged on receipt.
NOVEMBER 1991, VOLUME 38, NUMBER 9 1083 --- ···-··-······-·~---·--·-·· ------r--·--·-··-···-·-···---·----··--·--·-·····-···-··Letters to the Editor at producing research mathematicians is undoubtedly a place in society, and curious. It is my impression that a (among other things), but also ensuring an important one, for the activity that high school instructor should not that those students who go on to pur constitutes the normally understood se speak for more than three minutes sue other careers, leave Colby with a mantics of the word "teaching". But without asking a question. heightened awareness of the nature of this is not at all appropriate for the 2. Motivate interest in the topic. contemporary mathematics. kind of institution of primary concern Some concession must be made to But it will only be possible to sus to the AMS. People learn far more from the student who asks: Why would tain the momentum we have built up if example than from being shown "what anybody want to know this? Do all of us have a reasonable chance to se to do", cookbook style. Mathematics not give a normal classroom lec cure summer research funding. Without is a living, breathing, growing subject, ture. that, it will wither and die. Their small and to those who choose to learn it for 3. Prepare the talk. Transparencies size and intimate atmosphere makes the its own sake (i.e. not just as a utility), of diagrams and proofs should selective small colleges the best chance it should be "taught" as such, and that be made ahead of time. Help the nation has to produce new gener I maintain can only be done by some ful handouts should be duplicated ations of scientists of all disciplines. one active in research. (Of course, Mr. prior to the meeting. Physical de Students learn best from example. The Trautman has a point if that research vices to illustrate mathematical professor at the chalkboard is their role comes· in the way of student-professor applications should not be made model. Over their four years at the interaction, but that is another matter so crudely that they are disap college, the students can get to know altogether.) pointing. the professor extremely well. So, by Let me stress that, to the best of 4. Learn the level of the students' giving increased priority to the funding my knowledge, the people working at ability and speak at that level. of small college researchers, the NSF NSF are doing the very best they can. Most high school students need would be placing its limited resources But they can only operate within the long pauses between equations to into the sector most likely to produce budget they are allocated, and have to verify and understand them, and the long term results it surely aims for. set the priorities they think are best. their minds will wander when ap (And remember, I am not suggesting Maybe letters such as this can help parently true statements are rigor that the NSF gives priority to "second them as they argue the budget with the ously proved. class research". RUI proposals are sub government. As to setting priorities, I 5. If your talk is not especially in jected to the same initial peer scrutiny suspect that the voice of small college sightful, informative, or entertain as any other proposal.) research is not very well represented at ing, then don't give it. Having taught at both large research NSF, if at all. So, here is an offer to The following quotation is an ex the NSF. Let me offer my own services schools (in Britain, Germany, and North ample of what is highly desired in to try to explain to you just what America) and now at a small college, expository talks. It would be appropri is involved in maintaining an active I can confirm that it is at least an ate for a high school calculus class. order of magnitude more difficult to research program at a small teaching sustain an active research program at college. As a professor at such a school, [Isaac Newton's] Principia was a remote small college. Relatively few I don't really have the time of course, written almost entirely in the lan small college professors seem able to but given the stakes involved, I am guage of geometry; nearly all sustain it for long, given the huge effort prepared to take it on. I doubt that I subsequent progress in gravita it takes both to find enough time and am alone. tional astronomy has been made to keep in touch with one's colleagues. Keith Devlin by mathematical methods known Considering the tiny amounts of money Colby College as analysis [calculus, limits, infi involved (usually just summer salary (Received August 12, 1991) nite sequences, etc.]. In the ge and travel to another location) the fi ometrical treatment of an astro nancial savings to the nation achieved Speaking to High School Students nomical problem each step of the by scrimping on RUI support must be The collegiate and industrial profession reasoning is expressed in such paltry. The potential loss to the nation has a great deal to offer high school a way as to be capable of be is surely enormous, and constitutes a students in a 45-minute talk. The fol ing interpreted in terms of the tragic waste both of financial resources lowing suggestions (based on years of original problem, whereas in the and of natural talent. observing high school speakers) can analytical treatment the problem Incidentally, I disagree violently help maximize the impact of any talk is first expressed by means of with the views expressed by Dave to young people. algebraic symbols; these symbols Trautman in the same issue of Notices 1. Make the talk interactive by ask are manipulated according to cer (pp. 540-541) to the effect that there ing questions, or getting students tain purely formal rules, no regard is far too much mathematical research to guess or draw a conclusion being paid to the interpretation of being done and that we should con before it is stated, or by asking the intermediate steps, and the fi centrate instead on "teaching". There students to consider something nal algebraic result, if it can be
1084 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Letters to the Editor
obtained, yields on interpretation Strengthening Undergraduate Science on program, lean and lab-rich, faculty the solution of the original prob and Mathematics," the report of the enhancement activities, mathematics ... lem. The geometric solution of Project Kaleidoscope Committee. The is enhanced, enhance the learning com the problem, if it can be obtained, examples of officialese, sociologese, munity, set of K-12 experiences, labo is frequently shorter, clearer, and incongruous vocabulary, vogue words, ratory experiences, hands-on and lab more elegant; but on the other and overdone metaphors are so numer rich experiences, research experiences, hand, each special problem has to ous that one is tempted to throw the kinesthetic experiences in which stu be considered separately, whereas reports down and say "Enough!" dents use proprioceptive senses, student the analytic solution can be con Those who read "Moving Beyond led educational experiences, science ex ducted to a great extent accord Myths" must put up with phrases periences, enmeshing the teacher in a ing to fixed rules applicable in a like: Statewide mathematics articula laboratory setting, empowering learn larger number of cases. -Arthur tion, to replicate effective interven ers, may not be informed by a clear Berry, A Short History of Astron tion programs, to enable students to understanding, filtering action, a criti omy (John Murray, 1898; Dover interactively understand, the goal for cal pump in the career pipeline, science reprint, 1961) pages 247-248. each experience [experience is a new and mathematics pipeline, portrait of word for course], to mainstream stu leakage from the science pipeline, dis Michael Stueben dents, to remediate students, to sen aggregative enterprise, disaggregated Thomas Jefferson High School sitize teaching assistants, to educate by gender, gender make-up, degrees for Science and Technology intending teachers, pipeline population, by gender, facilitators, capstones, clus (Received September 3, 1991) a lens ... polished by their own educa ters, gatekeeper courses, varied menu tion, harmful myths about mathematics of courses, upper-class students will Style in Recent Reports metastasize to the body politic, interest socialize lower-level students, spaces I write to express my exasperation payments on the deficit of scholarly [i.e., rooms], shape the spaces, etc. etc. at the deplorable style of English in maturity balloon college enrollments, Since the authors of these reports which two recent reports about teaching etc. etc. have something important to say, why undergraduate mathematics are writ The Project Kaleidoscope report is don't they say it in plain English? They ten. The July/August 1991 issue of much worse. We find there: Hands-on find much to complain about, and it Notices, with the essay "Moving Be curriculum, hands-on learning, hands is well that there be no faults in them yond Myths" (pages 545-559), arrived on approach, hands-on research, hands who point out the faults of others. on the same day that I received the on learning experience, hands-on exper Anthony Lo Bello booklet "What Works: Building Natu iments, hands-on connections, hands-on Allegheny College ral Science Communities-A Plan for workshops, hands-on pedagogy, hands- (Received August 9, 1991) UMETRENDS News and Reports on Undergraduate Mathematics Education
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NOVEMBER 1991, VOLUME 38, NUMBER 9 1085 1991 Annual AMS-MAA Survey (First Report)
Report on the 1991 Survey of New Doctorates, Donald E. McClure Salary Survey for New Doctorates Faculty Salary Survey Doctoral Degrees Conferred, 1990-1991
Highlights This first report on the 1991 Survey includes a report on the 1991 survey of new doctorates, a report on salaries of new doctorates, salary data • U.S. institutions awarded 1074 doctorates in the math on faculty members in four-year colleges and universities, and a list of ematical sciences from July 1, 1990 to June 30, 1991, an names and thesis titles for members of the 199Q-1991 Ph.D. class. increase of 15 percent over last year's fall count and 26 The report is based on information collected from questionnaires distributed in May to departments in the mathematical sciences in percent more than the average of the fall counts for the last colleges and universities in the United States and Canada, and later to four years. the recipients of doctoral degrees granted by these departments between July 1990 and June 1991, inclusive. A further questionnaire • The number of U.S. citizens reported to have received was distributed in September, concerned with data on fall enrollments, doctorates in the mathematical sciences is 461, which is 15 majors, and departmental size. These data will appear in the second report on the 1991 Survey, in a spring 1992 issue of Notices. percent higher than the number earning doctorates last The 1991 Annual AMS-MAA Survey represents the thirty-fifth in an year and 27 percent higher than the record lows recorded annual series begun in 1957 by the Society. The 1991 Survey is under in 1986-87 and 1987-88. the direction of the AMS-MAA Data Committee whose members are Edward A. Connors, Lincoln K. Durst (consultant), John D. Fulton, • The number of non-U.S. citizens receiving doctorates in James F. Hurley, Charlotte Lin, Don 0. Loftsgaarden, David J. Lutzer, the mathematical sciences reached anew high of 600, well James W. Maxwell (ex officio), Donald E. McClure (chair), and Donald C. Rung. Comments or suggestions regarding this Survey may be over twice the number of noncitizens earning doctorates in directed to the committee. the U.S. ten years ago.
• Of the 461 U.S. citizen doctorates 10 are black. In 1989- For these reports, departments are divided into groups according to the highest degree offered in the mathematical sciences: 90 only 4 of the U.S. citizen doctorates were black.
Groups I and II include the leading departments of mathematics in the • Total employment of new doctorates in the U.S. increased U.S. according to the 1982 assessment of Research-Doctorate Pro from last year, but employment in some sectors decreased grams conducted by the Conference Board of Associated Research and the percentage of unemployed increased substantially. Councils in which departments were rated according to the quality of As of late September 1991, approximately 12 percent of their graduate faculty. 1 Group I is composed of 39 departments with scores in the 3.Q-5.0 the new doctorates were reported to be still seeking em range. ployment. The percentage unemployed is over twice the Group II is composed of 43 departments with scores in the 2.0-2.9 corresponding percentage reported last fall. range. Group Ill contains the remaining U.S. departments reporting a doc toral program. • The total number and the percentage of women among Group IV contains U.S. departments (or programs) of statistics, U.S. citizen new doctorates reached new highs in 1990-- biostatistics and biometrics reporting a doctoral program. 91. A total of 112 U.S. citizen women earned doctorates Group V contains U.S. departments (or programs) in applied mathe from U.S. universities, accounting for 24 percent of the matics/applied science, operations research and management sci doctorates awarded to U.S. citizens. ence which report a doctoral program. Group Va is applied mathematics/applied science; Group Vb is operations research and management science. • The median starting salary of new doctorates reporting Group VI contains doctorate-granting departments (or programs) in teaching (or teaching and research) was $33,000 for men the mathematical sciences in Canadian universities. and $33,200 for women. Group M contains U.S. departments granting a master's degree as the highest graduate degree. Group B contains U.S. departments granting a baccalaureate degree • In almost all cases, the mean salary by faculty rank only. reported for 1991-92 increased less than five percent over 'These findings were published In An Assessment of Research-Doctorate Programs in the that reported for 1990--91. Major exceptions were the United States: Mathematical and Physical Sciences, edited by Lyle V. Jones, Gardner 1991-92 mean salaries reported for associate and full Lindzey, and Porter E. Coggeshall, National Academy Press, Washington, D.C., 1982. The Information on mathematics, statistics and computer science was presented in digest form in professors in doctorate-granting departments of applied the April 1983 issue of Notices, pages 257-267, and an analysis of the above classifications was given in the June 1983 Notices, pages 392-393. For a listing of departments in Groups mathematics and operations research (Group V), which I and II see April 1988 Notices, pages 532-533. increased 9% and 7% respectively.
1086 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
Report on the 1991 Survey of New Doctorates Donald E. McClure
This report presents a statistical profile of new doctorates in the Table 2C records the number of new doctorates in the mathematical sciences awarded by universities in the United mathematical sciences in the U.S. from the years 1986--87, States and Canada during the period July 1, 1990 through June exclusiveofGroup Vb. TheresponserateforGroup Vb, which 30, 1991. It includes the employment status of recipients of includes departments in engineering and management science, 1990-91 doctorates in the mathematical sciences (as of Sep is the lowest of all groups. tember 20), an analysis of the data by sex, racial/ethnic group Groups I and II account for the largest part of the increase and citizenship, and reports trends in the number of doctoral shown in Table 2C. The count for Group I increased by 72 (20 degrees for each of Groups I through V (see box on preceding percent) and the count for Group II increased by 46 (33 percent) page for description of groups). Table 1 provides the response over the corresponding fall counts in the 1990 Annual Survey. rates for the 1991 Survey of New Doctorates. There was virtually no change in the fall counts for Group III. The fall count for Group IV (statistics) showed a modest TABLE 1: Response Rates decrease, though that finding must be interpreted cautiously in Group I 39 of 39 view of the lower response rate for Group IV. Group II 42 of 43 including 3 with 0 degrees Group Ill 80 of 86 including 27 with 0 degrees Table 2C: New Doctorates Group IV 53 of 75 including 5 with 0 degrees Awarded by Groups I-Va Group Va 12 of 16 86-87 87-88 88-89 89-90 90-91 Group Vb 18 of 33 I-Va 743 760 854 881 990** Group VI 27 of 31 including 8 with 0 degrees **This is a fall count. The other entries in Table 2C are spring counts. Table 2C will be updated to include a spring count for Doctorates Granted 1990-91 in a spring 1992 issue of Notices. The number of new doctorates reported in 1990-91 by U.S. and Canadian mathematical sciences departments is 1142. Table Employment Status of 2A gives the fall counts for the past five Annual Surveys. This New Doctorates, 1990-1991 year's fall count will be updated in the Second Report of the In 1990, the Annual Survey started adding new questions to 1991 Survey, to appear in a spring 1992 issue ofNotices. Table monitor the changing employment market. At the time, the 2B reports for comparison the fall and spring counts in the years AMS-MAA Data Committee was interested in collecting 1986--87 through 1989-90. baseline data against which the future shortages of Ph.D.s The total number of new doctorates increased substantially projected in the science press could be compared. In the past this year. The total count has been increasing steadily since two years, however, changing economic conditions and other 1984-85. This year's increase is the largest in absolute num perturbations of the employment market have refocused the bers (151) and in percentage(+ 15 percent) during this six-year interest of the mathematics community on a difficult job period. Cumulatively, the total number of new doctorates has market. In this report, we shall present a broader analysis than increased 49 percent since 1984-85. is customary to illuminate patterns of employment for new doctorates. Table 3A shows the employment status, by type of em Table 2A: New Doctorates, Fall Counts ployer and field of degree, of the 1142 recipients of doctoral 86-87 87-88 88-89 89-90 90-91 degrees conferred by the mathematical sciences departments u.s. 779 804 905 933 1074 in the U.S. and Canada between July 1, 1990, and June 30, Canada 66 52 53 58 68 1991. The names of these individuals are listed with their Total 845 856 958 991 1142 thesis titles in a later section of this First Report of the 1991 Annual Survey. Again this year we present the employment status of the 227 women new doctorates in Table 3B. The employment information was obtained initially from the de Table 28: New Doctorates, Fall and Spring Counts partments granting the degrees and subsequently from data provided by the degree recipients themselves. 86-87 87-88 88-89 89-90 90-91 Fall/Spring Fall/Spring FaiVSpring Fall/Spring FaiVSpring The first five rows of Table 3A give the numbers of new doctorates who have accepted appointments in U.S. doctorate u.s. 779 808 804 828 905 919 933 950 1074 * granting mathematical sciences departments (Groups I-V). Canada 66 66 52 55 53 62 58 59 68 * The next two rows give the numbers who have accepted Total 845 874 856 883 958 981 9911009 1142 * appointments in mathematical sciences departments granting *To appear in a spring 1992 issue of Notices. masters and bachelors as the highest degrees.
NOVEMBER 1991, VOLUME 38, NUMBER 9 1087 Annual AMS-MAA Survey
Table 3A: Employment Status of 1990-1991 New Doctorates in the Mathematical Sciences Linear or Algebra Real or Geometry Probability Applied Discrete Numeri- Non- or Complex or Logic or Math- Math or cal linear Other TOTAL Type of Employer Number Combi- Analysis Topology Statistics ematics Analysis Optimi- Theory natorics zation Group I 21 18 31 3 5 14 1 2 1 4 100 Group II 5 8 5 2 10 1 4 1 1 37 Group Ill 9 8 11 9 9 4 1 1 2 54 Group IV 37 2 39 Group V 5 7 1 2 1 1 17 Masters 18 12 7 15 9 7 3 2 6 79 Bachelors 17 17 27 2 14 18 6 5 1 18 125 Two-year Colleges 4 2 1 1 7 3 18 Other Academic Departments 3 1 1 3 17 14 2 2 2 17 62 Research Institutes 5 3 4 9 4 1 7 33 Government 2 7 10 2 1 2 24 Business and Industry 5 3 6 2 55 10 4 4 13 14 116 Canada, Academic 11 3 8 6 11 4 1 1 8 53 Canada, Nonacademic Foreign, Academic 14 20 10 3 28 11 1 2 4 11 104 Foreign, Nonacademic 1 4 1 1 3 10 Not seeking employment 1 1 4 1 3 3 13 Not yet employed 14 17 17 3 25 23 11 4 1 10 125 Unknown (U.S.) 3 4 2 4 8 2 2 7 32 Unknown (non-U.S.)* 19 16 21 4 14 11 4 4 3 5 101 Total 148 136 152 20 261 179 50 40 34 122 1142
*Non-U.S. citizens who returned to their country of citizenship and whose status is reported as "unknown" or "still seeking employment".
Table 38: Employment Status of 1990-1991 New Doctorates in the Mathematical Sciences Females Only Linear or Algebra Real or Geometry Probability Applied Discrete Numeri- Non- or Math or Type of Employer Complex or Logic or Math- cal linear Other TOTAL Number Analysis Topology Statistics ematics Combi- Analysis Optimi- Theory natorics zation Group I 3 4 3 1 1 2 1 15 Group II 3 1 1 2 1 1 9 Group Ill 2 1 2 3 8 Group IV 9 9 Group V 3 3 Masters 6 1 1 4 1 2 15 Bachelors 8 5 12 3 3 1 2 3 37 Two-year Colleges 1 2 3 Other Academic Departments 1 1 5 2 1 1 1 6 18 Research Institutes 2 3 5 Government 2 1 1 4 Business and Industry 1 16 3 1 3 2 26 Canada, Academic 1 1 1 1 4 Canada, Nonacademic Foreign, Academic 2 3 1 9 2 1 3 21 Foreign, Nonacademic Not seeking employment 1 1 2 Not yet employed 2 4 1 7 6 2 22 Unknown (U.S.) 1 3 4 Unknown (non-U.S.)* 3 3 6 1 3 3 1 2 22 Total 28 21 28 4 70 29 9 7 6 25 227
*Non-U.S. citizens who returned to their country of citizenship and whose status is reported as "unknown" or "still seeking employment"
1088 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·-----·"··-···""""'"'''····--·-··-·"·--···...... -...... ~.-~...... __ _ Annual AMS-MAA Survey
Most new doctorates accept academic positions. Of the 704 At the same time last year, 5.7 percent of the 1989-90 new new doctorates employed in the U.S., a total of 564 (80 percent) doctorates were reported as "not yet employed". The data in hold jobs in academia. For comparison, last year's First Report Table 3A were obtained in many instances early in the summer showed 678 new doctorates employed in the U.S., including of 1991 and do not reflect subsequent hiring. Nonetheless, the 571 in academic positions. The 564 academic positions this year-to-year comparision shows compelling evidence of the year include a total of 247 in U.S. doctorate-granting depart difficult job market faced by this year's new doctorates. An ments (Groups I-V). This number is only slightly smaller than update of Table 3A is planned for the Second Report in a spring last year (259 positions in Groups I-V) and remains above the 1992 issue of Notices. In a similar update last year, the corresponding numbers in the previous two years (240 in 1988- percentage of 1989-90 new doctorates who had reported not 89 and 207 in 1987-88). Among these Groups, the number finding employment was two percent (see Notices, November hired by Group I has been essentially constant for three years. 1990, page 1219, and May/June 1991, page 413). The numbers hired by Group Il and Group Ill both declined by The 1991 Survey sent to individual new doctorates asked nine (-20 percent and -14 percent, respectively). The number for information about the type of academic position held. Based of new doctorates employed by bachelor's degree-granting on an early response from 377 individuals who provided colleges and universities increased by 20 (19 percent) from information about their contract terms, 50 percent reported that 1989-90. their position is not tenure-eligible and 50 percent reported that ,Excluding those whose employment status is unknown, 22 their position is tenured or tenure-eligible. The respondents percent of the women and 25 percent of the men accepted include holders of academic positions everywhere, not exclu appointments in Groups I-V departments. sively within the U.S. The number of new doctorates taking jobs in U.S. Table 3C shows employment status, by type of employer nonacademic positions increased significantly this year. The and Group of the department granting the degree, of the 1142 140 positions in government, business and industry in the U.S. new doctorates. The results document patterns generally recog account for 20 percent of total U.S. employment. Last year at nized anecdotally. For example, Table 3C shows that 85 this time, the total of 107 U.S. nonacademic positions repre percent of the new doctorates obtaining academic positions in sented 16 percent of the U.S. total. Group I departments obtained their degree from a Group I A striking change has occurred in the numbers shown as department. Similarly, 85 percent of the new doctorates taking "not yet employed" in Tables 3A and 3B. Of those whose a position in a Group IV department obtained their degree from employment status is known, over 12 percent are unemployed. a Group IV department. New doctorates from a Group IV or a
TABLE 3C: Employment Status of 1990-1991 New Doctorates by type of granting department
TYPE OF DOCTORATE-GRANTING DEPARTMENT TOTAL EMPLOYED TYPE OF EMPLOYER Group I Group II Group Ill Group IV Group V Group VI BY TYPE OF Math Math Math Statistics Applied Math/OR Canada EMPLOYER Group I 85 7 1 2 3 2 100 Group II 18 9 3 1 6 37 Group Ill 29 8 10 6 1 54 Group IV 2 3 33 1 39 Group V 1 2 1 13 17 Masters 24 22 16 12 5 79 Bachelors 39 37 38 4 7 125 Two-year Colleges 3 4 9 1 1 18 Other Academic Departments 20 5 3 14 20 62 Research Institutes 14 2 1 9 6 1 33 Government 5 3 3 4 8 1 24 Business and Industry 15 15 11 39 36 116 Canada, Academic 16 4 2 2 29 53 Canada, Nonacademic Foreign, Academic 47 16 6 21 7 7 104 F()reign, Nonacademic 2 2 3' 3 10 Not seeking employment 3 6 1 3 13 Not yet employed 39 30 19 10 11 16 125 Unknown (U.S.) 10 3 3 16 32 Unknown (non-U.S.)* 56 8 6 6 13 12 101
TOTALS 426 185 136 170 157 68 1142 *Non-U.S. citizens who returned to their country of citizenship and whose status is reported as "unknown" or "still seeking employment".
------.... ·------~---~---··---····---·----- ...... ______~------··------·--·-·--- NOVEMBER 1991, VOLUME 38, NUMBER 9 1089 Annual AMS-MAA Survey
Group V department assume U.S. nonacademic positions in slightly higher for non-U.S. citizens (12.2 percent of those greater proportion than new doctorates from Groups 1-V over whose job status is known) than it is for U.S. citizens (10.4 all. The unemployment rates are different for each group. percent). Understandably, a much higher percentage of the Excluding those whose employment status is unknown, the noncitizens are found in foreign academic positions. The percentages who are reported to be still seeking employment percentage of U.S. citizens in U.S. nonacademic jobs is much are 10.8 percent for Group I, 17.2 percent for Group II, 15.0 higher than the percentage of noncitizens in the same category percent for Group III, 6.0 percent from Group IV, 8.6 percent (18.2 percent of citizens versus 11.3 percent of noncitizens for Group V and 28.6 percent for Group VI (Canadian depart whose job status is known). U.S. citizens hold positions in U.S. ments). academic doctorate-granting departments in lower proportion Table 3D shows the pattern of employment within broad job than do noncitizens (22.7 percent of citizens compared to 28.4 categories broken down by citizenship status for those new percent of noncitizens), while citizens hold positions in non doctorates earned from U.S. universities (Groups 1-V). The doctorate-granting U.S. departments in substantially higher citizenship status is known for 1029 of 1074 recipients of proportion than do noncitizens (41.0 percent of citizens com doctorates from U.S. institutions. The rate of unemployment is pared to 20.6 percent of noncitizens); here all percentages exclude new doctorates whose job status is unknown.
TABLE 30: Employment Status of 1990-1991 U.S. New Doctorates (Groups 1-V) by citizenship status*
TYPE OF CITIZENSHIP TOTAL DOCTORATES WHOSE CITIZENSHIP IS TYPE OF EMPLOYER U.S. Citizens Non-U.S. Citizens KNOWN* Number Percent Number Percent Number Percent
U.S. Academic, Ph.D. Department 96 21 149 26 245 24 U.S. Academic, non-Ph.D. Department 173 38 108 19 281 27 U.S. Research Institute 16 4 16 3 32 3 U.S. Nonacademic 77 17 59 10 136 13 Foreign Academic 12 3 109 19 121 12 Foreign Nonacademic 10 2 10 1 Not seeking employment 4 1 9 2 13 1 Unemployed and seeking employment 44 10 64 11 108 10 Unknown status (U.S. address) 28 6 4 1 32 3 Unknown status (foreign address) 51 9 51 5
TOTALS 450 100% 579 100%** 1029 100%**
* The adjusted total varies from that on Table 5 because the data are gathered on different surveys. •• Column percents are rounded to the nearest whole percent.
Acknowledgments The Annual AMS-MAA Survey attempts to provide an accurate appraisal and analysis of various aspects of the academic mathematical scene for the use and benefit of the mathematics community. Every year, college and university departments in the United States and doctorate-granting departments in Canada are invited to respond. The Annual Survey relies heavily for the quality of its information on the conscientious efforts of the dedicated staff members of these departments. On behalf of the AMS-MAA Data Committee and the Annual Survey staff, I thank the many secretarial and administrative staff members in the mathematical sciences departments for their cooperation and assistance in responding to the survey questionnaires. Several people have made essential contributions to the preparation of the reports on the 1991 Annual AMS-MAA Survey. I express special thanks to Monica Foulkes for her constant support and initiatives on all aspects of the Annual Survey. Jim Maxwell regularly offers insight and direction for the work of the Data Committee. Monica and Jim share credit for the companion articles on starting salaries of new doctorates and on faculty salaries. DonLoftsgaarden and Ed Connors contributed to the data analysis and bibliography.
1090 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
Table 3E and the accompanying chart show how employ doctorate production by U.S. universities. (Table 3E includes ment patterns have varied over time for the major categories of doctorates granted by Canadian universities and Table 5 does employment of new doctorates. See also Table 5 and the graph not.) Note that all years prior to 1982-83 include doctorates accompanying it for the corresponding longitudinal pattern of granted by computer science departments.
Table 3E: Employment of New Doctorates in the Mathematical Sciences, 1977-78 to 1990-91
TYPE OF 1977- 1978- 1979- 1980- 1981- 1982- 1983- 1984- 1985- 1986- 1987- 1988- 1989- 199Q- EMPLOYMENT 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991*
U.S. academic 524 508 489 509 497 454 470 435 441 456 478 554 595 564 U.S. nonacademic 210 202 204 197 170 129 134 122 136 123 110 119 122 140 Canadian 62 47 44 41 36 30 27 30 29 37 46 37 53 53 Foreign 120 98 93 131 115 141 126 157 156 164 177 177 137 114
Total known employed 916 855 830 878 818 754 754 744 762 780 811 887 907 871
Total doctorates granted 952 889 858 904 860 792 792 769 801 845 856 958 991 1142 (fall counts)
*1990-1991 employment status figures are fall counts; the entries for previous years are spring counts. 1990-1991 figures will be updated in the Second Report in a spring 1992 issue of Notices.
1000
c 900 ~c .II: 800 .!1! Ill :I 700 'tii Ill - 600 c -CD E >- 0 500 iS. • Foreign employment E CD 400 CD Ill 0 • Canadian employment s:. 300 •Ill 0 US nonacademic ~.. 200 0 1) B US academic 0 100 Q zI 0 ,.... CXl,.... Ol 0 C\1 C') It) tO CXl Ol 0 ~ co D? CXl """D? CXl CXl CXl Ol tp r-!.. ~ d: 6 c\i C') ..!- ,;, :6 ~ ob <» 0 ,.... ,.... ,.... CXl co CXl CXl CXl CXl CXl CXl CXl CXl Ol
NOVEMBER 1991, VOLUME 38, NUMBER 9 1091 Annual AMS-MAA Survey
TABLE 4: Sex, Racial/Ethnic Group, and Citizenship of New Doctorates July 1 , 1990 -June 30, 1991 U.S. DEGREES MEN WOMEN TOTAL CITIZENSHIP CITIZENSHIP Total Total RACIAUETHNIC GROUP Not Not Canada Other Men Canada Other Women u.s. Known u.s. Known Asian, Pacific Islander 17 2 306 5 330 14 64 1 79 409 Black 7 5 12 3 1 4 16 American Indian, Eskimo, Aleut 1 1 1 1 2 Mexican American, Puerto Rican, 2 28 30 4 7 11 41 or other Hispanic None of those above 299 12 120 2 433 85 1 32 1 119 552 Unknown 23 1 20 4 48 5 1 6 54
Total 349 15 479 11 854 112 1 105 2 220 1074
CANADIAN DEGREES MEN WOMEN TOTAL CITIZENSHIP CITIZENSHIP Total Total RACIAUETHNIC GROUP Not Not Canada Other Men Canada Other Women u.s. Known u.s. Known Asian, Pacific Islander 4 18 2 24 1 3 4 28 Black 3 3 3 American Indian, Eskimo, Aleut Mexican American, Puerto Rican, or other Hispanic None of those above 1 24 7 1 33 3 3 36 Unknown 1 1 1
Total 1 28 28 4 61 4 3 7 68
Sex, Minority Group, and Citizenship 91 count is 121 percent greater than the number awarded by of New Doctorates, 1990-1991 U.S. institutions ten years ago (272 in 1980-81). Table 4 presents a breakdown according to sex, racial/ethnic The percentage increases in the numbers ofU.S. citizen and group, and citizenship of the new doctorates. The information noncitizen new doctorates parallel each other. As a conse reported in this table was obtained from departments granting quence, the percentage that U.S. citizens represent of the total the degrees and in some cases from the recipients themselves. doctorates given by U.S. universities remains at the all-time Of the 1074 doctorates awarded by U.S. universities, the low of 43 percent attained in 1989-90. Data for the period citizenship is reported as known for 1061 recipients, with 461 1973-74 through 1990-91 are shown in Table 5. reporting U.S. citizenship. The number of U.S. citizen new Among the U.S. citizens receiving doctorates in the mathe doctorates is 15 percent greater than in 1989-90 and is the matical sciences, 10 were black (7 men, 3 women) and 6 were highest count since 1981-82. Still, the number ofU.S. citizens Mexican American, Puerto Rican or other Hispanic (2 men, 4 is substantially lower than it was throughout the 1970s. See women). Table 5 and the accompanying graphs. Women account for 24 percent of the U.S. citizens receiv At the same time that the number of U.S. citizens has ing doctorates in the mathematical sciences from U.S. univer increased, so has the number of noncitizen new doctorates. A sities. This is equal to the highest percentage ever reported. total of 600 noncitizens were granted doctorates by U.S. In absolute numbers, the count of 112 U.S. citizen women universities in 1990-91. This represents an increase of 14 earning doctorates is the highest number since the data on sex percent from the numberin 1989-90. The number ofnoncitizen were first reported in 1973-74. See Table 6. new doctorates has risen every year since 1978-79. The 1990- Note that in Table 5 and Table 6 all years prior to 1982-83 include doctorates granted by computer science departments.
1092 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
TABLE 5: U.S. Citizen Doctorates Adjusted Total* Total of Graph for Table 5: U.S. Citizen Doctorates of Doctorates Doctorates Total of Doctorates by Percent given by U.S. who are U.S. % universities citizens % 80 1973-1974 938 677 72 1974-1975 999 741 74 1975-1976 965 722 75 1976-1977 901 689 76 70 1977-1978 868 634 73 1978-1979 806 596 74 1979-1980 791 578 73 60 198D-1981 839 567 68 1981-1982 798 519 65 1982-1983 744 455 61 50 1983-1984 738 433 59 1984-1985 726 396 55 1985-1986 755 386 51 1986-1987 739 362 49 40 1987-1988 798 363 45 1973- 1978- 1983- 1988- 1990- 1988-1989 884 411 46 74 79 84 89 91 1989-1990 929 401 43 1990-1991 1061 461 43 *Number of doctorates whose citizenship is known. Total will vary from that on Table 3D because the data are gathered on different surveys.
Graph for Table 5: U.S. Citizen Doctorates 1100 TABLE 6: U.S. Citizen Doctorates, Male and Female
1000 Doctorates 0 who are U.S. Male Female /o Female 900 citizens 1973-1974 677 618 59 9 741 800 1974-1975 658 83 11 1975-1976 722 636 86 12 1976-1977 689 602 87 13 1977-1978 634 545 89 14 1978-1979 596 503 93 16 1979-1980 578 491 87 15 1980-1981 567 465 102 18 1981-1982 519 431 88 17 1982-1983 455 366 89 20 1983-1984 433 346 87 20 1984-1985 396 315 81 20 1985-1986 386 304 82 21 1986-1987 362 289 73 20 1987-1988 363 287 76 21 1973- 1978- 1983- 1988- 1990- 1988-1989 411 313 98 24 74 79 84 89 91 1989-1990 401 312 89 22 1990-1991 461 349 112 24 -- Adjusted total of doctorates given by U.S. universities - Total of doctorates who are U.S. citizens
NOVEMBER 1991, VOLUME 38, NUMBER 9 1093 Annual AMS-MAA Survey
Bibliography [19] Bernard L. Madison and Therese A. Hart, A Challenge of [1] Plans and Expectations for Retirement: Survey of TIAA-CREF Numbers: People in the Mathematical Sciences. National Academy Press, Participants Ages 55-70, Research Dialogues, Issue No. 25, April1990, Washington, DC, 1990. Teachers Insurance and Annuity Association, New York, NY. [20] National Research Council. Renewing U.S. Mathematics: A [2] National Science Foundation. Science and Technology Data Plan for the 1990s. National Academy Press, Washington, DC, 1990. Book, National Science Foundation, Washington, DC, 1989. [21] National Science Board. Science and Engineering Indicator~ [3] Rand Publication Series. Reports on teaching and education. 1989. U.S. Government Printing Office, Washington, DC, 1989 (NSB Beyond the Commission Reports: The Coming Crisis in Teaching. 89-1). R-3177-RC, July 1984. Steady Work: Policy, Practice and the Reform of [22] Commission on Professionals in Science and Technology. Sala American Education. R-3574-NIE/RC, February 1988. The Evolution of ries of Scientists, Engineers .and Technicians: A Summary of Salary Teacher Policy. JRE-01, March 1988. Assessing Teacher Supply and Surveys, 15th Ed., Washington, DC, 1991. Demand. R-3633-ED/CSTP, May 1988. [23] Commission on Professionals in Science and Technology. Pro [4] D. J. Albers, R. D. Anderson, and D. 0. Loftsgaarden, Under fessional Women and Minorities-1991. Washington, DC, 1991. graduate Programs in the Mathematical and Computer Sciences. The [24] 1990--1991 Faculty Salary Survey by Discipline. Office of 1985-1986 Survey, MAA Notes No.7. Institutional Research, Oklahoma State University, Stillwater, OK, 1991. [5] The Annual Report on the Economic Status of the Profession [25] Report on the National Science Foundation Disciplinary Work 1990--1991, Academe: Bulletin of the American Association of Univer shops on Undergraduate Education. Recommendations of the discipli sity Professors, March-April1991, Washington, DC. nary taskforces concerning critical issues in U.S. undergraduate education [6] The Underachieving Curriculum:Assessing U.S. School Mathe in the Sciences, Mathematics and Engineering. National Science Founda matics from an International Perspective, Stipes Publishing Co., Cham tion, Washington, DC, Apri11989. paign, illinois, January 1987. [26] Mathematical Sciences Education Board. Mathematics Educa [7] Competition for Human Resources in the 1990s, Proceedings of tion: Wellspring of U.S. Industrial Strength. Report of a Symposium held a Symposium, Commission on Professionals in Science and Technology, December 1988. National Research Council, 1990. May 1988. [27] David Blackwell and Leon Henkin, Mathematics: Report ofthe [8] National Science Foundation, Science and Engineering De Project 2061. Phase I Mathematics Panel. American Association for the grees: 1966--89, NSF 91-314, Washington, DC, 1991. Advancement of Science, Washington, DC, 1989 (AAAS Pub 89-03S). [9] National Science Foundation, Selected Data on Science and [28] National Academy of Sciences. Engineering Personnel Data Engineering Doctorate Awards: 1990, NSF 91-310, Washington, DC, Needs for the 1990s. National Academy Press, Washington, DC, 1988. 1991. [29] Commission on Professionals in Science and Technology. Pro [10] Educating Scientists and Engineers: Grade School to Grad ceedings ofa symposium "Human Resources in Science and Technology: School. U.S. Congress, Office of Technology Assessment, OTA-SET- Improving U.S. Competitiveness" held March 1990. CPST, Washington, 377, Washington, DC, June 1988. DC, July 1990. [11] National Research Council. Summary Report 1989, Doctorate [30] Roman Czujko and David Bernstein, Who Takes Science? A Recipientsfrom U.S. Universities, National Academy Press, Washington, Report on Student Coursework in High School Science and Mathematics. DC, 1990. American lost. of Physics, New York, NY, December 1989 (AlP Pub No. [12] Edward A. Connors, A Decline in Mathematics Threatens R-345). Science-and the U.S., The Scientist, November 28, 1988. [31] A Guide to NSF Science/Engineering Resources Data. Na [13] Edward A. Connors, America's Scientific Future is Threatened tional Science Foundation, Washington, DC, 1987. by the Decline in Mathematical Education, The Chronicle of Higher [32] Christine M. Matthews, Congressional Research Service Issue Education, January 11, 1989. Brief, Science, Engineering and Mathematics Precollege and College [14] National Research Council. Everybody Counts: A Report to the Education. Library of Congress, Washington, DC, 1991. Nation on the Future ofMathematics Education, National Academy Press, [33] Recruitment,Retentionand Utilization ofFederal Scientists and Washington, DC, 1989. Engineers. A report to the Carnegie Commission on Science, Technology [15] Higher Education for Science and Engineering: A Background & Governnment. National Academy Press, Washington, DC, 1990. Paper. U.S. Congress, Office of Technology Assessment, OTA-BP-SET- [34] National Research Council. Moving Beyond Myths: Revitaliz 52. Washington, DC, March 1989. ing Undergraduate Mathematics. National Academy Press, Washington, [16] Commission on Professionals in Science and Technology. Oc DC, 1991. casional Papers, prepared by Betty M. Vetter. Look Who's Coming to [35] Richard C. Atkinson, Supply and Demand for Scientists and School (89-0), December 1988. Women in Science. Progress and Prob Engineers: A National Crisis in the Making, Science, April27, 1990, 425- lems (89--1), February 1989. Recruiting Doctoral Scientists and Engi 432. neers (89-2), February 1989. American Minorities in Science and [36] Robert Pool, Who will do Science in the 1990s?, Science, April Engineering (89--3), September 1989. Replacing Science and Engineer 27,1990,433-435. ing F acuity in the 1990s (89-4), December 1989. Supply and Demandfor [37] Survey of Mathematics and Statistics Departments at Higher Engineers in the 1990s (90--1), April 1990. Who is in the Pipeline? Education Institutions. Higher Education Surveys Report, Survey Num Science, Math and Engineering Education (90--2), July 1990. Recruiting ber 5, December 1990. Sponsored by the National Science Foundation. Doctoral Scientists and Engineers for the Twenty-first Century (90--3), [38] Board on Mathematical Sciences. Action for Renewing U.S. October 1990. Women in Science andEngineering ,AnlllustratedProgress MathematicalSciencesDepartments. National Research Council, Wash Report (90-4) December 1990. Recruiting and Retaining a Diverse, ington, DC, 1990. Quality Technical Workforce (91-1) April1991. By the Year 2000: Myths [39] Board on Mathematical Sciences. Chairing the Mathematical and Facts (91-2) July 1991. CPST, Washington, DC. Sciences Departments of the 1990s. Proceedings of a Colloquium, [17] Meeting the Needs of a Growing Economy: The CORETECH October 27-28, 1989. National Academy Press, Washington, DC, 1990. Agenda for the Scientific and Technical Workforce. CORETECH, Wash [40] Board on Mathematical Sciences. Mathematical Sciences, ington, DC, 1988. Technology and Economic Competitiveness, ed. James G. Glimm. Na [18] Measuring National Needs for Scientists to the Year 2000. tional Academy Press, Washington, DC, 1990. Report to the National Science Foundation. Commission on Professionals [41] Allyn Jackson, Top Producers ofWomen Mathematics Doctor in Science and Technology, Washington, DC, July 1989. ates, Notices of the AMS, September 1991.
1094 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
Salary Survey for New Recipients of Doctorates, 1990-1991 The figures for 1991 were compiled from questionnaires sent to academic year in which the doctorate was received. M and F individuals who received a doctorate in the mathematical are Male and Female respectively. One year or less experience sciences during the 1990-91 academic year from universities in means that the persons had experience limited to one year or the United States and Canada. less in the same position or a position similar to the one Questionnaires requesting information on salaries and pro reported; some persons receiving a doctorate had been em fessional experience were distributed to 1124 recipients of ployed in their present position for several years. Quartile degrees using addresses provided by the departments granting figures are given only in cases where the number of responses the degrees. 523 individuals returned forms between late June is large enough to make them meaningful. and mid-September. Responses with insufficient data, or from Graphs. The horizontal line represents the median salary individuals who indicated they had part-time employment, for 1990 in hundreds of dollars. The points plotted are the were not yet employed, or were not seeking employment, were median salaries for each year converted to 1990 dollars using considered unusable. Numbers of usable responses for each the implicit price deflator prepared annually by the Bureau of salary category are reported on the following tables. Economic Analysis, U.S. Department of Commerce. (Because Readers should be warned that the data in this report are the deflator is not yet available for this year, the 1991 figures do obtained from a self-selected sample and inferences from them not appear on the graphs.) The boxes show the middle half of may not be representative of the population. For more compre the population, where the quartile data are available. hensive information on the recipients of new doctorates granted Note that salaries for teaching, or teaching and research, last year in the mathematical sciences in the U.S. and Canada, have yet to return to their high point of 1970, although steady see the preceding article by D. McClure. progress has been made since 1980. (For further details, see Key to Tables. Salaries are listed in hundreds of dollars. Donald Rung's article, "A Fifteen Year Retrospective on Aca Nine-month salaries are based on 9-10 months teaching and/or demic Salaries of U.S. Doctorate Holding Faculty," in the research, not adding extra stipends for summer grants or sum November 1985 issue of Notices, pages 772-773.) mer teaching or the equivalent. Years listed refer to the
Nine-Month Salaries Nine-Month Teaching or Reported Teaching and Research Ph.D. Min Median Q Max Median in Year ~ 3 1990$ TEACHING OR TEACHING AND RESEARCH 700 {188 men+ 54 women) 1960 49 65 80 276 600 1965 70 80 105 311 1970 85 110 195 344 1975 90 120 128 135 173 284 ....(/) 500 1980 105 155 171 185 250 262 ca 1985 170 230 250 270 380 296 0 1988 200 275 293 314 575 318 0 400 1989 200 290 310 330 478 323 1990 320 710 0 230 305 350 320 -(/) 1991 150 310 330 360 610 "0 300 ....Q) "0 1988M 200 274 290 315 520 c::: 1988F 216 275 299 314 575 :::J 200 I 1989M 200 290 305 330 478 1989F 220 295 310 330 470 100 1990M 230 306 320 350 710 1990F 250 300 325 360 493 0 60 65 70 75 80 85 90 1991M 150 310 330 360 610 1991F 260 310 332 360 550 One year or less experience (129 men + 43 women) 1991M 150 315 333 360 578 1991F 260 314 325 349 475
NOVEMBER 1991, VOLUME 38, NUMBER 9 1095 Annual AMS-MAA Survey
Nine-Month Salaries Nine-Month Research Reported Ph.D. Median Max Median in Year Min 1990$ RESEARCH (7 men+ 1 woman) 1960 52 65 80 277 Graph omitted because 1965 71 81 90 315 1970 78 105 160 329 sample size too small. 1975 100 110 1980 125 137 180 210 1985 205 235 250 279 1988 260 280 385 304 1989 235 270 330 281 1990 230 300 404 300 1991 260 295 470 1988M 260 280 385 1988F
1989M 235 270 330 1989F
1990M 230 300 404 1990F
1991M 260 290 360 1991F One year or less experience (6 men + 1 woman) 1991 M 260 280 300 1991F
Twelve-Month Salaries Twelve-Month Teaching Ph.D. Reported or Teaching and Research Year Min Q1 Median ~ Max Median in 1990$ 700 TEACHING OR TEACHING AND RESEARCH (20 men+ 5 women) 600 1960 ...... No data ...... 1965 78 104 121 405 1970 95 128 200 401 en 87 145 204 .... 500 1975 322 ctl 1980 143 195 350 299 1985 220 230 273 300 470 324 0 1988 220 313 330 360 480 358 0 400 1989 238 290 315 370 620 328 -0 1990 225 318 365 404 670 365 en 1991 290 310 350 408 758 "0 300 ....Q) I "0 1988M 220 308 330 355 480 c: ::J 1988F 329 335 350 365 441 :c 200 1989M 238 295 315 370 620 1989F 275 290 314 380 434 100 1990M 225 316 360 400 670 1990F 250 320 383 420 425 0 .I 60 65 70 75 80 85 90 1991M 290 310 350 400 530 1991F 300 310 472 530 758 One year or less experience (18 men + 2 women) 1991M 290 320 350 400 505 1991F - - --
1096 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
Twelve-Month Salaries Twelve-Month Research Reported Ph.D. Min Q Median Max Median in Year 1 Oa 700 RESEARCH 1990$ (25 men + 11 women) 600 1960 97 105 140 447 1965 81 93 107 362 1970 90 120 205 376 f!? 500 1975 90 119 180 264 ttl 1980 120 180 321 276 0 1985 190 295 342 400 520 406 0 400 1988 200 245 295 331 505 320 j 1989 180 250 317 385 623 330 1 1990 180 280 300 365 546 300 1991 190 277 320 380 480 ~~ 300+------+---+----r---+---~~ "0 1988M 200 240 280 330 505 c: ::J 200 1988F 280 320 330 350 360 :I: 1989M 180 250 300 393 623 1989F 200 295 350 373 400 100
1990M 180 280 300 360 546 1990F 330 330 365 400 400 o~~---+---r--~--+---~_, 60 65 70 75 80 85 90 1991M 190 290 310 360 480 1991 F 240 272 340 405 450 One year or less experience (22 men + 6 women) 1991M 250 300 310 360 480 1991 F 264 270 307 380 400
Twelve-Month Salaries Twelve-Month Government Reported Ph.D. Min Q Median ~ Max Median in Year 1 1990$ 800 GOVERNMENT (16 men + 4 women) 700 1960 72 93 130 396 1965 70 126 160 490 1970 100 150 223 470 600 1975 78 182 247 404 1980 156 244 501 374 1985 263 294 325 381 440 385 f!? 500 1988 240 298 343 405 436 372 ttl 1989 330 363 378 438 540 394 0 1990 320 345 378 430 587 378 0 400 1991 230 365 423 497 630 r---,_---;----+----+----r---~--~1 0 1988M 240 290 332 360 436 (/) 1988F 380 380 405 430 430 "0 300· ~ "0 1989M 330 363 378 438 540 1989F -- § 200 :I: 1990M 320 345 375 430 587 1990F 330 354 378 429 480 100
1991 M 230 345 424 497 630 1991F -- o.___l---1---1---1---+---+--~ One year or less experience (13 men+ 2 women) 60 65 70 75 80 85 90 1991 M 230 330 373 450 630 1991F------
NOVEMBER 1991, VOLUME 38, NUMBER 9 1097 Annual AMS-MAA Survey
Twelve-Month Salaries Twelve-Month Business and Industry Reported Ph.D. Min ~ Median Oa Max Median in 800 Year 1990$ BUSINESS AND INDUSTRY (43 men+ 10 women) 700
1960 78 110 150 468 1965 100 136 180 529 600 1970 96 170 235 532 1975 114 187 240 415 1980 190 284 400 436 .....(/) 500 1985 260 360 400 420 493 474 ca 1988 300 400 440 490 1100 477 0 ~ 1989 250 420 464 505 5250 483 Cl 400 1990 320 438 495 533 700 495 1991 235 480 510 573 830 -0 (/) ""0 Q) 300 1988M 300 400 431 490 1100 ..... ""0 1988F 375 437 454 495 660 r:::: ::J 200 1989M 250 420 464 513 5250 :I 1989F 375 430 470 500 516 100 1990M 320 443 490 533 630 1990F 390 440 500 525 700 0 1991M 330 500 520 587 830 60 65 70 75 80 85 90 1991F 235 420 481 554 720 One year or less experience (24 men + 6 women) 1991M 380 495 505 550 715 1991F 235 420 471 510 570
Faculty Salary Survey 1991-1992 Salaries
The charts on the following pages display faculty salary data for intervals. Reporting salary data in this fashion eliminates some Groups I-VI, M and B: faculty salary distribution by rank, of the concerns about confidentiality, but does not permit mean salaries by rank, information on quartiles by rank, and the determination of actual quartiles. What can be determined is number of usable returns for the group. the salary interval in which the quartiles occur, and this infor Departments were asked to report the number of faculty mation has been added to this year's report. The salary intervals whose 1991-92 academic-year salaries fell within given salary containing the quartiles are denoted by
1098 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey
55 FACULTY SALARIES 1991-1992 50 GROUP 1-Doctorate-granting departments of mathematics (39) 35 usable .,,.,,,nnc::oc:: .lll: c 45 ca Rank ..c :c 40 +------1 1------f Assistant Professor 200 .:!:: Associate Professor 207 ;: Full Professor 935 >- 35 '3 -() ca 30 D Assistant -1ii 0 25 0- 111'&1 Associate 20 c -Cl) f •Full Cl) 15 a. ca 10 Illca >- .:t:: 5 :I ()ca u.. 0
.II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 0 C\1 (') (') '<:t '<:t LC) LC) CD CD I'- I'- co co Ol Ol 0 0 C\1 C\1 I I I I I I I I .,.... .,.... .,.... .,.... .,.... ;:: ab 6 LC) 6 LC) 6 LC) 0 LC) 6 ab 0 LC) 0 I I 0 C\1 (') (') '<:t '<:t LC) LC) CD CD I'- I'- co co Ol LC) 6 LC) 6 ab Q) CD Ol 0 0 > cc .c0 1991-1992 Academic year salary <(
55 FACULTY SALARIES 1991-1992 50 GROUP II - Doctorate-granting departments of mathematics (43) 40 usable """~'""'"'"' .lll: c 45 ..ca Rank c 40 +------1 1------1 Assistant Professor 39,827 :c Associate Professor 43,021 .:t: ;: Full Professor 59,732 >- 35 .:t:: :I ()ca 30 D Assistant -1ii 0 25 0- rB Associate -c 20 ..~ • Full & 15 ca Illca 10 ~ :I () 5 3!. 0 .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: .II:: LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 LC) 0 0 C\1 '? (') "'t "'t 1.9 LC) C9 CD I'- I'- co co ~ Ol .,....0 .,....0 .,.... .,.... .,....C\1 C\1 LC) 0 ' LC) 0 LC) 6 LC) 6 ab 6 ab 6 LC) 6 ~ C\1 (') (') '<:t '<:t LC) LC) CD CD I'- I'- co co Ol ab 6 ab 6 ab Q) CD Ol 0 0 > cc .c0 1991-1992 Academic-year salary <(
NOVEMBER 1991, VOLUME 38, NUMBER 9 1099 Annual AMS-MAA Survey
55 LTV 1991-1992 GROUP Ill - Doctorate-granting departments of mathematics (86) 50 67 199Q-1991 .Ill: 45 c Rank Mean 1! c 40 Assistant Professor 426 <30,35> <35,40> <35,40> 35,872 34,977 :c Associate Professor 472 <35,40> <40,45> <45,50> 41,828 40,737 Full Professor 688 <45,50> <55,60> <60,65> 56,857 55,917 i 35 ~ G .! 30 I 25 .. 0 Assistant ...0 ....c 20 CD II Associate ~ & 15 ca • Full I 10 >- =:I l 5 0
.Ill: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ~ ..11: ..11: ..11: ..11: ll) 0 ll) 0 ll) 0 ll) 0 ll) 0 ll) 0 ll) 0 ll) 0 LO 0 ll) 0 0 C\1 v v ll) co co co CJ) 0 0 C\1 C\1 C? C? I I II? '9 ~ ,... ,... ,... ,... ,... ll) ll) !}, !}, !}, !}, J: 0 ll) 0 0 0 "'0 0 0 I I 0 C\1 C') C') v v ll) ll) co "'co co co CJ) ll) 0 ll)' 0 !}, Q) a; CJ) 0 0 ,... > "' "' ,... 0 Ill 1991-1992 Academic-year salary ..0 55 FACULTY SALARIES 1991-1992 50 GROUP IV - Doctorate-granting depts. of statistics, biostatistics, biometrics (73) 57 usable of73 .Ill: c 45 1990-1991 1! Rank Mean c 40 Assistant Professor 163 <35,40> <35,40> <40,45> 40,943 35,883 :c Associate Professor 159 <40,45> <45,50> <50,55> 47,241 45,118 i Full Professor 361 <50,55> <65,70> <75,80> 68,983 65,703 35 ~ :I u D Assistant .! 30 ii...... 0 25 Iii Associate 0 ... 20 c • Full 8 .. 15 CD Q. ca II) 10 ca >- :I 5 =u ~ 0 ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ..11: ll) 0 LO 0 ll) 0 ll) 0 ll) 0 0 ll) 0 ll) 0 LO 0 ll) 0 0 C\1 C') C') v v ll) ll) co co ~ co co CJ) CJ) 0 0 C\1 C\1 I I I I I I I I I I I I I ,... ,... ,... ,... ,... 3: ll) 0 ll) 0 ll) 0 ll) 0 "'ll) ll) 0 LO 0 I I 0 C\1 C') C') v v ll) ll) co co R co co CJ) ll) 0 !}, 6 !}, a; CJ) 0 0 ~ "' 0 Ill 1991-1992 Academic-year salary ..0 1100 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey 55 FACULTY SALARIES 1991-1992 50 GROUP V- Doctorate-granting depts. of applied mathematics and operations research (34) 27 usable .Ill: c 45 1990-1991 I! Rank Mean c :c 40 Assistant Professor 63 <40,45> <45,50> <45,50> 45,584 44,162 ... Associate Professor 74 <45,50> <50,55> <55,60> 53,741 49,156 "i Full Professor 153 70> <70,75> <85,90> 74,722 69,801 35 ~ :I u 30 .! D Assistant iii 0 25 ... II Associate 0 20 ...c CD •Full u... 15 c.CD Ill 10 Ill Ill >- 5 =:Iu Ill LL 0 .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: .lll:: 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 0 C\1 C') C') 10 10 NOVEMBER 1991, VOLUME 38, NUMBER 9 1101 Annual AMS-MAA Survey 55 FACULTY SALARIES 1991-1992 GROUP M- Master's degree granting departments of mathematics (264) 50 152 usable .II:c 199Q-1991 I! 45 Rank Mean c 40 Assistant Professor 730 <30,35> <30,35> <35,40> 35,507 34,517 :c Associate Professor 819 <35,40> <40,45> <45,50> 42,444 41,920 i Full Professor 946 <45,50> <50,55> <60,65> 53,152 52,736 >- 35 '5.. u J!! 30 ii D Assistant .. 25 ..0 -0 20 II Associate ..c CD ...u 15 CD • Full Cl. Ill 10 Ill Ill >- 5 =:::s u .f 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 10 0 10 0 10 0 10 0 10 ,..._0 10,..._ 0 10 0 10 0 10 0 10 0 0 C\1 ('I) ('I) " Q) m 0 III 1991-1992 Academic-year salary .0 <( 55 FACULTY SALARIES 1991-1992 GROUP B- Bachelor's degree granting departments of mathematics (1012) 50 477usable .II:c 199Q-1991 I! 45 Rank Mean c :c 40 Assistant Professor 1079 <25,30> <30,35> <35,40> 32,889 31,579 Associate Professor 974 <35,40> <35,40> <40,45> 39,967 38,066 i Full Professor 868 <40,45> <45,50> <55,60> 49,057 46,405 >- 35 ..'5 u J!! 30 ii D Assistant ...e 25 -0 20 F1A Associate ..c CD e 15 CD • Full Cl. Ill 10 Ill Ill >- 5 =:::s ~ 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 10 0 10 0 10 0 10 0 10 ,..._0 10,..._ 0 10 0 10 0 10 0 10 0 0 C\1 ('I) ('I) " T" T" 0 III .0 1991-1992 Academic-year salary <( 1102 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Doctoral Degrees Conferred 1990--1991 Arizona Jaksic, Vojkan, Solutions to some problems in The following list contains the names and mathematical physics. thesis titles of recipients of doctoral degrees Arizona State University (2) Mazorow, Moya Michelle, Extremal problems in the mathematical sciences (July 1, 1990 to in codes,finite sets, and geometries. June 30, 1991) reported in the 1991 Annual MATHEMATICS Shih, Tanchu, Bounds of fixed point ratios of AMS-MAA Survey by 227 departments in 157 Cole, George R., Triangles all of whose sides permutation representations of GLn(q) and universities in the United States and Canada. and medians are rational. Each entry contains the name of the recipient groups of genus zero. Pernice, Stephen G., Techniques for coloring and the thesis title. The number in parenthe Yue, Chengbo, Rigidity of three measure graphs with forbidden trees. ses following the name of the university is the classes on the ideal boundary of manifolds of number of degrees listed for that university. A University of Arizona (10) negative curvature. supplementary list, containing names received Zhang, Xiao-Dong, On spectral properties of since compilation of this list, will appear in a APPLIED MATHEMATICS spring 1992 issue of Notices. positive operators. Bernstein, Lisa J., Quantum theories of self localization. Claremont Graduate School (2) Crowe, Kathleen M., A discrete size-structured MATHEMATICS competition model. Gooley, Theodore Alan, Quantitative com Turner, Gregg H., Spectral conditions for parisons on statistical methods in image oscillations and stabilization of systems of Alabama reconstruction. differential equations with piecewise constant Jakobsen, Per Kristen, Stability and instability arguments. Auburn University (6) of two laser models. Velasco-Hernandez, Jorge Xicotencatl, Models Mazer, Arthur A., Design and analysis of ofChagas' disease: Stability, thresholds and ALGEBRA, COMBINATORICS asymptotic behavior. AND ANALYSIS mixing machines. Stapleton, David P., A technique for the Carnes, Nell Patrick, Cyclic antiautomor Naval Postgraduate School (l) analysis of the invariance of classical gauge phisms ofMendelsohn triple systems. field theory by means offunctional equations. OPERATIONS RESEARCH Ehme, Jeffrey Allen, Boundary value problems Su, Yu, Mathematical theory and computer for ordinary differential equations. Ressler, Richard, An investigation of non simulation of isoelectric focusing. linear controls and regression-adjusted esti El-Zanati, Saad 1., Graph designs. Wu, Chuntao, Percolation in half spaces and mators for variance reduction in computer Olson, Timothy Edward, On the nonexistence Markov fields on branching planes. simulation. of a basis of translates and approximation with wavelets. MATHEMATICS Stanford University (23) Adongo, Harun Paulo Kasera, Isomorphism of FOUNDATIONS, ANALYSIS AND ENGINEERING-ECONOMIC SYSTEMS TOPOLOGY automorphism groups of mixed modules over a complete discrete valuation ring. Beider, Perry Collin, All the good ones are Curry, Stephen Burton, One dimensional plane Lee, June Bok, Integral solutions in arithmetic taken: A search-theory analysis of multi-type continua with disjoint e-dense closed subsets. progression for elliptic curves. marriage markets. Yu, Joseph Yi-Chung, Automorphisms in the Courand, Gregory Joseph, Cooperation via Stone-Cech remainder of the non-negative California justification-based consensus formation pro real number line. cesses. University of Alabama, California Institute of de Klerk, Antonie Machiel, Decision incen Technology (10) Tuscaloosa (5) tives in major systems acquisition. APPLIED MATHEMATICS Hagen, Brian Wayne, Constructing discrete MANAGEMENT SCIENCE AND STATISTICS marginal distributions via redundant proba Hobson, Dana D., Point vortex models for bilistic assessment. Abedin, Zainul, Classical and Bayesian esti- modon dynamics. mators of exponential reliability function. Matheson, David Earnest, When should you Mudkavi, Vidyadhar Y., Numerical studies reexamine your frame? Kwon, 0-Joung, A real-time expert system for of nonlinear axisymmetric waves on vortex controlling packet switching networks. filaments. Poh, Hean Lee, A neural network approach for marketing strategies, research, and decision Lucy-Bouler, Thomas, Using autocorrela Pham, Thu, Numerical studies of incom tions, CUSUMs and Runs Rules for control pressible Richtmyer-Meshkov instability in a support. chart pattern recognition: An expert system stratified fluid. Shi, Xia, Modeling the Chinese economy in a approach. general equilibrium framework. Venkatachalam, A. R., A knowledge-based MATHEMATICS MATHEMATICS approach to design for manufacturability. Delatte, David Allen, Nonstationary normal forms for Anosov diffeomorphisms and skew Chuaqui, Martin, The Schwarzian derivative MATHEMATICS product transformations. in Riemannian geometry and quasiconformal Lee, Yong-Hoon, Ambrosetti-Prodi type re Gursky, Matthew J., Compactness of con reflections in spheres. sults for periodic solutions of second order formal metrics with integral bounds on Dai, Jiangang, Steady-state analysis of re ordinary differential systems. curvature. flected Brownian motion. NOVEMBER 1991, VOLUME 38, NUMBER 9 1103 Annual AMS-MAA Survey Lundelius, Rolf, Asymptotics of the determi Racer, Michael James, Coordinating inbound Lou, Zhong Ci, Vortex approximations of the nant of the Laplacian on hyperbolic surfaces and outbound vehicle routes within a decen Navier-Stokes equations in a boundary layer. offznite volume. tralized decision environment. Lum, Robert, Piecewise affine dynamics. Mo, Xiaokang, Gauss maps and moduli spaces Rhee, Jongtae, A neural-net knowledge-based McCarnmond, Jonathan Paul, The word prob of minimal surfaces in Euclidean spaces. system with instant-based rules. lem for Burnside semigroups: A positive Mullins, David, The generalized Casson in solution for a MATHEMATICS 2:: 6. variant oftwo-field covers ofthe three-sphere McSwiggen, Patrick Dennis, Invariant mani and the Jones polynomial. Bagarla, Juan P., Definable forcing and regu folds and infinitesimal foliations. larity properties ofprojective sets ofreals. Nagayama, Misao, On valued commutative Natarajan, Loki, Unitary highest weight repre regular rings and Boolean algebras. Baxter, William Erik, Chromatic framed link sentations of certain infinite-dimensional Lie Zhang, Dong, New results on geometric invariants and cabling. groups and Lie algebras. variational problems. Behrend, Kai Achim, The Lefschetz trace Patrick, George William, Two axially symmet formula for the moduli stack in principal OPERATIONS RESEARCH ric coupled rigid bodies: Relative equilibria bundles. stability. bifurcations, and a momentum Andrad6tter, Sigrun, Stochastic optimization Bernier, David Patrick, Quasicentral approx preserving symplectic integrator. with applications to discrete event systems. imate units relative to normed ideals for the Qi, Anmin, Three dimensional vortex methods Huang, Ying, Asymptotic pencils of linear discrete Heisenberg group. for the analysis of wave propagation on programs and Markov branching decision Bonet, Maria Luisa, The Lengths of proposi vortex filaments. chains. tional proofs and the deduction rule. Ruan, Yongbin, Gauge theory and its applica Leichner, Stephanie Ann, A strictly improving Bor, Gil, Non self-dual Yang-Mills fields. tion to Riemannian geometry. linear programming algorithm using least Brown, Alton Raymond, An analytical test for Sawin, Stephen French, Subfactorsfrom quan squares subproblems. chaos. tum groups. Munoz, David Fernando, Cancellation meth Calhoun, William Cooper, The lattice ofideals Schweitzer, Laurence Britt, Representations ods in the analysis of simulation output. of recursively enumerable degrees. of dense subalgebras of C* -algebras with Nakayama, Marvin Kunio, Simulation of Chopp, David Layne, Computing minimal applications to spectral invariance. highly reliable Markovian and non-Markovian surfaces via level set curvature flow. Shepard, Marc, The topology ofshortest curves systems. Despic, Mladen, Automorphisms of radical in surfaces. Nguyen, Phuong-Vien T., Heavy traffic analy convolution algebras. Shirman, Leon A., Construction of smooth sis of processing networks with parallel and sequential tasks. Feng, Yin Sun, Stability analysis ofsome root cun•es and surfaces from polyhedral models. free or algorithms for symmetric tridiagonal Stein, Harvey Jess, Singular morphisms, Schulz, Scott, Bias reducing steady-state matrices. estimates for parallel simulation. smoothness, and lifting lemmas. Franco, Zachary Martin, Diophantine approx Wamow, Tandy Jo, Combinatorial algorithms Shahabuddin, Perwez, Simulation and analysis imation and the qx + 1 problem. of highly reliable systems. for constructing phylogenetic trees. Gokhman, Dmitry M., Complex Hardy fields. Sokkappa, Padrnini R., The cost-constrained Yang, Jian Li, Adjoint spectrum ofAnosov dif traveling salesman problem. Goldstern, Martin Robert, Sets of reals and feomorphisms in logic and the methodology countable support iteration. of science. University of California, Gonzalez-Dorrego, Maria del Rosario, Curves University of California, Davis (8) Berkeley (49) on Kummer surfaces in p3. BIOSTATISTICS Gonzalo, Jesus, Large soap bubbles and MATHEMATICS isoperimetric regions in the product of Brodziak, Jon Kenton Tarsus, Theoretical Nielsen, Jens P., Kernel estimation ofdensities Euclidean space with a closed manifold. aspects of genetic stock identification. and hazards: A counting process approach. Grzegorczyk, Iwona Maria, Vector bundles on Hann, Kathleen Marie, The average number Parker, Jennifer D., The probability of cor algebraic curves. rectednessfrom the Poisson model of nearest of normals through a point in a convex body Hammond; John Todd, The lattice of sets neighbor distance and a multivariate analysis and a related Euler-type relationship. recursively enumerable in an oracle. of benzene pharmacokinetics. Kang, Wei, Extended controller normal form, Ilmanen, Tom, Motion of level sets and of Robinson, Laurence D., The effects of co invariants and dynamic feedback lineariza variafolds by mean curvature. variate adjustment upon precision for some tion of nonlinear control systems. common generalized linear models. Jeong, Joohee, On finitely decidable varieties. Savoye, Philip, An analysis of the equation of Shiboski, Stephen C., Statistical analysis of Kania-Bartoszynska, Joanna, Examples of dif a vibrating beam subject to elastic restoring HW infectivity based on partner study data. ferent 3-manifolds with the same invariants and axial compressive forces. of Witten and Reshetikhin-Turaev. Vakilian, Ramin, Application ofnumber theory INDUSTRIAL ENGINEERING AND Kuperberg, Gregory John, Invariants of links in the statistical mechanics of quasicrystals OPERATIONS RESEARCH and 3-manifolds via multilinear algebra and and existence and asymptotic properties of Chyu, Chiuh-cheng, Computing probabilities Hopf algebras. entire solutions of elliptic partial differential for probabilistic influence diagrams. Li, Yingchen, Picard bundles and the Brill equations. Cogez, Patrick Robert, Managing uncertainty Noether problem of higher rank. Young, Robin Carl, An extension of Glimm's in release decisions for semiconductor fabri Liu, Zhu-shiu, On the extended HR algorithm. method to third order in wave interaction. cation: A fuzzy logic based approach. Lopes, Helene Judith Nussenzveig, An es STATISTICS Makjamroen, Thanet, The self-organizing list timate on the Hausdorff dimension of a and processor problems under randomized concentration set for the incompressible 2-D Kvam, Paul Haak:on, Estimation based on policies. Euler equation. ranked set samples. 1104 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·--~··~--~-! 77'1 w Annual AMS-MAA Survey Prewitt, Kathryn Ann, Weak convergence of Shors, Douglas, Deforming reducible repre Wahlen, Bruce Edward, A non-parametric Gaussian processes in nonparametric curve sentations of knot groups in SL2( C). measure of independence. estimation. Soash, James Douglas, Systems ofindependent University of California, Markov chains. University of California, Irvine (3) Santa Barbara (7) Soong, Tien-Lun, On the existence of an MATHEMATICS extremalfimctionfor J. Moser's inequality. MATHEMATICS Barry, Ronald, Minimal and near-minimal Tsui, Waikin, Domain decomposition of bihar Chang, Shu-Chu, Two-sided equivalence with resolution IV designs. monic and Navier-Stokes equation. respect to subgroups of the modular group. DeBonis, Mark Jude, Contributions to omega White, Tad P., The geometry of the outer Lee, Cheng, Approximating the averaging stable groups. space. operator. Margulies, Caryl Ann, Existence of solutions Wu, Lixin, Stability of difference approxima Miranda, Hector Fernando, G-Majorization, to some semilinear equations. tions for initial boundary value problems. reflection groups and trace inequalities. University of California, Yeung, Wing, Essentially non-oscillatory Putnam, Thomas Craig, Combinatorial Gray method for Navier-Stokes type equations. through cer Los Angeles (26) code and Hamiltonian circuits University of California, tain Cayley graphs of the symmetric group. BIOSTATISTICS Riverside (5) So, Was in, Exponential formulas and spectral Fine, Gil David, Nonparametric estimation of indices. MATHEMATICS the receiver operating characteristic curve. STATISTICS AND APPLIED PROBABILITY Hemyari, Parichehr, Evaluating robustness of McMorran, Shawnee Lee, Expansive func Best approximations in the quartiles of survival times, reliability, tions and existence theorems for singular Chaturvedi, Prachi, with respect to stop and regression coefficients when the distri quasilinear differential equations. insurance mathematics butional assumption is violated. loss distances. STATISTICS Wan, Xinyuan, Inference for a semi parametric Nisenbaum, Rosane, Covariate measurement error in the exponential regression model. Anderson, Dale, Some time series models with problem. Rutter, Carolyn Ann, A comparison ofmethods non-additive structure. University of California, for the analysis of mapped rates. de Ruiz, Kaye, A mathematical model for a Santa Cruz (2) Wanek, Leslie Ann, Multistage Markov mod paired comparison experiment on a contin MATHEMATICS elling applied to malignant melanoma pro uum of response. gression. Kemple, William, Stratigraphic correlation as Fu, Xiang, Asymptotics of Toeplitz matrices a constrained optimization problem. with symbols of bounded variation. MATHEMATICS Yang, Su-Fen, Economic design ofjoint X and Robinson, Stephen Bruce, Semilinear elliptic Bisch, Dietmar Herbert, Subfactors, actions of R control charts: A Markov chain method. boundary value problems. groups and growth invariants. University of California, University of Southern Butler, David, Normal generation of vector San Diego (10) bundles over a curve. California (1) Chow, Richard Tao-hwa, Holomorphic mo MATHEMATICS MATHEMATICS surfaces. tions on Riemann Allen, Edward E., On a conjecture of Procesi Angelone, Maria E., Jones index for rings. Conley, Charles Henry, Representations of and a new basis of graded left regular finite length of semidirect product Lie groups. representation. Colorado Dadarlat, Marius, Homotopy invariants for Celniker, Nancy Jeanne, Combinatorial prop operator algebras. erties of finite, upper half-planes and an Colorado State University (2) Donat, Rosa, Propagation of error into regions improvement on the Tutle polynomial for STATISTICS of nonlinear approximations to hyperbolic coloring grey groups. equations. Garrett, Brett Taylor, Euclidean and hyper Khodadadi, Ahmad, Studies on a general Fatemi, Emad, Numerical solution of electron bolic surfaces determined by circle parkings. distribution and censoring procedure in life and hole transport. Kelly, Colleen Lauerl, A test of the Markov testing. Kitagawa, Koji, On standard p-adic L assumption in DNA sequence evolution and Li, Junfang, Sequential and optimal single functions offamilies of cusp forms. a generalization of the model to allow the stage factorial designs, with industrial appli Lafon, Frederic, Filtering methods for the sites to evolve to unequal rates. cations. Hamilton-Jacobi equation and hyperbolic Ram, Arun, Representation theory and char University of Colorado, Denver (4) systems of conservation laws. acter theory of centralizer algebras. Little, Richard E., Manifolds of almost nega Sethuraman, Bharath, Construction of val MATHEMATICS tive Ricci curvature. ued division algebras with applications to Bradford, Bert Larue, Fast Fourier transforms Liu, Xijian, Infinite reversible nearest parti indecomposability and elementary abelian for direct solution of Poisson's equation. cle systems in inhomogeneous and random crossed products. Henson, Van Emden, Fourier methods of environments. Shick, Johnathan, Quadratic forms over func image reconstruction. McClanahan, Kevin Paul, C* -algebras gener tion fields of elliptic and hyperelliptic curves. Lett, Gregory Scott, Domain decomposi ated by elements of a unitary matrix. Thomas, Carolyn Ann, Extension of classical tion preconditioners for thin rectangular Radulescu, Florin, Fundamental group for von results in one complex variable to several p-version finite elements. Neumann algebras associated to free groups. complex variables. Rasmussen, Craig W., Interval competition Robins, Sinai, Arithmetic properties of modu Velasquez, Elinor Laura, The Radon transform graphs of symmetric digraphs and two-step lar forms. onfmite groups. graphs of trees. NOVEMBER 1991, VOLUME 38, NUMBER 9 1105 Annual AMS-MAA Survey University of Colorado, Delaware STATISTICS Boulder (1) Kim, Ji-Hyun, Conditional bootstrap methods University of Delaware (2) APPLIED MATHEMATICS for censored data. Jones, Fred Byron, Property inherited by MATHEMATICAL SCIENCES Norris, James, Estimation of the number of classes of objects through presence/absence the two-dimensional unfoldings of one Hernandez, Jorge Eliezer, Global invertibility dimensional. data. in smooth and nonsmooth analysis. Young, Thomas, A new family of survival Connecticut Mehrotra, Devan, Circularity diagnostics for functions derived from a general cumula repeated measures designs. tive damage threshold crossing model for University of Connecticut (10) evolving structural systems of improving components with biomedical and accelerated MATHEMATICS District of Columbia life testing applications. Boman, Margaret Ann, A feasible algorithm American University (3) to determine whether a 3-manifold is Haken. University of Florida (4) Budney, Paul, Some applications of the P-X MATHEMATICS AND STATISTICS INDUSTRIAL AND SYSTEMS ENGINEERING dual. Awartani, Nehaya, The asymptotic behavior of Chang, Maoli, Polyharmonic cardinal Hermite Uzsoy, Reha, Production scheduling algo- linear regression M -estimators for censored rithms for semiconductor test operations. spline interpolation. data. Her, Hyeyoung, Multiple periodic solutions in Chen, Ling, Estimation of the mean of MATHEMATICS a hanging cable with periodic forcing. positively skewed distributions to estimation Fujimoto, Ichiro, CP-convexity and its appli Her, Min, Multilinear measure theory and its of exposure to contaminated soils. cations. applications. Winter, June Frances, Art and mathematics: Manseur, Zohra Z., Decomposition and inver Hu, Shu-An, The numerical range of opera Enhancing achievement through curricular sion of convolution operators. tors. design. McMillan, Timothy, Invariants ofantisymmet Liu, Guangyu, Some problems about joint ric tensors. ergodicity and uniform distributions. George Washington University (6) Tsatsomeros, Michael, Reachability of non University of Miami (1) OPERATIONS RESEARCH negative and symbiotic states for linear MATHEMATICS AND COMPUTER SCIENCE differential systems. Abel, Patricia, Information and the design of Vinel, Gerard Francois, On Lie triple super life tests. Siler, John, Connecting the student and the systems and symmetric supermanifolds. Balana, Arturo, Stochastic monotonicity and computer: Development and implementation Zou, Zhiming, Some results on jumps of comparison: Applications to provisioning of a lab component for calculus I. splittings of recursively enumerable sets. in nonstationary repairable-item inventory University of South Florida (5) systems. Wesleyan University (4) Boukari, Djamel, Nonalgorithmic sensitivity MATHEMATICS MATHEMATICS analysis and bounds on the parameters of Guan, Zhengyuan, On operators of monotone Hasfura-Buenaga, Julio Roberto, The equiv linear and nonlinear programs. type in Banach spaces. alence theorem for zd-actions of positive Hamed, Ammar Salah, Calculation of bounds Kaplan, David, Applications ofnonlinear anal entropy. on variables and underestimating convex ysis to the control of space with preassigned Johann, Patricia, Complete sets of transforma functions for nonconvex functions. responses. tions for unification problems. Palocsay, Susan, Topics in nonconvex frac- Pan, Kuochen Guoquan, Some extremal prob Kizanis, Ann, Epicompletions of archimedean tional programming. lems in approximation theory. lattice-ordered groups. STATISTICS, COMPUTER AND Shim, Jaedong, Optimal control problems in Trigos-Arrieta, Francisco Javier, Pseudocom- INFORMATION SYSTEMS delay differential equations. pactness on groups. Weng, Xinlong, Approximation methods for Palish, Yuko, K-group group multi-variate solving nonlinear equations in Banach Yale University (6) rank test and related estimators of group spaces. differences. MATHEMATICS Cockburn, Sally Patricia, The "(-filtration on Georgia the representation ring of a p-group. Florida Curtis-Budka, Cynthia Louise, A Casson-type Emory University (2) Florida State University (6) invariant counting S0(3)-representations. MATHEMATICS AND COMPUTER SCIENCE Dartnell, Pablo Ricardo, On the homology of MATHEMATICS groups ofjets. Fletcher, Raymond, Unique path property Choi, Junesang, Determinants of Laplacians digraphs. Gonzalez, Maria Jose, Uniformly perfect sets, and multiple gamma functions. Green functions, and fundamental domains. Gersdorff, Graham, Singular nonlinear second order boundary value problems. Laeng, Enrico, Analysis of orthogonal expan Raspopovic, Pedja, Incompressible surfaces in punctured Kleinbottle bundles. sions offunctions. Georgia Institute of Technology (1) Tajdari van der, Mohammad Sina, Singular STATISTICS complex periodic solutions of van der Pol's MATHEMATICS Sherman, Robert P., U -processes and semi equation of uniform approximations for the Postell, Floyd Vince, High order finite differ parametric estimation. solution ofLagerstrom's model problem. ence methods. 1106 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey University of Georgia (4) Krishnamurti, Deepa, Resource allocation Xu, YiJing, Topological classification of mechanisms for finite sets. weakly elliptic complete intersection sin MATHEMATICS Southern Illinois University, gularities. Ding, Li-Feng, Pairs of separating vectors Zadori, Laszlo, Posets, zigzags and monotone Carbondale (3) and reflexivity. clones. Sligar, John Christopher, On the minimal MATHEMATICS v-degree of the generalized Jones polyno University of Illinois, Lin, Cantian, Some properties of Hadamard Urbana-Champaign (13) mial. matrices. STATISTICS Sarker, Tejendra N., Numerical computation MATHEMATICS Su, Kuoliang, Law of large numbers and of the solution to certain exterior Dirichlet Amir, Abdelmadjid, Strong concergence to failure rate function estimation. problems having singular points and edges. diffusion processes with application to queue Wen, Miin-Jye, Single-stage multiple compar Wang, Tingxiu, Stability in abstract functional ring theory. ison procedures under heteroscedasticity. differential equations. Balmaceda, Jose, Multiplicity-free permuta University of Chicago (12) tion representations ofthe alternating groups. Hawaii Chiappari, Stephen Anthony, Proper holomor MATHEMATICS phic mappings of positive codimension in University of Hawaii (2) Bennett, Curtis, Affine A-buildings. several complex variables. MATHEMATICS Fisher, Tony Jared, Weight operators and Feuerman, Kenneth, The Hanna-Neumann grove geometries. conjecture: A flow detection approach. Zhou, Chiping, Maximum principles and Liou Goldstein, Daniel, Heeke algebra isomor Kezdy, Andre, Studies of connectivity. ville theorems for elliptic partial differential phisms/or tamely ramified characters. equations. Kim, Hobum, Geometries and dynamical Hui, Kin-Ming, A Fatou theorem for the properties ofRiemannian foliations. PUBLIC HEALTH SCIENCES solution of the heat equation at the corner McEachin, Raymond, Analysis ofan inequality Khan, Mahmudul, Theoretical approach to the points ofa cylinder and some F atou theorems concerning perturbation of self-adjoining problem of record linkage: Maximizing the for the generalized porous medium and fast operators. diffusion equations. use of blocking. Rogers, Allen Dale, Theory and applications Jantzen, Christopher, Degenerate principal of a functional from metric geometry. series for symplectic groups. Idaho Sanders, Robin, Graphs on which dihedral, Kumabe, Masahiro, On the Turing degrees of quaternion and abelian groups act vertex Idaho State University (1) generic sets. and/or edge transitively and applications to Manhi, Antonella, Dirichlet and Neumann MATHEMATICS tensor products. boundary value problems for Yang-Mills Scofield, Paul David, Symplectic and complex Siler, Jospeh R., Reflectors matrix-valued connections. foliations. inner products, and partial orders of equivariant charac Wicks, John, Calculating Seyfried, Michael, The zeta function of an Hermitian-preserving linear transformations. teristic classes. order in a general algebra. Illinois STATISTICS Wenzel, Christian, Classification of all para Chappell, Richard, Collection and analysis of bolic subgroup schemes of a semi-simple Illinois Institute of Technology (1) truncated censored data. linear algebraic group over an algebraically closed field ofpositive characteristic. MATHEMATICS Inclan, Carla H., Retrospective detection of sudden changes of variance in time series. Zhang, Liang-Cheng, Some important contin represen Maslanka, David J., A geometrical Liu, Jun, Correlation structure and conver ued fractions ofRamanujan and Selberg. for quantum tation of the sets of pure states gence rate of the Gibbs sampler. logics. Niu, Xufeng, Space-time arma models for Indiana Illinois State University (1) satellite ozone data. Indiana University (2) MATHEMATICS University of Illinois, Chicago (8) MATHEMATICS Lenney, Stephen, G.F.B. Riemann and Fourier MATHEMATICS, STATISTICS, AND series. COMPUTER SCIENCE Promislow, Keith, Construction and appli cation of approximate inertial manifolds Northern Illinois University (1) Bultman, William, Topics in the theory of for the Ginzburg-Landau partial differential machine learning and neural computing. MATHEMATICAL SCIENCES equation. Gupta, Ajay, On the complexity ofcomputation representa Dever, Mary Beth, Moebius transformations and learning in neural networks. Zou, Yi-Ming, Structure of some tions of quantum groups. in several dimensions. Hou, Xiang-dong, Covering radius of error Northwestern University (3) correcting codes. Purdue University (15) Mbateng, Gaston Ngantcheu, Optimum selec MATHEMATICS tion procedures for linear regression model. MATHEMATICS Dietz, Jill, Stable splittings of classifying Ramachandran, Mohan, Type 11 index theorems Ban, Chun-sheng, Whitney stratification, eq spaces ofmetacyclic p-groups. for manifolds with boundary. uisingular family and the aureole of quasi Haunsperger, Deanna, Projection and aggre Sompolski, Walter Robert, The second case ordinary singularity. gation paradoxes in nonparametric statisti of Fermat's Last Theorem for fixed irregular Benjamin, Chen-Famg Liang, Fixed point cal tests. prime exponents. indices, transfers, and path fields. NOVEMBER 1991, VOLUME 38, NUMBER 9 1107 Annual AMS-MAA Survey Cho, Sanghyun, On the extension of complex Yun, Jae-Heon, Numerical solution for the Zhao, Pei-Yi, Invariant links for knotted structures on compact pseudoconvex complex minimum norm solution to the first kind graphs in 3-space. manifolds. integral equation with a special kernel and Dwyer, David John, The spectrum of the efficient implementations of the Cholesky STATISTICS complex Laplacian for N -invariant pseudo factorization algorithm on the vector and Anderson-Sprecher, Richard, The statistical Kahlerian structures on en parallel supercomputers. analysis of wildlife radio-tracking data. Hong, Bum ll, High-order regularity and ap STATISTICS Galbiati-Riesco, Jorge Mauricio, Estimation of proximation for Hamilton-Jacobi equations. Biele, Jonathan, Sample-size-optimal Bayesian choice models under endogenous/exogenous Huang, Weiming, Differential invariant prop schemes in sequential sampling. stratification. erties of analytic spaces. Carley, Michael Ray, Knowledge-based sup Lee, Chang Soo, Time series models for the Li, Wei, Coverings of algebraic varieties and port systems for statistical software. credibility estimation ofinsurance premiums. the tame version ofZariski's Conjecture. Freire, Clarice Azevedo de Luna, Applications Oh, Kyung-Ho, On topology of quasi-ordinary of resampling methods to the estimation of Kansas singularities. ecological diversity. Sastry, Pramathanath, Regular differentials Homble, Patrick Rene, On the stability of Kansas State University (6) and relative duality. linear stochastic difference equations. Xu, Jianming, On the lifetime of conditioned Li, Seung-Chun, Some admissible nonpara MATHEMATICS Brownian motion. metric tests and a minimal complete class Ghoreishi, Afshin, Positive solutions of inter theorem. STATISTICS acting models in a heterogeneous environ Mundfrom, Daniel James, Estimating course ment under mixed boundary conditions. Bose, Sudip, Bayesian robustness with shape difficulty. Logan, Roger, A study of a two-species constrained priors and mixture priors. Nusser, Sarah Margaret, Failure time analyses competing interaction model in mathematical Huang, Su-Yun, Nonparametric density esti for data collected from independent groups biology. mation by spline projection kernels. of correlated individuals. Su, Yeong-Tzay, A sequential test for Markov Park, Heon Jin, Alternative estimators of the STATISTICS dependence. parameters of the autoregressive process. Hwang, Ching-Chang, Hypothesis testing in Tan, Ming, Shrinkage, GMANOVA, control Rathbun, Stephen Lyun, Estimation and statis linear models hewing nested error structure. varieties and their applications. tical inference for space-time point processes. Neogi, Debashis, Stochastic, fractal, and Ye, Keying, Noninformative priors in Bayesian Sarkar, Sahadeb, Nonlinear least squares esti chaotic modeling of multiphase flow systems. mators with differential rates of convergence. analysis. Ogunyeni, Theophilus Olabide, Simplified Shin, Dongwan, Estimation for the autore University of Notre Dame (7) two-stage estimators and a Bayes type gressive moving average model with a unit modification of maximum quasi-likelihood root. MATHEMATICS estimates. Vander Wiel, Scott Alan, Some aspects of Tashtoush, Suleirnan, Small sample power of Bardis, Emmanuel Theodore, The defect re monitoring and control ofunivariate dynamic aligned rank transform tests in fractorial lation for meromorphic maps defined on systems. covering parabolic manifolds. experimental design. Borberly, Albert, The Dirichlet problem at University of Iowa (12) infinity and vanishing curved manifolds. APPLIED MATHEMATICAL SCIENCES Kentucky Dennee, Paul, Constant mean curvature cylin Bematz, Richard, Development of the finite ders with embedded ends. analytic method for turbulent forced and free . University of Kentucky (6) Niebergall, Ross, Dupin hypersurfaces in ~ 5 convection. MATHEMATICS O'Shea, Julann, A defect relation for slowly MATHEMATICS moving target hypersurfaces. Branner, Frank, On the projective functor. Catepillan-Clares, Ximena, Canonically Koszul Buskirk, Robert, A universal completely reg- Pilkington, Anne B., Normal subgroups of invertible, Koszul invertible, and quasinor 4-dimensional hyperbolic orthogonal groups mal pairs of operators on Hilbert space. ular curve and inverse limits of locally over arithmetic domains. connected curves. Chien, David, Piecewise polynomial colloca Szoke, Robert, Mange-Ampere models. tion for integral equations on surfaces in Glunt, William, An alternating projection three dimensions. method for linear convex programming prob lems. Iowa Espina, Carlos, Stability of equilibria in some epidemic models. Yeomans, Charles, Quintic forms over finite Iowa State University (16) Ha, Kyung Soon Jung, On simple Lie algebras and local fields. of characteristic p and l-filtrations. MATHEMATICS STATISTICS Lee, Hosae, Multigrid method for integral Deng, Keng, The asymptotic behavior of equations. Fai, Hrong-Tai, Comparison of exact and approximate tests of hypotheses concerning solutions of some nonlinear initial-boundary Levin, Rebecca, Generalizations of GCD the first-stage factor in unbalanced nested value problems ofparabolic type. domains and related topics. Gaitan, Hernando, About quasivarieties of designs and the main plot factor in split-plot Olivares, Patricio, Exactness at the middle experiments with missing data. p-algebras and Wajsberg algebras. stage of the Koszul complex of commuting Vmayagamoorthy, Manickavasagar, Inversion pairs of Hilbert space operators, with ap Shen, Pao-Sheng, The study of efficiency of of multi-dimensional Laplace transform plications to 2-variable weighted shifts and some planned unbalanced designs for esti analytical and numerical techniques. triangular pairs. mation of quantitative genetic parameters. 1108 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY. Annual AMS-MAA Survey Louisiana Law, Chun-Chung, Statistical methods for the Kapitula, Todd, Stability of travelling waves analysis of interval censored data. with applications to Ginzburg-Landau equa Louisiana State University (6) Liu, Xin-Hua, Estimating functions in regres tions. MATHEMATICS sion models with error-in-covariates. Karlovitz, Max, Some solutions to overdeter mined boundary value problems on subdo Beaulieu, Patricia Wright, A new construction MATHEMATICAL SCIENCES mains of spheres. of subgroups inducing isomorphic represen Appel, Martin J., AB percolation. tation. Kelly, James, Confidentiality protection in two Busch, Ingrid K., Vehicle routing on acyclic Chen, Sheng, Constructing isospectral but and three-dimensional tables. networks. non-isometric Riemannian manifolds. Koutsoukos, Antonis, Probabilities of mod Kosansky, Alan J., Preparation cost structures Gu, Diana, Exterior vertices in graphs and erate and large deviations of test statistics in inspection games. realization ofplurality preference digraphs. and estimators in the presence of nuisance Rangaraj, Narayan, Nonsmooth optimization: parameters. Gubser, Bradley, Problems in matroid theory. Algorithms and applications. Pfeffer, Carolyn, Harmonic analysis on solv Lakey, Joseph David, Weighted norm inequal Steinsaltz, Steven J., Scheduling jobs on a manifolds. ities for the Fourier transform. machine subject to weardown. Stuart, Donna, A new conditions for arithmetic Lee, In-Ja Baik, A numerical treatment of Trenk, Ann N., Generalized perfect graphs. equivalence. generalized eigenvalue problems for Sturm Wang, Zhiping, Continuation methods for Liouville equations. Tulane University (7) solving the variational inequality and com Martin, Donald, Estimation of the period of MATHEMATICS plementarity problems. periodically correlated random sequences. Calzada, Maria Eugenia, A combustion model MATHEMATICS McGowan, Jill F., Lower bounds on the diameters of space forms. for incompressible flows. Furusawa, Masaaki, On Fourier coefficients of Huth, Michael Reiner, Projection-stable and Eisenstein series on G0(5, 2). Miner, Robert Roland, Affine manifolds with dilations. zero dimensional domains. Kramer, Richard, The periodic Hopf ring of Li, Xuefeng, A compressible vortex method connective Morava K -theory. Rivera, William, Discrete dynamical systems modeled by difference equations with appli for viscous gas dynamics and its numerical Tanabe, Michimasa, On certain periodic co cations to digital filters and neural networks. implementations. homologies ofChevalley groups. Segalla, Gabriella, Approximation theorems Yao, Dongyuan, Higher algebraic K -theory Sowers, Richard, New asymptotic results for for linear integra-differential equations in of admissible Abelian categories and local stochastic partial differential equations. Banach spaces. ization theorems. Stietz, Philip, Automorphisms of stable struc Song, Yu, Numerical methods for turbulent Zhou, Qien, The homology of the double loop tures. combustion problems. space of the Thorn space MU(2). Sweet, William, The metaplectic case of the Tran, Hong Thi, Boundary layer phenomena Weil-Siegel formula. for a turbulent model. University of Maryland, Takagi de Cristoforis, Masako, The Stone Villarreal, Karen Mary Zeringue, Fibered Baltimore (2) Weierstrass property in semi-simple commu products of homogeneous continua. MATHEMATICS AND STATISTICS tative branch algebras. University of Southwestern Abbad, Mohammed, Perturbation and stabil Trivedi, Hiren, Development of manpower Louisiana (7) ity theory for Markov control problems. planning models with known target size. Tsuchiya, Takuya, A priori and a posteriori MATHEMATICS Shyong, Wen-Jong, Homogenization and sym- metry in perforated elastic materials. error estimates of finite element solutions of Bourque, Anthony Keith, Matrices associated parametrized nonlinear equations. with classes of arithmetical functions. University of Maryland, Cobb, Shannon Sherlita, Quenching for para College Park (23) Massachusetts bolic mixed boundary-value problems. MATHEMATICS Fung, Tai-Wai, Dead cores and quenching for Boston University (7) semilinear reaction-diffusion systems. Chen, Sy-Mien, Robust tests in statistical Hu, Chenyi, Optimal preconditioners for the quality control. MATHEMATICS interval Newton method. Clemons, Curtis, Uniqueness results of semi linear elliptic equations. Brown, John, Analysis of a model of a sigma Vincent, Diana J., An inward harmonic contin delta modulator with an arbitrary input uation problem with biomedical application. Faulkenberry, Richard, On some interpola tion problems for rational matrix-valued signal. STATISTICS functions. Ramaswamy, Ratna, Techniques for analyzing Noorossana, Rassoul, An imperial Bayes Fletcher, Charles, Multiscale periodic homog ordinal scaled data. approach to statistical process control. enization of certain elliptic equations using Sanchez-Morgado, Hector, Lefschetz formulas Walsh, Dennis, A bounded distribution with viscosity solution methods. for Anosov flows. Poisson properties. Heller, William Harold, Frames of exponen Turpin, Mark, Rotation number properties of tials and applications. a class of annulus homeomorphisms with an Maryland Heyman, Robert, Interpolation of entire invariant indecomposable cofrontier. Walsh, James, Rotation vectors for maps and Johns Hopkins University (15) functions--infinite order. Hugger, Jens, Computational aspects and flows on compact surfaces. BIOSTATISTICS adaptive solution methods in the finite Whalen, Edward, The asymptotic distribution Karim, M. Rezaul, Generalized linear models element method for non-linear, parametrized of magnitude trimmed sums and related with random effects. problems. results. NOVEMBER 1991, VOLUME 38, NUMBER 9 1109 Annual AMS-MAA Survey Yu Kong, Wen Yuan, A general procedure for Burnol, Jean-Fran~ois, Weierstrass points on Hahnfeldt, Philip J., The suitability and the specification, estimation, and graphical arithmetic surfaces. formulation of a continuous-time, Markov presentations ofthe hazard regression model. Darmon, Henri, Refined class number formulas chain approach to cellular DNA radiation for derivatives of £-series. damage and repair. Brandeis University (6) Frenkel, Edward, Affine Kac-Moody algebras Hansen, Mark D., Results in computational MATHEMATICS at the critical level and quantum Drinfeld geometry: Geometric embeddings and query Sokolov reduction. retrieval problems. Boden, Hans, Representations of orbifold Hu, Yi, The geometry and topology of quotient groups and parabolic bundles. McKernan, James, On the hyperplane sections of a variety in projective space. varieties. Fong, Lung-Ying, Studies on the degeneration Iyer, Renganathan G., Modular and conformal of algebraic curves. Ramsay, Keith, Power-free values of polyno mials. invariance constraints in the representation Hughes, James, Peripheral link-homotopy theory of super-affine algebras. invariants. Schwartz, Andrew D., /gusa towers over Hilbert modular surfaces. Mascarenhas, Walter Figueiredo, On the con Kao, Shu-Jung, On values of Gauss maps of vergence of the Jacobi method for arbitrary complete minimal surfaces on annular ends. Spencer, Philip, Yang-Mills connections with asymptotically constant curvature. orderings. Lam, Ngau, A study of the geometry of Masson, Gfsli, Rings of differential operators algebraic curves and determinantal varieties. STATISTICS and Etale homomorphisms. Wu, Bing-Le, Jsoparametric submanifolds of Belin, Thomas Richard, Using mixture models Palmieri, John H., A chromatic spectral Lorentzian spaces. to calibrate error rates in record-linkage sequence to study Ext over the Steenrod procedures, with application to computer Harvard University (27) algebra. matching for census undercount estimation. Pedersen, Jan, Renormalization, singular cur APPLIED SCIENCES Brown, Constance Marie, Assessing associa rents, and representations of infinite dimen tion within a bivariate time series. Beaver, Donald R., Security, fault-tolerance, sional groups on quantized fields. · and communication complexity for dis Meng, Xiao-Li, Towards complete results for Piazza, Paolo, K -theory and index theory on tributed systems. some incomplete-data problems. manifolds with boundary. Faybusovich, Leonid, Dynamical systems that Massachusetts Institute of Schwabe, Eric J., Efficient embeddings and solve eigenvalue and linear programming Technology (34) simulations for hypercubic networks. problems. Thompson, Alan A., Sobolev estimates for OPERATIONS RESEARCH Feigin, Gerald E., Comparison methods for singular radon transforms. scheduling control ofmulticlass single server Ballman, Karla V., Cost-effectiveness of smart Wang, Frank Y. H., Conductors of fields queues. traffic signals. arising from Stark's conjecture. Hwang, Ten-Lee, Integrating visions modules Gau, Shiow-Hwa, Server management in West, Julian, Permutations with forbidden sub for moving edge analysis. queueing systems. sequences; and, stack-sortable permutation. Keeler, Kenneth C., Map representations and Goemans, Michel X., Analysis of linear Wu, Peiru, A singularity method for sedimen optimal encoding for image segmentation. programming relaxations for a class of tation and shear flow of suspensions. connectivity problems. Kochhar, Sandeep, Cooperative computer Wylie, Dorshka C., Condensation in a higher aided design: A paradigm for automating the Nakazato, Daisuke, Transient distributional core model. results in queues with applications to queue design and modeling of graphical objects. Yang, Bo-Yin, Two enumeration problems ing networks. Lee, Morris, Moment methods for recovering about Aztec diamonds. Richetta, Octavio, Ground holding strategies affine transformation in computer vision. Yang, Julia S., Symmetricfunctions,plethysm, for air traffic control under uncertainty. Lyuu, Yuh-Dauh, An information dispersal and enumeration. van Ryzin, Garrett, Stochastic and dynamic approach to issues in parallel processing. Yavin, David, The intersection homology with vehicle routing in Euclidean service regions. Marks, Joseph W., Automating the design of twisted coefficients oftoric varieties. Venkatakrishnan, C. S., Analysis and opti network diagrams. Zhang, Jian James, Theory ofquantum groups. mization of terminal area air traffic control Nitzberg, Mark, Depth from overlap. operations. Zhou, Yifan, Nonlinear instability of three Nowlin, William C., Tactile sensing with dimensional waves on shear flows. MATHEMATICS compliant manipulators. Northeastern University (6) Park, Frank C., The optimal kinematic design Biedrzycki, Witold R., Spinors over a cone ofmechanisms. Dirac operator and representations of Spin MATHEMATICS Sistare, Steven J., A graphical editor for (4,4). Bassiakos, Yiannis, The validity of the boot 3-dimensional constraint-based geometric Callejas-Bedregal, Roberto, Algebraic treat strap in the two-sample problem with right modeling. ment of the Whitney conditions. censoring. Tam, Va-on, Transaction management in data Chen, William Y. C., On the combinatorics of Fang, Guangxiong, Stability and instability of migration systems. plethysm. open coverings. Tsantilas, Athanasios, Communication issues Duval, ArthurM., Simplicialposets: !-vectors Halverson, Kimberly J., Multiple recurrence, in parallel computation. and free resolutions. alpha type, and sequences of integers for Edidin, Dan S., Brill-Noether theory in transformations with infinite invariant mea MATHEMATICS codimension-two. sure. Abramovich, Dan, Subvarieties of abelian Grigni, Michelangelo, Structure in monotone Ji, Lizhen, The spectral degeneration for varieties and ofJacobians of curves. complexity. hyperbolic Riemann surfaces. Aitken, Wayne, An arithmetic Riemann-Roch Grossberg, Michael D., Complete integrability Kui, Johnny, Analysis of neural networks for theorem for singular arithmetic surfaces. and geometrically induced representations. pattern recognition and associative memory. 1110 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY m ~~J1Hilj1!---=~- Annuai AMS-MAA Survey Piscitelle, Louis, Nested center manifolds for Zhang, Sixiang, Markov properties ofmeasure- Chun, Sungki, Weak convergence of zero a set of weather equations. indexed Gaussian random fields. measures of orthogonal polynomials in the case of a thin weight measure. Tufts University (1) University of Michigan, Corson, Jon M., Thesis in combinatorial group Ann Arbor (37) MATHEMATICS theory. Hwang, Eunmi C., The number of projective BIOSTATISTICS Ghamsari, Manouchehr, Extension domains. representations of a finite group over an Lee, Seungyeoun, Testing for and adjusting Kay, Leslie D., The Kobayashi-Royden metric arbitrary field. for dependent censoring in survival analysis. for ellipsoids and perturbations of the ball. Kim, Hoil, Stable vector bundles on Enriques University of Massachusetts, Park, Taesung, Estimation of the nonresponse models for categorical data. suifaces. Amherst (9) Petroni, Gina, A class of two-sample test Lee, Jong Bum, Generalized spherical space MATHEMATICS AND STATISTICS statistics for stochastically ordered distribu forms. Fuller, Mark, Investigations of Qk(>..): Some tion functions with interval censored data. Li, Wing Suet, On polynomially bounded notions of normality for filters ofpartitions. Schmaltz, Stephen, Inverse nonlinear estima operators. Morris, Brian C., Variational study ofinterstel tion in the presence of measurement error. Li, Zhongyan, On spherical CR manifolds lar magnetic gas clouds: Theory, modeling, Sereika, Susan, Techniques for analyzing with positive Webster scalar curvature. and computation. collinear censored data. Lou, Yu-Cai, Constructionsand3-deformations of2-polyhedra and group presentations. Olubummo, Yewande, Measures on empirical INDUSTRIAL AND OPERATIONS Pan, Yifei, Proper holomorphic mappings in logics and the properties of their associated ENGINEERING dual Banach spaces. eN Al-Sultan, Khaled, Nearest point problems: Tang, Ding Yi, Compact Lie group actions Seidel, Roger R., Slowly decreasing functions Theory and algorithms. and total mean curvatures of irreducible and closed ideals. symmetric subspaces. Arantes, Jose, Resolution of degeneracy in Soderborg, Nathan R., Quasiregular mappings generalized networks and penalty methods Wang, Kongming, Limit theorems and param and Royden algebras. for linear programs. eter estimation for the Q-state Curie-Weiss Stanoyevitch, Alexander, Geometry ofPoincare Potts model. Ben Kheder, Nejib, Economic lot-sizing in domains. just-in-time procurement systems. Wang, Sheng, Internal cnoidal waves in Wang, Mei, Local limit theorems and occupa continuously stratified fluids. Bourland, Karla, Production planning and tion times for perturbed random walks. control for the stochastic economic lot Xu, Zhong-Ling, Polynomial families with scheduling problem. STATISTICS multilinear uncertainties. Brown, Matthew, A mean-variance serial Sarkar, Jyotirmoy, Bandit problems with co Zalarnea, Fernando, Axiomatic enumeration replacement decision model. · variates: Sequential allocation of experi and parametrization: A category-theoretic ments. approach. Cho, Myeon-Sig, Design and peiformance analysis of trip-based material handling Zang, Xin-Min, Geometry of spherical mini Wayne State University (8) systems in manufacturing. mal submanifolds. Hahm, Juho. Economic lot production and MATHEMATICS Michigan delivery scheduling problem. Chen, Xu-Ming, Groups related to generalized Hsiao, Hongwei, Posture preferences and quadrangles. Michigan State University (10) postural behavior during static, seated, Chen, Zhi-Hong, Reductions of graphs and visual and manual tasks. spanning Euclidean sub graphs. MATHEMATICS Kim, Deok-Soo, Cones on Bezier curves and Jeon, Tae-ll, Limit theorems for nonlinear vec Cuckovic, Zeljko, Commutants of Toeplitz suifaces. tor functionals of vector Gaussian processes. operators on the Bergman space. Palmiter, Susan, Use of animated graphical in Jiang, Jing-Lin, Existence and regularity of Ding, Jiu, Finite approximations ofFrobenius structions to present procedural instruction. stochastic partial differential equations in Perron operators. Park, Yunsun, Average optimality in infinite Holder spaces. Gu, Dangsheng, Some operators and Carleson horizon optimization. Li, He, A generalized optimization problem measures on weighted norm spaces. Rim, Suk-Chul, Circular layout problems in with application to optimal design theory. Nah, Young-Chae, Dirichlet spaces on finitely manufacturing systems. Wu, Wen-Jun, Unequal arm chemical balance connected domains. Saldana, Norka, Designed evaluation ofa com weighing design. Wang, Xiaoshen, Homotopy methods for solv puter system operated by the workforce for Zhao, Guanghua, Banach* -algebras of com ing deficient polynomial systems. the collection of perceived musculoskeletal pletely bounded multilinear forms on locally discomfort: A tool for surveillance. compact groups. STATISTICS AND PROBABILITY Ulin, Sheryl, Development of guidelines for Zhong, Xiao-Hu, The radial limits offunctions Andhivarothai, Nupun, Sufficiency in the the use of powered hand tools using psy in star-invariant subspaces of weighted HP presence of nuisance parameters. chophysical data. BMOA. Kinateder, Kimberly, Strong Markov proper Yang, Kai, New iterative methods for linear Minnesota ties for Markov rdndomfields. inequalities. Mashayekhi, Mostafa, Stability ofsymmetrized University of Minnesota (26) probabilities and compact equivariant deci MATHEMATICS sions. Andreev, Valentin V., The Poincare inequality: MATHEMATICS Vasudaven, Mangalarn, Weak convergence of A necessary and sufficient condition. Barcelo, Bartolome, On the harmonic measure standarized Kaplan-Meier process in L 2 Chun, Hyesook, Hilbert series for graded for nondivergence elliptic equations with space. quotient rings of2-forms. lower order terms. NOVEMBER 1991, VOLUME 38, NUMBER 9 1111 Annual AMS-MAA Survey Cerutti, Cristina, Properties of Green's func Mississippi Well, Roark, Artificial intelligence methods tions and uniqueness for diffusions related to in utilizing low dimensional models of 2nd order elliptic operators with decontinu University of Mississippi (1) differential games. ous coefficients. MATHEMATICS Yan, Di, Methods for stochastic optimization. Collins, Charles Robert, Computation and Zhan, Wei, Noninteracting control with stabil analysis of twinning in crystalline solids. Norris, Paula Anell, Starlike functions with ity for nonlinear systems. Escauriaza, Luis, Boundary and interior regu indicator B. larity of gradients of solutions of parabolic Montana and elliptic problems. Missouri Hong, Dug Hun, Random walks with time St. Louis University (2) Montana State University (1) stationary random distribution function. Jang, Jaeduck, On spike solutions ofsingularly MATHEMATICS MATHEMATICAL SCIENCES perturbed semilinear Dirichlet problem. Hopfinger, Mark M., Nearly simple modules Fredenberg, VIrgil, Computer generated graph Kwak, Minkyu, Finite dimensional inertial for polycyclic-by-finite groups. ics in calculus and effect on student achieve forms for the 2D Navier-Stokes equations. Ikeda, Yutaka, A generalized Toponogov com ment. Lee, Jaejin, The combinatorics of the spin parison theorem. University of Montana (1) characters of the symmetric group. Mari-Beffa, Gloria, Poisson geometry of the University of Missouri, MATHEMATICAL SCIENCES Columbia (4) Virasoro algebra. Rummel, Steven, A procedure for obtaining Marin-Malave, Santiago, Fatou theorems for MATHEMATICS a robust regression employing the greatest some nonlinear elliptic partial differential Easley, Kevin, Local existence of warped deviation correlation coefficient. equations. product metrics. Matos, Joao, Some mathematical methods of Leranoz, Maria Camino, Uniqueness of un Nebraska mechanics. conditional bases in quasi-banach spaces. Pan, Tsorng-Whay, Analysis of shear flow University of Nebraska (3) instabilities in nematic liquid crystals. STATISTICS MATHEMATICS AND STATISTICS Reitich, Fernando Leiva, Topics in free bound Kaiser, Mark, Statistical models for limiting ary problems and phase transitions. factors in ecology. Jia, Bao Ping, Splitting of prime ideals and Rusewicz, Andrzej, Extending reasonable Summerville, John, Conditional properties of valuations. ideals to countably saturated ideals on some interval estimators. Li, Yuanzhang, Robust Bayesian analysis. small algebras of sets. Woerner, Edwin Louis, Self-similar solu Washington University (16) Sand, Mark P., The structure of the inverse of tions to the detonation equations in non layer potential operators. MATHEMATICS homogeneous media. Seppalainen, Timo, Large deviations for pro Chen, Zhenhua, Boundary regularity of the cesses with stationary random distributions. a-equation on convex domains. New Jersey Sheng, Li, Dynamics offluid sedimentation of Fan, Dashan, Hardy spaces on compact Lie spherical particles with inertial effects. Princeton University (7) groups. Shepard, Melissa, Some calculations in K theory with an application to the image of Gavosto, Estela Ana, Analysis on finite type MATHEMATICS the stable Hurwicz homomorphism in K domains. Axelrod, Scott, Geometric quantization of homology of infinite quaternionic projective Kellum, Mark, Uniformly quasiconformal fo Chern-Simons gauge theory. space. liations. Bertozzi, Andrea, Existence, uniqueness and a Su, Jianzhong, Delayed oscillation phenomena Lin, Nong, Galerkin method for the boundary characterization of solutions to the contour in the Fitz-Hugh-Nagumo equation. integral equations of the Dirichlet problems dynamics equations. Susanka, Lawrence, Potential theoretic and ofthe Laplace equation in Lipschitz domains. Fractman, Gabriel, On the product formula for stopping time methods for converse mean Ma, Daowei, Invariant metrics on domains. quadratic forms. value problems. Peloso, Marco Maria, Mobius invariant spaces Schwartz, Richard, The limit sets of some Zheng, Stephen, In''estigations on the question on the unit ball. infinitely generated Schottky groups. of finiteness for the solutions of Plateau's Wu, Zhijian, Hankel and Toeplitz operators on Shu, Wei-Ton, Spin-field equations and Yang problem. Dirichlet spaces. Mills equation. STATISTICS Zheng, Juneng, Some extremal problems in Steinke, John, The second variation of normal volving n points on the unit circle. Chattopadhyay, Manas, Dirichlet bandit prob currents. lems. SYSTEMS SCIENCE AND MATHEMATICS Sullivan, John, A crystalline approximation theorem for hyperswfaces. Chen, Chung-Nien, Model influence and influ Bouthellier, Paul, Analysis and design of ential observations in Bayesian statistics. discrete-time, linear time-varying systems. Rutgers University, Huang, Tze-Hsi, Statistical inferences on Ganguly, Sugato, Discrete time nonlinear_ New Brunswick (10) change point problems. feedback method on robot arm control. Kahng, Myung Wook, Inference and diagnos Geist, Daniel, Semantic control in continuous MATHEMATICS tics for nonlinear regression. time: Applications to aerospace problems. Caravella, Sandra, N onsingular affine surfaces Makris, Lukas, Modeling uncertainty in the Maserang, Daniel, Estimating R&D spillovers with unique C* action. predictive causalty assessment problem for in major defense contractors an application Chua, Seng Kee, Extension and restriction adverse drug reactions. of nonlinear filtering. theorems on weighted Sobolev spaces. 1112 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Fernandes, Jose C., Mean value and Har Loo, Saoping, Multicolor Ramsey numbers for BIOMETRICS nack inequalities for a class of degenerate disjoint unions of graphs. Feng, Ziding, Statistical inference using max parabolic equations. Mantzivis, Georgios, Circuits in bounded imum likelihood estimation and the gener Holt, Linda, Singularities produced in conor arithmetic. alized likelihood ratio under nonstandard mal wave interactions. Mishra, Sudakara, Rays of small integer conditions. Huang, Yi-Zhi, On the geometric interpreta of homogeneous ternary quadratic solutions MATHEMATICS tion of vertex operator algebras. equations. Destrempes, Francois, Invariants of virtual Kuplinsky, Julio Mario, Hard-to-color graphs Persinger, Sharon E., One-relator groups v.1ith lattices over group rings with applications to and mixed and restricted colorings. torsion virtually free-by-cyclic groups, and Galois module structure. Lohrenz, Terry M., Determinants on CR free-by-free groups. Friedman, Erich, First passage percolation on manifolds. Tien, Jonathan, Neural Petri nets and their a Poisson lattice. Lu, Guozhen, BMO estimates for eigenfunc applications to combinatorial games. Stephen, Holomorphic motions tions on Riemannian surfaces and degenerate Lieb, Gregory spaces. differential equations given by vector fields Clarkson University (2) and Teichmiiller satisfying Hormander's condition. Luo, Xiaolong, High dimensional annihilating MATHEMATICS AND COMPUTER SCIENCE random walks. Wang, Yuan, Algebraic differential equations branching and nonlinear control systems. Li, Guoqing, Edge crossing number problem Peterson, Todd Edmund, Convergence prop and interactive graph editing system. erties of the discontinuous Galerkin method STATISTICS Li, Wei, Applications of the Riemann-Hilbert for a scalar hyperbolic equation. Jou, Hann-Chang, Assessing interrater agree problem to colliding gravitational waves. Petrie, Emily Ruth, Convergence of power ment and treatment effect when data is series invariants for families ofp-adic Galois ordinal. Columbia University (11) representations. Senqupta, Ambar Niel, The Yang-Mills mea New Mexico MATHEMATICS sure for the two-sphere. Agboola, Adebisi, Abelian varieties and Ga Stafford, Seth, Harmonic functions on mani New Mexico State University (2) lois module structure in global fields. folds of non-negative Ricci curvature. Jiang, Renfang, On free actions on R-trees. Yakhnis, Alexander, Game-theoretic seman MATHEMATICAL SCIENCES Lee, Li, Freeness and discreteness of actions tics for concurrent programs and their Combs, Randel, Weighted norm inequalities on R-trees by finitely generated free groups. specifications. with general weights for multipliers on Lisca, Paolo, On smoothly embedded tori in Yakhnis, Vladimir R., Concurrent programs, functions with vanishing moments. four-manifolds. calculus of state-strategies and Gurevich El-Gawi, Salem, Aspects ofFatou-Julie theory Harrington games. Liu, Yingsheng, Commensurability groups of for rational functions of degree one to four. uniform trees. STATISTICS University of New Mexico (4) Qin, Zhenbo, Equivalence classes of ample Hsieh, Pushing, Performance of diagnostic divisors and moduli spaces of stable rank-2 setting. MATHEMATICS AND STATISTICS tests in a non-parametric bundles on ruled surfaces. Kane-Esrig, Yana, Information retrieval and Engman, Martin Feeney, The spectrum of a Rogers, Michael Kevin, On a multiplicative estimation with auxilary information. surface of revolution. additive Galois invariant and wildly ramified McCanna, Joseph E., Characterization of self extensions. New York University, Courant Institute (19) dual graphs and related topics in graph Zhang, Shouwu, Numerical criteria for am theory. pleness of arithmetical line bundles. MATHEMATICS Porter, Thomas Dale, Partitions of graphs. Asch, Mark, Analysis and numerical solution STATISTICS Robey, Thomas Howard, The mixed finite of a transport equation for pulse rejlectivn in element method. Quan, Hui, Diagnostic jackknife and bootstrap a randomlylayered medium. for the proportional hazards model and Calderon, Pablo, On the macroscopic behavior New York nonparametric estimation of a treatment of a large stochastic system. effect under biased sampling. Coffey, Mark, The cell discretization algorithm Adelphi University (1) Ray, Bonnie Kathryn, Fractionally differ for partial differential equations. MATHEMATICS AND COMPUTER SCIENCE enced ARMA processes: Seasonality and Cohn, Steve, Resonance and long time forecasting issues. existence for the quadratically nonlinear Gusack, Russell, Mathematical models for the Xue, Xing Xiong, The martingale representa Schrodinger equation. epidemiology ofAIDS. tion theorem for a class of Levy processes Coulter, Lisa Osterman, Piecewise smooth CUNY, Graduate Center (9) and its applications. spline interpolation and the numerical solu tion of the Riemann problem for materials (15) MATHEMATICS Cornell University undergoing a phase transition. Arcones, Miguel, On the asymptotic theory of APPLIED MATHEMATICS Filippas, Stathis, Center manifold analysis for the bootstrap. a semilinear parabolic equation arising in Danas, George, Crossed n-fold extensions and Laney, Culbert, Monotonicity and overshoot the study of the blow up Ut Au = uP. to cohomology. conditions for numerical approximations Firoozye, Nikan, Optimal translations and conservation laws. Fung, Terry, Fundamental domains ofmodular relaxations of some multiwell energies. subgroups using isometric circles. Park, Chang Kyun, Testing 'fuzzy indepen Lima, Paulo- Cupertino, The renormalization tables. Jiang, Wei-Hua, On the dynamics of>.. tanz. dence' in two-way contingency group in the local potential approximation. NOVEMBER 1991, VOLUME 38, NUMBER 9 1113 Annual AMS-MAA Survey McGrattan, Kevin, A comparison of the Schroeder, William, Geometric triangulations Teng, Lichen L., The probability of correct potential and the Euler formulations of the with application to fully automatic 3-D classification conditional on distance from equations of motion for transonic flow. generation. boundary. Morokoff, William, Quasi-Monte Carlo meth Wu, Xiao-Lei Charley, A computer software Yang, Chin-Chun, A minimum modeling strat ods for numerical integration and simulation. system for solving graph theory problem~ egy in prediction outside the range of Puppo, Gabriella, Prandtl's equations: Numer graph pack. observations. ical results about singularity formation and SUNY at Albany (4) Zhang, Fenggang, On numerical methods for a numerical method. solving singular integral equations. Rybka, Piotr, Dynamical modeling of phase MATHEMATICS AND STATISTICS MATHEMATICS transitions in solids by means of viscoelas Bomash, Gregory, Random analytic functions, ticity in many dimensions. their zero sets and singular measures. Gong, Guihua, Smooth extensions for finite Schevermann, John, Tabular equations of Kim, Seok-Chan, Properties of the family of CW complexes and index theory. state and their use in the solution ofRiemann analytic functions with subordination class Hidalgo, Ruben, On Schottky groups with problems. determined by rotations. automorphisms. Smith, Barry, Domain decomposition algo Rajia, Abbess, A new class of nonparametric Kasper, Brian, Examples of symplectic struc rithms for the partial differential equations Hazard rate function estimates. tures on fiber bundles. of linear elasticity. Weinraub, David, Cofinite induction and Lam, Tsz Kin, Spaces of real algebraic cycles Tahuildar-Zadeh, Abdoireza, Equivariant har Noether's theorem for Hopf orders in group and homotopy theory. algebras. monic maps of the Minkowski space. Liu, Zhong-dong, Nonnegative Ricci curvature Wang, Xiao, Singular solutions for the non SUNY at Binghamton (2) near infinity and geometry of ends. linear Schrodinger equation and Zatchanov MATHEMATICAL SCIENCES McHugh, Andrew, The space of super light equations. rays for complex conformal spacetimes. Militello, Robert, On the Cayley-Hamilton Xin, Xue, Existence and stability of travelling property in groups. Rong, Xiaochun, Collapsed 3-manifolds and waves in periodic media governed by a rationality of limiting 'T!-invariants. Moore, Theresa Engel, Deformation and bistable nonlinearity. rigidity along paths of manifolds. Shen, Zhongmin, Finite topological type Zingano, Paulo, Nonlinear stability analysis and vanishing theorems for Riemannian with decay rates of two classes of waves for SUNY at Buffalo (11) manifolds. consen•ation laws. INDUSTRIAL ENGINEERING Tan, Delin, On generalizations of ]r/Jrgensen's Zumbrun, Kevin, Asymptotic behavior for Dell, Robert Franklin, The development of inequality for Kleinian groups and some systems ofnonconvex conservation laws. equitable vehicle routes for overnight parcel topics on quasiconformal extension. Yu, Jinguo, The Euler equations of an incom Polytechnic University (4) deliveries. Jamil, Mamnoon, The !-center problem with pressible ideal fluid in a high-dimensional MATHEMATICS queueing. bounded region. Zeng, Xueqi, Clifford cohomology and El-Achkar, Issam, Regularity of probability Krishnamurthy, Nirup Naidu, Modeling block Kahler geometry. and deterministic measures and separation ing in automated guided vehicle systems. of lattices in classical statistical models. Zhu, Shun-hui, Bounding topology by Ricci MATHEMATICS curvature in dimension three. Gnecco, Clare, Bayesian decision theoretic Chang, Wen-dong, Quasi-periodic and peri designs for estimation using arithmetic loss. odic motions of a heavy rigid body about a Syracuse University (4) Siegel, Dale Alan, Weak regularity of prob fixed point. MATHEMATICS ability measures and of deterministic mea Chen, Bei-fang, Combinatorial studies of surements in extended classical statistical geometric measures on singular spaces. Fatica, Vincent Edward, On edge-critical models. Faro, Emilio, A categorical study of affine graphs and the notion ofvertex independence Whang, In-Hong, Lattice regular measures geometry. in graphs. and associated outer measures. Gao, Wei-zheng, Threshold behavior in a class Kantrowitz, Robert, Homomorphisms into Banach algebras ofcontinuous vector-valued Rensselaer Polytechnic Institute (7) of semidiscrete dynamic systems. Jiang, Hua-Qiong, Degenerate Hopf bifurca functions. DECISION SCIENCES AND ENGINEERING tion and isolas of periodic solutions in an Novak, Carolyn, A study to determine possi SYSTEMS enzyme-catalyzed reaction model. ble trends between students' problems and successes and instructors' and teaching as Gao, Zhengping, Performance analysis of Lu, Yin, Existence of temperature plateau and sistants' usage levels and concern stages contention protocols for local area networks. existence of multiple solutions in combustion theory. implementing calculators into class. Makuch, William, Optimizing the collection of Schembari, Nunzio P., Functions of general delinquent consumer credit. Tong, Mai, A strong modal set theory. ized bounded variation, generalized absolute Rather, Laurie, Information requirements for STATISTICS continuity and applications to Fourier series. integrated manufacturing planning and con Sankoh, Abdul, Some contributions to a trol: A theoretical model. Bayesian finite population model. University of Rochester (9) MATHEMATICAL SCIENCES SUNY at Stony Brook (16) MATHEMATICS Gingrich, Ross, A free boundary problem for a APPLIED MATHEMATICS AND STATISTICS Barrionuevo, Jose A., £ 2 estimates for some discontinuous semi-linear elliptic equation. Baus, Theresa A., A solution of the electro- Kakeya-type maximal functions. Schmidt, Raymond, Adaptive quadtree dis magnetic inverse scattering problem utilizing Marhuenda, Francisco, Microlocal analysis of cretizationfor fluid flow problems. the generalized pulse spectrum technique. some isospectral problems. 1114 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Sanchis, Gabriela Raquel, Large deviations Moneyhun, Kay Marie, lsoclinisms in Lie OPERATIONS RESEARCH algebras. in function space: An extension of Cramer's Liang, Huei-Mei, Retrial queues. theorem. Talmadge, Andrew VanSickle, A geometric Silberbush, Paul, Suspension orders and the formulation of the Higgs mechanism via Ohio stable decomposition of iterated loops on internal metric fields. spheres. Terrell, William Jennings, Observability and Bowling Green State University (5) Wong, Shiu-chun, The fibre of the iterated external description of linear time varying Freudenthal suspension. singular control systems. MATHEMATICS AND STATISTICS STATISTICS OPERATIONS RESEARCH Mohanty, Supriya, Structure theory of limited codes. Chen, Shande, Generalization of influence Al-Jazzaf, Mahdy 1., Multiplier methods with Selvavel, Kandasamy, Statistical inference for functions and their applications. partial elimination of constraints for nonlin ear programming. truncation parameter families. Dasu, Tamraparni, The proportional mean VanRie, Debra, Quasi-varietiesof1-metabelian residua/life model. Jan, Gwo-Ming, A new variant of the primal affine scaling algorithm for linear program lattice-ordered groups. Smethurst, Philip, Generalized spacings and ming. Varga, Tomas, Matrix variate elliptically entropy: Some theory and applications. Michael, David J., The optimal representation contoured distributions: Stochastic represen Svoronou, Alexandra, Multivariate Markov of activity networks as directed acyclic tation and inference. processes via the Green's Function Method. graphs. Weininger, David, Cartesian groups and their corresponding Bose-Mesner algebras. North Carolina STATISTICS Filloon, Thomas Gene, Improved curve esti Case Western Reserve University (6 Duke University (11) mation with smoothing splines through local cross-validation. OPERATIONS RESEARCH MATHEMATICS Fitz-Simons, Terence Rhette, Fitting a lognor Araar, Abdelaziz, Optimization of queueing An, Lianjun, Loss of hyperbolicity in elastic mal distribution to air quality data observed systems with service interruptions. plastic material at finite strains. with measurement error. Be.nmerzouga, Ali, Optimal group replacement Hsu, Lucas, Calculus of variations via the Hughes-Oliver, Jacqueline Mindy-Mae, Es policies. Griffiths formalism. timation using group-testing procedures: Biermann, Jeanette Aileen Stifel, An inquiry Johnson, Michael Joseph, Numerical methods Adaptive iteration. into the optimal loads on servers in a for semiconductor process simulation in two Khalil, Tarek Mohamed, A study of the doubly queueing network. spatial dimensions: A nonlinear diffusion gepmetric processes, stationary cases and a Dhamankar, Sunil Yashwant, An efficient problem with a free boundary. non-stationary case. group-theoretic algorithm for an assignment Polaski, Thomas William, Estimates for differ McCaffrey, Daniel Francis, Estimating Lya problem with a single knapsack constraint. ences and Harnack's inequality for functions punov exponents with nonparametric regres Kamrad, Bardia, A multinomial lattice op harmonic with respect to random walks. sion and convergence rates for feedforward tion pricing methodology for valuing risky Poznanski, Jonathan, A meta-analytic ap single hidden layer networks. ventures: Multiple sources of uncertainty. proach to estimating item difficulties. Meier, Kristen Louise, Estimating rate equa Singer, Ethan Lloyd, Modeling the mail Shin, Insun, Diffusion with periodic obstacles tions using nonparametric methods. survey response pattern and determining and applications to intracellular diffusion. Wisniewski, Michael Edward, Analysis oftime the optimal number of questionnaires: A Sun, Tien-Yu, A class of three dimensional series with missing values. Bayesian approach. Yu, Yanan, A Leslie model, threshold function, steady water waves generated by localized Kent State University (4) pressure disturbances. and uncertainty for chemical control of corn Wang, Feng, Numerical study of granular flow earworm. MATHEMATICS AND COMPUTER SCIENCE in a converging hopper. University of North Carolina, Li, Xiezhang, An adaptive method for solv- Ye, Yun-Gang, Relative Brill-Noether theory Chapel Hill (8) ing nonsymmetric linear systems involving and an infinitesimal version of the Harris application of SCPACK. BIOSTATISTICS Mumford problem. Masri, Ibrahim, Estimates for norms of mul Zhang, Qi, Adjunction for vector bundles, Atkinson, Susan Shearer, Analysis of categor tilinear Hankel operators and absolutely characterizations of uniruled varieties, and ical data for crossover design. summing multipliers. small contraction mappings. Davis, Vicki G., Subsampling strategies in Shura, Thaddeus J., The Lambda property in large studies of chronic diseases. Zhang, Taiyan, Periodic limit of inverse normed linear spaces. Edwards, Lloyd Jerome, Errors in variables scattering. Sorenson, Timothy, Characters which vanish and properties of statistical inference. on all but three conjugacy classes. North Carolina State University, Shemanski, Lynn Roberta, K-ratio tests with Raleigh (17) covariates. Ohio State University (19) MATHEMATICS MATHEMATICS MATHEMATICS Augustine, M. K., Monoids of Lie type and Coan, Boyd, Top exterior powers over com Blanchard, John, Integral equation analysis of their congruences. mutative rings. artificial dialectrics. Han, Jun Cheol, Involutions in left Artinian Tendian, Sonny, Deformation of cones over Druschel, Kimberly, Orbiford cobordism in rings. curves of high degree. variants. James, Douglas, Conjugate gradient methods White, Homer, Algorithmic complexity of Forrest, Alan, Recurrence in dynamical sys for constrained least squares. trajectories ofpoints in dynamical sytems. tems: A combinatorial approach. NOVEMBER 1991, VOLUME 38, NUMBER 9 1115 Annual AMS-MAA Survey Iwakata, Yasushi, Subschemes of group asso University of Oklahoma (1) Lehigh University (4) ciation schemes. MATHEMATICS MATHEMATICS Lari Lavassani, Ali, Multiparameter bifurca Chen, Chaorong, Networks and nonlinear tion with symmetry via singularity theory. Davidson, James Ross, Disconjugacy criteria phenomena in oxygen transport to tissue. Manoharan, Palanivel, A study of Frechet for a third-order linear differential equation. Schultes, Carla Nelson, Characteristic classes manifolds. Oregon of totally geodesic and Riemannian folia Mariasousai, William, Approximation by mul tions. tivariate polynomials offixed length. Oregon State University (4) Stoudt, Gary S., Sequence space properties Prabaharan, Kanagarajah, Topics in ergodic related to the Wilansky property. MATHEMATICS theory: Existence of invariant elements and Wang, Jian-hua, Extended canonical transfor ergodic decompositions ofBanach lattices. Choi, In-Kyeong, On straight line representa mations and their applications to systems of Prieto-Cox, Juan Pablo, Representations of tions of random planar graphs. partial differential equations. positive definite Hermitian forms. Crow, John Anthony, A nonlinear shallow wa Rodriguez-Villegas, Fernando, On the square ter wave equation and its classical solutions Pennsylvania State University (13) root of special values of certain L-series. of the Cauchy problem. MATHEMATICS Szabo, Laszlo, On ergodic and martingale Hwang, Daesik, Large deviation principles for Hajrnirzaahmad, Mojdeh, The spectral resolu theorems in Orlicz spaces. random measure. tion of Laguerre operators in right definite and left definite spaces. Tam, Laying, The general Euler-Bore[ summa STATISTICS bility method. Li, Wu, Continuous selections for metric Voon, Shu-nan, Genus ofSlz(Fq). O'Donnell, Robert P., Fisher and logistic dis projections injunction spaces. criminant function estimation in the presence Wang, Qi, Dynamics of viscoelastic slender Lo, Wing Tai, On super theta functions, super of co/linearity. free jets. elliptic functions, and the Weil representa Xia, Yining, Farrell-Tate cohomology of the University of Oregon (3) tion. mapping class group. Moriyoshi, Hitoshi, Chern characters and MATHEMATICS Yan, Zhongde, On the prophet inequality for noncommutative Chern-Weil theory. the transforms ofprocesses. . Deck, Karin M., A Galois theory for transcen Movahedi-Landkarani, Hossein, Minimal Lip dental field extensions. schitz embeddings. STATISTICS Hollingsed, Thomas, The lattice of closed Santa Gadea, Nicolas Alfredo, On the rank Kim, Dongjae, Distribution-free tests based subgroups of a topological group. and the crank moduli 8, 9, and 12. on placements and partially sequential treat Roehrle, Gerhard, Orbits in internal Chevalley Santos, Jose Plinio de 0., Computer algebra ments versus control procedures. modules. and identities of the Rogers-Ramanujan type. White, Susan Elizabeth, Robust multiple com Tom, Michael Mudi, Global well-posedness, parison procedures. Pennsylvania local smoothing, and dispersive blow-up of Zhou, Xiao hua, Robust procedures in survival some nonlinear dispersive equations. analysis and reliability. Carnegie Mellon University (9) Wei, Shi Yuan, On the combinatorics of representations of classical linear groups. Ohio University (2) MATHEMATICS Carrera, Maria-Cecilia Arce, A computational STATISTICS MATHEMATICS study of the set covering problem. Brown, Michael, A framework for evaluating Al-Huzali, Abdullah, A study on the weak Hu, Xiaohua, Covolume techniques for anistropic interim analysis rules in clinical trials. relative injectivity of rings and modules. media/application of spectral methods to a Deng, Min, Differential geometry in statistical Cai, Zhixiong, Anti-periodic boundary value Cahn-Hilliard model ofphase transition. inference. problems for differential equations with Struthers, Allan, Mobile phase boundaries in Liu, Zhijun; Some contributions to nonpara monotone operators in Banach spaces. elastic media. metric estimation and robust estimation. Serinko, Regis, The asymptotics of univariate University of Cincinnati (2) STATISTICS K -mean and K -median clustering under MATHEMATICAL SCIENCE Chen, Rong, Two classes of non-linear time some nonregular conditions. series models. Guo, Lijia, Stabilized numerical solution for Temple University (11) inverse head conduction problems. Ding, Ye, Capture-recapture census with uncertain matching. MATHEMATICS QUANTITATIVE ANALYSIS AND Etzioni, Ruth, Bayesian group-sequential sam Abeysinghe, Wadduwage, Reformation and INFORMATION SYSTEMS pling with applications to tax auditing. solution of some ranking problems. Roberts, Donna, Incorporating uncertainty Parmigiani, Giovanni, Optimal scheduling in Banh, Tong T., Fredholm maps and transver into data envelopment analysis. inspections with an application to medical sality. screening tests. Chandrakantha, M. W. Leslie, Testing random Oklahoma Peruggia, Mario, Iterated function systems and walk hypothesis using variance ratios. the propagation of rounding errors. Hedrick, Paul J., Path covers and the Hamilton Oklahoma State University (I) Wang, Lian, Topics in team decision theory. cover problem. Lee, Min-Young, Bonferroni-type inequalities. STATISTICS Drexel University (1) Maksum, Choiril, A new method for imputing Lin, Xu-Sen, Exchangeability in extreme value missing values when the probability of MATHEMATICS AND COMPUTER SCIENCE theory and some Poisson limit theorems. response depends on the variable being Sevy, Jonathan, Acceleration of convergence Shadur, Raphael, Poisson and Poisson related imputed. of sequences of simultaneous approximants. stochastic processes. 1116 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------~-~------~-~·- illli&¥illk W.i.ii~i-£1 Annual AMS-MAA Survey STATISTICS Martin, James, Numerical investigation of Tennessee Cheung, Siu Hung, On smoothing discrete three-dimensionally evolving jets. bivariate densities with applications to two Platt, Nathan, An investigation of chaotic Memphis State University (2) way contingency tables. Kolmogorov flows. MATHEMATICAL SCIENCES Ghosh, Krishnendu, Robust multivariate re Raphael, Christopher, Mathematics in radia gression analysis of complex-valued data. tion therapy treatment planning. Harris, John H., Hypertext vs. lineartext as learning tools. Goldberg, Kenneth M., Bivariate extensions Wang, Yun, Damping modeling and parameter of the box plot and distribution free quartile estimation in Timoshenko beams. Lin, Chiu-Chin Vickey, Robust studies on some time series models. based tests. Yang, Jichuan, Sensitivity analysis and para Sarranadasa, Hewa, Discriminant analysis metric optimization for stochastic systems. University of Tennessee (3) based on some concepts of experimental Zhou, Xiang, Coherence and chaos in a model MATHEMATICS designs. of turbulent boundary-layer flow. University of Pennsylvania (9) Condo, John T., LCM-stability ofpower series MATHEMATICS extensions characterizes Dedekind domains. MATHEMATICS Baragar, Arthur, The Markoff' equation and Im, Young Ho, Submanifold decompositions Alber, Mark, Geometric phases, geometric equations ofHunvitz. that induce approximate fibrations and ap asymptotics, and integrable systems. proximations by bundle maps. Chang, Xiang-Qian, Weighted norm equality Cai, Mingliang, On manifolds of almost non for martingales. Silva, Jacques A. Loureiro Da, Stability of negative Ricci curvature. nonlinear age structured models. Donohoe, William, Generalized Castelnuovo Dew, Eric, Fields of moduli of arithmetic Galois groups. inequalities. Vanderbilt University (5) Huang, Ying, Floquet theory for linear peri Giaquinto, Anthony, Deformation methods in MATHEMATICS quantum groups. odic differential delay equations. Aluthge, Ariyadasa, Properties ofp-hyponor Iaia, Joseph A., Isometric embeddings of Johnson, Brenda, The derivatives of homotopy theory. mal operators. surfaces with non-negative curvature in IR 3 . Hart, James Buford, Decompositions for rela Kamberov, George 1., Singular geometric University of Rhode Island (1) tively normal lattices. partial differential equations. Jones, Joel Lynn, The concordance extension Lu, Duojia, Homogeneous foliations ofspheres. MATHEMATICS theorem. STATISTICS Vlahos, Panagiotis N., Global attractivity in Knisley, Jeff Randell, The analytic model of Lim, Pilar, Measurement error in simultaneous delay difference equations. a semi-hyponormal operator with rank one qualitative response models. polar difference. Uziinogullari, Ulkii, Estimation of the hazard South Carolina Lyon, Bradford Franklin, On zeta functions as function and its derivatives under random sociated to the product of two Einstein series truncation models. and their Liz SL(2, Z)-spectral expansions. Clemson University (2) University of Pittsburgh (3) MATHEMATICAL SCIENCES Texas MATHEMATICS AND STATISTICS Brown, David Dean, Iterated presentations Rice University (14) Hong, Bin, Symmetry on solution manifolds of and module polynomials over extensions of parametrized equations. finite fields. MATHEMATICAL SCIENCES Hu, Tien-You, Fractal dimensions and singu Lundquist, Michael Edward, Zero patterns, larities of the Weierstrass type-functions. Bao, Gang, Microlocal regularity of an in chordal graphs and matrix completions. Ye, Xiu, Construction of divergence free space verse problem for the multidimensional wave equation. for Navier-Stokes equations. University of South Carolina (6) El-Bakry, Amr Saad, On the role of indica Rhode Island MATHEMATICS tors in identifying zero variables in linear programming. Brown University (16) Beintema, Mark, Gorenstein algebras with Kelley, Robert, Optical illusions and aug unimobal H-sequences. mented graphics for manned and robotic APPLIED MATHEMATICS Liu, Shih-haa, Boundary limits of generalized guidance and control. Fakhroo, Fariba, Legendre tau approximation Green potentials on the unit ball in Rn. Overley, H. Kurt, A new secant update for for an active noise control problem. Palmer, Susan, Algebra structures on resolu nonlinear constrained optimization. Fan, Jiang-ping, Characteristic multipliers of tions of rings defined by grade four almost Raydan, Marcos, Convergence properties of periodic solutions of singularly perturbed complete intersections. the Barzilai and Borwein gradient method. delay differential equations. Ren, Guanshen, On non-Archimedean normed Saigal, Sanjay, Optimizing over the cut cone: A Intrator, Nathan, Feature extraction using spaces. new polyhedral algorithm for the maximum an exploratory projection pursuit neural Still, Charles Herbert, Parallel methods for weight cut problem. network. unconstrained optimization. Intrator, Oma, Methods for exploring survival Samuelsen, Catherine, The Dikin-Karmarkar principle for steepest descent. data. STATISTICS Kossioris, Georgios, Propagation of singu Wu, Zhijun, A subgradient algorithm for non larities for solution of Hamilton-Jacobi Sa, Ping, Multiple comparisons with a control linear integer programming and its parallel equations. in response surface methodology. implementation. NOVEMBER 1991, VOLUME 38, NUMBER 9 1117 Annual AMS-MAA Survey MATHEMATICS Texas Tech University (3) Tintera, George Dunkin, On the stable rank of enveloping algebras. Anderson, John P., Harmonic diffeomorphisms MATHEMATICS between manifolds with bounded curvature. lakovidis, Ilias, Observability and the inverse University of Texas, Dallas (3) Cheng, Xiaoxi, Evolution problems in geomet problem in electrocardiography. ric analysis. MATHEMATICAL SCIENCES Jang, Ruey-Jen, The ideal structure of the Eisenlohr, John M., Fully transitive polyhedra algebraic Eigenspace to the spectral radius Feistel, Robert Fritz, Robust singular-value with crystallographic symmetry groups. of eventually compact, reducible, positive decomposition. Poon, Chi Cheung, Axially symmetric har linear operators. Gautam, Shiva Prasad, Applications of the t, monic maps and relaxed energy. Richards, Kendall Clyde, Majorization in the T2 and F statistics to ordinal categorical Tomlinson, Kathy A., An analog to the heat Bergman space. data. equation in complex space variables. Wildenhain, Kenneth Raymond, Inversion Zhou, Xiadong, Some static and dynamic University of Houston (3) techniques for wave velocity and density in an problems in plasticity. MATHEMATICS elastic medium with horizontal homogeneity. Southern Methodist University (11) Chen, Shui-Tain, On selected conjectures of Graffiti. Utah COMPUTER SCIENCE AND ENGINEERING Dionne, Benoit, Spatially periodic patterns in University of Utah (8) Fan, Chin-Feng, Design and performance two or three dimensions. optimization of a multi-risk execution model Tiballi, Terry R., Symmetric orthogonalization MATHEMATICS for parallel logic programs. of vectors in Hilbert space. Devoto, Jorge Andres, Finite group actions Gruenwald, Gia-Loi Le, Reload in a main memory database system: MARS. University of North Texas (3) and elliptic genera. Ferguson, Kenneth, A constructive approach Hickman, Betty L., Parallel algorithms for MATHEMATICS pure network problems and related applica to the SU(2) Witten invariant. Ali, Ismail A., Uniqueness ofpositive solutions tions. Izadi, Elham, On the moduli space of four for elliptic Dirichlet problems. Leff, Laurence L., Symbolic finite element dimensional principally polarized abelian Bozeman, Alan K., Weakly dense subsets of analysis and constructive solid geometry. varieties. homogeneous complete Boolean algebras. Lin, David Dah-Haur, An efficient environ Kinyon, Michael Kenneth, The adjoint prob May, Lee C., A solution-giving transformation mental support for heterogeneous distributed lem for coupled linear operators. for systems of differential equations. programming. Lundstrom, Ronald, Stochastic models and Lucks, Michael, A knowledge-based frame University of Texas, Arlington (2) statistical methods. work for the selection of mathematical Ma, Yonghao, A division algorithm over software. MATHEMATICS Z[xr, ... , Xn] and the first syzygies of Stewart, Bryan Douglas, Multi-tree algorithms Johnson, Ronald Duane, Some computational determinantal ideal. for efficient shortest-path computation. differential geometry questions in solid mod Wickham, Cameron Garth, Annihilation of Thiagarajan, Kumar, Fractional quadratic eling. homology of certain finite free complexes. zero-one programs for graph partitioning Pierce, Rebecca Lynn, On the choice of Wiskin, James, Integral equation and geo and hierarchical clustering. the prior distribution in hypergeometric metric methods for scattering in layered Wang, Zhiming, The shortest augmenting path sampling. media. algorithm for bipartite network problems. University of Texas, Austin (10) Yang, Cheng, A multi-layer design and load Virginia sharing algorithm for personal communica MATHEMATICS tion networks. Claus, Wilhelmina Christina, Essential lami George Mason University (1) nations in closed Seifertfibered spaces. MATHEMATICS OPERATIONS RESEARCH AND APPLIED Kohn, Peter, Linking and unlinking properties STATISTICS Zhang, Wen, Numerical solution of ordinary of two component links. differential equations with applications. Nanyes, Ollie, Proper knots are locally un Ndousse, Thomas, Queueing models of an Integrated packet voice and data network Texas A&M University (4) knotted and a new proof of Schubert's bridge number theorem. with congestion control. STATISTICS O'Leary, Robbin Lynn Lerch, Small solutions Old Dominion University (4) Chang, Kyung, Asymptotic expansions of the to inhomogeneous systems oflinear equations distributions of studentized test statistics over an algebraic number field. MATHEMATICS AND STATISTICS for the slope parameter in simple linear Saito, Masahico, Invariants of link cobordism. Arriola, Leon, A generalization of linear structural relationships. Seelinger, George Francis, Orthogonal matrix multistep methods. Hwang, Lie-Ju, An empirical Bayes approach invariants and generalized matrix concomi Casper, Jay, An extension of essentially non to variance function estimation. tants. oscillatory shock-capturing schemes to multi Jayasuriya, Bodhini Rasik:a, Testing for poly Semple, John, On a class of dual methods for dimensional systems of conservation laws. nomial regression using nonparametric re quadratic programming. DeRise, George, The Fokker-Plank and related gression techniques. Sun, Li, On some problems of chance equations in theoretical population dynamics. Parsa, Amba Rahulji, Analysis of contingency constrained programming. Wangler, Thomas, A mathematical model of tables with structural zeros and ordered Sun, Xingping, Multivariate interpolation us the dynamics ofan optically pumped codoped categories. ing ridge or related functions. solid state laser system. 1118 NOTICES OF lliE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey University of Virginia (19) Edwards, Erick, A Monte Carlo approach to Lin, Lillian Shengjung, Analysis of multivari hypothesis testing in nonparametric regres ate binary outcome data from a randomized APPLIED MATHEMATICS sion. clinical trial. Averick, Brett Mitchell, Solution of nonlinear Esinhart, James, Statistical inference on intra McGorray, Susan Patricia, Evaluation of Poisson-type equations. subject variability in bioequivalence studies. environmental and genetic components of Bradley, Mary Elizabeth, Local and global ex Hunsberger, Sally, Semiparametric regression disease susceptibility based on data obtained ponential stabilization results for nonlinearly in likelihood based model. from sibling pairs. perturbed plates models where nonlinearities Jung, Hyonggi, Interval estimation of the Watelet, Luc Freddy, Non-parametric esti appear on the boundary. median lethal dose using an up-and-down mation of component life distributions in England, Michael Rohn, A classification of method under a probit model. Meilijson's competing risk model. general helicoidal shells. MATHEMATICS Falgout, Robert Dean, Algebraic-geometric Virginia Polytechnic Institute and multigrid methods for Poisson-type equa State University (12) K won, Joong Sung, Some products of stochas tions. tic set functions. Ourada, Norman Lee, Uniform stabilization MATHEMATICS Lear, Dale, Extensions of normal functions for the Euler-Bernoulli equation with feed Fast, Stephen Hardin, Examples and theorems and asymptotics of the height pairing. back operator in only theNeumann boundary for generalized paracompact topological Wright, Stephen E., Convergence and ap condition. spaces. proximation for primal-dual methods in Russell, William Stuart, Analysis of the spiral Ge, Yuzhen, Studies of one-dimensional maps large-scale optimization. properties in prototype galaxies. in the chaotic regime. Yan, Dung Yung, On the Thom spectra over the loops on SU(n)jSU(n), and Mahowald's MATHEMATICS Hammer, Patricia, Parameter identification in parabolic partial differential equations using spectra. Cruz-Sampedro, Jaime, Boundary values at quasilinearization. infinity of solutions to the Schrodinger STATISTICS equation. Huang, Jiann-Shiun, One-to-one correspon Kahn, Michael Jay, Incorporating covariates dence between maximal sets of antisymmetry Herrin, Jeffrey, The Born-Oppenheimer ap into a beta-binomial model with applications and maximal projections of antisymmetry. proximation: Straight-up and with a twist. to medicare policy: A Bayes/empirical Bayes Kang, Jeongook, Interpolation problem for approach. Krason, Piotr, On the category of unstable rational matrix function with low McMillan modules modulo its nilpotents. Le, Nhu Dinh, Modeling and bootstrapping degree. for non-Gaussian time series. Lake, Douglas, Determining the motion of an object through variable time delay estima Lee, Gyou Bong, A study of the computation Newton, Michael Abbott, The weighted like tion. and convergence behavior of eigenvalue lihood bootstrap and an algorithm for bounds for self-adjoint operators. prepivoting. Linde, Darryl, Some operators on the Newton spaces. McCoy, Daisy C., Irreducible elements in Sheehan, Nuala Ann, Genetic restoration on algebraic number fields. complex pedigrees. Lu, 1-Li, Multivariate natural exponential families. Park, Young Wook, Large deviations theory Taplin, Ross Howard, Modelling agricultural for queueing systems. trials on the field in the presence of outliers Magnus, John, Lie ideals closed under non-Lie and fertility jumps. polynomials. STATISTICS Magnus, Teresa Deitz, Geometries over non Agard, David, Robust inferential procedures Wisconsin division rings. applied to regression. Morrisett (Clark), Julia, Relations between Marquette University (1) quadratic residue codes written in their Baik, JaiWook, X control charts in the MATHEMATICS, STATISTICS, AND defining field and certain other classical presence of correlation. COMPUTER SCIENCE codes. Kuzmak:, Barbara, An examination of outliers Ross, William T., Multiplication operators and interaction in a nonreplicated two-way Vachuska, Colleen Ann, Contributions on and invariant subspaces on Bergman spaces. table. completely regular semigroups. Torrence, Bruce, Submanifolds of products of Rozum, Michael, Effective design augmenta University of Wisconsin, real projective spaces. tion for prediction. Madison (30) Torrence, Eve, The coordinatization of a INDUSTRIAL ENGINEERING hexagonal Barbilian plane by a quadratic Washington Jordan algebra. Ferreira, Pedro, Intertemporal stability of Wassell, Stephen, The stability of a Hamilton- University of Washington (16) patient's quality judgments. ian system at high energy. Potthoff, Sandra, A comparison of two elic BIOSTATISTICS itation methodologies for modeling expert Virginia Commonwealth judgment. University (7) Ciol, Marcia Aparecida, An adaptive case cohort design. MATHEMATICS BIOSTATISTICS De Andrade, Mariza, Estimation of genotype Arvola, William A., The fundamental group Anderson, Randy, Robust linear regression parameters under nonnormal models. of the complement of an arrangement of with censored responses. Fellingham, Gilbert Warren, An analysis of complex hyperplanes. Bortey, Enoch, Hypothesis testing based on longitudinal models. Calbeck, William S., LP decomposition of ranks in multivariate linear models. Kosinski, Andrzej Stanislaw, A geometric view functions defined on C00 totally real sub Chien, Tsui-Hsien, Distribution-free tests for of iterative methods, matrix decompositions manifolds of C n into boundary values of interaction in a two-way design. and multiple case regression diagnostics. functions holomorphic in wedges. NOVEMBER 1991, VOLUME 38, NUMBER 9 1119 Annual AMS-MAA Survey Cholak:, Peter Abe, Automorphisms of the University of Wisconsin, McGill University (4) lattice of recursively enumerable sets. Milwaukee (5) MATHEMATICS AND STATISTICS Fan, Haitao, The existence, uniqueness and MATHEMATICAL SCIENCE stability of the Riemann problem of a system Chayet, Maurice, Some general estimates for of conservation laws of mixed type. Abeyratne, Athula 1., Limit distributions for the heat kernel on symmetric spaces and Gwanyama, Philip Wagala, A model of human a multitype branching process in a random related problems of integral geometry. mathematics-problem-resolution in analysis. environment. Chu, Ping-Tong David, Representations of Choo, Joshua Youngmyo, Stable high order lltis, Michael George, Asymptotics of large exact distribution of random volume from methods for solving elliptic equations with deviations for IJ.D. and Markov-additive beta type-2 random points. large first order terms. random variables in lR d. Funk, Jonathon Randall, Descent for cocom Hero, Michael W., A characterization of the plete categories. Keppelmann, Edward C., Periodic points on attracting center for dynamical systems on nilmanifolds and solvmanifolds. Sbihi, Mohammed Amine, Covering times for the interval and circle. random walks on graphs. Kim, Weonja, LP bounds for Hilbert trans Koker, John Joseph, Homological dimension forms along convex surfaces. of rings with Krull and Gabriel dimension. McMaster University (3) Landver, Avner, Singular Baire numbers and Rim, Seog Hoon, On semiperfect localizations. related topics. MATHEMATICS AND STATISTICS Shaw, Karl Elizabeth, Boundary behavior of Wyoming Schlitt, Gregory Mark Stephen, N -compact Besov functions. frames and applications. Siegel, Eli Adam, The representations of a University of Wyoming (10) Squire, Richard, Presheaf toposes and propo Heeke algebra of the affine group over a sitional logic. MATHEMATICS finite field. Zhang, Ying-Lan, Ore localizations and ir Stroomer, Jeffrey Dean, Combinatorics and Curran, Mark Charles, Numerical schemes reducible representations of the first Weyl the representation theory of GL(r, C) and for highly advective flows using finite algebra. Sp(2r,C). element collocation with adaptive local grid refinement. Queen's University (3) Sun, Shu Ming, Theory of surface waves in Li, Chao, Adaptive computation in convective the presence of surface tension. MATHEMATICS AND STATISTICS diffusion model with application to water Wright, James Robert, LP estimates for contamination. Kechagias, Epaminondas, Homology opera operators associated to oscillating plane Li, Gang, Finite element methods and error tions and modular invariant theory. curves. estimates for two dimensional chemical Tautz, Walter, Reduction of Abelian varieties Wu, Xuezheng, Smooth linearization near a flooding reservoir simulation. over number fields and supersingular primes. hyperbolic fixed point. Lin, Tao, Some direct numerical methods Wong, Cecilia Fung Yee, A non-classical first Ye, Zaifei, Holomorphic extension and. de for inverse problems of one dimensional order logical system for deductive reasoning. composition/rom a totally real manifold. parabolic equations. Simon Fraser University (5) Zhong, Ning, Generalized metric spaces and Sansiry, Prashant, A numerical scheme to track products. the growth of cavities in underground coal MATHEMATICS AND STATISTICS gasification. Zrotowski, Roman Jozef, Indescribability Das, Salil, Parameter estimation in oceano properties of large cardinals. Schumann, Shannon, Characterizations of decomposable and indecomposable inverse graphic flows and computation of flows driven by density gradient. STATISTICS limit spaces. Ekambaram, Thiru Sambandam, The Frobe Basu, Sabyasachi, Analysis offirst-order spa STATISTICS nius problem. tial bilateral ARMA models. Al-Sunduqchi, Mahdi, Determining the appro Song, Yuhe, Some three-dimensional problems Chen, Hanfeng, Efficiency of tests following priate sample size for inferences based on in the computational fluid dynamics of Box-Cox transformations. the Wilcoxon statistics. shallow areas. Chen, Jiahua, On minimum aberration frac Bromaghin, Jeffrey F., Sampling and parame Yu, Min-Li Joseph, Tree decompositions of tional factorial designs. ter estimation in avian nesting studies. complete graphs. Ho, Chiang-Hong, Topics in cumulative sum Gonzalez, Maria Liliana, Geostatistical hy Yu, Qinglin, Factors and factor extensions. procedures. pothesis testing. Universite Laval (4) Jones, Stephen, Designs for minimizing the Krehbiel, Timothy C., Sequential design and effect ofenvironmental variables. analysis of sm factorial experiments. MATHEMATIQUES ET STATISTIQUE Kim, Whasoo, Choosing response surface Canada Boivin, Sylvain, Simulation d' ecoulements designs for multiple responses. compressibles a nombre de Reynolds eleve. Lee, Jae-Won, Interim analyses with repeated Dalhousie University (2) Farhloul, Mohammed, Methodes d' elements measurements in clinical trials. finis mixtes et volumes finis. Shieh, Shwu-Rong, Some extensions of U- and MATHEMATICS, STATISTICS AND Guenette, Robert, Etudes theoriques et numer V-statistics. COMPUTER SCIENCE iques du modele de Leslie-Ericksen pour les Soo, Yuh-Wen, Spline-based regression for Ireland, Alice Marie, An intelligent decision cristaux liquides. nonlinear models with multiple responses. support system for debt management. N'Zi, Modeste, Proprietes asymptotiques Su, John(Qiang), Analysis of repeated mea Ye, Juan Juan, Optimal control of piecewise de certains champs ateatoires generalisant surements. deterministic Markov processes. l' aire de Levy. 1120 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Annual AMS-MAA Survey Universite de Montreal (10) Chang, Huakang, The steady Navier-Stokes PURE MATHEMATICS problem for low Reynold's number viscous Bigelow, David Carleton, Enclosings of Latin MATHEMATIQUES ET STATISTIQUES jets. squares and triple systems. Abbaoui, Salim, Theorie de points fixes, Xie, Winston Wenzheng, A sharp inequality Craigen, Robert William, Constructions for perturbations et iterations. for Poisson's equation in arbitrary domains orthogonal matrices. Allaire, Jerome, Etude de certaines mesures and its applications to Burger's equation. Kim, Goansu, Conjugacy and subgroup sepa- de liaison entre plusieurs vecteurs aleatoires. Zangeneh, Bijan, A semilinear stochastic rability of generalized free products. Bensebah, Ali, Sur certaines classes d' algebres evolution equation. University of Western Ontario (3) non associatives involutives et normees. Zhang, Xingru, Topics on Dehn surgery. Corvellec, Jean-Noel, Contribution aIa theorie APPLIED MATHEMATICS University of Calgary (4) des points critiques. Frank, Gregory William, Recovering the Lya Decoste, Helene, Series indicatrices d' especes MATHEMATICS AND STATISTICS punov exponent from chaotic time series. ponderes et q-analogues. He, Wenhua, Some mixed boundary value Sawchuck, Stephen Peter, Circular cylinder in Marchand, Eric, Estimation de la moyenne problems in the linear theory of elasticity. axial flow. multivariee avec contraintes. Ling, Joseph Ming-Tak, Amenable and ex STATISTICS AND ACTUARIAL SCIENCES Monga, M., La methode du rangement apres tremely amenable locally compact semi Lawry, Katherine, Topics in spatial sampling substitution appliquee un plan de carres a groups. and experimental design. latins. Nelson, Wayne H., Aspects ofZiglin analysis. Niyonsenga, Theophile, Estimation des para University of Windsor (1) Zhu, Xuding, Multiplicative structures. metres d' une population finie en tenant MATHEMATICS AND STATISTICS compte University of Guelph (1) Van Nguyen, Phu, Application ofcomplex vari de Ia non-reponse. MATHEMATICS AND STATISTICS ables in electromagneticfluiddynamic, mag Olivier, Patrick, Contributions a l' inegalite de netofluiddynamic and fluid dynamic flows. Ye, Liqian, Computer simulation studies of Bernstein et une formule de quadrature pour Viscoelastic boundary-layer theory. desfonctions entieres. lipid surface reactions in blood coagulation. Watt, Abdou! Ousmane, Des problemes University of Manitoba (2) extremaux pour certaines classes de poly Doctoral Degrees Conferred nomes. MATHEMATICS AND ASTRONOMY Guelzow, Andreas, Some classes of E-minimal 1988-1989 Universite du Quebec Supplementary List a Montreal (3) algebras of affine type. Nilpotent squags, P groups and nilpotent SQS-skeins. MATHEMATICS Teo, Siong Khow, Congruence lattices of The following list supplements the list of thesis Constantineau, Ivan, Calcul combinatoire de lattices. titles published in the November 1989 Notices, series indicatrices de cycle. pages 1169-1188, the May/June 1990 Notices, University of Saskatchewan (1) page 558, and November 1990, page 1250. Lalonde, Pierre, Contribution a l' etude des empilements. MATHEMATICS Melancon, Guy, Reecritures dans l' algebre Schulz, Eckart Robert, The stable rank of de Lie libre, dans le groupe libre et dans crossed products of sectional C* -algebras University of Windsor (2) l' algebre associative libre. by compact Lie groups. MATHEMATICS AND STATISTICS University of Alberta (7) University of Toronto (4) Hamdan, Mohammed Hafiz, Numerical simu lation offlow through porous media. MATHEMATICS MATHEMATICS Mian, Ijaz U.H., Statistical analysis offamilial Aiello, Walter Gordon, Time delay models of Farenick, Douglas Ronald, The matricial correlations. population growth with stage structure. spectrum and range, and C* -convex sets. Chen, Weiyu, Some inequalities in approxi Mai, Liem, The analytic rank of a family of mation theory. elliptic curves. Doctoral Degrees Conferred Lin, Xiaodong, Mathematical analysis ofsome Pravila, David William, Mathematical analy 1989-1990 models in ecology and epidemiology. sis of wave propagation in stratified media. Supplementary List Miao, Tianxuan, Amenability of locally com Sherman, Glen Aldridge, Allowable decompo- pact groups, subspaces and sets of invariant sitions for the doubling paradox. means. The following list supplements the list of thesis University of Waterloo (6) titles published in the November 1990 Notices, Riley, David Michael, On nilpotence and pages 1231-1250, and the May/June 1991 No dimension in group rings. APPLIED MATHEMATICS tices, page 419. Shen, Zuowei, Two studies on functions of Ma, Philip Kim-Hung, Similarity solutions to several variables. viscous fluid flow problems. Yu, Lao Sen, Positive decaying solutions of California nonlinear elliptic problems. COMBINATORICS AND OPTIMIZATION Stanford University (1) University of British Columbia (5) Metzlar, Alice, Minimum transversal of cycles in intercyclic digraphs. OPERATIONS RESEARCH MATHEMATICS Tan, Ruo Yang, Quadratic programming and Yao, Jen-Chih, Generalized quasi-variational Bermejo-Bermejo, Rodolpho, Analysis of a isotonic regression: Some efficient algo inequality and implicit complementarity Galerkin-characteristic. rithms. problems. NOVEMBER 1991, VOLUME 38, NUMBE~ 9 1121 ····~·~·····~·~·""~"'···"'···········--·~··~-··--"·--· .. ~~· .. ~··-··lti!MI&I.. I&IBIIJ.illllillllilil!ililil'di-llilllliltliilml•••••ii~E ~~·~··~· .. -~-...... ~.~······~············-······~-~ ...... - ... Annual AMS-MAA Survey Georgia New York Huang, Mei Ling, D numbers and the D distribution. University of Georgia (1) Syracuse University (1) Khan, Khushnood Alam, MRP P and MRBP rank tests-fourth moment based inference MATHEMATICS STATISTICS and empirical power performance. Su, Kuo-Liang, Laws of large numbers and Weinstein, Gilbert A., On rotating black holes failure rate function estimation. in equilibrium in general relativity. Indiana Canada Purdue University (1) University of Windsor (3) STATISTICS MATHEMATICS AND STATISTICS San Martin, Jaime, Stratonovich differential Bamwal, Rajesh Kumar, Analysis of one-way equations. layout of count data. APPLIED GEOMETRY AND DISCRETE MATHEMATICS: THE VICTOR KLEE FESTSCHRIFT Peter Gritzmann and Bernd Sturmfels, Editors This volume, published jointly with the Association for Computing Machinery, com prises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting triibute to one of the foremost leaders in discrete mathematics. All prices subject to change. Free shipment by surface; for 1991 Mathematics Subject Classifications: 05, 15, 28, air delivery, please add $6.50 per title. Prepayment 46, 51, 52, 57, 65, 68, 90. ISBN 0-8218·6593-5, required. Order from American Mathematical Society, LC 91-26934, 15SN 1052-1798,608 pages P.O. Box 1571, Annex Station, Providence, RI 02901·1571, (hardcover), June 1991; Individual member $68, or call toll free 800-321-4AMS (321-4267) in the continen List price $113, Institutional member $90, tal U.S. and Canada to charge with Visa or MasterCard. To order please specify DIMACS/4NA Please add 7% GST to all orders to Canada. 1122 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematics under Hardship Conditions in the Third World Neal Koblitz University of Washington, Seattle felt belief in the importance of education as a way to attain The following article is adapted from an AMS-MAA a better life personally and also as a way to modernize Invited Address, delivered by Koblitz at the Joint Summer their country. Students are better disciplined and more hard Meetings in Orono, Maine, on August 9, 1991. working than their American counterparts. They are not jaded, spoiled, or distracted to the same extent. This talk will be based largely on my experiences in Central In Vietnam, which is one of the poorest countries in the America, Vietnam, and India. I've never made a systematic world, a network of city-wide, regional, and national high study of science in the Third World, so I'm not going school math competitions has led to the selection of some to give you statistics, sociological analyses, or anything excellent teams for the International Olympiads. In Australia like a complete overall picture. Rather, what I say will be in 1988, for example, Vietnam took fifth place, ahead of the subjective and impressionistic. And some of what I say sixth place U.S. team. will be controversial. If this were a lunch-time address, In the area of university education, an example of then it would be encumbent upon me not to say anything excellence is provided by the Indian Institute of Technology outrageous, so as not to interfere with anyone's digestion. (liT) with its five campuses in different major cities of India. But since this is an early morning talk, my role is to wake Graduates of liT are comparable to the best that leading you up, and be provocative. U.S. universities can produce. First I'll discuss mathematics education, particularly in I'd like to insert a personal story here. When I was six Central America. Then I'll talk about mathematical research years old, my family spent a year in Baroda, India. I attended in the Third World, where most of my observations are based the Catholic school, which was the only English-medium on ten years of coordinating mathematical programs for a school in the city. The math standards there were higher nongovernmental organization called the U.S. Committee than in American schools. The next year, when I returned for Scientific Cooperation with Vietnam. to the U.S., I was so far ahead of my classmates that my teacher erroneously believed that I had a special gift for mathematics. Like other mistaken notions that teachers get Math Education into their heads, this sort of erroneous belief has a way of The most obvious thing to say is that throughout the becoming a self-fulfilling prophecy. As a result of all the Third World, most schools and universities suffer material encouragement after my return from India, I was on my way deprivation far worse than anything we might complain toward becoming a mathematician. Thus, I have a special about in the United States. Instructors generally receive personal debt to India, and to its schools. extremely low salaries, and they have to teach in antiquated But in some countries, the approach to teaching math classrooms, without enough textbooks or basic reference ematics is simply a disaster. Nicaragua is a case in point. books, with tiny chalkboards and no overhead projectors, Students are required to memorize bits and pieces of sophis with poor lighting, and frequent blackouts and brownouts. ticated mathematics without any understanding of what it's Most of the Third World is in the tropics, so dilring much all about or why it might be worthwhile. A colleague at the of the school year it gets oppressively hot during the day; if National Autonomous University in Managua said: the instructor and students are lucky, they have an overhead fan to at least keep the air circulating-provided that the You can understand why so many of these [Nicaraguan] electricity is working. students are just terrorized by mathematics. For exam Despite all this, at its best, education in many Third ple, I found that all of my students knew the Euclidean World countries is impressively good. There are some ad algorithm, but only in a mechanical way, with no un vantages, as well as disadvantages, for secondary and higher derstanding. It turned out that they had been required education in Asia, Africa, and Latin America. Educational to memorize the Euclidean algorithm as the way to attainments, such as advanced degrees, carry more prestige find the least common denominator when adding two in the Third World than in the U.S. People have a deeply fractions. -·-··--··----·------·----- NOVEMBER 1991, VOLUME 38, NUMBER 9 1123 Math in the Third World Here I have an audience of a few hundred mathemati a government based on such ideals as free medical care, cians. I'd like to ask: How many of you have ever in your universal literacy, and greatly increased access to higher lives added two fractions by first applying the Euclidean education. The democratization of higher education was a algorithm to the denominators? noble objective, but there was a problem that was ignored This isn't an isolated example. The same colleague told by the Sandinistas in their reformist zeal. Nicaragua had few me of passing a classroom and hearing the students repeat qualified professors, and a significant fraction of the best in unison after the professor: "An equivalence relation is a trained people-especially those coming from the wealthy relation that is reflexive, symmetric, and transitive." What classes-had fled to Miami after the Revolution. Even these words mean, why equivalence relations are important, more of the educated middle class left the country as the under what circumstances in their life in Nicaragua they Reagan Administration's contra war and economic sabotage might have occasion to use the definition of an equivalence took its toll on the quality of life in Nicaragua. Thus, the relation-all of this remained a mystery to the students. large increase in the size of Nicaraguan universities in the This story reminded me again of my school in India. 1980s occurred despite the small and diminishing number Every morning in the bus to school we children would of Nicaraguans who were competent to be instructors. recite the Lord's Prayer: " ... Forgive us our trespasses, as But I don't want to leave you with an entirely negative we forgive those who trespass against us ... the Father, the impression of Nicaragua. Despite the desperate material Son, and the Holy Ghost, Amen." In Nicaragua, which is conditions of their lives and the cruelly incompetent methods a Catholic country, the incantation of the Holy Trinity is a of teaching mathematics, the Nicaraguan math students I familiar ritual to the children. Then when they grow older, met were intelligent, hard-working, and eager to learn. They they learn that there is a second Holy Trinity whose incanta asked me good questions and listened carefully to everything tion also has a special mystical significance: " ... Reflexive, I said. They did not have a short attention span, they did not Symmetric, and Transitive"! expect to be entertained, and they never complained about But it would be unfair to blame the Catholic Church for my accent in Spanish-or that of any of the other foreign the sorry state of mathematical education in Nicaragua. The visitors or instructors. So the impression I have is that, in real culprits in this case were the mathematical communities many respects, Nicaraguan students are more mature than in North America and Europe, which in the 1960s pushed their U.S. counterparts. for the abstract, formalistic "New Math" approach that It is not only in Nicaragua that the imported "New came to dominate mathematical pedagogy in most of the Math" pedagogy made an already difficult situation even world. And the drawbacks that by now are well known worse. When I was in El Salvador recently, I discussed in the U.S.-boring material, unmotivated, unrelated to some questions in math education with the Academic real life, often taught by teachers who can't understand it Dean, Rene Zelaya of the Jesuit University Universidad themselves-all of this is magnified to absurd proportions Centroamericana, which is known by the acronym UCA. in the impoverished countries of the Third World, such as Zelaya used to be chairman of the math department, and Nicaragua. was moved up to his present position as Academic Dean Math majors in their last two years at the National when his predecessor, the distinguished psychologist Father Autonomous University of Nicaragua are required to spend Ignacio Martin-Bar6, was murdered. (Recall that in the thirty hours per week in math classes. The syllabus, taken middle of the night of November 16, 1989, a squad from the unaltered from European universities by the higher education First Brigade of the Salvadoran Army, which was trained bureaucracy, uses textbooks that would be considered too and equipped by the U.S., invaded the UCA campus and advanced for undergraduates in any U.S. university. The killed Martfn-Bar6, five other leading intellectuals of UCA, students are required to memorize long lists of definitions, their housekeeper, and her daughter.) The UCA professors, theorems, and proofs, none of which they could realistically such as Zelaya in the area of math education, are running a be expected to understand conceptually. Moreover, most special risk, because UCA has historically been a center of of the material is not even understood by their Nicaraguan efforts for peace and in opposition to U.S. military aid. The professors, whose own mathematical background is typically Jesuit professors are hated by the military. that of a weak B.A. degree. The result is what I'm tempted Rene Zelaya recounted to me how, when he graduated to call "Mathematics as a form of oppression." from the University of El Salvador in 1968, the "New Math" The hoops Nicaraguan math students are made to jump was just being introduced in the country. The curriculum through to get their degree bring to mind more a fraternity shifted to an emphasis on set-theoretic and ring-theoretic hazing than an education: If they endure the pain and get abstractions, even in the primary grades. He said that the through it, then they get their degree, join the club, and pass teachers were completely unprepared, and the Salvadoran from being the oppressed to being the oppressors of the next school system is still in the process of trying to recover generation of Nicaraguan students. from the misguided "reform" of 1968. When I was in San The lack of competent Nicaraguan math instructors is Salvador two months ago, the newspaper that was slipped a result of one of the many tragic ironies of Nicaraguan under my hotel door every morning was running a series of history. As you know, in 1979 the Sandinista movement articles on the confusion in elementary math education in succeeded in overthrowing the Somoza dynasty and installing El Salvador caused by the dispute over whether or not to 1124 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY --·-··················--·············--···-·····------······-.. ····-· .. ·····-····················-··-·-····------······-··················· ...... Math in the Third World continue focusing on set theory. Research The pedagogical dilemmas now facing Nicaragua and El Since time is short, I want to move on to discuss the research Salvador are consequences of the damage done by the "New environment in the Third World, especially in countries like Math" craze of the 1960s when it spread from the U.S. and Vietnam and India where there are large numbers of research France to the developing countries. Of course, these days, mathematicians (in Central America, on the other hand, there complaining about the failure of the New Math movement are not1). is like beating a dead horse. Nevertheless, there's a lesson Again the most obvious thing to say is that the material here: We should try not to colonize the Third World with conditions of our colleagues, especially in Vietnam, are every half-baked educational fad that sweeps through North unbelievably bad. To give you a very rough idea, I've made America and Europe. a table of the average monthly salary of a math professor I promised you some controversy this morning. So, in the U.S. and in three different developing countries. instead of beating a dead horse, I'd like to beat a horse These figures are based on my observations of a couple that's very much alive: the so-called computer revolution of years ago, and they're not very exact (especially since in math education. In the U.S., I think it's fair to say that the conversion rate from local currency to U.S. dollars can computers have been shamelessly oversold as a panacea fluctuate a lot). for the problems of math education. Pespite all the hype, it's hard to tell at this point whether the introduction of Typical Monthly Salary of a Math Professor computers in grade school through college has had, on (very rough estimate) balance, a positive or negative effect on math education. u.s.::::::! $4000 The primary measurable effect, as far as I'm aware, has India :::::J $400 been to bring in a lot of money to computer hardware and software companies. In the words of Michael Fellows, a Nicaragua :::::J $40 leading computer scientist who is active in grade school Vietnam :::::J $4 educational reform, "It would, in many (if not most) schools, be better to put the machines in the dumpster." I really like this chart, and find it useful to look at from Despite the acute lack of money for education in de time to time. If I ever start to feel demoralized because veloping countries, to some extent the computer craze has of the stinginess of the Washington State legislature in spread to the Third World. In February 1986, a major confer keeping our University of Washington salaries below those ence called "Informatics and the Teaching of Mathematics of most other state universities, all I have to do is think of in Developing Countries" was held in Tunisia. Participants how my Vietnamese colleagues are producing world-class came in large numbers from Northern Africa, and many mathematical research on a salary of $4 per month, and my came from the universities, institutes, and educational estab morale is restored! lishments of other regions of the Third World. I received Clearly, Vietnamese mathematicians cannot use their a copy of the proceedings of that conference. All of the salaries to buy books: A single book would cost a year's there mathematicians and math educators, without exception, sang wages! How do they equip their libraries? Well, from friends in other the praises of computers and pled for the rapid introduction are several ways: (1) donations countries, mainly the U.S. and France; (2) book purchases of computers into their school systems. Not a single note the Vietnamese make when they have a post-doc or visiting of skepticism, not a single troubling question was even professorship in Europe or North America; (3) journal raised, let alone explored in depth. One could have asked, exchanges (in which they can offer a subscription to the main for example: Are computers truly what schools in Africa Vietnamese math journal, Acta Mathematica Vietnamica). (If be introduced on a need? In practice, would computers you would like to get a subscription to Acta Mathematica for the general level, or only in a few of the elite schools Vietnamica for your library, please contact me, and I can wealthy? Could resources be better spent in other ways-to help you arrange it.) But even with the best efforts of the raise teachers' salaries, improve classroom blackboards and Vietnamese mathematicians, the math collections in Vietnam lighting, expand libraries? In any case, it seems to me bizarre remain spotty. that the Tunisia conference adopted as an axiom the notion It's not only the geographical isolation and lack of that the introduction of computers should be a priority for books and journals that make it difficult for Vietnamese elementary education in Africa. mathematicians to keep in touch with current developments. I should point out that much of the support for the In most fields, they are not part of the informal network of Tunisia conference came from the big French computer researchers that communicates by means of letters, phone companies. Thus, even though the conference was of little value for people seriously interested in educational issues, 1But Mexico and Cuba, tbe two Third World countries closest to tbe United I can see how the funding companies could have viewed it States, do have many research mathematicians. In tbe case of Cuba, tbe severe as a great success, holding open the possibility of lucrative U.S. government restrictions on travel to Cuba and visas for Cuban scientists have been an obstacle to contact between tbe two countries' mathematical new markets, particularly in the former French colonies of communities. For more information about tbis regrettable situation, see Seymour Northern Africa. Schuster's article in The Mathematicallntelligencer, Vol. 10, No. 4, 1988. ------·--·•••----·•··••--·•••""•-----·-•-•···---·-••·-••·•-·-•"""--•-·•-·•··•-••·••--·•·•-""·"-"""""-""-••••·-•- NOVEMBER 1991, VOLUME 38, NUMBER 9 1125 Math in the Third World calls, email, and casual conversations at conferences. There in this field, it is not easy to find a publisher. have been several cases of promising young mathematicians One can't help noticing a strong Eurocentric bias in returning to Vietnam from graduate school in Europe, only the publishing world. How many biographical articles, full to become demoralized by the harsh material conditions and length biographies, and histories have you seen about Third the isolation and then abandon research. But the remarkable World mathematicians? (Okay, several books have been thing is that, in most cases, the Vietnamese manage to written about Ramanujan. But what about the others?) For continue working at a high level, despite the obstacles. example, all of the mathematicians whose interviews were A list of publications of the members of the Hanoi Math included in the two volumes, Mathematical People and More Institute runs to over sixty pages. Most of the publications Mathematical People, live in Europe or North America. And, appeared in European and North American journals. The to be frank, I found some of the interviews almost put me list is comparable in quantity and quality to the list of to sleep. If I had been editor, I would have been tempted to publications by faculty members that one would expect to toss out the more soporific interviews and replace them with find at a large state university in the U.S. some oral history of mathematical people from other parts If we want to understand how the Vietnamese have been of the world. able to produce impressive accomplishments in mathematical Browsing through the stacks of any university math research and education under adverse conditions, we need library, you can easily find quite a few full-length autobi to talk with some of their senior mathematicians about ographies of prominent white male American mathematicians their own lives and the development of mathematics in that are real snoozers yet had no trouble finding publishers. Vietnam. In January 1989, I conducted a series of interviews But I have not yet been able to find a publisher for a pro with the then Director of the Hanoi Mathematical Institute, posed collection of reminiscences I would like to edit about Professor Hoang Tl;ly. Much of what he said was published the development of mathematics in Vietnam during the war in The Mathematical Intelligencer in an issue with the words years. In addition to recollections of Vietnamese mathemati "Mathematics in Vietnam" on the cover (Vol. 12, No. 3, cians, the collection would contain an English translation of 1990). the unpublished 1967 report by the great French mathema Hoang Tl;ly grew up in the south of Vietnam during tician Grothendieck, who gave a short course on abstract a turbulent period when many Vietnamese intellectuals, algebraic geometry in the jungles of North Vietnam, where including his family, were deeply involved in the struggle for the university had been evacuated during the bombing. independence from France. He was largely self-educated and Here I'd like to put in a word of appreciation for the late became a high school teacher in one of the "liberated zones" Walter Kaufmann-Bubier, who was one of the rare editors in the late 1940s, during the height of the anti-colonial war willing to take risks and publish unconventional things. He that was being waged by the Viet Minh guerrillas. In 1949, was math editor at Springer-Verlag when The Mathematical he wrote a high school geometry textbook in Vietnamese. Intelligencer was started. That journal has carried on in It was published by the Viet Minh press-perhaps the first the tradition of Kaufmann-Bubier, and is one place where math book ever published by a guerrilla movement. historical and cultural articles about the Third World can get Two years later, Hoang Tl;ly decided to leave home to published. study and teach in a rudimentary university that the Viet Just as most publishers ignore the Third World in their Minh guerrilla organization had set up in the far north. As publications on the history of mathematics, they also ignore Hoang Tl;IY relates: the needs of Third World mathematicians in their pricing of books and journals. As far as I know, there are no major In 1949, with Hanoi occupied [by the French] and the commercial publishers that offer special discounts to math university closed, some classes in university mathemat libraries in the Third World. 2 This is unfortunate, and hard ics had been established in the liberated zones in the to understand, because even from a narrow financial point mountains near the Chinese border ... The trek north of view it would be in the interest of the publishers to offer took three months ... We did everything possible to such discounts. The important thing to remember is that such lighten our load. We carried only rice and salt for food. arrangements would not cut into regular-price sales (unlike Before I left, I had taken my math books, removed the discount arrangements for mathematicians in the wealthier covers, and cut out the margins on every page so that countries). Hence, the financial aspect should be computed they would be lighter for the journey north. on the basis of the marginal cost of the copies for the In our discussions, Hoang Tl;IY recounted some amazing Third World-not including the fixed costs of producing things about his own life and the history of mathematics in the book or journal. I once talked about this with Walter Vietnam-please contact me if you would like me to send Kaufmann-Bubier, who was very sympathetic and optimistic you a copy of the full interview. about doing something. But we were unable to do anything I'm emphasizing this interview with Hoang Tl;IY to such before his untimely death. an extent because, unfortunately, it's one of the few things 2In a few places-mainly China and India-some publishers license local that have been published about the history of mathematical publishing houses to reprint books at greatly reduced cost. However, this institutions and personalities in the Third World. Little work system operates in only a handful of countries and it covers a relatively small has been done in this area, and when something is written number of books. 1126 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY - = Math in the Third World Another topic I'd like to address here is the "brain one, in fact-which they could use to transport visitors and drain"-a fundamental problem faced by almost all devel conduct other Institute business. The van had cost $12,000 oping countries. The term "brain drain" refers to the loss and had been paid for entirely by the individual contributions of mathematicians, scientists, and other professionals, who, of Institute members who had saved up portions of the salary after receiving most of their education in their own country they had earned while on post-docs or visiting professorships (usually through the undergraduate level), emigrate to a in the West. The mathematicians were proud that such a developed country (usually the U.S.) in search of a better large sum had been raised by purely voluntary contributions. life. The "brain drain" is in fact an important source of The second example concerns the algebraic topologist skilled professionals for the U.S., and for this reason the Huynh Mui, now a professor at Hanoi University. Exiled U.S. recently amended its immigration laws so as to make it from South Vietnam in the 1960s, he spent most of the easier for professionals to move here. Not long ago, I read war years in Japan, where he received his graduate training of a British study that attempted to put a dollar value on and his first job. Despite the horrible material conditions in the benefit to the U.S. of the brain drain. The conclusion Vietnam following the war, Mui returned to Hanoi in the was that the total of all U.S. foreign aid is slightly less than late 1970s to found a small school of algebraic topology. the total aid the U.S. receives in the form of well-educated One of the problems he faced was the lack of any living immigrants. Of course, as with any attempt to attach a dollar accommodations for his students and proteges from other figure to something that's not really quantifiable, there are parts of the country. To overcome this obstacle, he had some flaws in this study. It seems to me that, most likely, the friends from Japan send him a top-of-the-line bicycle, which study underestimates the benefit to the U.S. and understates he was able to sell for a handsome sum. (Bicycles are the even more the damage to the Third World of the brain drain. main form of transportation in Vietnam.) Mui then used the In fact, one can argue that the loss to the country of origin money from selling the bicycle to finance the construction is much greater than the gain to the U.S. because of the of a small guesthouse in the outskirts of Hanoi. way the brain drain undermines professional institutions and Huynh Mui is one of a small but important group morale. of mathematicians who were trained in the wealthy coun For example, when I was in Madras, India, I met a young tries and then decided to return to Vietnam and dedicate Indian physicist who had returned after graduate study in themselves to training the next generation of Vietnamese the U.S. He complained bitterly of the way most Indians mathematical researchers and educators. This flow of math assumed that he had returned because he wasn't good ematicians back to Vietnam has been a sort of "brain drain enough to make it in the U.S. If people have the perception, in reverse." correct or incorrect, that the best and the brightest emigrate Another representative of this group is the algebraist to the U.S., then the best young scientists will in fact feel Hoang Xuan Sinh, whose work in category theory was under pressure to leave, and the perception will become a partly inspired by Grothendieck's 1967 visit. She received self-fulfilling prophecy. her docteur d'etat in France about 20 years ago--she By the same token, when bright young scientists are actually wrote most of her thesis in Vietnam during the dissatisfied with the scientific institutions of their country, height of the bombing-and has since been teaching at the instead of staying and trying to effect reform from within, Hanoi Pedagogical Institute. Professor Sinh was also the first they are tempted to wash their hands of it and leave for the woman full professor of any scientific subject in Vietnam. U.S. Thus, the brain drain also drains away much of the She is a vice-president of the Vietnam Women's Union and human energy that could go into reform and modernization. has played a key role in encouraging young Vietnamese I believe that the material differences between life in the women to study mathematics. Third World and in the U.S. are not the only cause-and A large number of the mathematicians in Vietnam are not necessarily even the primary cause-of the brain received all or part of their advanced training in the Soviet drain. For example, even though Vietnamese mathematicians Union or Eastern Europe. And until recently, Vietnamese are the lowest paid mathematicians in the world (I believe math libraries could receive Soviet journals at nominal this is literally true), there has been virtually no brain charge. Both forms of assistance have now dried up. In fact, drain. The best Vietnamese mathematicians go abroad for when I was in Hanoi last January, I was told that the Russians several months or a year, and then invariably return. Let me now expect the Vietnamese to pay full price in dollars for mention in passing, that of the approximately 200 scientists Soviet journals. Of course, in practice this means that the from Vietnam whose visits to the U.S. have been arranged Vietnamese will have to drop all of their subscriptions to through the U.S. Committee for Scientific Cooperation with Soviet journals. The sudden vanishing of assistance from Vietnam, not a single visit has ended in a defection. The the Soviet Union and Eastern Europe is one of the reasons point is that in Vietnam-much more so than in India-the why help is badly needed from mathematicians in the West. scientists are held in tremendous popular esteem, and they I'd like to make a few general comments on mathemat have an impressive esprit de corps. ics in developing countries. Along with all the obstacles, I'd like to give two striking examples of this group mathematicians in the Third World have some things going spirit. When I was last in Hanoi in January, the Hanoi Math for them as well. For example, mathematics does not require Institute for the first time had a microbus-a brand new the infrastructure and material investment that most branches NOVEMBER 1991, VOLUME 38, NUMBER 9 1127 Math in the Third World of science need in order to function at a high level. Thus, should make all of their books and journals available at in many developing countries-Vietnam, China, and India, nominal cost to libraries in the Third World3 ; and (2) for example-mathematics seems to be the strongest area we should approach the commercial math publishers in an of science, with the most prestige and clout. In Vietnam, organized way and ask them to offer steeply discounted in fact, mathematicians are often consulted by the political sales to libraries in developing countries. leaders of the country. This contrasts with the U.S., where • Publishers should be more open-minded about possible mathematicians tend to have less clout in Washington than publications on the culture and history of mathematics other scientists. in the Third World. In addition, many developing countries have ancient • Mathematical institutions and individual mathematicians traditions in mathematics. We now know that a number of should limit their ties to only the best known research basic mathematical ideas and techniques were first discov centers. It is unfortunate that in India, for example, the ered in China, India, and the Middle East. An example university system is often neglected by foreign visitors, of early mathematical work in another part of the world, who traditionally have most of their ties with the namely Central America, is found among the Mayans, who various research institutes (especially the Tata Institute developed mathematical astronomy to an extent that was not in Bombay). duplicated in Europe until centuries later. As you probably • Finally, on an individual basis, one can cultivate relations know, the Mayans had excellent success predicting eclipses. with one or two math departments or institutes in the If we adopt a broad understanding of what constitutes Third World. I'm not suggesting becoming a one-person mathematical ideas, we find that mathematical thinking has foreign aid program or spreading oneself too thin. a long history in many indigenous cultures throughout the Rather, choose a place where you have a former student, Third World. This area of history of mathematics is often or where you know of a mathematician with similar called "ethnomathematics"-a term coined by the Brazilian research interests, or a region where you have family mathematician Ubiratan d' Ambrosio. The further study and ties, or a country where you have a longstanding cultural popularization of ethnomathematics could lead to a greater or political interest, or where you like the food and consciousness of the contributions to world mathematics that climate. Escape the New England winter every year by have been made in Asia, Africa, and Latin America. This giving a January "short course" of lectures in sunny realization could inspire a greater self-confidence among Madras, Maputo, or Montevideo! math students in developing countries, and a determination Why should we go to the trouble? Not for reasons of to leave behind the legacy of colonialism and once again altruism. Speaking personally, I find that what one gets out become major participants in world mathematical culture. of contacts with colleagues in the Third World is much more I'd like to conclude with a list of things we can do to valuable than whatever time, money, and energy one puts support our colleagues in the Third World. into it. You meet some tremendous people, you get a useful • We could develop sabbatical-like programs for Third perspective on your own professional life in the U.S., and World mathematicians so that they could spend, say, one you get a sense of having a real impact on the development out of every five or six years in a developed country. of our science in some farftung part of the world. That way, active researchers in developing countries One feature of mathematics of which we can be justifi would not be faced with the either-or choice: to emigrate ably proud is that it is the most international of all academic to the U.S. or to remain in their native country forever disciplines. Despite all the cultural differences-and all the isolated from the main centers of research. material differences between rich and poor.:__we really are on • We should make every effort to keep contact with our the same wavelength. We are interested in the same research former students who return to their countries of origin. problems and the same problems of mathematics education. The simple act of regular correspondence can go a long When we strengthen our ties with and organize support for way to keep them from being overcome by isolation. our colleagues in the Third World, we are contributing to • We could donate books and journals to institutes and the future vitality of the worldwide mathematical profession. universities in developing countries. Dumping one's old books and moldy copies of Notices is not helpful. Rather, • 31n the case of the AMS, the Committee on Service to Mathematicians in Developing Countries, which in the past has distributed books and journals we should find out what they really want and try to get to some countries on an ad-hoc basis, would be the appropriate group to it for them. In particular: (1) the AMS and the MAA coordinate the systematic distribution of AMS publications. 1128 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum Of course, in the short run, the economic slump figures large in explaining the lack of jobs. Many states-including The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between California, Maryland, Massachusetts, North Carolina, Penn 1000 and 2500 words long. Readers are invited to submit articles sylvania, and Virginia-are experiencing sizeable shortfalls for possible inclusion in Forum to: in revenues. The upshot is that many state universities, Notices Forum Editor which expected last fall to have a few "line" positions and American Mathematical Society several instructorships, in the end had no positions at all. P.O. Box 6248 Most private universities have been less severely affected, Providence, RI 02940 but the bad news will trickle down to them in a year or two. or electronically to [email protected] To make a long story short, in the academic year 1990- 1991 there were many more job candidates in mathematics than usual and many fewer jobs. However, we maintain that there are long term trends in the hiring policies of Some Observations about the mathematics departments-trends that have been developing Hiring Situation in Mathematics over the last twenty years-that have been eroding our Steven G. Krantz and Guido L. Weiss ability to hire good people and our ability to place our new Washington University Ph.D.s. Let us describe what some of these are. There have been significant increases in the last five to The academic year 1990-1991 was a bleak one in the ten years in the total number of instructorships and "postdoc" job market for young mathematicians. An informal poll In any given year, a large number of conducted by the American Mathematical Society between positions available. speaking, April and early May revealed that among twenty-eight top the new Ph.D.s land postdoc positions. Generally in January Ph.D.-producing math departments, only 48% of their new most of these positions are handed out quickly Ph.D.s seeking U.S. academic positions had accepted a and February. What becomes of the remaining new Ph.D.s? position as of the reporting. Furthermore, we estimated that, That is the rub. By convention, almost nobody hires new based on a number of anecdotal reports at the time, as many Ph.D.s as Assistant Professors anymore. We want to hire as 500 mathematicians, new and otherwise, were still seek either a "proven product" coming off a two or three year ing employment. At many good mathematics departments, postdoc or an Associate Professor at the beginning tenure including our own, we find ourselves turning to our new level. So this other half of the new crop of mathematicians Ph.D.s and saying "we're sorry, we don't understand why the ones who do not get postdocs--ends up with jobs in the job market is so bad." As a stopgap measure, we can non-research departments or in industry or, perhaps worst of keep some of these students in the graduate program for an all, with one-year make-do instructorships (there has been extra year (in many cases without support), but this is no an alarming increase in the number of one year jobs in the solution to the problem. And what is the problem? last few hiring seasons-this in spite of sanctions against The analysis made by the two David Reports (in 1984 that practice by the AAUP). and in 1989) was based on a situation that has been Part and parcel of the syndrome described in the last drastically changed by the enormous influx of excellent few paragraphs is the superstar mentality that we have all mathematicians from both China and eastern Europe. Many developed. Rather than hiring a promising young mathema of these immigrants are among the best in modem mathe tician fresh out of school and watching the candidate for six matics. Who wouldn't move heaven and earth (and in the years to see how he/she develops, we want to hire a proven process short-change our obligation to young scientists) in product. Tenure decisions are unpleasant and nobody wants order to grab one of these stars? But it is short-sighted and to face them. More to the point, we all want to hire stars. simplistic to think that this is the only, or even the main, Here is the crux: In every hiring season for the last cause of the problem. five or six years, about half a dozen candidates--each about NOVEMBER 1991, VOLUME 38, NUMBER 9 1129 Forum four years out--emerge as the stars of the moment. And all All of the problems described above have been exacer the best departments go after these same people. The end bated (and understandably so) in recent years because each result is a circus. Each candidate ends up with so many candidate sends out so very many applications. In the early offers that--due to a combination of lack of experience, 1970s, applying to forty or so schools was considered more immaturity, and hubris-he/she can no longer make an than sufficient (and there weren't any jobs then either). informed decision. Moreover, all the job searches at the But now there are word processors and a candidate thinks thirty or forty schools involved are tied up until these few nothing of applying to 200 or more schools. And since jobs candidates make up their minds. By the time the dust clears, are so tough to get, it makes sense to apply to a lot of it is the end of April and everyone throws in the towel places. Many good math departments received between 600 on hiring for that year. So a great many other deserving and 1200 applications this year. How can the members of candidates are left high and dry. [Even in the disastrous the hiring committee possibly evaluate all this information? season 1990-1991, a great many openings were left unfilled Of course they cannot, so they get on the telephone and due to the inefficiency of our hiring system.] It sounds silly the good old boy network comes into play. Again, this loop to commit these words to print, but they are true: We do only aggravates the travails suffered by most job seekers. not want to hire fresh Ph.D.s, certainly not as Assistant We would like to encourage the American Mathematical Professors, and yet we are all bemoaning the fact that Society to explore ways in which it can help to organize, our own Ph.D. students cannot find jobs. We would be the and to act as a clearing house for, the job seeking process first to admit that our own department has been guilty of for people who are zero to three years from the Ph.D. Fields participating in this syndrome. Medalists and Congress speakers need not be affected by To carry this point to an extreme, there has been this service. But the rest of the mathematics community will considerable mobility among senior mathematicians in their benefit enormously from a reevaluation of our value system late thirties and early forties in the last few years. Many and, particularly, of our hiring practices. There are no doubt hiring programs have been skewed in an attempt to make other devices that should be explored for alleviating the attractive offers to these famous people. Six figure salaries present hiring difficulties in mathematics. We wish to focus are the norm in these situations. Five figure discretionary attention in this essay on what the AMS might do to help. funds and reduced teaching loads are of course expected. The Forum article by Don Lewis that appeared in the Jobs for spouses, in-laws, and offspring ru;e often part of April 1991 issue of Notices, pages 296-297, advocates that the package. In some universities, graduate student positions strong measures be taken to increase the number of postdocs and junior faculty positions have been eliminated in order available in any given year. This may be a partial solution to amass the resources necessary to make these fabulous to the problems described here. We urge the American offers. The end result, obviously, is fewer opportunities for Mathematical Society and other organizations to explore young people. means by which the total number of postdocs may be We are suggesting that the lack of jobs, and the difficulty increased. in placing our own students, is not just a function of The present hiring situation, which shows no sign of im demographics (Chinese and eastern Europeans) and not just mediate improvement, will serve only to discourage young a function of shortfalls in state budgets. It is in fact a people from going into mathematics. The number of Amer corollary of the sociology of mathematics. And this is a ican students entering the profession is already alarmingly sociology that is recently evolved. Thirty-five years ago small. In our hiring efforts, we must take into account mathematicians were comfortable with waiting seven to ten not only the immediate needs and prestige of our own years for tenure-just like everyone else. Now we have to departments, but the infrastructure of the profession. Most give tenure to people who are four years out if we want to of us were hired at a time when mathematics departments be competitive. Of course, we cannot expect these people to were less star-struck. There is no reason to believe that direct theses or serve on committees or even know how to the current hiring system is any improvement. In fact, it teach well; after all, they are only four years from the Ph.D. has instead created an atmosphere in which everyone is But that is beside the point. We have to be competitive so always looking to move. As a result, mathematicians, during we can attract the stars. their most vigorous and productive years, tend to have no This is not the way that hiring is done in the medical commitment to their own departments. The long term effects profession, nor even in chemistry or physics or computer of such an attitude are bound to be calamitous. We owe science. In medicine, the national professional organizations it to ourselves and to our profession to rethink the hiring help to orchestrate the hiring process. It works well. And program in academic mathematics. while some young physicians do not get the position of their Editor's Note: The first report of the 1991 Annual choice, they at least all get a position. Most good computer AMS-MAA Survey, which includes the 1991 survey of science departments do not perform "star searches" to fill new doctorates, starting salaries of new doctorates, faculty their positions. They look over the dossiers that come in and salaries, and a list of names and thesis titles for members of they pick somebody. If he/she does not work out, then the the 1990-1991 Ph.D. class, starts on page 1086 of this issue candidate does not get tenure. of Notices. ------1130 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum Rigor in the Undergraduate textbooks, or employ a double standard, pretending to teach Calculus Curriculum rigor without demanding any true mathematical reasoning William G. McCallum from their students. Most of the textbook questions dealing with the abstract part of the course, are, in fact, as formulaic University of Arizona as drill problems about the chain rule: find the c such that About two years ago, I signed up on a five year odyssey f(b)- f(a) = f'(c)W- a); construct the Riemann sum with to reform the calculus curriculum, known as the Harvard 4 subdivisions (do not evaluate!). Calculus Consortium. We have so far survived the hazards As a result, we produce students who believe that of despair and dissension, but I see ahead clashing rocks mathematics is, in its essence, a matter of blind rules and between which we must pass: Scylla, the Student, protesting procedures; their main reaction to being asked to reason we demand too much mathematical reasoning, and Charyb mathematically is "When are we going to stop fooling dis, the Colleague, wailing that we have abandoned it. This around with these 'thought' questions and return to real article is an attempt to appease Charybdis; I haven't yet mathematics?" figured out what to do about Scylla. Bear in mind that among these same students, there In thinking about teaching mathematics, I find it useful are those, the better ones, who are expert in "taking the to have in mind the following rough hierarchy of the sorts derivative using the definition" and who can faithfully of things we teach: First, mathematical methods, second, reproduce the E - 8 definition of a limit. The trouble is that, intuition and analysis, and third, abstraction and rigor. from their point of view, there is no distinction between this Mathematical methods form· the lowest level, consisting sort of ability and the ability to use the chain rule; as far as of rules and procedures which are useful even if not they are concerned, all mathematics is method, regardless of fully understood, such as the quadratic formula or the meaning. chain rule. The next level, that of intuition and analysis, A case in point: In a traditional calculus course, we consists of modes of reasoning that enable the student to successfully teach a fair number of students how to interpret use the methods; for example, a sufficient understanding of the symbols infinitesimals to set up definite integrals that compute various physical quantities. The highest level, that of abstraction and J'(x) =lim f(x +h)- f(x) rigor, is the level where intuition and analysis are refined h->0 h into mathematics as we know it today. For example, once in the special case f(x) = x2 to derive f'(x) = 2x. However, the student has a sufficient intuitive grasp of the definite we never bother to check if they realize, in any practical integral, he or she is ready for the formal definition of the sense, that the derivative is a limit of difference quotients. Riemann integral. For an example of just how far their understanding is from About the first level, I don't have much to say. The what you think you are teaching, try asking your class for specific methods to be taught may vary with time; methods f'(2) when f(x) = x"'. What's shocking is not so much that of integration may become less important, interpolation half of them will answer 4, through a false application of methods more so, and there will from time to time be the power rule, but that they are utterly unconvinced when arguments about which methods should be dropped and you pull out a calculator and compute which admitted. But I don't think it is too hard for us to come to some agreement on this. Also, the main obstacle 2.001 2·001 - 22 to teaching mathematical methods, at least in calculus, is .001 = 6.779. that our incoming students lack basic skills. This problem, although formidable, must be tackled by a broader reform Another example: I asked my students to analyze the one than the one we are attempting. parameter family of functions e-"'2 fa in two stages. First, I think what's wrong with the way we teach calculus they were to use a computer graphing program to sketch can be stated fairly simply mterms of these categories: the graph of e-"'2 fa for various different values of a, and We mostly teach mathematical methods, but, to salve our describe the effect of varying a (Answer: The bell-shaped mathematical consciences, we throw in bits and pieces of curve is wide when a is large, narrow when a is small). abstraction and rigor; these mean nothing to the students, Then they were to find the inflection points (they are at since we have neglected to supply them with any intuition x = ±/0]2), and relate their discovery to the effect they or analysis. Worse, we misguidedly save them from what observed on the computer. Most students had no trouble little intuition they bring with them; we tell them that area with the first part; however, in the second part, many failed is a "concept" that requires definition, then come to their to use the product rule in calculating the second derivative, rescue with Riemann sums; that it is not at all obvious and concluded that there was only one inflection point, at that x2 approaches 4 as x approaches 2, then come to their x = 0. I wasn't surprised at the error, but I was profoundly rescue with epsilons and deltas. disturbed that they chose the evidence of their calculation In fact, I suspect that most mathematicians who teach over the evidence of their own eyes. calculus either surreptitiously relax their standards of rigor I am sure that most mathematicians who teach calculus and concentrate more on developing intuition, in spite of the have similar stories: I am not so sure that they diagnose the NOVEMBER 1991, VOLUME 38, NUMBER 9 1131 ································-···-····································-··················································-·················------Forum problem correctly. All too often I hear my colleagues shrug I will give two examples my students produced (without their shoulders and say "What can you do? They don't learn prodding from me) that I think are in the right spirit. anything in high school (watch too much TV, are idiots)." First, in answering the question about e- :1/ I a that I In fact, I think that we bear at least part of the blame. described above, some who failed to correctly find the I said above that teachers "surreptitiously" develop their second derivative nonetheless recognized that fact, and student's intuition, and I think that's the right word. Despite came up with the following analysis, which avoided any the fact that we use it all the time ourselves, we seem to feel discussion of inflection points: They observed that when a obliged to tell our students repeatedly that they shouldn't was large, the bell curve was flatter. They then looked at the trust intuition, that intuitive. arguments using infinitesimals first derivative may look appealing, but that they are a snare and a delusion. The fact of the matter is that intuitive arguments using f '( x ) ---e_ -2x x2/a infinitesimals work pretty well most of the time, and the few a pitfalls (using infinitesimal cylinders rather than frustra to and pointed out that when a was large, the derivative compute surfaces of revolution, for example) are instructive, had smaller values; this explained the flatness of the curve. not disastrous. Another problem I gave my students was to explain why, Consider the following problem, which I have just set for a smooth function f, the local extrema of f' coincide on the final exam of an experimental calculus class. with the inflection points of f. Most students demonstrated (a) There is a function used by statisticians, called the their attachment to simple but false rules by answering that error function, which is written y = erf(x ). Suppose both coincided with the zeroes off". But a couple gave the your calculator has a button for this function. Playing following answer, still only partially correct but much more with your calculator, you find that encouraging. They said that it was geometrically obvious that inflection points occur at the steepest part of the graph, erf(O) = 0 and that these correspond to the points where the absolute erf(l) = .84270079 value of the derivative is at a maximum, hence the derivative is at an extreme. Of course, they forgot that inflection points erf(.l) = .11246292 can also occur at the least steep part of the graph, but I think erf(.Ol) = .01128342. this argument shows a geometric understanding· that should be encouraged. Using this information alone, give an estimate for I suspect that there is enormous room for disagreement err' (0). Give as many decimal places as you feel among mathematicians on the demarcation between intuition reasonably sure of, and explain why you gave that and rigor, and on the correct mixture. One of my colleagues many. wondered how "we build confidence at level 2 [intuition (b) Suppose that you go back to your calculator, and and analysis] without venturing into level 3 [abstraction and find that rigor]", whereas another "firmly believe[s] that traditional erf(.OOl) = .00112838. rigor has no place in the introductory calculus sequence." However, I think this is clear: A calculus course, with or With this extra information, would you refine the answer without rigor, should be built from the ground up, adding you gave in (a)? what is necessary for understanding only as the necessity I will be delighted if any of my students answer part (b) for it becomes clear. By contrast, the curriculum we use by giving more decimal places, even though this answer is now looks like it was dismantled from the top down: It is unsupportable from a strict point of view; I want them to a reliquary for pieces of the True Calculus, full of proofs understand the notion of a limit intuitively before I challenge bowdlerized beyond common sense. that intuition. I discussed this question with a colleague, Before trying to teach students the sophisticated proof, who is sympathetic to my point of view, and he looked at we should make sure they grasp the naive one. We should not me and said: "I like it-but the gods of mathematics will abandon to mindless symbolic manipulation those students be displeased with you." My feeling is that we should give who can't or won't follow the rigorous approach. We should problems like this unashamedly, without worrying about the come up with probing questions that test for good intuition, gods of mathematics peering over our shoulder. and do our students the favor of both demanding and learning My experience this semester showed that it is not wildly to recognize mathematical thought in their arguments, flawed romantic to demand intuitive reasoning from our students. as they may be from a strict point of view. ------···--···--···------1132 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics Edited by Keith Devlin This month's column ematicians. Nevertheless, some theorem provers have been Computer-assisted proofs are the theme of this month's feature article, used to produce fully machine-checked proofs of mathe by William Farmer and Javier Thayer of the MITRE Corporation. This matically significant results; for examples, see [1, 2, 3, 8, is followed by two software reviews. Larry Riddle reviews Plot and 9]. Tevian Dray describes his experiences with the two programs Cube and Tess. In this article we discuss two proofs that were created Editor's address: with the help of a computer theorem proving system called Professor Keith Devlin IMPS (Interactive Mathematical Proof System), which is Department of Mathematics currently being developed at The MITRE Corporation. The and Computer Science fact that these results were proven using a computer is Colby College not in itself noteworthy. However, it is significant that Waterville, Maine 04901 the proof itself can be organized in a way which is at Correspondence by electronic mail is preferred, to: the same time comprehensible to a mathematically trained [email protected] person and recognizably valid to the computer. We want to conclude from this that computers can indeed support the standard techniques of mathematics and can provide strong organizational, as well as computational, assistance Two Computer-Supported Proofs for theorem proving. The two theorems proved are the following elementary in Metric Space Topology* results about the topology of metric spaces: William M. Farmer and Theorem 1. Let f be a continuous mapping from a metric F. Javier Thayer space M to a metric space N. If A~ M is connected, then The MITRE Corporation f(A) is likewise connected. Theorem 2. Let f be a continuous mapping from a metric space M to a metric space N. If A ~ M is sequentially compact, 1 then f(A) is likewise sequentially compact. 1. Introduction In Section 2, we shall discuss some of the facets of Every mathematician will agree that the discovery, analysis, IMPS that make it particularly suitable for formulating and and communication of theorems and proofs is at the heart of reasoning about mathematics. Then in Section 3 we shall his or her discipline. A number of computer programs (such describe the formal theory in which the theorems are stated as Maple or Mathematica) assist mathematicians in testing and proved. The proofs of the two theorems are given in conjectures and proving certain kinds of theorems, typically Section 4. The final section, Section 5, contains a short identities involving rational functions or trigonometric poly conclusion. nomials. These systems, however, were never intended for some of the most critical parts of the mathematical process: 2. IMPS formulation of concepts and theories and rigorous proof of The IMPS system is intended to provide computational general theorems. support for rigorous mathematical reasoning in a style that There are other programs, less well known in the math closely conforms to conventional practice. It can be used ematical community, that are designed to provide computer to formulate axiomatic theories and to prove theorems in support for the actual theorem proving process. These pro them. The major goal of the system is to provide users grams, usually called theorem provers, tend to be very with the means to develop machine-checked proofs that are specialized tools, aimed at discovering or checking proofs convincing and intelligible to a wide audience. in languages or logical systems not ordinarily used by math- 1We define a set to be sequentially compact if each one of its countable *Supported by the MITRE-Sponsored Research program. open covers has a finite subcover. NOVEMBER 1991, VOLUME 38, NUMBER 9 1133 --···········-·······-·--········-·········-···-·······-·-···--··"·················--·············-·············-····-···------Computers and Mathematics For a detailed overview of the IMPS system see [6]. In a number of facilities for using the axiomatic method in the rest of this section, we shall describe three aspects of the little theories style. Users of IMPS can freely formulate IMPS that facilitate the construction of intelligible proofs: its multiple axiomatic theories. Each theory consists of a logic, its support for the axiomatic method, and its style of formal language-specified by a set of atomic sorts and proof. constants-and a set of axioms expressed in the language. Theories are related to each other by theory interpretations. A theory interpretation is a syntactic device for translating 2.1 Logic the language of a theory T to the language of a theory In IMPS all concept formulation, calculation, and inference T' with the property that each theorem of T is translated is performed with respect to a formal logic that is a to a theorem of T'. Theory interpretations thus provide version of classical higher-order predicate logic. This logic a mechanism for "transporting" theorems from abstract provides strong support for specifying and reasoning about functions. In particular, functions may be higher order theories to more concrete theories. The IMPS theory and theory interpretation mechanisms (have arguments which are themselves functions) and partial should be useful in much of mathematical analysis, where (not defined on all arguments). In addition, formulas may reasoning is typically done at various levels of abstraction. contain arbitrary quantification (universal or existential) over For example, the proof of the Picard-LindelOf existence functions. Partial functions are handled in a direct manner, theorem for ordinary differential equations is often proved without introducing special error elements. This means that in textbooks by applying the fixed point principle for some terms, such as 2/0, have no value assigned to them. contractive mappings on a complete metric space.2 In the A direct approach to partial functions is very convenient for formalizing mathematics in which partial functions play a terminology of IMPS, that approach requires the construction prominent role. This is especially true for analysis where of a theory interpretation in which a metric space is partial higher-order functions, such as the differentiation interpreted as a space of continuous functions on an interval. operator on functions, occur naturally. The real work here consists of showing that this instantiation The IMPS logic is equipped with a hierarchy of objects is valid, which involves among other things, reasoning about called sorts which denote classes of elements. Sorts are used integrals of real-valued functions on intervals. to help specify the value of an expression and to restrict quantification. They are especially useful for reasoning with 2.3 Proofs respect to overlapping domains. For example, suppose Z IMPS produces formal proofs, but they are very different and R are sorts denoting the integers and the real numbers, from the formal proofs that are described in logic text respectively. Then the Archimedean principle for the real books. Usually a formal proof is a tree or graph constructed numbers can be expressed quite naturally as in a purely syntactic way from axioms, previously proved theorems, and a small number of low-level rules of inference. for every a : R for some n : Z a < n. Formal proofs of this kind tend to be composed of an For more information on the IMPS logic, see [4, 5, 7]. enormous number of small logical steps and for this reason are usually exceedingly hard to understand. In contrast, the steps in an IMPS proof can be very large, and most low 2.2 Axiomatic Method level inference in the proof is performed by an expression The axiomatic method comes in two basic styles. There is simplification routine. Since inference is described at a high the "big theory" style in which all reasoning is carried out level, proofs constructed in IMPS resemble informal proofs, within one theory-usually some highly expressive theory, but unlike an informal proof, all the details of an IMPS proof such as Zermelo-Fraenkel set theory. There is also the "little are machine-checked. theories" style in which results are proven in small abstract In IMPS, there are several devices for compressing com theories and then used in more concrete theories. This latter plex deductions into single units. Expression simplification style of the axiomatic method is employed extensively in carries out myriad low-level inferences in one step using al standard practice. For example, if a mathematician needed gebraic manipulation, term rewriting, and special algorithms a fact about multiplication over the nonzero elements in a for checking the definedness of terms. Theorem assumption field, he would usually not prove it in the context of fields allows one to assume intermediate assertions that have been if he could get away with proving it as a general result proved independently, either in the home theory of the in group theory. That is, he would prove a general result proof or in some appropriate outside theory. Collections in group theory, notice that multiplication over the nonzero of theorems can be automatically applied, in an organized elements has the structure of a group, and then appropriately manner, to a conjecture using macetes.3 Strategies call rules instantiate the general result to obtain the desired fact. In of inference-including simplification, theorem assumption, other words, a mathematician will typically prove a result in and macete application-in useful patterns; they are akin to a context free of unnecessary details, so that the result can what are called tactics in other systems. be used freely in a variety of more specialized contexts. Most theorem provers today support only the big theory 2 A proof of this latter result has been carried out in IMPS by Bob Givan. style of the axiomatic method. In contrast, IMPS provides 3In Portuguese, a macete is a clever trick. 1134 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ······················--······------~---- Computers and Mathematics These devices for packaging inferences help the IMPS (theory-from-definition user to raise the essential ideas of a proof to the surface, '(metric-spaces while suppressing the details that would normally not appear (component-theories b-o-real-arithmetic) in a written presentation of the proof. They also give the (language metric-spaces-language) user the means to initiate and control machine deduction. (axioms (positivity-of-distance 3. The Formal Theory "forall(x,y:points, O<=dist(x,y))") The formal proofs of Theorems 1 and 2 are carried out in a (point-separation-for-distance theory of metric space pairs. Before describing this theory, "forall(x,y:points, x=y iff dist(x,y)=O)") we need to describe two other basic theories that serve as (symmetry-of-distance building blocks for this theory. "forall(x,y:points, dist(x,y) = dist(y,x))") 3.1 Higher-Order Real Arithmetic (triangle-inequality-for-distance The IMPS theory of higher-order real arithmetic, called "forall(x,y,z:points, dist(x,z) h-o-real-arithmetic, axiomatizes the real number system as <=dist(x,y)+dist(y,z))")))) a complete ordered field and characterizes the integers and rationals as imbedded structures. This is a fairly extensive theory, so we only describe it informally here. The language These forms say the following: constants of this theory are of two kinds: • The theory metric-spaces includes h-o-real-arithmetic as • The function constants+,*,/, A' sub,-,<,~ that denote a subtheory (which, in particular, means completeness the arithmetic operations of addition, multiplication, arguments can be freely used). division, exponentiation, subtraction, negation, and the • The underlying set of the metric space is denoted by binary predicates less than and less than or equal to, the sort points. The function constant dist denotes the respectively. distance between two points in the metric space. (Note: • An infinite set of individual constants, one for each the sort R is entered at the keyboard by rr.) rational number. The atomic sorts of the language are Z, Q, R denoting 3.3 Metric Space Pairs the integers, rationals, and reals. Other constants and sorts The relevant theory for stating and proving Theorems 1 and can be added by definitions. 2 is called metric-space-pairs. The theory of a single metric The axioms of this theory are the usual field and order space is insufficient to formulate a completely general theory axioms as well as the completeness axiom which states of continuous functions between metric spaces, one that will that any predicate which is non-vacuous and bounded above include for instance continuous mappings between R3 to R2 has a least upper bound. This theory also contains the as a special case of the general theory. IMPS has a theory full second-order induction principle for the integers as an replication mechanism which allows users to automatically axiom. One can prove in this theory the basic facts about create a new theory which contains a fixed number of real numbers such as the archimedean principle stated above. imbedded copies of a given theory. By an imbedding we mean a theory interpretation as explained earlier in the paper. 3.2 Metric Spaces Theory replication is essential for doing interesting math The theory metric-spaces is a formal theory of a single ematics because most often one considers several instances metric space. It is sufficiently expressive to formulate the of the same structure and mappings between these structures. basic concepts of metric spaces, such as open and closed Thus, ordinarily mathematicians think of "ring theory" not sets, connectedness, sequential compactness (equivalent to as aformal theory of a single ring (which does not provide compactness for separable metric spaces), and continuity of much material for mathematical development) but at the real-valued functions. Results proven in this theory can be very least as a theory of rings and morphisms between them. transported, for example, to the theory of higher-order real The theory replication is specified in IMPS by the arithmetic. The theory is defined in IMPS by the two forms following form: (or s-expressions) given below. The first of these forms defines the language (i.e., the atomic sorts and constants (poly-replicate-theory-with-definitions which constitute the vocabulary of the theory), and the metric-spaces second form essentially just lists the axioms of the theory. (list 'first 'second) 'metric-space-pairs) (language-from-definition '(metric-spaces-language The theory metric-space-pairs includes h-o-real-arithmetic (embedded-languages b-o-real-arithmetic) plus the following additional components: (base-types points) • The additional atomic sorts (i.e., the atomic sorts of the (constants theory's language other than those in h-o-real-arithmetic) (dist (points points rr))))) are first.points and second.points. NOVEMBER 1991, VOLUME 38, NUMBER 9 1135 Computers and Mathematics • The additional constants are first....dist and second....dist. predicates are very close to the conventional ones adopted • The additional axioms of the theory are the metric in most textbooks. For example, the following expression is distance axioms (triangle inequality, symmetry, etc.) for the condition for x to be a connected subset of points. the functions first....dist and second....dist. for every a, b: sets[points] implication The procedure poly-replicate-theory-with-definitions also • conjunction creates a pair of translations from metric-spaces to metric • o open(a) space-pairs. Moreover, defined constants in the theory • o open(b) metric-spaces are automatically translated in two different • o empty?{anbnx} ways to similarly defined constants in the theory metric • ox~aub space-pairs. For example, the predicate open which is • disjunction defined in the theory metric-spaces is translated as two • ox~a predicates firsLopen and second_open, corresponding to e oX~ b. the property of being an open subset of first_points and The condition for a function f : firsLpoints ---+ second_points, respectively. second_points to be continuous can be given in several equivalent ways, but for our purposes, the most convenient 3.4 Indicators one is So far we have not discussed how to quantify over sets for every v : sets[second_points] implication of points in a way which would allow us to define • second_open(v) connectedness or sequential compactness. One possibility • firsLopen(f-1(v)). is to imbed the theory of metric space pairs in a larger Of course one can show in IMPS (with a certain amount theory such as Zermelo-Fraenkel set theory. This approach of user assistance) that this condition is equivalent to the is quite feasible but has the disadvantage that it requires a usual E, 8 condition for continuity. certain amount of preparatory work in set theory. Moreover, results in this larger theory can only be transported to other theories which are similarly imbedded in set theory. This 4. The Proofs considerably restricts the flexibility with which results can We describe in this section formal proofs of Theorems 1 and be moved around from theory to theory. 2 produced with IMPS. A proof in IMPS is represented by a In our development of metric spaces, we have adopted data structure called a deduction graph. A deduction graph the more direct approach of conceptually identifying a set is a directed graph with nodes of two kinds, representing S with a function f which takes on a fixed value (say formulas and inferences respectively. The formulas appearing the number 1) on S and is undefined everywhere else. We in a deduction graph are actually sequents consisting of a call such functions indicators. We have developed several single formula called the assertion together with a set of "generic" theories involving indicators which allow us to assumptions called the context. A sequent is considered to prove theorems about sets, covers, and inverse images in a be true if its context implies its assertion. very abstract setting. Since these theories have no axioms, There are two basic routines in IMPS for presenting the theorems proved in them can quite easily be transported to information contained in a deduction graph in a 1}3X format. other theories. One routine describes each logical inference recorded in the The following is an example of a useful fact (named deduction graph. The other routine is prescriptive: It presents direct-image-subset-conversion) which can be proved in one the deduction graph in terms of the user commands (i.e., of these generic theories. It allows us to replace, in certain rules of inference, macetes, and strategies) that were used cases, statements involving direct images with statements to construct the deduction graph. This is analogous to how involving inverse images. proofs are given in a lecture or in a textbook. Few details for every are provided by the lecturer, who limits him or herself to f : ind1 ---+ ind2, a: sets[ind!], b: sets[ind2] giving the information on how to reconstruct the proof. The implication proofs in the section are presented using this latter routine. • total(!, [ind1 ---+ ind2]) The formal statement of the first theorem is: • f(a) ~ b ~ a ~ J- 1(b). This is a useful result, since inverse images have nicer Theorem 1 properties than direct images. We make use of this result and for every f: firsLpoints---+ similar results in our computerassisted proofs of Theorems second_points, o: sets[firsLpoints] implication 1 and 2. • conjunction • o continuous(!) 3.5 Definitions • o total(!, [firsLpoints---+ second_points]) Theories can be enriched by sort and constant definitions. • o firsLconnected(o) The definitions we need to formulate Theorems 1 and • second_connected(f( o) ). 2 all define predicate constants which denote boolean We present the proof of Theorem 1 as it is actually valued functions. Our definitions of the requisite topological formatted by IMPS using the prescriptive proof presentation 1136 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY --·--····-·--···-············--·~···----········ ························-·······································-···········ueaaaaeeeam.'"IT§:~>~~·--··--··~······-·· ...... ----··-······------···-·············--············~---~-··· Computers and Mathematics routine. In this particular proof, the full deduction graph Sequent3. consists of I 8 sequent nodes. Before presenting the proof, we give the intuitive idea for every f : firsLpoints -+ second_points, o : sets[firsLpoints] implication behind it. The proof begins by expanding all definitions at • conjunction the top level of the expression. In this case, the defined con o Vv: sets[second_points] second_open(v) :J firsLopen(f- 1 (v)) o total(!, [firsLpoints -+ second_points]) stants are the predicates firsu:onnected, second_connected, oVa, b: sets[firsLpoints] (firsLopen(a) 1\ firsLopen(b) II empty?{a n b n and continuous. Since these constants are defined as A o}/\o ~aU b) :J (o~ aVo~ b) expressions (a A-expression is a fancy name for a term of • for every a0 , bo : sets[second_points] implication o second_open(ao) II second..open(bo) II empty?{f-1 (ao) n r 1(bo) no} II o ~ the form "the function which carries x, y, . . . to the expres r 1 (ao) u r 1 (bo) sion blah"), expanding the definitions merely replaces these 0 0 ~ r 1 (ao) v 0 ~ r 1(bo). constants with their defining A-expressions. We next have to apply the rule of ,6-reduction, which essentially plugs in values to the expressions which define the functions. This leaves us with an assertion which contains several Apply the strategy PROVE-BY-LOGIC-AND-SIMPLIFI subexpressions of the form f(a) ~ b. We now apply a CATION to the previous sequent. This completes the proof. user-defined macete which applies repeatedly a number of The formal statement of the Theorem 2 is almost identical generic (and very easy to prove) results on indicators, such as to that of the previous theorem except that "connected" the direct-image-subset-conversion lemma mentioned above. is replaced with "sequentially compact." Moreover, the Application of this macete turns these subexpressions into sequence of user commands required to prove Theorem 2 is subexpressions of the form a ~ f-1(b) and also uses the identical to that of Theorem 1. Of course, the actual TEX preservation properties of J-1. To complete the proof, we form of the proof is different because the goal formula and use an ending strategy. An ending strategy attempts to find all intermediate formulas are different. We omit the details. a proof of a goal sequent by successively applying rules of inference from a fixed list (depending on the strategy) and backtracking when a particular branch fails. Conclusion PROOF. Apply the strategy DEFINITION-EXPANSION to the In this article we presented computer-supported proofs of claim of the theorem. This yields the following new subgoal: two theorems in metric space topology. The theorems were stated within an axiomatic theory of metric space pairs Sequent 1. using familiar topological concepts such as open set and for every f : firsLpoints-+ second_points, o : sets[firsLpoints] implication continuous function which were defined in a very direct and • conjunction natural way. The proofs were constructed within a version o >.{! : firsLpoints -+ second_points IVv : sets[second_points] second..open(v) :J firsLopen(r 1 (v))} (f) of predicate logic with the help of the IMPS theorem proving o total(!, [firsLpoints -+ second_points]) system. Each proof was fully machine-checked and required o .>.{"' : sets[firsLpoints]l Va, b: sets[firsLpoints] (firsLopen(a) 1\ only four commands from the user. firsLopen(b)/\empty?{anbn.,}/1"' ~aU b) :J ("' ~ aV"' ~b)} (o) • .>.{"' : sets[second_points]i for every a, b : sets[second_points] implication The theorems and proofs were developed in the little o second..open(a) 1\ second..open(b) 1\ empty?{a n b n "'} 1\"' ~ aU b theories style of the axiomatic method. This approach o"'~av.,~b} (f(o)). benefited our proofs in two ways. First, both proofs utilized results proved outside of the theory of the proof, specifically results about converting statements involving direct images Apply the inference rule BETA-REDUCTION to the into statements involving inverse images. These results previous sequent. This yields the following new subgoal: were proved in a theory about abstract mappings, and the system determined on its own how and where to apply Sequent2. them. Second, the two theorems can be transported to any theory that contains structures which are metric spaces. for every f : firsLpoints-+ second_points, o : sets[firsLpoints] implication For example, they can be transported to the theory h-o • conjunction real-arithmetic by interpreting the two metric spaces of o Vv: sets[second_points] second_open(v) :J firsLopen(f- 1 (v)) metric-space-pairs as R3 and R2 • o total(!, [firsLpoints -+ second_points]) oVa, b: sets[firsLpoints] (firsLopen(a) 1\ firsLopen(b) 1\ empty?{a n b n The everyday practice of mathematics involves proving o} 1\ o ~aU b) :J (o ~aVo~ b) numerous elementary, but not entirely trivial results, which • for every ao, b0 : sets[second_points] implication are similar in complexity to Theorems 1 and 2. In fact, many o second_open(a0 ) 1\second_open(bo) l\empty?{a0 nb0 n f(o)} 11/(o) ~ ao U bo o f(o) ~ ao V f(o) ~ bo. substantial theorems are proved by just skillfully combining elementary facts. Systems such as IMPS, which can be effectively used to formulate, prove, and apply elementary theorems, thus have the potential to play a significant role in Apply the macete DIRECT-IMAGE-TO-INVERSE-IMAGE mathematics research. Moreover, they offer mathematicians CONVERSION-MACETE to the previous sequent. This yields a new technology for organizing, checking, and reusing their the following new subgoal: work. NOVEMBER 1991, VOLUME 38, NUMBER 9 1137 ------·······-·-······-····---·-··------Computers and Mathematics References or periodic functions as different parameters are varied. Plot [1] W. W. Bledsoe, Some automatic proofs in analysis, in Automated integrates both approaches in a way that is easy for students Theorem Proving: After 25 Years, American Mathematical Society, to learn and use. 1984, pp. 89-118. The program is organized around a sequence of keyboard [2] R. S. Boyer and J. S. Moore, A theorem prover for a computa tional logic, in lOth International Conference on Automated Deduction, activated menus. Many options for exploring an individual M. E. Stickel, ed., vol. 449 of Lecture Notes in Computer Science, graph are available from the Main Menu (see Figure 1). In Springer-Verlag, 1990, pp. 1-15. addition to drawing the graph of a function, the user can [3] S.-C. Chou, An introduction to Wu's method for mechanical the display next to the graph a table of numerical values, locate orem proving in geometry, Journal of Automated Reasoning, 4 (1988), zeros of Cartesian functions, or obtain the coordinates of pp. 237-267. local extreme points. In the menu for the latter option, a [4] W. M. Farmer, A partial functions version of Church's simple search interval restricts the independent variable, but one theory of types, Journal of Symbolic Logic, 55 (1990), pp. 1269-91. [5) --, A simple type theory with partial functions and subtypes. can search for the extreme values of different coordinates. Forthcoming. For Cartesian graphs, this is the coordinate of the dependent [6] W. M. Farmer, J. D. Guttman, and F. J. Thayer, IMPS: an in" variable. For polar graphs of the form r = f(q), one can teractive mathematical proof system, Tech. Rep. M90-19, The MITRE search for extreme values of the radius r, or extreme values Corporation, 1991. for either x or y. With parametric equations, one can search [7] J. D. Guttman, A proposed inteiface logic for verification envi for the extreme values of either x or y. When Extremes is ronments, Tech. Rep. M91-19, The MITRE Corporation, 1991. [8] N. Shankar, ProofChecking Metamathematics, Ph.D.thesis, Uni pressed for the first time, the program finds and displays versity of Texas at Austin, 1986. the coordinates for the first extreme point that it detects [9] C. A. Wick and W. W. McCune, Automated reasoning about ele and displays the graphic cursor at this point on the graph mentary point-set topology, Journal of Automated Reasoning, 5 (1989), (see Figure -2 next page). Pressing any key releases the pp. 239-255. program to find the next extreme point or to quit that menu. When there are extreme points that are too close together for both to be detected in the first pass, pressing Extremes again will break the search interval into more subintervals thereby increasing the likelihood that the extreme points Plot will be separated. You can also manually restrict the search Reviewed by Larry Riddle* interval if you are looking for a particular extreme point. The Intersection command in the Zeros menu works the Plot is primarily a two-dimensional plotter for Cartesian, same way as the Extreme command. Through these two polar, or parametric functions, with additional capabilities menu items students can quickly determine the roots of a for three-dimensional plots, implicit graphs, and differential function or solve max-min problems. equations. It was developed by Richard Parris, a teacher at Phillips Exeter Academy. I have used Plot extensively in precalculus and calculus courses and found it excellent for Main Menu classroom exploration and student use on homework and Y ..,XA3-4X+ 1 laboratory projects. -5.0000 ------·---···------·····----·------1138 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics the screen or sent to the printer. applied to whichever of the windows is currently active. The twelfth lesson maintains that students need ex perience controlling scale: "students need experience with Extreme Points strictly metric controls (e.g. specifying the exact borders Y ·XA3-4X+ 1 of the region of the plane they wish to examine) and -5.0000 NOVEMBER 1991, VOLUME 38, NUMBER 9 1139 Computers and Mathematics library of built-in functions, including a join function for easy dimensional representation is also given. Faces are rotated construction of piecewise defined graphs and an iteration by clicking on the center "square" (really a cube) of the function iter(n,f(x)) for plotting the nth iterate of f. The face and then clicking on an arrow indicating the direction user can also save his or her own specially built library of rotation. of functions on disk. When the program is waiting for r • File Edit Options Eaecute Processes 12:3018 ~ non-menu-specific input, a box will open on the screen to !i!D let the student know that some information must be entered. Numerical input may be entered in non-decimal form, such as sqr(3) or 2pi, for example. It is even possible to add text to the plots. This program has many features and menus, and a student Lower Layer Middle Layer Upper Layer :· will need some guidance on where commands are located. Fortunately, most of the basic graphing operations are found in the opening two menus. The minimal documentation for the program is two ascii files that come on the disk. The files describe all the features but have no table of contents or index. One can, however, view the documentation files ~ from within Plot and search for text strings. Plot is available free of charge by sending a formatted [@] disk and return mailer with postage to Richard Parris, An example of Cube. Phillips Exeter Academy, Exeter, NH 03833. Cube is really just a prelude to Tess (short for Tesseract, Reference another name for a hypercube), which gives the 3 x 3 x 3 x 3 [1] Goldenberg, E. Paul, The difference between graphing sqftware and generalization of the Rubik cube, displayed as three 3 x 3 x 3 educational graphing software, Visualization in Teaching and Learning cubes. Again, clicking on the center "cube" of a "face" (really Mathematics, W. Zimmermann and S. Cunningham, Eds., MAA Notes a hypercube and a cube, respectively), produces three axes #19 (1991), 77....!66. with arrows, so that the corresponding "face" (cube) can be rotated. r • File Edit Options Eaecute Processes 12:28@ ~ ~ hH Cube and Tess Reviewed by Tevian Dray* A square has 4 "faces", each of which is a line. A cube has 6 faces, each of which is a square. A (4-dimensional) hypercube has 8 "faces", each of which is a cube. Divide the square into 9 equal squares and you get a tic-tac-toe board. As we all know, the center square is different from the others, because it shares a "face" (edge) with the most neighbors. A similar division of the cube into 27 equal cubes results in the Rubik cube. Again, different cubes ("cubies") have different properties depending on their location. Divide • a hypercube similarly into 81 equal hypercubes and what do you get? An example of Tess. Cube and Tess are two Macintosh programs (distributed together by Atlantic Software for $39.95) which model the Although the instructions do not discuss the hypercube Rubik cube and its 4-dimensional generalization, the "Rubik itself in any detail, careful thought (draw pictlires!) should hypercube", respectively. I ran them on a Mac SE, but enable the mathematically inclined to determine how the Atlantic Software claims that the programs will run on any given 3-dimensional representation corresponds to the 4- Mac. dimensional "reality". Cube gives the 3 x 3 x 3 Rubik cube in a 2-dimensional The programs come with very good directions, including representation consisting of three 3 x 3 squares. A 3- a section for Mac hackers giving the defaults and how to change them. Both programs use virtually identical *Tevian Dray is an Associate Professor of Mathematics at Oregon State commands. One of the nicest features of the programs is University. He is an expert on the uses of algebraic computing in the field of that one can define (and save) macros, which are called general relativity. His current research involves classifying spacetimes based on their symmetry groups using the symbolic manipulation package SHEEP, Processes. Anyone who has ever played with a Rubik cube which is particularly good at manipulating tensors. will appreciate the desirability of this feature! Other nice 1140 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics features are the abilities to Undo the previous move (but only A minor criticism of both programs is that the Quit one), to Scramble to a random starting configuration, and, command is not self-explanatory: A dialog box appears, of course, to Restore the original configuration. Numerous with "Save state before quitting" checked, with a similar exercises with solutions on disk are provided. box for processes. If you want to simply quit, without saving It is highly recommended that one try Cube first, as this anything, it is necessary to first uncheck these boxes, then provides good practice with the format of the programs and confirm. A yes/no decision would have been both faster and thus prepares one for Tess. more obvious. I am reasonably competent with the (original) Rubik There are precisely n axes in n dimensions parallel to cube-it takes me 5-10 minutes to unscramble a cube. which one can slice an n-dimensional cube into (n I) Nevertheless, my first effort with Cube took well over an dimensional cubes. One such slicing is given originally, hour. The reason for this is that it is not simple to turn and the Reslice command allows you to choose any of the the entire cube around (see previous page), so that I had others. Unfortunately, the action of the Reslice command is difficulty figuring out where I was. However, this merely very hard to visualize, so that it may be hard to predict indicates that the ability to visualize in 3-dimensions is not exactly what the result of a given reslicing will be. However, necessarily helpful when solving a 2-dimensional puzzle! some trial and error should result in the desired reslicing With practice, my time did improve somewhat, although I being achieved. Since it is usually (there is one exception) never did develop a 2-dimensional intuition for what I was necessary to use Reslice if you wish to rotate the entire doing; this was at least partly due to lack of time on my (hyper)cube, this does mean that it is difficult to perform part. a particular rotation quickly. Furthermore, Reslice reverses A minor criticism of Cube is that rotation of the right the orientation of the cube, e.g. the 3-dimensional Reslice and left faces is counterintuitive, as it does not correspond to command performs an operation which is impossible with a the "obvious" rotations of the 3-dimensional cube, but rather Rubik cube. While these are not major drawbacks, it does to their inverses. For instance, having selected the right mean that one's experience with the Rubik cube may or face, clicking on the right portion of the arrow produces may not prove helpful-I at least am constantly turning the a counterclockwise rotation (as seen from the right, which whole Rubik cube around when I work with it. In fact, once is the displayed perspective of the cube) instead of the the I figured out how to write simple macros to rotate the entire expected clockwise rotation. Although there is a detailed cube about any of the three axes (only one of these rotations example given in the instructions, which should be carefully is built into Cube), I made progress much more quickly. The studied, I can find no reason why the opposite convention examples of the Reslice command in the instructions merit couldn't have been chosen, which I believe would merely careful study. correspond to swapping the displayed positions of the upper Overall, I recommend these two programs highly to all and lower layers in the 2-dimensional representation. Mac users who enjoy the Rubik cube, as well as anyone interested in learning more about 4-dimensional geometry. Planning to Apply Geometry to Computer Science~ Vision Geometry Offers You State-of-the-Art. Editors Robert A. Melter, Azriel This timely new book is valuable to 1980 Mathematics Subject Classifications: 51, 68 ISBN 0-8218-5125-X, Rosenfeld, and Prabir Bhattacharya computer scientists who study: 237 pages (softcover), bring you Vision Geometry, volume List price $87, Institutional member $70, • image processing 119 in the American Mathematical Individual member $52. • computer vision To order, please specify CONM/119NA Society series, Contemporary • pattern recognition Mathematics. To order, call800 321-4267 in the continental and mathematicians who study United States and Canada (VISA and MasterCard). Write American Mathematical Society, Post geometry as it is applied to computer Office Box 1571, Annex Station, Providence, science. Rhode Island 02901-1571. All prices subject to change. Prepayment is required. Free shipment Gain new insight into how geom by surface; for air delivery, add $6.50 per title. etry is applied to problems in com Please add 7% GST to all orders being shipped to puter vision today. Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1141 Inside the AMS The AMS Marketing Division documents which will have an even broader appeal than our and the Nineties current list. The Marketing Division and the Publications Group Jeremy Soldevilla are already working very closely in conjunction with the Director ofMarketing production staff to identify new publishing opportunities and Over the last several years, the AMS has been growing at technologies. technologies, a rapid pace. New publications, cutting edge In order to attract more authors and to reach a more di on a global and increasing involvement with mathematicians verse audience, the promotional program is being re~amped. 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It For further information, or for assistance accessing and supports arbitrary document types, revision control and using e-MATH services, send email to: annotation, and grammar-based bi-directional SGML-~ [email protected]. STRUCTURAL PROPERTIES OF POLYLOGARITHMS Mathematical Surveys and Monographs, Volume 37 • '"e • I '" I e About ten years ago, the handful of peculiar numerical dilogarithmic identities, known since the time of Euler and Landen, gave rise to new discoveries concerning cyclotomic equations and related polylogarithmic ladders. These discoveries were made mostly by the methods of classical analysis, with help from machine computation. About the same time, starting with Bloch's studies on the application of the dilogarithm in algebraic K-theory and algebraic geometry, many important discoveries were made in diverse areas. This book seeks to provide a synthesis of these two streams of thought. In addition to an account of ladders and their association with functional equations, the chapters include applications to volume calculations in Lobatchevsky geometry, relations to partition theory, connections with Clausen's function, new functional equations, and applications to K-theory and other branches of abstract algebra. This rapidly-expanding field is brought up to date with two appendices, and the book concludes with an extensive bibliography of recent publications. About two-thirds of the material is accessible to mathematicians and scientists in many areas, while the remainder requires more specialized background in abstract algebra. 1991 Mathematics Subject Classification: 39 All prices subject to change. Free shipment by surface; for air ISBN 0-8218-1634-9, LC 91-18172, ISSN 0076-5376 delivery, please add $6.50 per title. Prepayment required. 419 pages (hardcover), July 1991 Order from American Mathematical Society, P.O. Box 1571, Individual Member $77, List Price $128, Annex Station, Providence, Rl 02901-1571, or call toll free Institutional member $102 800-321-4AMS (321-4267) in the continental U.S. and To order please specify SURV /3 7NA Canada to charge with Visa or MasterCard. Please add 7% GST to all orders being shipped to Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1143 News and Announcements Raviart Receives Prize tion at the National Science Foundation aged those in the mathematical sciences Le Comite du Rayonnement Franc;ais (NSF). In this newly-created position, community who have an interest in ed has awarded its Prix des Sciences Barrett will serve as primary advisor ucation to get in touch with EHR, Physiques et Mathematiques for 1991 to the Assistant Director for Education to inquire about serving as rotators, to Pierre Arnaud Raviart, professor of and Human Resources (EHR), Luther reviewers, or members of reviewing mathematics at l'Ecole Polytechnique. Williams, to provide analysis and coor panels. Professor Raviart was recognized dination of NSF educational programs. Barrett's position also involves co for building an exceptional body of The position is aimed at two goals: ordination and cooperation with other work in numerical analysis. The cita first, to examine the range of NSF Washington organizations that deal with tion for the prize noted that his work educational programs and formulate an education. For example, she has at has been useful to engineers and re overview of what's being done and tended meetings of a Congressional searchers and possesses an aestheti what gaps there might be, and second, committee that's examining standards cally pleasing clarity and simplicity. to act as a facilitator to insure that for educational testing. She will act as His work concerns the theory of finite the various EHR programs complement a liaison with the National Governor's element methods, parabolic problems, and enhance one another. Association, which has been active in and nonlinear hyperbolic equations. Barrett says that one of her first educational matters in the past couple Professor Raviart's influence on the projects will be a report on existing of years. In addition, she will keep discipline has been profound, not only school programs. "There are a lot of abreast of activities at the Department because of his own research but also problems in education, but there are of Education and the National Research because of his mentorship of a group also a lot of answers," she notes. She Council (NRC), particularly the Math of young numerical analysts who have will be analyzing the components of ematical Sciences Education Board and gone on to research centers and indus school programs in mathematics and the NRC's newly-created Coordinating tries in France and around the world. science to determine the ingredients that Council on Education. Le Comite du Rayonnement Fran make them successful. "We need to see Barrett's prior positions include serv c;ais was founded in 1893 and its pur what makes them work, how dependent ing as dean at Mississippi State Univer is to recognize and illuminate the pose they are on a particular setting, whether sity and as associate provost at North achievements of French researchers, they are translatable to other settings." ern Illinois University. She was on the artists, and writers. This committee She will also be looking at net mathematics faculty of the University awards a range of prizes each year in working programs that link teachers, of Tennessee at Knoxville for nineteen various fields of endeavor. Le Prix des schools, and organizations and trying to years, serving as department chair from Sciences Physiques et Mathematiques determine how such programs can be 1973 to 1980. She was president of the of 50,000 FF is awarded each year to an Mathematical Association of America outstanding researcher in mathematics used to disseminate information about during 1989 and 1990. or one of the physical sciences, includ educational projects. Electronic com ing physics, chemistry, earth science, munications will likely play a key role The timing of the creation of her and astronomy. in this area. NSF position is linked with the large The EHR staff now has a substantial increases in funding the education di representation in mathematics. "There rectorate has received from Congress Lida Barrett is as much mathematics as science at over the last few years. Part of the mo Takes NSF Position the school level, so we ought to be tivation of creating this position, Barrett Lida K. Barrett, Dean of the College heavily represented," she remarks. "I says, is to figure out "how to best use of Arts and Sciences at Mississippi would say that half the staff should be the interest and fiscal support com State University, has taken a position in mathematics, but that's me talking ing from Congress." As for grumblings as Senior Advisor on Precollege Educa- as a mathematician!" She also encour- from the NSF research divisions over 1144 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements the increases EHR has received, Barrett Materials Development, Research, posals through the National Science comments that "the research divisions and Informal Science Education Foundation Important Notice 107, is and EHR are working well together, es Joan Leitzel, Division Director sued August 29, 1990. These format pecially in mathematics . . . In the long 202-357-7073 revisions of Important Notice 107 were run, this attention to education will help EHR now has a substantial cadre of fully implemented on January 1, 1991 everyone." mathematicians on its staff. Among the and will be in effect for research pro incoming visiting scientists are Lida posals submitted for the coming fiscal Mathematics Staff in K. Barrett, Dean of the College of year. NSF's Education Directorate Arts and Sciences, Mississippi State Processing of proposals and con The Directorate for Education and Hu University. She will serve in a newly tinuing increments will be significantly man Resources (EHR) of the Na created position of Senior Advisor to delayed if items are missing or in an tional Science Foundation sponsors a the Director of EHR, Luther Williams inappropriate format for review. Two range of programs that support educa (see accompanying news item in this distinct components were implemented tional projects in mathematics, science, section of Notices). on January 1, 1991: and engineering. Listed below are the Other incoming staff this year are 1. All renewal proposals, as part names and telephone numbers of those Geeslin from the University of New of the summary of progress under EHR program officers whose field is Hampshire, Lightbourne from West Vir prior awards, must contain a state in the mathematical sciences or mathe ginia University, Cozzens from North ment about the impact on education matics education. These individuals can eastern University, Enneking from Port and human resource development of provide information about the programs land State University, and Leiva the NSF-supported project; all progress they oversee, as well as information from the University of North Carolina reports on continuing awards must con about other EHR programs of interest Charlotte. tain a similar statement; to mathematicians. The community expresses its thanks 2. For all proposals, the format for Young Scholars Program, for a job well done to outgoing rotators the biographical sketch that accompa Division of Research Career Thomas Berger, who has returned to the nies the proposal has been revised. Development University of Minnesota; John ("Spud") The expectations of the Division of William Geeslin, 202-357-7538 Bradley, who is now associate execu Mathematical Sciences with respect to tive director of AMS and managing these changes were outlined in the Course and Curriculum Program, editor of Notices; Joan Ferrini-Mundy, Dear Colleague letter of December Division of Undergraduate Science, who has returned to the University of 1990. To assist principal investigators Engineering, and Mathematics New Hampshire; Christian Hirsch, who in their proposal preparation, this let Education has returned to Western Michigan Uni ter encloses an abbreviated Checklist James Lightbourne, 202-357-7051 versity; and Glenda Lappan, who has for the Preparation of Disciplinary Re Faculty Enhancement Program, returned to Michigan State University. search Proposals for submission to the Division of Undergraduate Science, Program officers in EHR can be Division of Mathematical Sciences. All Engineering, and Mathematics reached through electronic mail. To principal investigators should examine Education form an individual's address, take the Grants for Research and Education in William Haver, 202-357-7051 first initial and last name, and append Science and Engineering, An Applica Instructional Materials Development @nsf.gov for Internet, or @nsf for tions Guide (NSF90-77, August 1990) Program, Division of Materials Bitnet. For example, to contact William for greater detail on proposal prepara Development, Research, and Geeslin on the Internet, use the address tion. Informal Science Education [email protected]. Sincerely, Margaret Cozzens, 202-357-7066 The mailing address is Directorate Judith S. Sunley, Director Teacher Enhancement Program, for Education and Human Resources, National Science Foundation, 1800 G Division of Mathematical Sciences Division of Teacher Preparation August 1991 and Enhancement Street, NW, Washington, DC 20550. Marjorie Enneking, 202-357-7751 The Checklist to which this letter refers was sent to all mathematical sci Teacher Preparation Program, Open Letter on ences departments in the U.S. Copies Division of Teacher Preparation Proposal Format Changes of the Checklist are also available upon and Enhancement What follows is an excerpt from an request from the Division of Mathe Miriam Leiva, 202-357-7069 open letter sent to mathematical sci ences departments in the U.S. matical Sciences, Room 339, National The EHR administrative staff includes: Science Foundation, 1800 G Street, Office of the Assistant Director for Dear Colleague: NW, Washington, DC 20550. EHR Early in the fall of 1990 you and Those intending to send propos Lida K. Barrett, Senior Advisor on your institution were informed about als to DMS should be aware that the Precollege Education, 202-357-7926 changes in the format of NSF pro- changes in proposal format are quite NOVEMBER 1991, VOLUME 38, NUMBER 9 1145 News and Announcements substantive. In particular, the 1991 (Princeton), John Hubbard (Cornell), It is planned that there be no sched changes require that: Harvey Keynes (Minnesota), Benoit uled talks, apart from an initial intro • proposers provide a list of sug Mandelbrot (IBM and Yale), Albert ductory round of five-minute talks the gested reviewers (and preferred non Marden (Minnesota), John Milnor first day. Rather, the large number of reviewers) for the proposal (otherwise, (Stony Brook), David Mumford (Har Geometry Center desks, workstations the principal investigators will be asked vard), Charles Peskin (Courant), Jean (NeXTs, Sun Spares, Irises and two for such information when the proposal Taylor (Rutgers), William Thurston Macll's), small and large conference is received); (Berkeley), Allan Wilks (AT&T Bell rooms, whiteboards, and video equip • those submitting renewal propos Labs). Albert Marden is Director, Wil ment plus the open layout of the Center als include an education and human liam Thurston is Codirector, Richard will be used to promote one-on-one and resource impact statement and a list McGehee is Science Advisor, and small group interactions. We hope that of graduate students involved in the Harvey Keynes is Education Director. participants will be able to demonstrate project; Full time technical staff are Scott Bertil their programs in action, either on the • proposers limit publication lists son, Charlie Gunn, Silvio Levy, Stu workstations or on videotape, and to to the five publications most relevant art Levy, Tamara Munzner, and Mark discuss issues of modelling, program to the research proposed and up to Phillips. ming, etc. five additional publications; no other The visitor program in research will publication lists should be included involve theoretical and practical issues Visualization of Invariant Sets for in the proposal. With regard to other related to computation and visualiza Symplectic Maps in Dimension 4, biographical information, faculty-level tion. Mathematicians or computer sci March 9-20, 1992. The organizer is investigators must list their own gradu entists interested in organizing small Richard McGehee, University of Min ate and postdoctoral advisors, their co working "teams" to consider particu nesota, mcgehee@ geom.umn.edu. Most authors over the past forty-eight months lar problems concerning the organiza questions about the dynamics of sym and long-time collaborators, and any tion, implementation, or development plectic maps in dimension 4 remain one who might benefit if the proposal of algorithms and software (including unanswered. Even the basic problem of leads to an award. related theory) in mathematics or com determining the stability of an elliptic Proposals that do not meet the for puter science are invited to apply for fixed point is unresolved, a problem mat guidelines will be returned as unac funding. which is rooted in the classic question ceptable. To avoid unnecessary delays, The Center also supports curricu of the stability of the solar system. proposers are urged to carefully follow lum development (including course This workshop will bring together re the new guidelines. ware). Small "teams" focused on par searchers interested in exploring these ticular projects in education are invited questions through computer simulation to apply for funding as well. and visualization. Talks w,ill be limited News from the Elsewhere in this issue please find to two hours per day; most of the time Geometry Center the advertisement for the Center listing will be devoted to informal discussions University of Minnesota available positions. centered around computer simulations This is the first year of the National For the current year, the following of symplectic maps. Science and Technology Research Cen two special programs are being orga Topics will include: (1) The break ter for Computation and Visualization nized. For information about participa down of invariant two-dimensional tori. of Geometri.c Structures. It is funded at tion, please contact the organizer. Com (2) The computation of Arnold's the rate of about $2 million per year by putational Crystal Growers Work "whiskered tori", which, in this case, shop, February 24-29, 1992. The orga the National Science Foundation, De are invariant circles. (3) The computa nizer is Jean Taylor, Rutgers University, partment of Energy, Minnesota Tech tion of stable and unstable manifolds taylot@ geom.umn.edu. Computational nology, Inc., and the University of Min for hyperbolic periodic orbits and for nesota. The Center will support mathe models are playing a central role in the hyperbolic invariant circles. Committed matics and computer science research, analysis of crystal growth, whether the participants include Michael Herman mathematics education and communi approach is from mathematics, materi cation, and software development in als science, or physics. Indeed, compu and Jiirgen Moser. support of research and education. The tational methods have led to theoretical The Geometry Center has a good principal investigators/permanent fac advances and vice versa. The intent of collection of graphics workstations run ulty of the Center are: Fred Alm this workshop is to get together many ning locally developed visualization gren (Princeton), Jim Cannon (Brigham of the people, from each of the three software. There is an ongoing develop Young), Bernard Chazelle (Princeton}, disciplines, that are actively working ment of software specific to the visu John Conway (Princeton), David Dob on various computational models for alization of invariant two-dimensional kin (Princeton), Adrien Douady (Or various types of crystal growth, and manifolds in It'. It is expected that this say), David Epstein (Warwick), Michael thereby to facilitate the exchange of project will stimulate and be stimulated Freedman (UCSD), Pat Hanrahan ideas, algorithms, and results. by the participants of the workshop. 1146 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements News from the solution. Methods that are particularly For more information, contact: SMF Institute for Mathematics efficient on modem computer architec (Prix d'Alembert), ENS, Tour L, 1 rue and Its Applications tures will be emphasized. The meeting Maurice Arnoux, 92120 Montrouge; University of Minnesota is sponsored jointly with the Minnesota telephone (1)40-84-80-54. The 1991-1992 academic year program Supercomputer Institute. The last day of at the IMA is Applied Linear Alge the workshop will be a celebration ded New Upgrades in TeX bra. The Coordinators for this pro icated to Gene Golub on the occasion Software from AMS gram are R.A. Brualdi, G. Cybenko, of his sixtieth birthday. This activity is The AMS has made available new A. George, G. Golub, M.B. Luskin and being arranged by Jack Dongarra and versions of three software products that P. Van Dooren. The Advisory Com Paul van Dooren. utilize the 1}3X typesetting language. mittee is A. Bjorck, T. Kailath, V. The IMA 1992 summer program -4MS-1}3X, -4MS-MJEX, and AMSFonts Klee, J. McKenna, and R. Ward. Fall will be Environmental Studies: Math have all been upgraded to incorporate quarter activities, presently underway, ematical, Computational and Statisti several enhancements. are concentrating on Discrete Matrix cal Analysis, July 6-31. The Orga -4MS-'IEX 2.1 The ..4w5'-1EX macro Analysis with emphasis on the mathe nizing Committee is Mary Wheeler package provides advanced mathemat matical analysis of sparse matrices and (Chair), Julius Chang, Michael Ghil, ics typesetting capabilities, as well as combinatorial structure. David McTigue, John Seinfeld and easy access to an extended set of math The winter quarter Applied Lin Paul Switzer. More details concerning fonts (see AMSFonts below) which ear Algebra program will concentrate the Environmental Studies program and are not typically available with nor on Matrix Computations with special the rest of the Applied Linear Algebra mal 'lEX installations. Version 2.1 fixes emphasis on iterative methods for solv program will appear in future issues of bugs reported in version 2.0, and adds ing systems of linear equations and Notices. a new file, amspptl.tex, that provides computing the eigenvalues of sparse, Important sources for IMA aca backward compatibility with documents possibly structured matrices. demic year and summer programs are written under amsppt.sty version 1. During January 13-17 there will be program proposals and ideas for pro -4MS-IDEX 1.1 The -4MS-MIEX a Workshop Linear Algebra, Markov posals submitted by members of the macro package provides advanced math Chains, and Queueing Models orga research community. If you are inter ematics typesetting capabilities to users nized by John McKenna, Robert J. ested in submitting a proposal for a familiar with the MIEX environment, as Plemmons and G. W. Stewart. Markov future IMA program please contact the well as easy access to the AMSFonts. chains and qt~:eueing models are playing Director, Avner Friedman. Also provided are two documentstyles an increasing role in the understanding Fpr more information about IMA (amsart and amsbook), which are based of complex systems such as computer, activities, see the Meetings and Con on the standard MIEX article and book communication, and transportation sys ferences section of this issue or contact styles, but with AMS specifications. tems. Three areas are important in the the IMA at the University of Minnesota, Version 1.1 fixes bugs reported in ver construction and numerical solution of 514 Vincent Hall, 206 Church St., sion 1.0. these problems: linear algebra, Markov S.E., Minneapolis, MN 55455-0436; AMSFonts 2.1 The AMSFonts font chains, and queueing network models. 612-624-6066; Fax: 612-626-7370; or set is a collection of fonts suitable The object of this workshop is to bring [email protected]. for use with 1}3X and any output de together experts from these three areas vice. Fonts provided include Cyrillic, to share their different points of view Euler (including German (Frak.tur)), ex of the subject. Call for Nominations tra math symbols, and additional point The workshop Iterative Methods for d'Alembert Prize sizes of some Computer Modem math for Sparse and Structured Problems Every two years, the Societe Mathema fonts. Version 2.1 has several enhance organized by Gene Golub, Anne Green tique de France awards the Prix d' Alem ments. One of these is an improvement baum, and Mitchell Luskin, will be held bert for a popularization of mathematics in the bold Euler fonts that makes them February 24-March 1. Large systems aimed at the general public. The prize darker and more extended and there of matrix equations arise frequently in may be for an article, book, television fore more easily distinguishable from applications and they have the property or radio broadcast, film, or other project the regular, non-bold fonts. Version 2.1 that they are sparse and/or structured. that promotes increased understanding also fixes many bugs reported in ver Important applications await techniques of mathematics and recent mathemati sion 2.0, and, because of the nature for solving large nonsymmetric sys cal developments. of these bug fixes, users are strongly tems of linear equations and eigenvalue Only French-language works are encouraged to upgrade to version 2.1. problems. The purpose of this work eligible for the prize. Nominations may There are two ways to obtain the shop is to bring together researchers be made by the candidates themselves new versions of these software prod in numerical analysis and various ap or by others and must be received ucts. For many users, the easiest way plication areas to discuss where such by December 31, 1991. The prize of is by anonymous FTP from the Soci problems arise and possible methods of 15,000FF will be awarded in May 1992. ety's Internet node e-MATH.ams.com NOVEMBER 1991, VOLUME 38, NUMBER 9 1147 News and Announcements (130.44.1.100). In addition to the three For those who do not have FTP price of $13; AMSFonts is $251ist, $22 software packages, Metafont sources access, the software can be obtained on for members. In addition, until April for all AMSFonts and guidelines for Macintosh or ffiM high-density 5.25 1, 1992, present users of AA4S' -'lEX, preparing electronic manuscripts in inch diskettes (special orders for 3.5 AA45'-rn}3X, and AMSFonts can obtain AA45'-1EX and in AA45'-rnBX are also inch or low-density diskettes will also free upgrades on diskette; there is a on e-MATH. For assistance on how be accepted). The Metafont sources shipping and handling charge of $8 per to transfer files from e-MATH using are also available on diskette. The request. For more information, contact FTP, see your local support personnel prices for the software on diskettes have Customer Services, American Mathe or send electronic mail to support@ been substantially reduced: AA45'-1EX, matical Society, P.O. Box 6248, Provi e-math.ams.com. AA45'-rn}3X, and Metafont sources now dence, RI 02940-6248; or call toll-free have a list price of $15 and a member 1-800-321-4AMS (321-4267). What Do You Know About China•s Contribution to Probability Theory~ Probability Theory and its Applications in China, edited by Yan Shi-Jian, Yang Chung-Chun, and Wang Jia Gang, offers you the answer. With Probability Theory and its Applications in China, a new 1991 title in the series Comtemporary Mathematics, you will benefit with the latest news on these 18 topics: 1. stochastic analysis 9. interacting particle systems 15. strong approximations 2. stochastic differential equations 10. entropy production of Markov processes 16. large deviations 3. Dirichlet forms 11. renewal sequences and p-functions 17. stochastic control systems 4. Brownian motion and diffusion 12. multi-parameter stochastic processes 18. probability problems in information theory 5. potential theory 13. stationary random fields 14. limit theorems 6. geometry of manifolds 7. semi-martingales 2 ways to order 8. jump Markov processes 1. Call 800 321-4267 in the continental United States and Canada (VISA and MasterCard). 2. Write: American Mathematical Society, Post Office Box 1571, 1980 Mathematics Sub;ect Classifications· 60 82 62 93 94 58 .... ~~. Annex Station, Providence, Rhode Island 02901-1571 J • ' ' ' ' ' '~r'!.}. .1..(0 53, 31, 35, ISBN 0-8218-5126-8, 352 pages (softcover), &• ••••o•••. :1<"' All prices subject to change. Prepayment is required. Free Individual member $28, Institutional member $37, List price $46. ij ~ S ~ shipment by surface; for air delivery, add $6.50 per title. Please To order, please specify CONM/118NA ~ • • ~ add 7% GST to all orders being shipped to Canada. •. \':~~;§§§w... 0liNDEt> \~ AMERICAN MATHEMATICAL SOCIETY ·---·--·------·--- 1148 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information for the Mathematical Sciences NSF Revamps PYI Program engineering, to enhance the academic hers. The Fellows will use the awards The National Science Foundation (NSF) careers of recent doctorates by provid to undertake self-designed, innovative has established two new programs for ing flexible support for research and research and teaching projects, to es young researchers: NSF Young Inves teaching, and to foster contact and tablish research and teaching programs, tigators (NYI) and Presidential Faculty cooperation between academia and in and to pursue other activities appropri Fellows (PFF). Together, these two ac dustry. Approximately 150 new NYI ate for outstanding faculty. tivities replace the Presidential Young awards will be made in this year's The awards will carry a grant from Investigator Program (PYI) that oper competition. Because these awards are NSF of $100,000 per year for five years, ated from 1984 to 1991. intended to develop teaching as well as subject to availability of funds. Thirty NYI and PFF will operate inde research, NYI awardees are expected to awards are planned, of which fifteen pendently, will have separate submis maintain standard teaching responsibil will be in engineering and fifteen in sion deadlines, and will require sep ities. science. Nominations must be submit arate nominations. The PFF awards Only department chairs or analo ted by the president or chief academic will be made first, and successful gous administrative officials may nom officer of the nominating institution. nominees who have also been nom inate faculty members for the NYI For further information, contact inated for the NYI competition will awards. Each award will be for up to Mary F. Sladek, Program Manager, have their nominations administratively five years and will consist of an an PFF/NYI Programs, National Science withdrawn from the latter. nual base grant of $25,000 from NSF Foundation, 1800 G Street, NW, Wash (At the time of this writing, the pro plus up to $37,500 of additional funds ington, DC 20550; telephone 202-357- gram announcements for the NYI and per year on a dollar-for-dollar matching 7536. Email requests for the pro PFF programs were not in final form. basis frem industrial and not-for-profit gram announcement may be sent to Those interested in these programs are sources, resulting in total annual sup [email protected] (Internet) or pubs@nsf urged to consult the Federal Register or port of up to $100,000. (Bitnet); request publication NSF91- obtain a program announcement from Presidential Faculty Fellows. These 112 for the NYI announcement and the address listed below.) awards will recognize and support the NSF91-1 03 for the PFF announcement NSF Young Investigators. The NYI scholarly activities of outstanding young It will be mailed out within two days awards are intended to recognize out science and engineering faculty mem- of the receipt of the request. standing young faculty in science and NOVEMBER 1991, VOLUME 38, NUMBER 9 1149 1992 AMS Elections Nominations by Petition Vice-President or Member-at-Large The new members will be elected in a preferential ballot. One position of vice-president and member of the Council The President will name at least six candidates for these ex officio for a term of two years is to be filled in the three places, among whom may be candidates nominated by election of 1992. The Council intends to nominate at least petition in the manner described in the rules and procedures. two candidates, among whom may be candidates nominated The candidate's assent and petitions bearing at least 100 by petition as described in the rules and procedures. valid signatures are required for a name to be placed on Five positions of member-at-large of the Council for a the ballot. In addition, several other rules and operational term of three years are to be filled in the same election. considerations, described below, should be followed. The Council intends to nominate at least ten candidates, among whom may be candidates nominated by petition in the manner described in the rules and procedures. Rules and Procedures Petitions are presented to the Council, which, according Use separate copies of the form for each candidate for vice to Section 2 of Article VII of the bylaws, makes the president, member-at-large, or member of the Nominating and nominations. The Council of 23 January 1979 stated the Editorial Boards Committees. intent of the Council of nominating all persons on whose 1. To be considered, petitions must be addressed to Robert M. Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island behalf there were valid petitions. 02940, and must arrive by 28 February 1992. Prior to presentation to the Council, petitions in support 2. The name of the candidate must be given as it appears of a candidate for the position of vice-president or of in the Combined Membership List. If the name does not appear member-at-large of the Council must have at least 50 valid in the list, as in the. case of a new member or by error, it must signatures and must conform to several rules and operational be as it appears in the mailing lists, for example on the mailing considerations, which are described below. label of the Notices. If the name does not identify the candidate uniquely, append the member code, which may be obtained from the candidate's mailing label or the Providence office. 3. The petition for a single candidate may consist of several Editorial Boards Committee sheets each bearing the statement of the petition, including the Two places on the Editorial Boards Committee will be filled name of the position, and signatures. The name of the candidate by election. There will be four continuing members of the must be exactly the same on all sheets. Editorial Boards Committee. 4. On the next page is a sample form for petitions. Copies The new members will be elected in a preferential ballot. may be obtained from the Secretary; however, petitioners may The President will name at least four candidates for these make and use photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that of the member two places, among whom may be candidates nominated by whose name and address is given in the left-hand column. petition in the manner described in the rules and procedures. 6. The signature may be in the style chosen by the signer. The candidate's assent and petitions bearing at least 100 However, the printed name and address will be checked against valid signatures are required for a name to be placed on the Combined Membership List and the mailing lists. No attempt the ballot. In addition, several other rules and operational will be made to match variants of names with the form of name in considerations, described below, should be followed. the CML. A name neither in the CML nor on the mailing lists is not that of a member. (Example: The name Robert M. Fossum is that of a member. The name R. Fossum appears not to be.) 7. When a petition meeting these various requirements ap Nominating Committee pears, the Secretary will ask the candidate whether he is willing Three places on the Nominating Committee will be filled to have his name on the ballot. Petitioners can facilitate the by election. There will be six continuing members of the procedure by accompanying the petitions with a signed statement Nominating Committee. from the candidate giving his consent. 1150 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY NOMINATION PETITION FOR 1992 ELECTION The undersigned members of the American Mathematical Society propose the name of as a candidate for the position of (check one): D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 1993. Name and Address (printed or typed) Signature Signature Signature Signature Signature Signature NOVEMBER 1991, VOLUME 38, NUMBER 9 1151 CALL FOR SUGGESTIONS There will be a number of contested seats in the 1992 AMS elections. Your suggestions are wanted by THE NOMINATING COMMITTEE for vice-president, trustee, and five members-at-large of the council and by THE PRESIDENT for three Nominating Committee members and two Editorial Boards Committee members In Addition THE EDITORIAL BOARDS COMMITTEE requests suggestions for appointments to various editorial boards of Society publications. Send your suggestions for any of the above to: Robert M. Fossum, Secretary American Mathematical Society Department of Mathematics University of Illinois 1409 West Green Street Urbana, IL 61801 Joint Mathematics Meetings January 8-11, 1992 Supplement to Announcement in October Notices Please refer to the Preliminary Announcement for this There are many choices, depending on the view one takes meeting which begins on page 951 of the October 1991 issue of the proper mix of the Society's activities between its of Notices. The Important Deadlines from the preliminary various missions, e.g., serving research; education; and announcement are reproduced below for convenience. The public information. There are also many challenges in forms for Preregistration/Housing, MAA Minicourses, and creating lasting partnerships with different players in the the Employment Register are located at the back of this mathematics enterprise, and to bring these partnerships to issue. bear on creative solutions that will benefit the nation's youth. The panel discussion will center around a discussion of these AMS Invited Adresses issues, with adequate time for questions from the audience. The first two Colloquium Lectures by Robert P. Langlands It is hoped that an active dialogue will result. are titled Automorphic forms and Hasse-Weil zeta junctions, and the third lecture is titled Finite models for percolation. Other AMS Events The title of William Browder's Retiring Presidential There will be a reception in honor of reviewers (past and Address is In search of symmetry. present) for Mathematical Reviews (MR) on Friday, January 10, 6:00 p.m. to 7:00 p.m. All reviewers are encouraged By invitation of the AMS Program Committee for to come to the reception, and others who are interested National Meetings there will by an additional invited address in MR are also invited. Members of the MR Editorial by I. Gelfand, Rutgers University. Committee and MR editorial staff will be present to discuss MR's editorial policies and other items of interest (and Other AMS Sessions amusement) to reviewers and users of MR. Refreshments Committee on Education Panel: In the last few years there will be provided. has been a growing awareness that serious effort is needed from the mathematics community in seeking solutions to MAA Invited Addresses the crisis in mathematics education which confronts the The Invited Address by David H. Carlson is titled Teaching nation. What role should the AMS play in these efforts? linear algebra; must the fog always roll in? The Invited Address by James W. Demmel is titled IMPORTANT DEADLINES Linear algebra, geometry, and supercomputing. AMS Abstracts For Consideration for Special Sessions Expired MAA Minicourses Of Contributed Papers Expired The times for Minicourse #7, Using NETPAD software to MAA Abstracts teach and learn about graphs have been changed. Part A has Of Contributed Papers Expired been moved from Thursday morning to Thursday evening, EARLY Preregistration and Housing Expired ORDINARY Preregistration/Housing/Tickets November18 7:00 p.m. to 9:00 p.m., and Part B from Saturday morning Employment Register to Saturday afternoon, 1:00 p.m. to 3:00p.m. (Applicants & Employers) November 18 MAA Minicourse Preregistration November18 Other MAA Sessions Motions for AMS Business Meeting DecemberS Hotel Changes and Cancellations The Student Workshop on Environmental mathematics is with Service Bureau December 10 being organized by B. A. Fusaro, Salisbury State University. FINAL Preregistration (no housing or tickets) December 10 Cancellations for all Banquets (50% refund) December30 Other MAA Events Preregistration Cancellations (50% refund) January 3 The Reception for Elementary School Teachers has been Employment Register Cancellations (50% refund) January3 cancelled. NOVEMBER 1991, VOLUME 38, NUMBER 9 1153 Meetings The display of John von Neumann memorabilia and The National Association of Mathematicians' session on photographs from the Vonneuman family has been canceled. Presentations by recent doctoral recipients has been moved from Friday morning to Saturday afternoon, 1:00 p.m. to AMS-MAA Events 3:00p.m. Social for First-time Attendees: The correct spelling of The NAM panel discussion on Friday morning, The fate the name of the Chairman of the MAA Committee on of minority mathematics students, is now cosponsored by Membership is Susan Forman. MAA. Activities of Other Organizations Social Events The Association for Women in Mathematics Emmy Noether Ramesh A. Gangolli, University of Washington, Seattle, Lecture given by Nancy Kopell is titled Oscillators and will be the featured speaker at the Banquet to Honor 25-year networks of them: which differences make a difference?. Members of the AMS on Saturday evening. The title of The AWM panel discussion on graduate education will his talk is Mathematics education: challenge or temptation?; be moderated by Carol Wood, Wesleyan University. The AMS in the garden of delights. The Board on Mathematical Sciences' panel discussion, The menu for the NAM luncheon on Friday includes Educating mathematicians, is now cosponsored by the AMS. soup du jour, grilled flank steak with sherry sauce, potato, It has been moved from Wednesday morning to Friday vegetable, rolls and butter, and double chocolate mousse. afternoon, 2:00 p.m. to 3:30 p.m. Tickets are $22 each; the price includes tax and gratuity. Joint Meeting with the London Mathematical Society Preliminary information Cambridge, England, June 29-July 1, 1992 The two Societies are very gratified by the interest that has the scientific program, will appear in the January 1992 been shown in the Joint Meetings to be held in Cambridge, Notices. It will specify preregistration by 1 May 1, 1992. England, from Monday, June 29, to Wednesday, July l, All participants must preregister in advance of the meeting. 1992. It seems possible that more people will wish to Intending participants are urged to preregister at the earliest attend the meeting than had been originally expected. Whilst opportunity. If the number of preregistrations approaches the this is welcomed, it might cause problems in Cambridge greatest number that the Local Organizing Committee feels both with housing and with lecture room accommodation. can be accommodated in Cambridge, then the two Soceities The first announcement of the meeting, with details of might have to consider closing preregistration. 1154 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1992 Summer Seminar in Applied Mathematics Exploiting Symmetry in Applied and Numerical Analysis Colorado State University, July 26-August 1 The twenty-second AMS-SIAM Summer Seminar in Applied of Minnesota; and the local organizers Eugene L. Allgo Mathematics will be held July 26-August 1, 1992, at wer (Co-chairman), Kurt Georg (Co-chairman), and Rick Colorado State University, Fort Collins, Colorado. The Miranda (Co-chairman), Colorado State University. seminar will be sponsored by the American Mathematical Those interested in attending the Seminar should send Society, the Society for Industrial and Applied Mathematics the following information to Donna Salter, Conference Co and the Department of Mathematics at Colorado State ordinator, American Mathematical Society, P.O. Box 6887, University. It is anticipated that it will be supported by grants Providence, R.I. 02940, email: [email protected], from federal agencies. The proceedings of the seminar will before May 6, 1992. Please type or print the following: be published by the American Mathematical Society in the Lectures in Applied Mathematics series. 1. Full name; The aim of the conference is to provide a wide 2. Mailing address; ranging survey of the exploitation of symmetry in applied 3. Telephone number and area code for office and home; and numerical analysis. The seminar will have both an 4. email address if available; entry level summer school component intended for young 5. Anticipated arrival and departure dates; researchers and a frontier level research aspect. A number 6. Your scientific background relevant to the topic of the of the anticipated participants will be experts from foreign seminar; countries. 7. Financial assistance requested (please estimate cost A purpose of the seminar is to stimulate interaction be of travel), indicate if support is not required, and if tween aspects of Applied Mathematics (e.g., PDE's, integral interested in attending even if support is not offered. equations, bifurcation), Numerical Mathematics (e.g., numer ical linear algebra, boundary and finite element methods), Participants who wish to apply for a grant-in-aid should Pure Mathematics (e.g., representation theory of groups), so indicate; however, funds available for the seminar are very and Classical Physics (e.g., Taylor and Benard problems). limited and individuals who can obtain support from other The Organizing Committee consists of Martin Gol sources should do so. Graduate students who have completed ubitsky, Univerity of Houston; Klaus W. Kirchgassner, at least one year of graduate school are encouraged to University of Stuttgart, Germany; Peter J. Olver, University participate. QUANTUM LINEAR GROUPS Brian J. Parshall and Jian-pan Wang • Memoirs of the AMS, Volume 439 This volume begins with a general discussion of the theory of quantum groups. The authors view the theory as a natural extension of the theory of affme group schemes. They establish a number of foundational results, including the theory of induced representations and spectral sequences for quantum group cohomology. They then apply these results to give a detailed study of the quantum general linear group and its representation theory. Some of the central topics included are a development of quantum determinants, Frobenius kernels and their representation theory, high weight theory, and the generalization of various important theorems concerning the cohomology of vector bundles on the flag manifold. Finally, the authors use the theory to give a treatment of q-Schur algebras, proving, for example, that q-Schur algebras are quasi-hereditary. 1980 Mathematics Subject Classifications: 20, 14 All prices subject to change. Free shipment by ISBN 0-8218-2501-1, LC 90-19310, surface; for air delivery, please add $6.50 per title. ISSN 0065-9266 Prepayment required. Order from American Math 168 pages (softcover), January 1991 ematical Society, P.O. Box 1571, Annex Station, Individual Member $14, List Price $23, Providence, RI 02901-1571, or call toll free 800-321- Institutional Member $18 4AMS (321-4267) in the continental U.S. and Canada To order please specify MEM0/439NA to charge with Visa or MasterCard. Please add 7% GST to all orders bei!li _shipped to Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1155 Joint Summer Research Conferences in the Mathematical Sciences Mount Holyoke College, South Hadley, Massachusetts, June 13 to July 24, 1992 The 1992 Joint Summer Research Conferences in the Math Please type or print the following: ematical Sciences will be held at Mount Holyoke College, 1. Title and dates of conference desired South Hadley, Massachusetts, from June 13 to July 24. It is 2. Full name anticipated that the series of conferences will be supported 3. Mailing address by grants from the National Science Foundation and other 4. Telephone number and area code for office, home and agencies. electronic-mail addresses, FAX number There will be nine conferences in nine different areas 5. A short paragraph describing your scientific back of mathematics. The topics and organizers for the confer ground relevant to the topic of the conference ences were selected by the AMS, Institute of Mathematical 6. Financial assistance requested; please estimate cost of Statistics (IMS), and -the Society for Industrial and Applied travel Mathematics (SIAM) Committee on Joint Summer Research 7. Indicate if support is not required and if interested .in Conferences in the Mathematical Sciences. The selections attending even if support is not offered. were based on suggestions made by the members of the The deadline for receipt of requests for information is committee and individuals submitting proposals. The com March 2, 1992. Requests to attend will be forwarded to the mittee considered it important that the conferences represent Organizing Committee for each conference for consideration diverse areas of mathematical activity, with emphasis on after the deadline of March 2. All applicants will receive areas currently especially active, and paid careful attention a formal invitation, Brochure of Information, notification to subjects in which there is important interdisciplinary of financial assistance, and a tentative scientific program activity at present. (if the Chairman has prepared one in advance; otherwise The conferences emulate the scientific structure of those programs will be distributed at registration) from the AMS held throughout the year at Oberwolfach. These conferences by April 15. Funds available for these conferences are are intended to complement the Society's program of annual limited and individuals who can obtain support from other Summer Institutes and Summer Seminars, which have a sources should do so. The allocation of grant funds is larger attendance and are substantially broader in scope. The administered by the AMS office, and the logistical planning conferences are research conferences and are not intended for the conferences is also done by the AMS. However, to provide an entree to a field in which a participant has not it is the responsibility of the Chairman of the Organizing already worked. Committee of each conference to determine the amount of It is expected that funding will be available for a limited support participants will be awarded. This decision is not number of participants in each conference. Others, in addition made by the AMS. Women and members of minority groups to those funded, will be welcome, within the limitations of are encouraged to apply and participate in these conferences. the facilities of the campus. In the spring, a brochure of Any questions concerning the scientific portion of the information will be mailed to all who are requesting to attend conference should be directed to the chair or any member the conferences. The brochure will include information on of the Organizing Committee. room and board rates, the residence and dining hall facilities, The Joint Summer Research Conferences in the Mathe travel, local information, and a Residence Housing Form to matical Sciences are under the direction of the AMS-IMS use to request on-campus accommodations. Information on SIAM Committee on Joint Summer Research Conferences off-campus housing will also be included in the brochure. in the Mathematical Sciences. The following committee Participants will be responsible for making their own housing members chose the topics for the 1992 conferences: John A. and travel arrangements. Each participant will be required Bums, Fan R. K. Chung, Leonard Evens, Martin Golubit to pay nominal registration and social fees. sky, Anthony W. Knapp, Peter W. K. Li, Emanuel Parzen, Those interested in attending one of the conferences Stewart B. Priddy, Michael Shub and Gregg J. Zuckerman. should send the following information to the Summer Research Conference Coordinator, Meetings Department, N.B. Lectures begin on Sunday morning and run American Mathematical Society, Post Office Box 6887, Prov through Thursday. Check-in for housing begins on idence, RI 02940 or by email: [email protected] on Saturday. No lectures are held on Saturday. the Internet. 1156 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences Saturday, June 13 to Friday, June 19 Saturday, July 4 to Friday, July 10 Conformal field theory, topological field theory, and quan Commutative algebra: Syzygies, multiplicities and tum groups birational algebra MosHE FLATO (University de Dijon), Co-Chair WILLIAM HEINZER (Purdue University), Co-Chair JAMES LEPOWSKY (Rutgers University), Co-Chair CRAIG HUNEKE (Purdue University), Co-Chair PAUL SALLY (University of Chicago), Co-Chair JUDITH D. SALLY (Northwestern University), Co-Chair Saturday, June 20 to Friday, June 26 Cohomology, representations and actions offinite groups Saturday, July 11 to Friday, July 17 JON F. CARLSON (University of Georgia), Chair Change-point problems Saturday, June 20 to Friday, June 26 EDWARD CARLSTEIN (University of North Carolina), Co-Chair Nielsen theory and dynamical systems HANS-GEORG MULLER (University of California, Davis), CHRISTOPHER McCORD (University of Cincinnati), Co-Chair Chair DAVID SIEGMUND (Stanford University), Co-Chair Saturday, June 27 to Friday, July 3 The Penrose transform and analytic cohomology Saturday, July 11 to Friday, July 17 in representation theory Control and identification ofpartial differential equations ROBERT J. BASTON (Oxford University, England) Co-Chair H. T. BANKS (University of Southern California), MICHAEL G. EASTWOOD (Adelaide University, Australia) Co-Chair Co-Chair K. ITo (University of Southern California), Co-Chair Saturday, June 27 to Friday, July 3 Saturday, July 18 to Friday, July 24 Wavelets and applications CHARLES K. CHUI (Texas A & M University), Co-Chair Adaptive designs STEPHAN MALLAT (Courant Institute of Mathematical STEVE DURHAM (University of South Carolina), Co-chair Sciences, New York University), Co-Chair NANCY FLOURNOY (The American University), Co-chair Many-particle Hamiltonians: r-= ~ "\ g9"\ -----,_ Spectra and Scattering NE.\N fO Advances in SOVIET edited by R. A. Minlos MATHEMATICS This collection of papers deals with several different topics related to the construction and spectral analysis of Hamiltonians of various systems arising in mathematical physics. Volume 5 You will benefit from these topics: • Disposition and character of resonances for certain operators • Perturbation of Hamiltonians in fermion systems Many-particle Hamiltonians: • Construction of the Hamiltonian for three different pointwise Spectra and Scattering interacting quantum particles R. A Minlos • Lower branches of the Hamiltonian of the lattice model for chromodynamics Editor • Problems related to the spectrum of finite-particle lattice Hamiltonians. Contributors: J. I. Abdullaev, S. N. Lakaev, D. Botvich, V. A. Malyshev, A. M. Melnikov, R. A. Milnos, E. A. Zhizhina, A. I. Mogil'ner 1991 Mathematics Subject Classifications: 47, 82, 81; 34 ISBN 0-8218-4104-1, 194 pages, September 1991, Ust price $75, Institutional member $60, Individual member $45 To order, please specify ADVSOV/SNA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. American Mathematical Society Prepayment required. Order from American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Please add 7% GST to all orders being shipped to Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1157 Invited Addresses and Special Sessions Invited Addresses Organizers and Topics at AMS Meetings 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 som~ meetings, the list of speakers is incomplete. this issue of Notices went to the printer. The section below entitled Information for Organizers describes the timetable for announcing the existence of Special Sessions. Baltimore, MD, January 1992 Please refer to the first announcement beginning on page 951 in the October Notices, as well as updated information January 1992 Meeting in Baltimore, Maryland on this meeting elsewhere in this issue. Associate Secretary: Lance W. Small Deadline for organizers: Expired Deadline for consideration: Expired Springfield, MO, March 1992 Please refer to the first announcement beginning on page 951 in the October Notices, as well as updated information Alexander Eremenko Peter J. Olver elsewhere in this issue. Julia Knight Ernst A. Rub March 1992 Meeting in Tuscaloosa, Alabama Tuscaloosa, AL, March 1992 Southeastern Section Associate Secretary: Joseph A. Cima Jane M. Hawkins Serge Ochanine Deadline for organizers: Expired Charles A. Micchelli Peter M. Winkler Deadline for consideration: December 12, 1991 Richard C. Brown, Spectral theory of ordinary and partial differential operators Bethlehem, PA, April1992 Jon M. Corson, Martyn Russell Dixon, Martin J. Evans and Jean-Luc Brylinski Edward Y. Miller Frank Roehl, Infinite groups and group rings Ingrid Daubechies Douglas C. Ravenel Dwight A. Duffus and Peter M. Winkler, Combinatorial problems on partially ordered sets Cambridge, England, June 1992 Jane M. Hawkins, Karma Kajani, Karl Petersen and Mate (Joint meeting with the London Mathematical Society) Wierdl, Theory and dynamical systems Alan Hopenwasser and Cecelia Laurie, Operator algebras John M. Ball Nigel J. Hitchin Vo Thanh Liem and Bruce S. Trace, Geometric topology Lawrence Craig Evans Edward Witten Kai-Ching Lin, Harmonic analysis and related topics Benedict H. Gross Charles A. Micchelli and R. A. Zalik, Approximation theory: modern methods Dayton, OH, October 1992 Martin Golubitsky Louis H. Kauffman March 1992 Meeting in Springfield, Missouri Jonathan I. Hall J. T. Stafford Central Section Associate Secretary: Andy R. Magid Deadline for organizers: Expired Invited addresses at Sectional Meetings are selected by Deadline for consideration: December 12, 1991 the Section Program Committee, usually twelve to eighteen Nakhle Habib Asmar and Stephen John Montgomery-Smith, months in advance of a meeting. Members wishing to nomi Harmonic analysis nate candidates for invited addresses should send the relevant Margaret M. Bayer, Combinatorics and discrete geometry information to the Associate Secretary for the Section who Wenxiang Chen and Shou Chuan Hu, Partial differential will forward it to the Section Program Committee. equations 1158 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ····---~~~--111!111-7 ------~~·~~· ...... --··-~·········--·-····~-···-~--·····--····-·-······----···-··--····-- Invited Addresses and Special Sessions William J. Heinzer, Craig Hunecke and Kishor M. Shah, March 1993 Meeting in Knoxville, Tennessee Commutative algebra Southeastern Section Luis Hernandez and Ernst A. Ruh, The geometry of connec Associate Secretary: Joseph A. Cima Deadline for organizers: June 26, 1992 tions Deadline for consideration: To be announced Jerry A. Johnson and Benny D. Evans, Microcomputers in the upper division and graduate curriculum April1993 Meeting in Salt Lake City, Utah Niky Karnran and Peter J. Olver, Lie algebras, cohomology, Western Section and new applications to quantum mechanics Associate Secretary: Lance W. Small Deadline for organizers: July 9, 1992 Ellen Maycock Parker, C*- algebras and algebraic topology Deadline for consideration: To be announced Boris M. Schein, Semigroups Vera B. Stanojevic, Fourier analysis May 1993 Meeting in DeKalb, Illinois Xingping Sun and Xiang Min Yu, Approximation theory Central Section David Wright, Automorphisms of affines spaces Associate Secretary: Andy R. Magid Deadline for organizers: August 21, 1992 Deadline for consideration: To be announced April1992 Meeting in Bethlehem, Pennsylvania Eastern Section Associate Secretary: W. Wistar Comfort August 1993 Meeting in Vancouver, Deadline for organizers: Expired British Columbia, Canada Deadline for consideration: January 2, 1992 Associate Secretary: Lance W. Small Edward F. Assmus, Jr. and Jennifer D. Key, Finite geometry Deadline for organizers: November 11, 1992 Grahame Bennett, JeffreyS. Connor and Andrew K. Snyder, Deadline for consideration: To be announced Sequence spaces October 1993 Meeting in College Station, Texas Jean-Luc Brylinski and Dennis A. McLaughlin, Character- Central Section istic classes, algebraic K-theory and field theory Associate Secretary: Andy R. Magid Donald M. Davis and Douglas C. Ravenel, Homotopy theory Deadline for organizers: January 22, 1993 David L. Johnson and Penny D. Smith, Geometric analysis Deadline for consideration: To be announced Xiao-Song Lin, Tavan T. Trent, James Li-Ming Wang and Zhijian Wu, New invariants of links and 3-manifolds January 1994 Meeting in Cincinnati, Ohio Associate Secretary: Joseph A. Cima Lee J. Stanley, Set theory Deadline for organizers: April 5, 1993 Joseph E. Yukich, Stochastic processes Deadline for consideration: To be announced June 1992 Meeting in Cambridge, England March 1994 Meeting in Lexington, Kentucky (Joint Meeting with the London Mathematical Society) Southeastern Section Associate Secretary: Robert M. Fossum Associate Secretary: Joseph A. Cima Deadline for organizers: Expired Deadline Deadline for organizers: June 18, 1992 for consideration: February 7, 1992 Deadline for consideration: To be announced Bela Bollobas and Ronald L. Graham, Probabilistic combi- natorics March 1994 Meeting in Manhattan, Kansas John Coates, Number theory Central Section _ Richard D. James, The microstructure of crystals Associate Secretary: Andy R. Magid Deadline for organizers: June 25, 1993 W. B. Raymond Lickorish, Geometric topology in low Deadline for consideration: To be announced dimensions William M. Kantor and Jan Saxl, To be announced January 1995 Meeting in Denver, Colorado Associate Secretary: Andy R. Magid October 1992 Meeting in Dayton, Ohio Deadline for organizers: April 20, 1994 Central Section Deadline for consideration: To be announced Associate Secretary: Andy R. Magid Deadline for organizers: January 30, 1992 Deadline for consideration: July 13, 1992 March 1995 Meeting in Chicago, Illinoin Central Section Joanne M. Dombrowski and Richard Mercer, Operator Associate Secretary: Andy R. Magid theory and operator algebras Deadline for organizers: June 24, 1994 Anthony B. Evans and Terry A. McKee, Combinatorics and Deadline for consideration: To be announced graph theory Louis H. Kauffman, Knots and topological quantum field January 1996 Meeting in Orlando, Florida theory Associate Secretary: Lance W. Small Deadline for organizers: April 12, 1995 Deadline for consideration: To be announced January 1993 Meeting in San Antonio, Texas Associate Secretary: W. Wistar Comfort Information for Organizers Deadline for organizers: April 13, 1992 Special Sessions at Annual and Summer Meetings are held Deadline for consideration: September 17, 1992 under the supervision of the Program Committee for National ------·----~------NOVEMBER 1991, VOLUME 38, NUMBER 9 1159 ~~·--~~··-~··------·------·-·-·------····-··-·•••••••••alliill:illmllffiBBIImllii··~········--·~···· ···········-··--····························· ·······································"·····-"····················· Invited Addresses and Special Sessions Meetings (PCNM). They are administered by the Associate Proposals for Special Sessions to the Secretary in charge of that meeting with staff assistance from Associate Secretaries the Meetings Department in the Society office in Providence. The programs of Sectional Meetings are arranged by the According to the "Rules for Special Sessions" of the Associate Secretary for the section in question: Society, Special Sessions are selected by the PCNM from Western Section a list of proposed Special Sessions in essentially the same Lance W. Small, Associate Secretary Department of Mathematics manner as individuals are selected to give Invited Addresses. University of California, San Diego The number of Special Sessions at a Summer or Annual La Jolla, CA 92093 Electronic mail: [email protected] Meeting is limited. The algorithm that determines the number (Telephone 619-534-3590) of Special Sessions allowed at a given meeting, while Central Section simple, is not repeated here, but can be found in "Rules for Andy R. Magid, Associate Secretary Special Sessions" on page 614 in the April 1988 issue of Department of Mathematics University of Oklahoma Notices. 601 Elm PHSC 423 Each person selected to give an Invited Address is Norman, OK 73019 invited to generate a Special Session, either by personally Electronic mail: [email protected] organizing one or by having a Special Session organized by (Telephone 405-325-6711) Eastern Section others. Proposals to organize a Special Session are sometimes W. Wistar Comfort, Associate Secretary requested either by the PCNM or by the Associate Secretary. Department of Mathematics Other proposals to organize a Special Session may be Wesleyan University Middletown, CT 06457 submitted to the Associate Secretary in charge of that Electronic mail: [email protected] meeting (who is an ex-officio member of the committee and (Telephone 203-347 -9411) whose address may be found below). These proposals must Southeastern Section be in the hands of the PCNM at least nine months prior to Joseph A. Cima, Associate Secretary Department of Mathematics the meeting at which the Special Session is to be held in University of North Carolina, Chapel Hill order that the committee may consider all the proposals for Chapel Hill, NC 27599-3902 Special Sessions simultaneously. Proposals that are sent to Electronic mail: [email protected] the Providence office of the Society, to Notices, or directed (Telephone 919-962-1050) As a general rule, members who anticipate organizing Special Sessions at to anyone other than the Associate Secretary will have to be AMS meetings are advised to seek approval at least nine months prior to the forwarded and may not be received in time to be considered scheduled date of the meeting. No Special Sessions can be approved too late for acceptance. to provide adequate advance notice to members who wish to participate. Proposals for Special Sessions at the June 29-July I, 1992, meeting in It should be noted that Special Sessions must be an Cambridge, England, only, should be sent to Professor Fossum at the Department nounced in Notices in such a timely fashion that any member of Mathematics, University of Illinois, Urbana, IL 61801, Telephone: 217-244- of the Society who so wishes may submit an abstract for 1741, Electronic mail: [email protected] consideration for presentation in the Special Session before the deadline for such consideration. This deadline is usually Information for Speakers three weeks before the deadline for abstracts for the meeting A great many of the papers presented in Special Sessions at in question. meetings of the Society are invited papers, but any member Special Sessions are very effective at Sectional Meetings of the Society who wishes to do so may submit an abstract and can usually be accommodated. The processing of for consideration for presentation in a Special Session, proposals for Special Sessions for Sectional Meetings is provided it is received in Providence prior to the special handled in essentially the same manner as for Annual early deadline announced above and in the announcements of and Summer Meetings by the Section Program Committee. the meeting at which the Special Session has been scheduled. Again, no Special Session at a Sectional Meeting may be Contributors should know that there is a limitation in size approved so late that its announcement appears past the of a single Special Session, so that it is sometimes true that deadline after which members can no longer send abstracts all places are filled by invitation. Papers not accepted for for consideration for presentation in that Special Session. a Special Session are considered as ten-minute contributed papers. The Society reserves the right of first refusal for the Abstracts of papers submitted for consideration for pre publication of proceedings of any Special Session. These sentation at a Special Session must be received by the proceedings appear in the book series Contemporary Math Providence office (Meetings Department, American Mathe ematics. matical Society, P. 0. Box 6887, Providence, RI 02940) by More precise details concerning proposals for and orga the special deadline for Special Sessions, which is usually nizing of Special Sessions may be found in the "Rules for three weeks earlier than the deadline for contributed papers Special Sessions" or may be obtained from any Associate for the same meeting. The Council has decreed that no Secretary. paper, whether invited or contributed, may be listed in the 1160 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···········~-~~Y11iW!IfiH11~ ?-·-·-······-~·············----···-----·---~~~···· Invited Addresses and Special Sessions program of a meeting of the Society unless an abstract of the more than once. An author can speak by invitation in more paper has been received in Providence prior to the deadline. than one Special Session at the same meeting. Electronic submission of abstracts is available to those An individual may contribute only one abstract by title who use the 1E;X typesetting system. Requests to obtain in any one issue of Abstracts, but joint authors are treated the package of files may be sent electronically via the as a separate category. Thus, in addition to abstracts from Internet to [email protected]. Requesting the two individual authors, one joint abstract by them may also files electronically will likely be the fastest and most be accepted for an issue. convenient way, but users may also obtain the package on IBM or Macintosh diskettes, available free of charge Site Selection for Sectional Meetings by writing to: Electronic Abstracts, American Mathematical Sectional Meeting sites are recommended by the Associate Society, Publications Division, P.O. Box 6248, Providence, Secretary for the Section and approved by the Committee RI 02940, USA. When requesting the abstracts package, of Associate Secretaries and Secretary. Recommendations users should be sure to specify whether they want the plain are usually made eighteen to twenty-four months in ad 'IE;X, .J\A,i5-1E;X, or the I5IEX package. vance. Host departments supply local information, ten to twelve rooms with overhead projectors for contributed pa per sessions and Special Sessions, an auditorium with twin Number of Papers Presented overhead projectors for invited addresses, and registration Joint Authorship clerks. The Society partially reimburses for the rental of Although an individual may present only one ten-minute facilities and equipment, and for staffing the registration contributed paper at a meeting, any combination of joint desk. Most host departments volunteer; to do so, or for more authorship may be accepted, provided no individual speaks information, contact the Associate Secretary for the Section. Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory (Contemporary Mathematics, Volume 120) Robert S. Doran, Editor This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Opera tor Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S. Muhly (which will be published in a CBMS Regional Confer ence Series volume), there were twenty-eight lectures delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, there are over one hundred problems and questions scattered through out this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory. 1991 Mathematics Subject Classification: 22, 46, 47; 05, 06, 18, 20, 57 ISBN 0-8218-5127-6, LC 91-19767, ISSN 0271-4132; 215 pages (softcover), July 1991 Individual member $29, List price $49, Institutional member $39 To order please specify CONM/120NA 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 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-321-4AMS (321-4267) in the continental U.S. and Canada to charge with Visa or MasterCard. Please add 7% GST to all orders being shipped to Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1161 Winter Meeting of the Canadian Mathematical Society December 7-10, 1991 Tentative Pro gram The Canadian Mathematical Society (CMS) and the Uni Classical analysis (in honour of P. G. Rooney's 65th versity of Victoria cordially invite all mathematicians to birthday), David W. Boyd, University of British Columbia; the 1991 Winter Meeting of the Society. All events will and Mourad E. H. Ismail, University of South Florida, take place at the Victoria Convention Centre/Empress Hotel co-organizers; complex in downtown Victoria, British Columbia. Kenneth F. Andersen, University of Alberta; Richard Askey, University of Wisconsin, Madison; David W. Boyd, Scientific Program University of British Columbia; Charles Dunkl, University of Virginia; John J. F. Fournier, University of British Principal Speakers Columbia; George Gasper, Jr. Northwestern University; The names and affiliations of the principal speakers and the Hans P. Heinig, McMaster University; Mourad E. H. Ismail, tentative days and times they will talk are as follows: University of South Florida; Paul G. Rooney, University of Andrew J. Casson, University of California, Berkeley, Toronto; Eric T. Sawyer, McMaster University; Sunday, 2:00p.m.- 3:00p.m.; Discrete aspects of Lie theory, Arturo Pianzola, University Stephen Grossberg, Boston University, Sunday, 9:00 of Alberta, organizer; a.m. - 10:00 a.m.; Stephen Berman, University of Saskatchewan; Murray Ian G. Macdonald, Queen Mary College, Monday, 9:00 R. Bremner, University of Toronto; Daniel J. Britten, Uni a.m.- 10:00 a.m.; versity of Windsor; Robert L. Griess, Jr., University of Benjamin Muckenhoupt, Rutgers University, Tuesday, Michigan; Victor Kac, Massachusetts Institute of Technol 2:00 p.m. - 3:00 p.m.; ogy; Frank W. Lemire, University of Windsor; Kailash Marc A. RietTel, University of California, Berkeley, C. K. Misra, North Carolina State University; Robert Tuesday, 9:00 a.m. - 10:00 a.m. V. Moody, University of Alberta; J. Patera, Universire de Montreal; Dale H. Peterson, University of British Columbia; Coxeter-James Lecture Louis Solomon, University of Wisconsin; The Coxeter-James Lecture will be given by Kumar Murty, Harmonic analysis/operator algebras, Anthony T. Lau, University of Toronto, on Monday, December 9, at 2:00 University of Alberta, organizer; p.m. Lawrence W. Baggett, University of Colorado; Ching Chou, SUNY at Buffalo; Edward G. EtTros, University of Symposia California, Los Angeles; Brian E. Forrest, University of Special Sessions in five domains will take place with session Waterloo; F. Ghahramani, University of Manitoba; John organizers and invited speakers as follows: E. Gilbert, University of Texas, Austin; Colin Graham, Lakehead University; Edmond E. Granirer, University of Applied non-linear differential equations, Reinhard Illner British Columbia; Kathryn E. Hare, University of Waterloo; and Pauline Van Den Driessche, University of Victoria, Paul Milnes, University of Western Ontario; Ole E. Nielsen, co-organizers; Queen's University; Alan L. T. Paterson, University of Stavros N. Dusenberg, Harvey Mudd College; John Mississippi; Arlan B. Ramsay, University of Colorado; M. Chadam, McMaster University; Herbert I. Freedman, Keith F. Taylor, University of Saskatchewan; Martin E. University of Alberta; John G. Heywood, University of Walter, University of Colorado; British Columbia; Josef Hofbauer, University of Vienna; Charles D. Levermore, University of Arizona; Robert M. Low dimensional topology, Steven P. Boyer, Universire du Miura, University of British Columbia; Michael Shearer, Quebec, Montreal, organizer; North Carolina State University; Marshall Slemrod, Uni David M. Austin, University of British Columbia; versity of Wisconsin, Madison; Hal L. Smith, Arizona State Steven A. Bleiler, Portland State University; Charles D. University; C. Sulem, University of Toronto; Frohman, University of Iowa; David Gabai, California 1162 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Winter Meeting of the Canadian Mathematical Society Institute of Technology; C. M. Gordon, University of Texas, Preliminary activities will be held at the Empress Austin; Joel Hass, University of California, Davis; David Hotel/Convention Centre on December 6 and 7 as follows: Darren Long, University of California, Santa Barbara; Erhard Luft, University of British Columbia; Andrew J, Nicas, McMaster University; D. Rolfson, University December6 2:30p.m. CMS Executive Meeting of British Columbia; Martin G. Scharlemann, University Empress Hotel Board Room of California, Santa Barbara; Denis Sjerve, University of British Columbia; Kevin Walker, Mathematical Sciences Research Institute; Xingru Zhang, University of British December7 Columbia; 9:30a.m. CMS Executive Meeting A session on Mathematics education has been organized (if necessary) by Katherine Heinrich, Simon Fraser University. Empress Hotel Board Room 2:30p.m. CMS Executive Meeting Contributed papers of 15 minutes' duration are invited. Empress Hotel Board Room 6:00 p.m. - 9:00 p.m. Evening Registration Convention Centre Plaza Hotel Accommodations Prefunction Area Rooms have been booked at the Empress Hotel at a cost 7:00p.m. Cash Bar Reception of $93.50 CDN (single or twin) excluding applicable taxes. Convention Centre Plaza Rates are given in Canadian dollars. Reservations should be Prefunction Area made directly with the Empress Hotel. Reservation cards for the Empress will be sent to you with your confirmation of registration or can be obtained from the CMS Office, Scientific Programme Committee 577 King Edward, Ottawa, Ontario, Canada K1N 6N5. The Kee Y. Lam, University of British Columbia (Chairman); telephone number for the Empress is 604-384-8111. David W. Boyd, University of British Columbia; Steven P. Boyer, Universire du Quebec, Montreal; Reinhard lllner, University of Victoria; Mourad E. H. Ismail, University of Miscellaneous Information South Florida; Anthony Lau, University of Alberta; Pauline Social events include a welcoming reception with cash Van Den Driessche, University of Victoria. bar at the Plaza Prefunction Area of the Convention Centre Further information and registration forms may be on Saturday, December 7th, beginning at 7:00 p.m., and a obtained from C. R. Miers, Local Organizer, Depart banquet at the Crystal Ballroom of the Empress on Monday, ment of Mathematics and Statistics, University of Vic December 9th, beginning at 7:00p.m. toria, Victoria, British Columbia, V8W 3P4; telephone Air travel: Victoria International Airport is about 25 604-721-7463; FAX 604-721-8962; email: CRMIERS@ km north of downtown Victoria and is served by both Air UVVM.UVIC.CA. Canada and Canadian Airlines connector flights. Busses meet each flight and the cost of bus transportation to downtown Victoria is $10. Taxi fare for the same trip is about $40. One may also fly from Seattle to the airport via Horizon Air Registration Fees (in Canadian dollars) and from Seattle to the inner harbour of Victoria (adjacent to the Empress) via Lake Union Air Service. Before After November 9 November Car and/or passenger ferry travel: There is frequent CMS/AMS/MAA Members ferry service (approximately every two hours) provided with grants $145 $175 by B. C. Ferries between Tsawassen, which is just south CMS/AMS/MAA Members of Vancouver, and Schwartz Bay, which is just north of without grants 70 100 Victoria. Victoria may also be reached from Anacortes, Non-Members with grants 190 220 Washington, via the Washington State Ferries, and from Non-Members without grants 95 125 Port Angeles, Washington, via the Black Ball ferry Coho. Grads/PDFs/Retired Faculty 40 40 The Victoria Clipper provides daily passenger ferry service Banquet Tickets for between Seattle and Victoria. There is also bus service accompanying persons 40 40 from VancouverNancouver Airport to downtown Victoria, One Day Fee 65 including the ferry trip, provided by Pacific Coach Lines. Weather: Weather in Victoria in December is cool with (The one day fee is intended for anyone who wishes to take the average high/low being 7°C/3°C, and may also be damp part for only one day of the meeting. All fees except the with an average December rainfall of 111 mm. one day fee include a ticket to the Monday night banquet.) ·------·------· ------NOVEMBER 1991, VOLUME 38, NUMBER 9 1163 Mathematical Sciences 3-9. Mengenlehre, Oberwolfach, Federal Republic of Germany. (Jul./Aug. 1990, p. 746) Meetings and Conferences 4-8. Second SIAM Conference on Geomet ric Design, Tempe, AZ. (Nov. 1990, p. 1289) 4-8. Les Processus Stochastiques en Theorie des Epidemies, Centre International de Ren contres Mathematiques. (May/Jun. 1991, p. 474) 9. Differential Geometry Day, Eastern illi nois University, Charleston, IL. (May/Jun. 1991, p. 474) . 9-10. Western Section, University of Cali fornia, Santa Barbara. INFORMATION: W. Drady, American Math THIS SECTION contains announcements of meetings and conferences of interest to some ematical Society, P.O. Box 6887, Provi segment of the mathematical public, including ad hoc, local, or regional meetings, and dence, RI 02940. meetings or symposia devoted to specialized topics, as well as announcements of regularly scheduled meetings of national or international mathematical organizations. (Information on 11-15. IMA Workshop on Combinatorial meetings of the Society, and on meetings sponsored by the Society, will be found inside the and Graph-Theoretic Problems in Linear front cover.) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, and specifies Algebra, University of Minnesota, Minneapo the place, date, subject (when applicable), and the speakers; a second full announcement lis, MN. (Oct. 1990, p. 1140) will be published only if there are changes or necessary additional information. Once an 15-17. Fourth Annual International. Con announcement has appeared, the event will be briefly noted in each issue until it has been ference on Technology in Collegiate Mathe held and a reference will be given in parentheses to the month, year, and page of the issue in matics, Portland, OR. (Jul./Aug. 1991, p. 642) which the complete information appeared. Asterisks (*) mark those announcements containing new or revised information. 17-23. Singularitaten der Kontinuums IN GENERAL, announcements of meetings and conferences held in North America carry mechanik: Numerische und Konstruktive only date, title of meeting, place of meeting, names of speakers (or sometimes a general Methoden zu Ihrer Behandlung, Oberwol statement on the program), deadlines for abstracts or contributed papers, and source of fach, Federal Republic of Germany. (Jul./Aug. further information. Meetings held outside the North American area may carry more detailed 1990, p. 746) information. In any case, if there is any application deadline with respect to participation in 18-21. DIMACS Workshop on Planar the meeting, this fact should be noted. All communications on meetings and conferences in the mathematical sciences should be sent to the Editor of Notices, care of the American Graphs: Structures and Algorithms, Cen Mathematical Society in Providence. ter for Discrete Mathematics, Rutgers, The DEADLINES for entries in this section are listed on the inside front cover of each issue. In State University of New Jersey. (Oct. 1991, order to allow participants to arrange their travel plans, organizers of meetings are urged to p. 1006) submit information for these listings early enough to allow them to appear in more than one 18-22. Workshop on Discrete Groups, issue of Notices prior to the meeting in question. To achieve this, listings should be received Number Theory and Ergodic Theory, Math in Providence SIX MONTHS prior to the scheduled date of the meeting. ematical Sciences Research Institute (MSRI), EFFECTIVE with the 1990 volume of Notices, the complete list of Mathematical Sciences Meetings and Conferences will be published only in the September issue. In all other issues, Berkeley, CA. (May/Jun. 1991, p. 474) only meetings and conferences for the twelve-month period following the month of that issue 18-22. Supercomputing '91, Albuquerque, will appear. As new information is received for meetings and conferences that will occur later NM. (Mar. 1991, p. 243) than the twelve-month period, it will be announced at the end of the listing in the next possible 20-26. C*-Aigebren, Oberwolfach, Federal issue. That information will not be repeated until the date of the meeting or conference falls Republic of Germany. (Jul./Aug. 1990, p. 746) within the twelve-month period. 21-22. MSI/Stony Brook Conference on Nonlinear Analysis and Computation, Stony Brook, NY. (Sep. 1991, p. 835) 1991-1992. Mittag-Leffler Institute Aca Theory and Algorithms, Center for Discrete 24-30. Numerische Methoden der Approx demic Program for 1991-1992: Combi Mathematics, Rutgers, The State University imationstheorie, Oberwolfach, Federal Re natorics, Djursholm, Sweden. (Apr. 1991, of New Jersey. (Oct. 1991, p. 1005) public of Germany. (Jul./Aug. 1990, p. 746) p. 359) 25-29. Seminaire Sud-rhodanien de Geome * 1991-1992. 1991-1992 Special Year on Au trie, Centre International de Rencontres Math tomorphic Forms in Number Theory, Centre ematiques. (May/Jun. 1991, p. 474) de Recherches Mathematiques, Universite de November 1991 26-29. Conference on Representation Theo Montreal. (Please note corrections to Sep. ries of Lie Groups and Lie Algebras, Misasa, 1991, p. 832) 1-2. Sixth Annual Pi Mu Epsilon Re Tottori, Japan. (May/Jun. 1991, p. 474) gional Undergraduate Mathematics Confer CHAIRMAN: R. Murty (McGill Univ.), ence, St. Norbert College, DePere, WI. (Sep. previously incorrectly listed as J. Arthur. 1991, p. 834) INVITED SPEAKERS: J. Arthur (Univ. of 1-3. Partial Differential Equations and Toronto) will be the principle speaker December 1991 (Aisenstadt Chair) during the Spring of Mechanics, Southern illinois University, Car 1992. bondale, IL. (May/Jun. 1991, p. 474) Fourth International Conference on Numer 3-6. ORSAITIMS Joint National Meeting, ical Combustion, St. Petersburg, FL. (Feb. 1991-1992. DIMACS Special Year: Graph Anaheim, CA. (May/Jun. 1991, p. 474) 1991, p. 146) 1164 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 1-7. Statistik Stochastischer Prozesse, Ober in Geophysics, Monteray, CA. (Oct. 1990, Applications of Geometry and Topology", wolfach, F.R.G. (Jul./Aug. 1990, p. 746) p. 1141) Baltimore, MD. (Jul./Aug. 1991, p. 643) 2-4. Fourth International Conference on Spring 1992. IMACS Symposium on Math 6-17. Topology Workshop, Pontifical Catho Numerical Combustion, St. Petersburg, FL. ematical Modelling, Wiener Neustadt, Ger lic University, Rio de Janeiro, Brazil. (Oct. (May/Jun. 1991, p. 474) many. (May/Jun. 1991, p. 475) 1991, p. 1007) 2-4. Titre aPreciser, Centre International de Spring 1992. Third IMACS International 6-17. International Research Workshop on Rencontres Mathematiques. (May/Jun. 1991, Conference on Expert Systems in Numer Banach Space Theory, Merida, Venezuela. p. 474) ical Computing, Purdue University, West (Jul./Aug. 1991, p. 643) 2-6. Workshop on Statistical Methods in Lafayette, IN. (May/Jun. 1991, p. 475) 8-11. Joint Mathematics Meetings, Balti Imaging, Mathematical Sciences Research Spring 1992. DIMACS Workshop on Ex more, MD. (including the annual meetings of Institute, Berkeley, CA. (Oct. 1990, p. 1140) pander Graphs: Theory and Applications, the AMS, AWM, MAA and NAM) 2-9. SIAM Conference on Combustion, St. Center for Discrete Mathematics, Rutgers, The INFORMATION: H. Daly, AMS, P.O. Box Petersburg, FL. (Nov. 1990, p. 1289) State University of New Jersey. (Oct. 1991, p. 1007) 6248, Providence, Rl 02940. 6-7. The Midwest Conference on Differ ential Equations, University of Iowa, Iowa 12-18. Applied Dynamics and Bifurcation, City, lA. (Jul./Aug. 1991, p. 642) Oberwolfach, Federal Republic of Germany. 7-10. Canadian Mathematical Society Win January 1992 (Jan. 1991, p. 51) ter Meeting, Victoria, B.C., Canada. (Oct. 1-11. Mathematische Optimierung, Ober 13-15. DIMACS Workshop: Graph Em 1990, p. 1141) wolfach, Federal Republic of Germany. (Jan. beddings and Parallel Architectures, Center 8-14. Stochastic Geometry, Geometric 1991, p. 51) for Discrete Mathematics, Rutgers, The State University of New Jersey. (Oct. 1991, p. 1007) Statistics, Stereology, Oberwolfach, Federal 3-6. International Conference on Ran Republic of Germany. (Jul./Aug. 1990, p. 746) dom Mappings, Partitions, and Permuta 13-17. IMA Workshop on Linear Algebra, 9-13. Femmes et Mathematiques-Congres tions, University of Southern California, Los Markov Chains, and Queuing Models, Uni Europeen, Centre International de Rencontres Angeles, CA. (Sep. 1991, p. 835) versity of Minnesota, Minneapolis, MN. (Oct. 1990, p. 1141) Mathematiques. (May/Jun. 1991, p. 475) * 3-6. Short Conference on Topology, Kansas 10-12. Ninth Biennial Conference on Mod State University, Manhattan, KS. 15-17. Workshop on Stochastics and Anal elling and Simulation, Queensland, Australia. ysis, Universitiit Ziirich, Ziirich, Switzerland. (May/Jun. 1991, p. 475) PROGRAM: Professor A.V. Arhangel'skii (May/Jun. 1991, p. 475) of Moscow Univ. will give four hour-long Research Work 17. Joint Meeting with the Edinburgh 12-16. NATO Advanced lectures on "The concept of cleavability of Topology and Algebraic International Centre shop: Algebraic a topological space". This is a relatively Mathematical Society, Louise, Alberta, Canada. Sciences, Edinburgh, Scot K-Theory, Lake new concept that should be of interest to for Mathematical 1008) (Jul./Aug. 1991, p. 642) many topologists, especially those at the land. (Oct. 1991, p. 15-21. Quantenstochastik, Oberwolfach, early stages of their research careers. The 19-25. Modelltheorie, Oberwolfach, Federal Federal Republic of Germany. (Jul./Aug. conference will also feature talks by other Republic of Germany. (Jan. 1991, p. 51) 1990, p. 746) participants on a wide range of topics in 26-February 1. Applied and Computational 23-26. International Conference on Gen topology. It has been timed to immediately Convexity, Oberwolfach, Federal Republic of eralized Functions and Their Applications, proceed the Joint Mathematics Meetings Germany. (Jan. 1991, p. 51) Banaras Hindu University, Varanasi, India. of the AMS and MAA to be held in 27-29. Third ACM-SIAM Symposium on (Dec. 1990,p. 1458) Baltimore, January 8-11, 1992. Discrete Algorithms, Orlando, FL. (Feb. *27-31. Holiday Symposium on the Impact ORGANIZING COMMITTEE: G. Strecker, 1991, p. 146) of Software Systems in Mathematical Re Y.-L. Lee, T. Muenzenberger, J. Maginnis, D. Yetter. * 27-31. Conference on Scientific Computing, search, New Mexico State Univ., Las Cruces, Benin-City, Nigeria. NM. (Please note changes from Jul./Aug. INVITED SPEAKERS: W.W. Comfort, B. 1990, p. 746) Fitzpatrick, G. Gruenhage, J. Heath, R. PROGRAM: The conference language is Heath, E. Michael, J. Nikiel, P. Nyikos, English. The scientific program will con PROGRAM: A second principle speaker J. Roitman, M.E. Rudin, R. Smithson, F. sist of invited and contributed talks. There has been added to the Holiday Sympo Tall, H. Wicke, and S. Williams. will be morning and afternoon lectures sium. J.S. Devitt of the University of INFORMATION: Organizing Committee, of 60 minutes for invited lectures and 20 Saskatchewan will join J.L. Selfridge of Short Conference on Topology, Dept. of minutes for contributed papers. Florida Atlantic University in presenting Math., Kansas State Univ., Manhattan, KS ORGANIZING COMMITTEE: S. 0. Fatunla the symposium. 66506-2602. (Benin-City, Nigeria), B. Russell (Burn aby, Canada), J. Pryce (Swindon, UK). 3-7. Seventh Texas International Sympo CONFERENCE TOPICS: Ordinary differ sium on Approximation Theory, Austin, TX. ential equations, partial differential equa 1992 (Sep. 1991, p. 835) tions, parallel methods, interval arithmetic, 1992. IMACS Symposium on Symbolic 5-8. Second Caribbean Conference on computational fluids, nonlinear dynamical Computation in Engineering Design, IDN, the Fluid Dynamics, University of the West systems and chaos, numerical software, Lille, France. (Jul./Aug. 1990, p. 746) Indies, St. Augustine, Trinidad. (Jan. 1991, seismic analysis, supercomputing, compu IMACS International Conference on Com p. 51) tational meterology, computer algebra. putational Physics, University of Colorado, 5-8. Second International Symposium on INVITED SPEAKERS: CANADA: J. Verner Boulder, CO. (Oct. 1990, p. 1141) Artificial Intelligence and Mathematics, Fort (Kingston), B. Russell (Burnaby), P. Sharp Spring 1992. International Conference on Lauderdale, FL. (Oct. 1991, p. 1007) (Kingston); ENGLAND: J. Pryce (Swin Finite Elements and Boundary Elements 6-7. AMS Short Course on "New Scientific don); SCOTLAND: S. McKee (Glas- NOVEMBER 1991, VOLUME 38, NUMBER 9 1165 Meetings and Conferences gow); THE NETHERLANDS: M.N. Spi (10-20 lines single spaced) of a paper by (Jul./Aug. 1991, p. 644) jker (Leiden), P. Van Der Houwen (Ams January 17, 1992. 5-6. Twenty-third SIGCSE ('92) Technical terdam), K. Dekker (Amsterdam); ITALY: INFORMATION: F. Hoffman, Dept. of Symposium, Kansas City, MO. (Jul./Aug. E. Spedicato (Bergamo); JAPAN: M. Math., Florida Atlantic Univ., Boca Ra 1991, p. 644) Nakashim (Kagoshima), T. Tsuboi (Ky ton, FL 33431; 407-367-3345 or 407-367- oto); U.S.A.: R. O'Malley, Jr. (Seattle), V. 3341 or via email: [email protected] 8-14. Mathematische Stochastik, Oberwol Pereyra (Los Altos), D. Kannan (Athens); or [email protected]. For registration fach, Federal Republic of Germany. (Jan. GERMANY: M. Rump (Hamburg); NIGE information, contact the Division of Con 1991, p. 52) RIA: C.O.A. Sowunmi (Ibadan), M.A. tinuing Education, at 407-367-3090. 13-14. Southeastern Section, University of Ibiejugba (llorin), P. Onumanyi (llorin), Alabama, Tuscaloosa, AL. S. Ibiyemi (llorin), R.O. Ayeni (Ogbo 9-15. Numerical Methods for Parallel Com mosho), K. Aderogba (Lagos), A. Ojo puting, Oberwolfach, Federal Republic of INFORMATION: W. Drady, American Math (Ibadan). Germany. (Jan. 1991, p. 51) ematical Society, P.O. Box 6887, Povi CALL FOR PAPERS: Potential contribu 10-11. Workshop on Amenable Ergodic dence, Rl 02940. Theory, Mathematical Sciences Research In tors should submit a one-page abstract 13-15. Permian Basin Supercomputing stitute (MSRI), Berkeley, CA. (May/Jun. * (together with their registration form) Conference 1992, University of Texas of 1991, p. 475) to Fatunla, Russell, or Pryce. The one the Permian Basin, Odessa, TX. page abstract should include the title 16-22. Funktiontheorie, Oberwolfach, Fed and (list of) author(s) in a form suit eral Republic of Germany. (Jan. 1991, p. 51) PROGRAM: The purpose of this confer able for direct inclusion in the book of 17-22. Informatics '92, Havana, Cuba. (Sep. ence is to bring together researchers in abstracts. If possible, submit abstracts by 1991, p. 836) all fields of supercomputing, high perfor email to B. Russell, Dept. of Math. and mance computing, and parallel computing 23-29. p-Adische Analysis und Anwen Stat., Simon Fraser Univ., Canada; rus for an effective exchange of ideas and dis dungen, Oberwolfach, Federal Republic of [email protected] or J. Pryce, Computational cussion of recent developments and future Germany. (Jan. 1991, p. 51) and Applied Math. Group, Royal Military directions of research. College, Shrivenham, Swindon, England; 24-28. IEEE Computer Society COMP ORGANIZERS: M. Paprzycki (Univ. of [email protected] or by telex to CON Spring '92, San Francisco, CA. (Jan. Texas), F. Khosraviyani (Univ. of Texas), S. Fatunla at 41365 UNIBEN NG. Dead 1990, p. 62) M. Melander (SMU). line: November 30, 1991. 24-28. Elliptic Curves and Related Topics, INVITED SPEAKERS: Tentative: C. Bisch INFORMATION: S. ola Fatunla, Director Sainte-Adele, Quebec, Canada. (Please note of (ANL), J. Diaz (Univ. of Tulsa), I. of Conference, Benin City, Nigeria, Telex: correction to Sep. 1991, p. 836) Gladwell (SMU), D. Kincaid (Univ. of 41365 UNffiEN NG. 24-March 1. IMA Workshop on Iterative Texas), G. MacMechan (Univ. of Texas), Methods for Sparse and Structured Prob 30-February 1. International Meeting on R. Plemmons (Wake Forest Univ.), D. lems, University of Minnesota, Minneapolis, Sorensen (Rice Univ.), R. van de Geijn Nonlinear Boundary Value Problems in Sci MN. (Jul./Aug. 1991, p. 643) ence and Engineering: Analytic Methods, (Univ. of Texas). University of Wollongong, New South Wales, CALL FOR PAPERS: Three copies of de Australia. (Jul./Aug. 1991, p. 643) tailed abstract (not to exceed 1000 words) March 1992 should be received by December 20, 1991. INFORMATION: Conference Chairman, M. March 1992. 1992 ASL Annual Meeting, Paprzycki, Dept. of Math. and Comp. Sci., February 1992 Duke University, Durham, NC. (Apr. 1991, UT Permian Basin, Odessa, TX 79762; p. 366) 2-8. Thermodynamische Materialtheorien, 915-367-2244; Fax: 915-367-2115; email: Oberwolfach, Federal Republic of Germany. 1-7. Klassifizierende Raume und Anwen [email protected] or (Jan. 1991, p. 51) dungen der Steenrod-Algebra, Oberwolfach, [email protected]. Germany. (Jan. 1991, p. 52) 3. Joint Meeting of the ICMS and the 15-21. Regelungstheorie, Oberwolfach, Fed Royal Society of Edinburgh, International * 2--6. Workshop on Interfaces between eral Republic of Germany. (Jan. 1991, p. 52) Centre for Mathematical Sciences, Edinburgh, Physics and Mathematics, University of Vi Scotland. (Oct. 1991, p. 1008) enna, Austria. 20-21. Central Section, Southwest Missouri 3-7. Eighth International Conference on PROGRAM: A list of invited speakers and State University, Springfield, MO. Data Engineering, Phoenix, AZ. (Jul./Aug. their topics: A. Connes: Noncommutative INFORMATION: W. Drady, American Math 1991, p. 643) geometry; L. Faddeev: Exchange alge ematical Society, P.O. Box 6248, Provi * 3-7. Twenty-third Southeastern Interna bras; J. Froehlich: Gauge symmetry in dence, Rl 02940. tional Conference on Combinatorics, Graph condensed matter physics; K. Gawedzki: Theory, and Computing, Florida Atlantic Title to be announced; W. Thirring: Quan 21-27. Workshop on Fluid Dynamics and University, Boca Raton, FL. tum ergodic theory; I. Todorov: Confor Statistical Physics, Institute for Advanced mal quantum field theory; A. Trautman: Study, Princeton, NJ. (Jul./Aug. 1991, p. 644) INVITED SPEAKERS: L. Babai, Eotvos Spinors; A. Vinogradov: Geometry of par Univ. and Univ. of Chicago; P. Erdos, Hun 22-28. Teichmiiller-Theorie und Modul tial differential equations; J. Wess: Q\lan raume Riemannscher Flachen, Oberwolfach, garian Academy of Sciences; D. Goren tum groups. stein, Rutgers Univ. and DIMACS; K. Federal Republic of Germany. (Jan. 1991, INFORMATION: H. Narnhofer, Institute of p. 52) O'Hara, Univ. of Iowa; and D. Stinson, Theoretical Physics, University of Vienna, Univ. of Nebraska. Boltzmanngasse 5, A-1090 Wien, Austria. 22-28. Georgia Tech.-UAB International CALL FOR PAPERS: There will be fifteen Conference on Differential Equations and minute sessions for contributed papers. 3-5. ACM 1992 Computer Science Con Mathematical Physics, Atlanta, GA. (Jul./Aug Please submit the title and an abstract ference, Kansas City, Missouri. 1991, p. 644) 1166 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences * 24-26. Data Compression Conference- public of Germany. (Jan. 1991, p. 52) Colloquium, University of Strathclyde, Glas nee '92, Snowbird, Utah. 29-April 5. Sixth International Conference gow, Scotland, UK. CONFERENCE TOPICS: Coding theory, on Geometry, University of Haifa, Israel INVITED SPEAKERS: C. MeA. Gordon quantization theory, parallel compression (postponed from March 1991 because of the (Austin), E.H. Lieb (Princeton), J.H. van algorithms and hardware, lossless and Gulf War). (Jul./Aug. 1991, p. 644) Lint (Eindhoven), I. Anderson (Glasgow), lossy compression algorithms for specific * 30-31. IMA International Conference on I.N. Baker (Imperial College), S. Bren types of data (including text, images, Mathematics in Industrial Maintenance, Ed ner (Liverpool), J. Carr (Heriot-Watt), E. video, speech, music, maps, instrument inburgh, Scotland. Cusack (BT Labs), E.B. Davies (King's data, graphics, animation, and bit-maps), INFORMATION: A.H. Christer, Dept. of College), S.J. Gardiner (Univ. College), J. data compression standards, hi-level cod Math. and Comp. Sci., Univ. of Salford, Greenlees (Sheffield), J. Hawkes (Swan ing, transform methods, wavelet and frac Lanes., M5 5WT, UK; or L.C. Thomas, sea), J.M. Howie (St. Andrews), M.N. tal techniques, string searching and manip Dept. of Business Studies, Univ. of Ed Huxley (Cardiff), P.B. Kronheimer (Ox ulation, closet-match retrieval, theory of inburgh, William Robertson Building, 50 ford), M.A.H. MacCallum (QMW), D. minimal length encoding and applications George Square, Edinburgh, EH8 9JY, UK. MacHale (Cork), D.B. Pearson (Hull), to learning, system issues relating to data R.M. Thomas (Leicester), J. Truss (Leeds), compression (including error control, data 30-April 2. Thirty-fourth British Theoret P.M.H. Wilson (Cambridge). security, and indexing), medical imagery, ical Mechanics Colloquium, University of INFORMATION: A.C. McBride, Dept. of scientific and space archives. Keele, England. (Sep. 1991, p. 836) Math., Univ. of Strathclyde, Livingstone CALL FOR PAPERS: Submit 4 copies of 30-April 3. Workshop on Statistical Meth Tower, 26 Richmond St., Glasgow G 1 an extended abstract of 8 to 10 pages ods in Molecular Biology, Mathematical Sci 1XH, Scotland, UK; tel: 041-552-4400, (please include your affiliation, address, ences .Research Institute, Berkeley, CA. (Sep. ext. 3647; email: [email protected] telephone number, fax number, and email 1991, p. 836) address) by November 15, 1991 to the 7-10. Twenty-third Annual Iranian Mathe address below. matics Conference, Razi University, Bakhta INFORMATION: M. Cohn, Comp. Sci. ran, Iran. (Sep. 1991, p. 836) Dept., Brandeis Univ., Waltham, MA April1992 *7-10. Statistics in Public Resources and 02254; 617-736-2705; FAX: 617-736-2741; April 1992. Eighth International Confer Utilities, and in Care of the Environment email: [email protected]. ence on Mathematical and Computer Mod (SPRUCE), Lisbon, Portugal. elling, United States. (Sep. 1990, p. 939) 24-28. GAMM Annual Meeting, Leipzig, INFORMATION: V. Barnett, Dept. Prob. Germany. (Sep. 1991, p. 836) * 3-4. 1992 Dlinois Number Theory Confer- and Stat., The University, Sheffield S3 ence, University of lllinois, Urbana, IL. 7RH, UK. 24-28. Algebraic Groups and Their Rep resentations, University of California, Los INVITED SPEAKERS: P.T.D.A. Elliott (Col 9-11. Symplectic Topology, University of Angeles. (Oct. 1991, p. 1008) orado), F. Garvan (Dalhousie/Florida), A. Arkansas, Fayetteville, Arkansas. (Sep. 1991, Granville (Georgia). * 25-28. International Conference on Hamil p. 837) CALL FOR PAPERS: Interested persons tonian Dynamical Systems, University of are invited to submit a brief abstract for 11-12. Eastern Section, Lehigh University, Cincinnati, Cincinnati, Ohio. a 20-minute talk. Deadline: February 3, Bethlehem, PA. PURPOSE: To bring together researchers 1992. INFORMATION: W. Drady, American and students from diverse areas with a MISCELLANEOUS: Hotel Reservations: A Mathematical Society, P.O. Box 6887, common interest in Hamiltonian systems. block of rooms has been reserved at the Providence, RI 02940. PROGRAM: There will be plenary ad University Inn, 302 E. John St., Cham dresses and contributed papers. The pro paign, 217-384-2100. Contact the hotel 12-18. Mathematische Logik, Oberwolfach, ceedings will be published in the IMA directly for reservations, mentioning the Federal Republic of Germany. (Feb. 1991, Volumes in Mathematics and its Applica conference for $52/night rate. Deadline: p. 146) tions. March 3, 1992. Dinner: A dinner is sched 13-17. Workshop on Lie Groups, Ergodic ORGANIZERS: S. Dumas, K. Meyer, and uled Friday April 3, at the University Inn Theory, and Geometry, Mathematical Sci D. Schmidt. costing under $20.00. Make reservations ences Research Institute (MSRI), Berkeley, CONFERENCE TOPICS: Recent advances with the conference organizers. Deadline: CA. (May/Jun. 1991, p. 476) March 3, 1992. in bifurcation theory, heteroclinic orbits, 19-25. Arbeitsgemeinschaft mit Aktuellem INFORMATION: H.G. Diamond, UIUC reduction, properties of area preserving Thema, Oberwolfach, Federal Republic of Math. Dept., 1409 West Green St., Urbana, mappings, integrable systems, stability, Germany. (Feb. 1991, p. 146) Nekhoroshev theory, with applications to IL 61801; 217-333·0379; Fax: 217-333- * 26-28. Conference on Applied Statistics in physics and celestial mechanics will be 9576; [email protected]. Agriculture, Kansas State University, Man presented at the conference. 5-11. Algebraische K-Theorie, Oberwol hattan, KS. INFORMATION: K. Meyer, Institute for fach, Federal Republic of Germany. (Feb. Dynamics, Dept. of Math. Sci.,Univ. of 1991, p. 146) INFORMATION: G.A. Milliken, Kansas Cincinnati, Cincinnati, OH 45221-0025; State Univ., Dept. of Stat. and Stats. Lab., Fax: 513-556-3417. 5-11. Informationstheorie, Oberwolfach, Dickens Hall, Manhattan, KS 66506. Federal Republic of Germany. (Jul./Aug. 27-28. Eighth South-EasternAnalysis Meet 1991, p. 644) 26-May 2. Gruppentheorie, Oberwolfach, ing (SEAM VIII), University of Tennessee, 6-10. IMA Workshop on Linear Algebra Federal Republic of Germany. (Feb. 1991, Knoxville, TN. (Sep. 1991, p. 836) for Signal Processing, University of Min p. 146) 29-April 4. Topologische Methoden in der nesota, Minneapolis, MN. (Oct. 1990, p. 1141) 30-May 1. Twenty-third Annual Pittsburgh Gruppentheorie, Oberwolfach, Federal Re- * 6-10. Forty-fourth British Mathematical Conference on Modeling and Simulation, NOVEMBER 1991, VOLUME 38, NUMBER 9 1167 Meetings and Conferences University of Pittsburgh, PA. (Jul./Aug. 1991, 17-23. Quadratische Formen, Oberwolfach, 31-June 6. Singularitaten, Oberwolfach, p. 644) Federal Republic of Germany. (Feb. 1991, Federal Republic of Germany. (Feb. 1991, p. 146) p. 147) * 18-22. Eighth International Conference on 31-June 6. Free Resolutions in Alge May 1992 the Numerical Analysis of Semiconductor braic Geometry and Representation Theory, May 1992. Conference on Classification Devices and Integrated Circuits: NASEC Oberwolfach, Federal Republic of Germany. of Algebraic Varieties, L' Aquila, Italy. (Apr. ODE Vill, City Club, Vienna, Austria. (Feb. 1991, p. 147) 1991, p. 366) CONFERENCE TOPICS: process simu 3-9. Wavelett (Signalverarbeitung), Ober lation, device modelling, circuit analy wolfach, Federal Republic of Germany. (Feb. sis, physical aspects, computational tech June 1992 1991, p. 146) niques, mathematical analysis, Monte Carlo June 1992. IMACS Symposium on Numer 4--6. 1992 ACM Symposium on the Theory simulations, quantum effects, energy trans port models, code validation against real ical Computing and Mathematical Mod of Computing, Victoria, British Columbia, elling, Bangalore, India. (Oct. 1990, p. 1141) Canada. (Oct. 1991, p. 1009) devices and processes. CALL FOR PAPERS: For papers: Potential June 1992. Continuum Models for the Mi * 4--6. 1992 IEEE Symposium on Research in contributors should submit an abstract crostructure of Crystals, International Centre Security and Privacy, Oakland, CA. (one page, 500 words maximum) which for Mathematical Sciences, Edinburgh, Scot PROGRAM: The purpose of this sympo must clearly state the purpose of the land. (Oct. 1991, p. 1009) sium is to bring together researchers and work, the specific results obtained and 1-5. Seventh International Conference on developers who work on secure computer their significance. For sessions: Potential Graph Theory, Combinatorics, Algorithms, systems. The symposium will address ad organizers should submit the title(s) of the and Applications, Western Michigan Univer vances in the theory, design, implementa sessions they propose. A typical session sity, Kalamazoo, MI. (May/Jun. 1991, p. 476) tion, evaluation and application of secure consists of six 20-minute papers. 1-5. IMA Workshop on Linear Algebra for computer systems. INFORMATION: J. Miller, NASECODE Control Theory, University of Minnesota, CONFERENCE TOPICS: Secure systems, Secretariat, 26 Temple Lane, Dublin 2, Ire Minneapolis, MN. (Oct. 1990, p. 1141) network security, database security, au land; Telefax: (+353-1) 679-2469; 7-13. Computational Group Theory, Ober thentication, privacy issues, formal mod Tel: (+353-1) 679-7655; email: jmiller@ wolfach, Federal Republic of Germany. (Feb. els, access controls, data integrity, infor vaxl.tcd.ie; telex: 30547 SHCN EI (Ref: 1991, p. 147) mation flow, viruses and worms, security NASECODE). verification and validation, auditing and 8-11. Sixth SIAM Conference on Discrete intrusion detection. 18-23. Second European Conference on Mathematics, University of British Columbia, CALL FOR PAPERS: Send six copies of Compute.r Vision, Santa Margherita Ligure, Vancouver, Canada. (May/Jun. 1991, p. 476) your paper, panel session proposal, and Italy. (Jul./Aug. 1991, p. 645) 8-13. Zero-dimensional Schemes, Ravello, position papers to J. McLean at address 18-23. Low-Dimensional Topology, Knox Italy. (Sep. 1991, p. 837) below. Deadline: November 8, 1991. ville, TN. (Oct. 1991, p. 1009) * 10-16. Geometric Topology Workshop, INFORMATION: D. Cooper, General Chair, * 20-June 5. Workshop on Automorphic Technion, Haifa, Israel. Unisys Corp., 5731 Slauson Ave., Culver Forms and L-functions, Institute for Ad CONFERENCE TOPICS: Geometry and City, CA 90230; 213-338-3727; cooper@ vanced Studies, Hebrew Univ. of Jerusalem, topology of low dimensional manifolds. culv.unisys.com; T. Lunt, Vice Chair, SRI Israel. International, EL245, 333 Ravenswood INVITED SPEAKERS: J. Birman, F. Bona Ave., Menlo Park, CA 94025; 415-859- PROGRAM: One or two lectures a day. bon, A. Casson, D. Gabai, C.M. Gordon, 6106; [email protected]; J, McLean, Pro Invited participants include J. Bernstein, J. Hass, P. Scott, P. Shalen, V. Touraev. gram Co-Chair, Naval Research Lab., R. Howe, D. Kazhdan, S. Kudla, S. Rallis, INFORMATION: Y. Moriah, B. Wajnryb, Code 5543, Washington, PC 20375; 202- K. Ribet, P. Sarnak, and others. Dept. of Math., Technion, Haifa, Is 767-3852; [email protected]; R. INFORMATION: S. Gelbart, Dept. of Math., rael; email: [email protected] or Kemmerer, Program Co-Chair, Comp. Weizmitnn Institute of Science, Rehovot, [email protected]; Fax: 972-4-324- Sci. Dept., Univ. of California, Santa Bar Israel; email: mtgelbar@weizmann, or I. 654; C. Gordon, 512-471-7711, email: bara, CA 93106; 805-893-4232; kemrn@ Piatetski-Shapiro, Dept. of Math., Yale [email protected]. cs.ucsb.edu; J. Jacob, European Contact, Univ., New Haven, CT 06520; email: [email protected]. 12-14. Canadian Mathematical Society Oxford Univ. Computing Lab., 11 Keble Summer Meeting, York University, North Rd., Oxford, England OXl 3QD; +44 24--30. Kommutative Algebra und Alge York, Ontario, Canada. (Nov. 1990, p. 1289) 865 272562; Fax: +44 865-273839; braische Geometrie, Oberwolfach, Federal * 13-16. Conference in Geometric Group [email protected]; D. Bai Republic of Germany. (Feb. 1991, p. 146) ley, Cipher Editor, USDOE, WQD, P.O. Theory, Ohio State University, Columbus, Box 5400, Albuquerque, NM 87115; 25-28. NATO Advanced Research Work OH. 505-845-4600; db@ lanl.gov. shop: Asymptotic-Induced Numerical Meth PROGRAM: This conference is part of ods for PDE's, Critical Parameters, and Do a special semester in Geometric Group 10-16. Geschichte der Mathematik, Ober main Decomposition, Beaune, France. (Sep. Theory. wolfach, Federal Republic of Germany. (Feb. 1991, p. 837) ORGANIZING COMMITTEE: R. Charney, 1991, p. 146) 28-30. ICCI '92-Fourth International Con M. Davis, M. Shapiro. 11-13. Fourth SIAM Conference on Opti ference on Computing and Information, CONFERENCE TOPICS: Hyperbolic mization, Chicago, IL. (Feb. 1991, p. 146) Toronto, Canada. (Oct. 1991, p. 1009) groups, automatic and combable groups, 11-15. IUTAM Symposium on Inverse 29-31. Twenty-first International Sympo group actions on R-trees, complexes of Problems in Engineering Mechanics, Tokyo, sium on Multi-Valued Logic, Sendai 980, groups and spaces of non-positive curva Japan. (Sep. 1991, p. 837) Japan. (Jan. 1990, p. 62) ture. 1168 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences INFORMATION: M. Shapiro, Math. Dept., of Chicago; A. Beer, Purdue Univ.; C. GRADUATE SUMMER SCHOOL LEC Ohio State Univ., Columbus, OH 43210; Farhat, Univ. of Colorado, Boulder; P. Fis TURERS: L. Caffarelli (lnst. for Ad email: [email protected]. cher, Brown Univ.; R. Glowinski, Univ. vanced Study), A. Chang (UCLA), R. of Houston; G.H. Golub, Stanford Univ.; Schoen (Stanford), L. Simon (Stanford), 14-20. Fifth International Symposium on W. Gropp, Argonne Nat'l Lab.; D. Keyes, M. Struwe (ETH Zurich). Statistical Decision Theory and Related Top Yale Univ.; Yu. A. Kuznetsov, Moscow; APPLICATIONS: A limited number of ics, Purdue University, West Lafayette, IN. U. Langer, Technical Univ. of Chemitz; fully funded slots will be available in the (Sep. 1990, p. 938) P. Le Tallec, Univ. de Paris Dauphine; three programs open to applicants in 1992. 14-20. Freiformkurven und Freiform P. Leca, ONERA; D. Marini, Univ. di APPLY EARLY! Application forms will ftachen, Oberwolfach, Federal Republic of Genova and I.A.N.-C.N.R.; S.V. Nepom be available after November 15, 1991 by Germany. (Feb. 1991, p. 147) nyaschikh, USSR Academy of Sciences; phone, mail, or email. Recommendation * 15-18. Wave Phenomena II: Modern The J.E. Pasciak, Brookhaven National Lab.; letters will be required for undergraduate ory and Applications, Edmonton, Alberta, J. Periaux, Avions Marcel Dassault; R. and graduate students, and postdoctorates. Canada. Plemmons, Wake Forest Univ.; B. Smith, Applications and recommendation letters Argonne Nat'l Lab.; J. Sun, Academia may be submitted via email. Deadline: INFORMATION: Canadian Applied Mathe Sinica; T. Tezduyar, Minnesota Super February 15, 1992. matics Society Conference, Applied Math computer lnst.; O.B. Widlund, Courant INFORMATION: H. Clemens, Institute Di ematics Institute, Univ. of Alberta, Ed Inst.; J. Xu, Penn State Univ.; D.P. Young, rector, L. Hitchens, Institute Coordina monton, Alberta, Canada T6G 2G 1. The Boeing Co. tor, Summer Geometry Institute, Dept. of CALL FOR PAPERS: Extended abstracts Math., 210 JWB, Univ. of Utah, Salt Lake 15-19. Twenty-first International Confer of a maximum of 1000 words on topics City, Utah 84112; 801-585-3488; Fax: ence on Stochastic Processes and their Ap related to the conference are invited by 801-581-4148; email: [email protected]. plications, Toronto, Canada. (May/Jun. 1990, December 1, 1991. p. 613) INFORMATION: Sixth Domain Decompo 22-25. Seventh Annual IEEE Symposium 15-19. Fourth Conference on Formal sition Conference, I.A.N.-C.N.R., Palazzo on Logic in Computer Science, Santa Cruz, Power Series and Algebraic Combinatorics, dell 'Universita', Corso Carlo Alberto, 5, CA. (Sep. 1991, p. 838) Universite du Quebec a Montreal. (Sep. 1991, 27100 Pavia, Italy; Fax: +39-382-28079; * 22-25. Seventh Annual Conference on p. 837) email: [email protected]. Structure in Complexity Theory, Boston * 15-19. Sixth International Conference on University, Boston, MA. Domain Decomposition Methods in Science 17-20. Fourth International Conference and Engineering, Como, Italy. on Computers and Learning, ICCAL '92, PROGRAM COMMITTEE: D. Barrington, Acadia University, Nova Scotia, Canada. (Feb. G. Brassard, L. Hemachandra, D. Leivant, PROGRAM: The conference will host 1991, p. 147) T. Long, N. Nisan, J. Royer, 0. Watanabe. about 30 invited lectures, as well as CONFERENCE TOPICS: All areas of com about 30 contributed presentations and 21-27. Porous Media, Oberwolfach, Federal putational complexity theory, including: a poster session. Domain decomposition Republic of Germany. (Feb. 1991, p. 147) Structure of complexity classes, relativiza is an increasingly important part of sci tions, independence results, applications of * 21-July 10. Summer Geometry Institute, entific computing. Algorithms based on recursion theory, descriptive complexity, Park City, Utah. this approach have attracted the attention interactive proof systems, cryptographic of many numerical analysts and com SPONSORS: Univ. of Illinois at Chicago, complexity, parallel complexity classes, putational scientists. Parallel computing Univ. of Texas at Austin, Univ. of Utah, and circuit complexity. systems are rapidly becoming more pow Rice Univ., and Univ. of Washington. CALL FOR PAPERS: Send 9 copies of erful and they already offer cost effective PROGRAM: The Institute, sponsored by an extended abstract or a full draft paper alternatives to supercomputers for solving the NSF, is a multi-university endeavor to the program chair: T. Long, Dept. of many problems in the natural and engi to integrate the subject of geometry, from Comp. Sci., New Mexico State Univ., neering sciences. Domain decomposition high school education to advanced re Box 30001/Dept. 3CU, Las Cruces, NM methods appear to offer the best promise search. To this end, the three week insti 88003-0001; Deadline: January 21, 1992. for the effective use of this powerful new tute will bring together geometers from INFORMATION: J. Royer, Dept. of Comp. technology. all sectors of geometry education and re and Inf. Sci., Syracuse Univ., Syracuse, CONFERENCE THEMES: Numerical anal search, in a unique and congenial setting. NY 13244; [email protected]. ysis of domain decomposition, block and The program is designed to foster commu substructuring methods, multilevel meth nication and deeper insight into geometry * 22-26. Fifth International Meeting on ods, domain decomposition for time de at all levels. The conference will consist Statistical Climatology (SIMSC), Toronto, pendent problems, interface conditions of four programs operating concurrently; Canada. for heterogeneous domain decomposition, high school teachers of geometry, under parallel implementation, multibody dy graduate students, graduate students and INFORMATION: F.W. Zwiers, Numeri namics, decomposition methods in micro postdoctorates, and researchers in geome cal Modeling Division, Canadian Climate electronics, environmental sciences, appli try. Centre, 4905 Dufferin St., Downsview, cations in science and engineering. CONFERENCE TOPICS: The topic for Ontario, Canada M3H 5T4. INVITED SPEAKERS: V.I. Agoshkov, Mos the graduate/postdoctorate Summer School * 22-26. Twelfth Conference on Probability cow; R. Bank, Univ. of California, San will be nonlinear partial differential equa and Statistics in the Atmospheric Sciences, Diego; J.H. Bramble, Cornell Univ.; A.B. tions in differential geometry. Topics for Toronto, Canada. Brandt, Weizmann lnst. of Science; C. the research program will be related. Un Canuto, Politecnico di Torino; T.F. Chan, dergraduate topics will continue to cover INFORMATION: P. Mielke, Jr., Dept. of Univ. of California, Los Angeles; M. classical geometry and use of computers Stat., Colorado State Univ., Fort Collins, Dryja, Warsaw Univ.; T. Dupont, Univ. in mathematics. co 80523. NOVEMBER 1991, VOLUME 38, NUMBER 9 1169 Meetings and Conferences * 22-26. The Twelfth Dundee Conference binatorial Computing, Perth, Western Aus 26-August 1. AMS-SIAM Summer Seminar on Ordinary and Partial Differential Equa tralia. on Exploiting Symmetry in Applied and Nu tions, Dundee, Scotland. merical Analysis, Colorado State University, INFORMATION: K. Vijayan, Dept. of Fort Collins, CO. PROGRAM: The purpose of the conference Math., University of Western Australia, is to bring together research workers with WA 6009, Australia; email: vijayan@ INFORMATION: D.L. Salter, AMS, P.O. a common interest in differential equations madvax.maths.uwa.oz.au. Box 6887, Providence, RI 02940. and their applications. The conference will also honor the mathematical contributions * 6-10. Thirty-Sixth Annual Meeting of the Australian Mathematical Society, Perth, that Douglass Jones has made to acous August 1992 tics, electromagnetic theory and general Western Australia. ized functions. Particular attention will be INFORMATION: W.S. Perriman or P.F. August 1992. The International Confer focused on recent developments in the Siew, School: of Math. and Stat., Curtin ence Lobachevsky and Modern Geome theory of nonlinear differential equations Univ. of Technology, Bentley, WA 6102, try devoted to the 200th Anniversary of and their applications to biological phe Australia; email: [email protected]. Lobachevsky's birthday, Kazan, USSR. (Feb. nomena, wave propagation and dynamical 1991, p. 147) systems. 6-31. IMA Summer Program on Environ August 1992. Kinetics of Phase Transi INVITED SPEAKERS: I.D. Abrahams, A.T. mental Studies: Mathematical, Computa tions, International Centre for Mathematical de Hoop, W.N. Everitt, A.V. Holden, D.S. tional, and Statistical Analysis, Institute for Sciences, Edinburgh, Scotland. (Oct. 1991, Jones, M. Lapidus, M.J. Lighthill, D.A. Mathematics and its Applications, University p. 1010) Rand, G.F. Roach, W. Rundell. of Minnesota. (Sep. 1991, p. 838) 2-8. Algebraische Zahlentheorie, Oberwol INFORMATION: R.J. Jarvis, Dept. of Math. 6-August 14. Summer Program in Math fach, Federal Republic of Germany. (Feb. and Comp. Sci., The University, Dundee ematical Physiology, Mathematical Sciences 1991, p. 147) DD1 4HN, Scotland, UK; email: rjjarvis@ Research Institute, Berkeley, CA. (Sep. 1991, uk.ac.dund.mcs. 3-7. Sixth Workshop on Lie-Admissible p. 838) Formulations, Clearwater, FL. (Mar. 1991, 23-26. Homotopy Theory, Sorrento, Italy. 11-18. St. Andrews Colloquium, University p. 244) (Jul./Aug. 1991, p. 645) of St. Andrews, Scotland. (Jul./Aug. 1991, 3-7. Fifth International Meeting of Statis 28-July 4. Hyperbolic Systems of Conser p. 645) tics in the Basque Country, San Sebastin, vation Laws, Oberwo1fach, Federal Republic 12-17. International Colloquium on Spain. (Jul./Aug. 1991, p. 646) of Germany. (Feb. 1991, p. 147) Automata, Languages and Programming, 3-7. Second Meeting of the International 29-30. International Conference on the Vienna, Austria. (Jul./Aug. 1991, p. 645) Linear Algebra Society (ILAS), University Development of Mathematics from 1900 to 12-18. Arithmetic Algebraic Geometry, of Lisbon, Portugal. (Sep. 1991, p. 839) 1950, Luxembourg. (Sep. 1991, p. 838) Oberwolfach, Federal Republic of Germany. 9-15. Jordan-Algebren, Oberwolfach, Fed 29-July 1. Joint Meeting with the London (Feb. 1991, p. 147) eral Republic of Germany. (Feb. 1991, p. 147) Mathematical Society, Cambridge, England. 19-24. SIAM Annual Meeting (SIAM's 13-17. First Colloquium on Numerical INFORMATION: H. Daly, American Math 40th Anniversary), Los Angeles, CA. (Feb. Analysis, Plovdiv, Bulgaria. (Oct. 1991, ematical Society, Post Office Box 6248, 1991, p. 147) p. 1011) Providence, Rhode Island 02940. 19-25. Lower-Dimensional Theories and 16-22. Reelle Analysis, Oberwo1fach, Ger Domain Decomposition Methods in Me many. (Jul./Aug. 1991, p. 646) 29-July 5. Nineteenth International Collo chanics, Oberwolfach, Federal Republic of * 17-21. The Sixth International Confer quium on "Group Theoretical Methods in Germany. (Feb. 1991, p. 147) ence on Boundary and Interior Layers Physics", Salamance, Spain. (May/Jun. 1991, 19-25. Applications of Nonstandard-Analy Computational and Asymptotic Methods p. 476) sis to Analysis, Functional Analysis, and (BAIL VI), Summit County, Colorado. Probability Theory, Heinrich Fabri-Institut CONFERENCE. TOPICS: Stiff systems of der Universitiit Tiibingen, Blaubeuren (Ulm), July 1992 ordinary differential equations, numeri Federal Republic of Germany. (Jul./Aug. cal and asymptotic methods for bound 1-10. Stochastic Analysis Workshop of 1991, p. 645) ary and interior layers, singular perturba Guadeloupe-Silivri, Pointe-a-Pitre, France. 20-24. The Fifth International Conference tions, shocks, multiphase problems, soli (Jul./Aug. 1991, p. 645) on Fibonacci Numbers and their Applica tary waves, bifurcation, chaos, singular 5-11. Mathematische Modellierung und tions, University of St. Andrews, St. Andrews, perturbations in biology, chemistry, con Simulation Elektrischer Schaltungen, Ober Scotland. (May/Jun. 1991, p. 476) trol theory, engineering, mathematics and wolfach, Germany. (Jul./Aug. 1991, p. 645) 20-24. Algorithms for Approximation, physics. 5-August 1. NSF Regional Geometry Insti Cranfield Institute of Technology, Oxford. CALL FOR PAPERS: For papers: Potential tute: Computational Algebraic Geometry, (Sep. 1991, p. 839) contributors must submit an abstract (one page, 500 words maximum) which must Amherst College, Amherst, MA. (Oct. 1991, 20-26. International Conference on Alge clearly state the purpose of the work, the p. 1010) braic Geometry, Universite Paris-Sud. (Please specific results obtained and their signif note date change from Apr. 1991, p. 363) 6-10. European Congress of Mathematics, icance. For sessions: Potential organizers Paris, France. (May/Jun. 1991, p. 476) 26-31. Eighteenth International Sympo must submit the title(s) of the sessions 6-10. Mathematical Conferences in Perth, sium on Rarefied Gas Dynamics (RGD18), they propose. A typical session consists University of Western Australia. (Sep. 1991, University of British Columbia, Vancouver, of six 20-minute papers. p. 838) Canada. (May/Jun. 1991, p. 477) INFORMATION: J. Miller, BAIL Secre * 6-10. Eighteenth Australasian Conference 26-August 1. Variationsrechnung, Ober tariat, 26 Temple Lane, Dublin 2, Ireland; on Combinatorial Mathematics and Com- wolfach, Germany. (Feb. 1991, p. 147) Telefax: (+353-1) 679-2469; Tel: (+353- 1170 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 1) 679-7655; email: [email protected]; 6-12. Topologie, Oberwolfach, Federal Re Federal Republic of Germany. (Feb. 1991, telex: 30547 SHCN EI (Ref: BAll.,). public of Germany. (Feb. 1991, p. 148) p. 148) 8-11. IMA Thtorial: Introduction to Linear 30--November 1. Central Section, Right 17-21. The Alan Day Conference on Lat * Multivariable Control, Optimal Design, and State University, Dayton, OH. tices and Algebras, McMaster University, Parameter Estimation, Institute for Math Hamilton, Ontario, Canada. INFORMATION: W. Drady, American Math· ematics and its Applications, University of ematical Society, P.O. Box 6887, Povi Minnesota. (Sep. 1991, p. 839) PURPOSE: This conference is being held dence, RI 02940. to honor the memory of Dr. Alan Day. The * 9-11. Royal Statistical Society Full Confer- conference will provide an international ence, Sheffield, UK. forum for the exchange of ideas and November 1992 results in lattice theory, universal algebra, INFORMATION: P.J. Diggle, Math. Dept., and related topics. Lancaster Univ., Lancaster LAl 4YF, UK; 1-7. Kombinatorik, Oberwolfach, Federal INVITED SPEAKERS: S. Burris, R. Freese, email: [email protected]. Republic of Germany. (Feb. 1991, p. 148) R. Goldblatt, R. Greechie, C. Herrmann, 13-19. 4-Dimensional Manifolds, Oberwol 8-14. Numerische Integration, Oberwol J. Jezek, E. Kiss, G. McNulty, J.B. Nation, fach, Federal Republic of Germany. (Feb. fach, Federal Republic of Germany. (Feb. P.P. Palfy, D. Pickering, S. Tschantz. 1991, p. 148) 1991, p. 148) INFORMATION: W. Lampe, Dept. of Math., * 9-13. IMA Workshop on Control and Univ. of Hawaii, Honolulu, HI 96822. * 14-18. Twentieth European Meeting of Statisticians, Bath, UK. Optimal Design of Distributed Parameter Systems, Institute for Mathematics and its 17-23. Seventh International Congress on INFORMATION: R. Sibson, School of Applications, University of Minnesota. (Please Mathematical Education (ICME-7), Uni Mathematics, University of Bath, Claver note date change from Sep. 1991, p. 840) versite Laval, Quebec, Canada. (Sep. 1991, ton Down, Bath BA2 7AY, UK. p. 839) 14-16. The Third Biennial Conference of the Allahabad Mathematical Society, Alla 18-22. Third Colloquium on Differential 16-18. Second SIAM Conference on Con habad, India. (May/Jun. 1991, p. 477) Equations, Plovdiv, Bulgaria. (Oct. 1991, trol in the 90s, Minneapolis, MN. (Feb. 1991, p. 1011) p. 148) 15-21. Komplexitatstheorie, Oberwolfach, Federal Republic of Germany. (Feb. 1991, * 19-26. World Congress of Nonlinear Ana 17-19. International Conference on Group p. 148) lysts, Melbourne, FL. (Please note additions Theory, University of Timisoara, Romania. to Nov. 1990, p. 1289) (Jul./Aug. 1991, p. 646) 16--20. International Congress on Numer 20--26. Funktionalgeichungen, Oberwol ical Methods in Engineering and Applied INVITED SPEAKERS: A. Bensoussan, H. fach, Federal Republic of Germany. (Feb. Sciences, University of Concepci6n, Con Brezis, W. Brock, F. Browder, S. Emely 1991, p. 148) cepci6n, Chile. (Jul./Aug. 1991, p. 646) anov, A. Friedman, J. Hale, F. John, G. 21-25. IMA Workshop on Robust Control 16--20. IMA Period of Concentration: Flow Kallianpur, H. Keller, I. Kevrekidis, L. Control, Institute for Mathematics and its Knopoff, P. Kokotovic, M. Krasnosel' skii, Theory, Institute for Mathematics and its Applications, University of Minnesota. (Sep. Applications, University of Minnesota. (Sep. J.-L. Lions, A. Majda, L. Markus, Yu. 1991, p. 840) Mitropolsky, J. Necas, L. Nirenberg, C. 1991, p. 839) Olech, I. Prigogine, P. Rabinowitz, W. 27-0ctober 3. DarstellungstheorieEndlicher 29-December 5. Theory of Large Devia Rheinboldt, R.T. Rockafellar, R. Sagdeev, Gruppen, Oberwolfach, Federal Republic of tions, Oberwolfach, Federal Republic of Ger A. Samarsky, A.N. Shiryaev, V. Skorohod, Germany. (Feb. 1991, p. 148) many. (Feb. 1991, p. 148) S. Smale. CALL FOR PAPERS: Deadline: April 30, 1992. October 1992 The following new announcements will not be repeated until the criteria in the last 22-28. Eighteenth International Congress 4-10. Funktionalanalysis, Oberwo1fach, Fed paragraph in the box at the beginning of of Theoretical and Applied Mechanics, eral Republic of Germany. (Feb. 1991, p. 148) this section are met. Technion-Israel Institute of Technology, Haifa, 11-17. Arbeitsgemeinschaft mit Aktuellem Israel. (Jan. 1991, p. 52) Thema, Oberwolfach, Federal Republic of 1993 23-29. Mathematical Finance, Oberwolfach, Germany. (Feb. 1991, p. 148) Federal Republic of Germany. (Feb. 1991, 12-16. IMA Workshop on Control Systems * 1992-1993. Mittag-Leffler Institute's Aca p. 147) Design for Advanced Engineering Systems: demic Program for 1992-1993: Special Prob 26-28. IMACS RM2S '92 Kobe, Kobe Uni Complexity, Uncertainty, Information, and lems in Mathematical Physics, Djursholm, versity, Kobi, Japan. (May/Jun. 1991, p. 477) Organization, Institute for Mathematics and Sweden. 30--September 5. Komplexe Analysis, Ober its Applications, University of Minnesota. PROGRAM: Emphasis will mainly be on wolfach, Federal Republic of Germany. (Feb. (Sep. 1991, p. 840) SchrOdinger operators. Application dead 1991, p. 147) 16--19. Second SIAM Conference on Dy line for postdoctoral fellowships: April 1, namical Systems, Salt Lake City, UT. (Jul./ 1992 to the Mittag-Leffler Institute, Au Aug. 1991, p. 646) ravligen 17, S-182 62 Djursholm, Sweden. 18-24. Geometrie, Oberwolfach, Federal INFORMATION: A. Jensen, Dept. of Math. Republic of Germany. (Feb. 1991, p. 148) and Comp. Sci., Aalborg Univ., Fr. Bajers September 1992 22-30. Forty-sixth Conference and Con Vej 7, DK-9220 Aalborg, 0, Denmark. September 1992. IMACS· 2nd Interna gress of the International Federation for Information and Documentation, Madrid, tional Conference on System Simulation January 1993 and Scientific Computing-BICSC '92, Bei Spain. (May/Jun. 1991, p. 477) jing, China. (May/Jun. 1991, p. 477) 25-31. Stochastische Analysis, Oberwolfach, * 25-29. IMA Workshop on Robotics, In- NOVEMBER 1991, VOLUME 38, NUMBER 9 1171 Meetings and Conferences stitute for Mathematics and its Applications, INFORMATION: Institute for Mathematics University of Minnesota, Minneapolis, MN. and its Applications, University of Min nesota, 514 Vincent Hall, 206 Church St., June 1993 INFORMATION: Institute for Mathematics S.E., Minneapolis, MN 55455-0436; 612- and its Applications, University of Min * 7-11. IMA Tutorial: Mathematical The 624-6066; FAX: 612-626-7370; email: nesota, 514 Vincent Hall, 206 Church St., ory which Has become an Integral Part of [email protected]. S.E., Minneapolis, MN 55455-0436; 612- Modern Financial Economics, Institute for Mathematics and its Applications, University 624-6066; FAX: 612-626-7370; email: * 12-16. IMA Workshop on Adaptive Con of Minnesota, Minneapolis, MN. ima_staff@ima. umn.edu. trol, Filtering, and Signal Processing, In stitute for Mathematics and its Applications, INFORMATION: Institute for Mathematics University of Minnesota, Minneapolis, MN. and its Applications, University of Min February 1993 nesota, 514 Vincent Hall, 206 Church St., INFORMATION: Institute for Mathematics S.E., Minneapolis, MN 55455-0436; 612- * 1-3. IMA Minisymposium on Biological and its Applications, University of Min 624-6066; FAX: 612-626-7370; email: Control of Movement, Institute for Math nesota, 514 Vincent Hall, 206 Church St., [email protected]. ematics and its Applications, University of S.E., Minneapolis, MN 55455-0436; 612- Minnesota, Minneapolis, MN. 624-6066; FAX: 612-626-7370; email: * 14-18. IMA Workshop on Mathematical INFORMATION: Institute for Mathematics ima_staff@ima. urnn.edu. Finance, Institute for Mathematics and its and its Applications, University of Min Applications, University of Minnesota, Min * 19-20. IMA Minisymposium on Fuzzy nesota, 514 Vincent Hall, 206 Church St., neapolis, MN. Control, Institute for Mathematics and its S.E., Minneapolis, MN 55455-0436; 612- Applications, University of Minnesota, Min INFORMATION: Institute for Mathematics 624-6066; FAX: 612-626-7370; email: neapolis, MN. and its Applications, University of Min [email protected]. nesota, 514 Vincent Hall, 206 Church St., INFORMATION: Institute for Mathematics S.E., Minneapolis, MN 55455-0436; 612- * 16-25. IMA Workshop on Nonsmooth and its Applications, University of Min 624-6066; FAX: 612-626-7370; email: Analysis and Geometric Methods in Con nesota, 514 Vincent Hall, 206 Church St.. [email protected]. trol, Institute for Mathematics and its Appli S.E., Minneapolis, MN 55455-0436; 612- cations, University of Minnesota, Minneapo 624-6066; FAX: 612-626-7370; email: lis, MN. [email protected]. August 1993 INFORMATION: Institute for Mathematics and its Applications, University of Min * 9-12. Joint Statistical Meetings, San Fran- nesota, 514 Vincent Hall, 206 Church St., cisco, CA. May 1993 S.E., Minneapolis, MN 55455-0436; 612- INFORMATION: American Statistical As 624-6066; FAX: 612-626-7370; email: * 3-7. IMA Tutorial: Verification Issues in sociation, 1429 Duke St., Alexandria, VA ima_staff@ima. urnn.edu. Discrete Event Systems, as well as Perfor 22314-3402. mance and Control, Institute for Mathematics and its Applications, University of Minnesota, * 25-September 3. Forty-ninth Biennial Ses March 1993 Minneapolis; MN. sion of the International Statistical Institute, Firenze, Italy. * 15-19. IMA Workshop on Systems and INFORMATION:' Institute for Mathematics Control Theory for Power Systems, Insti and its Applications, University of Min INFORMATION: lSI Permanent Office, 428 tute for Mathematics and its Applications, nesota, 514 Vincent Hall, 206 Church St., Prinses Beatrixlaan, P.O. Box 950, 2270 University of Minnesota, Minneapolis, MN. S.E., Minneapolis, MN 55455-0436; 612- AZ Voorburg, Netherlands. 624-6066; FAX: 612-626-7370; email: INFORMATION: Institute for Mathematics [email protected]. and its Applications, University of Min October 1993 nesota, 514 Vincent Hall, 206 Church St., * 10-14. IMA Workshop on Discrete Event 3-11. The International Congress of Math S.E., Minneapolis, MN 55455-0436; 612- Systems, Manufacturing Systems, and Com ematicans 1994, ZUrich, Switzerland. (Mar. 624-6066; FAX: 612-626-7370; email: munication Networks, Institute for Mathe 1991, p. 244) [email protected]. matics and its Applications, University of Minnesota, Minneapolis, MN. March 1995 April1993 INFORMATION: Institute for Mathematics and its Applications, University of Min 24-25. Central Section, DePaul University, *5-9. IMA Tutorial: Design and Analysis of nesota, 514 Vincent Hall, 206 Church St., Chicago, IL. Adaptive Systems, Institute for Mathematics S.E., Minneapolis, MN 55455-0436; 612- and its Applications, University of Minnesota, 624-6066; FAX: 612-626-7370; email: INFORMATION: W.S. Drady, AMS~ P.O. Minneapolis, MN. ima_staff@ima. urnn.edu. Box 6887, Providence, RI 02940. 1172 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications the historical development of the theory of subfactors and the A MANUAL FOR TRANSLATORS OF ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and MATHEMATICAL RUSSIAN, REVISED Kauffman polynomials, introduces statistical mechanical methods EDITION on knot diagrams, and attempts an analogy with conformal field S. H. Gould theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected Revised Edition Edited by R. P. Boas interconnections between different parts of mathematics and This manual is intended for mathematicians who are fairly physics. well acquainted with Russian and have a need to translate Contents into English. Both of the editors worked mathematical materials von Neumann algebras; Group actions and subfactors; Values of the in the process of their extensively with such translations and, index, Virasoro algebra; Construction of examples, further structure; The both grammatical and stylistic, work, kept records of problems, braid group and its representations; Knots and links; The knot polynomial up. The main part of the booklet presents that commonly turned VL; Knots and statistical mechanics; The algebraic approach. typical examples: First the Russian text is given, then the faulty translation, an acceptable translation, and usually some 1991 Mathematics Subject Classifications: 16S99, 46L 10, 57M25, comments. Although such a manual cannot be exhaustive, it 81P05,81R10;46L37,46L40,57M15,81T05. does deal with many common mistakes and misconceptions. The ISBN 0-8218-0729-3, LC 91-24438, ISSN 0160-7642 examples are taken from the mathematical literature, making 113 pages (softcover), November 1991 All individuals $26, List price $43 interest to mathematicians; however, it the manual of particular To order, please specify CBMS/80N should also be useful to physicists, chemists, engineers, and anyone else concerned with the translation of scientific Russian into English. SCATTERING AND APPLICATIONS Contents INVERSE David Sattinger, Editor Introduction; Part One: General remarks on grammar and style; Part (Contemporary Mathematics, Volume 122) Two: Russian words and phrases; Part Three: English words and phrases; English index; Russian index; Cyrillic transliteration table. This book contains the proceedings of an AMS-IMS-SIAM Summer Institute on Inverse Scattering and Applications, held 1991 Mathematics Subject Classifications: 01-00; OOA20 1990. The papers cover ISBN 0-8218-0172-4, LC 91-20605 in Amherst, Massachusetts in June 42 pages (softcover), December 1991 the current state of the art in inverse conductivity problems, Individual member $12, List price $20, applications of inverse scattering theory to integrable systems, Institutional member $16 three-dimensional inverse scattering, inverse monodromy To order, please specify MTR/N problems, and nonlinear waves, among other topics. Intended for researchers working in inverse scattering theory, inverse conductance problems, and completely integrable systems, this book presents results by some of the major experts in the field. KNOTS SUBFACTORS AND Contents Vaughan Jones T. Aktosun and C. van der Mee, Wiener-Hopf factorization in Number 80 (CBMS Regional Conference Series, multidimensional inverse Schrodinger scattering; R. Beals and D. Supported by the National Science Foundation) Sattinger, Complete integrability of "Completely Integrable" systems; This book is based on a set of lectures presented by the R. Carroll, On the determinant theme for tau functions, Grassmannians, author at the NSF-CBMS Regional Conference, Applications of and inverse scattering; M. Cheney and D. Isaacson, An overview Operator Algebras to Knot Theory and Mathematical Physics, of inversion algorithms for impedance imaging; H. Frahm, On the held at the U.S. Naval Academy in Annapolis in June 1988. construction of integrable XXZ Heisenberg models with arbitrary The audience consisted of low-dimensional topologists and spin; G. F. Helminck, A geometric construction of solutions of matrix operator algebraists, so the speaker attempted to make the hierarchies; R. Herman, Lax pairs, recursion operators, and the material comprehensible to both groups. He provides an perturbation of nonlinear evolution equations; A. R. Its, A. G. lzergin, extensive introduction to the theory of von Neumann algebras and V. E. Korepin, Time and temperature dependent correlation function and to knot theory and braid groups. The presentation follows of an impenetrable Bose gas field correlator in the impenetrable Bose Use the order form in the back of this issue or call 800-321-4AMS (800-321-4267) in the U.S. and Canada to use VISA or MasterCard. NOVEMBER 1991, VOLUME 38, NUMBER 9 1173 New AMS Publications gas; S. Klchenassamy, Breathers and the sine-Gordon equation; study investigates a number of new features of this relation B. G. Konopelchenko and V. G. Dubrovsky, Localized solitons for and its generalization to multicyclic permutations (modelling the lshimori equation; J. Palmer, Tau functions; J. Sylvester and G. finite unions of periodic orbits) and combinatorial patterns Uhlmann, Inverse problems in anisotropic media; S. Venakides, The (modelling finite invariant sets). A central theme is the role of Toda shock problem. reductions and extensions of permutations. Results include: (i) a "combinatorial shadowing theorem" and its application to 1991 Mathematics Subject Classifications: 34B25, 35P25, 35R30 approximating permutations by cycles in the forcing relation; ISBN 0-8218-5129-2, LC 91-26094, ISSN 0271-4132 133 pages (softcover), November 1991 (ii) the distribution of different representatives of a given cycle in Individual member $25, List price $41, one (adjusted) map; (iii) characterization of the forcing-maximal Institutional member $33 permutations and patterns of fixed degree; and (iv) a calculation To order, please specify CONM/122N of the asymptotic growth rate of the maximum entropy forced by a permutation of given degree. Contents DIFFERENTIAL OPERATORS AND HIGHEST Adjusted maps; Equivalence and essential patterns; Reductions WEIGHT REPRESENTATIONS and extensions of patterns; Irreducible patterns and Markov graphs; Mark G. Davidson, Thomas J. Enright, and Horseshoe patterns and fold type; Extensions of cycles; Combinatorial Ronald J. Stanke shadowing; Transitive patterns; Representatives of cycles; Forcing and (Memoirs of the AMS, Number 455) degree; Entropy estimates. This work concerns the representation theory of semisimple 1991 Mathematics Subject Classifications: 58F20, 54 H20, 26A18 Lie groups. From the algebraic perspective, the theory of ISBN 0-8218-2513-5, LC 91-27263, ISSN 0065-9266 unitarizable highest weight modules is highly developed. The 120 pages (softcover), November 1991 classification was given in 1981, and, more recently, even Individual member $13, List price $21, the character and nilpotent cohomology formulas have been Institutional member $17 determined for G of classical type. However, from the analytic To order, please specify MEM0/456N point of view, as originally presented by Harish-Chandra, unitarizable highest weight modules occur as subspaces of certain spaces of vector-valued polynomials, or, equivalently, as subspaces of holomorphic sections for vector bundles on MULTIPLICATIVE HOMOLOGY OPERATIONS GjK. The main results of this book offer characterizations of AND TRANSFER unitary highest weight representations as solutions to systems of Norihiko Minami differential operators. (Memoirs of the AMS, Number 457) Contents In this work, the author presents a completely new treatment Vector bundles and algebraic conventions; Conjugate pairings and 0 reproducing kernels; t -irreducibility of the system of differential operators; of the homology operations QS . This approach employs the p +-cohomology for the exceptional groups; Notational conventions Burnside rings and produces results that are much sharper and a lemma; The cone decomposition; The oscillator representation, than previous results. As an application, the author improves harmonic polynomials and associated affine varieties; Young products Tsuchiya's claim and generalizes Priddy's multiplicative and a refinement of the factorization theorem; The fundamental system Kahn-Priddy theorem to apply to any prime. of differential operators; Explicit forms of the systems of differential 1991 Mathematics Subject Classifications: 55P47, 55P91, 55S12 operators for the classical groups; The ladder representation examples; ISBN 0-8218-2518-6, LC 91-28757, ISSN 0065-9266 Kc -orbits in p + and the Wallach representations. 80 pages (softcover), November 1991 1991 Mathematics Subject Classifications: 22E45, 22E47; 20G05, Individual member $11, List price $18, 32M15 Institutional member $14 ISBN 0-8218-2509-7, LC 91-27804, ISSN 0065-9266 To order, please specify MEM0/457N 108 pages (softcover), November 1991 Individual member $12, List price $20, Institutional member $16 To order, please specify MEM0/455N LVAPUNOV THEOREMS FOR OPERATOR ALGEBRAS Charles A. Akemann and Joel Anderson COMBINATORIAL PATTERNS FOR MAPS (Memoirs of the AMS, Number 458) OF THE INTERVAL In 1940, A. A. Lyapunov published his celebrated discovery Michal Misiurewicz and Zbigniew Nitecki that the range of a nonatomic vector-valued measure is convex (Memoirs of the AMS, Number 456) and compact, This book presents the result of a systematic generalization of Lyapunov's theorem to the setting of operator In recent years, motivated by Sharkovskii's theorem, algebras. The authors' point of view follows that of Lindenstrauss, researchers have realized that a good deal of information about so that, in their terminology, Lyapunov's theorem asserts that the dynamics of a map on the interval can be deduced from the if 'I' is a weak* continuous map of a nonatomic abelian von combinatorial structure of its periodic orbits. This data can be Neumann algebra.#' into C n, and B denotes the positive part formulated as a "forcing" relation between cyclic permutations of the unit ball of .AI; then for each a E B there is an extreme (representing "orbit types" of periodic orbits). The present point p of B (i.e., a projection) with 'I' (p) = qi (a). We begin 1174 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications by studying an affine map 'I' of a convex subset Q of a linear I •: lBIIIJll space,2'into a linear space)': If 'I'(E) = 'I'(Q), where E NONLINEAR SECOND-ORDER PARTIAL denotes the extreme points of Q, we say a Lyapunov theorem of type 1 holds. lf$fis a normed space, we say a Lyapunov theorem DIFFERENTIAL EQUATIONS of type 2 (r~sp. type 3) holds if 'I' (E) is norm dense (resp. Guangchang Dong E-dense) in 'I' (Q). Roughly speaking, a Lyapunov theorem of (Translations of Mathematical Monographs, Volume 95) type 4 asserts that 'I' maps at least one element of E "away This book addresses a class of equations central to many from the boundary." Results of all four types are obtained. In areas of mathematics and its applications. Although there is no some cases (notably, when2'is a nonatomic von Neumann routine way of solving nonlinear partial differential equations, algebra), Q may be a face of B, or the entire unit ball of 2'. effective approaches which apply to a wide variety of problems If'¥ is a singular map and2'is a purely infinite, countably are available. This book addresses a general approach that decomposable von Neumann algebra, then the range of 'I' consists of the following: Choose an appropriate function space, may be infinite-dimensional. define a family of mappings, prove this family has a fixed Contents point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori An abstract Lyapunov theorem; Lyapunov theorems for nonatomic estimates. By focusing on a particular approach that has proven von Neumann algebras; Lyapunov theorems for C.* -algebras; useful in solving a broad range of equations, this book makes a Lyapunov theorems for atomic von Neumann algebras; Simultaneous useful contribution to the literature. approximations; Lyapunov theorems for singular maps; Noncommutative Contents range; Applications to the paving problem. The first boundary value problem for second-order quasilinear parabolic equations with principal part in divergence form; A periodic boundary 1991 Mathematics Subject Classifications: 46L05, 46L30, 46L1 0; 28B05, value problem for a nonlinear telegraph equation; The initial value 46B99,46G10,49E15,52A20,60A10,93C15 problem for a nonlinear Schrodinger equation; Multi-dimensional ISBN 0-8218-2516-X, LC 91-28168, ISSN 0065-9266 subsonic flows around an obstacle; The initial-boundary value problem for 96 pages (softcover), November 1991 Individual member $11, List price $19, degenerate quasilinear parabolic equations; The speed of propagation of Institutional member $15 the solution of a degenerate quasilinear parabolic equation; Aleksandrov To order, please specify MEM0/458N and Bony maximum principles for parabolic equations; The density theorem and its applications; Fully nonlinear parabolic equations; Fully nonlinear parabolic equations (continued). 1991 Mathematics Subject Classifications: 35K, 35L FINITENESS THEOREMS FOR LIMIT CYCLES ISBN 0-8218-4554-3, LC 91-27853, ISSN 0065-9282 Yu. S. ll'yashenko 251 pages (hardcover), November 1991 (Translations of Mathematical Monographs, Volume 94) Individual member $82, List price $136, Institutional member $109 To order, please specify MMON0/95N This book is devoted to the following finiteness theorem: A polynomial vector field on the real plane has a finite number of limit cycles. To prove the theorem, it suffices to note that limit cycles cannot accumulate on a polycycle of an analytic vector COMBINED MEMBERSHIP LIST field. This approach necessitates investigation of the monodromy transformation (also known as the Poincare return mapping or This CML is a comprehensive directory of the membership the first return mapping) corresponding to this cycle. To carry out of the AMS, the Mathematical Association of America, and this investigation, this book utilizes five sources: The theory of the Society for Industrial and Applied Mathematics. The list is Dulac, use of the complex domain, resolution of singularities, the distributed on request as a privilege of membership to AMS geometric theory of normal forms, and superexact asymptotic members in even-numbered years and the MAA members in series. In the introduction, the author presents results about this odd-numbered years. The CML is an invaluable reference for problem that were known up to the writing of the present book, keeping in touch with colleagues and for making connections in with full proofs (except in the case of results in the local theory the mathematical sciences community in the United States and and theorems on resolution of singularities). abroad. There are two lists of individual members. The first is Contents a complete alphabetical list of all members in all three organizations. For each member, the CML provides his or her Decomposition of a monodromy transformation into terms with address, title, department, institution, and telephone number (if noncomparable rates of decrease; Function-theoretic properties of available), electronic address (if indicated), and also indicates the regular functional cochains; The Phragmen-Lindelof theorem for regular mathematical organizations to which the individual belongs. The functional cochains; Superexact asymptotic series; Ordering of functional second lists individual members according to their geographic cochains on a complex domain. locations. In addition, the CML lists all academic and institutional members and provides addresses and telephone numbers of 1991 Mathematics Subject Classifications: 34-02, 34C05; 34C20, 34C35, mathematical sciences departments. 57R25, 14E15,41A60 1991 Mathematics Subject Classification: 00 ISBN 0-8218-4553-5, LC 91-27411, ISSN 0065-9282 ISBN 0-8218-0170-8 288 pages (hardcover), November 1991 584 pages (softcover), November 1991 Individual member $118, List price $196, Individual member $27, List price $45, Institutional member $157 Institutional member $36 To order, please specify MMON0/94N To order, please specify CMU91/92N NOVEMBER 1991, VOLUME 38, NUMBER 9 1175 New AMS Publications SOCIETE MATHEMATIQUE DE FRANCE, ASTERISQUE PRIVILEGE NUMERIQUE UNIFORME (Asterisque, Number 194-195) The AMS distributes Asterisque only in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF, Ecole Normale This book examines a uniform bound for particular solutions Superieure, Tour L, 1 rue Maurice Arnoux, 92120 Montrouge, France, of linear systems with complex analytic coefficients defined or to OFFILIB, 48 rue Gay-Lussac, 75240 Paris Cedex 05, France. on a domain of CP. The bound is given in terms of the norm Individual members of either AMS or SMF are entitled to the member of the right hand side, on a compact disk varying in the price. (ISSN 0303-1179) domain of definition of the coefficients. This is equivalent to a "uniform and numerical" version of Douady's privilege theory. The tools used are a "uniform and numerical" version of Hironaka's division theorem, the semi-continuity of Newton's ALGORITHMIQUE, TOPOLOGIE, ET diagram, and the related stratification. An appendix sketches an application to a generalization of Serre's "GAG/Ji' theorem for GEOMETRIE ALGEBRIQUES non-proper algebraic varieties, which makes use of a "moderate" Claude Hayat Legrand and Francis cohomology defined in the book. Sergeraert, Editors (Asterisque, Number 192) Contents This book contains papers presented during the International Relations d'ordre et filtres associes; Variation des exposants privilegies; Congress of Sevilla, held in August-September 1987, and during Theoreme de division numerique uniforme par un ideal; Theoreme the Colloquium of Toulouse in December 1988. The papers focus de privilege numerique uniforme; Appendice 1-Fonctions moderees; on recent results in algorithmic problems arising in algebraic Appendice II-Theoreme de privilege numerique uniforme pour un geometry and algebraic topology. morphisme de modules coherents; Appendice 111-Cohomologie moderee Contents et "GAGA" non propre. Mitsuyuki Ochiai, Nontrivial projections of the trivial knot; Felice Ronga, Recherche de solutions d'inequations polynomiales; Marie-Fran9olse 1991 Mathematics Subject Classification: 32 Roy, Computation of the topology of a real curve; Julio Rubio et ISSN 0303-1179 Francis Sergeraert, Supports acycliques et a/gorithmique; Francis 368 (softcover), 1991 Individual AMS or SMF member $37, List price $53 Sergeraert, Functional coding and effective homology; Katsuyuki To order, please specify AST/194/195N Shibata, Micro-computer Prolog as a handy tool for formal algebraic computations; Martin C. Tangora, Computing with the lambda algebra. 1991 Mathematics Subject Classifications: 14, 55, 57 ISSN 0303-1179 94 (softcover), 1991 Individual AMS or SMF member $9, List price $13 To order, please specify AST/192N e-MATH is a node on the INTERNET providing mathematicians with the ability to electronically communicate with a central information source. e-MATH offers a searchable, on-line Combined Membership List; a professional register for employment and postdoctoral opportunities; a repository of AMS-supported TEX software; the new Mathematical Reviews classification scheme and more. To successfully connect toe-MATH, you need: • A connection to an INTERNET host; • VT100 connectivity in communications software and host operating system; • Terminal tabs set at every eight columns. To access e-MATH: telnet e-math.ams.com (or telnet 130.44.1.100). Login and password are e-math. 1176 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications Bylaws of the American Mathematical Society Article I Article III Officers Committees Section 1. There shall be a president, a president-elect Section 1. There shall be nine editorial committees as (during the even-numbered years only), an ex-president follows: committees for the Bulletin, for the Proceedings, (during the odd-numbered years only), three vice-presidents, for the Colloquium Publications, for the Journal, for Mathe a secretary, four associate secretaries, a treasurer, and an matical Surveys and Monographs, for Mathematical Reviews; associate treasurer. a joint committee for the Transactions and the Memoirs; a Section 2. It shall be a duty of the president to deliver committee consisting of the representatives of the Society an address before the Society at the close of the term of on the Board of Editors of the American Journal of Mathe· office or within one year thereafter. matics; and a committee for Mathematics of Computation. Section 2. There shall be a Science Policy Committee. Article II Section 3. There shall be a communications committee Board of Trustees called the Committee to Monitor Problems in Communica tion. Section 1. There shall be a Board of Trustees consisting Section 4. The size of each committee shall be deter of eight trustees, five trustees elected by the Society in mined by the Council.. accordance with Article VII, together with the president, the treasurer, and the associate treasurer of the Society ex officio. The Board of Trustees shall designate its own Article IV presiding officer and secretary. Council Section 2. The function of the Board of Trustees shall be to receive and administer the funds of the Society, to Section 1. The Council shall consist of fifteen members have full legal control of its investments and properties, at-large and the following ex officio members: the officers of to make contracts, and, in general, to conduct all business the Society specified in Article I, except that it shall include affairs of the Society. only one associate secretary, the chairman of each of the Section 3. The Board of Trustees shall have the power editorial committees and of the communications committee to appoint such assistants and agents as may be necessary and of the Science Policy Committee, any former secretary or convenient to facilitate the conduct of the affairs of for a period of two years following the terms of office, the Society, and to fix the terms and conditions of their and members of the Executive Committee (Article V) who employment. The Board may delegate to the officers of remain on the Council by the operation of Article VII, the Society duties and powers normally inhering in their Section 4. respective corporative offices, subject to supervision by the The chairman of any committee designated as a Coun Board. The Board of Trustees may appoint committees cil member may name a deputy from the committee as to facilitate the conduct of the financial business of the substitute. The associate secretary shall be the one charged Society and delegate to such committees such powers as with the scientific program of the meeting at which the may be necessary or convenient for the proper exercise of Council meets except that at a meeting associated with no those powers. Agents appointed, or members of committees scientific meeting of the Society the secretary may designate designated, by the Board of Trustees need not be members the associate secretary. of the Board. Section 2. The Council shall formulate and administer Nothing herein contained shall be construed to empower the scientific policies of the Society and shall act in an the Board of Trustees to divest itself of responsibility for, or advisory capacity to the Board of Trustees. legal control of, the investments, properties, and contracts Section 3. In the absence of the secretary from any of the Society. meeting of the Council, a member may be designated NOVEMBER 1991, VOLUME 38, NUMBER 9 11n Bylaws of the American Mathematical Society as acting secretary for the meeting, either by written discussed by the Council. authorization of the secretary, or, failing that, by the presiding If, at a meeting of the Council, there are present twelve officer. members, then the prior notification to the secretary may be Section 4. All members of the Council shall be voting waived by unanimous consent. In such a case, a unanimous members. Each member, including deputies and the desig favorable vote by those present shall empower the Council nated associate secretary, shall have one vote. The method to speak in the name of the Society. for settling matters before the Council at any meeting shall The Council may also refer the matter to a referendum by be by majority vote of the members present. If the result of mail of the entire membership of the Society, and shall make a vote is challenged, it shall be the duty of the presiding such reference if a referendum is requested, prior to final officer to determine the true vote by a roll call. In a roll call action by the Council, by two hundred or more members. vote, each Council member shall vote only once (although The taking of a referendum shall act as a stay upon Council possibly a member of the Council in several capacities). action until the votes have been canvassed, and thereafter Section 5. Any five members of the Council shall no action may be taken by the Council except in accordance constitute a quorum for the transaction of business at any with a plurality of the votes cast in the referendum. meeting of the Council. Section 6. Between meetings of the Council, business Article V may be transacted by a mail vote. Votes shall be counted as specified in Section 4 of this Article, "members present" Executive Committee being replaced by "members voting." An affirmative vote Section 1. There shall be an Executive Committee of by mail on any proposal shall be declared if, and only if, the Council, consisting of four elected members and the (a) more than half of the total number of possible votes following ex officio members: the president, the secretary, is received by the time announced for the closing of the the president-elect (during even-numbered years), and the polls, and (b) at least three-quarters of the votes received ex-president (during odd-numbered years). by then are affirmative. If five or more members request Section 2. The Executive Committee of the Council postponement at the time of voting, action on the matter shall be empowered to act for the Council on matters at issue shall be postponed until the next meeting of the which have been delegated to the Executive Committee by Council, unless either (1) at the discretion of the secretary, the Council. If three members of the Executive Committee the question is made the subject of a second vote by mail, request that any matter be referred to the Council, the matter in connection with which brief statements of reason, for and shall be so referred. The Executive Committee shall be against, are circulated; or (2) the Council places the matter responsible to the Council and shall report its actions to the at issue before the Executive Committee for action. Council. It may consider the agenda for meetings of the Section 7. The Council may delegate to the Executive Council and may make recommendations to the Council. Committee certain of its duties and powers. Between meet Section 3. Each member of the Executive Committee ings of the Council, the Executive Committee shall act for shall have one vote. An affirmative vote on any proposal the Council on such matters and in such ways as the Council before the Executive Committee shall be declared if, and may specify. Nothing herein contained shall be construed as only if, at least four affirmative votes are cast for the empowering the Council to divest itself of responsibility for proposal. A vote on any proposal may be determined at a formulating and administering the scientific policies of the meeting of the Executive Committee, but it shall not be Society. necessary to hold a meeting to determine a vote. Section 8. The Council shall also have power to speak in the name of the Society with respect to matters affecting the Article VI status of mathematics or mathematicians, such as proposed or enacted federal or state legislation; conditions of employment Executive Director in universities, colleges, or business, research or industrial Section 1. There shall be an Executive Director who organizations; regulations, policies, or acts of governmental shall be a paid employee of the Society. The Executive agencies or instrumentalities; and other items which tend to Director shall have charge of the central office of the Society, affect the dignity and effective position of mathematics. and shall be responsible for the general administration of With the exception noted in the next paragraph, a the affairs of the Society in accordance with the policies favorable vote of two-thirds of the entire membership of that are· set by the Board of Trustees and by the Council. the Council shall be necessary to authorize any statement Section 2. The Executive Director shall be appointed in the name of the Society with respect to such matters. by the Board of Trustees with the consent of the Council. With the exception noted in the next paragraph, such a vote The terms and conditions of employment shall be fixed by may be taken only if written notice shall have been given the Board of Trustees. to the secretary by the proposer of any such resolution not Section 3. The Executive Director shall work under later than one month prior to the Council meeting at which the immediate direction of a committee consisting of the the matter is to be presented; and the vote shall be taken president, the secretary, and the treasurer, of which the not earlier than one month after the resolution has been president shall be chairman ex officio. The Executive Director 1178 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Bylaws of the American Mathematical Society shall attend meetings of the Board of Trustees, the Council, Executive Committee (see Article V, Section 1) shall be and the Executive Committee, but shall not be a member eligible for election to the Executive Committee. In case of any of these bodies. The Executive Director shall be a a member is elected to the Executive Committee for a voting member of the Committee to Monitor Problems in term extending beyond the regular term on the Council, Communication but shall not be its chairman. that person shall automatically continue as a member of the Council during the remainder of that term on the Executive Committee. Article Vll Section 5. The president and vice-presidents shall not be Election of Officers and Terms of Office eligible for immediate re-election to their respective offices. Section 1. The term of office shall be one year in the A member-at-large or an ex officio member of the Council case of the president-elect and the ex-president; two years shall not be eligible for immediate election (or re-election) in the case of the president, the secretary, the associate as a member-at-large of the Council. secretaries, the treasurer, and the associate treasurer; three Section 6. If the president of the Society should die years in the case of vice-presidents and members-at-large of or resign while a president-elect is in office, the president the Council, one vice-president and five members-at-large elect shall serve as president for the remainder of the year retiring annually; and five years in the case of the trustees. and thereafter shall serve the regular two-year term. If the In the case of members of the editorial committees and president of the Society should die or resign when no appointed members of the communications committees, the president-elect is in office, the Council, with the approval term of office shall be determined by the Council. The term of the Board of Trustees, shall designate one of the vice of office for elected members of the Executive Committee presidents to serve as president for the balance of the regular shall be four years, one of the elected members retiring presidential term. If the president-elect of the Society should annually. All terms of office shall begin on February 1 die or resign before becoming president, the office shall and terminate on January 31 with the exception that the remain vacant until the next regular election of a president officials specified in Articles I, II, ill, N, and V (excepting elect, and the Society shall, at the next annual meeting, the president-elect and ex-president) shall continue to serve elect a president for a two-year term. If the ex-president until their successors have been duly elected or appointed should die or resign before expiration of the term of office, and qualified. the Council, with the approval of the Board of Trustees, Section 2. The president-elect, the vice-presidents, the shall designate a former president of the Society to serve as trustees, and the members-at-large of the Council shall be ex-president during the remainder of the regular term of the elected by written ballot. An official ballot shall be sent to ex-presidency. Such vacancies as may occur at any time in each member of the Society by the secretary on or before the group consisting of the vice-presidents, the secretary, the October 10, and such ballots, if returned to the secretary in associate secretaries, the treasurer, and the associate treasurer envelopes bearing the name of the voter and received within shall be filled by the Council with the approval of the Board thirty days, shall be counted. Each ballot shall contain one of Trustees. If a member of an editorial or communications or more names proposed by the Council for each office committee should take temporary leave from duties, the to be filled, with blank spaces in which the voter may Council shall then appoint a substitute. The Council shall substitute other names. A plurality of all votes cast shall be fill from its own membership any vacancy in the elected necessary for election. In case of failure to secure a plurality membership of the Executive Committee. for any office, the Council shall choose by written ballot Section 7. If any eleCted trustee should die while in among the members having the highest number of votes. office or resign, the vacancy thus created shall be filled for The secretary, the associate secretaries, the treasurer, and the the unexpired term by the Board of Trustees. associate treasurer shall be appointed by the Council in a Section 8. If any member-at-large of the Council should manner designated by the Council. Each committee named die or resign more than one year before the expiration of in Article III, Section 1 or 3, shall be appointed by the the term, the vacancy for the unexpired term shall be filled Council in a manner designated by the Council. Each such by the Society at the next annual meeting. committee shall elect one of its members as chairman in a Section 9. In case any officer should die or decline to manner designated by the Council. serve between the time of election and the time to assume Section 3. The president becomes ex-president at the office, the vacancy shall be filled in the same manner as if end of the term of office and the president-elect becomes that officer had served one day of the term. president. Section 4. On or before February 15, the secretary shall Article VIII send to all members of the Council for a mail vote a ballot Members and Their Election containing two names for each place to be filled on the Executive Committee. The nominees shall be chosen by Section 1. Election of members shall be by vote of the a committee appointed by the president. Members of the Council or of its Executive Committee. Council may vote for persons not nominated. Any member Section 2. There shall be four classes of members, of the Council who is not an ex officio member of the namely ordinary, contributing, corporate, and institutional. NOVEMBER 1991, VOLUME 38, NUMBER 9 1179 Bylaws of the American Mathematical Society Section 3. Application for admission to ordinary mem dues and with membership extending over at least twenty bership shall be made by the applicant on a blank provided years may, by giving proper notification to the secretary, by the secretary. Such applications shall not be acted upon have dues remitted. Such a member shall receive the No until at least thirty days after their presentation to the tices and may request to receive Bulletin as privileges of Council (at a meeting or by mail), except in the case of membership during each year until membership ends. members of other societies entering under special action of Section 9. An ordinary or contributing member shall the Council approved by the Board of Trustees. receive the Notices and Bulletin as privileges of membership Section 4. An ordinary member may become a con during each year for which dues have been discharged. tributing member by paying the dues for such membership. Section 10. The annual dues of ordinary, contributing, (See Article IX, Section 3.) and corporate members shall be due by January 1 of the Section 5. A university or college, or a firm, corporation, year to which they apply. The Society shall submit bills for or association interested in the support of mathematics may dues. If the annual dues of any member remain undischarged be elected a corporate or an institutional member. beyond what the Board of Trustees deems to be a reasonable time, the name of that member shall be removed from the list of members after due notice. A member wishing Article IX to discontinue membership at any time shall submit a Dues and Privileges ofMembers resignation in writing to the Society. Section 1. Any applicant shall be admitted to ordinary Section 11. Any person who has attained the age of membership_ immediately upon election by the Council 62 and has been a member for at least twenty years may (Article VITI) and the discharge within sixty days of election become a life member by making a single payment equal to of the first annual dues. Dues may be discharged by payment five times the dues of an ordinary member for the coming or by remission when the provision of Section 7 of this year. Insofar as there is more than one level of dues for Article is applicable. The first annual dues shall apply to ordinary membership, it is the highest such dues that shall be the year of election, except that any applicant elected after used in the calculation, with the exception for members by August 15 of any year may elect to have the first annual reciprocity noted in the following paragraph. A life member dues apply to the following year. is subsequently relieved of the obligation of paying dues. Section 2. The annual dues of an ordinary member of The status and privileges are those of ordinary members. the Society shall be established by the Council with the (This section does not affect those persons who became approval of the Trustees. The Council, with the approval of life members before October 25, 1941. They remain life the Trustees, may establish special rates in exceptional cases members with the status and privileges of ordinary members. and for members of an organization with which the Society When the class of them is empty, this parenthetical remark has a reciprocity agreement. is to be removed.) Section 3. The minimum dues for a contributing mem A member of the Society by reciprocity who has reached ber shall be three-halves of the dues of an ordinary member the age of 62, has been a member for at least 20 years, per year. Members may, upon their own initiative, pay larger has been a member by reciprocity for at least 15 of those dues. 20 years and asserts the intention of continuing to be a Section 4. The minimum dues of an institutional mem member by reciprocity may purchase a life membership by ber shall depend on the scholarly activity of that member. a one-time payment of a special rate established by the The formula for computing these dues shall be established Council, with the approval of the Trustees. from time to time by the Council, subject to approval by the Board of Trustees. Institutions may pay larger dues than the Article X computed minimum. Section 5. The privileges of an institutional member Meetings shall depend on its dues in a manner to be determined by Section 1. The annual meeting of the Society shall be the Council, subject to approval by the Board of Trustees. held between the fifteenth of December and the tenth of These privileges shall be in terms of Society publications to February next following. Notice of the time and place of be received by the institution and of the number of persons this meeting shall be mailed by the secretary or an associate it may nominate for ordinary membership in the Society. secretary to the last known post office address of each Section 6. Dues and privileges of corporate members of member of the Society. The times and places of the annual the Society shall be established by the Council subject to and other meetings of the Society shall be designated by approval by the Board of Trustees. the Council. There shall be a business meeting of the Section 7. The dues of an ordinary member of the Society at the annual meeting and at the summer meeting. A Society shall be remitted for any years during which that business meeting of the Society shall take final action only member is the nominee of an institutional member. on business accepted by unanimous consent, or business Section 8. After retirement from active service on ac notified to the full membership of the Society in the call count of age or on account of long term disability, any for the meeting, except that the business meetings held at ordinary or contributing member who is not in arrears of either the annual meeting or the summer meeting may take 1180 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ~~-·-~·----···~ .. ~,.------~~--,-~--.ri:V~~Ii :~__..------·~· Bylaws of the American Mathematical Society final action on business which has been recommended for mathematical research. It shall also cooperate in the conduct consideration by the Council and has been accepted by the of the American Journal of Mathematics. It shall publish a vote of four-fifths of the Society present and voting at such news periodical known as the Notices of the American Math a meeting. Such notification shall be made only when so ematical Society, containing programs of meetings, items of· directed by a previous business meeting of the Society or news of particular interest to mathematicians, and such other by the Council. materials as the Council may direct. Section 2. Meetings of the Executive Committee may Section 2. The editorial management of the publications be called by the president. The president shall call a meeting of the Society listed in Section 1 of this article, with at any time upon the written request of two of its members. the exception of the Notices, and the participation of the Section 3. The Council shall meet at the annual meeting Society in the editorial management of the American Journal of the Society. Special meetings of the Council may be called of Mathematics shall be in the charge of the respective by the president. The president shall call a special meeting editorial committees as provided in Article ill, Section 1. at any time upon the written request of five of its members. The editorial management of the Notices shall be in the No special meeting of the Council shall be held unless hands of a committee chosen in a manner established by the written notice of it shall have been sent to all members Council. of the Council at least ten days before the day set for the meeting. Section 4. The Board of Trustees shall hold at least Article XII one meeting in each calendar year. Meetings of the Board of Trustees may be called by the president, the treasurer, Communications or the secretary of the Society upon three-days' notice of The Committee to Monitor Problems in Communication such meetings mailed to the last known post office address shall perform such tasks in the field of communication of of each trustee. The secretary of the Society shall call a mathematics as are assigned to it by the Council. meeting upon the receipt of a written request of two of the trustees. Meetings may also be held by common consent of all the trustees. Article XIII Section 5. Papers intended for presentation at any meet ing of the Society shall be passed upon in advance by a I ndemni.fication program committee appointed by or under the authority of Any person who at any time serves or has served as a the Council; and only such papers shall be presented as shall trustee or officer of the Society, or as a member of the have been approved by such committee. Papers in form un Council, or, at the request of the Society, as a director or suitable for publication, if accepted for presentation, shall be officer of another corporation, whether for profit or not for referred to on the program as preliminary communications profit, shall be indemnified by the Society and be reimbursed or reports. against and for expenses actually and necessarily incurred in connection with the defense or reasonable settlement of any action, suit, legal or administrative proceeding, whether Article XI civil, criminal, administrative or investigative, threatened, pending or completed, to which that person is made a Publications party by reason of being or having been such trustee, Section 1. The Society shall publish an official organ officer or director or Council member, except in relation to called the Bulletin of the American Mathematical Society. matters as to which the person shall be adjudged in such It shall publish four journals, known as the Journal of action, suit or proceeding to be liable for negligence or the American Mathematical Society, the Transactions of misconduct in the performance of official duties. Such right the American Mathematical Society, the Proceedings of the of indemnification and reimbursement shall also extend to American Mathematical Society, and Mathematics of Com the personal representatives of any such person, and shall be putation. It shall publish a series of mathematical papers in addition to and not in substitution for any other rights to known as the Memoirs of the American Mathematical Soci which such person or personal representatives may now or ety. The object of the Journal, Transactions, Proceedings, hereafter be entitled by virtue of the provisions of applicable Memoirs, and Mathematics of Computation is to make law or of any other agreement or vote of the Board of known important mathematical researches. It shall publish a Trustees, or otherwise. periodical called Mathematical Reviews, containing abstracts or reviews of current mathematical literature. It shall publish a series of volumes called Colloquium Publications which Article XIV shall embody in book form new mathematical developments. Amendments It shall publish a series of monographs called Mathematical Surveys and Monographs which shall furnish expositions These bylaws may be amended or suspended on recom of the principal methods and results of particular fields of mendation of the Council and with the approval of the NOVEMBER 1991, VOLUME 38, NUMBER 9 1181 Bylaws of the American Mathematical Society membership of the Society, the approval consisting of an the Council, and provided notice of the proposed action and affirmative vote by two-thirds of the members present at a of its general nature shall have been given in the call for the business meeting or of two-thirds of the members voting in meeting or accompanies the ballot in full. a mail ballot in which at least ten percent of the members As amended December 1990 vote, whichever alternative shall have been designated by AMS Funds, Prizes, Officers and Lecturers Colloquium Lecturers C. B. Morrey, Jr., 1964 E. B. Wilson, 1930 A. P. Calderon, 1965 P. W. Bridgman, 1931 James Pierpont, 1896 Samuel Eilenberg, 1967 R. C. Tolman, 1932 Maxime Bocher, 1896 D. C. Spencer, 1968 Albert Einstein, 1934 W. F. Osgood, 1898 J. W. Milnor, 1968 Vannevar Bush, 1935 A. G. Webster, 1898 Raoul H. Bott, 1969 H. N. Russell, 1936 Oskar Bolza, 1901 Harish-Chandra, 1969 C. A. Kraus, 1937 E. W. Brown, 1901 R. H. Bing, 1970 Theodore von Karman, 1939 H. S. White, 1903 Lipman Bers, 1971 Sewall Wright, 1941 F. S. Woods, 1903 Armand Borel, 1971 Harry Bateman, 1943 E. B. Van Vleck, 1903 Stephen Smale, 1972 John von Neumann, 1944 E. H. Moore, 1906 John T. Tate, 1972 J. C. Slater, 1945 E. J. Wilczynski, 1906 M. F. Atiyah, 1973 S. Chandrasekhar, 1946 Max Mason, 1906 E. A. Bishop, 1973 P. M. Morse, 1947 G. A. Bliss, 1909 F. E. Browder, 1973 Hermann Weyl, 1948 Edward Kasner, 1909 Louis Nirenberg, 1974 Norbert Wiener, 1949 L. E. Dickson, 1913 John G. Thompson, 1974 G. E. Uhlenbeck, 1950 W. F. Osgood, 1913 H. Jerome Keisler, 1975 Kurt Gtidel, 1951 G. C. Evans, 1916 Ellis R. Kolchin, 1975 Marston Morse, 1952 Oswald Veblen, 1916 Elias M. Stein, 1975 Wassily Leontief, 1953 G. D. Birkhoff, 1920 I. M. Singer, 1976 K. 0. Friedrichs, 1954 F. R. Moulton, 1920 Jiirgen K. Moser, 1976 J. E. Mayer, 1955 L. P. Eisenhart, 1925 William Browder, 1977 M. H. Stone, 1956 Dunham Jackson, 1925 Herbert Federer, 1977 H. J. Muller, 1958 E. T. Bell, 1927 Hyman Bass, 1978 J. M. Burgers, 1959 Anna Pell-Wheeler, 1927 Philip A. Griffiths, 1979 Julian Schwinger, 1960 A. B. Coble, 1928 George D. Mostow, 1979 J. J. Stoker, 1961 R. L. Moore, 1929 Julia B. Robinson, 1980 C. N. Yang, 1962 Solomon Lefschetz, 1930 Wolfgang M. Schmidt, 1980 C. E. Shannon, 1963 Marston Morse, 1931 Mark Kac, 1981 Lars Onsager, 1964 J. F. Ritt, 1932 Serge Lang, 1981 D. H. Lehmer, 1965 R. E. A. C. Paley, 1934 Dennis Sullivan, 1982 Martin Schwarzschild, 1966 Norbert Wiener, 1934 Morris W. Hirsch, 1982 Mark Kac, 1967 H. S. Vandiver, 1935 Charles L. Fefferman, 1983 E. P. Wigner, 1968 E. W. Chittenden, 1936 Bertram Kostant, 1983 R. L. Wilder, 1969 John von Neumann, 1937 Barry Mazur, 1984 W. H. Munk, 1970 A. A. Albert, 1939 Paul H. Rabinqwitz, 1984 E. F. F. Hopf, 1971 M. H. Stone, 1939 Daniel Gorenstein, 1985 F. J. Dyson, 1972 G. T. Whybum, 1940 Karen K. Uhlenbeck, 1985 J. K. Moser, 1973 Oystein Ore, 1941 Shing-Thng Yau, 1986 Paul A. Samuelson, 1974 R. L. Wilder, 1942 Peter D. Lax, 1987 Fritz John, 1975 E. J. McShane, 1943 Edward Witten, 1987 ArthurS. Wightman, 1976 Einar Hille, 1944 Victor W. Guillemin, 1988 Joseph B. Keller, 1977 Tibor Rad6, 1945 Nicholas Katz, 1989 Donald E. Knuth, 1978 Hassler Whitney, 1946 William P. Thurston, 1989 Martin D. Kruskal, 1979 Oscar Zariski, 1947 Shlomo Sternberg, 1990 Kenneth G. Wilson, 1980 Richard Brauer, 1948 Robert D. Macpherson, 1991 Cathleen S. Morawetz, 1981 G. A. Hedlund, 1949 Elliott W. Montroll, 1982 Deane Montgomery, 1951 Samuel Karlin, 1983 Alfred Tarski, 1952 Gibbs Lecturers Herbert A. Simon, 1984 Antoni Zygmund, 1953 Michael 0. Rabin, 1985 M. I. Pupin, 1923 Nathan Jacobson, 1955 L. E. Scriven, 1986 Robert Henderson, 1924 Salomon Bochner, 1956 Thomas C. Spencer, 1987 James Pierpont, 1925 N. E. Steenrod, 1957 David P. Ruelle, 1988 H. B. Williams, 1926 J. L. Doob, 1959 Elliot H. Lieb, 1989 E. W. Brown, 1927 S. S. Chern, 1960 George B. Dantzig, 1990 G. H. Hardy, 1928 G. W. Mackey, 1961 Michael F. Atiyah, 1991 Saunders Mac Lane, 1963 Irving Fisher, 1929 1182 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers Presidents T. H. Hildebrandt, 1945, 1946 R. G. D. Richardson, 1921-1940 Einar Hille, 1947, 1948 J. R. Kline, 1941-1950 J. H. Van Amringe, 1889, 1890 J. L. Walsh, 1949, 1950 E. G. Begle, 1951-1956 J. E. McClintock, 1891-1894 John von Neumann, 1951, 1952 J. W. Green, 1957-1966 G. W. Hill, 1895, 1896 G. T. Whybum, 1953, 1954 Everett Pitcher, 1967-1988 Simon Newcomb, 1897, 1898 R. L. Wilder, 1955, 1956 Robert M. Fossum, 1989- R. S. Woodward, 1899, 1900 Richard Brauer, 1957, 1958 E. H. Moore, 19!H, 1902 E. J.McShane, 1959,1960 Treasurers T. S. Fiske, 1903, 1904 Deane Montgomery, 1961, 1962 T. S. Fiske, 1890, 1891 W.E Osgood, 1905,1906 J. L. Doob, 1963, 1964 Harold Jacoby, 1892-1894 H. S. White, 1907, 1908 A. A. Albert, 1965, 1966 R. S. Woodward, 1895, 1896 Maxime Bacher, 1909, 1910 C. B. Morrey, Jr., 1967, 1968 Harold Jacoby, 1897-1899 H. B. Fine, 1911, 1912 Oscar Zariski, 1969, 1970 W. S. Dennett, 1900--1907 E. B. Van Vleck, 1913, 1914 Nathan Jacobson, 1971, 1972 J. H. Tanner, 1908-1920 E. W. Brown, 1915, 1916 Saunders Mac Lane, 1973, 1974 W. B. Fite, 1921-1929 L. E. Dickson, 1917, 1918 Lipman Bers, 1975, 1976 G. W. Mullins, 1930--1936 Frank Morley, 1919, 1920 R. H. Bing, 1977, 1978 P. A. Smith, 1937 G. A. Bliss, 1921, 1922 Peter D. Lax, 1979, 1980 B. P. Gill, 1938-1948 Oswald Veblen, 1923, 1924 Andrew M. Gleason, 1981, 1982 A. E. Meder, Jr., 1949-1964 G. D. Birkhoff, 1925, 1926 Julia B. Robinson, 1983, 1984 W. T. Martin, 1965-1973 Virgil Snyder, 1927, 1928 Irving Kap1ansky, 1985, 1986 E P. Peterson, 1973- E. R. Hedrick, 1929, 1930 George Daniel Mostow, 1987, 1988 L. P. Eisenhart, 1931, 1932 William Browder, 1989, 1990 A. B. Coble, 1933, 1934 Michael Artin, 1991, 1992 Solomon Lefschetz, 1935, 1936 R. L. Moore, 1937, 1938 G. C. Evans, 1939, 1940 Secretaries Marston Morse, 1941, 1942 T. S. Fiske, 1888-1895 M. H. Stone, 1943, 1944 E N. Cole, 1896-1920 Endowment Fund 198-219; and to Solomon Lefschetz for his memoir, On certain numerical invariants with applications to Abelian In 1923 an Endowment Fund was collected to meet the varieties, Transactions of the American Mathematical So greater demands on the publication program of the Society, ciety, volume 22 (1921), pp. 407-482. demands caused by the ever-increasing number of important mathematical memoirs. Of this fund, which amounted to Third award, 1928: To J. W. Alexander for his memoir, approximately $94,000 in 1960, a considerable proportion Combinatorial analysis situs, Transactions of the American was contributed by members of the Society. In 1961, upon Mathematical Society, volume 28 (1926), pp. 301-329. the death of the last legatees under the will of the late Robert Fourth award, 1933: To Marston Morse for his memoir, Henderson-for many years a Trustee of the Society-the The foundations of a theory of the calculus of variations entire principal of the estate was received by the Society, in the large in m-space, Transactions of the American thereby bringing the total of the Endowment Fund to Mathematical Society, volume 31 (1929), pp. 379-404; and approximately $648,000. to Norbert Wiener for his memoir, Tauberian theorems, Annals of Mathematics, Series 2, volume 33 (1932), pp. Prize Funds 1-100. The Bocher Memorial Prize Fifth award, 1938: To John von Neumann for his memoir, This prize was founded in memory of Professor Maxime Almost periodic functions and groups. I, II, Transactions of Bacher with an original endowment of $1,450. It is awarded the American Mathematical Society, volume 36 (1934), pp. every five years for a notable research memoir in analysis 445-492, and volume 37 (1935), pp. 21-50. that has appeared during the past five years. Either the Sixth award, 1943: To Jesse Douglas for his memoirs, recipient is a member of the Society or the Memoir is Green's function and the problem of Plateau, American published in a recognized North American journal; this Journal of Mathematics, volume 61 (1939), pp. 545-589; provision, introduced in 1971, is a liberalization of the terms The most general form of the problem of Plateau, American of the award. Journal of Mathematics, volume 61 (1939), pp. 590-608; and First (preliminary) award, 1923: To G. D. Birkhoff for Solution of the inverse problem of the calculus of variations, his memoir, Dynamical systems with two degrees offreedom. Proceedings of the National Academy of Sciences, volume Transactions of the American Mathematical Society, volume 25 (1939), pp. 631-637. 18 (1917), pp. 199-300. Seventh award, 1948: To A. C. Schaeffer and D. C. Spencer Second award, 1924: To E. T. Bell for his memoir, for their memoir, Coefficients of schlicht functions. I, II, III, Arithmetical paraphrases. I, II, Transactions of the Amer N, Duke Mathematical Journal, volume 10 (1943), pp. 611- ican Mathematical Society, volume 22 (1921), pp. 1-30, 635, volume 12 (1945), pp. 107-125, and the Proceedings of NOVEMBER 1991, VOLUME 38, NUMBER 9 1183 AMS Funds, Prizes, Officers and Lecturers the National Academy of Sciences, volume 32 (1946), pp. of numbers, respectively, under restrictions similar to those 111-116, volume 35 (1949), pp. 143-150. for the Bocher Prize. Eighth award, 1953: To Norman Levinson for his contribu First award, 1928: To L. E. Dickson for his book Algebren tions to the theory of linear, nonlinear, ordinary, and partial und ihre Zahlentheorie, Orell Ftissli, Ztirich and Leipzig, differential equations contained in his papers of recent years. 1927. Ninth award, 1959: To Louis Nirenberg for his work in Second award, 1931: To H. S. Vandiver for his several partial differential equations. papers on Fermat's last theorem published in the Transactions of the American Mathematical Society and in the Annals of Tenth award, 1964: To Paul J. Cohen for his paper, On a Mathematics during the preceding five years, with special conjecture ofLittlewood and idempotent measures, American reference to a paper entitled On Fermat's last theorem, Journal of Mathematics, volume 82 (1960), pp. 191-212. Transactions of the American Mathematical Society, volume Eleventh award, 1969: To I. M. Singer in recognition of 31 (1929), pp. 613-642. his work on the index problem, especially his share in two Third award, 1939: To A. Adrian Albert for his papers joint papers with Michael F. Atiyah, The index of elliptic on the construction of Riemann matrices published in the operators. I, III, Annals of Mathematics, Series 2, volume Annals of Mathematics, Series 2, volume 35 (1934) and 87 (1968), pp. 484-530, 546-604. volume 36 (1935). Twelfth award, 1974: To Donald S. Ornstein in recognition Fourth award, 1941: To Claude Chevalley for his paper, La of his paper, Bernoulli shifts with the same entropy are theorie du corps de classes, Annals of Mathematics, Series isomorphic, Advances in Mathematics, volume 4 (1970), pp. 2, volume 41 (1940), pp. 394-418. 337-352. Fifth award, 1944: To Oscar Zariski for four papers on Thirteenth award, 1979: To Alberto P. Calderon in recog algebraic varieties published in the American Journal of nition of his fundamental work on the theory of singular Mathematics, volumes 61 (1939) and 62 (1940), and in the integrals and partial differential equations, and in particu Annals of Mathematics, Series 2, volumes 40 (1939) and 41 lar for his paper Cauchy integrals on Lipschitz curves and (1940). related operators, Proceedings of the National Academy of Sciences, USA, volume 74 (1977), pp. 1324-1327. Sixth award, 1946: To H. B. Mann for his paper, A proof of the fundamental theorem on the density of sums of sets of Fourteenth award, 1984: To Luis A. Caffarelli for his positive integers, Annals of Mathematics, Series 2, volume deep and fundamental work in nonlinear partial differential 43 (1942), pp. 523-527. equations, in particular his work on free boundary problems, vortex theory and regularity theory. Seventh award, 1949: To Richard Brauer for his paper, On Artin's L-series with general group characters, Annals of Fifteenth award, 1984: To Richard B. Melrose for his Mathematics, Series 2, volume 48 (1947), pp. 502-514. solution of several outstanding problems in diffraction theory and scattering theory and for developing the analytical tools Eighth award, 1951: To Paul Erdos for his many papers in needed for their resolution. · the theory of numbers, and in particular for his paper, On a new method in elementary number theory which leads to an Sixteenth award, 1989: To Richard M. Schoen for his elementary proof of the prime number theorem, Proceedings work on the application of partial differential equations to of the National Academy of Sciences, volume 35 (1949), differential geometry, in particular his completion of the pp. 374-385. solution to the Yamabe Problem in Conformal deformation of a Riemannian metric to constant scalar curvature, Journal Ninth award, 1954: To Barish-Chandra for his papers of Differential Geometry, volume 20 (1984), pp. 479-495. on representations of semisimple Lie algebras and groups, and particularly for his paper, On some applications of the universal enveloping algebra of a semisimple Lie algebra, The Frank Nelson Cole Prize in Algebra Transactions of the American Mathematical Society, volume The Frank Nelson Cole Prize in Number Theory 70 (1951), pp. 28-96. These prizes were founded in honor of Professor Frank Tenth award, 1956: To John T. Tate for his paper, The Nelson Cole on the occasion of his retirement as secretary of the American Mathematical Society after twenty-five years higher dimensional cohomology groups of class field theory, Annals of Mathematics, Series 2, volume 56 (1952), pp. of service and as editor-in-chief of the Bulletin for twenty 294-297. one years. The original fund was donated by Professor Cole from moneys presented to him on his retirement, was Eleventh award, 1960: To Serge Lang for his paper, Un augmented by contributions from members of the Society, ramified class field theory over function fields in several and was later doubled by his son, Charles A. Cole. The variables, Annals of Mathematics, Series 2, volume 64 present endowment is $2,250. The prizes are awarded at (1956), pp. 285-325; and to Maxwell A. Rosenlicht for his five-year intervals for contributions to algebra and the theory papers, Generalized Jacobian varieties, Annals of Mathe- 1184 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·~~~-~--~~~--"----.ill n m lili AMS Funds, Prizes, Officers and Lecturers matics, Series 2, volume 59 (1954), pp. 505-530, and A Twentieth award, 1982: To Robert P. Langlands for pio universal mapping property of generalized Jacobians, Annals neering work on automorphic forms, Eisenstein series and of Mathematics, Series 2, volume 66 (1957), pp. 80-88. product formulas, particularly for his paper Base change for GL(2), Annals of Mathematics Studies, volume 96, Princeton Twelfth award, 1962: To Kenkichi Iwasawa for his paper, University Press, 1980; and to Barry Mazur for outstanding Gamma extensions ofnumber fields, Bulletin of the American work on elliptic curves and Abelian varieties, especially Mathematical Society, volume 65 (1959), pp. 183-226; and on rational points of finite order, and his paper Modular to Bernard M. Dwork for his paper, On the rationality of the curves and the Eisenstein ideal, Publications Mathematiques zeta function of an algebraic variety, American Journal of de l'Institut des Hautes Etudes Scientifiques, volume 47 Mathematics, volume 82 (1960), pp. 631-648. (1977), pp. 33-186. Thirteenth award, 1965: To Walter Feit and John G. Twenty-First award, 1985: To George Lusztig for his Thompson for their joint paper, Solvability of groups of odd fundamental work on the representation theory of finite order, Pacific Journal of Mathematics, volume 13 (1963), groups of Lie type. In particular for his contributions pp. 775-1029. to the classification of the irreducible representations in Fourteenth award, 1967: To James B. Ax and Simon characteristic zero of the groups of rational points of B. Kochen for a series of three joint papers, Diophantine reductive groups over finite fields, appearing in Characters problems over local fields. I, IT, III, American Journal of of reductive groups over finite fields, Annals of Mathematics Mathematics, volume 87 (1965), pp. 605-630, 631-648, and Studies, volume 107, Princeton University Press, 1984. Annals of Mathematics, Series 2, volume 83 (1966), pp. Twenty-Second award, 1987: To Dorian M. Goldfeld for 437-456. his paper, Gauss's class number problem for imaginary Fifteenth award, 1970: To John R. Stallings for his paper, quadratic fields, Bulletin of the American Mathematical On torsion-free groups with infinitely many ends, Annals of Society, volume 13, (1985), pp. 23-37; and to Benedict H. Mathematics, Series 2, volume 88 (1968), pp. 312-334; and Gross and Don B. Zagier for their paper, Heegner points and to Richard G. Swan for his paper, Groups of cohomological derivatives of L-Series, Inventiones Mathematicae, volume dimension one, Journal of Algebra, volume 12 (1969), pp. 84 (1986), pp. 225-320. 585-610. Twenty-Third award, 1990: To Shigefurni Mori for his Sixteenth award, 1972: To Wolfgang M. Schmidt for outstanding work on the classification of algebraic varieties the following papers: On simultaneous approximation of and, in particular, for his paper Flip theorem and the existence two algebraic numbers by rationals, Acta Mathematica of minimal models for 3-folds, Journal of the American (Uppsala), volume 119 (1967), pp. 27-50; T-numbers do exist, Mathematical Society, volume 1 (1988), pp. 117-253. Symposia Mathematica, volume IV, Academic Press, 1970, pp. 1-26; Simultaneous approximation to algebraic numbers The Oswald Veblen Prize in Geometry by rationals, Acta Mathematica (Uppsala), volume 125 This prize was established in 1961 in memory of Professor (1970), pp. 189-201; On Mahler's T-numbers, Proceedings Oswald Veblen through a fund contributed by former students of Symposia in Pure Mathematics, volume 20, American and colleagues. The fund was later doubled by the widow Mathematical Society, 1971, pp. 275-286. of Professor Veblen, bringing the fund to $2,000. The first two awards of the prize were made in 1964 and the next in Seventeenth award, 1975: To Hyman Bass for his paper, 1966; thereafter, an award will ordinarily be made every five Unitary algebraic K-theory, Springer Lecture Notes in Math years for research in geometry or topology under conditions ematics, volume 343, 1973; and to Daniel G. Quillen for his similar to those for the Bocher Prize. paper, Higher algebraic K-theories, Springer Lecture Notes in Mathematics, volume 341, 1973. First award, 1964: To C. D. Papakyriakopoulos for his papers, On solid tori, Annals of Mathematics, Series 2, Eighteenth award, 1977: To Goro Shimura for his two volume 66 (1957), pp. 1-26, and On Dehn's lemma and the papers, Class fields over real quadratic fields and Heche asphericity of knots, Proceedings of the National Academy operators, Annals of Mathematics, Series 2, volume 95 of Sciences, volume 43 (1957), pp. 169-172. (1972), pp. 130-190; and On modular forms of half integral weight, Annals of Mathematics, Series 2, volume 97 (1973), Second award, 1964: To Raoul Bott for his papers, The pp. 440-481. space of loops on a Lie group, Michigan Mathematical Journal, volume 5 (1958), pp. 35-61, and The stable homo Nineteenth award, 1980: To Michael Aschbacher for his topy of the classical groups, Annals of Mathematics, Series paper, A characterization of Chevalley groups over fields 2, volume 70 (1959), pp. 313-337. of odd order, Annals of Mathematics, Series 2, volume Third award, 1966: To Stephen Smale for his contributions 106 (1977), pp. 353-398; and to Melvin Hochster for his to various aspects of differential topology. paper Topics in the homological theory of commutative rings, CBMS Regional Conference Series in Mathematics, Number Fourth award, 1966: To Morton Brown and Barry Mazur 24, American Mathematical Society, 1975. for their work on the generalized Schoenflies theorem. NOVEMBER 1991, VOLUME 38, NUMBER 9 1185 AMS Funds, Prizes, Officers and Lecturers Fifth award, 1971: To Robion C. Kirby for his paper, theory for nonlinear elliptic equations, and applications of his Stable homeomorphisms and the annulus conjecture, Annals work to the theory of minimal surfaces in higher dimensions. of Mathematics, Series 2, volume 89 (1969), pp. 575-582. Fourth award, 1978: To Garrett Birkhoff for bringing the Sixth award, 1971: To Dennis P. Sullivan for his work methods of algebra and the highest standards of mathematics on the Hauptvermutung summarized in the paper, On the to scientific applications. Hauptvermutung for manifolds, Bulletin of the American Mathematical Society, volume 73 (1967), pp. 598-600. Fifth award, 1978: To Mark Kac for his important con tributions to statistical mechanics and to probability theory Seventh award, 1976: To William P. Thurston for his work and its applications. on foliations. Sixth award, 1978: To Clifford A. Truesdell for his out Eighth award, 1976: To James Simons for his work on standing contributions to our understanding of the subjects minimal varieties and characteristic forms. of rational mechanics and nonlinear materials, for his efforts Ninth award, 1981: To Mikhael Gromov for his work to give precise mathematical formulation to these classical relating topological and geometric properties of Riemannian subjects, for his many contributions to applied mathematics manifolds. in the fields of acoustic theory, kinetic theory, and nonlinear elastic theory, and the thermodynamics of mixtures, and for Tenth award, 1981: To Shing-Tung Yau for his work in his major work in the history of mechanics. nonlinear partial differential equations, his contributions to the topology of differentiable manifolds, and for his work on Seventh award, 1983: To Paul R. Garabedian for his the complex Monge-Ampere equation on compact complex important contributions to partial differential equations, to manifolds. the mathematical analysis of problems of transonic flow and Eleventh award, 1986: To Michael H. Freedman for his airfoil design by the method of complexification, and to the development and application of scientific computing to work in differential geometry and, in particular, the solution problems of fluid dynamics and plasma physics. of th~ four-dimensional Poincare conjecture. Twelfth award, 1991: To Andrew J. Casson for his work on Eighth award, 1988: To Elliott H. Lieb for his profound the topology of low-dimensional manifolds, and to Clifford analysis of problems arising in mathematical physics. H. Taubes for his foundational work in Yang-Mills theory. The Norbert Wiener Prize The George David Birkhoff Prize in Applied Mathematics in Applied Mathematics This prize was established in 1967 in honor of Professor This prize was established in 1967 in honor of Professor Norbert Wiener and was endowed by a fund amounting to George David Birkhoff. The initial endowment of $2,066 $2,000 from the Department of Mathematics of the Mas was contributed by the Birkhoff family and there have sachusetts Institute of Technology. The prize is normally been subsequent additions by others. It is normally awarded awarded every five years, beginning in 1970, for an out every five years, beginning in 1968, for an outstanding standing contribution to "applied mathematics in the highest contribution to "applied mathematics in the highest and and broadest sense." The award is made jointly by the Amer broadest sense." The award is made jointly by the American ican Mathematical Society and the Society for Industrial and Mathematical Society and the Society for Industrial and Applied Mathematics. The recipient must be a member of Applied Mathematics. The recipient must be a member of one of these societies and a resident of the United States, one of these societies and a resident of the United States, Canada, or Mexico. Canada, or Mexico. First award, 1970: To Richard E. Bellman for his pio First award, 1968: To Jiirgen K. Moser for his contributions neering work in the area of dynamic programming, and for to the theory of Hamiltonian dynamical systems, especially his related work on control, stability, and differential-delay his proof of the stability of periodic solutions of Hamiltonian equations. systems having two degrees of freedom and his specific applications of the ideas in connection with this work. Second award, 1975: To Peter D. Lax for his broad contributions to applied mathematics, in particular, for Second award, 1973: To Fritz John for his outstanding his work on numerical and theoretical aspects of partial work in partial differential equations, in numerical analysis, differential· equations and on scattering theory. and, particularly, in nonlinear elasticity theory; the latter work has led to his study of quasi-isometric mappings as Third award, 1980: To Tosio Kato for his distinguished well as functions of bounded mean oscillation, which have work in the perturbation theory of quantum mechanics. had impact in other areas of analysis. Fourth award, 1980: To Gerald B. Whitham for his broad Third award, 1973: To James B. Serrin for his fundamental contributions to the understanding of fluid dynamical phe contributions to the theory of nonlinear partial differential nomena and his innovative contributions to the methodology equations, especially his work on existence and regularity through which that understanding can be constructed. ------·------·--·------1186 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers Fifth award, 1985: To Clifford S. Gardner for his contri August 1972: To William J. Ellison for his paper, War butions to applied mathematics in the areas of supersonic ing's problem, American Mathematical Monthly, volume 78 aerodynamics, plasma physics and hydromagnetics, and (1971), pp. 10-36. especially for his contributions to the truly remarkable de August 1972: To Lawrence F. Payne for his paper, Isoperi velopment of inverse scattering theory for the solution of metric inequalities and their applications, SIAM Review, nonlinear partial differential equations. volume 9 (1967), pp. 453-488. Sixth award, 1990: To Michael Aizenman for his outstand August 1972: To Dana S. Scott for his paper, A proof of ing contribution of original and non-perturbative mathemat the independence of the continuum hypothesis, Mathematical ical methods in statistical mechanics by means of which Systems Theory, volume 1 (1967), pp. 89-111. he was able to solve several long open important prob lems concerning critical phenomena, phase transitions, and January 1975: To Lipman Bers for his paper, Uniformiza quantum field theory; and to Jerrold E. Marsden for his out tion, moduli, and Kleinian groups, Bulletin of the London standing contributions to the study of differential equations Mathematical Society, volume 4 (1972), pp. 257-300. in mechanics: he proved the existence of chaos in specific January 1975: To Martin D. Davis for his paper, Hilbert's classical differential equations; his work on the momentum tenth problem is unsolvable, American Mathematical Monthly, map, from abstract foundations to detailed applications, has volume 80 (1973), pp. 233-269. had great impact. January 1975: To Joseph L. Taylor for his paper, Measure The Leroy P. Steele Prizes algebras, CBMS Regional Conference Series in Mathemat These prizes were established in 1970 in honor of George ics, Number 16, American Mathematical Society, 1972. David Birkhoff, William Fogg Osgood, and William Caspar August 1975: To George W. Mackey for his paper, Ergodic Graustein, and are endowed under the terms of a bequest theory and its significance for statistical mechanics and amounting to $145,000 from Leroy P. Steele. From 1970 probability theory, Advances in Mathematics, volume 12 to 1976 one or more prizes were awarded each year for (1974), pp. 178-286. outstanding published mathematical research; most favorable August 1975: To H. Blaine Lawson for his paper, Fo consideration was given to papers distinguished for their liations, Bulletin of the American Mathematical Society, exposition and covering broad areas of mathematics. In volume 80 (1974), pp. 369-418. 1977 the Council of the AMS modified the terms under which the prizes are awarded. Since then, up to three prizes 1976, 1977, 1978: No awards were made. have been awarded each year in the following categories: January 1979: To Salomon Bochner for his cumulative (1) for the cumulative influence of the total mathematical influence on the fields of probability theory, Fourier analysis, work of the recipient, high level of research over a period of several complex variables, and differential geometry. time, particular influence on the development of a field, and influence on mathematics through Ph.D. students; (2) for a January 1979: To Hans Levy for three fundamental papers: book or substantial survey or expository-research paper; (3) On the local character of the solutions of an atypical for a paper, whether recent or not, that has proved to be of linear differential equation in three variables and a related fundamental or lasting importance in its field, or a model of theorem for regular functions of two complex variables, important research. Annals of Mathematics, Series 2, volume 64 (1956), pp. 514-522; An example of a smooth linear partial differential August 1970: To Solomon Lefschetz for his paper, A page equation without solution, Annals of Mathematics, Series 2, of mathematical autobiography, Bulletin of the American volume 66 (1957), pp. 155-158; On hulls of holomorphy, Mathematical Society, volume 74 (1968), pp. 854-879. Communications in Pure and Applied Mathematics, volume August 1971: To James B. Carrell for his paper, written 13 (1960), pp. 587-591. jointly with Jean A. Dieudonne, Invariant theory, old and August 1979: To Antoni Zygmund for his cumulative new, Advances in Mathematics, volume 4 (1970), pp. 1-80. influence on the theory of Fourier series, real variables, and August 1971: To Jean A. Dieudonne for his paper, Algebraic related areas of analysis. geometry, Advances in Mathematics, volume 3 (1969), pp. August 1979: To Robin Hartshorne for his expository 223-321, and for his paper, written jointly with James research article Equivalence relations on algebraic cycles and B. Carrell, Invariant theory, old and new, Advances in subvarieties of small codimension, Proceedings of Symposia Mathematics, volume 4 (1970), pp. 1-80. in Pure Mathematics, volume 29, American Mathematical August 1971: To Phillip A. Griffiths for his paper, Periods Society, 1975, pp. 129-164; and his book Algebraic geometry, of integrals on algebraic manifolds, Bulletin of the American Springer-Verlag, Berlin and New York, 1977. Mathematical Society, volume 76 (1970), pp. 228-296. August 1979: To Joseph J. Kohn for his fundamental paper: August 1972: To Edward B. Curtis for his paper, Simplicial Harmonic integrals on strongly convex domains. I, II, Annals homotopy theory, Advances in Mathematics, volume 6 of Mathematics, Series 2, volume 78 (1963), pp. 112-248 (1971), pp. 107-209. and volume 79 (1964), pp. 450-472. NOVEMBER 1991, VOLUME 38, NUMBER 9 1187 AMS Funds, Prizes, Officers and Lecturers August 1980: To Andre Weil for the total effect of his in generalized recursion theory and descriptive set theory: work on the general course of twentieth century mathemat Arithmetical predicates and function quantifiers, Transactions ics, especially in the many areas in which he has made of the American Mathematical Society 79 (1955), pp. fundamental contl;ibutions. 312-340; On the forms of the predicates in the theory August 1980: To Harold M. Edwards for mathematical of constructive ordinals (second paper), American Journal exposition in his books Riemann's zeta function, Pure and of Mathematics 77 (1955), pp. 405-428; and Hierarchies Applied Mathematics, number 58, Academic Press, New of number-theoretic predicates, Bulletin of the American York and London, 1974; and Fermat's last theorem, Graduate Mathematical Society 61 (1955), pp. 193-213. Texts in Mathematics, number 50, Springer-Verlag, New August 1983: To Shiing-Shen Chern for the cumulative York and Berlin, 1977. influence of his total mathematical work, high level of August 1980: To Gerhard P. Hochschild for his significant research over a period of time, particular influence on work in homological algebra and its applications. the development of the field of differential geometry, and influence on mathematics through Ph.D. students. August 1981: To Oscar Zariski for his work in algebraic geometry, especially his fundamental contributions to the August 1984: To Elias M. Stein for his book, Singular algebraic foundations of this subject. integrals and the differentiability properties of functions, Princeton University Press (1970). August 1981: To Eberhard Hopf for three papers of funda mental and lasting importance: Abrweigung einer periodis August 1984: To Lennart Carleson for his papers: An inter chen Losung von einer stationaren Losung eines Differential polation problem for bounded analytic functions, American systems, Berichte tiber die Verhandlungen der Sachsischen Journal of Mathematics, volume 80 (1958), pp. 921-930; Akademie der Wissenschaften zu Leipzig. Mathematisch Interpolation by bounded analytic functions and the Corona Naturwissenschaftliche Klasse, volume 95 (1943), pp. 3- problem, Annals of Mathematics (2), volume 76 (1962), pp. 22; A mathematical example displaying features of turbu 547-559; and On convergence and growth of partial sums of lence, Communications on Applied Mathematics, volume 1 Fourier series, Acta Mathematica volume 116 (1966), pp. (1948), pp. 303-322; and The partial differential equation 135-157. Ut + uu, = p,u,.,, Communications on Pure and Applied August 1984: To Joseph L. Doob for his fundamental work Mathematics, volume 3 (1950), pp. 201-230. in establishing probability as a branch of mathematics and August 1981: To Nelson Dunford and Jacob T. Schwartz for his continuing profound influence on its development. for their expository book, Linear operators, Part I, General August 1985: To Michael Spivak for his five-volume set, A theory, 1958; Part II, Spectral theory, 1963; Part III, Spectral Comprehensive Introduction to Differential Geometry (second operators, 1971, Interscience Publishers, New York. edition, Publish or Perish, 1979). August 1982: To Lars V. Ahlfors for his expository work August 1985: To Robert Steinberg for three papers on in Complex analysis (McGraw-Hill Book Company, New various aspects of the theory of algebraic groups: Represen York, 1953), and in Lectures on quasiconformal mappings tations of algebraic groups, Nagoya Mathematical Journal, (D. Van Nostrand Co., Inc., New York, 1966) and Conformal volume 22 (1963), pp. 33-56; Regular elements ofsemisimple invariants (McGraw-Hill Book Company, New York, 1973). algebraic groups, lnstitut des Hautes Etudes Scientifiques, August 1982: To Tsit-Yuen Lam for his expository work Publications Mathematiques, volume 25 (1965), pp. 49-80; in his book Algebraic theory of quadratic forms (1973), and and Endomorphisms of linear algebraic groups, Memoirs of four of his papers: K 0 and K 1---an introduction to algebraic the American Mathematical Society, volume 80 (1968). K-theory (1975), Ten lectures on quadratic forms over fields (1977), Serre's conjecture (1978), and The theory of ordered August 1985: To Hassler Whitney for his fundamental work fields (1980). on geometric problems, particularly in the general theory of manifolds, in the study of differentiable functions on closed August 1982: To John W. Milnor for a paper of fundamental sets, in geometric integration theory, and in the geometry of and lasting importance, On manifolds homeomorphic to the the tangents to a singular analytic space. ?-sphere, Annals of Mathematics (2) 64 (1956), pp. 399-405. January 1986: To Donald E. Knuth for his expository August 1982: To Fritz John for the cumulative influence of work, The Art of Computer Programming, 3 Volumes (1st his total mathematical work, high level of research over a Edition 1968, 2nd Edition 1973). period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students. January 1986: To Rudolf E. Kalman for his two fundamen tal papers: A new approach to linear filtering and prediction August 1983: To Paul R. Halmos for his many graduate problems, Journal of Basic Engineering, volume 82, (1960), texts in mathematics and for his articles on how to write, pp. 35-45; and Mathematical description of linear dynamical talk and publish mathematics. systems, SIAM Journal on Control and Optimization, volume August 1983: To Steven C. Kleene for three important 1 (1963), pp. 152-192; and for his contribution to a third papers which formed the basis for later developments paper, (with R. S. Bucy) New results in linear filtering and 1188 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY c.itx.,. AMS Funds, Prizes, Officers and Lecturers prediction theory, Journal of Basic Engineering, volume 83D August 1990: To Raoul Batt for having been instrumental (1961), pp. 95-108. in changing the face of geometry and topology, with his January 1986: To Saunders Mac Lane for his many contri incisive contributions to characteristic classes, K-theory, butions to algebra and algebraic topology, and in particular index theory, and many other tools of modem mathematics. for his pioneering work in homological and categorical August 1991: To Jean-Fran9ois Treves for Pseudodiffer algebra. ential and Fourier Integral Operators, Volumes 1 and 2 August 1987: To Martin Gardner for his many books and (Plenum Press, 1980). articles on mathematics and particularly for his column August 1991: To Eugenio Calabi for his fundamental "Mathematical Games" in Scientific American. work on global differential geometry, especially complex August 1987: To Herbert Federer and Wendell Fleming for differential geometry. their pioneering paper, Normal and integral currents, Annals of Mathematics, volume 72 (1960), pp. 458-520. August 1991: To Armand Borel for his extensive contribu tions in geometry and topology, the theory of Lie groups, August 1987: To Samuel Eilenberg for his fundamental their lattices and representations and the theory of auto contributions to topology and algebra, in particular for morphic forms, the theory of algebraic groups and their his classic papers on singular homology and his work on representations and extensive organizational and educational axiomatic homology theory which had a profound influence efforts to develop and disseminate modem mathematics. on the development of algebraic toplogy. August 1988: To Sigurdur Helgason for his books Dif The Delbert Ray Fulkerson Fund ferential Geometry and Symmetric Spaces (Academic Press, 1962), Differential Geometry, Lie Groups, and Symmetric Gifts of friends of the late Professor Fulkerson have provided Spaces (Academic Press, 1978); and Groups and Geometric a fund in excess of $7,000. Part or all of the proceeds is to Analysis (Academic Press, 1984). be used jointly by the Mathematical Programming Society and the American Mathematical Society for the award of one August 1988: To Gian-Carlo Rota for his paper On the or more prizes in discrete mathematics at regular intervals. foundations of combinatorial theory, I. Theory of Mobius functions, Zeitschrift fiir Wahrscheinlichkeitstheorie und Ver First award, 1979: To Richard M. Karp, for On the com wandte Gebiete, volume 2 (1964), pp. 340-368. putational complexity of combinatorial problems, Networks, August 1988: To Deane Montgomery for his lasting impact volume 5 (1975), pp. 45-68; to Kenneth Appel and Wolfgang on mathematics, particularly mathematics in America. He is Haken, for Every planar map is four colorable, Part I: Dis one of the founders of the modem theory of transformation charging, Illinois Journal of Mathematics, volume 21 (1977), groups and is particularly known for his contributions to the pp. 429-490; and to Paul D. Seymour, for The matroids with solution of Hilbert's fifth problem. the max-flow min-cut property, Journal of Combinatorial Theory, Series B, volume 23 (1977), pp. 189-222. August 1989: To Daniel Gorenstein for his book Finite Sim ple Groups, An Introduction to their Classification (Plenum Second award, 1982: To D. B. Judin and A. S. Nemirovski1, Press, 1982); and his two survey articles The Classification for Informational complexity and effective methods of solution of Finite Simple Groups and Classifying the Finite Simple for convex extremal problems, Ekonomika i Matematicheskie Groups, Bulletin of the American Mathematical Society, Metody 12 (1976), 357-369, and to L. G. Khachiyan for volume 1 (1979) pp. 43-199, and volume 14 (1986) pp. A polynomial algorithm in linear programming, Akademiia 1-98, respectively. Nauk SSSR. Doklady 244 (1979), 1093-1096; to G. P. Egorychev, for The solution of van der Waerden's problem for August 1989: To Alberto P. Calderon for his paper Unique permanents, Akademiia Nauk SSSR. Doklady 258 (1981), ness in the Cauchy Problem for Partial Differential Equations, 1041-1044, and D. I. Falikman, for A proof of the van der American Journal of Mathematics, volume 80 (1958), pp. Waerden conjecture on the permanent of a doubly stochastic 16-36. matrix, Matematicheskie Zametki 29 (1981), 931-938; and to August 1989: To Irving Kaplansky for his lasting impact on M. Gr6tschel, L. Lovasz and A. Schrijver, for The ellipsoid mathematics, particularly mathematics in America. By his method and its consequences in combinatorial optimization, energetic example, his enthusiastic exposition, and his overall Combinatorica 1 (1981), 169-197. generosity, he has made striking changes in mathematics and has inspired generations of younger mathematicians. Third award, 1985: To J6zsef Beck, for Roth's estimate of the discrepancy of integer sequences is nearly shmp, August 1990: To R. D. Richtmyer for his book Difference Combinatorica 1 (4), 319-325, (1981); and H. W. Lenstra, Methods for Initial-Value Problems (Interscience, 1st Edition Jr., for Integer programming with a fixed number ofvariables, 1957 and 2nd Edition, with K. Morton, 1967). Mathematics of Operations Research 8 (4), 538-548, (1983); August 1990: To Bertram Kostant for his paper, On the ex and Eugene M. Luks for Isomorphism of graphs of bounded istence and irreducibility of certain series of representations, valence can be tested in polynomial time, Journal of Computer Lie Groups and their Representations (1975), pp. 231-329. and System Sciences 25 (1), 42-65, (1982). NOVEMBER 1991, VOLUME 38, NUMBER 9 1189 AMS Funds, Prizes, Officers and Lecturers Fourth award, 1988: To Eva Tardos for A strongly poly Special Funds nomial minimum cost circulation algorithm, Combinatorica, volume 5 (1985), pp. 247-256; and to Narendra Karmarkar AMS Centennial Fellowship Fund for A new polynomial-time algorithm for linear programming, This fund was established by the Society in 1973 and Combinatorica, volume 4 (1984), pp. 373-395. provides one-year Research Fellowships awarded each year in March. The number of fellowships granted each year Fifth award, 1991: To Martin Dyer, Alan Frieze, and depends on the contributions the Society receives, matched Ravi Kannan for A random polynomial time algorithm for by a contribution from the Society of not more than approximating the volume of convex bodies, Journal of the $30,000. Through the academic year 1983-1984, this was Association for Computing Machinery, volume 38/1 (1991) a postdoctoral fellowship, restricted to persons only a few pp. 1-17; to Alfred Lehman for The width-length inequality years past the Ph.D. In the competition of January 1984, it and degenerate projective planes, W. Cook and P. D. was changed to an early mid-career fellowship, for persons Seymour (eds.), Polyhedral Combinatorics, DIMACS Series five to ten years past the Ph.D. At the same time, the in Discrete Mathematics and Theoretical Computer Science, stipend was substantially increased. For the 1988 award, the volume 1, (American Mathematical Society, 1990) pp. 101- name of the fellowship was changed from AMS Research 105; and to Nikolai E. Mnev for The universality theorems Fellowship to AMS Centennial Fellowship in honor of the on the classification problem of configuration varieties and Society's Centennial. convex polytope varieties, 0. Ya. Viro (ed.), Topology and Geometry-Rohlin Seminar, Lecture Notes in Mathematics First award, 1974-1975: Fred G. Abramson and James 1346 (Springer-Verlag, Berlin, 1988) pp. 527-544. Li-Ming Wang. Second award, 1975-1976: Terence J. Gaffney, Paul Nevai, The Ruth Lyttle Satter Prize in Mathematics and George M. Reed. The prize was established in 1990 using funds donated by Third award, 1976-1977: Fredric D. Ancel and Joseph A. Joan S. Birman in memory of her sister, Ruth Lyttle Satter. Sgro. Professor Birman requested that the prize be established to honor her sister's commitment to research and to encouraging Fourth award, 1977-1978: Steven Kalikow, Charles Patton, women in science. The prizes are awarded every two years Duong-Hong Phong, and David Vogan. to recognize an outstanding contribution to mathematics Fifth award, 1978-1979: Alan Dankner, David Harbater, research by a woman in the previous five years. Howard Hiller, Steven P. Kerckhoff, and Robert C. McOwen. First award, 1991: To Dusa McDuff for her outstanding work during the past five years on symplectic geometry. Sixth award, 1979-1980: Scott W. Brown, Jeffrey E. Hoff stein, Jeffry N. Kahn, James E. McClure, Rick L. Smith, and Mark Steinberger. Award for Distinguished Public Service Seventh award, 1980-1981: Robert K. Lazarsfeld, Thomas To provide encouragement and recognition to those individ H. Parker, and Robert Sachs. uals who contribute their time to public service activities in support of mathematics, the Council of the Society es Eighth award, 1981-1982: Lawrence Man-Hou Bin and tablished the Award for Distinguished Public Service. The Mark Williams. award was established in response to a recommendation by the Society's Committee on Science policy. The award is Ninth award, 1982-1983: Nicholas J. Kuhn. presented every two years to a research mathematician who Tenth award, 1983-1984: Russell David Lyons. has made a distinguished contribution to the mathematics profession during the preceding five years. Eleventh award, 1984-1985: Richard Timothy Durrett. First Award, 1990: Kenneth M. Hoffman Twelfth award, 1985-1986: R. Michael Beals. Thirteenth award, 1986-1987: Dinak:ar Ramakrishnan Citation for Public Service Fourteenth award, 1987-1988: Richard Hain and Bill Jacob To provide encouragement and recognition for contributions to public service. activities in support of mathematics, Fifteenth award, 1988-1989: Stephen R. Bell, Don M. the Council of the Society established the Citation for Blasius, and David Gabai Public Service. The award was established in response to Sixteenth award, 1989-1990: Isaac Y. Efrat, John M. Lee, a recommendation by the Society's Committee on Science and Ralf J. Spatzier Policy. One to three citations are presented each year for notable contributions to the mathematics profession through Seventeenth award, 1990-1991: Michael Anderson, Car public service. olyn Gordon, Steven Mitchell First award, 1991: Andre Z. Manitius Eighteenth award, 1991-1992: Daniel Bump, Karl Vilonen ·-··------~------· 1190 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Funds, Prizes, Officers and Lecturers The Levi L. Conant Fund that will focus on fundamental concepts in the forefront of Levi L. Conant bequeathed a sum of $9,500 which the mathematics. Trustees incorporated with the permanent endowments for prize funds. The Joseph Fels Ritt Memorial Fund From the estate of Estelle F. Ritt, the income from a fund of The Karl Menger Fund $22,500 is available for the publication of works in the field The family of the late Karl Menger were the major con of mathematics as shall be determined by the governing tributors to a fund established at Duke University totalling bodies of the Society. $40,000. The majority of the income from this fund is to be The Waldemar J. Trjitzinsky Fund used by the Society for annual awards at the International Science and Engineering Fair. A bequest of $189,000 was received in 1988 from the estate of Barbara G. Trjitzinsky to establish a fund in memory of her husband, Waldemar J. Trjitzinsky. The income from this The Eliakim Hastings Moore Fund fund is to be used for needy students studying in the field This fund was donated in 1922 in honor of Professor of mathematics. Eliakim Hastings Moore on the occasion of the twenty-fifth anniversary of the Chicago (Western) section of the Society. Friends of Mathematics Fund The fund is $2,575 and the income from the fund is to A Friends of Mathematics Fund has been created to incor be used at the discretion of the Council for the publication porate monetary gifts to the Society of a general nature. The of important mathematical books and memoirs and for the principle of this fund is now $123,572. The proceeds of the award of prizes. fund are a part of the invested assets of the Society. The following gifts are components of this fund: $1,000 from the The C. V. Newsom Fund estate of Professor Ernest William Brown; $1,000 from the In 1990 the Society received a bequest of $100,000 from estate of Genevra B. Hutchinson; $3,000 from Solomon A. the estate of Carroll V. Newsom. The bequest was made to Joffe; $650 from the estate of Professor Helen A. Merrill; memorialize John von Neumann and his accomplishments. $23,600 from the estate of Dean Marion Reilly; $1,000 from The income from this fund is to be used to support a qua the estate of James K. Whittemore; and $2,700 from an drennial symposium, called the von Neumann Symposium, anonymous donor. Several Complex Variables and Complex Geometry Eric Bedford, John P. D'Angelo, Robert E. Greene, and Steven G. Krantz, Editors (Proceedings of Symposia in Pure Mathematics, Volume 52) This three-volume set contains the proceedings of the Summer Research Institute on Several Complex Variables andComplex Geometry, held at the University of California at Santa Cruz in July 1989. The institute explored recent developments in the geometry and function theory of several complex variables. An attempt was made to stimulate interactions among the different methodologies in the subject, such as differential geometry, algebraic geometry. partial differential equations, harmonic analysis, and classical methods. The topics covered include function theory, complex geometry, partial differential equations, functional analysis, and analysis in manifolds. With contributions by some of the world's top experts in several complex variables and complex geometry, this book provides readers with insight into the current state of this field. 1991 Mathematics Subject Classification: 32 (Part 1), 32, 53 (Part 2), 32, 35, 53 (Part 3) ISBN (Set) 0-8218-1488-5; ISBN (Part 1) 0-8218-1489-3; ISBN (Part 2) 0-8218-1490-7; ISBN (Part 3) 0-8218-1491-5, LC 91-11227, ISSN 0082-0717; 262 pages (Part 1); 625 pages (Part 2); 368 pages (Part 3), (hardcover}, July 1991 Set: Individual member $131, List price $219, Institutional member $175 Part 1: Individual member $35, List price $58, Institutional member $46 Part 2: Individual member $66, List price $110, Institutional member $88 Part 3: Individual member $43, List price $72, Institutional member $58 To order please specify PSPUM/52NA (Set) PSPUM/52.1NA (Part 1), PSPUM/52.2NA (Part 2}, PSPUM/52.3NA (Part 3) 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 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS (321-4267) in the continental U.S. and Canada to charge with Visa or MasterCard. Please add 7% GST to all orders being shipped to Canada. NOVEMBER 1991, VOLUME 38, NUMBER 9 1191 Miscellaneous Personals Monroe D. Donsker, of New York 758; May/June 1990, p. 621. Alberto Seeger, of the University of University-Courant Institute, died on Farag Attia, (Egypt and Kuwait), Barcelona, Spain, has accepted the po June 8, 1991, at the age of 66. He was Portland State University, Statistics, sition of Professor of Mathematics at a member of the Society for 46 years. 8/90-8/92. the University of Avignon, France. John M. Reiner, of Denver, Col Yunping Cheng, (People's Repub orado, died on July 19, 1991, at the age lic of China), Portland State Univer of 71. He was a member of the Society sity, Computational Mathematics, 1/91- Deaths for 26 years. 12/91. Albert Carson, of Dayton, Ohio, died Hai-gon Je, (Korea), Portland State on March 17, 1990, at the age of 82. Visiting Mathematicians University, Real Analysis and Measure He was a member of the Society for 54 Supplementary List Theory, 12/91-12/92. years. Mathematicians visiting other institu Kwang-Bok Lee, (Korea), Portland Nancy Cole, Associate Professor tions during the 1990-1991 and 1991- State University, Analytic Functions, Emeritus of Syracuse University, died 1992 academic years have been listed 12/91-12/92. on July 7, 1991, at the age of 89. She in recent issues of Notices: Octo V. Pestov, (USSR), University of was a member of the Society for 62 ber 1991, p. 1016; September 1991, Victoria, Topological Algebra, Model years. p. 858; July/August 1991, p. 656; Theory, and Mathematical Physics, 9/91- Allen Byron Cunningham, of West May/June 1991, p. 494; December 5/92. Virginia University, died on May 3, 1990, p. 1466; November 1990, p. Gao Qiuxian, (People's Republic 1991, at the age of 79. He was a 1295; October 1990, p. 1148; Septem of China), Portland State University, member of the Society for 50 years. ber 1990, p. 959; July/August 1990, p. Biostatistics, 10/91-4/92. t!!~DIMACS Series in Discrete Mathematics and Theoretical Computer Science The Series VolumeS This stimulating and useful series covers the newest Reliability of Computer developments in these fields and Communication Networks Frank Hwang, Clyde Monma, and Fred Roberts, Editors • Discrete and computational geometry This workshop, held at Rutgers University, emphasized the latest • Discrete optimization trends and important open problems concerning the reliability of • Computational number theory and cryptology increasingly complex modem systems of telecommunications, • Finite groups and permutation groups information transmissions, transportation, and distribution. Partici • Recursive function theory and mathematical logic pants of the workshop included theoretical mathematicians, computer • Boolean functions scientists, and electrical engineers from academia and industry. The success of the workshop in fostering many new interactions among researchers and practitioners is reflected in the proceedings, which provide an exciting look at some of the major advances at the All prices subject to change. Free shipment by surface: for air delivery, please add forefront of this important field of research. $6.50 per title. Prepayment required. Order from American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 1991 Mathematics Subject Classifications: 05, 68, 90, 94 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. ISBN 0-8218-6592-7, 259 pages (hardcover), 1991 Ust price $43, lnstitution81. member Please add 7% GST to all orders being shipped to Canada. $34, Individual member $26. To order specify DIMACS/5NA 1192 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS ORDINARY MEMBERS Joan-Carol J Carrafiello, John Wiley Gary L Gray, Univ of Wisconsin, Michele Louise Koskiniemi, Tucson, Aaron Abrams, San Jose, CA & Sons, New York, NY Madison AZ Lokesh M Aggarwal, Staten Island, Benjamin P Carter, Manhattan William E Gripentrog, Kindred Kenneth K Kovacs, Ann Arbor, MI NY Beach, CA Public School, ND Vadim D Kryakvin, Rostov-on-Don, Ahmed M Al-Ghabban, Manhattan, Larry T Cassidy, Sault Ste Marie, MI Aaron Gross, Univ of California USSR KS Dario Castellanos, Valencia, Santa Barbara Ratnesh Kumar, Univ of Kentucky, Natalia H Guersenzvaig, Buenos Pablo Sebastian Armas, Buenos Venezuela Lexington Aires, Argentina John Brian Clifford, Fort Walton Aires, Argentina Nguyen Anh Ky, Bulgarian Academy Oretha W Hargro, Vacaville, CA of Science, Sofia Mercedes Arribas, Univ de Zaragoza, Beach, FL David B Hartvigsen, Northwestern Harold L LaRock II, Rochester, NY Spain James Maurice Cobb, Wheeling, WV Univ, Evanston, IL Johan M Larnmens, SUNY at George Arvanitopoulos, Athens, Herbert E Cohen, Randallstown, MD James F Hartzell, Scarsdale, NY Buffalo, NY Greece John Bryant Collings, Alamosa, CO Eugene J Hebert Jr, Philadelphia, PA Richard C LeBome, San Diego, CA Bruce Allen Babcock, Mount Laurel, Ronald A Collins, Riverdale, MD Eduardo A Hernandez, Univ of Miriam A Leiva, Washington, DC NJ Robert C Cox, Round Rock, TX Santiago, Chile Janny M Y Leung, Univ of Arizona, Anne-Marie J Balboni, Glocester, RI John William Craig, Anaheim, CA James Logan Higgins, Wichita, KS Tucson Bassarn Abbas Bamieh, Rice Univ, David J Crisp, Adelaide, Australia James Alan Hoffman, Catoosa, OK Jin Kun Lin, Nankai Univ, Tianjin, Houston, TX Frank D'Agosta, Jonesport, ME Jeff David Hoft, Iowa City, lA People's Republic of China Dorys Josefina Barban, Ridgewood, James A Dare, Fort Wayne, IN Lori G Holcombe, Chico, CA 0 Lipovan, Timisoara, Romania NJ Rhonda Laverne Datcher, College David Holland, McMaster Univ, Mu Lan Liu, Academia Sinica, Line Baribeau, Univ of Laval, Park, MD Hamilton, Ontario Canada Beijing, People's Rep~blic of Quebec, Canada Zhen Xi Dong, Peking Univ, Pui-Larn Hon, Waterloo, Ontario China Ronald L Barndt, West Newton, MA Beijing, People's Republic of Canada Shu Lin Liu, Academia Sinica, Erik Bell, Arden, NC China Ali Hooshyar, Univ of Texas at Beijing, People's Republic of Douglas A Drake, Hebron, NE Yu M Berezanskii, Ukrainian Dallas, Richardson China Theresa Mary DuRapau, New Academy of Sciences, Kiev, Sharyn Nancy Hoover, Charlotte, NC Estela S Llinas, Univ of Orleans, LA USSR Mary Ann Hom, Univ of Virginia, Pittsburgh-Greensburg, Richard Timothy Eakin, Austin, TX Walter Bernard, Providence, RI Charlottesville Greensburg, PA Javier Echeverria, Univ of Pais Rajendra Bhatia, Indian Statistical Eric Hughes, Berkeley, CA John E Long, Minneapolis, MN Vasco, San Sebastian, Spain Institute, New Delhi Ann Marie Huntz, Woburn, MA Thomas Koji Maadie, Whittier, CA Frances A Elliott, North Barrington, William C Hiester, Lawrence Cullen L Inman, Newton, NJ Lakshminarayanan Mahadevan, IL Livermore National Laboratory, James N Issos, Tallahassee, FL Stanford Univ, CA Nathan Elliott, Livingston Univ, AL CA Adrien C Jarni, Paris, France Babak Mahbod, Computech, Sushil Kumar Bissu, Sukhadia Univ, Elaine Cook Ensign, College, AK Sherry Anne Jaques, Bolivar, NY Portland, OR Udaipur, India Rosemary Carroll Farley, Yonkers, Michael Joseph Johnson, Endwell, Tinyaw Mak, Indiana Univ of M L Blank, USSR Academy of NY NY Pennsylvania, Indiana, PA Science, Moscow Leonard Feldman, Berkeley, CA Kathy Jones, Pasadena, MD Rafael Maradiaga, Tegucigalpa, David A Blohm, Mathsoft Juan C Ferrando Perez, Univ Gregory Singh Juneja, Framingham, Honduras Incorporated, Cambridge, MA Politecnica de Valencia, Spain MA Leandro Marin-Munoz, Murcia, Michael J Bockelie, Hampton, VA Jeffrey J Fetterman, Bangor, PA Alexander Karsen, Beckman Spain John Cecil Bower, Silver Spring, Daniel Alberto Figueroa, Atlantida, Instruments, Brea, CA Wilfreda Martinez, Rio Grande, PR MD Honduras Constantine Kelesoglou, Marathon Cameron Mashayekhi, Sandy, UT Stephen Homer Boyd, Richmond John L Flanagan, New York, NY Oil, Littleton, CO January August May Jr, Muncie, IN Hill, GA Kevin J Francis, Worth, IL Alaa M Khalil, Cinncinnati, OH Jan F McGarry, National Aeronautics James J Brendle, Oakton, VA Bosco Garcia-Archilia, Univ of Paula Kim, Santa Clara, CA & Space Administration, A V Buchvalov, Leningrad, USSR Valladolid, Spain Peter H Kleban, Univ of Maine, Greenbelt, MD Joseph M Bugajski, Ypsilanti, MI Constantinos Georghiou, Univ of Orono Frederick Martin Medak, Ames, lA V N Burkov, Moscow, USSR Patras, Greece Yukio Kobayashi, Fayettesville, AR John-Paul Timothy Menard, Daniel G Caldi, Univ of Cambridge, Richard G Gibson, Berkeley, CA Albert Erik Kolman, Saint Mary's Danville, CA England E Paul Goldenberg, Educational College, Winona, MN Jill Menzies, Auburn, AL Mark Robert Cambisios, Astoria, NY Development Center, Newton, B G Konopelchenko, Institute of David John Michael, Raleigh, NC Jia-Ding Cao, Fudan Univ, MA Nuclear Physics, Novosibirsk, John Joseph Michels, Mililani, HI Shanghai, People's Republic of Donald I Good, Austin, TX USSR Ashish J Modhera, Wilmington, DE China David Lee Gordon, Tokyo, Japan Kenneth William Koput, Univ of Jan Montgomery, Camp Hill, PA Harry Caplan, Danville, CA Per 0 Grape, Stockholm, Sweden California Berkeley Augusto Moraes, Troy, NY NOVEMBER 1991, VOLUME 38, NUMBER 9 1193 New Members of the AMS John J Morgan, Huntington Beach, Mohanuned Salem Sanunan, Jeddah, Stephen G Worotynec, Toronto, Sociedad Matematica Mexicana CA Saudi Arabia Ontario Canada Alberto Alonso Mohammad Mozaffari, Houston, TX Luis M Sanchez Ruiz, Univ Ives J Wu, Silver Spring, MD Bertha Alicia Madrid Nuiiez Barbara Lee Mudloff, Skokie, ll.. Politecnica de Valencia, Spain Victor Yancsek, Edison, NJ Sociedad de Matematica de Chile Kathleen Denise Naylor, Kettering, Jonathan Sheffer Sandberg, George Yossif, Birmingham, AL OH Princeton, NJ Eugene J Zak, Bedford Hills, NY Carmen Cortazar David W Newhouse, Amarillo, TX Hermann Roland Schichl, Wien, Andrei V Zelevinsky, Northeastern Jaime Ricardo San Martin Thomas Edward Nordahl, Davis, CA Austria Univ, Boston, MA Sociedade Brasileira de Matematica Mikhail Nikhailovich Novikov, Jeffrey S Scroggs, North Carolina Walter G Zinman, Syosset, NY Aplicada e Computacional Bowling Green, KY State Univ, Raleigh Dalcidio M Claudio Carroll Jay Nunn, Chapel Hill, NC Jonathan Reed Senning, Univ of Julianne September Nuzman, Virginia, Charlottesville Societat Catalano de Matematiques Aberdeen, MD Farhana Shaheen, Quaid-E-Azam Jose Ignacio Burgos Gil Julie K Orr, College Park, MD Univ, Islamabad, Pakistan Frederic Udina Jennifer Steichen Ortiz, San Jose, Ahmad Shayganmanesh, Iran Univ RECIPROCITY MEMBERS Unione Matematica Italiana CA of Science & Technology, Patrizia Berti Allahabad Mathematical Society Pamela L Overfelt, Inyokern, CA Tehran Bruno Gabutti Anargyros Papageorgiou, City Maziar Shirvani, Univ of Alberta, Khanindra Chandra Chowdhury Luciano Lomonaco College (CUNY), New York, Edmonton, Canada Deutsche Mathematiker-Vereinigung NY Iftimie A Simion, Jackson Heights, Armando Majorana e .. V. Young-June Park, Seoul, Korea NY Pietro Rigo Felix Leinen Mark James Paton, Karen L Simmons, Bonneau, SC Wiskundig Genootschap Lutz Mattner Buckinghamshire, England Catherine M Smith, Kalamazoo, M1 Wieb Bosma Dominikus Noll Karen Whitney Patterson, Salisbury Carole P Sokolowski, Merrimac, MA Theodorus Van Der Walt State Univ, MD George Robert Spahl, Jacksonville, Helmut Pfeiffer Christopher Bishop Pedonesi, Tampa, FL Alan David Rendall 6sterreichische Mathematische Gesellschaft FL Sandra Linck Spain, Hampton, VA Iranian Mathematical Society John C Peterson, Knoxville, TN Russell L Staley, Deer Park, TX Franz Halter-Koch Mohanunad-Ali Asadi Karen D Phillips, Tuscaloosa, AL John David Starrett, Denver, CO Michel Plathey, Thorey-en-Plaine, Michael Stessin, Northwestern Univ, Korean Mathematical Society France Evanston, ll.. Tae HwaKim Anthony Joseph Plozai, Marquette, Jurgen Olivier Stigter, Delft, Seung Kab Yang Ml Netherlands ll Yoo Wayne N Polyzou, Univ of Iowa, Douglas J Strand, Westborough, MA Ki-Jo Yoo Iowa City Karl Strehmel, MLU Mathematical Society of Japan Daniel B Pouquet-Barthez, Halle-Wittenberg, Germany NOMINEE MEMBERS Avranches, France Hasegawa Takemitsu, Fukui Univ, Yoshiaki Ito Alexander A Premet, Academy of Japan Koji Kikuchi Colorado State University Sciences of the Belorussian SSR, Grey M Tarkenton, Austin, 'IX Hideyasu Sumihiro Houcine Zeleity Minsk, USSR Michael Wayne Thomas, Stillwater, Humio Suzuki Concordia University Cam Van Quach-Hongler, Gland, OK Shukichi Tanno Rodney Joseph Shaughnessy Switzerland Lewis D Thorson, Duncan Energy Toshio Umezawa Maharishi International University Michael F Quinn, Pasadena, CA Company, San Francisco, CA Masafumi Yoshino Niranjan Ramachandran, Brown Ton Tran-Cong, Port Melbourne, K Richard Weller Mathematical Society of the Republic Univ, Providence, Rl Australia University Nac Autonoma de Mexico of China Lisanne Renee Raymos, San Marcos, Chan-Nhu Trinh, Collinsville, ll.. Oscar Cuauhtemoc Esperanza TX Daniel Joseph Tucker, James Yi-YongNie University of Colorado, Boulder Gary L Regensburg, North Wales, Madison Univ, Harrisonburg, Norsk Matematisk Foreningros Jennifer P Hyndman PA VA Nils Henrik Risebro M Erik Reid, Pittsburgh, PA Dorothy I Tymczyszyn, Bayonne, University of Kentucky Polskie Towarzystwo Matematyczne Duane R Renner, Telford, PA NJ Weiming Zhang Kathleen T Renwick, Utica, NY Roy F Unger, Deptford, NJ Jozef Zajac University of Montana Richard G Rhinehart Jr, North Mary Vasconcelos, Miami, FL Societe Mathematique de France Peiyong Qu Jackson, OH Ellen Venable, Santa Cruz, CA Gerard Debeaumarche Heather L Rider, Virginia Beach, VA Theodore Vlachos, Arta, Greece Francois Goichot University of Oregon Charles William Robertson IT, Duo Wang, Tsinghua Univ, Beijing, Kamel Hamdache Jon M Clauss Baltimore, MD People's Republic of China University of Regina Julio Daniel Rossi, Buenos Aires, Ellen Keer Weingarten, Jean-Francois Mattei Argentina Cinnaminson, NJ Marianne Morillon Chenkuan Li Larry M Russ, Stevens Institute of John Gregg White, Huntington, WV Charles Camille Notari Western Illinois University Technology, Hoboken, NJ Jody T Wilson, Seneca, SC Remi Lucien Saumont MingXu 1194 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements SUGGESTED _USES for classified advertising are positions available, books or lecture notes for an exceptional record in research including re sale, books bemg sought, exchange or rental of houses, and typing services. search grants and a record of good teaching. THE 1991 RATE IS $55.00 per inch on a single column (one-inch minimum), calculated from Preference will be given to candidates whose the top of the type; ~25 for each additional !Jz inch or fraction thereof. No discounts for multiple research is compatible with that of our current ads or the same ad 1n consecutive issues. For an additional $10 charge, announcements can be faculty: this includes dynamical systems dif placed anonymously. Correspondence will be forwarded. f~rential geometry, mathematical physics, 'non A~vertise~ents in the "Positions Available" classified section will be set with a minimum linear analysis, partial differential equations one-li~e hea~l.me, consisting of the institution name above body copy, unless additional headline inclu_ding numerical p.d.e., and topological dy copy IS spec1~1ed by the adve~iser. Advertisements in other sections of the classified pages will namics. To apply please send a curriculum be set accord1_n_g to the advertisement insertion. Headlines will be centered in boldface at no extra vitae, selected reprints, and at least three letters ~harg~. Cl_assifled rates are calculated from top of type in headline to bottom of type in body copy of reference. Senior applicants may request that 1n?lud1ng li~es and spaces ~ithin: Any fractional text will be charged at the next Ih_ inch rate. Ad~ the Search Committee contact the references Will appear 1n the language 1n wh1ch they are submitted. please make that clear in the cover letter. Send Prep~¥ment is r~qui~ed of individuals but not of institutions. There are no member discounts applications to the following address: for class1f1ed ads. D1~at1on over t~e ~elephone will not be accepted for classified advertising. Search Committee DEADLINES are listed on the 1ns1de front cover or may be obtained from the AMS Advertising Department of Mathematics Department. University of Alabama at Birmingham . ~- S. LA~S PR~~IB~! di~~riminati~n in employment on the basis of color, age, sex, race, Birmingham, AL 35294-2060 religion or nat1o_nal ong1n. Pos1t1ons Available" advertisements from institutions outside the U.s. For full consideration applications should be c~nn~t _be published unless they are accompanied by a statement that the institution does not received by February 15, 1992. UAB is an d1scr~m1nate on these grounds whether or not it is subject to U. S. laws. Details and specific Affirmative Action/Equal Opportunity Employer. word1ng m_ay be found near the Classified Advertisements in the January and July/August issues of the Nottces. SITUATIONS WANT~D ADVERTISEMENTS from involuntarily unemployed mathematicians ~reaccepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) 1n the U.S. and Canada for further information. ARIZONA SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence NORTHERN ARIZONA UNIVERSITY Rho~e Island 02940. AMS location for express delivery packages is 201 Charles Street' Prov~dence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not Flagstaff, Arizona requ1red to do so. AMS FAX 401-455-4004. The Department of Mathematics announces tenure-track openings for Fall 1992. Ordinary Differential Equations. Assistant POSITIONS AVAILABLE AUBURN UNIVERSITY Professor with specialty in the geometric theory Department ·of Algebra, of dynamical systems supporting work of our Combinatorlcs and Analysis existing special research focus, especially pla nar systems with polynomial right hand sides ALABAMA Applicants in combinatorics are sought for a and bifurcation theory. Mathematics Education. Professor with AUBURN UNIVERSITY tenure-track appointment at the rank of assis tant professor expected to be made in beginning commensurate record of research, leadership at Division of Mathematics September 1992. Preference given to candi the university and national level, and experience Department of Foundations, dates in discrete optimization, coding theory, with teacher education programs. Analysis, and Topology cryptology, extremal set theory, or association Sta~istics. Assistant Professor with strong schemes. theoretical background and interest in intramural We anticipate having two or more tenure track Some temporary one-year appointments at consulting; with preference given to those with positions at the Assistant Professor or possibly the rank of assistant professor are also expected actuarial expertise. higher rank available for fall 1992. Primary beginning September 1992. Preference given Each requires a doctorate, demonstrated ~onsideration will be given to filling positions to applicants in differential equations. Those in potential for a productive, quality research 1n each of the areas of Discrete Geometry algebra, analysis, combinatorics, linear algebra program, and substantial evidence of high and Harmonic Analysis. If we fail to find highly or probability considered. Research interest quality teaching. qualified applicants in these areas or more compatible with current faculty. Flagstaff is located in the cool pine forests positions become available we will give sec Ph.D. and excellence in both teaching and of Northern Arizona, near high mountains and ondary consideration to applicants in the areas research required for all positions. Send re numerous natural attractions. NAU has an on of Set Theory, Dynamical Systems, and Anal sume and arrange for at least three letters campus enrollment of approximately 14,000. ysis. Successful applicants will have earned of recommendation to be sent to James The Department of 31 faculty offers Bachelor's a Ph.D. degree in Mathematics and will have R. Wall, 120 Math Annex, Auburn University, AL and Master's degree programs. ~emonstrated potential for teaching and ability 36849-5307. Minorities and Women are encour Send vita, direct three letters of reference 1n research in their area. We will begin our aged to apply. Auburn University is an Equal to: Screening Committee, Department of Math selection process on January 1, 1992. Opportunity Affirmative Action Employer. ematics, P.O. Box 5717, NAU, Flagstaff, AZ Send vita and have three letters of recom 86011. The searches will remain open until mendation sent to George Kozlowski, Head, the positions are filled; however, the Screening Department of Foundations, Analysis, and Committee will begin reviewing applications on Topology, Auburn University, AL 36849-5310. THE UNIVERSITY OF ALABAMA January 3, 1992. Northern Arizona University is Minorities and women are encouraged to apply. AT BIRMINGHAM an Equal Opportunity/Affirmative Action Institu Auburn University is an Equal Opportu Department of Mathematics tion. Women and minorities are encouraged to nity/Affirmtive Action Employer. apply. Applications are invited for tenure track po sitions at all levels to begin September 1992. Applicants for a junior level position should have strong research potential as well as a commit NORTHERN ARIZONA UNIVERSITY ment to teaching undergraduate and graduate Department Chair students. Applicants with post-doctoral expe rience are especially welcome. Applicants for The Department of Mathematics seeks a dy senior level positions with tenure should have namic individual to lead a progressive depart- NOVEMBER 1991, VOLUME 38, NUMBER 9 1195 Classified Advertisements ment with a balanced teaching-research-service analysis, nonlinear science, number theory, and CALIFORNIA POLYTECHNIC mission in a growing comprehensive university. probability. STATE UNIVERSITY Qualifications include an earned doctorate in Postdoctoral Fellowships (Research As mathematics, or mathematics through the doc sociate). Applicants with strengths in all areas Lecturers, Full-lime, Mathematics Department. toral qualifying level plus a doctorate in mathe compatible with department interests are en Salary commensurate with qualifications and matics education or statistics; a record of high couraged to respond. In addition, special Center experience. Available (pending funding) for the quality university teaching and research; exten of Excellence Awards in nonlinear optics and 1992-93 academic year. Teaching load is 12 sive professional service including leadership fluid mechanics are available. units per quarter plus 3 units of instructionally re roles; excellent administrative skills; excellent The Mathematics Department will also have lated responsibilities. Doctorate in mathematics communication and interpersonal skills; recent, several visiting positions for next year. required; strong commitment to both teaching extensive experience in a mathematics de We encourage early application. Deadline and research expected. Closing date: January partment; and broad knowledge of academic date will be December 15, 1991 or whenever 1, 1992. Additional information or application, mathematics, mathematics education and sta positions are filled. Women and minority appli contact Screening Committee Chair. Mathemat tistics. The starting date is July 1, 1992. cants are especially welcome. Send application, ics Department, CAL POLY, San Luis Obispo, The department of 32 permanent faculty of which should include a letter of interest, cur CA 93407. AAIEOE. fers degree programs through the master's level riculum vitae with a list of publications, and a with emphasis in mathematics, mathematics minimum of three (3) letters of recommendation education, statistics and actuarial science. Our (enclose or arrange to be sent), to: programs have experienced consistent strong Alan C. Newell, Chairman CALIFORNIA POLYTECHNIC growth during the last several years. Faculty Personnel Committee STATE UNIVERSITY have active research interests in algebra, analy Department of Mathematics Tenure-Track Position, Mathematics Depart sis, combinatorics, geometry, mathematics edu University of Arizona ment. Salary commensurate with qualifications cation, statistics and topology. Special research Tucson, Arizona 85721, USA & experience; assistant professor preferred. concentrations have recently been established The University of Arizona is an Affirmative Duties & responsibilities include teaching math in combinatorics and dynamical systems. In Action/Equal Opportunity Employer. ematics courses including methods & content addition, the department is actively involved in for K-12 teachers. Full description of duties & initiatives of regional and national interest in responsibilities available from Screening Com cluding calculus reform, use of technology and mittee Chair. Doctorate in Mathematics Edu participation of minorities. cation & Master's Degree in Mathematics or NAU has a current on-campus enrollment of CALIFORNIA equivalent required. Pre-college teaching expe about 14,600 students. It lies on the southern rience & background in educational technology edge of Flagstaff, a city of about 45,000, at an CALIFORNIA INSTITUTE OF TECHNOLOGY desirable. Closing date: January 1, 1992. For altitude of 7000 feet. The setting is mountain Applied Mathematics further information and application form con ous, pine-forested and cool, with four distinct tact: Screening Committee Chair, Mathematics seasons, a relatively dry climate, abundant blue Postdoctoral positions as Research Fellow for Department, CAL POLY, San Luis Obispo, CA skies and generous winter snows. Nearby at one or pof?sibly two years doing joint research 93407. AAIEOE. tractions include spectacular canyons, national under the direction of senior faculty are avail forests, high mountains, large recreation areas, able. The research is sponsored and frequently numerous national parks and monuments, and involves large scale computations in some area Indian ruins. of continuum mechanics and fluid dynamics. CALIFORNIA STATE POLYTECHNIC To apply, send letter of application, vita Research in numerical analysis and parallel computing is also active. Current salaries are UNIVERSITY and statement of academic philosophy and di Pomona, CA rect four letters of reference to: Mathematics about $30,000 for 11 months. Send detailed vita, bibliography and three letters of reference Chair Screening Committee, College of Arts The College of Science invites applications and to The Executive Officer, Applied Mathematics and Sciences, P.O. Box 5621, Northern Ari nominations for the position of Chair of the Math 217-50, Caltech, Pasadena, CA 91125. Caltech zona University, Flagstaff, AZ 86011-5621. The ematics Department. Doctorate in Mathematics is an Equal Opportunity/Affirmative Action Em search will remain open until the position is or equivalent degree. Record of successful ad ployer. Women and minorities are encouraged filled; however, the screening committee will ministrative, teaching and scholarly research begin reviewing applications on December 13, to apply. required. Evidence of commitment to promoting 1991. teaching, research, and other scholarly activ NAU IS AN EQUAL OPPORTUNITY/AFFIR ities. Application, resume, copy of transcripts MATIVE ACTION INSTITUTION. WOMEN AND and three current letters of reference to be MINORITIES ARE ENCOURAGED TO APPLY. CALIFORNIA INSTITUTE OF TECHNOLOGY received by 12/15/91 . For additional information Applied Mathematics or to apply contact: Search Committee, Mathe matics Department, California State Polytechnic The Applied Mathematics program at Caltech University, 3801 W. Temple Ave., Pomona, CA invites applications for a tenure-track or possibly 91768-4033. (714) 869-3487. EOE/AA UNIVERSITY OF ARIZONA tenured appointment in the case of exception Department of Mathematics ally well-qualified applicants. Candidates should Tucson, Arizona 85721 have a demonstrated ability to carry out high quality research in their fields of Applied Math MILLS COLLEGE The Mathematics Department at the University ematics and be willing to participate in the Department of Mathematics of Arizona is happy to announce several po teaching program at graduate and undergradu and Computer Science sitions which will be available beginning Fall ate levels. Applicants should submit a detailed Oakland, California 94613 1992. curriculum vitae and list of publications with Tenure-track positions. Excellent research at least three letters of recommendation or Mills College is seeking outstanding candidates record or potential, stron commitment to teach the names of referees to The Executive Of for· two tenure-track positions, commencing Fall ing required. Fields should complement but ficer, Applied Mathematics 217-50, Caltech, 1992. The first is Assistant Professor of Com not duplicate existing department research Pasadena, CA 91125. Caltech is an Equal Op puter Science. A Ph.D. in Computer Science strengths in algebra, arithmetic geometry, com portunity/Affirmative Action Employer. Women is required. The second is Assistant Professor putational science, differential equations, dy and minorities are encouraged to apply. of Computer Science and Director of the Inter namical systems, fluid mechanics, differen disciplinary Computer Science Master's Degree tial geometry, mathematical physics, nonlinear Program. A strong computer science back- 1196 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements ground, a Ph.D. in a related field, and the UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA ability to guide students, with quite diverse AT BERKELEY AT BERKELEY backgrounds, in a master's degree program Department of Mathematics Department of Mathematics are required. Candidates for both positions Bereley, CA 94720 Berkeley, CA 94720 must submit evidence of superior teaching and Tenured Position Temporary Postdoctoral Positions research abilities. Salary will depend on experi ence and qualifications. The initial contract will We invite applications for one or more positions Several temporary positions beginning in Fall be for three years, subject to final administrative effecttive July 1, 1992 at tenure level (Associate 1992 are anticipated for new and recent Ph.D.s approval. Please send vita, and direct three or full Professor), subject to bugetary approval, of any age. In the areas of algebra, analysis, letters of reference, to: in the areas of algebra, analysis, applied mathe applied mathematics, foundations, or geometry Chair, Computer Science Search matics, foundations, or geometry and topology. and topology. The terms of these appointments Committee Demonstrated leadership in research is ex may range from one to three years. Applicants Mills College pected of applicants. Applicants should send for NSF or other postdoctoral fellowships are Oakland, California 94613 a curriculum vitae, list of publications, a few encouraged to apply for these positions; com The deadline for applications is January 10, selected reprints or preprints, and the names of bined teaching/research appointments may be 1992. Mills College is an Equal Opportunity three references to The Vice Chair for Faculty made for up to three years. Mathematicians Employer. Affairs at the above address. We should receive whose research interests are close to those of this material no later than January 15, 1992. The regular department members will be given some University of California is an Equal Opportunity, preference. Applicants should send a resume, Affirmative Action Employer. and reprints, preprints, and/or dissertation ab STANFORD UNIVERSITY stract, and ask three people to send letters of Department of Mathematics recommendation to The Vice Chair for Faculty Affairs at the above address. We should receive Assistant Professorships in honor of Gabor this material no later than January 15, 1992. The Szego. UNIVERSITY OF CALIFORNIA University of California is an Equal Opportunity, The Department of Mathematics expects to AT BERKELEY Affirmative Action Employer. make one or more appointments in 1992-1993 Department of Mathematics for these special two-year positions. Applicants Berkeley, CA 94720 are expected to show outstanding promise in Assistant Professorships research and clear evidence of achievement. UNIVERSITY OF CALIFORNIA, IRVINE They should have received the Ph.D. prior to We invite applications for one or more positions Department of Mathematics the start of the appointment but not before effective July 1, 1992, at the· tenure-track Irvine, CA 92717 1990. Stanford is committed to excellence in Assistant Professor level, subject to budgetary teaching, and applicants should count this as approval, in the areas of algebra, analysis, Applications are invited for up to five positions one of their goals. Candidates should send a applied mathematics, foundations, or geometry effective July 1 , 1992 at the tenure-track level letter of application with a curriculum vitae, a and topology. Applicants are expected to have in the areas of algebra, analysis, applied math list of publications and information concerning demonstrated outstanding research potential, ematics, foundations, geometry, probability, sta teaching experience, and should arrange to normally including major contributions beyond tistics, or topology. Demonstrated leadership in have three letters of recommendation sent to the doctoral dissertation. Applicants should research is expected of applicants at the tenure Prof. Solomon Feferman, Chairman, Dept. of send a resume, and reprint or preprints, and/or (Associate or Full Professor) levels. Applicants Mathematics, Stanford University, Stanford, CA dissertation abstract, and ask three people at these levels should send a curriculum vitae, 94305-2125, by January 1, 1992. Stanford is an to send letters of recommendation to The list of publications, a few selected reprints or Equal Opportunity, Affirmative Action Employer, Vice Chair for Faculty Affairs at the above preprints, and the names of three references and welcomes applications from women and address. We should receive this material no to Peter Li, Chair of the Recruitment Com minorities. later than January 15, 1992. The University of mittee, at the above address. Applicants at California is an Equal Opportunity Affirmative the tenure-track level are expected to have Action Employer. demonstrated outstanding research potential, and should send a resume, reprints, preprints STANFORD UNIVERSITY and dissertation abstract, and ask three people Department of Mathematics to send letters of recommendation to Peter Li. UNIVERSITY OF CALIFORNIA We should receive all these materials no later The department expects to make at least one AT BERKELEY than March 1, 1992. The University of Califor tenure-track or tenured appointment beginning nia is an Equal Opportunity/Affirmative Action Department of Mathematics September 1992, among the following fields: (1) employer. The Department of Mathematics wel analysis, (2) geometry or topology, (3) algebra, Berkeley, CA 94720 comes applications from women and minority number theory, or logic, (4) applied mathematics Charles B. Morrey, Jr. candidates. or probability; in the last case there are also Assistant Professorships possibilities for joint appointments with other departments. At the tenured level, preference We invite applications for these special two would go to individuals in the early years of year (nontenure-track) positions effective July UNIVERSITY OF CALIFORNIA, their ranks, though a more senior appointment 1, 1992. Applicants should have a recent Ph.D. LOS ANGELES may be possible for an extremely well-qualified in the areas of algebra, analysis, applied mathe Department of Mathematics individual. Candidates should send a letter of matics, foundations, or geometry and topology, application and a curriculum vitae with a list and should have demonstrated superior re TEMPORARY POSITIONS of publications, and arrange to have three let search potential. Applicants should send a (1) One or two E. R. Hedrick Assistant ters of recommendation and some evidence of resume, reprints, preprints and/or dissertation Professorships. Applicants must show very commitment to teaching sent to Prof. Solomon abstract, and ask three people to send letters of strong promise in research and teaching. Salary Feferman, Department of Mathematics, Stan recommendation to The Vice Chair for Faculty $39,600. Three year appointment. Teaching ford University, Stanford, CA, 94305-2125 by Affairs at the above address. We should receive load: four quarter courses per year, which may January 1, 1992. Stanford is an Equal Opportu this material no later than January 15, 1992. The include one advanced course in the candidate's nity, Affirmative Action Employer, and welcomes University of California is an Equal Opportunity, field. Preference will be given to applications applications from women and minorities. Affirmative Action Employer. completed by January 1, 1992. (2) Subject to administrative approval, sev eral Research Assistant Professorships in Com- NOVEMBER 1991, VOLUME 38, NUMBER 9 1197 Classified Advertisements putational and Applied Mathematics. Applicants ics, University of California, Los Angeles, CA Visiting positions (at all levels) and postdoctoral must show very strong promise in research 90024-1555. Attn: Staff Search. UCLA is an appointments will also be available. and teaching. Salary $39,600. One year ap equal opportunity/affirmative action employer. The Department of Mathematics also seeks pointment, probably renewable up to two times. to fill at least one tenured position at the senior Teaching load: at most four quarter courses per level. Successful applicants will have an out year, which may include one advanced course standing record of mathematical research and in the candidate's field. Preference will be given UNIVERSITY OF CALIFORNIA, scholarship, and proven administrative skills for to applications completed by January 1, 1992. SANTA BARBARA academic leadership. Applications should be (3) Subject to administrative approval, one Department of Mathematics mailed to: Chair of Appointments Committee, or two Adjunct Assistant Professorships in the Department of Mathematics, ORB 155, Uni Program in Computing (PIC). Applicants must Applications are invited for the KV FAN AS versity of Southern California, Los Angeles, show very strong promise in teaching and SISTANT PROFESSORSHIP. The Ky Fan as CA 90089-1113. USC is an Equal Opportu research, preferably in the general area of logic sistant professorship is a special two-year non nity/Affirmative Action employer. Women and and computation. Teaching load: four quarter renewable position which carries a research minorities are especially encouraged to apply. programming courses and an advanced quarter stipend. Appointment is effective July 1, 1992. course of the candidate's choice per year. Two Candidates must possess a Ph.D by Septem year appointment, possibly renewable once. ber 1992. Selection will be based primarily on Salary range $39,600-$47,000. Preference will demonstrated research achievement. Teaching CONNECTICUT be given to applications completed by February experience is desirable. Teaching load will con 1, 1992. sist of four quarter courses per year. To apply FAIRFIELD UNIVERSITY (4) Subject to administrative approval, a send vita and publication list, and arrange to Department of Mathematics Lectureship in the Program in Computing (PIC). have 3 letters of recommendation sent to: Ky and Computer Science Fan Faculty Search Committee, Department Applicants must show very strong promise in North Benson Rd. of Mathematics, University of California, Santa the teaching of programming. M.S. in Computer Fairfield, CT 06430-7524 Science or equivalent degree preferred. Teach Barbara, CA 931 06. All applications received ing load: five quarter programming courses per by January 10, 1992 will be given thorough Asst. Prof. Math; tenure-track; 9 hours teaching year. One-year appointment, possibly renew consideration. UCSB is an Equal Opportu per week plus research; start Sept. 1992; Ph.D. able up to five times, depending on the needs nity/Affirmative Action employer. Proof of U.S. in Math required with teaching competence of the program. Salary is based on experience citizenship or eligibility for U.S. employment will in Statistics desirable; salary competitive; full and begins at $34,248. Preference will be given be required prior to employment (Immigration consideration until Feb. 1, 1992; vitae and 3 to applications completed by February 1, 1992. Reform and Control Act of 1986). letters of reference to Joseph B. Dennin, Chair (5) Subject to administrative approval, a of Department. Fairfield is a Jesuit University 60 few Adjunct Assistant Professorships. One year minutes from New York University. appointments, probably renewable once. Strong UNIVERSITY OF CALIFORNIA, research and teaching background required. SANTACRUZ Salary $35,900-$40,500. Teaching load: five quarter courses per year. Department of Mathematics DISTRICT OF COLUMBIA (6) Subject to administrative approval, sev The Mathematics Department at the University eral positions for visitors and lecturers. of California, Santa Cruz, expects to have J. TRINITY COLLEGE To apply, write to Thomas M. Liggett, Chair, W. T. Youngs Assistant Professorships in Math Division of Mathematics Department of Mathematics, University of Cal ematics beginning Fall 1992. These recently and Natural Science ifornia, Los Angeles, CA 90024-1555. Attn: established Assistant Professorships in Math Washington, D.C. 20017 Staff Search. UCLA is an equal opportu ematics are named in honor of our founding nity/affirmative action employer. chairman, J. W. T. Youngs. Appointees will be Tenure-track position at the Assistant Professor expected to teach, pursue their research, and level beginning Fall 1992 (subject to funding perform some department or university service. appropriations). Qualifications include a Ph.D., These positions are available for a two-year with specialization in analysis or statistics pre UNIVERSITY OF CALIFORNIA, period with the possibility of an extension for ferred. Strong interest in teaching necessary. LOS ANGELES a third year. Minimum Qualifications: Ph.D. in Send letter of application with vita, transcripts Department of Mathematics Mathematics and a demonstrated excellence in and three letters of recommendation to Dr. research and teaching or potential for excel Marlene Lawson, Division of Mathematics and REGULAR POSITIONS IN PURE AND AP lence. Salary Range: $35,900-$37,400 com Natural Science, Trinity College, Washington, PLIED MATHEMATICS mensurate with qualifications and experience. D.C. 20017. Subject to administrative approval, one or Available: Fall 1992. Application Deadline: De Trinity College is a liberal arts college for two regular positions in pure and applied math cember 15, 1991. Please refer to position #T91- women under Catholic auspices. Applications ematics. The six specific search areas are as 04. Applicants should send vitae, three letters of from women and minorities are strongly encour follows: 1) statistics; 2) applied and computa reference, and information about their teaching aged. AAIEOE. tional mathematics; 3) logic and mathematical and research experience to: Recruitment Com computer science; 4) geometry and topology mittee, Mathematics Department, University of (including dynamical systems and geomet California, Santa Cruz, CA 95064. UCSC is an ric partial differential equations); 5) analysis affirmative action/equal opportunity employer. FLORIDA and differential equations (including Lie groups, mathematical physics, probability and game STETSON UNIVERSITY theory); 6) algebra, number theory and com Department of Mathematics binatorics (including algebraic geometry and UNIVERSITY OF SOUTHERN CALIFORNIA, and Computer Science representation theory). Very strong promise in LOS ANGELES research and teaching required. Positions ini Applications are invited for a tenure track posi tially budgeted at the assistant professor level. The Department of Mathematics has available tion in mathematics at the Assistant Professor Sufficiently outstanding candidates at higher several tenure-track or tenured positions at level beginning Fall 1992. A Ph.D. in mathe levels will also be considered. Teaching load: the Assistant and/or Associate Professor level. matics is required. Applicants should have a averaging 1.5 courses per quarter, or 4.5 quar Applicants must show strong research promise strong commitment to undergraduate teaching ter courses per year. To apply, write to Thomas and possess excellent communications skills for in a liberal arts environment. Teaching load: M. Liggett, Chair, Department of Mathemat- teaching undergraduate mathematics courses. 9-10 hrs/wk. Responsibilities include teaching 1198 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements mathematics courses at all levels of the un ics. Ph.D. in mathematics required. Research Probability, Partial Differential Equations, and dergraduate curriculum, and continuing schol is desirable but is neither required nor heavily Topology. Northwestern is an affirmative action, arly activity. The department currently has 10 weighed. equal opportunity employer committed to fos full-time faculty members. Stetson University, The ideal candidate will show a strong tering a diverse faculty, so women and minority located in Central Florida, is a small, private, mastery of the discipline, a commitment to candidates are especially encouraged to apply. comprehensive university of 2500 students. Its professional growth and development, an ability Candidates should arrange that at least three three schools-the College of Arts and Sci for and commitment to excellence in teaching, letters of recommendation be sent to Prof. D. ences, the School of Business, and the School and the potential and desire to enhance the G. Saari, Chair, Personnel Committee, Depart of Music-are dedicated to excellence in teach college's intellectual community. ment of Mathematics, Northwestern University, ing and are united by a commitment to the The Mathematics Department has sixteen Evanston, Illinois 60208-2730. Alternatively, ap liberal arts. Send vitae and three letters of tenure-track positions. There is a new B.S. in plications and supporting documentation can be recommendation to: Professor Dennis Kletz Mathematics, dual major programs with other sent via email to "[email protected]." In ing, Department of Mathematics and Computer departments, and several minor programs. The order to receive full consideration, applications Science, Stetson University, Deland, Florida bulk of the teaching is in service courses. should be received by February 15, 1992. Hir 32720. Deadline for applications is December Southern Tech is a state supported senior ing is contingent upon eligibility to work in the 31, 1991, or until position is filled. Stetson college in the University System of Georgia. United States. University is an Equal Opportunity Employer Situated on a 230 acre site 15 miles northwest of and enthusiastically solicits applications from Atlanta, the college enrolls about 4,000 students women and minority candidates. in technically oriented programs through the Master's level. UNIVERSITY OF ILLINOIS A complete application consists of a letter AT URBANA-CHAMPAIGN of application, a curriculum vitae, transcripts of Department of Mathematics all college work, and a minimum of two letters of reference. The deadline for applications is Applications are invited for one or more tenure EMORY UNIVERSITY February 1, 1992; applications not completed track or tenured faculty positions commencing ATLANTA, GA 30322 by that date will not be considered. Applicants in August 1992. We are particularly interested in Department of Mathematics who are not U.S. citizens should state visa type hiring in the areas of applied mathematics, com binatorics, optimization, partial differential equa and Computer Science and authorization for permanent employment in the U.S.; an application will not be conisdered tions, and probability. Outstanding candidates The Department of Mathematics and Computer complete without such a statement. in all fields of mathematics are encouraged to Science has three openings in mathematics to Applications and inquiries should be ad- apply and will be seriously considered. Some begin September 1 , 1992. The positions are dressed to: visiting appointments for the 1992-93 academic at the level of tenure-track assistant professor. Dr. James C. Kropa year are also anticipated. Salary and teaching Applicants must have a Ph.D. in mathematics Mathematics Department load are competitive. Candidates must have and a strong record (or promise) of research. Southern College of Technology completed the Ph.D. by the time the appoint The areas of geometric analysis, algebra Marietta, Georgia 30060-2896 ment begins. Candidates should send a letter of and combinatorics are of particular interest to Southern College of Technology is an equal application, curriculum vitae and publication list, · us. The teaching load is 6 hrs./wk, including opportunity/affirmative action employer. and arrange to have three letters of reference graduate and undergraduate courses. sent directly to Please send vita and names of three refer C. Ward Henson, Chair ences to the above address, and have reference Department of Mathematics letters forwarded to us. Screening of applica University of Illinois at tions will begin Jan. 20, 1992. Urbana-champaign Emory University is an equal opportu ELMHURST COLLEGE 1409 W. Green St. nity/affirmative action employer. Urbana, Illinois 61801 Tenure-track position beginning fall1992 (pend tel. (217)333-3352 ing approval of the Board of Trustees). Qualifi In order to ensure full consideration, all ap cations desired: Ph.D. in mathematics, interest plication materials including letters of reference GEORGIA INSTITUTE OF TECHNOLOGY in continued scholarship, and a strong com should be received by December 2, 1991. In mitment to undergraduate teaching in a liberal terviews may be conducted prior to December The School of Mathematics expects to have arts college. Teaching load: 6 courses per year. 2, but completed applications received by that some visiting and tenure-track positions in sev Elmhurst College is a four-year private institu date will receive full consideration. Candidates eral areas, including probability and statistics, tion located in the western suburbs of Chicago. are expected to present evidence of excellence, at various levels beginning in Fall 1992. Candi Applications should include a curriculum vitae or potential for excellence, in research and dates with strong research and teaching records and three letters of reference. Please send teaching. Applications from women and minority or potential should send a resume, at least three to Dr. Jon L. Johnson, Dept. of Mathematics, candidates are especially encouraged. The Uni letters of reference, and a summary of future re Elmhurst College, Elmhurst, IL 60126. Elmhurst versity of Illinois is an Affirmative Action/Equal search plans to the Hiring Committee, School of College is an Equal Opportunity Employer. Opportunity Employer. Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160. Georgia Tech, a member of the University System of Geor NORTHWESTERN UNIVERSITY gia, is an Equal Opportunity/Affirmative Action Employer. Department of Mathematics INDIANA Evanston, Illinois 60208-2730 INDIANA UNIVERSITY· Applications are invited for one or more antici PURDUE UNIVERSITY SOUTHERN COLLEGE OF TECHNOLOGY pated tenure-track positions starting September AT INDIANAPOLIS (IUPUI) 1992. Priority will be given to young, excep Department of Mathematical Sciences MATHEMATICS-The Mathematics Department tional research mathematicians (no more than of the Southern College of Technology seeks several years after the Ph.D.). However, more The Department of Mathematical Sciences at applicants for one or more tenure-track posi senior candidates with very exceptional creden IUPUI is seeking applicants for three tenure tions at the rank of Assistant Professor. The tials may be considered for a tenured position. track positions to begin in August 1992. Rank Department desires faculty who can contribute Fields of interest .within the department in is open depending on qualifications. Applicants to the newly created B. S. program in Mathemat- clude Algebra, Analysis, Dynamical Systems, must have an earned doctorate by the starting NOVEMBER 1991, VOLUME 38, NUMBER 9 1199 Classified Advertisements date, either a strong research record or excel UNIVERSITY OF IOWA UNIVERSITY OF KANSAS lent research potential, and a commitment to Department of Mathematics quality graduate and undergraduate teaching. The Mathematics Department of the University Some preference may be given to applicants in of Iowa invites applications for the following Applications are invited for tenure-track posi discrete mathematics, scientific computing and positions: tions at the assistant or associate professor applied statistics. However, strong applicants 1. One tenure-track appointment at the As level and for visiting positions at the assistant from all areas of mathematical sciences are sistant or beginning Associate Professor level professor level (pending on funding), beginning encouraged to apply. starting in the 1992-93 academic year. The August 17, 1992 or as negotiated. Field is IUPUI is a comprehensive urban university position is to be filled by a specialist in some unrestricted but preference will be given to can with over 28,060 students. The department aspect of harmonic analysis/representation the didates whose specialties mesh well with those offers programs of study leading to Purdue ory, probability theory/stochastic analysis, or already represented in the department. Candi University B.S., M.S., and Ph.D. degrees and topology of manifolds/dynamical systems. Se dates must have a Ph.D. or its requirements we anticipate significant growth in our faculty lection will be based on evidence of outstanding completed by August 15, 1992. Postdoctoral ex during the next few years. The university offers research accomplishments or potential, and perience for tenure-track positions is preferred competitive salaries and provides excellent teaching ability. A Ph.D. or equivalent training is but optional. fringe benefits. Send resume and three letters required. Application, detailed resume with description of recommendation to Prof. Bart S. Ng, Chair, 2. Pending availability of funds, one or of research, and three recommendation letters Department of Mathematical Sciences, IUPUI, more visiting positions for all or part of the should be sent to C. J. Himmelberg, Chairman, 1125 E. 38th Street, Indianapolis, IN 46205- 1992-93 academic year. Selection will be based Department of Mathematics, 405 Snow Hall, 2810. Closing date: January 15, 1992. Late on research expertise and teaching ability. University of Kansas, Lawrence, KS 66045- applications will be considered until positions Preference will be given to applicants whose 2142. are filled. scholarly activity is of particular interest to Deadlines: December 1, 1991 for first con IUPU/ is an Affirmative Action/Equal Oppor members of current faculty. sideration, then monthly until August 1, 1992. tunity Employer. Women and minority candi Women and minority candidates are espe The University of Kansas is an equal oppor dates are encouraged to apply. cially urged to apply for the above positions. The tunity/affirmative action employer. University of Iowa welcomes the employment of highly-qualified professional couples on its faculty and staff, permits the appointment of faculty couples within the same department, and permits the sharing of a single appointment by a faculty couple. Formal screening will begin January 2, 1992. XAVIER UNIVERSITY OF LOUISIANA IOWA To apply, send a complete vita and have three College of Pharmacy letters of recommendation sent to: IOWA STATE UNIVERSITY Professor Richard Randell, Chair A nontenured track faculty position at the rank Department of Mathematics Department of Mathematics of assistant professor in biostatistics is avail University of Iowa able immediately. Competitive salary and fringe Subject to the availability of funds, the Depart Iowa City, Iowa 52242 benefits. A Ph.D. in biostatistics or other re ment of Mathematics of Iowa State University The University of Iowa is an Equal Em lated statistical area is required with preference expects to fill one tenure track position at the ployment Opportunity and Affirmative Action given to those with specialization in experimen assistant professor level in applied partial dif Employer tal design, computational statistics, and/or data ferential equations for the 1991-92 academic analysis and data collection procedures. The year. Start up funds will be available for the appointee will be expected to conduct indepen successful applicant. The successful candidate dent research, serve as a consultant to phar is expected to have a strong interest in teaching macy faculty, and teach biostatistic course(s) to at both the graduate and undergraduate level KANSAS pharmacy students. Letter of application, a cur and maintain an active research program. rent vita, and three letters of recommendation Iowa State is the closest member institution KANSAS STATE UNIVERSITY should be sent to: Chairman, Division of Ba to the NSF Institute for Mathematics and its Department of Mathematics sic Pharmaceutical Sciences, Xavier University Applications in Minneapolis. The Department College of Pharmacy, New Orleans, LA 70125. strongly encourages its faculty and graduate Subject to budetary approval, applications are Xavier University, a historically Black Catholic students to participate in the Institute's programs invited for several tenure-track and visiting University, is an Equal Opportunity Employer. and provides direct and indirect support for them positions commencing August 18, 1992; rank to do so. and salary commensurate with qualifications. We will begin screening applications January All fields will be considered, but for some of the 15, 1992. However we shall continue to accept tenure-track positions, preference will be given applications until the positions are filled. to candidates in Numerical Analysis, Differential MARYLAND A number of visiting positions in diverse Equations, and Global Analysis. Applicants areas of mathematics and applied mathematics must have strong research credentials and a THE JOHNS HOPKINS UNIVERSITY are expected to be available and applications commitment to excellence in teaching. A Ph.D. Department of Mathematical Sciences · for them are also encouraged. Preference will in mathematics or a Ph.D. dissertation accepted be given to those applicants whose interests with only formalities to be completed is required. Applications are invited for a faculty position in are similar to those of the current faculty. Letter of application, current vita, description of OPERATIONS RESEARCH or OPTIMIZATION Iowa State University is an Affirmative Ac research and three letters of recommendation to begin in Fall 1992. Within these areas, tion/Equal Opportunity Employer. Women and should be sent to: either a stochastic or a deterministic emphasis minorities are encouraged to apply. Louis Pigno is of interest. Applicants at all levels will be Applications and three letters of recommen Department of Mathematics considered. dation should be sent to Howard A. Levine, Cardwell Hall 137 Selection is based on demonstration and Chair, Department of Mathematics, Iowa State Kansas State University promise of excellence in research, teaching, University, Ames, Iowa 50011. Manhattan, KS 66506 and innovative application. AA/EOE. Deadline: February 1, 1992 Applicants are asked to furnish a curriculum vitae, transcripts Ounior applicants only), reprints (if available), a letter describing professional -----·------·----·-~-.~.------~~·------1200 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements interests and aspirations, and to arrange for to persons (regardless of age) who have had nearing, Chemical Engineering, Geology, and three letters of recommendation to be sent to: their doctorate less than two years. There will Metallurgical & Materials Engineering, engaged John C. Wierman, Chair also be some positions available at the level in an active program of research in Fluid Me Department of Mathematical Sciences of instructor. Please send a resume and ar chanics. This position will carry an appointment 220 Maryland Hall range to have three letters of recommendation as Associate Professor or Professor. Candi The Johns Hopkins University sent to: Professor Richard E. Phillips, Chair, dates should have an active research record Baltimore, MD 21218-2689 Department of Mathematics, Michigan State in Fluid Mechanics and Applied Mathematics. University, East Lansing, Ml48824-1027: email A good funding record and experience with [email protected]. It would be helpful if Ph.D. students is required. The position starts in resume includes appropriate Mathematics Sub September 1992. Send a curriculum vitae and THE JOHNS HOPKINS UNIVERSITY ject Classification number(s) and (if possible) three letters of recommendation to Recruitment Department of Mathematics electronic address. Applications received by Committee, Department of Mathematical Sci Applications are invited for a position beginning January 4, 1992 will be given more attention. ences, Michigan Technological University, 1400 Fall1992 at the Associate or Assistant Professor MSU is an Affirmative Action/Equal Oppor Townsend Drive, Houghton, Ml 49931-1295. level in partial differential equations or related tunity Institution. Applications will be accepted until February 3, areas. Outstanding research accomplishments 1992. MTU is an equal opportunity educational institution/equal opportunity employer. · and commitment to teaching are required. Applications will be considered from candidates MICHIGAN STATE UNIVERSITY who have received a Ph.D. in mathematics prior Department of Mathematics to 12/89. East Lansing, Ml 48824-1027 Minority and women candidates are strongly encouraged to apply. The Johns Hopkins Uni The Department is seeking applicants for sev SAINT LOUIS UNIVERSITY versity is an Affirmative Action/Equal Opportu eral tenure-track positions; openings are avail nity Employer. able at each of the Assistant, Associate, and Department of Mathematics Applications and recommendation letters Full Professor levels. Excellence in research and Computer Science should be sent to: POE Search Committee, and teaching is essential and applicants in all Saint Louis, MO 63103 Department of Mathematics, The Johns Hopkins areas of research will be considered. Please University, Baltimore, MD 21218. send a resume and arrange to have three letters One or more tenure-track appointments, to of recommendation sent to Professor Richard begin in the Fall of 1992. Candidates should E. Phillips, Chair, Department of Mathematics, have a Ph.D. in mathematics and be com Michigan State University, East Lansing, Ml mitted to teaching and research. Preference 48824-1027: Email [email protected]. given to researchers in analysis, especially It would be helpful if resume includes ap harmonic analysis, Lie group representations, WELLESLEY COLLEGE propriate Mathematics Subject Classification and functional analysis. If more than one ap Department of Mathematics number(s) and (if possible) electronic address. pointment is made, researchers in the area Wellesley, MA 02181 Applications received by January 4, 1992 will of group theory will also be given preference. be given more attention. The Department currently has 13 members, all Two or three tenure-track positions at the Asst. MSU is an Affirmative Action/Equal Oppor of whom are active in research. Representa Professor level beginning Fall1992. The teach tunity Institution. tives of the Department will be present at the ing load is currently four courses per year. joint mathematics meetings in Baltimore. Dead Requirements include a Ph.D. in mathemat line for full consideration is 2/1/92. Send vita ics (completed, or expected by June 1992), (with email address if available) and three let excellence in and commitment to both under MICHIGAN TECHNOLOGICAL UNIVERSITY ters of reference to Bradley Currey, Chair, Facul graduate teaching and mathematical research Mathematical Sciences Department ty Search Committee, (email: curreybn@ in a liberal-arts environment. Candidates with sluvca.slu.edu). Saint Louis University is an The Department of Mathematical Sciences is research interests in any area of mathematics equal opportunity employer; minorities and seeking a tenure track position in Applied Sta will be considered. Applicants should send a women are encouraged to apply. tistics at the Associate or Full Professor level. curriculum vitae and arrange for at least three The department currently offers Bachelor's and letters of recommendation that address both Master's degrees in Statistics. Applicants must teaching and research. Applications and rec have established research, teaching, and fund ommendation letters should be sent to arrive ing records and be able to provide leadership by December 6, 1991 , to ensure full consid for an expanding statistics group. Duties include eration. Reply to: Search Committee, Dept. UNIVERSITY OF NEVADA, RENO teaching, research, and consulting. The position of Math., Wellesley College, Wellesley, MA Department of Mathematics starts in September 1992. Send a curriculum 02181. Wellesley College is an Equal Opportu Chair Wanted vitae and three letters of recommendation to nity/Affirmative Action Employer and particularly Recruitment Committee, Department of Mathe encourages applications from women and mi Do you have what it takes to lead a Math matical Sciences, Michigan Technological Uni nority candidates. Department boldly into the future? Would you versity, 1400 Townsend Drive, Houghton, Ml welcome the opportunity to make an impact on 49931-1295. Applications will be accepted until an entire state? If you answered "yes" to these February 3, 1992. MTU is an equal oppor questions, then UNR invites your application! tunity educational institution/equal opportunity The Department of Mathematics is seeking employer. a dynamic, well-rounded individual to be its MICHIGAN STATE UNIVERSITY Chair. Currently the department has 15 faculty. Department of Mathematics Among these are three recipients of distin East Lansing, Ml48824-1027 MICHIGAN TECHNOLOGICAL UNIVERSITY guished teaching awards and one outstanding Mathematical Sciences Department researcher award. More faculty members will One or more Postdoctoral fellowships in Mathe be added in the near future, and the chair will matics. The appointment is for two years. Duties The Department of Mathematical Sciences is play a key role in making those hires. include teaching one course each semester of seeking a director for the Fluids Research We offer B.A., M.S., and M.A.T.M. degrees in the academic year with the expectation that Oriented Group (F.R.O.G.). F.R.O.G. is an mathematics. We are committed to excellence in the fellow will devote remaining time to re interdisciplinary group, involving Departments teaching at all levels, especially in the university search. These fellowships are normally offered of Mathematical Sciences, Mechanical Engi- wide core curriculum math courses. We are ·also NOVEMBER 1991, VOLUME 38, NUMBER 9 1201 Classified Advertisements working to increase the quantity and quality of STATE UNIVERSITY OF NEW YORK our research output. NEW MEXICO AT BUFFALO We intend that this position be filled by Department of Mathematics someone with the qualifications of a full profes NEW MEXICO STATE UNIVERSITY sor, so an applicant must have a substantial and Las Cruces, New Mexico The Department of Mathematics anticipates the continuing record of scholarly achievement, re Department of Mathematical Sciences appointment of several tenured or tenure-track search, and demonstrated interest in teaching. faculty members beginning September 1, 1992. Salary will be competitive and commensurate Possible visiting and tenure-track positions in Salary will be competitive. We seek applicants with qualifications of the applicant. pure and applied mathematics and statistics in all areas with excellent research accomplish Applications should include biographical in for 1992-93, primarily assistant professor level. ments/potential and a strong commitment to formation and names, addresses (including Strong commitment to both research and teach teaching. email, if appropriate), and telephone numbers ing required. Applications from women and Applicants should send supporting infor of five references. Please send to Don Pfaff, De members of minority groups welcome. Applica mation, including their relevant primary and partment of Mathematics, University of Nevada, tions kept on file through hiring period. Arrange secondary AMS subject classification numbers, Reno, Reno, NV 89557, [(702) 784-6775; email for vita, short research description, and three and have four letters of recommendation sent address: [email protected]; FAX: 702-784-1478]. reference letters to be sent to: Hiring Commit to: Review of applications will begin November 15, tee, Department of Mathematical Sciences, New Dr. Lewis A. Coburn 1991; the search will continue until the position Mexico State University, Las Cruces, NM 88003. Search Committee Chairman is filled. Equal Opportunity/Affirmative Action Employer. Department of Mathematics The University of Nevada, Reno is an Equal SUNY/Buffalo Opportunity, Affirmative Action employer and 1 06 Diefendorf Hall does not discriminate on the basis of race, Buffalo, New York 14214 creed, color, sex, age, national origin, veteran The deadline for applications is December status or handicap in any program or activity 1 , 1991 . Late applications will be considered it operates. The University of Nevada employs NEW YORK until positions are filled. only United States citizens or aliens lawfully SUNY/Buffalo is an Equal Opportunity/Af authorized to work in the United States. COLLEGE OF STATEN ISLAND (CUNY) firmative Action Employer. We are interested in identifying prospective minority and women Department of Mathematics candidates. No person, in whatever relationship A tenure-track position in mathematics is avail with the State University of New York at Buffalo able for Fall1992. Requirements: Ph.D., strong shall be subject to discrimination on the basis commitment to undergraduate teaching and to of age, creed, color, handicap, national origin, NEW HAMPSHIRE a productive research program. All mathematics race, religion, sex, marital or veteran status. research areas will be considered with special UNIVERSITY OF NEW HAMPSHIRE preference given to areas of strength within the department. These areas include probability, The University of New Hampshire, Department group theory and applied mathematics. The of Mathematics invites applications for tenure position is budgeted at the assistant professor track, Assistant Professor to begin September level. The College of Staten Island is a senior 1992. Applied Mathematics Ph.D. is required in NORTH CAROLINA college in CUNY. Send resume and three letters field of specialty. Strong commitment to teaching of reference to Dr. Jane Coffee, Chairperson, NORTH CAROLINA STATE UNIVERSITY in both graduate and undergraduate programs Mathematics Department, College of Staten Is is expected. Send resume (hiring is contingent Department of Mathematics land, 130 Stuyvesant Place, Staten Island, N. Y. upon eligibility to work in the U.S.) and names Research Instructor - Mathematical Physics 10301, by January 15, 1992. AAIEOE Employer. of three references by December 1, 1991 to: The Department of Mathematics at North Car Professor Donovan H. Van Osdol, Chairman, olina State University is soliciting nominations University of New Hampshire, Department of and applications for a Research Instructor in Mathematics, M312 Kingsbury Hall, Durham, Mathematical Physics. The position is avail NH 03824. UNH is an AA!EOE employer. able for 2 years beginning in the Fall of SUNY COLLEGE AT BROCKPORT 1992. The applicant should not have received Brockport, NY 14420 his/her doctorate prior to 1990. The position Department of Mathematics requires a strong commitment to research and no more than 6 credit hours of teaching per Tenure-track assistant professorship in Math semester. The applicant's research interests NEW JERSEY ematics available September 1992. Ph.D. in should be compatible with those of the Depart STOCKTON STATE COLLEGE Mathematics (or Ph.D. in Statistics with strong ment's existing Mathematical Physics group. An component), one year of teaching expe international symposium will be held at the Uni Department of Mathematics math rience, demonstrated ability to carry out and versity honoring Cornelius Lanczos during the Mathematics-Assistant Professor/Instructor. publish scholarly research in the discipline re candidate's tenure in December 1993. To en Tenure-track, Sept. 1992. Required: Ph.D. for quired. Expertise in Prob/Stat, Discrete Math, or sure full consideration candidates should send Assistant Professor; ABO for Instructor. To be Applied Math preferred; other areas considered. a vitae, a description of research, visa status, part of a strong, nine-person mathematics de Strong commitment to teaching a culturally di and at least 3 letters of recommendation, one of partment. Salary competitive. Area of specialty ve~se student body at undergraduate and Mas which discusses his/her teaching qualifications, is open. Screening begins immediately. Send ter's levels. For further details: call N. Bloch, to Professor R. 0. Fulp, Dept. of Mathematics, letter of application, resume and 3 letters. of Chair, at (716)395-2194. Send application, tran Box 8205, N.C. State University, Raleigh, NC reference to Dr. Barbara Byrne, Dean, Natu scripts, resume, and three letters of reference 27695-8205 on or before January 15, 1992. ral Sciences and Mathematics, Stockton State by November 25, 1991 to: Office of Faculty/Staff For foreign candidates the offer of employ College, AA76, Pomona, NJ 08240. Stockton Relations, SUNY College of Brockport, Brock ment is contingent upon an appropriate visa is an AA!EOE, Women and minorities are port, NY 14420. Late applications considered status. Women and minorities are especially encouraged to apply. until position is filled. AAIEOE. encouraged to apply. NCSU is an AA/EOE. 1202 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements UNIVERSITY OF NORTH CAROLINA Columbus, Ohio 43210. Review of resumes will ysis. Postdoctoral experience is desirable, but AT CHAPEL HILL begin immediately. not essential. Department of Mathematics The Ohio State University is an Equal Op For the postdoctoral and visiting positions we Chapel Hill, NC 27599-3250 portunity/Affirmative Action employer. Qualified especially encourage, in addiiion to the above women and minority candidates are encouraged areas, applicants in Number Theory, Functional Applications are invited for one faculty ap to apply. Analysis and Banach Spaces, Lie Groups and pointment effective Fall1992. Rank and salary Representation Theory, Numerical Analysis and depend on qualifications and budget consider Approximation Theory. ations. Ph.D. in mathematics highly preferred, For full consideration, send a resume and exceptionally strong research program and com THE OHIO STATE UNIVERSITY arrange to have three confidential letters of mitment to excellent teaching required. Send Department of Mathematics reference sent by December 15, 1991 to Robert Myers, Appointments Committee Chairman, De curriculum vitae, abstract of current research Research Instructorships in Mathematics program and four letters of recommendation to partment of Mathematics, Oklahoma State Uni Search Committee Chairman, Math. Dept., CB The Department of Mathematics of The Ohio versity, Stillwater, OK 74078-0613. OSU is an #3250 Phillips Hall, UNC at Chapel Hill, Chapel State University hopes to have available a few affirmative action equal opportunity employer Hill, NC 27599-3250. EO/AA Employer. Women research instructor positions for the academic committed to multicultural diversity. and minorities are encouraged to identify them year 1992-93. Candidates should hold a Ph.D. selves voluntarily. Completed applications re (or equivalent) in mathematics and show strong ceived by February 15, 1992 are assured of full research promise. consideration. Please send credentials and have letters of recommendation sent to Professor Dijen Ray Chaudhuri, Department of Mathematics, The PENNSYLVANIA Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210. The Ohio State Univer COMMUNITY COLLEGE OF PHILADELPHIA OHIO sity is an Equal Opportunity/Affirmative Action Department of Mathematics employer. INSTITUT DE CALCUL MATHEMATIQUE Mathematics Dept. invites applications for a KENT STATE UNIVERSITY tenure-track Asst. Professorship position begin ning Fall 1992. The Dept. is actively engaged B. Beauzamy, P. Enflo and P. Wang wish to OHIO UNIVERSITY in course development. It has recently received develop their research group on Quantitative grants from NSF and CASET. Teaching load is Department of Mathematics estimates for polynomials in one or several 12 credit hours per semester. Candidates must variables and they encourage applications for have a Ph.D. or Master's +3 years teaching Ph.D. studies (These) in this direction. The Department of Mathematics anticipates the appointment of one tenure-track assistant, as in Mathematics, and a commitment to qual The topic has direct applications to Analysis ity teaching, both remedial and college level. (Fourier Analysis, Harmonic Analysis), to Num sociate or full professor beginning September 1, 1992. Salary (at least $30,000 per year) and Demonstrated strength in course development ber Theory, and Computer Science (Symbolic is essential. Candidates should provide clear Computation, Massively Parallel Programming). rank dependent on candidate's qualification and experience. The appointment of associate full evidence of strong background in Mathematics, It is supported by the National Science Founda together with ability to bring to the first 2 years, tion (U.S.A.), the C.N.R.S. (France), the Ministry professor rank may be contingent on budgetary constraint. Applicants must have a Ph.D. in mathematical topics usually delayed until later. of Defense (France), and DIGITAL Eq. Corp. Outstanding benefits. Send curriculum vitae The applicants should be citizens either of Mathematics before September 1, 1992 and have research interests in general topology or with 3 letters of recommendation by January the U.S. or of one of the countries of the 31, 1992 to: Head, Dept. of Mathematics, COM European Community. They will have to work set theory with possible applications to topology. Only exceptionally well-qualified individuals will MUNITY COLLEGE OF PHILADELPHIA, 1700 either in Paris or in Kent, and may have to travel Spring Garden St., Phila., PA 19130. AA/EOE. between both places. be considered for the associate or full profes Please write to: Prof. Bernard Beauzamy, sor rank. Send resume and have three letters lnstitut de Calcul Mathematique, Universite de of recommendation sent to Shih-liang Wen, Paris 7, 2 Place Jussieu, 75251 Paris Cedex Chairman, Department of Mathematics, Ohio 05, France, or to Prof. Per Enflo, Prof. Paul University, Athens, Ohio 45701. The deadline for applications is January 1, 1992. Ohio Univer Wang, Department of Mathematical Sciences, LEHIGH UNIVERSITY Kent State University, Kent, Ohio 44242, U.S.A. sity is an Equal Opportunity/Affirmative Action Employer. Department of Mathematics The Department of Mathematics at Lehigh University invites applications and nominations THE OHIO STATE UNIVERSITY for two tenure-track positions beginning with Department of Mathematics OKLAHOMA the Fall Semester 1992. Both positions are at the level of Assistant Professor. Preference will The Department of Mathematics of The Ohio OKLAHOMA STATE UNIVERSITY be given to researchers in the continuum from State University hopes to have available sev Department of Mathematics algebraic topology through differential geometry eral positions, both visiting and permanent, to global analysis and in algebra, specifically effective Autumn Quarter 1992. Candidates in Several tenure-track, postdoctoral, and visiting in an area overlapping combinatorics, discrete all areas of applied and pure mathematics, positions are anticipated for Fall 1992. Normal mathematics, and computational algebra. including those with demonstrated interest in duties include research and at most six hours Candidates for the positions must have an pedagogical matters, are invited to apply. Signif teaching per semester. Minimum qualifications earned doctorate in mathematics and an excel icant mathematical research accomplishments are a Ph.D. in Mathematics or a related field, lent record in teaching and research. Applicants or exceptional promise, and evidence of good evidence of research achievement or potential, should send a curriculum vita, reprints of pub teaching ability, will be expected of successful and a commitment to teaching. lished papers (or accepted for publication), and applicants. For the tenure-track positions all areas are at least three letters of recommendation to Please send credentials and have letters of under consideration; we especially encourage Search Committee, Department of Mathematics recommendation sent to Professor Dijen Ray applicants in Differential Geometry, Algebraic (Bldg 14), Lehigh University, Bethlehem, PA Chaudhuri, Department of Mathematics, The Geometry, Algebraic and Geometric Topology, 18015. Applications from minorities and women Ohio State University, 231 W. 18th Avenue, Several Complex Variables, and Harmonic Anal- are strongly encouraged. The selection process NOVEMBER 1991, VOLUME 38, NUMBER 9 1203 Classified Advertisements will begin in January 1992, and continue until application, resume, transcript and three {3) gebra/combinatorics, analysis, computational the positions are filled. current letters of recommendation to: math, operations research and statistics. Prefer Lehigh University is an equal opportunity Search Committee, Chairperson ence will be given to candidates having a strong and affirmative action employer. Mathematics Department background in algebra with some research in Slippery Rock University terest in combinatorics. Desirable attributes for Slippery Rock, PA 16057 candidates include an interdisciplinary research To ensure consideration, application mate orientation in the mathematical sciences and an MUHLENBERG COLLEGE rials should be received by January 31, 1992. interest in innovative applications. Candidates Truman Koehler Professorship Applications will be accepted until the position is should have strong potential or demonstrated of Mathematics filled. Slippery Rock University is an Affirmative capability for effective research and teaching. Action/Equal Opportunity Employer. All of the above areas of the mathematical Mathematics Department seeks nominations/ sciences are integrated into degree programs applications for this tenure track professorship at the BS, MS, PhD levels. In addition, the department jointly administers a PhD program beginning August 1992. Requirements include TEMPLE UNIVERSITY doctorate in mathematics sciences, minimum in Management Science with the Department of five years college/university teaching, publi Department of Mathematics Management. Applications received by Febru cation record and demonstrated competence Faculty Position ary 15, 1991, will be given highest priority, but in teaching and student research/independent others will be considered until position is filled. The Mathematics Department anticipates a study. Please send application letter, resume, Applicants should indicate in the cover letter tenure-track position opening at the junior level and names of three references to Dr. John their research specialities. Vita and names of beginning Fall 1992. Preferred fields are Sev Meyer, Head, Dept. of Mathematics, Muhlen three references should be sent to address eral Complex Variables and Geometry/Topology. berg College, Allentown, PA 18104. Screening below. Reference letters will be requested when Vita and three letters of reference should be begins in early January, with preliminary inter necessary. AA/EOE sent by December 31, 1991 to Search Com views possible at Baltimore meetings. EOE. Professor R. D. Ringeisen, Head mittee, Department of Mathematics, Temple File A University, Philadelphia, PA 19122. Department of Mathematical Sciences Women and Minorities are especially en Clemson University couraged to apply. Temple University is an Clemson, SC 29634-1907 PENNSYLVANIA STATE HARRISBURG Affirmative Action and Equal Opportunity STATISTICs-Penn State Harrisburg. The Math Employer. ematical and Computer Science program of Penn State Harrisburg solicits applications for WINTHROP COLLEGE a tenure-track position in Statistics. Applicants UNIVERSITY OF PITTSBURGH Department of Mathematics should have a Ph.D. in statistics; a specializa Department of Mathematics Winthrop College is seeking a tenure-track fac tion in one or more of the following areas: linear and Statistics and nonlinear regression, experimental design, ulty member at the associate or assistant level. industrial engineering, and quality control; a The department invites applications for the Applicants in the area of applied statistics are strong interest in teaching; and a willingness following positions, which will be available for encouraged to apply. Special consideration will to teach a variety of courses. Promotion and September 1992 if funding permits. be given to applicants with documentation of tenure criteria include teaching effectiveness, 1. Assistant Professor in pure mathematics. teaching excellence. Winthrop is a state sup research, scholarship, and service. Penn State We have a significant interest in someone in ported comprehensive college of SC, located Harrisburg, an upper division and graduate col algebra, topology, or geometry. approximately 20 miles south of Charlotte, NC, lege with an enrollment of approximately 2000 2. Visiting Assistant Professor in mathemat with an enrollment of 5000 students. An applica undergraduates and 1500 graduate students, is ical biology. Here we have a preference for an tion, vita, and three letters of recommendation located in a suburban setting near the state cap individual with a strong computational aspect are required. The reviewing of applications will ital. The program offers undergraduate degrees to their research. There is a possibility that begin February 3, 1992. Winthrop College is an in mathematical sciences, both undergraduate the person appointed to this position will be EOI and an AAE. Applications are to be sent and graduate degrees in computer science, and considered for a tenure-track position for the to: Dr. Ron C. Goolsby, Chair, Department of service courses for undergraduate and graduate following year. Mathematics, Winthrop College, Rock Hill, SC students in engineering, business, and educa Requirements include outstanding research 29733 tion. Send resume, copies of college transcripts, accomplishment and potential commensurate and three letters of reference by 15 January with experience, and ability and interest in 1992 to Statistics Search Committee, c/o Ms. excellent teaching. Sandra Jackson, Penn State Harrisburg, 777 W Applicants should send resume and arrange TENNESSEE Harrisburg Pike, Middletown, PA 17057-4898. to have at least three letters of recommendation AN AFFIRMATIVE ACTION/EQUAL OPPOR sent to: S. Hastings, Chairman, Department UNIVERSITY OF TENNESSEE, TUNITY EMPLOYER. WOMEN AND MINORI of Mathematics and Statistics, University of Mathematics Department TIES ARE ENCOURAGED TO APPLY. Pittsburgh, Pittsburgh, PA 15260. Knoxville, TN 37996-1300 The University of Pittsburgh is an equal opportunity/affirmative action employer. Women The Mathematics Department of the University and minorities are especially encouraged to of Tennessee, in an effort to significantly improve SLIPPERY ROCK UNIVERSITY apply. its research position, seeks to fill a tenure-track Mathematics Department Faculty assistant professorship in harmonic analysis, several complex variables, function theoretic Tenure-track, full-time position available be operator theory, differential geometry, numer ginning fall semester, 1992. Faculty rank ne SOUTH CAROLINA ical mathematics, theoretical probability and gotiable. Duties include teaching an average stochastic processes. Employment begins Au of twelve {12) semester hours of undergrad CLEMSON UNIVERSITY gust 1992. Substantial research as well as ded uate mathematics courses per semester and Clemson,SC ication to teaching are paramount. Interested participating in department activities. Ph.D. in applicants should arrange to have a vita, three mathematics and college mathematics teaching Applicants are invited for a tenure-track po reference letters, and a research statement experience required. Minorities and women are sition at the assistant professor level. The sent to Professor John B. Conway, Mathemat especially encouraged to apply. Send letter of department encompasses the areas of al- ics, University of Tennessee, TN 37996-1300. 1204 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements Review of applications will begin December 1 Committee, Department of Mathematics, Rice of recommendation to be sent to Professor and will continue until the position is filled. University, P.O. Box 1892, Houston, TX 77251. Gladwell. UTK is an EEO/AAfTitle IX Section 504/ADA Applications received by December 31, 1991 SMU is an equal opportunity/affirmative ac- Employer. will be assured full consideration. tiomtle IX employer. Rice University is an Equal Opportunity/Af I. Gladwell's email addresses: firmative Action Employer. [email protected] h5n 1001 @smuvm1.bitnet VANDERBILT UNIVERSITY h5nr1 001 @vm.cis.smu.edu Department of Mathematics RICE UNIVERSITY 1326 Stevenson Center Griffith Conrad Evans Nashville, TN 37240 THE UNIVERSITY OF TEXAS AT AUSTIN Instructorships Department of Mathematics ASSISTANT PROFESSOR. Specialization in Austin, Texas 78712 approximation theory, computer-aided design, Postdoctoral appointments for two to three years for promising research mathematicians with re or numerical analysis. This position is intended Openings are expected for Fall 1992 at all for a person whose primary research involves search interests in common with the active levels, including Instructor, Assistant Professor, research areas at Rice, particularly geometric computing. It is an initial 3 year appointment Associate Professor and Professor. Candidates topology, geometric analysis, differential geom beginning Fall 1992. It is renewable and tenure should have outstanding research ability and etry, mathematical physics and ergodic theory. track. Outstanding research potential and ev concern for teaching. Duties include teaching Duties will include research and classroom idence of effective teaching is required. Have undergraduate and graduate courses and con teaching. Applications received by December vita and 4 letters of recommendation (including ducting independent research. Applicants at all 31, 1991 will receive full consideration. Rice one about teaching) sent to Professor Glenn levels are expected to have completed the University is an Equal Opportunity/Affirmative Webb, Chair. Ph.D. by August 31, 1992. Salaries are com Action Employer and strongly encourages ap VANDERBILT UNIVERSITY IS AN EQUAL petitive. If you have access to email, request OPPORTUNITY/AFFIRMATIVE ACTION EM plications from women and minority group a form from [email protected]. Oth members. Inquiries and applications should be PLOYER erwise please send vita, detailed summary of addressed to Chair, Evans Committee, Depart research interests and three recommendation ment of Mathematics, Rice University, PO Box letters to address above, directed as follows: 1892, Houston, TX 77251-1892. Instructor and Assistant Professor: c/o VANDERBILT UNIVERSITY Recruiting Committee; Associate Professor Department of Mathematics and Professor: c/o Efraim P. Armendariz, 1326 Stevenson Center SOUTHERN METHODIST UNIVERSITY Chairman Nashville, TN 37240 Department of Mathematics The University of Texas at Austin is an equal opportunity employer. Minorities and women are ASSISTANT PROFESSOR. Ph.D. required with The Department of Mathematics at Southern encouraged to apply. two-year appointment beginning Fall1992. This Methodist University invites applications for a is not a tenure track appointment but is intended senior level and a junior level tenure-track po for a person with demonstrated research poten sition, with employment beginning in Fall 1992. THE UNIVERSITY OF TEXAS AT DALLAS tial who would like to spend time in a department The applicants must be active researchers, Faculty Position in with a vigorous research atmosphere. We are -must have a strong commitment to undergrad Mathematical Sciences especially interested in someone who works uate teaching and must be ready to teach in one of the areas of departmental strengths advanced courses in the doctoral program in Applications are invited for an anticipated tenure which include universal algebra, differential applied mathematics, numerical analysis and track assistant professorship faculty position in equations, approximation theory, operator the scientific computation. The senior applicants Applied Mathematics or Statistics beginning Fall ory, mathematical biology, applied mathematics, must have research interests in applied math 1992. Ph.D. in relevant field is required. Ap graph theory, and topology. Applicants should ematics, must be ready to supervise doctoral plicants must demonstrate research potential. have a strong commitment to teaching. Have dissertations, and must have a strong grant Particular fields of interest are inverse scat vita and four letters of recommendation (includ record. The junior applicants must be active in tering, robust statistics, systems and control, ing one about teaching) sent to Professor Glenn research in numerical analysis. The standard signal processing and statistical computing. Re Webb, Chair. teaching load is two courses (six hours) per sponsibilities include research, teaching, and VANDERBILT UNIVERSITY IS AN EQUAL semester. direction of Ph.D. dissertations. Excellent com OPPORTUNITY/AFFIRMATIVE ACTION EM Departmental research interests include fluid puting facilities. Salary competitive. Applicants PLOYER. mechanics, numerical analysis of differential should send a curriculum vita and at least equations, mathematical software, asymptotic three letters of reference (indication of sex and and perturbation methods, nonlinear waves, bi ethnicity for Affirmative Action statistical pur furcation theory, combustion theory, dynamical poses is requested but not required) to: The TEXAS systems, and mathematical biology. Thirteen University of Texas at Dallas, Academic'Search of the sixteen faculty are applied or numerical #2003, P. 0. Box 830688, Richardson, Texas RICE UNIVERSITY mathematicians. Senior faculty include W. E. 75083-0688. Applications accepted until2/1/92, Department of Mathematics Ferguson (numerical partial differential equa or later if position not filled. The University is an tions), I. Gladwell (mathematical software), R. Affirmative Action/Equal Opportunity employer. Applications are invited for a tenure-track assis Haberman (nonlinear waves), G. W. Reddien tant professorship. There is a possibility of an (numerical bifurcation theory), D. A. Reinelt upgrade to associate or full professorship for an (fluid mechanics), and L. F. Shampine (numer exceptional senior candidate. Candidates must ical ordinary differential equations). Southern UTAH have an extremely strong research background Methodist University has a 20 processor Se and good teaching skills. Preference will be quent Symmetry for research use. given to applicants in geometric topology, ge The application deadline is January 15, BRIGHAM YOUNG UNIVERSITY ometric analysis, partial differential equations, 1992. Send a letter of application and a vita to: Department of Mathematics and algebraic geometry. Duties will include Professor I. Gladwell, Chairman, Department research and classroom teaching. of Mathematics, Southern Methodist University, Applications are invited for one position in the Please send a curriculum vitae and at least Dallas, Texas 75275 (Tel. (214) 692-2506). specialty of nonlinear POE and computational 3 letters of recommendation to: Appointments Applicants should arrange for three letters mathematics. NOVEMBER 1991, VOLUME 38, NUMBER 9 1205 .. -········-·---···---·-·------Classified Advertisements Selection will be based upon a proven record 24061-0123. Women and minorities are en D. Gunzburger, Department of Mathematics, of research and teaching ability. Applications will couraged to apply. Virginia Tech is an Equal Virginia Tech, Blacksburg, VA 24061-0123. be accepted until1 February 1992. Please send Opportunity/Affirmative Action Employer. Virginia Tech is an Equal Opportunity, Affir a curriculum vitae and have three letters of mative Action Employer. In keeping with Virginia reference sent to: Tech's commitment to providing equal opportu Donald W. Robinson nity for all, women, minorities, and the disabled 292 TMCB VIRGINIA POLYTECHNIC INSTITUTE are especially encouraged to apply. Brigham Young University AND STATE UNIVERSITY Provo, UT 84602 Department of Mathematics BYU is an Equal Opportunity/Affirmative Action VIRGINIA POLYTECHNIC INSTITUTE employer. Applications are invited for a tenure-track ap pointment at the level of Assistant Professor in AND STATE UNIVERSITY the general area of Dynamical Systems begin Department of Mathematics ning with the 1992-93 academic year. A Ph.D. po and strong research potential are required. A Applications are invited for a tenure-track sition in Geometry (differential or algebraic, or likelihood of productive interaction with current Because VIRGINIA senior faculty members, such as the group related areas) beginning Fall 1992. we seek applicants who will be able to de in partial differential equations and continuum promotion MARY WASHINGTON COLLEGE mechanics, would be helpful. Since the posi velop a strong case for eventual and tenure, preference will be given to those Department of Mathematics tion involves teaching duties of approximately with postdoctoral or instructorship experience six hours per week, there should be strong and established research programs. Please Applications are invited for at most two tenure indications that the candidate is or will become send vita and brief description of research and track Assistant Professor positions effective an effective teacher. Applicants should send a sent to Prof. 8/15/92. Candidates should have a Ph.D. in vita and arrange to have three letters of refer have three letters of reference Frank Quinn, Chair, Geometry Search Commit Mathematics and be committed to teaching. ence submitted to Kenneth B. Hannsgen, Chair, Tech, Those who also desire to continue their re Dynamical Systems Search Committee, Depart tee, Department of Mathematics, Virginia Blacksburg, VA 24061-0123. Applications will search (in any area) or to make significant ment of Mathematics, Virginia Tech, Blacksburg, position service contributions (to the Department and VA 24061-0123. Applications will be accepted be accepted until March 15, or until is filled. Virginia Tech is an Equal Opportu College) are particularly encouraged to apply. for as long as a position remains available but University The Department has ten full-time faculty. The no later than May 1, 1992. nity/Affirmative Action Employer. The and usual teaching load is four courses per semester Virginia Tech is an Equal Opportunity, Affir takes its affirmative action mission seriously applications with ~ 25 students per lower-level course and~ mative Action Employer. In keeping with Virginia is especially interested in receiving from women and people of color. 14 students per upper-level. Mary Washington Tech's commitment to providing equal opportu College is a small <~ 3500) undergraduate nity for all, women, minorities, and the disabled liberal arts college, and the Department has are especially encouraged to apply. 70+ majors. Areas of faculty (research) activ VIRGINIA POLYTECHNIC INSTITUTE ity include semigroups, graph theory, topology, AND STATE UNIVERSITY number theory, and differential geometry. Send Department of Mathematics vita to: VIRGINIA POLYTECHNIC INSTITUTE Marie Sheckels AND STATE UNIVERSITY The department invites applications in the Department Search Committee Department of Mathematics area of partial differential equations. Applicants Dept. of Mathematics should have a strong theoretical background in Mary Washington College The Department of Mathematics at Virginia Tech partial differential equations and a demonstrated Fredericksburg, VA 22401 is seeking qualified applicants for a tenure-track interest in applications. We are particularly in The review of applicants will begin in Novem position at the rank of Assistant Professor in the terested in applicants at the assistant professor ber 1991, and will continue until the positions area of Computational Mathematics/Numerical level. Applicants should submit a curriculum are filled. Mary Washington College is an Equal Analysis. The position should be available vitae and list of publications and arrange three Opportunity/Affirmative Action Employer. beginning with the 1992-1993 academic year. letters of recommendation to be sent to Michael A Ph.D. and strong research potential are Renardy, Chair, Applied POE Search Commit required. tee, Department of Mathematics, Virginia Tech, The Department currently includes a large Blacksburg, VA 24061-0123. Applications ac group of Applied Mathematicians including a cepted until March 15, 1992 or until position number of numerical analysts and computa is filled. Virginia Tech is an Equal Opportu tional scientists. Also, through the Interdisci nity/Affirmative Action Employer. The University VIRGINIA POLYTECHNIC INSTITUTE plinary Center for Applied Mathematics, mem takes its affirmative action mission seriously and AND STATE UNIVERSITY bers of the Department have developed close is especially interested in receiving applications Department of Mathematics collaborations with numerous scientists and from women and people of color. engineers throughout the University. We seek The Department of Mathematics is actively applicants who will be able to interact with the seeking applications for a tenure-track position present staff and aid in the further development in the area of discrete mathematics, combi of the Computational Mathematics/Numerical WEST VIRGINIA natorics, and graph theory beginning with the Analysis program in the Department. The posi 1992-93 academic year. Candidates with an tion involves teaching duties of approximately WEST VIRGINIA UNIVERSITY interest in computing are especially encouraged six hours per week; thus, there should be strong Department of Mathematics to apply. A Ph.D. and strong research poten indications that an applicant is or will become tial are required. Preference will be given to an effective teacher. The Department of Mathematics intends to candidates with postdoctoral experience. Appli The deadline for applications is March 15, make two faculty appointments at the Assistant cations will be accepted until March 15, 1992 1992; after that date, applications will be en Professor rank that will commence August 1992. or until the position is filled. Applicants should tertained only if the position remains unfilled. A Candidates are expected to have a Ph.D. in send a curriculum vitae and arrange to have curriculum vitae, description of research inter mathematics or equivalent with a strong record three letters of reference submitted to Chair, ests, including a synopsis of the dissertation, or demonstrated potential in both research and Discrete Math Search Committee, Department three letters of recommendation and any other teaching. Preference will be given to applicants of Mathematics, Virginia Tech, Blacksburg, VA supporting materials should be sent to Max whose research interests complement those 1206 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements currently in the Department. One appointment algebras, representation theory and related The research groups in mathematical comput will be in analysis, applied analysis, or numeri subjects ing and VLSI architectures are also members cal analysis. The other, pending funding, will be • Ability to establish constructive working of two inter-university research centres: CI in algebra or discrete mathematics. Normal re relations with students and colleagues CMA(Centre lnteruniversitaire en Calcul Math sponsibilities include research and a two course DESIRABLE: ematiques Algebrique) and GRIAO(Groupe de teaching assignment per semester at the grad • Background of efficient and effective Recherche lnteruniversitaire en Architecture uate or undergraduate level. Applications and teaching at University level des Ordinateurs de Haute Performance et inquiries should be directed to Michael Mays, • Compatability with and willingness to join VLSI). In particular, CICMA promotes research Department of Mathematics, West Virginia Uni a research team led by Professor lan Raeburn. in algebraic computing, combinatorics and com versity, Morgantown, WV 26506. Applicants SALARY: Salary will be in the range putational group theory. The department also should submit a vita and have three letters of $47,500-$55,000 depending on qualifications intends to strengthen its activities in software reference sent. To insure consideration, applica and experience. systems. To promote the development of new tion materials must be received by January 15, GENERAL: For further information please faculty members, the university has a program 1992. WVU is an affirmative action/equal oppor contact Professor I. Raeburn by telephoning to provide seed grants for their research in the tunity employer. Qualified women and minorities (049) 215535 or via overseas fax number first three years. are especially encouraged to apply. 0011+61+49+216900. Concordia is committed to Employment Eq Applications close 15th December, 1991. uity and encourages applications from women, GENERAL INFORMATION: Further informa aboriginal peoples, visible minorities and dis tion concerning conditions of employment may abled persons. All things being equal, women be obtained by contacting the Recruitment Unit, candidates shall be given priority. Interested ap telephone (049) 215444. plicants should send a resume and the names Applications quoting the appropriate posi of at least three references to WYOMING tion number and including the full details of Chair, Department Personnel qualifications and experience, and the names, Committee THE UNIVERSITY OF WYOMING addresses and telephone numbers of three Department of Computer Science Department of Mathematics referees should be addressed to reach the Concordia University Position in Mathematics undermentioned by the date specified above. 1455 de Maisonneuve West The Staff Office, The University of Newcas Montreal, Quebec H3G IM8 Applications are invited for a tenure-track po tle, NSW. 2308 Canada sition in Applied Mathematics or Analysis at The University is an Equal Opportunity Fax (514)848-2830 the rank of assistant professor. Strong consid Employer and has a policy of no smoking in the email: [email protected] eration will be given to, but not limited to, the workplace. In accordance with Canadian Immigration following areas: partial differential equations, requirements, priority shall be given to Canadian numerical linear algebra, applied functional citizens and permanent residents of Canada. analysis, and numerical analysis. Salary is com petitive and commensurate with experience and CANADA qualifications. Candidates should demonstrate McMASTER UNIVERSITY accomplishment and potential in research and CONCORDIA UNIVERSITY Department of Mathematics teaching. Department of Computer Science Applicants should send vita, three let & Statistics ters of recommendation, and brief descrip We are looking for new faculty members with Applications are invited for the Britton Post tion of his/her research plans to: Dr. John either strong research records or excellent re Doctoral Fellowship in Mathematics. Named George, Chairman, Department of Mathemat search potential to fill two tenure track positions after Dr. Ronald Britton, the Britton Fellowship ics, University of Wyoming, Laramie, Wyoming in the Assistant or Associate Professor rank. is intended for talented, young research math 82071. Email inquiries should be sent to Applicants must have an interest and ability ematicians who have recently completed the [email protected]. Applications to teach effectively at both the undergradu Ph.D. degree. The Britton Fellowship is open completed by January 15, 1992 will receive ate and graduate levels. Selected candidates to candidates of any nationality and selection first consideration. The University of Wyoming will be expected to carry out independent re will be based upon the candidate's research is an AAIEOE. search and other academic duties associated potential. Preference will be given to candi with our bachelor's, master's and Ph.D. pro dates working in partial differential equations grams. To fit our needs, priorities will be given or harmonic analysis. The Britton Fellowship is to the following areas: software engineering, tenable for a period of two years with effect from programming languages, expert systems and July 1, 1992 at a salary of $34,000 per year combinatorial computing. However, truly excep plus a research grant of $5,000. Applications, tional candidates in all computer science areas including three letters of reference, should be are encouraged to apply. AUSTRALIA completed by January 31, 1992 and sent to: Dr. The university is located in Montreal which I. Hambleton, Chairman or V. P. Snaith, Sc.D., UNIVERSITY OF NEWCASTLE is well known for its cultural diversity and F.R.S.C., Britton Professor of Mathematics, beauty. The department houses approximately Senior Lecturer Dr. P. Guan, Dr. E. Sawyer, Department of 600 undergraduates, 90 Masters and 30 Ph.D. Department of Mathematics Mathematics & Statistics, McMaster Univer students. While the undergraduate program em sity, Hamilton, Ontario, Canada, L8S 4K1. The appointee would be expected to be able phasizes both fundamental and practical skills, to make a significant contribution to teaching, our graduate research concentrates in artificial play a major role in sholarship, research and/or intelligence, combinatorics, computer algebra, professional activities, and have significant rel databases, distributed computing, large-scale McMASTER UNIVERSITY evant experience and a demonstrated record of scientific computing, pattern recognition, pro Department of Mathematics scholarship and professional achievement. gramming languages, software engineering and & Statistics This position has been created to support VLSI architecture. There are twenty-six full time the recently appointed Chair of Mathematics. faculty positions supporting these activities. The Department of Mathematics and Statistics ESSENTIAL: The department has established CENPARMI will sponsor applicants for the new NSERC • Ph.D. in Mathematics (Centre for Pattern Recognition and Machine International Fellowships. These fellowships • Strong research record in modern math Intelligence) with specialization in patter recog provide an opportunity to spend up to two ematics with research interests in operator nition and related expert systems research. years engaged in research, and are particularly NOVEMBER 1991, VOLUME 38, NUMBER 9 1207 Classified Advertisements suitable for talented, young mathematicians who formation should be received by January 31, UNIVERSITY OF TORONTO have recently completed the Ph.D. degree. 1992. Department of Mathematics The Fellowships are open to non-Canadian The University of Toronto encourages both candidates of any nationality and selection women and men to apply. The Department solicits applications for two will be based upon the candidate's research limited term Assistant professorships at the potential. downtown (St. George) campus, each for the Starting July 1, 1992, the stipend will be three-year period from July 1, 1992 to June 30, $29,000 plus a $3,000 grant for research 1995. Duties consist of teaching and research, expenses. UNIVERSITY OF TORONTO and candidates must demonstrate clear strength Applications and three letters of reference Department of Mathematics in both. should be sent by November 30, 1991 to: I. Applicants should send their complete C. Hambleton, Chairman, Department of Math The Department solicits applications for a V. including a list of publications and any ematics & Statistics, McMaster University, tenure-stream appointment in Analysis. Pref appropriate material about their teaching, and Hamilton, Ontario, Canada, LSS 4K1. erence will be given to researchers in the areas arrange to have at least four letters of reference of harmonic analysis, geometric analysis and sent directly to Professor J. Repka, Associate differential equations. Chair, Department of Mathematics, University of The appointment is at the downtown (St. Toronto, Toronto, Canada M5S 1A 1. At least one George) campus at the level of Assistant letter should deal with the candidate's teaching. THE UNIVERSITY OF BRITISH COLUMBIA Professor, to begin July 1, 1992. Candidates are To insure full consideration, this information Department of Mathematics expected to have at least three years experience should be received by January 31 , 1992. Assistant Professorship in teaching and research after the Ph.D., and to The University of Toronto encourages both be able to demonstrate excellence in each. In women and men to apply. In accordance with The Mathematics Department is seeking an particular, a candidate's research should show Canadian immigration requirements, priority will outstanding candidate for a tenure-track Assis clearly the ability to make significant original be given to Canadian citizens and permanent tant Professorship to begin July 1, 1992. Our and independenrcontributions to Mathematics. residents. highest priority is for a candidate in one of Applicants should send their complete C. the following fields: Real or Complex Analysis, V. including a list of publications and any ap Operator Algebras, Functional Analysis, Partial propriate material about their teaching, and Differential Equations. Applicants should have a arrange to have at least four letters of reference HONG KONG proven research record of high quality and have sent directly to Professor J. Repka, Associate demonstrated interest and ability in teaching. Chair, Department of Mathematics, University THE HONG KONG UNIVERSITY Preference will be given to candidates who have of Toronto, Toronto, Canada, M5S 1A 1. At least OF SCIENCE AND TECHNOLOGY one or more years of postdoctoral experience. one letter should deal with the candidate's Department of Mathematics This position is subject to final budgetary ap teaching. To insure full consideration, this in proval. In very exceptional circumstances, this formation should be received by January 31, The Hong Kong University of Science and position may be upgraded. The salary will be 1992. Technology is a new publicly funded research commensurate with experience and research The University of Toronto encourages both University. The first intake of students will record. In accordance with Canadian Immi women and men. to apply. In accordance with be in October 1991 at both undergraduate gration requirements, priority will be given to Canadian immigration requirements, priority will and graduate levels including the doctorate. Canadian citizens and permanent residents of be given to Canadian citizens and permanent Enrollment is expected to grow to 7,000 FTE Canada. UBC encourages qualified women and residents. by 1996-1997. The medium of instruction is minority applicants. Applicants should send a English. Applications are invited for the following C.V. including list of publications, statement of positions: research and teaching interests and arrange Professor : Minimum US$79,600 p.a. for three letters of recommendation to arrive Reader :'US$58,200- US$77,300 p.a. before January 1 , 1992 to the attention of: UNIVERSITY OF TORONTO Senior Lecturer: US$55,800- US$74,900 Head, Department of Mathematics, The Uni Department of Mathematics p.a. versity of British Columbia, Room 121 - 1984 Lecturer : US$35,900 - US$60,000 p.a. Mathematics Road, Vancouver, B.C., Canada The Department solicits applications for up to The Department will place major emphasis V6T 1Z2. three limited term Assistant professorships at on applications with an appropriate component the Erindale campus, each for the three-year of pure mathematics to preserve the integrity period from July 1, 1992 to June 30, 1995. of the discipline. Research areas will be highly Duties consist of teaching and research, and interdisciplinary and will include sCientific com UNIVERSITY OF TORONTO candidates must demonstrate clear strength in putation, statistics, fluid and solid mechanics, Department of Mathematics both. mathematical physics, analysis, algebra, geom Applicants should send their complete C. etry, etc. The Department solicits applications for a V. including a list of publications and any ap Applicants should have a Ph.D. degree in the tenure-stream position in Analysis at the down propriate material about their teaching, and relevant fields. Appointees at the senior level town (St. George) campus to begin on July 1, arrange to have at least four letters of reference are expected to have a distinguished record 1992. Preference will be given to researchers sent directly to Professor J. Repka, Associate in research and have demonstrated an ability working in Harmonic Analysis, or Ordinary or Chair, Department of Mathematics, University to develop research programs; appointees at Partial Differential Equations. of Toronto, Toronto, Canada, M5S 1A1. At least Lecturer level are expected to have outstanding Duties include teaching and research, and one letter should deal with the candidate's potential to develop research in his/her own candidates are expected to demonstrate excel teaching. To insure full consideration, this in fields. Responsibilities include undergraduate lence at each. formation should be received by January 31, and postgraduate teaching of not exceeding Applicants should send their complete C. 1992. two courses per semester. Applications for V. together with a list of publications, and ar The University of Toronto encourages both earlier positions will automatically be reviewed range to have at least four letters of reference women and men to apply. In accordance with and such candidates need not reapply. sent directly to Professor J. Repka, Associate Canadian immigration requirements, priority will Generous fringe benefits including medical Chairman, Department of Mathematics, Univer be given to Canadian citizens and permanent and dental benefits, annual leave, and chil sity of Toronto, Toronto, Canada, M5S 1A1. At residents. dren's education allowances are provided. Air least one letter should deal with the candidate's passage, housing or private tenancy allowance teaching. To insure full consideration, this in- are also provided where applicable. Initial ap- 1208 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------~-----~--~"""'!D!illi!IDIIII!IDIIII!IDIIII!IDIII?I!illTI!IDIIIDI!illi!IDIIII!IDIIII!IDIIII!IDIIIFTI!IDIIII!ill=rrR~~----· Classified Advertisements pointments will generally be on a three-year six published articles, five patented inventions. Dept., Box 5116, U. of North Texas, Den contract which is renewable subject to mu Over twenty years experience in teaching and ton, TX 76203. Phone: 817-565-2155. Email: tual agreement. A gratuity of an amount equal academic and industrial research. Permanent [email protected] or [email protected] to 25% of the total basic salary drawn will be resident. References upon request. Available FAX: 817-565-4919. payable upon successful completion of contract. immediately. Dmitry Keselman, 2572 Lenox It is the intention of the University to introduce a Rd., B-7, Atlanta, GA 30324. (404-237-2228). superannuation scheme and arrangements will be made for eligible staff to join the scheme as MATH SCI PRESS, 53 Jordan Rd., Brook appropriate. Approved sabbatical leave will be line, MA 02146, 617-738-0307. GEOMETRIC at full salary. COMPUTING SCIENCE: FIRST STEPS, by Applications/nominations should be sent MISCELLANEOUS R. Hermann. $85. 394 pages. Interdisciplinary with a complete CV together with the names Mathematics, vol. 25. and addresses of at least three referees to: Director of Personnel Prepare -4A.45-Il'TEX Documents FAST with The Hong Kong University 100s of shortcuts: of Science and Technology Default header/input, troff-style dot com 12/F, World Shipping Centre mands, user commands, user abbr., short EQN We buy periodicals in mathematics and many 7 Canton Road format, Greek letters, symbols, and many more. other subjects. Please call 1-(800) 521-0061 Tsim Sha Tsui Mix and match with TEX commands. Generates or (713) 556-0061. Lists of available material Kowloon, Hong Kong full -4A.45-~TE)<. Help utility included. may be sent to fax number (713) 556-1406 Fax No.: (852) 735-7806 TEX consulting Service. or to: Research Periodicals & Book Services, The search will continue until suitable ap IBM compatible. Program disk (state 5"13") Inc., P.O. Box 720728, Houston, Texas 77272, pointments are made. +manual: $30 ~TE)<, $25 -4A.45-TEX, $40 both. U.S.A. LaZTE)<, PO Box 1151, Lisle, IL 60532. PUBLICATIONS WANTED --•P•O-SI;..;,T,;,;;;IO•N•S-W...,.A.;;N:,:,T;:E;:;,D_ BLICATIONS FOR S MATHEMATICS PROFESSOR, Wanted: Mathematical books, journals, reprints, TEACHING AND RESEARCH ephemera. Contact R. K. Dennis, Math. Dept., MATHEMATICAL REVIEWS. Complete set from White Hall, Cornell U., Ithaca, NY 14853-7901. Ph.D. 1978, USSR. Specialty: Graph theory, volume 1 to present, including indices. Excel Tel: 607-255-4027, FAX: 607-255-7149. email: logic, applied statistics and probability. Twenty- lent condition. Contact J. Neuberger, Math. [email protected] COMPUTER-AIDED VEBIPICATIOl\T '90 E. M. Clarke and B. P. Kurshan, Editors Proceedings of a DIMACS Workshop, Volume 3 This volume, publishedjointly with the Machinery, contains the proceedings of the second workshop on Computer-Aided T"\T,,Jii!ilfll'lo at Rutgers University in June 1990. The motivation for the workshop on effective algorithms or methodologies for formal vA1r>ir1'n::~ii '"'""w.l-•~.,, attributes of logics or formal languages). The theoretical ~-.,,,Lll""' verif'ica>ticln methods include advances in the use of binary decision proof-checking in controller vAlr>ifin~ The general focus of this volume ~rerific:at:ion feasible for various models of computation. Specific emphasis st.T'•ihllt.P.n programs, protocols, and digital circuits. The general test of it into a verification tool and to exercise that tool on realistic examples. This tlll!lfi-r•P.tin::~.l advances in this exciting and important area of research. All prices suQject to $6.50 per title. Prl~ps,JT1Il!3nt Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321- 4AMS (321-4267) in the continental U.S. and Canada to charge with Visa or MasterCard. Please add 7% GST to all orders being shipped lo Canada. 1991 Mathematics Subject Classification: 68. ISBN 0-8218-6594-3, LC 91-8815, ISBN 1052-1798, 628 pages (hardcover), May 1991 Individual member $88, List price $96, Institutional member $77, To order please specify DIMACS/3NA NOVEMBER 1991, VOLUME 38, NUMBER 9 1209 Applications and nominations are invited for a full-time position as an Associate Editor of Mathematical Reviews (MR), to commence January 1, 1992 and continue for a term of two years. An individual with considerable breadth in pure or applied mathematics is sought and preference will be given to those applicants with expertise in number theory, Lie algebras and Lie groups, complex analysis and global analysis. The Mathematical Reviews office of the American Mathematical Society is located in Ann Arbor, Michigan, not far from the campus of the University of Michigan. The editors, although employees of the AMS, enjoy many privileges at the University. At present, MR employs fifteen mathematical editors, about six consultants and over sixty nonmathematicians.lt produces Mathematical Reviews, Current Mathemati cal Publications, various indexes, the on-line service MathSci and MathSci Disc. The responsibilities of an Associate Editor fall primarily in the day-to-day operations of selecting articles and books suitable for review, classifying these items, assigning .them to reviewers, editing the reviews when they are returned, and correcting the galley proof. The ability to write good English is essential and the ability to read mathematics in major foreign languages is important. (The ability to read mathematical articles in Russian or Chinese is especially desirable.) The twelve-month salary is negotiable and will be commensurate with the experience the applicant brings to the position. Persons interested in this position are encouraged to write (or telephone) for further information. Persons interested in taking leave from an academic appointment to accept the position as Associate Editor are encouraged to apply. Applications (including curriculum vitae, bibliography and name, address, and phone number of at least three references) and nominations should be sent to: Dr. G. J. Janusz, Executive Editor Mathematical Reviews P. 0. Box 8604 Ann Arbor, MI 48107-8604 Telephone: 313-996-5255 FAX: 313-996-2916 INTERNET: [email protected] Interested applicants are urged to inquire without delay. The American Mathematical Society is an equal opportunity employer. INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS announces a program on CONTROL THEORY AND ITS APPLICATIONS ADVISORY COMMITTEE: J. S. Baras, A Bensoussan, R. W. Brockett, C. Foias, R. V. Kohn, H. J. Kushner, A J. Laub, J. L. Lions, A. Z. Manitius, J. E. Marsden, S. K. Mitter, R. T. Rockafellar, E. D. Sontag, G. Stein, P. P. Varaiya, C. Willems COORDINATORS: H. J. Sussmann (Chairman), W. H. Fleming, P. P. Khargonekar, P. R. Kumar, D. L. Russell, S. E. Shreve A one-year program with three parts: (1) Fall: September 8-December 30, 1992, Linear and Distributed Parameter Systems; (2) Winter: January 2-March 30, 1993, Nonlinear Systems and Optimal Control; (3) Spring: April1-June 30, 1993, Stochastic and Adaptive Systems. POSTDOCTORAL MEMBERSHIPS* All requirements for a doctorate should be completed by September 1, 1992. Applicants must show evidence of mathematical excellence, but they do not need to be specialists in the field. The following materials must be submitted (all material should arrive by January 15, 1992): (1) Personal statement of scientific interests, research plans, and reasons for wishing to participate in the Control Theory program. (This is an essential part of the application.) (2) Curriculum vitae and a list of publications. (3) Three letters of recommendation, to be sent directly to the IMA. SENIOR MEMBERSHIPS Preference will be given to supplementary support for persons with sabbatical leaves, fellowships, or other stipends. POSTDOCTORATES IN INDUSTRIAL MATHEMATICS IMA announces at least 4 one-to-two-year positions in Industrial Mathematics, effective September 1, 1992. These appointments are in addition to the regular IMA postdoctoral program and are funded jointly by the NSF and participating industries. They are designed to prepare mathematicians for research careers involving industrial interaction. Applicants should have fulfilled all requirements for a Ph.D. in Mathematics or Applied Mathematics by September 1, 1992. Familiarity with pde and/or numerical analysis is desired, but no knowledge in engineering is required. Postdoctorates* will spend 50% effort working with industrial scientists on one of the following topics: (1) Signal processing and computational ocean acoustics; (2) Diffractive optics; Maxwell equations in periodic structure; (3) Computational fluid mechanics: viscous free-surface flows; (4) Scattering ofelectromagnetic waves from complex objects; (5) Magneto-optic recording media; the writing process; (6) Semiconductors; (7) Solid state physics & computational chemical physics; (8) Problems in mathematical photography, both traditional and electrophotography; (9) Air quality modeling; (10) Control thoery; and 50% effort in the regular IMA program. Requirements and application procedure are the same as for the postdoctoral memberships listed above. *The actual hiring title will be "Research Associate". All correspondence should be sent to either VISITING MEMBERSHIP COMMITTEE or INDUSTRIAL MATHEMATICS POSTDOCTORATE MEMBERSHIP COMMITTEE Institute for Mathematics and its Applications University of Minnesota 514 Vincent Hall 206 Church St. S.E. Minneapolis, MN 55455-0436 IMA PARTICIPATING INSTITUTIONS: Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Michigan State University, Northern Illinois University, Northwestern University, Ohio State University, Pennsylvania State University, Purdue University, University of Chicago, University of Cincinnati, University of Houston, University of Illinois (Chicago), University of Illinois (Urbana), University of Iowa, University of Kentucky, University of Manitoba, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, Wayne State University IMA, PARTICIPATING CORPORATIONS: Bellcore, Cray Research, Eastman Kodak, Ford, Hitachi, General Motors, Honeywell, ffiM, Kao, Motorola, Siemens, 3M, UNISYS Announcing a new journal - 1992 Journal of Algebraic Geometry Editors: V.I. Arnold(Moscow), A. Beauville(Orsay), S. J. Bloch(Chicago), E. Brieskom(Bonn), F.M.E. Catanese(Pisa), D. Eisenbud(Waltham), H. Hironaka(Cambridge), J. Kollar(Salt Lake City), U D.T.(Paris), S. Mori(Kyoto), K. Saito(Kyoto), S. S.-T. Yau (Managing editor, Univ. of illinois at Chicago,Box 4348,Chicago,IL 60680 USA) Associate Editors : G. Faltings(Princeton), W. Fulton(Chicago), J. Harris(Cambridge) The Journal ofAlgebraic Geometry will be published four times per year; volume 1 is the 1992 volume, with the frrst issue appearing in October of 1991. Please make your subscription now to AMS. 1992 Subscription Rates List price $138, Individual price $110 Postage Surcharge: India $15; other foreign $10 Optional Delivery: First class $12; Airmail $20 Prepayment required. Send charge orders to: AMS, P.O. Box 6248, Providence, RI 02940-6248, Attn: Customer Services Department. NOTE: Subscription to AMS journals are sold only on a calendar year basis (January-December). Split year subscription orders will not be accepted. Orders with remittances, send to: American Mathematical Society, Annex Station, P.O. Box 1571, Providence, RI 02901-1571 USA. Charge by phone in the continental U.S. and Canada 800-321-4AMS (321-4267) Algebraic geometry and singularity theory have made remarkable of singularities, Mumford's work on moduli schemes, Artin and progress in the last several decades. In the early 1940s, Van der Grothendieck's introduction ofetale cohomology, and Deligne's proof Waerden, Well, Zariski, and others established solid foundations for ofWeil's conjecture on zeta functions are some of the highlights of this algebraic geometry. Weil' s methods opened new applications to number era. theory, culminating in his proof of the Riemann hypothesis for curves over a fmite field. Hodge and de Rham developed the transcendental The study of singularities of differentiable maps goes back to ideas of method of studying algebraic varieties of arbitrary dimension, initiating Whitney, Thorn, Mather and Arnold. Singularities of differentiable maps the theory of harmonic integrals. These results were further developed are closely related to singularities of analytic maps and therefore to by Kodaira, Weil, and others and were applied to various classical algebraic geometry. Moreover, in this field of studies, important work problems in the field. of the last two decades has produced a surprising interplay between algebraic geometry, in particular Mixed Hodge theory, Picard-Lefschetz The theory of sheaves invented by Leray was developed by H. Cartan, theory,and deformation theory, Lie algebras, Lie groups and locally who employed coherent analytic sheaves and their cohomology groups. symmetric spaces, arithmetic of quadratic forms, braid groups, and other Serre transplanted these methods to lay new foundations for algebraic important fields of mathematics as well as science and engineering. geometry and also applied these methods to obtain such results as the comparison thoerem of algebraic and analytic geometry. The theory of This diverse and highly interconnected melange of activity has produced coherent analytic sheaves, combined with the potential theoretic an explosion of work of unprecedented depth and excellence. The methods, produced many important results on compact complex Journal of Algebraic Geometry will provide a forum for the best work manifolds. In the mid-1950s, Hirzebruch frrst proved the Riemann in algebraic geometry, the study of singularities, and related frelds, such Roch theorem for a nonsingular projective variety by using Thorn's as number theory, commutative algebra, projective geometry,complex cobordism theory. Later, Atiyah and Singer also produced a proof, this geometry, Kaehler geometry, and geometric topology. time in the case of an arbitrary compact complex manifold, by using their index theorem for elliptic operators on a compact manifold. The Journal will focus on research that clearly exhibits the symbiotic relationship among techniques of algebra, geometry, analysis, and In the late 1950s, Grothendieck introduced schemes, which generalized topology. Committed to serving as the journal of record for important the concept of an algebraic variety as a ringed space, and clarified the new results that stimulate interactions among these fields, the Journal relationship of algebra and geometry in full generality. The new of Algebraic Geometry will establish and maintain the highest methods had a strong influence on algebraic geometry and offered new standards of innovation and quality. techniques for classical problems. Hironaka's results in the resolution New in 1991 from Birkhauser New! G.-Q. Zhang, University of Georgia, Athens S. Lojasiewicz, Jagiellonian University, Cracow, Poland Logic of Domains Introduction to Complex A thorough study of some important logical aspects of domains as used Analytic Geometry in the denotational semantics of programming languages. Against a background of a well developed and sophisticated domain theory, the The subject of this book is analytic geometry, understood as the geometry author builds logical frameworks from domains and uses them for the of analytic sets (or, more generally, analytic spaces), i.e. sets described derivation of program logics. The reader will gain from this work a broad locally by systems of analytic equations. Though many of the results are and deep understanding of the state of knowledge in this vital area of relatively modem, they are alreadypartoftheclassical tool-kitofworkers theoretical computer science. in analytic and algebraic geometry and in analysis. The book is an 1991/259 pp./Hardcover/$49.50/ISBN 0-8176-3570-X introduction that aims to familiarize the reader with the basic range of Progress in Theoretical Computer Science problems, using means as elementary as possible. At the same time, the author's intention is to give the reader access to complete proofs without the need to rely on so-called "well-known" facts. New! 1991/537 pp./Hardcover/$118.00/ISBN 0-8176-1935-6 W. Barker, Bowdoin College, Brunswick, Maine, and P. Sally, University of Chicago (Eds.) New! Harmonic Analysis on Reductive Groups H. Triebel, Freidrich-Schiller-Universitat Jena, Germany Reflects accurately most of the major developments in harmonic analysis Theory of Function Spaces II on both real and p-adic groups since the well-knoWn landmark AMS Summer Symposium at Williamstown, MA. Builds on a well-established This book deals with the theory of function spaces of type B' pq and F pq as bodyofliterature,inparticularthedeepandpenetratingworkofHarish it stands at the end of the 1980's. These two scales of spaces cover many Chandra, but contains much mathematics that was developed entirely well-known function spaces such as Holder-Zygmund spaces, (frac within the past twenty years. tional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely Based on material presented at the Bowdoin Conference, the authors connected with Morrey-Campanato spaces. This monograph is self have made a serious effort tro give a complete exposition of their topics contained, although it may be considered an update of the author's in order to make them accessible to a wider audience. Readers will earlier book of the same title. find here a vivid illustration of continuity and vitality of modern 1991/Approx. 380 pp./Hardcover/$118.00 (tent.)/ISBN 0-8176-2639-5 mathematics. Monographs in Mathematics, Volume 84 1991/Approx. 400 pp./Hardcover/$60.00 (tent.)/ISBN 0-8176-3514-9 Progress in Mathematics, Volume 101 K.L. Alexander and J.C. Watkins, University of Southern California Spatial Stochastic Processes R. Kadison, University of Pennsylvania, and J.R. Ringrose, University A Festschrift in Honor of Ted Harris of Newcastle on His Seventieth Birthday Fundamentals of the Theory of Ted Harris has been one of the most significant and inventive contribu Operator Algebras, Volume III tors to the field of probability theory and stochastic processes. He has Elementary Theory- An Exercise Approach influenced the direction of all the areas covered in this volume -branch ing processes, percolation, interacting systems, stochastic cellular au The many readers of the highly acclaimed treatise on which this volume tomata, stochastic flows - as well as a host of related topics. This is is based will enthusiastically welcome the authors' decision to share with mixture of surveys, recent results, and ideas forfutureworkshould prove them their detailed solutions to the stimulating and penetrating exercises useful to a broad spectrum of professional mathematicians, physicists that appeared in the first volume. With clarity, thoroughness, and depth, and computer scientists. The color plates illustrating various phe these solutions supplement the basic theory and provide an invaluable nomena occurring in cellular automata are particularly attractive and tool for students and researchers in mathematics and theoretical physics illuminating. and engineering. They provide models which test understanding and 1991/Approx. 256 pp./Hardcover/$84.50(tent.)IISBN 0-8176-3477-0 suggest alternate methods and styles for producing further solutions and Progress in Probability, Volume 19 extending knowledge in such areas as functional analysis and quantum physics. 1991/283 pp/Hardcover/$34.50/ISBN 0-8176-3497-5 R. Durrett, Cornell University, Ithaca, NY; and H. Kesten, Cornell University, Ithaca, NY (Eds.) Random Walks, Brownian Motion Three Easy Ways to Order! and Interacting Particles Systems Call: Toll-Free 1-800-777-4643. In NJ please call (201) 348-4033. Your reference number is Y516. Write: Send payment plus $2.50 for postage and handling to: Birkhliuser, Order Fulfillment This collection of articles is dedicated to Frank Spitzer on the occasion of Dept. Y516, P.O. Box 2485, Secaucus, New Jersey 07096-2491. his sixty-fifth birthday. They are intended to demonstrate the major Visit: Your Local Technical Bookstore. influence he has had on probability theory for the last 30 years, dealing Visa, MasterCard, American Express and Discover charge cards as well as personal checks and with properties of Brownian motion, fluctuation theory and potential money orders arP acceptable forms of payment. All orders will be processed upon receipt. If theory for random walks and interacting particle systems. About one an order cannot be fulfilled within 90 days, payment will be refunded. Prices quoted are third of the papers focus on treating problems of statistical mechanics payable in U.S. currency or its equivalent. with rigorous probabilistic tools. 1991/Approx. 400 pp./Hardcover/$65.00 (tent.)IISBN 0-8176-3509-2 Progress in Probability, Volume 28 NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF MATHEMATICS Applications are invited for teaching appointments at the Lecturer or Senior Lecturer level from candidates who are able to teach in one or more of the following areas: Pure Mathematics Applied Mathematics Operational Research Statistics Candidates should possess a PhD degree in Mathematics and have strong commitment to teaching and research. Gross annual emoluments range as follows: Lecturer S$50,390- 64,200 Senior Lecturer S$58,680 -100,310 (US$1.00 = S$1.71 approximately) The commencing salary will depend on the candidate's qualifications, experience and the level of appointment offered. Leave and medical benefits will be provided. Depending on the type of contract offered, other benefits may include: provident fund benefits or an end-of-contract gratuity, a settling-in allowance of S$1 ,000 or S$2,000, subsidised housing at nominal re!"!tals ranging from S$1 00 to S$216 p.m., education allowance three children subject to a maximum of S$16,000 per annum per child, passage assistance and baggage allowance for the transportation of personal effects to Singapore. Staff members may undertake consultation work, subject to the approval of the University, and retain consultation fees up to a maximum of 60% of their gross annual emoluments in a calendar year. The Department of Mathematics is a department in the Faculty of Science. There are eight faculties in the National University of Singapore with a current student enrolment of some 1 5,000. All departments are well-equipped with a wide range of faci I ities for teaching and research. All academic staff have access to the following computer and telecommunication resources: an individual microcomputer (an IBM AT-compatible or Apple Macintosh); an IBM mainframe computer with 16 MIPS of computing power; an NEC SX supercomputer with 665 MFLOPS of computing power; departmental laser printers; a wide spectrum of mainframe and microcomputer software; on-line library catalogue; voice-mail; the international computer networks-BITNET and INTERNET, linking academic institutions and research centres all over the world. The campus-wide network, which is based on the high speed optical fibre based FDDI technology, enables the academic community to access the computing resources in the University from the convenience of the individual workstation. Application forms and further information on terms and conditions of service may be obtained from: The Director The Director Personnel Department North America Office National University of Singapore National University of Singapore 1 0 Kent Ridge Crescent 55 East 59th Street Singapore 0511 New York, NY 10022, USA Tel: (212) 751-0331 Enquiries may also be sent through BITNET to: PERPL @ NUS3090, or through Telefax: (65) 7783948 Then consider joining a highly talented group of Statistics, Cornbinatorics and more. And they function as a mathematicians whose job it is to deduce structure where true community, exchanging ideas and working with some of structure is not apparent, to find patterns in seemingly the finest minds-and most powerful computers-in the country. random sets, to create order out of chaos. If you love problem-solving and like the idea that those These are the mathematicians of the National Security solutions will be applied to real world look into a Agency. They contribute to the solution of cryptologic career with NSA. Send your resume to National problems using Number Theory, Group Theory, Finite Field the address below or contact your Security Theory, Linear Algebra, Probability Theory, Mathematical campus placement office. Agency The Opportunities of a Lifetime Attn: M322 (AEH), Ft. Meade, Maryland 20755-6000 An equal opportunity employer. U.S. citizenship required for applicant and immediate family memhers. Jou:maf of Jllppfiea !Matliematic.s tmtf Swclio.stic Jl4na/jjsis ------. AN INTERNATIONAL QUARTERLY JOURNAL PRINCIPAL EDITOR J.H. Dshalalow, USA SCOPE OF THE JOURNAL MANAGING EDITOR The Journal of Applied Mathematics and Stochastic Analysis publishes significant re R.F. Melka, USA search papers on the theory and applications of NONLINEAR ANALYSIS, STOCHASTIC ADVISORY EDITORS ANALYSIS, BOUNDARY VALUE PROBLEMS, STOCHASTIC MODELS AND APPROXIMATION Y. Berezanskl, Ukraine THEORY. The journal is concerned with concepts and techniques, and it is oriented to B. Fusaro, USA wards a broad spectrum of mathematical, physical and engineering interests. M. Krasnoselskil, USSR A SELECTION OF RECENT AND FORTHCOMING PAPERS C. Heyde, Australia Conditional D. Konig, Germany Limit Theorems for Branching Processes, L. Takacs; Nonlinear Evolution V. Lakshmikantham, USA Equations in Banach Space, N. Aluned; Wecessary and Sufficient Conditions for Ergo R. Uptser, USSR dicity of Markov Chains, L. Abolnikov and A. Dukhovny; Impulsive Integral Equations A. Martynyuk, Ukraine in Banach Spaces, D. Guo; Renewal Characterization of Markov Modulated "Poisson V. Matrosov, USSR Processes, M Neuts, U. Sumita and Y. Takahashi· To the Theory of One-Side Models in M. Neuts, USA Spaces with Arbitrary Cones, A. Martynyuk and A. Obolenskj; Relative Stability and A. Skorohod, Ukraine Weak Convergence in Nondecreasing Stochastically Monotone Markov Chains, P. To dorovic; TopoTogical Structures in COmputer Science, ASSOCIATE EDITORS E. Khalimsky, Queues, Random L Abolnikov, USA Graphs and Branching Processes, L. Taliilcs; Neural Networks with Memory, T. Burton; J. Becker, Germany On Some Queue Length Controlled Stochastic Processes, L. Abolnikov, J. Dshalalow P. Bremaud, France and A. Dukhovny. H. Daduna, Germany EDITORIAL POLICY W. Derrick, USA Papers in triplicate should be sent to: ].H. Dshalalow, Principal Editor, JAMSA, De K. Farahmand, UK partment of Applied Mathematics, Florida Institute of Technology, Melbourne, D. W. Fausett, USA FL C. T. Fulton, USA 32901, U.S.A.. c. Gunther, USA SUBSCRIPTION INFORMATION Z. A. Karian, USA The Journal ofApplied Mathematics and Stochastic Analysis (ISSN 1 048-9533) is pub E. Khalimsky, USA lished four times a year. Volume 5 (1992). Institutional rates: US $125.00 for US/Cana A. Krasnoselskil, USSR da, $135.00 elsewhere. Individual rates: US $50.00 for US/Canada, $60.00 elsewhere. W. Lee, USA Mail orders to: I. Malyshev, USA D. Konwinski, Financial Director, JAMSA, Department of Mathemat N. Papageorgiou, USA ics, University of Pittsburgh at Bradford, PA 16701, U.S.A.. A. Rosalsky, USA © 1991, The Society of Applied Mathematics, Modeling and Simulation KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN 31261, SAUDI ARABIA DEPARTMENT OF MATHEMATICAL SCIENCES NEEDS FACULTY MEMBERS FOR TEACHING GRADUATE AND UNDERGRADUATE COURSES IN ALL AREAS OF MATHEMATICAL SCIENCES. PH.D. IN MATHEMATICS IS REQUIRED. CANDIDATES MUST HAVE STRONG RESEARCH POTENTIAL OR ACCOMPLISHMENTS AND DEMONSTRATED EXCELLENCE IN TEACHING. PREFERRED AREAS OF RESEARCH ARE APPLIED MATHEMATICS AND NUMERICAL ANALYSIS. KFUPM offers attractive salaries commensurate with qualifications and experience, and benefits that include free furnished airconditioned accommodation on campus, yearly repatriation tickets, ten months duty each year with two months vacation salary. Minimum regular contract for two years, renewable. Interested applicants are requested to send their Curriculum Vitae with supporting documents not later than one month from the date of this publication, to: DEAN OF FACULTV AND PERSONNEL AFFAIRS KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPT NO. 9108 DHAHRAN 31261, SAUDI ARABIA The Geometry Center The National Science lr Technology Research Center for Computation and VIsualization of Geometric Structures The Geometry Center is based at the academic worlds. University of Minnesota in Minneapolis in Based on his or her interests and the needs 15,000 square feet of space overlooking the of the Center, an apprentice will work with also be willing to supervise student assistants Mississippi.. senior staff or faculty on a primary project and otherwise participate in the education The Geometry Center is looking for highly related to the areas listed above. In addition, program of the Center. talented and motivated individuals with a each apprentice will assist in visitor strong background in mathematics or orientation and related tasks. Research Professorships computer science. The Center has created a The salary will be at the level of a full time Application is encouraged and welcomed unified computing environment centered on graduate student, between $20,000 and from those with full or partial independent math and supporting: $25,000/year according to background. funding who would like to consider resi - math and computer science research, dence in the intensive computer environment - software and tool development, Postdoctoral Fellowships of the Center. A few grants may be available - application development, Up to three fellowships will be awarded for up to half-salary or $30,000. - mathematical visualization, start up to Fall, 1992. They are for one year - video animation production, and with the possibility of a one year extension. Applications - high school and college math education. Remuneration will be approximately To apply, please send a letter of interest $40,000/12 months if there is no other including a description of your research Apprentices support. program along with a resume and letters of In the past, successful apprentices have Applicants will be accepted from all recommendation as appropriate to: included those who wish to take time off branches of the mathematical sciences; Angie Vail, Sr. Admin. Dir. from college to get work experience, and preference may be given to those whose The Geometry Center those who have graduated from college and work relates to current interests of the 1300 South Second Street want to get more experience before deciding Center. A very high level of accomplish Minneapolis, MN 55454 on a future career or further graduate ment and breadth of education is expected Please address letters of inquiry regarding education. The unique Center environment from the applicants and also a substantial research professorships to Professor Albert reflects elements of both the corporate and computing background. Applicants should Marden, Director, The Geometry Center. v_g..(Io/f£2{$ I rTf]' 0 lf :J{Qg..((j 1(09\L(j Chair ofMathematics(Ref. 91/92-14) Applications are invited for the Chair of Mathematics, and the average is HK$848,040 (approx. US$1=HK$7.80, as tenable from 1 January 1992. of 24 September 1991). At current rates, salaries tax will not exceed 15% of gross income. Housing at a charge of 7.5% Applicants should be mathematicians with an outstand of salary, children's education allowances, leave, and medical ing research record in a main area of mathematics and with benefits are provided. some administrative experience. The successful candidate is expected to provide academic leadership in teaching and Further particulars and application forms may be research, and may be appointed as Head of Department. obtained from: Appointments (39910) The University would prefer to make a permanent Association of Commonwealth Universities appointment, but consideration may also be given to 36 Gordon Square applications for appointment on fiXed or secondment terms London WCJH OPF, UK of preferable not less than three academic years. or from: Appointments Unit, Registry The University reserves the right not to fill the Chair or University of Hong Kong to fill the Chair by invitation or to make an appointment at Hong Kong a lower level. (Fax (852)-5592058 E-mail: [email protected]) Annual salary (superannuable) will be within the professional range, of which the minimum is HK$685,620 Closes 31 December 1991. D-modules and New in paperback Topics in To Infinity and Spherical Noncommutative Beyond Representations A Cultural History of the Infinite FrecJeric Bien Geometry Eli Maor The theory of D-modules deals with Yuri I. Manin Eli Maar examines the role of infinity t!'e algebraic aspects of differential equa There is a well-known correspondence in mathematics and geometry and its tions. The book provides a general intro between the objects of algebra and cultural impact on the arts and sciences. duction to the theory of D-modules on geometry. In this book Yuri Manin Above all, the book describes the flag varieties, and it describes spherical addresses a variety of instances in which mathematician's fascination with infinity- D-modules in terms of a cohomological the application of commutative algebra a fascination mingled with puzzlement. formul~. Using microlocalization of repre cannot be used to describe geometric "~ascinating and enjoyable•••• places sentations, the author derives a criterion objects, emphasizing the recent upsurge the ideas of Infinity in a cultural context for irreducibility. The relation between of activity in studying noncommutative and shows how they have been es- multiplicities and singularities is also rings as if they were function rings on poused and molded by mathematics." discussed at length. "noncommutative spaces." -Science Mathematical Notes, 39 M. B. Porter Lectures, Rice Universily. Over 160 illustrations. Paper: $22.50 ISBN 0-691-02517-7 Department of Mathematics Paper: $16.95 ISBN 0-691-02511-8 In Japan order from United Publishers Services Cloth: $35.00 ISBN 0-691-08588-9 Available from Princeton only In the u.s. and Canada. l>~U~l>IIUf 41 WIWAM ST. • PRINCETON, NJ 08540 • (609) 258-4900 ORDERS: 800-PRS-ISBN (7n-4726) • OR FROM YOUR LOCAL BOOKSTORE Foundations of Computmg Series, Research Reports and Notes ~\ MATHEMATICS FACULTY ". Now Available for text use Basic Category Linear Network Theory for Optimization Anticipated tenure-track positions beginning September 2 Computer Scientists Algorithms and ~ 992. C~rrent research interests in the department Benjamin C. Pierce Codes mclude d1~cr~te r:nathematics, statistics, differential geom 100 pp. $17.95 softcover etry, opt1m1za_t1.~n theory, and algebraic topolog . Dimitri P, Bertsekas Computer fac1llt1es are available for teaching a~d Categories, Types, This book explains research pu_rposes. Ph.D. required; eligibility for appoint and Structures important recent ment at Assistant Pro~essor rank, a strong commitment to An Introduction to algorithms such as undergraduate teachmg and establishment of an active auction and relaxation, research program are expected. Category Theory for the proposed by the author Working Computer and others forthe William P~terson College, on a 250-acre suburban cam Scientist pus 20 miles !rom New York City, is an accredited state solution of these college offen'!g 50 un_dergraduate and graduate pro Andrea Asperti and problems. Giuseppe Longo grams. WPC IS an affirmative action/equal opportunity 384 pp, $39.95 325 pp. $32.50 en:pl~yer an~ energetically solicits applications from mmonty candidates. Logic Programming The Art of the Please submit letter of application, current vitae and and Nonmonotonic Metaobject three (3) le~!~rs of reference concerning teaching and Reasoning research ab1ht1es by January 30, 1992, to Protocol Proceedings of the First Gregor Kiczales, Jim des DR. E. PHADIA, Chair, International Workshop Rivifres. and Daniel Bobrow Department of Mathematics edited by Ani! Nerode, Wiktor 335 pp. $45.00 cloth, WILLIAM PATERSON Marek, and V. S. Subrahmanian $24.95 softcover WPC COLLEGE 290 pp. Drawer AMS Wayne, New Jersey 07470 Application for Membership 7992 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ...... Please read the reverse side of this form to determine what member Fields of Interest ship category you are eligible for. 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Account numbar &plrlltion date M2NO Membership Categories Reciprocating Societies Please read the following to determine what membership category you D Allahabad Mathematical Society are eligible for, and then indicate below the category for which you are D Asociaci6n Matem6tica Espanola applying. D Australian Mathematical Society For ordinary members whose annual professional income is below $45,000, D Berliner Mathematische Gessellschaft e.V. the dues are $78, for those whose annual professional income is $45,000 or D Calcutta Mathematical Society more, the dues are $104. D Dansk Matematisk Forening The CMS Cooperative Rate applies to ordinary members of the AMS who D Deutsche Mathematiker-Vereinigung e.V. are also members of the Canadian Mathematical Society and reside outside of D Edinburgh Mathematical Society the U.S. For members whose annual professional income is $45,000 or less, D Gesellschaft fur Angewandte the dues are $66 and for those whose annual professional income is above Mathematik und Mechanik $45,000, the dues are $88. D Glasgow Mathematical Association For a joint family membership, one pays ordinary dues, based on his or her income, and the other pays ordinary dues based on his or her income, D Indian Mathematical Society less $20. (Only the member paying full dues will receive the Notices and the D Iranian Mathematical Society Bulletin as a privilege of membership, but both members will be accorded all D Irish Mathematical Society other privileges of membership.) D fslenzka Staer8frae6afelagi6 Minimum dues for contributing members are $156. D Israel Mathematical Union For either students or unemployed individuals, dues are $26, and annual D J6nos Bolyai Mathematical Society verification is required. D Korean Mathematical Society The annual dues for reciprocity members who reside outside the U.S. and D London Mathematical Society Canada are $52. To be eligible for this classification, members must belong to D Malaysian Mathematical Society one of those foreign societies with which the AMS has established a reciprocity D Mathematical Society of Japan agreement, and annual verification is required. Reciprocity members who reside in the U.S. or Canada must pay ordinary member dues ($78 or $104). D Mathematical Society of the Philippines The annual dues for external members, those who reside in developing D Mathematical Society of the Republic of China countries which do not have any mathematical society, are $55. D New Zealand Mathematical Society Members can purchase a multi-year membership by prepaying their cur D Nigerian Mathematical Society rent dues rate for either two, three, four or five years. This option is not D Norsk Matematisk Forening available to either unemployed or student members. D Osterreichische Mathematische Gesellschaft D Polskie Towarzystwo Matematyczne 1992 Dues Schedule (January through December) D Punjab Mathematical Society For any category of membership where more than one dues level is given, D Ramanujan Mathematical Society see the above for descriptions of Members' Categories. D Real Sociedad Matem6tica Espanola D Sociedad Colombians de Matem6tica Ordinary member ...... •...... •...•••.•• $78 $104 D D D Sociedad de Matem6tica de Chile CMS Cooperative rate ...... •..•.••...... D $66 D $88 D Sociedad Matem6tica de Ia Republica Dominicans Joint family member (full rate) ••••...... •.•.•...... D $780 $104 D Sociedad Matematica Mexicana D Sociedade Brasileira Matem6tica Joint family member (reduced rate) ••••...•.•.••..••••. D $58 D $84 D Sociedade Brasileira de Matematica Contributing member (minimum $156) ••.••.•..•..•••...•••••..•. D Aplicada e Computacional D Sociedade Paranaense de Matematica Student member (please verify) 1 •••••••••••••••••••••••••••• D $26 D Sociedade Portuguese de Matem6tica D Societat Catalans de Matematiques Unemployed member (please verify)2 •••••••••••••••••••••••• D $26 D Societe de Mathematiques Appliquees Reciprocity member (please verify)3 •••••••••••• D $52 D $78 D $104 et lndustrielles D Societe Mathematique de Belgique External member ••.••.•••.•..•...... •.•.....••.•.•••.• D $55 D Societe Mathematique de France Multi-year membership •..•••••.•••..••..... $ ...... for •.•.•. years D Societe Mathematique Suisse D Southeast Asian Mathematical Society 7 Student Verification (sign below) D Suomen Matemaattinen Yhdistys D Svenska Matematikersamfundet I am a full-time student at ...... •.•.•.••...•.•••.•.•••••• D Union Mathem6tica Argentina .••..•...... currently working toward a degree. 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Box 6248 Providence, RI 02940-6248 lll •• ml.ll.l ••• l •• lllu.l.l •• l.lml •• l •• ll.ll •• 1l Fold here MathSci®Disc Mathematics Reference Collection on Two Compact Discs Search eleven+years of Mathematical Reviews (MR) and Current Mathematical Publi cations (CMP) on MathSci®Disc. 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Over 80 dramatic illustrations in both black and white and striking full color take you on a journey through fantastic land scapes and poetic images. Fomenko himself acts as your guide, describing in accompanying text the mathematical motivation behind each illustration, as well as the emotional, histori cal, or mythical subtexts they evoke. Winner of the Printers Industry Association oftheSouth Award ofExcellence 1980 Mathematics Subject Classification: 00 ISBN 0-8218-0162-7, LC 90-47514 194 pages (hardcover), December 1990 List price $45 To order, please specify MATIMP/NA 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. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800- 321-4AMS (321-4267) in the continental U. S. and Canada to charge with Visa or MasterCard. MAA Minicourse Preregistration Form, Baltimore, Maryland ~anuary 8-11, 1992 NOTE: This Is NOT an AMS Short Course Form. Please use the Joint Meetings Preglstration/Housing Form to preregister for the AMS Short Course. To register for MAA Minicourse(a), please complete THIS FORM or a PHOTOCOPY OF THIS FORM and return it with your payment to: Linda Heineman Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, DC 20036 Telephone: 202-387-5200 ---:::-:----:--:--::::------::::------:::~:7.""------Telephone: ------(Please print) Surname First Middle Street address City State Zip • Deadline for MAA Minicourse preregistration: November 18, 1991 (After this date, potential participants are encouraged to call the MAA headquarters at 800-331-1622.) • Deadline for cancellation in order to receive a 50% refund: December 30, 1991 • Each participant must fill out a separate Minicourse Preregistration form. • Enrollment is limited to two Minicourses, subject to availability. • Please complete the following and send both form and payment to Linda Heineman at the above address: I would like to attend 0 1 Minicourse 0 2 Minicourses Please enroll me in MAA Minicourse(s): #--and#-- In order of preference, my alternatives are: #-- and #-- • PAYMENT Check enclosed: $ __ Credit card type: 0 MasterCard 0 Visa Credit card#------Expiration date:------ Your Employing Institution Signature (as it appears on credit card) Minicourse Number and Name Organized by Fee 1. Alternatives to the lecture method in collegiate mathematics Julian Weissglass $36 2. The Harvard calculus reform project: Hands-on experience with the Deborah Hughes Hallett, Sheldon P. Gordon, $36 project materials William McCallum & Thomas Tucker 3. Using history in teaching calculus V. Frederick Rickey $36 4. Environmental Modeling Robert McKelvey $36 5. Using group projects in calculus Stephen Hilbert, John Maceli, Eric Robinson, $36 Diane Schwartz & Stanley Seltzer 6. Introduction to research in the teaching and learning of undergraduate Joan Ferrini-Mundy & Kathleen Heid $36 mathematics: Examples in calculus 7. Using NETPAD software to teach and learn about graphs Nathaniel Dean & Joseph G. Rosenstein $60 8. CAS laboratory projects for first year calculus using DERIVE Carl L. Leinbach & Marvin L. Brubaker $60 9. Learning abstract algebra by programming in ISETL Ed Dubinsky & Uri Leron $60 10. How to make effective use of inexpensive pocket computers to develop Franklin Demana & Bert K. Waits $36 the concepts and techniques of calculus 11. Instituting a mathematics placement program: Creating order out of Philip C. Curtis, Jr. $36 chaos in freshman mathematics 12. Mathematical modeling with a spreadsheet Stephen D. Comer & Hughes B. Hoyle Ill $36 13. Integrating calculus and physics for freshmen Joan R. Hundhausen & F. Richard Yeatts $36 14. The Fibonacci and Catalan numbers Ralph P. Grimaldi $36 15. Why, when and how to use CAS calculators in calculus and linear John Kenelly & Donald R. LaTorre $36 algebra instruction 16. Challenging students with research projects in calculus Douglas Kurtz & David Pengelley $36 17. Advanced workshop on DERIVE David R. Stoutemyer $30 n I plan on preregistering for the Baltimore, Maryland meetings ONLY in order to attend the MAA Minicourse(s) indicated above. It is my understanding tnat, should the course(s) of my choice be filled, full refund of the Baltimore meetings preregistration fee will be made. n I would like to preregister for the free Student Workshop organized by the MAA Committee on Student Chapters and the Ad hoc Committee on 'Kl&thematics and the Environment. REARRANGEMENTS OF SERIES IN BANACH SPACES V .M. Kadets and M.I. Kadets Translations of Mathematical Monographs, Instructions for Applicant's Form on facing page Volume86 The form. Applicants' forms submitted for the Em ployment Register by the November 18 deadline will In a contemporary course in mathematical be photographically reproduced in the December 1991 Information in the Mathematical analysis, the concept of series arises as a natural issue of Employment Sciences {ElMS). Resumes of only those attending will generalization of the concept of a sum over be posted at the meeting. finitely many elements, and the simplest proper The forms must be carefully typed using a fresh ties of finite sums carry over to infinite series. black ribbon. The best results are obtained with a Standing as an exception among these properties carbon-coated polyethylene film ribbon, but satisfac may be obtained using a ribbon made of is the commutative law, for the sum of a series tory results nylon or other woven fabric if suitable care is exer can change as a result of a rearrangement of its cised. It is important that the keys be clean and make terms. This raises two central questions: for which a sharp, clear impression. Do not erase-it causes series is the commutative law valid, and just how smudges which reproduce when photographed. Use a can a series change upon rearrangement of its correcting typewriter or correction tape or fluid if nec essary. Submit the original typed version only. Copies terms? Both questions have been answered for all will not reproduce properly and are not acceptable. finite-dimensional spaces, but the study of Hand lettered forms will be returned. Do not type rearrangements of a series in an infinite-dimen outside the box. sional space continues to this day. Applicants' forms must be received by the Society In recent years, a close connection has by November 18, 1991 in order to appear in the spe· cial issue of ElMS and must be accompanied by the between the theory of series and been discovered Preregistration/Housing Form printed in this issue, if the so-called finite properties of Banach spaces, attending the meeting. unified theory from making it possible to create a @ Specialties the numerous separate results. This book is the AL = Algebra AN = Analysis first attempt at such a unified exposition. BI = Biomathematics BS = Biostatistics This book would be an ideal textbook for CB = Combinatorics CM = Communication advanced courses, for it requires background only CN = Control CS = Computer Science CT = Circuits DE = Differential Equations at the level of standard courses in mathematical EC = Economics ED = Mathematical Education analysis and linear algebra and some familiarity FA= Functional Analysis FI =Financial Mathematics with elementary concepts and results in the theory FL = Fluid Mechanics GE = Geometry HM = History of Math LO = Logic of Banach spaces. The authors present the more MB = Mathematical Biology ME = Mechanics advanced results with full proofs, and they have MO = Modelling MP = Mathematical Physics included a large number of exercises of varying MS =Management Science NA =Numerical Analysis NT= Number Theory OR= Operations Research difficulty. A separate section in the last chapter is PR = Probability SA = Systems Analysis devoted to a detailed survey of open questions. ST = Statistics TO = Topology The book should prove useful and interesting both @ Career Objectives to beginning mathematicians and to specialists in AR = Academic Research AT = Academic Teaching functional analysis. NR = Nonacademic R&D NC = Nonacad. Consulting NS =Nonacademic Supervision @ (!)Duties Subject Classifications: 46 1980 Mathematics T =Teaching U = Undergraduate ISBN 0-8218-4546-2; LC 91-6522; ISSN 0065-9282 G =Graduate R =Research 122 pages (hardcover), Apri11991 C = Consulting A = Administration Individual member $43, S = Supervision IND = Industry List price $72, Institutional member $58 GOV = Government DP = Data Processing To order please specify MMON0/86NA Location E =East S = South C =Central M =Mountain W =West 0 =Outside U.S. I = Indifferent 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 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-321-4AMS (321-4267) in the continental U.S. and Canada to charge with Visa or MasterCard. Please add 7% GST to all orders being shipped to Canada. MATHEMATICAL SCIENCES EMPLOYMENT REGISTER APPLICANT FORM JANUARY 8-10, 1992 BALTIMORE, MARYLAND 1. Form must be typed. (Please see instructions on facing page. No other format will be accepted.) 2. This form CANNOT be submitted by electronic mail. 3. Hand lettered forms will be returned. Do not type beyond the box 4. Please check if Preregistration/Housing Form previously sent D S. Return form with payment with your Preregistration/Housing Form by November 18 to AMS, P.O. Box 6887, Providence, RI 02940, to be included in the December issue of ElMS. APPLICANT: Nrun~------CODE: Mailing address (include zip code) ------ @Specialties______@ Career objectives and accomplishments ACADEMIC: D Research, D Teaching NON-ACADEMIC: D Research and Development, D Consulting, D Supervision Near-term career goals ______ Significant achievements or projects, including rol"------ Honomandoffice~------ Other (e.g., paper to be presented at THIS meeting)------ Selected titles of papers, reports, books, patents______ @ Degree Year Institution @No. of abstracts, internal report,.,___ __ ------@ No. of papers acceptea______------® No. of books and patent,~------EMPLOYMENT HISTORY: Present Previous Previous @ Employe.______------Position @Duties Years ______to'------______to'------______to'------DESIRED POSITION:; ______CD Dutie"------0 Available mo. ___ /yr.___ Location ______@References (Name and Institution) © Citizenship: (check one) D U.S. Citizen D Non-U.S. Citizen, Permanent Resident D Non-U.S. Citizen, Temporary Resident @ AVAILABLE FOR INTERVIEWS: (Interviews for Session 4 scheduled on the basis of employer's request only.) Session 1 D Session 2 D Session 3 D Session 4. D Thurs. AM 9:00-11:15 Thurs. PM 12:4.5-4.:30 Fri. AM 9:00-11:15 Fri. PM 12:4.5-4.:30 I do not plan to attend the Baltimore meetings D EMPLOYER FORM MATHEMATICAL SCIENCES EMPLOYMENT REGISTER BALTIMORE, MARYLAND JANUARY 8-10, 1992 This form CANNOT be submitted by electronic mail •. INS1RUCTIQNS· Please read carefully before completing form below. Circled letters identify corresponding items in the FORM and the SUMMARY S1RIP; abbreviations to be used are provided in the notes below. Please print or type in black ink. Block capitals are suggested. The FORM itself will be placed on display at the Register exactly as submitted. The SUMMARY S1RIP (be sure to complete) will be used to prepare a computer printed list of summaties for disuibution at the Register. Employers are encouraged to provide more than one interviewer when they are able to do so, in order to increase the number of interviews which may be scheduled. Please take care to indicate on the Form.the number of interviewers for whom simultaneous interviews may be scheduled. (If all interviewers will be interviewing for the same position, or for the same set of positions, ouly one form should be submitted and ouly one employer code number will be assigned; therefore, each interviewer would then receive a separate computer schedule and separate table number.) More than one employer code will be required if some interviewers will not interview for all positions. Thus, if there are two disjoint sets of positions, two forms are required and two employer codes will be assigned. (Please refer to the section on the Employment Register following the Baltimore meeting announcement.) Return form with payment with your preregistrtioo/Housing form by November 18. EMPLOYER CODE Institution Dept Name of lnterviewer(s) 1. 2. 3. 4. City, State, Zip @ Title(s} ofPosition(s) @ Number of Positions Number of People Supervised ©Starting I @ Term of Appointment @ Renewal ( ) Possible Tenure Track Position Date ~ ~~~.------~s. ( ) Impossible Yes ( ) No ( ) Teaching hrs./wk ® Specialties Sought @ Degree Preferred @ Degree Accepted CDDuties ___ Ci)Experience ® Citizenship Restriction © Available for Interviews Session 1 ( ) Session 2 ( ) Session 3 ( ) Session 4 ( ) * Thurs. AM, 9:00-11:15 Thurs. PM, 12:45-4:30 Fri. AM, 9:00-11:15 Fri. PM, 12:45-4:30 @ Number of Interviewers Interviewers Interviewers Interviewers Interviewers @start Institution City State ® Title of position ® No. mo. I ~· I I I I I I I I I I I I I I I I I I I I ll I I I I I I I I I I I I I I I I I,[IJ,II I I 1,1I I I I,[IJ[D![Il @ @ ® Specialities sought @ @ CDDuties CDExperience @ © Sessions D,D,ITJ[IJ [IJ ITJITJ,ITJ [IJ [IJ [IJ ITJ,D,D, I I I I ll I I I 1,1I I I 1,11I I 1,ITLDDD D NOTES: @ Inst, Lect, Ass! Prof, Asso Prof, Prof, Dean, Open, MTS (Member Technical Staff), OPAN (Operations Analyst), PREN (Project Engineer), RESC (Research Scientist); @) Date e.g. 01/92; ® Possible=P, hnpossible=I; ® Algebra=AL, Analysis=AN, Biomathematics=BI, Biostatistics=BS, Combinatorics=CB, Communication=CM, Control=CN, Computer Science=CS, Circuits=CT, Differential Equations=DE, Econornics=EC, Mathematical Education=ED, Functional Analysis=FA, Financial Mathematics=FI, Fluid Mechanics=FL, Geometry=GE, History of Mathematics=HM, Logic=LO, Mathematical Biology=MB, Mechlinics=ME, Modeling=MO, Mathematical Physics=MP, Management Science=MS, Numerical Analysis=NA, Number Theory=NT, Operations Research=OR, Probability=PR, Systems Analysis=SA, Statistics=ST, Topology=TO; @@ Bachelor=B, Master=M, Doctor=D; (!) (J)Teaching=T, Undergraduates=U, Graduates=G, Research=R, Consulting=C, Administration=A, Supervision=S, lndustry=lND, Govemment=GOV, Data Processing=DP, no experience required=N; @ U.S. Citizen~U.S. Citizen or permanent resident=CP, No resuiction=NR; (!) Periods available for interviews: Check I, 2, 3, and/or 4, see the FORM above. * Interviews are scheduled in this session on the basis of employers request ouly. Preregistration/Housing Form, Baltimore, Maryland January 8-11, 1992 Please complete this form and return it with your payment to Mathematics Meetings Service Bureau P.O. Box 6887, Providence, Rhode Island 02940- Telephone: (401) 455-4143-Telex: 797192 DEADLINES: Room Lottery Qualification October 29, 1991 Joint Meetings & AMS Short Course Preregistration/Employment Register/Hotel Reservations/Tickets November 18, 1991 Final Preregistration ONLY (No housing, Employment Register, and/or tickets) December 10, 1991 Housing Changes/Cancellations December 10, 1991 50% Refund Preregistration/Employment Register/ AMS Short Course January 3, 1992 (no refunds after this date) Other Changes to Preregistration December 30, 1991 50% Refund on Tickets December 30, 1991 (no refunds after this date) REGISTRATION FEES Preregistration by December 10, 1991 JOINT MATHEMATICS MEETINGS $ Member of AMS, CMS, MAA 105 Nonmember 163 * Student, Unemployed, or Emeritus 25 AMS SHORT COURSE Member /Nonmember 60 * Student, Unemployed, or Emeritus 25 Preregistration by November 18, 1991 EMPLOYMENT REGISTER -Employer fee (1st Interviewer) 125 -Employer fee (2nd/ 3rd Interviewer) 60 - Applicant fee 30 - Posting fee for job descriptions for noninterviewing employers 30 (N.B.: A separate form appears in this issue for preregistration for MAA Minicourses) * See section on "How to Preregister" in the Notices or Focus for definition of "student", "unemployed", or "emeritus" status. PREREGISTRATION SECTION: Please check the function(s) for which you are preregistering: Joint Meetings 0 AMS Short Course (January 6-7, 1992) 0 Employer 0 Co-Interviewer 0 Applicant 0 Posting 0 1) Telephone: ------(Please print) Surname First Middle 2) (Mailing address) (E-mail address) I do not wish my badge, program, and/or Employment Register material to be mailed; however, the mailing address for my acknowledgement is given above. 0 3) Badge information: Affiliation------4) I am a student at 5) Emeritus member 0 Unemployed 0 MR Classification # MR Reviewer 0 6) Member of AMS 0 CMS 0 MAA 0 Nonmember 0 Member of other organizations: AWM 0 NAM 0 7) Joint Meetings fee$ 8) AMS Short Course fee$ 9) Employer fee(s) $ 10) Co-Interviewer fee(s) $ --- 11) Applicant fee$ 12) Posting fee$ 13) Hotel deposit$ (necessary ONLY if p~ing deposit by check) 14) __ AMS 25-Year Banquet tkt(s) @ $25 each=$ Veg. meal 015) __ NAM Luncheon tkt(s) @ $20 each = $ Veg. meal 0 16) __ MER Banquet tkt(s) @ $26 each=$ Veg. meal 0 17) __ AWM Banquet tkt(s) @ $26 each=$ Veg. meal 0 18) TOTAL AMOUNT ENCLOSED FOR 7 through 17 $ NOTE: May be paid by check payable to AMS (Canadian checks must be marked "U.S. Funds") or VISA or MasterCard credit cards. 0 original institutional purchase order attached Credit card type: Card number: Expiration date: ------If this is your credit card, please print your name as it appears on the credit card on the line below as well as sign your name. If this is not your credit card, please print card holder's name as it appears on the credit card on the line below, and have the card holder sign: (Printed name) (Signature) Please complete the appropriate sections on the reverse. For office use only: Codes: Options: Hotel: Room type: Dates: Hotel Deposit Total Amt. Paid: Special Remarks: for for you you 1992 1992 made made BELOW BELOW a.m./p.m. a.m./p.m. be be 8-11, 8-11, accepted accepted available, available, will will be be rates. rates. LISTED LISTED January January will will longer longer no no - NOT NOT these these is is cards cards assignment assignment for for rates) rates) + + + + + + + + credit credit the the 125+ 125+ 200+ 200+ 200+ 200+ 205+ 205+ 205+ 205+ 325+ 325+ 325+ 325+ 275+ 275+ 275+ 275+ requested requested Suites* Suites* 185 185 185 185 225 225 225 225 - qualify qualify other other (starting (starting rate rate to to hotels, hotels, DATE DATE No No HOTEL/MOTEL HOTEL/MOTEL at at the the A A 0 0 If If Focus) Focus) only). only). AT AT ranked ranked wfcot wfcot or or 109 109 130 130 123 123 133 133 103 103 123 123 rate. rate. N/A N/A NfA NfA NfA NfA NfA NfA NfA NfA Quad Quad - reservation. reservation. the the beds beds spouse spouse N/A** N/A** N/A** N/A** and and DEPARTURE DEPARTURE 2 2 housing housing at at --- only. only. Notices Notices room room STAYING STAYING your your type type (for (for below.) below.) below.) below.) of of below.) below.) 85 85 75 75 the the filled filled is is BE BE below.) below.) beds beds 115 115 108 108 118 118 103 103 123 123 140 140 135 135 115 115 116 116 135 135 Quad Quad 2 2 of of room room been been Express Express Maryland Maryland - WILL WILL information information Categories Categories Categories Categories categories categories section section confirmation confirmation wfcot wfcot occupants occupants have have 99 99 99 categories categories YOU YOU requested requested 110 110 108 108 118 118 108 108 N/A N/A NfA NfA N/A N/A N/A N/A N/A N/A for for tax. tax. 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PLEASE PLEASE Participant Participant be be The The an an Reservations Reservations will will *** *** Special Special ** ** * * Please Please I I HOUSING HOUSING room room Please Please GUARANTEE GUARANTEE at at will will 0 0 NORTH-HOLLAND MATHEMATICS STUDIES Edited by L. Nachbin ANNALS OF DISCRETE MATHEMATICS General Editor: P.L. Hammer LECTURE NOTES IN NUMERICAL AND APPLIED ANALYSIS General Editors: H. Fujita, M. Yamaguti STUDIES IN COMPUTATIONAL MATHEMATICS Editors: C. Brezinski, L. Wuytack ADVANCED STUDIES IN PURE MATHEMATICS EditorinChief: H. Morikawa CWI MONOGRAPHS . J.-R. Managing Editors: J. W. de Bakker, Honorary Editors: F.P. M. Hazewinkel, J.K. Lenstra P. Erd6s COLLOQUIA MATHEMATICS DIFFERENTIAL G SOCIETATIS JANOS BOLYAI APPLICATIONS Editor-in-Chief: D. STUDIES IN MATHEMATICS AND ITS APPLICATIONS DISCRETE APPLIED Editors: J.L. Lions, G.C. Papanicolaou, Operations Combinatorial H. Fujita, H.B. Keller Computer Science Editor-in-Chief: P.L. 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Gamkrelidze, Institute for Scientific Information, P.E. Kloeden, Murdoch University, Murdoch, Australia; Moscow, USSR (Ed.) E. Platen, Akademie der Wissenschaften, Berlin, Geometry I Germany Basic Ideas and Concepts of Differential Geometry Numerical Solution of Stochastic Contibutors: D.B. Alekseevskij, V.V. Lychagin and Differential Equations A.M. Vinogradov Provides an introduction to stochastic calculus and stochastic Since the early work of Gauss and Riemann, differential differential equations, in both theory and applications, geometry has grown into a vast network of ideas and emphasizing the numerical methods needed to solve such approaches. In this volume of the Encyclopedia of equations. To help the reader develop an intuitive under Mathematical Sciences, the authors give a tour of the standing of the underlying mathematics and hand-on nu principal areas and methods of modem differential geom merical skills, problems and over 100 PC-exercises are etry. It is structured so that the reader may choose parts of included. Many new results are presented on higher-order the text to read and still take away a completed picture of methods for strong sample path approximations, including some area of differential geometry. Beginning at the intro implicit, predictor-corrector, extrapolation and variance ductory level with curves in Euclidean space, the sections reduction methods. Offers the reader ready access to a become more challenging, arriving finally at the advanced large number of potential research problems in a field that topics which form the greatest part of the book. is expanding rapidly and is widely applicable. 1991/264 pp., 62 illus.!Hardcover/$59.00 1991/590 pp., 85 illus.!Hardcover/$73.00(tent.) ISBN 0-387-51999-8 ISBN 0-387-54062-8 Encyclopedia of Mathematical Sciences, Volume 28 Applications of Mathematics, Volume 23 M. Mignotte, UniversiteLouis Pasteur, Strasbourg, France L.R. Foulds, University of Waikato, New Zealand Mathematics for Computer Graph Theory Applications Algebra Offers a final-year undergraduate or first-year graduate Organized into two parts, Mathematics for Computer level introduction to the theory of graphs and its application Algebra presents the basic mathematical tools used in in engineering and science. The first part covers main computer algebra. The first part deals with arithmetical graph theoretic topics such as: connectivity, planarity, operations on large integers and elementary results in coloring, networks, matrices of a graph, graph theoretic number theory which have direct applications in modem algorithms, and matroids. In the second part, these con cryptography. The second part examines the factorization cepts are applied to problems in engineering, operations of polynomials with integer coefficients. This leads to the research, and science as well as to an interesting set of detailed study of polynomials over different rings, com miscellaneous problems. Some effort has been made to plex numbers, real numbers, finite fields, and rational present applications that use not merely the notation and integers. Also contains many exercises, classic as well as terminology of graph theory but the actual mathematical recent theorems, and useful earlier results. results of the subject. 1991/355 pp.!Hardcover/$39.00(tent.) 1991/416 pp., 90 illusJSoftcover/$48.00 ISBN 0-387-97675-2 ISBN 0-387-97599-3 Universitext J.K. Hale, Georgia Institute of Technology, Atlanta, GA; H. Ko~ak, University of Miami, Coral Gables, FL C.K.R.T. Jones, Brown University, Providence., RI; Dynamics and Bifurcations U. Kirchgraber, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland; H.O. Walther, University of In recent years, due primarily to the proliferation of com Munich, Germany (Managing Editors) puters, dynamical systems has once more turned to its roots in applications. It is the aim of this book to Rrovide a Dynamics Reported foundation of knowledge in dynamics and bifurcations of Volume 1 New Series ordinary differential equations for undergraduate and be Expositions in Dynamical Systems ginning graduate students in mathematics and engineering. Dynamics Reported is a series of books dedicated to the Equations in one and two dimensions constitute the majority exposition of the mathematics of dynamical systems. Its of the text. In particular, the basic notion of stability and aim is to make the recent research accessible to advanced bifurcations of vector fields are easily explained for scalar students and beginning researchers. There is an emphasis autonomous equations. on examples and explanations, but theorems appear with 1991/640 pp., 214 illus.!Hardcover/$49.00 their proofs. The focus is on the analytic approach to ISBN 0-387-97141-6 dynamical systems, emphasizing the origins of the subject Texts in Applied Mathematics, Volume 3 in the theory of differential equations. Written in a style that is best described as expository, Dynamics Reported Order Today! provides an excellent foundation for seminars on dynami > • Call: Toll-Free 1-800-SPRINGE(R): 1-800-777-4643. In NJ call cal systems. 201-348- 4033 (8:30AM-4:30PM EST). Your reference number is S981. • Write: Send payment plus $2.50 for postage and handling to: 1991/288 pp., 46 illus.!Hardcover/$59.00 Springer Verlag New York Inc•• Dept. #S981 , PO Box 2485, Secaucus. ISBN 0-387-54193-4 NJ 07096-249 I. • Visif: Your local technical bookstore. 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