OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

Strategic Planning for the Society page 17

JANUARY 1991 , VOLUME 38, NUMBER 1 Providence, Rhode Island, USA ISSN 0002-9920 ' Calendar of AMS Meetings and Conferences

This calendar lists all meetings which have been approved prior to the Mathematical Society in the issue corresponding to that of the Notices date this issue of Notices was sent to the press. The summer and annual which contains the program of the meeting, insofar as is possible. Ab­ meetings are joint meetings of the Mathematical Association of America stracts should be submitted on special forms which are available in many and the American Mathematical Society. The meeting dates which fall departments of mathematics and from the headquarters office of the So­ rather far in the future are subject to change; this is particularly true of ciety. Abstracts of papers to be presented at the meetir1g must be re­ meetings to which no numbers have been assigned. Programs of the ceived at the headquarters of the Society in Providence, Rhode Island. meetings will appear in the issues indicated below. First and supple­ on or before the deadline given below for the meeting. Note that the mentary announcements of the meetings will have appeared in earlier deadline for abstracts for consideration for presentation at special ses­ issues. sions is usually three weeks earlier than that specified below. For ad­ Abstracts of papers presented at a meeting of the Society are published ditional information, consult the meeting announcements and the list of in the journal Abstracts of papers presented to the American organizers of special sessions.

Abstract Program Meeting# Date Place Deadline Issue 864 tt March 15-16. 1991 South Bend, Indiana Expired March 865 * March 22-23,1991 Tampa, Florida Expired March 866 * June 13-15, 1991 Portland, Oregon March 26 May/June 867 * August 8-11, 1991 Orono. Maine May 22t July/August (94th Summer Meeting) 868 * October 12-13, 1991 Philadelphia, Pennsylvania August 1 October 869 * October 25-26, 1991 Fargo. North Dakota August 1 October 870 * November 9-11, 1991 Santa Barbara, California August 1 October 871 * January 8-11, 1992 Baltimore, Maryland October 2 December (98th Annual Meeting) March 13-14, 1992 Tuscaloosa, Alabama tt March 20-21, 1992 Springfield, Missouri June 29-July 1, 1992 Cambridge, England (Joint Meeting with the London Mathematical Society) January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) August15-19, 1993 Vancouver, British Columbia (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) January 12-15, 1994 Cincinnati, Ohio (1 OOth Annual Meeting) January 10-13, 1996 Orlando, Florida ( 102nd Annual Meeting) * Please refer to page 33 for listing of Special Sessions. t Please note this deadline is earlier than previously published. tt These dates are earlier than previously published. Conferences

January 14-15, 1991 : AMS Short Course on Probabilistic July 7-26, 1991: AMS Summer Research Institute on Combinatorics and Its Applications, San Francisco, Algebraic Groups and their Generalizations, University California. of Pennsylvania, University Park. Pennsylvania. June 22-August 2, 1991: Joint Summer Research Conferences in the Mathematical Sciences, University of Washington, Seattle, Washington. Events Cosponsored by the Society

February 14-20. 1991: Section A (Mathematics) Sessions at the AAAS Annual Meeting, Washington, D.C. Deadlines

March Issue April Issue May/June Issue July/August Issue Classified Ads* January 31, 1991 February 28. 1991 April25, 1991 June 17. 1991 News Items January 22, 1991 February 21, 1991 April 15, 1991 June 10, 1991 Meeting Announcements** January 24, 1991 February 25, 1991 April 15, 1991 June 13,1991 * 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. ------· 1 OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS FEATURE COLUMNS 3 Letters to the Editor 5 Forum 8 Computers and Mathematics Jon Barwise 21 News and Announcements This month's column is devoted to an article on "logical framework 25 Funding Information for the systems," (LFs), by N. G. de Bruijn, followed by comments from the editor. Mathematical Sciences 26 1991 AMS Elections 17 Inside the AMS 29 Meetings and Conferences of Though the discipline of mathematics, the mathematical community, and the theAMS world around it have seen great changes in the past seventy years, the South Bend, IN stated mission of the Society has remained the same. In what ways should March 15-16, 29 the AMS adapt and what are its long-range goals? Allyn Jackson discusses Tampa, FL a newly-appointed Strategic Planning Task Force, which will begin work March 22-23, 31 to assess the Society's strengths and resources and formulate a three- to Invited Speakers, 33 five-year strategic plan. AAAS Annual Meeting, 37 Joint Summer Research 19 Washington Outlook Conferences in the Mathematical Lisa A. Thompson examines "The Excellence in Mathematics, Science, and Sciences, 39 Engineering Education Act," which authorizes over $150 million for new and 1991 Summer Research existing programs in science and mathematics education, including $125 Institute, 41 million for education and human resources programs at the National Science 43 Mathematical Sciences Meetings Foundation. and Conferences 53 New AMS Publications 55 New Members of the AMS 57 Miscellaneous Personal Items, 57 Deaths, 57 58 AMS Policy on Recruitment Advertising 59 Classified Advertising 91 Forms

-·-··------·-----·---·-··---·········-···-····-·----·-···-----·---- JANUARY 1991, VOLUME 38, NUMBER 1 1 From the Executive Director ...

BEYOND THE REPORTS -DEPARTMENTAL ACTION

The last few years have seen a plethora of reports on all aspects of the nation's AMERICAN MATHEMATICAL SOCIETY mathematical sciences enterprise. These reports are useful in providing a springboard for debate, in distributing important information, and outlining means for change. However, it is now time to move beyond the reports and into action. Mathemati­ cal sciences departments are the natural institutions to take actions to bring about substantial, long-term change within the community. EDITORIAL COMMITIEE Robert J. Blattner (Forum Editor) Mathematics education, renewing the profession, resources for research, the reward Michael G. Crandall structure-these issues are not new. However, they are being raised with a new ur­ Robert M. Fossum (Chairman) gency as the result of various forces influencing the mathematical sciences: computers, Lucy J. Garnett, D. J. Lewis economic conditions, changing demographics, scientific and technological needs, and Nancy K. Stanton Robert E. L. Turner (Letters Editor) the growing importance of interdisciplinary research. Mathematical sciences depart­ ments need to reassess their responsibilities to adapt to the changing climate. MANAGING EDITOR Major national initiatives are now addressing these issues. The community, as never Donovan H. Van Osdol before, is involved in a systematic approach to the revitalization of the profession. For ASSOCIATE EDITORS example, at the National Research Council, the Board on Mathematical Sciences has Ronald L. Graham, Special Articles launched a national plan for departmental renewal, centered on the recommendations Jeffrey C. Lagarias, Special Articles of the update of the David Report. Another example is the Mathematical Sciences Education Board's national plan for reform of mathematics education, which includes SUBSCRIPTION INFORMATION state coalitions to facilitate local efforts and provide national coordination. How should Subscription prices for Volume 38 (1991) are mathematical sciences departments respond to efforts like these? How can linkages $121 list; $97 instiMional member; $73 individual be established? member. (The subscription price for members is in­ cluded in the annual dues.) A late charge of 10% To a great degree, the success of efforts targeted toward a national approach to the of the subscription price will be imposed upon or­ revitalization of the mathematical sciences depends upon the "fit" between these pro­ ders received from nonmembers alter January 1 grams and the college and university departments that train tomorrow's scientists, of the subscription year. Add for postage: Surface delivery outside the United States and lndia-$15; teachers, and researchers. Faculty must become involved to help insure the "fit" is a to lndia-$27; expedited delivery to destinations in good one. Crucial to this effort is departmental commitment: a few individual faculty North America-$28; elsewhere-$67. Subscrip­ members, working without departmental support and recognition, cannot fully address tions and orders for AMS publications should be the problems we are facing. Many different levels and modes of faculty involvement addressed to the American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl are possible, but departmental support of the entire effort is the only way to insure 02901-1571. All orders must be prepaid. lasting change. Departments should initiate open discussions of self-evaluation as a way of work­ ADVERTISING ing toward specific actions. A discussion could center on some very basic questions, Notices publishes situations wanted and classified advertising, and display advertising for publishers such as: What are the department's responsibilities in education (continuing, graduate, and academic or scientific organizations. undergraduate, and precollege)? What is the department's responsibility to interdisci­ Copyright @ 1991 by the American Mathematical plinary activities (interaction with other departments or with industry)? What is the Society. All rights reserved. Printed in the United department's responsibility in increasing the number of women and underrepresented States of America. minorities who succeed in mathematics? How well is the department fulfilling its The paper used in this journal is acid-free and falls responsibilities? If the department is ,not responsible for some of these activities, is within the guidelines established to ensure perma­ any other body acting on them? nence and durability. § Most of this publication was typeset using the TEl< typesetting system. In addressing these questions, the department will need to face the issue of recognition [Notices of the American Mathematical Society is and reward for an expanded definition of scholarship and professional activity. In this published monthly except bimonthly in May, June, area, too, a national movement can be seen: recently, the Carnegie Foundation for July, and August by the American Mathematical So­ the Advancement of Teaching issued a report suggesting fundamental changes in the ciety at 201 Charles Street, Providence, Rl 02904- 2213. Second class postage paid at Providence, faculty-reward system to place scholarly, professional, and educational activity on an Rl and additional mailing offices. POSTMASTER: equal footing with research. How will the mathematical sciences community respond Send address change notices to Notices of the to this national trend? American Mathematical Society, Customer Service Department, American Mathematical Society, P. 0. The climate for change is here. As the mathematical sciences become increasingly Box 6248, Providence, Rl 02940-6248.] Publication important to economic competitiveness, education and training, and scientific research, here of the Society's street address, and the other mathematical sciences departments will play an important role in the changes to come. information in brackets above, is a technical require­ Departments must act now with careful self-evaluation and strong action plans based ment of the U. S. Postal Service. All correspon­ dence should be mailed to the Post Office Box, NOT on broad departmental support and commitment. the street address. William Jaco

2 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The current proportion of Asian to the education of Black mathemati­ Letters students (American and foreign) in our cians. graduate program in Mathematics is Your commitment to equal rights to the Editor about 35%, and the corresponding fig­ goes far beyond academia and the field ure for UCLA as a whole is about 22%. of mathematics. In the late 1940s you Both the University and the Mathemat­ led a tenants group in the fight to ics Department are firmly committed to desegregate Stuyvesant Town in New enhancing the diversity of the student York City. You lost your position at a Asian Bias at UCLA? body in all respects and at the same major university after inviting a Black Recently the U.S. Office of Civil Rights time would be eager to address and family to live in an apartment you (OCR) completed an extensive review correct any validly determined findings retained in Stuyvesant Town. of graduate admissions at UCLA, fo­ of discrimination. We look forward to You are now Professor Emeritus cusing on the admission of Asian Amer­ the appeal process that we believe will of Mathematics at York University, ican students (excluding East Indians completely vindicate our admissions Toronto, Canada, where you began and Pakistani). After reviewing nearly decisions in Mathematics. teaching in 1968, and have also taught 100 programs (involving over 30,000 Alfred W. Hales, Chair at Fisk, Philander Smith, Wesleyan and admissions files), they concluded that University of California, the University of Alberta. You have one program (Mathematics) was not Los Angeles been a Visiting Professor or Research in compliance under Title VI, i.e. that (Received October 30, 1990) Scientist at the University of California illegal discrimination was present in at Berkeley, NYU's Courant Institute the admissions process, based on five and the Academy of Sciences of the cases in 1987 and 1988. Their findings USSR, among others. have been reported, with varying detail Lee Lorch Honored When Townsend Harris founded and accuracy, in a number of different Members of the AMS may be interested The City College in 1847 he defined places in the media. in the following citation accompanying its mission with these words: 'Open the The University has been very sup­ an honorary degree of Doctor of Hu­ doors to all-let the children of the rich portive of the Mathematics Department mane Letters which was conferred by and the poor take their seats together throughout and plans to appeal this vi­ the City University of New York on olation finding on our behalf. As we Professor Lee Lorch on May 25, at the are preparing for litigation, I should not commencement exercises of the City Policy on Letters to the Editor discuss the details of the case at this College of New York, the senior cam­ Letters submitted for publication in Notices are reviewed by the Editorial Committee, whose task time. Nevertheless I do want to make pus among its 20 campuses. is to determine which ones are suitable for pub­ some statement now to the mathemati­ "You are a distinguished mathe­ lication. The publication schedule normally re­ cal community. matician and educator who has made quires from two to four months between receipt of the letter in Providence and publication of the I have personally reviewed all of major contributions to the fields of earliest issue of Notices in which it could appear. the files involved in the OCR investi­ Fourier Analysis and Real Analysis. Publication decisions are ultimately made by gation in Mathematics and believe that You have had an equally profound majority vote of the Editorial Committee, with their charges are entirely unfounded. impact on the lives of minority and ample provision for prior discussion by commit­ tee members, by mail or at meetings. Because of Their findings appear to be based on women mathematicians who have ben­ this discussion period, some letters may require at least three faulty aspects of their ap­ efited from your efforts to expand op­ as much as seven months before a final decision proach: naive statistical methods which, portunities within the American mathe­ is made. Letters which have been, or may be, among other things, overlook statisti­ matical community. published elsewhere will be considered, but the Managing Editor of Notices should be informed cally valid tests showing that there In a letter to Science Magazine in of this fact when the letter is submitted. is no significant difference between 1951 you said: 'the scientific societies, The committee reserves the right to edit let­ admission rates of comparable Asian with their talk of the international char­ ters. Notices does not ordinarily publish com­ and non-Asian applicants; a failure to acter of science, must recognize its plaints about reviews of books or articles, al­ systematically interview those respon­ interracial character and put an end to though rebuttals and correspondence concerning sible for the admissions decisions in discriminatory practices.' As a mem­ reviews in Bulletin of the American Mathemat­ question; and a too rigid view of the ber of the Council of the American ical Society will be considered for publication. All published letters must include the name of admissions process which ignores the Mathematical Society, you led a suc­ the author. complex interplay of factors used by cessful struggle to end the Society's Letters should be typed and in legible form the individual who made the final de­ reciprocity agreements with the South or they will be returned to the sender, possibly resulting in a delay of publication. cisions in each case. This individual African Mathematical Society. Letters should be mailed to the Editor of No­ has also reviewed each of the files in Howard University honored you for tices, American Mathematical Society, P.O. Box question and stands by the legitimate, demonstrating 'exemplary courage and 6248, Providence, RI 02940, or sent by email to nondiscriminatory reasons for each of personal sacrifice in the struggle for hu­ [email protected], and will be acknowl­ edged on receipt. the decisions. man rights' and for your contributions

-----.. ------··------·----- JANUARY 1991, VOLUME 38, NUMBER 1 3 Letters to the Editor and know of no distinction save that of resentation, Biomechanics, and Appli­ formulate sentences about mathemati­ industry, good conduct, and intellect.' cations of Category Theory, Logic and cal objects we must determine precisely City College is today part of The other parts of Algebra to Theoretical the nature of these objects. (In such City University of New York, the most Computer Science? an effort we succeed with bitstreams, ethnically and racially diverse univer­ As Dr. Sunley reports in the same but we do not with sets.) Suppose a sity in America. CUNY is dedicated to issue of Notices, the mathematical world mathematician rebuilding the founda­ expanding opportunities and building seems to have reached a plateau in tion of mathematics proclaims that it is bridges among people. terms of resources available to it: Might the symbolic language of meaningless For your distinguished contribu­ this deliberate (and long-standing!) re­ signs and sentences (formed according tions in the field of mathematics and buff to the BE side of the current to rules of formation) which determine for your lifelong dedication to human research scene be explanation enough? the mathematical objects. Suppose fur­ rights, justice and equality, The City Robert Hermann ther that this mathematician proclaims University of New York takes great Boston University not to require the notion of truth and pride today in conferring upon you the (Received October 15, 1990) that we are dealing with a formal game degree of Doctor of Humane Letters." only, which nonetheless is bound to be We are gratified that Lee Lorch's Mathematics in the News significant. As a justification for this many contributions have been recog­ I read with interest Ethan Bolker's grandiose plan, he promises to provide nized, even belatedly. We only wish letter "Mathematics in the News," in us with a proof of consistency of the to note that the "major university" re­ the September 1988 issue of Notices. formal game. ferred to was Penn State (see N.Y. Bolker ruminates about his students' Can his numerous followers ever Times, April 10, 1950, p. 1; editorial, inability to recognize the 'nonsense' imagine that one reason truth cannot be April 11, 1950). He was, previously to they have written. In response, I should defined could be that truth was lacking that, dropped from the faculty of City like to share a few thoughts. in the first place? Will his followers College without explanation and after Surely, students "struggle hard at ever concede that there is a possibil­ having officially been recommended for the edge of what they can comprehend." ity that the reason for the lack of an promotion by department vote. At that The question is: "Can they possibly un­ absolute proof of consistency could be time, he was the only officer of the derstand what they are supposed to the presence of a contradiction? Are Tenant Committee to End Discrimina­ comprehend?" Professor Bolker cites students ever taught that the predicate tion in Stuyvesant Town who was on a problems with "for all" and "there ex­ calculus lacks precision because "for public payroll. ists," the universal and existential quan­ all" and "there exists" remain semanti­ Joseph Auslander tifiers of (first order) predicate logic. I cally undefined? Are students ever told Raymond L. Johnson question whether all the teachers and that in artificial programming languages University of Maryland writers of textbooks really know what (such as Pascal) we do have a precise (Received October 1, 1990) these words (or symbols) mean. syntax as well as a precise semantics? How come? The predicate calcu­ No! Not to my knowledge. Students Renewing U.S. Mathematics lus (or symbolic logic) is supposed to are told that the notions "for all" and As one who has been involved for be the precise (artificial) language of "there exists" are intuitively clear, and over thirty years with mathematical re­ "Mathematics." In a sense, the predicate that's it, and that's what the "success" search that strongly interacts with both calculus is as precise as can be, namely of mathematics is all about. More often the physics and electrical engineering as far as the syntax is concerned. Yet, than not, students are told that consis­ (BE) world, I would like to question there is precision lacking. Why? Math­ tency is assured by established wisdom the wisdom of the monolithic empha­ ematicians may, or may not, agree with and that a proof of consistency, elusive sis on Physics and traditional Applied me that the three most important no­ or not, is an unnecessary luxury. So Mathematics in the Report "Renew­ tions in (classical) mathematics as a much for intellectual honesty-in the ing U.S. Mathematics" in the Octo­ discipline are truth, proof, and infin­ classroom or elsewhere. It has been ber 1990 Notices and the lack of any ity. Can we have all three of these said that "to teach is to tell little white sense of contact with the current re­ without conflict? In most instances, the lies once in a while." Could it be that search scene in Electrical Engineering predicate calculus is a transfinitist's lan­ "little white lies" make it so hard for in that Report. Where are such sub­ guage. It was created for this purpose. the student to comprehend mainstream jects as Control, Robotics, Computer Is this language the best we can do? mathematics? Vision, the Relation between Symbolic Suppose a philosopher of mathe­ Gerhard F. Kohlmayr and Numerical Computation, Computer matics, or a philosopher of language, Mathmodel Consulting Bureau Programming Theory, Knowledge Rep- demands that before we even attempt to (Received October 9, 1990)

4 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum

more than a decade, and more than half the new doctorates are going to foreign nationals." The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between The picture suggested by these insights is one in which, 1000 and 2500 words long. Readers are invited to submit articles should such trends continue, mathematics faculty could be for possible inclusion in Forum to: reduced to teaching lower level courses, for the most part, Notices Forum Editor if we have any students left at all. Hence, Garfunkel and American Mathematical Society Young sound the alarm and seek, via a survey of disaffected P.O. Box 6248 departments outside mathematics, to diagnose the problem. Providence, Rl 02940 Apparently, if one can discover why an engineering depart­ or electronically to [email protected] ment, for example, offers its own mathematics coursework, rejecting the mathematics department for this service, then perhaps we can meet their criticisms and reclaim "our" students. The main criticisms that emerge from their survey Mathematics Inside Mathematics Departments focus on what is perceived as a poor treatment of applica­ Toni Kasper tions on our part, and a tendency to be too theoretical (i.e., bound to rigor and logical foundations). While we are told Borough of Manhattan Community College that, in calculus, we should emphasize skills and not the City University of New York reasoning and logical organization, we also get the complaint that students are not able to use their mathematical skills in problem solving, that "What appears to be ... lacking is the Editor's Note: In response to "Mathematics Outside Mathematics ability to formulate a problem quantitatively and then to solve Departments," by Solomon A. Garfunkel and Gail S. Young (No­ it using the tools they learned in their calculus course." tices, April1990, pages 408-411 ), the City University of New York The problems we face are much more serious, however, Mathematics Discussion Group sponsored a panel discussion of the issues raised by the authors. Dr. Young served as modera­ than what is suggested by Garfunkel and Young or by tor of the panel which otherwise consisted of Dr. Garfunkel, John the complaints of responding non-mathematics departments. Goodlet (Engineering Technology Department at the City College The rise, twenty-five years ago, in mathematics enroll­ of New York), and Toni Kasper (Mathematics Department at the ments reported by the authors-more than doubling in the Borough of Manhattan Community College). Kasper felt that, al­ 1960s-coincided with a great expansion in higher educa­ though the audience was of good size for the occasion, the impor­ tion occurring at that time. Since the number of college tance of the issues discussed required a more extensive broad­ cast. Accordingly, she wrote the following article examining the students increased greatly (both in absolute numbers and as questions and criticisms presented by Garfunkel and Young. a percentage of the population), there would of course be a corresponding increase in the number of students majoring in mathematics, especially since a growth in higher educa­ In their article "Mathematics Outside Mathematics Depart­ tion provided many job opportunities for college teaching. ments," Solomon A. Garfunkel and Gail S. Young report But then, the authors tell us, the number of mathematics that, although more and more students are taking advanced bachelor degrees fell during the 1980s back to the 1960s undergraduate mathematics courses, fewer and fewer of these level. This should come as no surprise. There had to come courses are being taught within the confines of mathematics a time when the growth in higher education would level off. departments. Moreover, the ·stmfents taking these courses are This in fact occurred, and hence the subsequent complaints not enrolled in mathematics programs per se but are, rather, that new Ph.D.s had little chance for academic employment. majoring in agriculture, business, engineering, science, and People who major in mathematics expect to teach, especially social science. Indeed, they remind us, "the number of math­ those who terminate their formal studies at the pre-doctoral ematics Ph.D.s awarded each year has dropped steadily for level. Given the poor reputation of secondary schools for

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salary and job status afforded, it is not such a shock that practice of requiring high school students to pass a course in mathematics major enrollments suffered so steep a decline intermediate algebra in order to graduate. Moreover, the new during the 1980s, especially when we also consider the Chancellor of City University, Dr. W. Ann Reynolds, has allure of large salaries being offered by the commercial voiced support for a corresponding approach at the college sector to graduates in business, law, finance, etc. entry level. When we consider that the present level of mathematics These are encouraging developments, but, while we have bachelor degrees, although at the 1960s level, now includes the patient opened, let's do the whole job. For one thing, foreign nationals, it becomes all too clear that a real loss in let's end the absurd practice, begun at least by the 1950s, mathematics study has taken place. This is not a tolerable of pretending that the people of our time can do what Isaac situation and we must identify the contributing causes in Newton could not: take calculus too soon. Newton entered order to supply a remedy. Trinity College, Cambridge, in 1661 and graduated in 1664. Since no population is uniform in its characteristics, the During his first two years there he studied elementary admission of a larger percentage of people to college stud­ mathematics. With that, and the lectures on geometry given ies required a relaxation of restrictive selection procedures. by his teacher (Dr. Isaac Barrow), he gained the insights Recall that, in 1970, The City University of New York that led shortly after to his famed discoveries. So admirable instituted its open admissions policy, whereby acceptance is the calculus and its many extensions, that it is probably into one of its colleges is guaranteed to any New York City natural for us to want our students to experience this pleasing student holding a high school diploma (or its equivalent). We subject as soon as possible. Given the awkwardness of some now have a student population different not only in numbers, of the techniques of analytic geometry, for example, as but in kind. For one thing, their exposure to mathematics is opposed to the more facile approach offered by the "new" much less than used to be the case. For example, a prerequi­ method, it is understandable that the traditional studies in site for admission to my own college, unti11970, was three analytic geometry began to suffer. Also, students faced a years of high school mathematics that included plane ge­ greater number of college level math courses than did their ometry, intermediate algebra, and trigonometry. After 1970, predecessors, as the field of mathematics itself grew. Thus, . admittance required no mathematics study at all, although whereas students had once taken separate high school courses a student might be obliged to undertake remedial work in in algebra (intermediate and perhaps advanced), trigonometry arithmetic and/or some elementary algebra. Throughout the (plane and spherical), and geometry (Euclidean, solid, and 1970s and 1980s, then, gaining access to higher education analytic), much of this became condensed or eliminated gradually became more a problem of affording the cost than altogether. ·Intermediate algebra and trigonometry became of qualifying on a scholastic basis. Access became more one course, for example, and what was left of analytic democratic academically (though few complained about the geometry became a short introduction to the calculus. growing financial elitism). In response, no doubt, to the This approach deprived students of the fuller exposure to increasing numbers of poorly prepared students, standards mathematics that must occur if the mathematical "maturity" were weakened, especially in "tougher" courses, mathe­ required for the study of the calculus is to take place. It is no matics being a conspicuous example. Thus, one college in wonder, then, that one of Garfunkel and Young's respondents our area changed its bachelor degree requirement from one complains that "Engineering has further suffered by the loss college level mathematics course to either a math or science of more preparatory subjects such as analytic geometry." course (and the latter could be satisfied with a rather soft Moreover, it is equally unremarkable that we have what science course, at that). many describe today as a crises in the teaching of calculus. Once colleges weakened their mathematics demands, Along with insufficient preparation, the study of calculus what support remained at the secondary level for the received another blow, in more recent years, when it began vigorous pursuit of mathematics study? Not surprisingly, to be used as a tool for inappropriate (if not downright then, as the last two decades have rolled over us, incoming nefarious) purposes, i.e., as evidence of a certain kind freshmen demonstrate less mathematical training, and fewer of intellectual power (often called mathematical maturity) students express any interest in mathematics itself. How deemed requisite for courses not involved with calculus at does a student discover such an interest (or talent) for a all. Thus, we see majors in computer science (who need subject if deprived-by declining standards-of the chance to study discrete methods), business, veterinary medicine, to experience the subject matter? Sadly, the effect of this etc., obliged to pass a calculus course, to the misery of could be only to deepen the unfortunate tendency already themselves and their instructors. How curious that, at the present at the college level. same time that we undermine the study of mathematics at There are signs that the nation is resetting its educational the lower levels, we demand the ability to perform at the compass. Recognition has come that the global economy higher levels. (I suspect that what this strange dichotomy that is now a fact of life necessitates a citizenry that is reveals is a basic lack of interest in mathematics itself but knowledgable, not just credentialed. As a local example, also a desire to gain respectability for one's subject matter but an important one nevertheless, Joseph A. Fernandez, by mathematizing the presentation to whatever extent is the Chancellor of the New York City school system, has possible). Then, for the final coup de grace, we pack these recently expressed an interest in returning to the previous unmotivated and undermined students by the hundreds into

6 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ______,_,______,,_.,_,___ , ______, __ , _____ , ___ ,,,... Forum

huge lecture sections where they are finished off. demanded, of the fuller exposure afforded by more So the problem, then, is not so much whether math­ preparatory coursework. ematics faculty know and treat applications, despite the 3. Abuses with respect to calculus coursework: complaints of the respondents to Garfunkel and Young's (a) using calculus as a screening device rather than survey. Yes, we could enliven our presentations by refer­ for its own sake in an appropriate setting. This causes ence to applications, and we should do so just to make it resentment among students who blame the mathematics more interesting (to ourselves as well as the student body). department, which may or may not be responsible for But that does not require us to relinquish our experience setting this obstacle to their goals. with mathematics on an esthetic basis as some engineering faculty, for example, would have us do just because they (b) the practice of employing gargantuan sized classes don't relate to the subject matter in the same fashion. The and teaching assistants who, either by inexperience or complainants also make the criticism that the mathematics poor English language skills, are incapable of compen­ material their students need is spread out over too many sating for the neglect engendered by the mass treatment. mathematics courses, that the items they want treated "span Indeed, their use often exacerbates the problem. too many math courses." The reason for that is simple and To stem the loss of students to mathematics study, we inevitable: the topics required are logically unrelated and must make the investment of providing reasonable class size, therefore would not naturally occur in a single mathematics thorough preparation at the secondary level, and we must course. These subjects represent tools to be used in an require students to undertake such study. Moreover, given the uncritical fashion, and that is just not how mathematicians demographic changes that are underway in the United States treat-or should treat-their subject. today, we must take deliberate steps to nurture those students In summary, while training in mathematics is becoming who could do well but have not traditionally undertaken more necessary, the failures in mathematics education grow, deeper studies in mathematics, female and minority students. and these are the consequences of several practices: It is especially important to support these groups at the 1. Failure to require students to take meaningful mathe­ higher levels, butthere is where they experience the saddest matics coursework at the lower levels, with the result neglect. Unless we are ready to refocus and, to some extent that they develop little interest or skill. reclaim older virtues, the numbers of students participating 2. Depriving students, of whom higher mathematics is in mathematics will continue to dwindle to a precious few.

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JANUARY 1991, VOLUME 38, NUMBER 1 7 Computers and Mathematics

Edited by Jon Barwise

This month's column Automated Checking vs. Automated Proving ~t the· intersection of mathematics, logic, and computer science, there The idea of formal proof checking is much older than the IS currently a great deal of activity in what are called "logical frame­ computer. Leibniz and Boole had already played with the work systems," or LFs. These systems aim at providing a computer idea to replace thinking by a kind of algebraic manipulation, environment witiiin which to do everything we do in matiiematics. In intent, at least, tiiey go far beyond programs like Maple and Mathe­ but in their time they did not have the means to carry matica. The most obvious difference is that tiiese systems provide a this out beyond the level of simple details of mathematical facility for the justification of everything, including the checking of all discourse. As we see it today, in order to cope with all proofs and constructions. possible mathematical situations one needs some feeling A pioneer in this program, one far ahead of his time, was Profes­ for formal languages as well as for language processing sor N. G. de Bruijn, of tlle Netiierlands. Starting in 1966, he led tiie algorithms. It is not so much the availability of computers, development of the Automatll project. This system is tiie grandfather of current logical framework systems. This month's column is devoted but rather the experience acquired around computers that to an article on these systems, written by de Bruijn, especially for tiie led to the design of what I like to call justification systems. column. Following his article, I add some comments of my own, to I prefer this term over proof checking systems since they spark some debate. handle much more than proofs. Some of these systems can check complete theories including whether definitions and axioms are well-formed, they can check relations between different theories, and the material that can be checked can go beyond what is called mathematics today. Checking Mathematics The activity of theorem proving should not be confused with Computer Assistance with the one of proof checking. A justification system is not expected to invent proofs, but to verify whether some input N. G. de Bruijn* is correct mathematics or not. ---···--·-··-----·-----·--·-····--······-·-·--·-· Automated theorem proving seems to be older than In recent years researchers have gained considerable ex­ automated proof checking. In a general sense automatic perience with computer systems for checking mathematics. production of proofs for all provable theorems is a very hard These have aroused practical and theoretical interest among task, but in limited areas it might be feasible and sometimes logicians and computer scientists, very little among mathe­ even easy. maticians. In this paper I try to inform a general mathematical Automatic theorem provers may occasionally do amazing readership about such systems, about their why and how, things, but they have their limitations. A justification system, about the possibility that some of these systems may alter on the other hand, is expected to be able to handle everything the views on how to formalize mathematics, and why they that is offered: every correct piece of mathematics should may eventually alter even the scope of mathematics. get the system's approval, and all incorrect or incomplete The matter has a large number of aspects and the reader material is to be rejected. An automatic theorem prover is should not think that these are all tightly linked. One may a kind of automated professor, a justification system a kind reject some of the opinions espoused in this paper and accept of automated student. The professor does the harder work some of the others. but has the advantage of being allowed to select topics and I will not always be able to avoid duplication with methods. The student seems to have the easier job, but is the paper in Notices by Shankar [S], which I recommend supposed to digest whatever is served. reading. Motives for Justification *N. G. de Bruijn is professor emeritus of the Department of Mathematics What motives can one invent for setting up a justification and Computer Science, Eindhoven University of Technology, PO Box 513, 5600MB Eindhoven, The Netherlands. He can be reached by email at system? (I say "invent" since motives are often afterthoughts: [email protected]. one starts something when it seems attractive and promises

8 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics some success, motives are invented afterwards as a kind of And apart from the computer's qualities in precision and defense.) An obvious motive is protection against human in speed, it has its influence in forcing us into an absolutely oversight in long chains of arguments. Usually mathe­ rigorous form of formalization. If we are unable to leave maticians do not need such checks: in most mathematical something to a computer, then it has not yet been sufficiently situations there are many possibilities to verify intermediate formalized. steps as well as final results by means of examples and But not all justification systems are equally good in analogies. But there are cases where a chain gets too long helping us to teach better. I feel that we learn much more to be grasped by a single brain in a limited time, which is from "framework" systems (to be discussed in this paper) particularly worrying when the chain has not been produced than from classical systems. by. a single person but by a group, possibly of both people What one is forced to learn anyway is to draw a strict and machines. Then the poor reader has to rely on mechan­ borderline between language and metalanguage. Mixing ical verification of all details. I use the word "mechanical" language and metalanguage is a well known source of in the old sense of human machine-like action. In that sense errors and paradoxes. The language is the only thing the we can do pencil-and-paper work without having to think verification system checks, the metalanguage helps us to all the time about the meaning. But in order to have any understand what we are doing. value at all, such mechanical checking should be perfectly organized. A very important class of applications can be the area of correctness proofs for computer software. In the near future this may be a kind of work that requires and deserves the Absolute Safety? attention of many mathematicians. One of the first questions people ask when hearing about a Another motive is to lighten the burden of referees of justification system is whether it would guarantee absolute mathematical papers. If a justification system is so easy to dependability. This can mean two things. In the first place handle that the average author can use it with little effort there is the matter of absolute dependability of mathematics, (at present no systems are that good) then the referees (or whatever the foundations may be. I think there is little hope the thesis supervisors) can require that the authors provide ever to get final answers to that question. a version of their paper directly in the language of the The second thing it can mean is this: once we have justification system so that the referees can run it on their accepted a rigorous formalization of some piece of math­ own machines. Then they need not bother about correctness ematics, and we have accepted the idea that "mechanical" and can concentrate on whether the paper is interesting and verification gives a kind of absolute guarantee of correct­ new. The question whether it is new, might profit from the ness, we ask whether this guarantee would be weakened system as well: once there is a good justification system used by leaving the mechanical verification to a machine. This on a large scale, one can think of organizing an enormous is a very reasonable, relevant and important question. It mathematical encyclopedia, a data bank of verified results, is related to proving the correctness of fairly extensive and such a bank can answer all sorts of questions about its computer programs and checking the interpretation of the contents. specifications of those programs. And there is more: the Quite a different motive is the matter of understanding hardware, the operating system have to be inspected thor­ mathematics. This can mean several things. oughly, as well as the syntax, the semantics and the compiler One way in which a justification system helps under­ of the programming language. And even if all this would standing was explained by Shankar [S]: by being forced to be covered to satisfaction, there is the fear that a computer convince a machine, a mathematician can sometimes trans­ might inake errors without indicating them through some form proofs with subtle errors and duplications into faultless total breakdown. elegant proofs. And elegance supports understanding and I do not see how we ever can get to an absolute insight. But it can also work out differently. Since a machine guarantee. But one has to admit that compared to human does not explicitly require elegance and shortness, there is mechanical verification, computers are superior in every the temptation to take the easy way as soon as the machine respect. has accepted correctness: just go on, without bothering about Another question people ask is whether a justification polishing. system can justify itself I think this is asking too much. But in a more general sense the system that we use A justification system can never justify more than certain for explaining mathematics to a machine can give insights fragments of itself or certain interpretations of itself. into the structure of mathematics and in the difficulties that Philosophically, I hardly think that the question of self­ beginners have in learning to play the game of mathematics. justification, if it has a meaning at all, is very relevant. I have to admit that teaching a student is not the same thing If someone tries to convince us with some story, then our as teaching a machine, but if teachers are unable to arrange doubts should not be allowed to melt away if the narrator their arguments in a way acceptable to a machine, then declares in the same convincing tone to be absolutely sure their teaching of students may be an illusion, not beyond about the truth. We should prefer to get support from a "teaching by intimidation and learning by imitation". different person.

--··-----······---· ···-·-----··---·--·-···--·------·------JANUARY 1991, VOLUME 38, NUMBER 1 9 Computers and Mathematics

Doing It Like Humans Finally, at the end of the belt the Checker does the final Some of the principles of the organization of justification verification. The work might be done by a human with an systems are copied from what we have always been doing unusual amount of endurance, but it is much better and as humans. cheaper to leave it to a computer. We explain things to our automatic student in terms of This picture of an assembly line may be a novelty for a language and according to the rules of that language we many mathematicians, since they hardly ever delegated parts write a book, consisting of a sequence of lines, or at least of their work to people below their own level. This is quite a tree-shaped arrangement of lines, which excludes circular different in other sciences. reasoning. The organization of memory in a justification system usually follows the human pattern too. We work with short Platonism and long range memory in our brain, directly accessible Some people feel that mathematical thinking depends on the written memory on our desk, books on our shelves and books existence of a real world of mathematical objects, an idea in possibly far away libraries. In a computer justification called Platonism. For communication between mathemati­ system we may observe a similar organization of memory. cians this idea is irrelevant: in a mathematical discussion Another aspect in which human behavior is followed between a believer and a non-believer none of the two closely is the production of mathematics, starting from a notices their different backgrounds. And of course it is kind of raw material, clever but vague ideas, and ending irrelevant in mathematical communication with a machine. with a final product of stupid but strictly precise formalities. The machine does not store the mathematical objects we are The process looks like an assembly line in a factory. In the talking about. The only thing it may have to store is what beginning of the conveyor belt there is the Mathematical has been said thus far. Genius who puts his ideas on the belt. Next there is the It is instructive to compare a justification system for Brilliant Mathematician who is able to write it all up in mathematics with a verification system for chess. The latter today's publication style. The next place along the belt is has to be able to read a chess game, consisting of a sequence taken by the Competent Mathematician. He knows the tricks of lines representing the moves. It has to find out whether of the subject, is able to supply necessary material that that sequence of moves produces a legitimate chess game his predecessor did not even mention, and is able to write or not. The chess moves are intended to update the position meticulously in every detail. on the board, and actually the rules of the game express In presenting mathematics to human students we usually legitimacy of the next move with respect to the updated do not give that ultimate form, and it is questionable position (including a few extra bits of information since whether we should. Mter all, students should learn to fill we have to know who's move it is, as well as a few gaps themselves. If we keep chewing all food for them details on castling and capturing "en passant"). The chess they will never develop proper teeth. Nevertheless they can verification system will of course store the position like learn a great deal from chewed material. In this connection a kind of Platonic reality and can even forget about all I mention the way Edmund Landau wrote his books on previous moves. So we get the feeling that the sequence of analysis and number theory. moves talks about the positions, that board and pieces form So the final product of the Competent Mathematician is the reality and that the given sequence of moves is just some a mathematical text that requires no specialized knowledge abstract coding of the sequence of positions. or experience from the reader. Let me call it Landau style. The difference with a mathematics verifier is striking. In The next stages along the belt have people who transform mathematics we have nothing but the discussion, and even this product into the language of the justification system. if a mathematical reality would exist, none of it would be Again it will turn out that gaps have to be filled, in particular stored in or consulted by the machine. since the Competent Mathematician did not bother to give The language of mathematics is not talking about a the proper references all the time and certainly did not always limited number of things. If it were, a justification system mention the logical derivation rules. After all, generations might try to take a kind of model-theoretical approach of mathematicians have done their work efficiently even by testing every statement in that world of objects. The without consciously knowing their derivation rules! language of mathematics cannot be verified on the objects: The work may be subdivided. One can think of a first there are too many of them. The only thing we can do stage where a person with some mathematical training inserts is apply the rule that things are correct if they have been a number of intermediate steps whenever there is a risk that correctly said. The notion of correctness is not formulated further workers along the belt might have trouble, and a in terms of a mathematical reality, but involves rules about second stage where the logical inference rules are supplied how a statement should be related to material that has and the actual coding is carried out. For the latter piece of been said before. Many non-mathematicians who hear about work one might think of a person with just some elementary verification systems get the idea that such systems can handle mathematics training or of a computer provided with some only "constructive" situations like finite mathematics. This artificial intelligence. But we should not be too optimistic confusion depends on that wrong idea of implementing about that: programming such jobs is by no means trivial. mathematical reality.

10 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ..------r--- Computers and Mathematics

I believe that every Platonist would be converted at once Doing It Efficiently when having to explain his mathematics to a machine. A very important feature of efficient justification systems is linearity. This refers to the length of a complete account of Doing It Naturally a piece of mathematics in standard language (Landau style) I think that in formalizing mathematics and, in particular, in compared to its translation in the language of the justification preparing mathematics for justification, it is usually elegant system and compared to the time a computer needs for as well as efficient to do everything in the natural way. That verification. In a bad system the latter two items may grow word of course does not mean "like in nature"; it can at exponentially compared to the first one, in a good system most mean "like normally in our culture". the relation is linear. It can be linear if the system makes Justification can be achieved step by step, like in full use of all the definitions, abbreviations, lemmas and the assembly line mentioned before. Putting a piece of theorems that the standard mathematical language already mathematics into a justification system is a process of provides. successive refinement. We begin by a rough sketch and in If the piece of mathematics in standard language contains various rounds we supply more and more details. The first gaps, however, or if it tacitly appeals to experience the few of these rounds belong to our cultural habits. I would student is assumed to have acquired thus far, then the call it "natural" if we proceed by successive refinement of text for the justification system might become considerably those first rounds and "unnatural" if the line of attack has longer. But then it is not fair to put the blame on the system. to be completely overthrown or remodelled. In that sense Without linearity, verification would never be feasible. Boolean logic is unnatural and natural deduction is natural. In the Automath project in the early 1970s, feasibility was Boolean logic comes down to replacing reasoning by put to a test. The test was to push a full mathematics an algebraic machinery that is not a refinement of what textbook through the justification system. The book chosen it is supposed to implement. Similarly Descartes' analytic was E. Landau's "Grundlagen der Analysis", and Landau geometry did not refine geometric proofs but replaced them was followed in every detail. No attempt was made to by algebraic ones with completely different structure. Both simplify or to modernize the text. The translation was Descartes and Boole created a beautiful and powerful theory, carried out by L. S. van Benthem Jutting [J] and the test but I would not call their work "natural". was completely successful. Linearity from the beginning to But of course, since the word "natural" means "cultural", the end. And computer technology of the early 1970s was it is subject to change. Set theory is an example for this. In good enough for this. The speed was never a problem, but my private opinion, it is unnatural to base mathematics on memory limitations were (and would still be). type-free set theory, where almost all mathematical notions Checking a Landau-like text is not always exactly what are coded as elements of the Zermelo-Fraenkel universe (to we have in mind. There is not always a Landau so kind be referred to as ZF). When it started, it reorganized much of as to write books in a systematically detailed form. Most the existing structure of mathematics, and could not be seen mathematicians hate to do that, and it should be said that as a refinement. But later generations of mathematicians in some parts of mathematics that work is more unattractive had often been exposed to ZF very early in life and would than in others. In some areas all the steps are equally elegant therefore call it quite natural. and interesting, whereas in.other areas we see elegant steps Some even believe (like Cantor possibly did) that the with a lot of dull work in between. At least there should ZF universe is not fiction but Platonic reality. This seems have been done dull work in between, usually suppressed to be in conflict with the popular slogan "everything is a by the author. In such areas people are likely to hate formal set". That slogan means that very many things (of course verification. not everything) can be coded in ZF. In a case like the one of the real number system, various different codings are in use. Filling Gaps Platonism of course wants to consider the reals as a kind We would like to have an automatic student who behaves of reality that is independent of the way we talk about it. like an intelligent human student and not like one that does So we have the picture of the Platonic reals, with injections "mechanical" checking without "understanding". (the codings) into the Platonic ZF universe. In that picture This indicates what we have to require from justification the real reals are no sets at all. systems in the future. In the first place they should be able Coming back to the idea of refinement, I must confess to deal with all the small gaps in any piece of mathematics, that it is difficult to keep it pure in the long run. The Genius in particular gaps which can simply be filled by an appeal at the beginning of the assembly line may look with one eye to a logical derivation rule. And in cases where references at what happens at the other end of the line and may adapt to previous material are needed, the machine should be able his ideas to the needs of the technology displayed there. to find those, possibly guided by hints in the text. Technical realization can have influence on design. Whatever a human student finds easy should be auto­ Moreover I am not sure that the idea of systematic mated, possibly by means of some artificial intelligence. refinement has an eternal value worth fighting for. After all, This kind of automation is hard, but I think it can be done it is extremely conservative, and there is nothing against a and will be done in some of the efficient systems which are revolution now and then. being developed today.

JANUARY 1991, VOLUME38, NUMBER 1 11 --·---···------Computers and Mathematics

But there is more. A good human student is not just proof, but nevertheless it is open for human inspection. We assumed to have a general aptitude in mathematical reasoning can inspect the general organization and if we select any in general, but is also assumed to learn from the particular detail we can convince ourselves that the proof of that part subject that is presented, recognizing situations that have is perfect. This is not very different from the situation in been understood before. This may amount to building a standard language in cases of exceedingly long proofs that kind of subconscious library of lemmas that have not been we have not written ourselves. formulated explicitly in the text or even a subconscious The use of machines for obtaining theorems was never library of methods. I think one is still very far from full questioned in the matter of numerical calculations. If, for automation of learning processes, so it will be a long time example, as a step in a mathematical proof we need the fact before we can automate the brilliant student. But for many that the product of 239 and 4649 equals 1111111, then it purposes it may suffice to automate the average student. is not customary to require a formal proof in mathematical Many mathematicians dislike pushing formalization to formalism. But it is reassuring to know that the process we the extreme. The idea is that it kills intuitive thinking. carry out by the pencil-and-paper multiplication algorithm I do not entirely agree. It may be true that unnatural for­ can be refined to a proof and it is not hard to have that malization replaces intuitive thinking by an entirely different refined proof produced automatically. process of formula manipulation, but natural formalization supports intuition rather than destroying it. Formalization and intuition should be each other's best friends rather than Frameworks enemies. When designing a justification system for mathematics, there But part of what we call intuitive thinking is not of is the crucial question how to start. In our present society it the kind that can be refined to proofs. That part cannot be is more or less accepted to say (often only as lip service) formalized. Our brain processes are not based on logic or that mathematics is founded on a basis of classical predicate any other foundation of mathematics, and nevertheless they logic and ZF set theory. Are we to base the justification produce wonderful things. But all mathematicians agree system on that foundation? Accepting this, we get what I that the results of intuitive thinkil'lg have to be justified shall call a "classical system". But there is the alternative by rigorous reasoning, even though there may be different to start off from a more primitive level, with the possibility opinions about the level of formality. to present logic and set theory as explained material in the system, on an equal footing with the presentation of all other mathematical material. In that case I use the term What Is a Proof? "framework system". Such a set-up means that "the usual Can a justification system check the computer proof of the way'' becomes an option, possibly along with others, and four color theorem? Or, rather, is that proof really a proof? that the user is allowed to be critical about the usual way. Instead of the spectacular four color theorem I prefer The rules of the game in a framework system have to discussing a simpler case. Imagine a combinatorial problem express how to handle mathematics and logic, more or less for which a computer search establishes the theorem that independently of the contents. Here "handling" involves how there are 24103 solutions. Do we consider that as a proof? to work with things like definitions, assumptions, axioms, Let us assume that there are correctness proofs, not just of free and bound variables, substitution, proof rules, proofs, the computer program, of the computer language compiler theorems. When designing the framework one has to bother and operator system, but even that there is a complete about what it means to apply a definition or a theorem or description of the hardware specifications. We now buy a a proof rule and not about what particular rules or axioms computer, trusting that it satisfies the specifications, we let are to be taken as a basis. It is not very customary among it run and get as output that there are 24103 solutions. Is mathematicians and logicians to discuss that framework: it that a proof? is usually assumed to be available before mathematics and Of course it is not. At most we have a proof for a more logic start off. But when trying to instruct a computer to complex statement: "if the abstract execution of the program follow our mathematical habits we are forced to be explicit on an abstract machine with the prescribed hardware leads about these matters. to 24103 solutions, then there are 24103 solutions". This statement does not even have the form of the one we have in mind; it is a companion theorem in some kind of Typing metalanguage. When I started working on a justification system around But it is reasonable to ask whether the computer search 1966, I wanted to make something of a universal nature. can be refined to a proof in the ordinary sense. I think that I gave a great deal of thought to the framework and that in many combinatorial search problems such a proof by led me in a quite natural way to giving a central place to refinement can be written (in the language of a justification the idea of typing; i.e., attaching a type to every expression. system) by a machine and that the program producing that The result was the system to be called Automath [dB 1]. proof can be obtained by refinement of the computer search To insiders it might be described as natural deduction program. That machine-produced proof can be checked by with (typed) variables and lambda-typed lambda calculus the justification system. Possibly no human will read that (lambda-typed means that the types may again be lambda

12 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics terms), with argumentation structure depending on the idea a+ b. Let us say that p(a +b) > 3 was proved earlier. We of "proofs as objects" (others use the term "propositions as satisfy the machine's inquisitiveness by referring to a place types" but I consider that to be unfortunate). where that proof 'Y is to be found. The machine checks this My interpretation of typing is related to the use of "is reference and then accepts all this as a proof of q( a+ b) < 5. a" in English. John is a soldier, London is a town, q is a So we have supplied a + b, which is a real number, and rational number and P is a point. Now let us call "soldier" a "f, which is a proof for p(a +b)> 3. In both cases we have type and "John" an inhabitant of that type. In English these the phrase "is a", and I interpret that as typing. The types types play the role of substantives. are "real number" and "proof for p(x) > 3". Proceeding in Replacing the "is a" by a colon, one gets "John: soldier", this style we note that proofs get the same treatment as "London : town", "q : rational number" and "P : point". objects and in manipulations like substitution, the machine But unlike typed lambda calculus, natural language does not treats the two in exactly the same way. It does not even have uniqueness of types. "John : soldier" is in no way in have to know whether expressions stand for objects or for conflict with "John : Canadian". Of course one may try to proofs. say that "soldier" and "Canadian" are subtypes of "man" The idea to treat proofs in the same way as mathematical and that "man" is the ultimate type, the archetype. But that expressions, as representing objects, is quite natural even if does not work. In a different context one claims that John we do not think of a machine that requires information from is a human being or that John is a living being. It is hard to us. It can be discussed in ordinary mathematics too. Instead pretend that there is something like an ultimate most general of getting to theorem q( a+ b) < 5 by application of theorem typing for John. T, we can get it by considering the proof ofT as a blueprint In mathematics things are different. I would describe that we just have to copy (with the proper adaptations) in the situation as follows. At some point in the discussion a order to get a proof for the application T1• So the new proof type A is introduced for the first time and subtypes of A is obtained by substitution into an old proof, and that is just are introduced later. But after A has been created, it is not like substituting into a function. possible to create a type B and to say that B is a supertype With this parallelism we get the full structure of math­ of A. Of course there can be situations that mathematicians ematical reasoning at once. A definition has the form want to have it that way, but then the rule of the game is f := P : Q, where f is a new name, P an acceptable that they have to start all over again, creating B first and expression and Q its type. In the proof world this form introducing A as a subtype of B. corresponds to a theorem, where P expresses the proof, Q In the typed justification systems the types are essen­ expresses (via "proof of") the proved statement, and f is the tially unique. So they are a kind of implementation of the name of the proof. The introduction of a typed variable x : Q archetypes mentioned above. Subtyping is not to be consid­ corresponds to an assumption. There Q represents (again via ered as typing, but has to be described by an archetype plus "proof of") the proposition that is assumed and x is a name a predicate. we can handle, during the lifetime of the assumption, as if it were a proof of the assumption, completely parallel to the Typing Can Implement Reasoning real variable x that is treated (during its lifetime) as if it Let me try to explain how a typed framework system can were a real number. handle mathematical reasoning. Instead of trying to build There is a second kind of parallelism on a different up a complete picture, I start somewhere in the middle. We level: types can be treated the same way as objects, in have some theorem T and want to apply it in a particular the sense that they can depend on variables and also act case; that application is a theorem T1• In theorem T there are as variables. Accordingly we have a kind of construction, some variables and some assumptions; let us just take one similar to functions of several variables, where some of the of each and have as an example "Let x be a real number, variables are on the level of objects or proofs, and others assume that p(x) > 3. Then q(x) < 5" (p and q are supposed are on the level of types. And the values of the functions to be known functions). Later we have an application. We can be objects as well as types. have real numbers a and b, we know that p(a +b) > 3, So we have two levels of typing. On the one level ("low" and our new theorem T, is that q( a + b) < 5. How do we typing) we say things like "3 is a natural", on the other one convince a machine that this is an acceptable application? ("high typing") "natural is a type". The machine wants to know several things. First it needs Such a simple systematic framework for dealing with a reference to the place where theorem T was proved. typing, enriched with facilities (typed lambda calculus) for It sees that the theorem contains a typed variable and an handling situations with dummy variables, is sufficiently assumption. It wants to know from us what we want to take simple to be natural, yet rich enough to express almost for x, and we say a+ b. The machine is able to check that anything we want. To take an example: the world of this has the right type: it is a real number indeed (typing Greek geometry did not only handle geometrical objects is unique and can be found by straightforward calculation, and proofs, but geometrical constructions too. And a text for which the machine needs no references or hints). Next describing a construction and proving that its result is the the machine requires a proof of the assumption, not of the one we wanted, handles three kinds of low typing. Apart original p(x) > 3 but of the one we get upon replacing x by from the two mentioned before (with objects and proofs) we

----·---·------······--···-----··-···---· JANUARY 1991, VOLUME 38, NUMBER 1 13 --··-----·------!"'"""'Computers and Mathematics get a third one, of the form ". . . is a construction for ...". instantiation. It has the effect that material written in some And the three domains are happily intermingled, referring context can be used later outside that context, without any to one another all the time. The combination of various appeal to lambda abstraction. theories into a single formalism can be called integration One might say, roughly, that until the 19th century (see [dBS]). mathematics needed no lambda calculus. Almost all of I think that this is much more natural then encoding it might have been written in terms of the ·lambda-free geometrical constructions as points in the ZF universe. fragment (PAL) of Automath, using the instantiation device for the description of explicit functions. It was only during the 19th century that the notion of a function moved very Typed Sets vs. Untyped Sets slowly from the metalanguage into the language, and that These frameworks based on typing can cover a very large made the lambda notation indispensable. part of formalizable mathematics, at least as much as what one has been doing with ZF. Actually, one of the things one can describe by means of the framework is ZF. But Scope of Mathematics we have the alternative to build mathematics on types (with A justification system is expected to be able to handle all sets as subtypes). In a way that gives much more, since formalizable mathematics. But the typed framework being types can depend on all sorts of parameters (including type as simple and rich as it is, we have the right to tum the parameters), can be freely created as primitives (like we do tables, and say: whatever the framework can describe, is to with axioms), and can be introduced as variables. The only be called formalizable mathematics. In particular it contains thing that we do not do is to create all our types in one all logic and computer science. stroke, by a single set of axioms. That is a very essential The claim is not so pedantic as it seems, since formal­ difference with ZF. ization does not encompass all mathematical activity. There The type structure is also rich enough to enable us to are other wonderful things like intuitive thinking, mental add entirely new areas of application. I mentioned objects, pictures, heuristics, metalanguage and interpretations. proofs, geometrical constructions, but there can be much more. Like algorithms in general (of which the geometric constructions are a special case). And we might get closer to Experiences fulfilling Leibniz' dream of a general language for science. It may be instructive to tell something about the experience we got in Eindhoven with teaching students to handle the Automath system. In the period 1971-1984 I gave A Word about the Lambda Calculus an introductory course on Automath almost every year. Almost everything in framework systems depends on the Students could get credits for that course, not by passing notations of the lambda calculus. That is something that still an examination but by doing practical work. Quite often seems to scare the majority of today's mathematicians. Very we gave them some material they were acquainted with strange, since the lambda notation is such a great help in and required them to have it checked by the system. No writing mathematics. It seems rather clumsy to live without treatment of preceding theories was required: all known it, in particular in fields like functional analysis. I can think material used in the proofs could be introduced by means of of only one reason why mathematicians still don't use it: it axioms. The students were usually mathematics majors with is because Bourbaki did not do it! about 4 years of training in pure and applied mathematics The theory of lambda calculus may have difficult aspects, and no training at all in logic. The general rule was that they but the notation itself is simple. It just amounts to the use had to spend about 100 hours on their job, which included of a quantifier with a bound variable in order to build a the time for attending the course. Most of them did rather function that is given by its values. Instead of introducing well, and delivered a complete machine-checked proof. the symbol f for the function that sends every x of a Examples of such pieces of mathematics were: the set S to x2 + x - 3, we can talk directly about that f as elements of group theory, the Banach-Steinhaus theorem AxEs(x2 + x- 3). So we do not need the letter f and we do of functional analysis, Dirichlet's pigeonhole principle, the not need the extra sentence which defines f by its values (it Konig-Hall theorem of combinatorics, Van der Waerden's is a sentence in the metalanguage). theorem on arithmetic progressions. One student wrote a It is amazing how much can be written in terms of master's thesis ·in Automath, treating a new theory of the lambda expressions! In particular I refer to [dB4] where it is real number system. It took him 9 months to deliver a fully explained how a complete book written in the language of checked text plus a report about the work. It would not have a justification system can be considered as a typed lambda taken him much less time to organize and finish the same expression and where the notion of correctness of the whole material in ordinary textbook style. book just reduces to the notion of correctness of that single In general it can be said that the more abstract the piece expression. of mathematics, the smaller the gaps and the easier the Nevertheless we can do at least some mathematical justification. Less abstract fields, like combinatorics, can be reasoning without lambda's. In contrast to most other frame­ hard since they may contain simple intuitive ideas for which work systems, Automath has a (very natural) feature of there is no tradition of formalization.

14 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Looking Around [HP] Huet, G. and Plotkin, G. (editors), Proceedings of the First It was the main purpose of this paper to try to explain Workshop on Logical Frameworks, Cambridge University Press, to ap­ what justification systems are and not to enter into details of pear 1991. systems. But here are some references for readers who might [S] Shankar, N., "Observations on the Use of Computers in Proof like Checking", Notices of the American Math. Soc., Vol. 35, Number 6, to have some real information about various systems. 1988. For the Boyer-Moore system I refer to [S]. For a survey of the Automath project to [dB3], for the Nuprl system to [C], for the Calculus of Constructions to [CH]. A way to put many framework systems in a common scheme was Some Thoughts on Mathematics, described in [B] (a similar scheme was already given in [dB2]). Logic, and Computers Finally, the collection [HP] can give a good impression of what is going on in the field. I already mentioned that I see a future in techniques of As recently as 1977, I was able to write, in the introductory automated gap-filling in order to make justification systems chapter of the Handbook of Mathematical Logic, (p. 22) "that useful for the working mathematician. For that particular there is a mathematically precise notion of ''-P is provable activity I think it makes little difference whether we take from T' which completely captures the intuitive notion '1.p a classical or a typed approach. In both cases one will do follows from T by the laws of logic alone,' for first-order roughly the same thing. 1.p and T." I went on to expand on this by explaining and But different justification systems may have different giving a proof of the Godel Completeness Theorem for views on the output. I would prefer the case where the first-order logic. machine's output is: "I have been able to fill the gap and A lot has happened in the mean time to shake my faith in here is the proof written in your own language". Other the spirit, if not the letter, of my claim.* Part of it has to do systems might say: "OK, I have been able to fill the gap to with experience gained by people working on systems like my satisfaction, but my proof would have been unreadable the ones de Bruijn describes. Justification systems that are for you, and has been put in the garbage already". I would useful for doing even a small part of standard mathematics call those systems "black box systems". They might work just do not fit into the framework of first-order logic and very fast, but slightly counter to the ethical principles of its proof theory. As de Bruijn indicates, one needs a wide justification. range of additional representational devices, including the lambda calculus notation and typing, as well as to admit of proofs themselves as objects of reference, alongside numbers, functions, what-have-you. None of this fits within References the first-order scheme. [B] H.P. Barendregt. "Introduction to generalized type systems," de Bruijn is not a mathematical realist. He thinks that no Proceedings 3rd Italian Conference on Theoretical Computer Science, one would be who tried to teach mathematics to a machine. Eds. A. Bertoni a.o., World Scientific, Singapore 1989. Well, he may be right. But I am a mathematical realist, one [dBl] Bruijn, N.G. de, "The mathematical language Automath, its who rejects the analogy between justification systems and usage, and some of its extensions," Symposium on Automatic Demon­ teaching. stration (Versailles, December 1968), Lecture Notes in Mathematics I think that mathematics is about something other vol. 125, Springer Verlag 1970, pp. 29-61. than symbols, equations or mental acts. I think it is about [dB2] -,"A framework for the description of a number of mem­ numbers, functions, sets, and the like. More generally, I bers of the Automath family," Memorandum 1974-08, Department of think mathematics is what Lynn Arthur Steen has called "the Mathematics, Eindhoven University of Technology, 1974. science of patterns." These patterns are real and they are the [dB3] -, (1980) "A survey of the project Automath," To H.B. ultimate subject matter of mathematics. As mathematicians, Curry: Essays in combinatory logic, lambda calculus and formalism, pp. we seek to discover the truths 579-606, Academic Press, 1980. about them and prove them [dB4] -, "Generalizing Automath by means of a lambda-typed to be so. lambda calculus." Mathematical Logic and Theoretical Computer Sci­ What justifies a given law of logic? On the realist ence, Lecture Notes in Pure and Applied Mathematics, Vol. 106 (ed. conception, the laws of logic are those moves that are D. W. Kueker, E.G.K. Lopez-Escobar, C.H. Smith) pp. 71-92. Marcel guaranteed to preserve truth: if the assumptions are true, Dekker, New York 1987. then so clearly is the conclusion. Any move that has this [dBS] -,"The use of justification systems for integrated seman­ property is legitimate. The Completeness Theorem for first­ tics," Colog-88 (ed. P. Martin-LOf, G. Mints), Lecture Notes in Com­ order logic attempts to give an puter Science, Vol 417, pp. 9-24, Springer Verlag, 1990. analysis of this notion. [C] Constable, R.L., et.al., Implementing Mathematics with the Nuprl Part of de Bruijn's quarrel with realism is that numbers ProofDevelopment System, Prentice-Hall Inc., 1986. and so on cannot be put in a machine. But then neither can [CH] Coquand, T. and Huet, G., "The calculus of constructions", they be put in a brain. What brains and machines can do is Information and Computation, Vol. 76, 95-120, 1988. [J] Jutting, L.S. van B., Checking Landau's "Grundlagen" in the *Here I should mention The Concept of Logical Consequence, by John Automath system, Mathematical Centre Tract Number 83, Amsterdam Etchemendy, Harvard University Press, 1990, which has done as much as 1979. anything to shake up my complacency.

JANUARY 1991, VOLUME 38, NUMBER 1 15 ~.~~_.~.~v~",_",~~~v."",~~,·~,.~~.~~~"~,""_"",_"",,,~,,,"~'".,""••".",."••" ••••••••••• ••: 1I••·lmlIIIU_.r.flllillill' 1' ······..·· ··..···..· ··· ···..···· ·· · M ..M· " ,"v.."."N ·,,'..~""..N. " ,,'~ ~.·.vw,,"~ Computers and Mathematics represent mathematical objects. What de Bruijn's work, and will never be a justification system that is observationally others following him, shows is that the first-order predicate complete. Why? Because, by definition, any such system calculus is a grossly inadequate way to model the way is going to be stuck using a given set of representational mathematicians represent mathematical objects. devices for representing mathematical objects and proofs, I have been drawn to the same conclusion by studying whereas mathematicians are not so constrained. We can, the role of diagrams in proofs and in working on Hyperproof, and do, create new forms of representation on the fly. And a (still very small) justification system that uses diagrams. with any new form of representation, certain moves will be On the traditional perspective, diagrams are only heuristic clearly seen to be laws of logic. aids to the construction of a formal proof. But why should In making this claim, I do not intend to cast doubt on the this be so? Why aren't diagrams as legitimate a tool for value of work on the sorts of systems de Bruijn describes. representing mathematical situations as sentences in a formal I think a great deal can be learned from such work. And language? And if they are, why can't there be laws of logic I expect that these systems will eventually become useful that are perspicuous from this point of view that would not mathematical tools, alongside, or incorporating, programs be perspicuous if recast in terms of sentences in a formal like Maple and Mathematica. Indeed, just as we can fruitfully language? make use of a computer algebra program without expecting It seems to me that there are such moves. This, however, the program to solve all our problems, we should not dismiss is not the place to go into that. Rather, what is relevant here work on logical framework systems just because the systems is the connection with the observation that mathematics is are limited. What I do want to cast doubt on' is th~ idea open-ended. The Godel Incompleteness Theorem assures us that any such system will ever meet the proclaimed goal of of that at a theoretical level. It tells us that no formal system observational completeness. is ever going to be complete for doing mathematics. Work on Mathematics just is not like chess, with its fixed set justification systems, those based on formal languages, with of rules. There will always be new patterns to discover or without the use of diagrams, shows that this theoretical and computers can help us discover them. As they are possibility is a real one. We are always looking for new discovered, they become grist for the mathematician's mill. representational devices and the laws of logic that go with We attempt to discover their truths. In this search, we will them. always be looking for novel ways of representing these Let us call a justification system observationally com­ patterns, ways appropriate to the mathematical objects at plete if it meets the proclaimed aim of such systems: to be hand. Each such representational scheme carries with it its able to digest and swallow any valid piece of mathematics own clearly valid laws of logic, moves that we can use in that humans find clear and digestible. My claim is that there giving proofs.

Announcing.... ·1991 MATHEMATICS SUB,IECT CLASSIFICATION

The editors ofMathematical Revie'ws announce the adoption of the revised Mathematics Subject Classification (MSC), prepared in cooperation with the editors of Zentralblatt filr Mathematik, for use in AMS publications, including Math­ ematicalRevieM's and CurrentMathematical Publications, beginning in 1991. The new classification contains significant changes in the areas

13 Commutative Rings and Algebras 16 Associative Rings and Algebras 33 Special Functions 49 Calculus of Variations and Optimal Control; Optimization 52 Convex Sets and Related Topics 81 Quantum Mechanics 82 Statistical Physics, Structure of Matter 92 Biology and Other Natural Sciences, Behavioral Science

Most ofthe other sections have been revised and expanded; approximately 600 more 5-digit classification lines represents a 14% increase in the size ofthe revised scheme. Section 19, K-theory, will be used for primary classification (it had been used only as a secondary classification in the 1985 version of the 1980 MSC).

A listing ofthe new classification can befound in the 1990AnnualIndexolMathernaticalReviel1's andonthe AMS e-MATH system with email addresstelnete-math.ams.com (see Notices ofthe AMS, October 1990, p. 1029 for more information about access to e-MATH).

16 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Strategic Planning for the Society "The membership needs to think about what they want the AMS to be, whether they're happy with this mission, or whether the mission should include some other kinds of This article is intended to inform the AMS membership of some recent important initiatives of the AMS Long Range Planning objectives, such as the dissemination of mathematical ideas Committee. The members of the Committee are listed below. to other sciences, to the general public, and to students.'' Robert M. Fossum, University of Illinois, Urbana-Champaign The Society has been called upon to take action in Ronald L. Graham, AT&T Bell Laboratories many areas, from precollege education to the support of William H. Jaco, Executive Director, AMS research, from the deterioration of academic libraries to Franklin P. Peterson, Massachusetts Institute of Technology public awareness of mathematics, from the human rights of Hugo Rossi (chair), University of Utah mathematicians to increasing the representation of women William P. Thurston, Princeton University and minorities in the profession. Thurston notes that dis­ M. Salah Baouendi, University of California, San Diego cussion of such issues often boils down to the question of Frederick W. Gehring, University of Michigan, Ann Arbor whether or not they fit into the Society's mission. Because The AMS Long Range Planning Committee (LRPC) was the Society has no clearly-stated goals, the entire decision­ formed in 1984 to formulate long-term plans, priorities, making process is slowed down. Says Thurston, "One thing and goals for the Society. At its most recent meeting in we want to accomplish [through the Task Force] is to come November 1990 at AMS headquarters in Providence, the to a decision on what the mission and goals are and what LRPC conferred with the AMS Executive Committee and we want to be doing over the next five years." Board of Trustees (ECBT) to consider ways in which Thurston sees communication as one of the central the Society could adapt to better serve the needs of its issues. "Mathematical ideas circulate within a group of membership. The ECBT decided to appoint a Strategic mathematicians, but not among the groups and not to other Planning Task Force to reexamine the Society's mission and sciences and the public," he notes. "We have a warehouse to formulate specific goals for the AMS over the next three stockpiled with concepts, ideas, and theorems, but there's to five years. no system of distribution... I think some change in the During a discussion of strategic planning, the ECBT mathematical culture needs to take place to establish more was asked to comment on the stated mission of the Society, communication." "the furtherance of the interests of mathematical scholarship Hugo Rossi, chair of the LRPC and of the Task Force, and research," and to assemble a set of goals for the believes that the strategic plan should articulate the role next several years. This discussion generated suggestions of the AMS in addressing some of the problems facing for rewording the mission to include such activities as the mathematical sciences community. "The Task Force disseminating mathematical information, promoting public will examine the role of the researcher in mathematical awareness and education, and supporting mathematics in a education, and how that role should be coordinated with broad professional sense, as well as a number of possible other professional groups already working in that area," he long-term goals for the Society. The Task Force will develop notes. "There are also a variety of roles the AMS could play and give shape to these ideas, eventually prioritizing the in support of research. It could support research directly, goals and developing an action plan. or through publications, or through public relations and national policy. The AMS is already doing some of these things. One purpose of the Task Force is to decide which The Need for a Strategic Plan are the most important." The AMS adopted its mission when it was incorporated in The AMS has come this far without a strategic plan; 1923, and although many aspects of the discipline and the why does it need one now? "The profession is in a state world around it have changed, the original stated mission of flux," Rossi points out. "Among the forces that are has not. Says outgoing LRPC chair William P. Thurston, causing it to change are the increasingly interdisciplinary

JANUARY 1991, VOLUME 38, NUMBER 1 17 ----··------~------Inside the AMS nature of mathematical research, the decrease in the number the recommendations before taking any action. of people entering the profession, and the need to find The Task Force will consist of the present LRPC, the next generation of mathematicians from populations not AMS President Michael Artin, and Past-President William traditionally associated with the profession. In addition, there Browder. In addition, approximately five more members will is an increasing tendency for federal funding for research to be appointed to the Task Force to broaden the experience shift from emphasis on individual, self-generating projects to and interests of the group. The AMS Trustees have approved large-scale, programmatic ones. The AMS needs to decide the hiring of a strategic planning facilitator, who will assist how it is to deal with this flux: where to try to arrest it, the Task Force and work with AMS staff to coordinate where to help propel it, where and how to react to it. In interviews, meetings, and communications connected with order to do this, the AMS needs to be guided by a clear and the planning activities. The AMS has been awarded a dynamic conception of its mission." $25,000 grant from the Exxon Education Foundation to One of the most important considerations is coordinating support the strategic planning activities and is seeking Society goals with the programs and plans of other orga­ additional underwriting of this project. nizations such as the Mathematical Association of America (MAA) and the Society for Industrial and Applied Math­ Timetable for the Plan ematics (SIAM). The Task Force will try to formulate a Development of the strategic plan will take place over the plan that does not compete or conflict with existing efforts, coming months and will be centered on a specific set of but rather complements and builds upon them. "We will be activities. The first phase will consist of an audit to assess getting input from other organizations as part of the planning the current resources and projects of the AMS and bring process," says Thurston. "I think there is a lot of sentiment into focus the key issues around which the strategic plan within the AMS that more communication and cooperation will be developed. To get a sense of which issues are with MAA and SIAM would be beneficial all around ... considered to be the most important, AMS leadership and There may be some philosophical differences in how the staff will be interviewed and a portion of the membership MAA or SIAM would set up a program as opposed to how will be surveyed. Phase two of the activities will be the the AMS might do it, but I think these differences are less development and writing of a multi-year strategic plan. important than the significance of everyone cooperating in a In conjunction with these activities, the AMS will united front." begin actions to achieve the goals as delineated in the plan. AMS staff, as well as Society members, will be Activities of the Task Force involved in this implementation process. "The Society is a The Task Force will help the Society formulate a coherent significant resource for the support of the broad mathematics approach to issues facing the mathematical sciences com­ community," notes AMS Executive Director William H. munity in a way that builds upon and enhances existing Jaco. "It is very exciting that we are undertaking a thorough efforts. In addition, a strategic plan will help to insure that process to investigate and plan how to best serve the day-to-day and longer-term decisions made by AMS staff community." would be part of a clearly articulated plan. Most of all, it The Task Force is scheduled to complete its work by will help the AMS to prioritize its activities to best utilize the summer, at which time it will present its report to the Society resources. Board of Trustees. Over the next several months, reports "By generating discussions on these issues, and trying of the activities of the Strategic Planning Task Force will to achieve a consensus, the Task Force will set a mis­ be reported in Notices. Members who have thoughts and sion statement for the Society which takes into account comments on this process are encouraged to communicate the changing environment and the end results the AMS them to: Strategic Planning Task Force Project Manager, wants to achieve," says Rossi. "They will formulate specific Timothy Goggins, American Mathematical Society, P.O. goals consistent with the mission and specific strategies to Box 6248, Providence, RI 02940; telephone 401-455-4110; achieve those goals." These strategies may take the form electronic mail [email protected]. of recommendations to the Executive Director, the Coun­ cil, or various AMS committees. Because the Task Force is Allyn Jackson an instrument of the Board of Trustees, the Board will review Staff Writer

18 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook

education and considering undergraduate instruction when This month's column is written by Lisa A. Thompson, determining faculty compensation and promotion, as well as who is the Assistant for Governmental Affairs of the Joint demonstration that the faculty member has kept current with Policy Board for Mathematics (JPBM). research in his or her field. Institutions that receive grants will be designated Centers of Excellence for Undergraduate In its waning days, the 101st Congress passed comprehensive Teaching. science and mathematics education legislation, the result of The new law also authorizes a gradual increase in numerous hearings over the past two years on at least a NSF spending on graduate fellowships to bring the number dozen proposals from House and Senate Members, as well awarded to 1200 per year by FY 93, for a total cost of $37.9 as President Bush. Although it endured the usual partisan million this year (FY 91) and $67.8 million in FY 93. It also sniping and interbranch differences of opinion, the package directs the NSF to ensure that the number of fellowships survived on its merits through the concerted efforts of going to women and minorities increases substantially every influential legislators who made mathematics and science year through the year 2000. NSF is also authorized to spend education a top priority. The bill was passed by ·a Congress $10 million this year on a graduate traineeship program that shares with the scientific community a belief that high for colleges and universities that are attended by few NSF quality mathematics and science education at all levels is fellows, but are committed to upgrading their capacities for absolutely crucial to the future of the Nation's security and high quality research and to graduating significant numbers prosperity. of women and minorities in mathematics, science, and "The Excellence in Mathematics, Science, and Engineer­ engineering. ing Education Act" authorizes over $150 million for new NSF's women and minorities programs are to be ex­ and existing programs, including $125 million for educa­ panded with $17 million in increased support this year for tion and human resources programs at the National Science institutions to make women and minority faculty members Foundation (NSF). Declaring that the federal government available to those that have few such faculty; for colleges has a "significant role in promoting the study of mathematics and non-research universities to attract and retain women and science," the package is designed to encourage Ameri­ and minority faculty members; and for alliances among can students to pursue careers in mathematics, science, and research universities and institutions with predominantly engineering; improve the quality of teaching in mathematics minority enrollment. and science made available to all Americans; have American The Department of Education, in cooperation with NSF, students rank first in the world in mathematics and science; is authorized by the act to spend almost $10 million this substantially increase the number of graduates with degrees year and increased amounts in following years on three new in mathematics, science, and engineering; and, substantially scholarship programs that would provide money to over increase the number of women and minorities pursuing 6000 undergraduates every year after the fourth year of full careers in mathematics, science, and engineering. enactment of the programs. National Science Scholarships Addressing Congressional concern that some U.S. uni­ are to be awarded each year to two high school seniors, versities place too much emphasis on research at the expense at least one of whom is female, from every Congressional of education, the act provides for a new NSF program of district. Each award will be up to $5000 per academic year competitive, merit-based grants to college and university for four years, depending on the recipient's cost of attendance professors with records of excellence in teaching. The grants and on the amount appropriated to the Department to spend are to be used for developing innovative curriculum or teach­ on the program. Scholars are to be chosen on the basis of ing methods, purchase of educational equipment, support for demonstrated achievement in the physical, life, or computer research or professional activities, and support of teaching sciences, mathematics, or engineering and must continue fellows. Criteria for the awards specifically include the to major and excel in one of these fields to receive the commitment of the institution to improving undergraduate funds. From among nominations by state review panels, the

JANUARY 1991, VOLUME38, NUMBER 1 19 ------·----· Washington Outlook

President, in consultation with the Secretary of Education nominees and the promotion of participation by minorities and the Director of NSF, selects the recipients. and persons with disabilities. The Robert Noyce Scholarships are for undergraduates At the precollege level, the new law allows for new in the third and fourth years of study majoring in and and expanded programs at both NSF and the Department of demonstrating high academic achievement in physical, life, Education, agencies Congress would like to see cooperate or computer sciences, mathematics, or engineering degree more in the area of mathematics and science education. This programs. From among nominations submitted by a merit section of the legislation is also designed to encourage the review panel, the President selects up to 500 recipients every formation of alliances among states, state education agencies, year. After graduation scholarship awardees, to be known as colleges, universities, nonprofit associations, and industry. the Robert Noyce Mathematics and Science Teaching Corps, The Department is authorized to make competitive, merit­ will be required to teach in U.S. secondary or elementary based awards totalling $17 million to a network of regional schools for two to four years, depending on the number of consortia to disseminate exemplary instructional materials award-years, or to repay the amount awarded plus interest. and provide technical assistance for their implementation in Each award will be up to $5000 per academic year required mathematics and science classes in elementary and secondary to earn the degree, and if necessary, up to $5000 for another schools. These consortia would work with a Department­ year to complete education courses required to fulfill the supported national clearinghouse for educational programs obligations of the award. The amount of each scholarship and materials, to which curricula developed with federal will depend on the recipient's cost of attendance and on the funds would be deposited. The regional consortia and the amount appropriated to the Department. national clearinghouse are required to obtain non-federal The National Science, Space, and Technology Corps is contributions. to be selected from among nominations by members of the The Department is also provided with authority to make House of Representatives. Every year, one high school senior grants to model programs for training and instruction in who has excelled in and plans to major in the physical, life, the use of computers as part of precollege mathematics or computer sciences, mathematics, or engineering will be and science curricula, with emphasis on programs that chosen from every Congressional district and will receive integrate higher order analytical and problem-solving skills up to $5000 per academic year for four years, depending into the curricula. The NSF is authorized to undertake on the recipient's cost of attendance and on the amount a complementary, merit-reviewed program to develop and appropriated to the Department to spend on the program. expand the uses of innovative technologies for mathematics Awardees can attend any U.S. institution of higher education, and science instruction. and those institutions enrolling members of the corps will NSF is also authorized to spend $17 million more this be members of the National Academy of Science, Space, year on informal mathematics, science and technology ed­ and Technology. Members of the corps will be required to ucation in the form of grants to public science-technology spend four years working in the physical, life, or computer centers-museums, planetariums, libraries, zoos, aquariums, sciences, mathematics or engineering in the employ of the etc.-for the development of interactive exhibits and pro­ United States or a U.S. company or pursuing postgraduate grams; replication and dissemination of effective programs; education in one of these fields. Those failing to complete and development of new centers. And the law states that $17 the service obligation will be required to repay the amount million more can be spent on grants to education agencies of the awards with interest. All three scholarship programs for systemic reform of mathematics and science education, provide for special consideration of the financial need of a program undertaken just recently by NSF.

20 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Wtadyslaw Orlicz He became the main editor of Com­ to thirty scientists and engineers. Sev­ 1903-1990 mentationes Mathematicae in 1955, and eral of the awardees who may be of Wladysl:aw Orlicz (May 24, 1903- in 1962 assumed the same position interest to Notices readers: George F. August 9, 1990) was born in Okocim for Studia Mathematica. Orlicz lec­ Carrier of Harvard University, Stephen in the district of Cracow, Poland. tured in Canada, West Germany, and C. Kleene of the University of Wis­ He studied mathematics in the Fac­ China (in Peking in 1963 there re­ consin at Madison, and John McCarthy ulty of Philosophy at the Jan Kaz­ sulted a 138-page book in Chinese: Lin­ and Patrick Suppes, both of Stanford imierz University in Lw6w. The Lw6w ear Functional Analysis, unfortunately University. A more extensive piece on School had been founded by Stefan Ba­ never translated into English). Among the awardees is being prepared for a nach and Hugo Steinhaus, and among other awards, Orlicz was presented the future issue of Notices. Orlicz's colleagues were Z. W. Birn­ Alfred Jurzykowski Foundation Award, baum, M. Kac, S. Mazur, J Schauder, and has honorary degrees from York and S. Ulam. He was a participant University, the Poznan Technical Uni­ Fulbright Scholars Named The Council for International Exchange in the regular meetings at t}J.e "Scot­ versity, and the University of Adam of Scholars has announced that 936 aca­ tish Cafe", chronicled by Ulam (1957, Mickiewicz. demics, professionals, and independent 1977) and by Mauldin (1981). Orlicz supervised 39 doctoral the­ scholars have received awards under the From 1922 through 1929 Orlicz ses and published 170 papers in many areas of mathematics. His name is as­ Fulbright Scholar Program to lecture, was a teaching assistant in mathematics consult, or conduct research abroad in at the Jan Kazimierz University. He sociated with many key ideas (among them Orlicz spaces, the Orlicz category 1990-1991. (Because of the crisis in obtained his Ph.D. degree in 1928, his the Middle East, the United States In­ thesis dealing with some problems in theorem, and Orlicz-Pettis theorem). In 1988, on the occasion of his 85th birth­ formation Agency has suspended the the theory of orthogonal series. At the 1990-1991 programs in Bahrain, Iraq, University of Gottingen (1929-1931) day, PWN-Polish Scientific Publishers published his "Collected Papers" in two Jordan, Kuwait, Qatar, Saudia Arabia, he studied with H. Bohr, M. Born, R. the United Arab Emirates, and Yemen.) Courant, and E. Landau. He served on volumes. He remained active in mathe­ matics throughout his life, finishing the The Fulbright program is financed the faculty of the Lw6w Technical Uni­ galley proof of a paper only one hour and administered by the United States versity from 1931 to 1937, when he before he died. We will always remem­ Information Agency. Support is also was nominated as Associate Professor ber Orlicz not only for his important provided by participating governments at the University of Poznan. The Sec­ contributions to mathematics but also and by host institutions in the United ond World War interrupted his work, for his generosity, enthusiasm, and in­ States and abroad. but he returned to his position in May terest in the work of others. Following are the names of this 1945. In 1948 Orlicz was appointed full Lech Maligranda year's American Fulbright scholars in professor, since which time he worked IVIC, Caracas the mathematical sciences, with the both as a faculty member at the Uni­ Lars Erik Persson names of their home institutions and the versity of Adam Mickiewicz and as a Lulea, Sweden countries in which they are lecturing or researcher in the Mathematical Institute conducting research. of the Polish Academy of Sciences. RAYMOND G. AYOUB, Pennsylva­ In 1961 he became a full member of nia State University, Syria; RANAN the Polish Academy of Sciences. Orlicz National Medals B. BANERJI, St. Joseph's University, officially retired in 1974, but continued of Science Awarded Austria; BRUCE A. BARNES, Univer­ his seminar at the Mathematical Insti­ On November 13, 1990, President Bush sity of Oregon, Greece; THEODORE tute of the Polish Academy of Sciences presented National Medals of Science A. BURTON, Southern Illinois Univer­ in Poznan. and National Medals of Engineering sity at Carbondale, Hungary; JOSEPH

JANUARY 1991, VOLUME 38, NUMBER 1 21 News and Announcements

A. CIMA, University of North Car­ the nominee on the following criteria: widely to the mathematical community olina at Chapel Hill, Ireland; G RE­ quality of performance in mathematics, by the Joint Policy Board for Mathe­ GORY M. CONSTANTINE, University exhibition of real interest in mathemat­ matics. Check with the chair of your of Pittsburgh, Trinidad and Tobago; ics, ability for independent work, and department to get more ideas for activ­ STEVEN D. CUTKOSKY, University of performance in mathematical compe­ ities. Missouri at Columbia, India; BRUCE titions at the local or national level, Since its inception in 1986, Math­ R. EBANKS, University of Louisville, if any. Supporting materials should be ematics Awareness Week has gained Hungary; VIRGINIA B. FLACK, Uni­ enclosed with the nominations. Nom­ momentum each year and is begin­ versity of California at Los Angeles, inations must be postmarked no later ning to make a cumulative impact on Guatemala; ERDOGAN GUNEL, West than March 29, 1991 and sent to Pa­ the nation. Help to make this year's Virginia University, Turkey; 0TOMAR tricia Cross, Executive Director, AWM, celebration the biggest ever. HAJEK, Case Western Reserve Univer­ Box 178, Wellesley College, Wellesley, sity, Germany; R. NEAL HART, Sam MA 02181. Congress Passes NSF Budget Houston State University, Oman; ALAN In November 1990, Congress signed R. HAUSRATH, Boise State Univer­ Mathematics Awareness Week: into law a bill that contains the ap­ sity, Botswana; THOMAS F. HIGGIN­ April21-27 propriation for the National Science BOTHAM, Southeastern Louisiana Uni­ This year, Mathematics Awareness Week Foundation (NSF) for fiscal year 1991. versity, Malta; CHARLES B. HUGHES, will be held April 21-27, 1991. This The total appropriation for the NSF Vanderbilt University, United King­ national event provides an opportu­ was $2.3 billion, an increase of about dom; WILLIAM A. KINCAID, Wilm­ nity for local and regional activities 11% over last year. The Research and ington College, Iceland; ALLEN KLING­ that heighten public awareness of the Related Activities portion of the bud­ ER, University of California, Los An­ beauty and usefulness of mathematics. get was up about 6% to $1.7 billion. geles, India; HOWARD W. LAMBERT, The theme this year, "Mathematics: As has been usual in recent years, Eastern New Mexico University, Costa It's Fundamental," was chosen because Congress appropriated more money for Rica; LINDA M. LESNIAK, Drew Uni­ the applications of mathematics, which educational programs that the Founda­ versity, Hungary; JOHN A. MITCHEM, are fundamental to progress in science, tion asked for: a rise of 46% to $322 San Jose State University, Botswana; technology, industry, and society, are million. VOJIN G. OKLOBDZIJA, San Fran­ not fully appreciated by the public. At the time of this writing, the cisco State University, Peru; JoN H. Mathematics Awareness Week provides budget of the Division of Mathematical PEARCE, San Jose State University, a forum for the mathematical commu­ Sciences (DMS) had not been finalized. Zimbabwe; ALFRED S. POSAMENTIER, nity to communicate with the public on However, DMS officials estimate the City College, City University of New this timely theme. increase for the Division will be 3- York, Austria; WALTER READ, Cali­ Mathematics departments and fac­ 4% over last year's budget of about fornia State University at Fresno, ulty can observe Mathematics Aware­ $69 million. The percentage increase Czechoslovakia; ANDREW J. SIMO­ ness Week in many ways: sponsoring a for DMS is about the same as for the SON, King College, Botswana; JEROME mathematics competition for students other divisions in the Mathematical and SPANIER, Claremont Graduate School, in nearby high schools; serving as Physical Sciences Directorate. Another New Zealand; GORDON A. STEGINK, a guest speaker at a nearby elemen­ action that will likely affect the DMS Hope College, Malawi; JOSEPH E. tary, middle, or secondary school; fly­ funding sitUation is the removal of YUKICH, Lehigh University, France. ing a banner proclaiming Mathematics the salary cap of $95,000 on principal Awareness Week above the door of investigator grants. Nominations for the your department; sponsoring a public Alice T. Schafer forum where members of your com­ European Mathematical Mathematics Prize munity can discuss proposed changes Society Founded The Association for Women in Math­ in mathematics education; or holding a In October 1990, the European Math­ ematics (AWM) calls for nominations mathematical art contest for students in ematical Society came into existence for the Alice T. Schafer Mathematics your department or geographic area. under an initiative of some thirty math­ Prize. This $1000 award is made an­ Last year, colleges and universities ematical societies from virtually every nually to an undergraduate woman for across the country participated in Math­ country of the European continent from excellence in mathematics. All mem­ ematics Awareness Week with a variety the Atlantic Ocean to the Ural Moun­ bers of the mathematical community of activities, from showing mathemat­ tains. The Society, founded at a historic are invited to submit nominations for ical films and videos, to writing opin­ juncture in European affairs, is anum­ the Prize, to be awarded in April 1991. ion pieces about mathematics for local brella organization that will focus on The nominee may be at any level newspapers, to holding a mathematical activities that are best handled by an in her undergraduate career. The let­ "murder mystery" contest. Packets of international organization. ter of nomination should include, but information for use during Mathemat­ The Society's Statutes state, "The not be limited to, an evaluation of ics Awareness Week were distributed purpose of the Society is to promote the

22 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements development of all aspects of mathe­ tor, she is responsible for managing (University of California at Davis), and matics in the countries of Europe, with the review procedure for and mak­ F. Franek (McMaster University). particular emphasis on those which are ing recommendations on grant propos­ The Center will be funded by var­ best handled on an international level. als which seek to improve the qual­ ious foundations and through private The Society will concentrate on those ity of mathematics instruction in the contributions from the United States activities which transcend national fron­ schools through programs that enhance and other countries. Recently, Westing­ tiers and it will in no way seek to teacher effectiveness while serving as house Foundation awarded a $25,000 interfere with the national activities of prototypes for other inservice projects. grant to support the Center's devel­ the member societies. In particular, the Lacampagne can be reached at the opment. The Center has also received Society will, in the European context, Division of Teacher Preparation and funds from the Czech and Slovak Civic aim to promote mathematical research Enhancement, Room 638F, National Forum Foundation. (pure and applied), assist and advise on Science Foundation, 1800 G Street, Among the workshops planned for problems of mathematical education, NW, Washington, DC 20550; electronic the next two years are: Winter School concern itself with the broader rela­ mail [email protected] (Internet) or on Abstract Analysis (January 12-26, tions of mathematics to society, foster clacampa@nsf (Bitnet); telephone 1991), Workshop on Evolution of In­ the interaction between mathematicians 202-357-9527; fax 202-357-7009. terstellar Matter and Star Formation of different countries, establish a sense (May 21-25, 1991), and Workshop on of identity amongst European math­ Center for Theoretical Study Phase Transitions: Physics, Mathemat­ ematicians, and represent the mathe­ in Prague ics, Biology, and Society (1992). More matical community in supra-national Charles University in Prague, Czecho­ information about the Center may be institutions." slovakia is developing a Center for The­ obtained from H. Woolf, Institute for Membership is open to organiza­ oretical Study for advanced theoretical Advanced Study, Princeton, NJ 08540; tions primarily concerned with pro­ research in mathematics, the natural electronic mail hwoolf@ guiness.ias.edu. moting research in pure or applied sciences, and the humanities. The Cen­ Members of the mathematical sciences mathematics in Europe, as well as to ter is intended to help bridge the natural community may also wish to contact individuals. The Society is planning a separation among these disciplines and Thomas Jech, Department of Mathe­ major Congress in Paris in the early to provide a forum for integrated re­ matics, 215 McAllister Building, Penn­ summer of 1992, and the possibility of search. The organization will also help sylvania State University, University a journal and a newsletter are being to further Czechoslovak science and Park, PA 16802; telephone 814-865- investigated. scholarship in the international arena. 7527; email: [email protected]. The Officers of the Society are: F. The Center's director is Ivan M. The address of the Center is: Center Hirzebruch (president), Cz. Olech and Havel, a computer scientist and brother for Theoretical Study, Charles Univer­ A. Figa-Talamanca (vice-presidents), C. of Vaclav Havel, president of the Czech sity, Ovocny trh 5, 116 36 Praha 1 - Lance (secretary), and A. Lahtinen and Slovak Federative Republic. The Stare Mesto, Czechoslovakia (address (treasurer). The members of its Ex­ Center's activities will begin with a for visitors is Celetna 20, Praha 1). ecutive Committee are: E. Bayer, A. small number of projects coordinated Kufner, P.-L. Lions, L. Marki, and A. by scholars and scientists from Czecho­ News from the St. Aubyn. slovakia and abroad. To establish long­ Mathematical Sciences Institute For legal purposes, the Society has term programs, an international advi­ Cornell University been established under Finnish law, sory board has been formed. The many aspects of partial differential with its seat in Helsinki. For more Senior and postdoctoral researchers equations are being explored in a spe­ information, contact: D. A. R. Wal­ will hold positions at the Center lasting cial program of invited lectures at the lace, Publicity Officer, European Math­ from three months to one year. There Mathematical Sciences Institute (MSI). ematical Society, Department of Math­ will also be short-term visiting scholars, This past fall we heard from P. Con­ ematics, University of Strathclyde, Liv­ as well as seminars and workshops on stantin (Univ. of Chicago) on PDE's ingstone Tower, 26 Richmond Street, topics emphasizing cross-disciplinary and Fluid Mechanics, from A. Eden Glasgow G1 1XH, Scotland, UK. activity. (Arizona State Univ.) on Exponential Havel says he is pleased to re­ Attractors for Navier-Stokes Equations Lacampagne Joins port that the Center is now particularly and from G. Ponce (Pennsylvania State NSF Staff strong in mathematics, having among Univ.) on Dispersive Equations. Carole Lacampagne, associate profes­ its scholars-in-residence Bohuslav Bal­ On February 1, 1991 E. DiBenedetto sor of mathematical sciences at North­ car (topological dynamics, Boolean al­ (Northwestern University) will give a em Illinois University, has taken a gebras) and Roman Kotecky (math­ lecture on Porous Media Type Equa­ position as a rotator in the Division ematical physics). Arrangements for tions: How the Solutions Behave Lo­ of Teacher Preparation and Enhance­ short term visits have also been made cally and Asymptotically. From Febru­ ment at the National Science Foun­ with with Thomas Jech (Pennsylvania ary 8-15, 1991, David Hoff (Indiana dation (NSF). As a program direc- State University), Washek F. Pfeffer University) will give a series of three

JANUARY 1991, VOLUME 38, NUMBER 1 23 News and Announcements

lectures on Discontinuous Solutions of Dispersive Waves, and C.l. Foias (Indi­ 1991. Other visits are being planned. the Navier-Stokes Equations for Com­ ana Univ.) will discuss A Normal Form For further information, please contact pressible Flow. J.-C. Saut (Universite for the Navier-Stokes Equations and B.S. Titi at Suite 321, 409 College Paris-Sud) will give a series of nine its Connection to Turbulence during a Avenue, Ithaca, NY 14850-4697; 607- lectures from March 25, 1991 through series of four lectures from June 5-15, 255-8005; Fax: 607-255-9003. Aprill2, 1991 on Linear and Nonlinear

Now in Paperback

INTRODUCTION TO ALGEBRAIC CURVES TRANSLATIONS OF MATHEMATICAL MONOGRAPHS, VOLUME 76 Phillip A. Griffiths

Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. However, the majority of books written on the subject discuss algebraic curves and compact Riemann surfaces separately, as parts of distinct general theories. Most texts and university courses on curve theory generally conclude with the Riemann-Roch theorem, despite the fact that this theorem is the gateway to some of the most fascinating results in the theory of algebraic curves. This book is based on a six-week series oflectures presented by the author to third- and fourth-yearundergraduates and graduate students at Beijing University in 1982. The lectures began with minimal technical requirements (a working knowledge of elementary complex function theory and algebra together with some exposure to topology of compact surfaces) and proceeded directly to the Riemarm-Roch and Abel theorems. This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises and two exams, this book would make an excellent introductory text. 1980 Mathematics Subject Classification: 14; ISBN 0-8218-4530-6, LC 89-7000, ISSN 0065-9282; (Hardcover) 500 pages, July 1989; Individual member $59, All prices subject to change. Free shipment by surface; for air delivery, List price $99, Institutional member $79 please add $6.50 per title. Preptl)·mel!l required. Order from American To order, please specify MMONOn6NA Mathematical Society, P.O. Box 1571, Annex Station, Providence. RI ISBN 0-8218-4537-3, December 1990 02901-1571, or call toll free 800-321-4AMS (321-4267) in the (Softcover) 500 pages, Individual member $34, List price $56 continental U.S. and Canada to charge with VISA or MasterCard. To order, please specify MMONOSn6NA

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

Deadline for Faculty ateships at NIST during the 1991-1992 Technology, Administration Building, Enhancement Program academic year. The Fellowships are in­ Room A337, Gaithersburg, MD 20899; The Faculty Enhancement Program at tended for senior researchers, while the telephone 301-975-2839. Women and the National Science Foundation (NSF) Associateships are for advanced gradu­ minorities are encouraged to apply. supports seminars and conferences for ate students and recent Ph.D.s. groups of faculty from a number of un­ In particular, the program seeks dergraduate institutions to learn about fellows with a strong interest in collab­ new developments and techniques in orative, cross-disciplinary research in OTA Congressional their fields. The workshops may focus process modeling and optimization. Ar­ Fellowship Program on recent developments in the mathe­ eas of research that fit NIST's research The Office of Technology Assessment matical sciences which have implica­ mission and facilities include: statis­ (OTA) is seeking outstanding candi­ tions for instruction in lower or upper tical approaches in materials process­ dates from academia, business and in­ level courses. Alternatively, they could ing and bioprocessing research; on-line consider how better to teach introduc­ dustry, and the public sector for its quality control in automated flexible Congressional Fellowship Program. Up tory courses for majors or non-majors. manufacturing; analysis of lifetime data In either case, participants learn some to six Fellows will be selected for one­ from multifactor experiments; sources year appointments in Washington, DC, new mathematics and bring their new of variability in physical measurement ideas back to their own institutions and beginning in September 1991. procedures; calibration for manufactur­ OTA provides congressional com­ regions. ing process control; variance compo­ The deadline for proposals is April mittees with objective analyses of the nents; design of experiments; errors in emerging, difficult, and often highly 15, 1991. A list of the 1990 awardees in variable regression; graphical data anal­ this program appears in the May/June technical issues of today. Assessments ysis; and statistical image processing. are conducted in such areas as eco­ 1990 issue of Notices, page 582-583. Stipends for the Senior Research For more information on the program, nomic competitiveness, international se­ Fellows will be commensurate with contact: William Haver, Faculty En­ curity, energy, advanced materials, bio­ qualifications and experience, and fringe hancement Program, Room 639, Na­ technology, neuroscience, agriculture, benefits will be provided. Appointments tional Science Foundation, 1800 G advanced medical technologies and ser­ will last four to nine months. Appli­ Street, NW, Washington, DC 20550; vices, telecommunications and informa­ cations are due January 15, 1991 for 202-357-7051; email [email protected] tion technologies, environment, educa­ (Internet) or whaver@nsf (Bitnet). Fellows and February 15, 1991 for As­ tion, and science policy. sociates. For application information, Candidates must have significant contact Carolee Bush, ASA/NSF/NIST experience in technical fields or man­ Fellowships at NIST Research Program, American Statis­ agement or have completed research The American Statistical Association tical Association, 1429 Duke Street, at the doctoral level. The deadline (ASA) announces the ASA/NSF/NIST Alexandria, VA 22314-3402; telephone for applications is January 31, 1991. Senior Research Fellowship Program, 703-684-1221. For information on re­ For more information, contact: Con­ which is cosponsored by the National search topics and other aspects of the gressional Fellowships, Personnel Of­ Science Foundation (NSF) and the Na­ program contact Ruth Varner, Coordi­ fice, Office of Technology Assessment, tional Institute of Standards and Tech­ nator, ASA/NSF/NIST Research Pro­ Congress of the United States, Wash­ nology (NIST). The program invites ap­ gram, Statistical Engineering Division, ington, DC 20510-8025; telephone 202- plications for Fellowships and Associ- National Institute of Standards and 224-8713.

JANUARY 1991, VOLUME 38, NUMBER 1 25 1991 AMS Elections Nominations by Petition

----·------·- Vice-President or Member-at-Large The new members will be elected in a preferential ballot. The Pres­ One position of vice-president and member of the Council ex officio ident will name at least six candidates for these three places, among for a term of two years is to be filled in the election of 1991. The whom may be candidates nominated by petition in the manner de­ Council intends to nominate at least two candidates, among whom scribed in the rules and procedures. may be candidates nominated by petition as described in the rules and The candidate's assent and petitions bearing at least 100 valid sig­ procedures. natures are required for a name to be placed on the ballot. In addition, Five positions of member-at-large of the Council for a term of three several other rules and operational considerations, described below, years are to be filled in the same election. The Council intends to nomi­ should be followed. nate at least ten candidates, among whom may be candidates nominated by petition in the manner described in the rules and procedures. Petitions are presented to the Council, which, according to Section Rules and Procedures 2 of Article VII of the bylaws, makes the nominations. The Council Use separate copies of the form for each candidate for vice-president, of 23 January 1979 stated the intent of the Council of nominating all member-at-large, or member of the Nominating and Editorial Boards persons on whose behalf there were valid petitions. Committees. 1. To be considered, petitions must be addressed to Robert M. Prior to presentation to the Council, petitions in support of a can­ Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island 02940, didate for the position of vice-president or of member-at-large of the and must arrive by 28 February 1991 . Council must have at least 50 valid signatures and must conform to 2. The name of the candidate must be given as it appears in the several rules and operational considerations, which are described be­ Combined Membership List. If the name does not appear in the list, as low. in the case of a new member or by error, it must be as it appears in the mailing lists, for example on the mailing 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. Editorial Boards Committee 3. The petition for a single candidate may consist of several sheets Two places on the Editorial Boards Committee will be filled by elec­ each bearing the statement of the petition, including the name of the tion. There will be four continuing members of the Editorial Boards position, and signatures. The name of the candidate must be exactly the Committee. same on all sheets. The new members will be elected in a preferential ballot. The Pres­ 4. On the next page is a sample form for petitions. Copies may be ident will name at least four candidates for these two places, among obtained from the Secretary; however, petitioners may make and use whom may be candidates nominated by petition in the manner de­ photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that of the member whose scribed in the rules and procedures. name and address is given in the left-hand column. The candidate's assent and petitions bearing at least 100 valid sig­ 6. The signature may be in the style chosen by the signer. However, natures are required for a name to be placed on the ballot. In addition, the printed name and address will be checked against the Combined several other rules and operational considerations, described below, Membership List and the mailing lists. No attempt will be made to match should be followed. variants of names with the form of name in 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 notto be.) 7. When a petition meeting these various requirements appears, the Nominating Committee Secretary will ask the candidate whether he is willing to have his name on Three places on the Nominating Committee will be filled by election. the ballot. Petitioners can facilitate the procedure by accompanying the There will be six continuing members of the Nominating Committee. petitions with a signed statement from the candidate giving his consent.

------26 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY NOMINATION PETf110N FOR 1991 ELECTION

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

as a candidate for the position of (check one): D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 January, 1992.

N arne and Address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

JANUARY 1991, VOLUME 38, NUMBER 1 27 CALL FOR SUGGESTIONS

There will be a number of contested seats in the 1991 AMS elections. Your suggestions are wanted by

THE NOMINATING COMMITTEE for president-elect, 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 South Bend, Indiana Indiana University at South Bend March 15-16 First Announcement

The eight-hundred-and-sixty-fourth meeting of the American Noncommutative ring theory, GAIL R. LETZTER, PE­ Mathematical Society will be held at Indiana University at TER MALCOLMSON, and FRANK 0KOH, Wayne State South Bend, South Bend, Indiana on Friday, March 15, and University. Saturday, March 16, 1991. All special sessions will be held Hilbert spaces of analytic function, JOHN E. Mc­ in Northside Hall and all invited addresses will be in Room CARTHY, Indiana University at Bloomington. 113 of Northside Hall. Probability and prediction theory, MOHSEN POURAH­ MADI, Northern Illinois University. Abstracts for consideration for these sessions should Invited Addresses have been submitted by the December 13, 1990 deadline. By invitation of the Central Section Program Committee, This deadline was previously published in the Calendar of there will be four invited one-hour addresses. The speakers, AMS Meetings and CC'Tlferences and in the Invited Speakers their affiliations, and the titles of their talks where available and Special Sessions section of Notices. are: LEONID G. MAKAR-LIMANOV, Wayne State Univer­ Contributed Papers sity, title to be announced. There will also be sessions for contributed ten-minute DoNALD G. SAARI, Northwestern University, Dynamics papers. Abstracts for consideration of these sessions should and symmetry applied to paradoxes of voting and the social have been submitted by the January 3, 1991 deadline sciences. previously published in the Calendar of AMS Meetings and STEPHEN D. SMITH, University of Illinois at Chicago, Conferences. Late papers will not be accommodated. title to be announced. DEANE YANG, Columbia University, Questions relating Registration Riemannian geometry and the topology of3-manifolds. The meeting registration desk will be located in the south Special Sessions wing (main entrance) of Northside Hall and will be open from 8:00 a.m. to 5:00 p.m. on Friday, March 15, and from By invitation of the same committee, there will be eight 8:00 a.m. to noon on Saturday, March 16. The registration special sessions of selected twenty-minute papers. The fees are $30 for members of the AMS, $45 for nonmembers, topics of these sessions, and the names and affiliations of and $10 for students or unemployed mathematicians. the organizers, are as follows: Mathematical economics and dynamical systems, CHAR­ Petition Table ALAMBOS D. ALIPRANTIS, Indiana University and Purdue University, and CARL P. SIMON, University of Michigan. A petltton table will be set up in the registration area. Simp tical complexes associated to finite groups and their Additional information about petition tables can be found in a box in the San Francisco meeting announcement in the representations, JONATHAN L. ALPERIN, University of October 1990 issue of Notices. Chicago, and STEPHEN D. SMITH. Model theory, STEVEN A. BUECHLER, University of Notre Dame. Accommodations Geometric topology, FRANK X. CONNOLLY, University Rooms have been blocked for participants at The Works of Notre Dame. Hotel, the Holiday Inn - Downtown, and the Ramada Inn. Algebraic topology, WILLIAM G. DWYER, University Participants should make their own reservations and directly of Notre Dame, and ANTHONY D. ELMENDORF, Indiana mention the AMS meeting to obtain the rates listed below. University at South Bend. All rates are subject to a ten percent tax. The AMS is

JANUARY 1991, VOLUME 38, NUMBER 1 29 Meetings not responsible for rate changes or the accommodations within 1.5 miles of the campus. Complete listings will be offered by these hotels/motels. available at the meeting registration desk. Other motels located on U.S. Route 31/33 North near the Ramada Inn are: Budgeteer Motor Inn (219-272-9000); Best Parking Inns of America (219-277-7000); Days Inn (219-277-0510); Free parking will be available in the student lot (PI) located Knights Inn (219-277-2960); and Motel 6 (219-277-2960). north of Northside Hall. Holiday Inn - Downtown (2.8 miles from campo~) 213 W. Washington Street, South Bend, IN 46601 Travel and Local Information Telephone: 219-232-3941 The deadline for reservations is February 27. Michiana Regional Airport is served by several major airlines. Free shuttle service is available to the Holiday Flat rate $55 Single, Double, Triple Inn - Downtown and the Works Hotel. Transportation to Restaurant/lounge, indoor pool, and free parking. For the Ramada Inn or other accommodations can be arranged free van transportation from airport, dial 6 from courtesy through United Limo or cab service at the airport. phone located at baggage pick-up. TRANSPO buses serve the IUSB campus from the downtown area of South Bend. Bus #9 leaves the downtown The Works Hotel (2.5 miles from campus) transfer center at approximately ten minutes before the hour 475 N. Niles Avenue, South Bend, IN 46617 (Monday-Friday), and every half-hour (Monday-Saturday) Telephone: 219-234-1954 beginning at 5:00 a.m. The bus ride from downtown to Deadline for reservations is March 1. the IUSB bus stop at Mishawaka Avenue and Greenlawn Avenue takes about ten minutes. Bus #10 for the return trip Single $48 Each additional adult $7 leaves the corner of Mishawaka and Greenlawn Avenues Free continental breakfast, restaurant adjacent, and free at approximately five minutes before the hour (Monday­ parking. For free van transportation from airport, call motel. Saturday). TRANSPO bus service back to the downtown The Ramada Inn (6.3 miles from campus) area ends at 9:33 p.m. on Friday and 6:26 p.m. on Saturday. 52890 U.S. Route 33 North, South Bend, IN 46637 TRANSPO service is not available to or from the Ramada Telephone: 219-272-5220 Inn area. The deadline for reservations is February 22. Weather Single $51 Double $59 A wide range of weather is possible in the Michiana area Restaurant/lounge, indoor pools, sauna, jacuzzi. in March. Participants are advised to note regional forecasts near the time of the meeting. Food Service Andy Roy Magid The IUSB Cafeteria (UC2) will be serving breakfast and Associate Secretary lunch on Friday, March 15. Other restaurants are located Norman, Oklahoma

This Is the second edition of The Joy of T£)(, the user-friendly 1980 Mathemmics Subject Classifications: 00, 68 guide to A_MS-TE)<, which is a software package based on the ISBN 0-8218-2997-1, LC 90-1082 Jhe C revolutionary computer typesetting language TE)<. A.MS-TEX 320 pages (saftcover), September 1990 was designed to simplify the typesetting of mathematical Individual member $30, List price $38, quantities, equations, and displays, and to format the output Institutional member $34 J0· 01 according to any of various preset style specifications. This To order, please specify JOYT/NA second edition of Joy has been updated to reflect the changes t ~4~ introduced in Version 2.0 of the A;WS'-TEX macro package. ..1> ' ., The first two parts of the manual, "Starters" and "Main Courses," teach the reader how to typeset the kind of text and mathematics one ordinarily encounters. "Sauces and Pickles," EXSero00 Edltloo the third section, treats more exotic problems and includes A a 60-page dictionary on special techniques. The manual Gourmet Guide also includes descriptions of conventions of mathematical typography to help the novice technical typist. Appendices to Typesetting list handy summaries of frequently used and more esoteric All prices subject to change. Free shipment by withtheAMS-lEX symbols. surface; for air delivery, please add $6.50 pertille. This manual will prove useful for technical typists as well as Prepayment required. Order from American macro package scientists who prepare their own manuscripts. For the novice, Mathematical Society, P.O. Box 1571, Annex exercises sprinkled generously throughout each chapter Station, Providence, Rl 02901-1571, or call toll free encourage the reader to sit down at a terminal and learn 800-321-4AMS (321-4267) in the continental U.S. M. D. SPIVAK, Ph.D. through experimentation. and Canada to charge with VISA or MasterCard.

30 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Tampa, Florida University of South Florida, Tampa March 22-23 First Announcement

The eight-hundred-and-sixty-fifth meeting of the American Several complex variables, PAUL M. GAUTHIER, Uni­ Mathematical Society will be held at the University of South versity of Montreal. Florida (USF), Tampa, Florida, on Friday, March 22, and Microcomputers and workstations in mathematics: teach­ Saturday, March 23, 1991. All scientific sessions will be held ing and research, LADNOR D. GEISSINGER, WILLIAM in the Chemistry, Engineering and Math/Physics buildings. H. GRAVES, and L. SENECHAL, Institute for Academic Computing, University of North Carolina, Chapel Hill. Invited Addresses Probability on algebraic and topological structures, JOSEPH GLOVER and ARUNAVA MUKHERJEA, Univer­ By invitation of the Southeastern Section Program Com­ sity of South Florida, Tampa. mittee, there will be four invited one-hour addresses. The Fractal and spectral geometry, MICHEL J. LAPIDUS; speakers, their affiliations, and the titles of their talks where and ROBERT S. STRICHARTZ, Cornell University. available are: Operator methods for control problems, SUNG J. LEE JOSEFINA ALVAREZ, New Mexico State University, andY. You, University of South Florida, Tampa. Title to be announced. Nonlinear boundary value problems, R. KENT NAGLE RONALD A. DEVORE, University of South Carolina, and MARY E. PARROTT, University of South Florida, Columbia, Compression from wavelet decompositions. Tampa. MICHEL L. LAPIDUS, University of California, River­ Hypergeometric functions on domains of positivity, jack, side and Yale University, Can one hear the shape ofa drum? polynomials, and applications, DONALD ST. P. RICHARDS. From the Weyl-Berry conjecture to the Riemann hypothesis. Abstracts for consideration for these sessions should DONALD ST. P. RICHARDS, University of Virginia, have been submitted by the December 13, 1990 deadline. Hypergeometric functions ofpositivity and applications. This deadline was previously published in the Calendar of AMS Meetings and Conferences and in the Invited Speakers Special Sessions and Special Sessions section of the Notices.

By invitation of the same committee, there will be twelve Contributed Papers special sessions of selected twenty-minute papers. The topics of these sessions, and the names and affiliations of There will also be sessions for contributed ten-minute the organizers, are as follows: papers. Abstracrs for consideration for these sessions should Harmonic analysis and applications, JOSEFINA AL­ have been submitted by the January 3, 1991 deadline VAREZ. previously published in the Calendar of AMS Meetings and Mathematical issues in biologically motivated comput­ Conferences. Late papers will not be accommodated. ing, W. EDWIN CLARK, JOSEPH L. LIANG, GREGORY L.MCCOLM, JOHN F. PEDERSEN, and W. RICHARD Council STARK, University of South Florida, Tampa. The Council of the Society will meet at 7:00 p.m. on Approximation theory, RONALD A. DEVORE; EDWARD Thursday, March 21, 1991, at the Holiday Inn - Busch B. SAFF and B. SHEKTMAN, University of South Florida, Gardens, 2701 E. Fowler Avenue, Tampa, FL 33612. Tampa. Finite groups and related topics, DAVID A. DRAKE, Registration CHAT YIN Ho, and GEOFFREY R. ROBINSON, University of South Florida, Tampa. The registration desk will be located in the lobby of the Differential geometry and mathematical physics, PAUL Math/Physics building and will be open from 8:00 a.m. to E. EHRLICH and STEPHEN J. SUMMERS, University of 5:00p.m. on Friday, March 22, and from 8:00a.m. to noon Florida. on Saturday, March 23. The registration fees are $30 for

JANUARY 1991, VOLUME 38, NUMBER 1 31 Meetings members of the AMS, $45 for nonmembers, and $10 for participants. The Empty Keg is located in the basement of students or unemployed mathematicians. the University Center which is within short walking distance the meeting rooms. The Empty Keg offers a soup and salad Petition Table bar, pizza, and various sandwich platters. Also open in the University Center from 7:30 a.m until 3:00 p.m. will A petition table will be set up in the registration area. be Sweet Sensations, a pastry and coffee shop. Complete Additional information about petition tables can be found in listings of other restaurants will be available at the meeting a box in the San Francisco meeting announcement in the registration desk. October 1990 issue of Notices. Parking Accommodations Free parking will be available to conference participants in Rooms have been blocked for participants at the following lots 8A and 8B on the campus of USE These lots are in hotels or motels in the area. Because of the large number close proximity to the conference site. of tourists during the winter month, hotel/motel reservations should be made as soon as possible. Participants should Travel and Local Information make their own reservations directly and mention the AMS meeting. The AMS is not responsible for rate changes or Tampa International Airport (TIA) is served by all major the accommodations offered by these hotels. All rates are airlines and located 15 miles from the USF campus. Travel subject to a ten percent sales tax. to the campus can be secured by calling Tampa Tours (telephone 813-621-6667) prior to arrival and give the date, Embassy Suites Hotel (.5 miles from campus) airline. flight number, and estimated time of arrival. The 11310 North 30th Street, Tampa, FL 33612 cost is $9 for one person one-way, $7 each for two to four Telephone: 1-800-EMBASSY persons one-way, and $30 for five to ten people one-way. Deadline for reservations is March 7. Other transportation from TIA to USF can be obtained Single $79 Double $89 through limousine service (Mannone's Limousine Service@ Complimentary full breakfast and cocktail reception, 813-932-1797 or Limo Inc.@ 1-800-282-6817) or taxi. The pool and jacuzzi, free shuttle service up to a three mile cost of a taxi is approximately $24. Most major car rental radius, and free parking. companies have agencies at Tampa International Airport. Directions for participants driving to the meeting are as Holiday Inn - Busch Gardens (1/4 mile from campus) follow: 2701 E. Fowler Avenue, Tampa, FL 33612 If traveling by automobile, participants should take I-75 Telephone: 1-800-99-BUSCH around Tampa and exit west at either the Fletcher Avenue Deadline for reservations is March 1. or the Fowler Avenue exit. The university is approximately three miles west. The campus can also be reached by taking Single $65 Double $65 I-275 through Tampa and exit east on either Fletcher Avenue Shoney's Inn- Tampa (2.5 miles from campus) or Fowler Avenue. The university is approximately one-and­ 8602 Morris Bridge Road, Tampa, FL 33617 one-half miles to the east. Bus service is available around Telephone: 1-800-222-2222 the university by Hartline and bus schedules will be made Deadline for reservations is March 5. available at the meeting registration desk. FROM THE AIRPORT: Participants should take Memo­ One-Four People $43-$45 rial Highway south to Interstate 275 and exit north to Fowler Complimentary coffee and cocktail reception, pool, and Avenue directly to USE free parking. Quality Suites Busch Gardens (1/2 mile from campus) Weather and Local Attractions 3001 University Center Drive, Tampa, FL 33612 The weather in Tampa in March is usually mild. The average Telephone: 1-800-228-5151 maximum temperature is 76.1 °F and the average minimum Deadline date for reservations is March 1. temperature is 57.2°E The average rainfall for March is Suites (One-Four persons) $69 three inches. Complimentary buffet breakfast and cocktail reception, Beaches, golf courses, Busch Gardens, Disney World, pool, and free parking. and many other attractions are located within an hour drive of the Tampa area. Food Service Joseph A. Cima The University Center Food Service will keep the Empty Associate Secretary Keg open from 11 :00 a.m. to 2:00 p.m. for conference Chapel Hill, North Carolina

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

Invited Speakers Invited addresses at Sectional Meetings are selected at AMS Meetings by the Section Program Committee, usually twelve to The individuals listed below have accepted invitations to eighteen months in advance of a meeting. Members wishing address the Society at the times and places indicated. For to nominate candidates for invited addresses should send some meetings, the list of speakers is incomplete. the relevant information to the Associate Secretary for the Section who will forward it to the Section Program Committee. South Bend, IN, March 1991 Leonid G. Makar-Limanov Stephen D. Smith Donald G. Saari Deane Yang Organizers and Topics of Special Sessions Tampa, FL, March 1991 The list below contains all the information about Special Josefina Alvarez Michel L. Lapidus Sessions at meetings of the Society available at the time Ronald A. De Yore Donald St. P. Richards 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. Portland, OR, June 1991 Dinakar Ramakrishnan V. S. Varadarajan March 1991 Meeting in South Bend, Indiana Gunther A. Uhlmann Central Section Associate Secretary: Andy R. Magid Deadline for organizers: Expired Orono, ME, August 1991 Deadline for consideration: Expired H. W. Lenstra Richard M. Schoen Charalambos D. Aliprantis and Carl P. Simon, Mathematical (Progress in Mathematics (Progress in Mathematics economics and dynamical systems Lecture) Lecture) Jonathan L. Alperin and Stephen D. Smith, Simplicial com- plexes associated to finite groups and their representations Steven A. Buechler, Model theory Philadelphia, PA, October 1991 Frank X. Connolly, Geometric topology Michael T. Anderson Majorie Senechal William G. Dwyer and Anthony D. Elmendorf, Algebraic Abbas Bahri Panagiotis E. Souganidis topology Gail R. Letzter, Peter Malcolmson and Frank Okoh, Non­ Fargo, ND, October 1991 commutative ring theory Ian D. Macdonald Henry C. Wente John E. McCarthy, Hilbert spaces of analytic functions Harald Upmeier Sylvia M. Wiegand Mohsen Pourahmadi, Probability and prediction theory

March 1991 Meeting in Tampa, Florida Baltimore, MD, January 1992 Southeastern Section Michael E. Fisher Associate Secretary: Joseph A. Cima (Gibbs Lecture) Deadline for organi=ers: Expired Deadline for consideration: Expired Josefina Alvarez, Harmonic analysis and applications Cambridge, England, June 1992 Ronald A. DeVore, Edward B. Saff and B. Shektman, (Joint meeting with the London Mathematical Society) Approximation theory John M. Ball Benedict H. Gross David A. Drake, Chat Yin Ho and Geoffrey R. Robinson, Lawrence Craig Evans Nigel J. Hitchin Finite groups and related topics

JANUARY 1991, VOLUME 38, NUMBER 1 33 Invited Speakers and Special Sessions

Paul E. Ehrlich and Stephen J. Summers, Differential geom­ James F. Davis, Ronnie Lee and Julius L. Shaneson, Surge1y etry and mathematical physics theory Paul M. Gauthier, Several complex variables Leon Ehrenpreis and Eric L. Grinberg, Geometric analysis Ladnor D. Geissinger, William H. Graves and L. Senechal, Janos Galambos, Extreme value theory Microcomputers and workstations in mathematics: teach­ David R. Hill, Computational experiments for numerical ing and research analysis instruction Joseph Glover and Arunava Mukherjea, Probability on Nicholas Ranges and A. Alexandrou Himonas, Applications algebraic and topological structures of microlocal analysis to partial differential equations Michel L. Lapidus and Robert S. Strichartz, Fractal and Bruce A. Kleiner and Robert B. Kusner, Variational problems spectral geometry in low dimensional geometry Sung J. Lee and Y. You, Operator methods for control Martin Lorenz and Shari A. Prevost, Rings and representa­ 'problems tions R. Kent Nagle and Mary E. Parrott, Nonlinear boundary Doris Schattschneider, Tilings value problems Halil Mete Soner and Panagiotis E. Souganidis, Phase John F. Pedersen, W. Edwin Clark, W. Richard Stark, Joseph transitions and/or front propagation J. Liang and Gregory L. McColm, Mathematical issues Daniel B. Szyld, Numerical linear algebra in biologically motivated computing Donald St. P. Richards, Hypergeometric functions on domains ofpositivity, jack polynomials, and applications October 1991 Meeting in Fargo, North Dakota Central Section Associate Secretary: Andy R. Magid June 1991 Meeting in Portland, Oregon Deadline for organizers: January 25, 1991 Western Section Deadline for consideration: July 11, 1991 Associate Secretary: Lance W. Small Joseph P. Brennan and Sylvia M. Wiegand, Commutative Deadline for organizers: Expired Deadline for consideration: March 5, 1991 algebra Donald G. Babbitt, Meromorphic differential equations ADogan Comez, Ergodic theory M. Paul Latiolais, Combinatorial group theory and low Kendall E. Nygard, Operations research dimensional topology James H. Olsen and Mark Pavicic, Mathematical foundations M. Sergei Prishepionok, Harmonic mappings and their of computer graphics applications Warren E. Shreve, Graph theory Dinakar Ramakrishnan, Cycles and poles of L-functions Vasant A. Ubhaya, Approximation theory Kenneth A. Ross, Fourier analysis Abraham Ungar, Lorentz transformations and spacetime John Sylvester and Gunther A. Uhlmann, Inverse problems geometry and applications Harald Upmeier, Multivariate operator theory in symmetric domains August 1991 Meeting in Orono, Maine Associate Secretary: Joseph A. Cima November 1991 Meeting in Santa Barbara, California Deadline for organizers: Expired Deadline for consideration: May 1, 1991 Western Section (Please note that this deadline has changed) Associate Secretary: Lance W. Small Deadline for organizers: February 7, 1991 Henrik Bresinsky, Commutative Noetherian rings with appli- Deadline for consideration: July 11, 1991 cations in algebraic geometry John C. Mayer, Continuum the01y and dynamical systems Ali E. Ozluk and William M. Snyder, Analytic number the01y January 1992 Meeting in Baltimore, Maryland Stanley Rabinowtiz, Geometric inequalities for polytopes Associate Secretary: Lance W. Small Gerald Schwarz, Symmetry and differential analysis Deadline for organizers: April 8, 1991 Deadline for consideration: September 11, 1991 Chuu-Lian Terng and Karen Uhlenbeck, Variational methods and symmet1y Toma V. Tonev, Function algebras and function spaces March 1992 Meeting in Tuscaloosa, Alabama Southeast Section October 1991 Meeting in Philadelphia, Pennsylvania Associate Secretary: Joseph A. Cima Eastern Section Deadline for organizers: June 13, 1991 Associate Secretary: W. Wistar Comfort Deadline for consideration: To be announced Deadline for organizers: January 10, 1991 Deadline for consideration: July 11, 1991 Michael T. Anderson and Jeff Cheeger, Recent progress in March 1992 Meeting in Springfield, Missouri Ricci curvature and related topics Central Section Associate Secretary: Andy R. Magid Boris A. Datskovsky and Marvin I. Knopp, Modular forms, Deadline for organi:ers: June 26, 1991 arithmetic algebraic geometly Deadline for consideration: To he amwunced

34 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···--··-····-··-····----... -...... -...... ,_,___ ,_,,.•.. --..... _...... ---··-----···----.------Invited Speakers and Special Sessions

June 1992 Meeting in Cambridge, England It should be noted that Special Sessions must be an­ (Joint Meeting with the London Mathematical Society) nounced in Notices in such a timely fashion that any member Associate Secretary: Robert M. Fossum of the Society who so wishes may submit an abstract for Deadline for organizers: September 28, 1991 Deadline for consideration: To be announced consideration for presentation in the Special Session before the deadline for such consideration. This deadline is usually three weeks before the deadline for abstracts for the meeting January 1993 Meeting in San Antonio, Texas Associate Secretary: W. Wistar Comfort in question. Deadline for organizers: April 13, 1992 Special Sessions are very effective at Sectional Meetings Deadline for consideration: To be announced and can usually be accommodated. The processing of proposals for Special Sessions for Sectional Meetings is August 1993 Meeting in Vancouver, handled in essentially the same manner as for Annual British Columbia, Canada and Summer Meetings by the Section Program Committee. Associate Secretary: Lance W. Small Again, no Special Session at a Sectional Meeting may be Deadline for organizers: November 11, 1992 approved so late that its announcement appears past the Deadline for consideration: To be announced deadline after which members can no longer send abstracts for consideration for presentation in that Special Session. January 1994 Meeting in Cincinnati, Ohio The Society reserves the right of first refusal for the Associate Secretary: Joseph A. Cima publication of proceedings of any Special Session. These Deadline for organizers: April 5, 1993 Deadline for consideration: To be announced proceedings appear in the book series Contemporary Math­ ematics. January 1996 Meeting in Orlando, Florida More precise details concerning proposals for and orga­ Associate Secretary: Lance W. Small nizing of Special Sessions may be found in the "Rules for Deadline for organizers: April 12, 1995 Special Sessions" or may be obtained from any Associate Deadline for consideration: To. be announced Secretary.

Information for Organizers Proposals for Special Sessions to the Special Sessions at Annual and Summer Meetings are held under the supervision of the Program Committee for National Associate Secretaries Meetings (PCNM). They are administered by the Associate The programs of Sectional Meetings are arranged by the Secretary in charge of that meeting with staff assistance Associate Secretary for the section in question: from the Meetings and Editorial Departments in the Society Western Section Lance W. Small, Associate Secretary office in Providence. Department of Mathematics According to the "Rules for Special Sessions" of the University of California, San Diego Society, Special Sessions are selected by the PCNM from La Jolla, CA 92093 a list of proposed Special Sessions in essentially the same Electronic mail: [email protected] (Telephone 619-534-3590) manner as Invited Speakers are selected. The number Central Section of Special Sessions at a Summer or Annual Meeting Andy R. Magid, Associate Secretary is limited. The algorithm that determines the number of Department of Mathematics Special Sessions allowed at a given meeting, while simple, University of Oklahoma is not repeated here, but can be found in "Rules for Special 601 Elm PHSC 423 Norman, OK 73019 Sessions" on page 614 in the April 1988 issue of Notices. Electronic mail: [email protected] Each Invited Speaker is invited to generate a Special (Telephone 405-325-6711) Session, either by personally organizing one or by having a Eastern Section Special Session organized by others. Proposals to organize a W. Wistar Comfort, Associate Secretary Special Session are sometimes requested either by the PCNM Department of Mathematics Wesleyan University or by the Associate Secretary. Other proposals to organize a Middletown, CT 06457 Special Session may be submitted to the Associate Secretary Electronic mail: [email protected] in charge of that meeting (who is an ex-officio member of the (Telephone 203-347-9411) committee and whose address may be found below). These Southeastern Section proposals must be in the hands of the PCNM at least nine Joseph A. Cima, Associate Secretary Department of Mathematics months prior to the meeting at which the Special Session is University of North Carolina, Chapel Hill to be held in order that the committee may consider all the Chapel Hill, NC 27599-3902 proposals for Special Sessions simultaneously. Proposals that Electronic mail: [email protected] are sent to the Providence office of the Society, to Notices, (Telephone 919-962-1050) or directed to anyone other than the Associate Secretary will As a general rule, members who anticipate organizing Special Sessions at AMS meetings are advised to seek approval at least nine months prior to the have to be forwarded and may not be received in time to be scheduled date of the meeting. No Special Sessions can be approved too late considered for acceptance. to provide adequate advance notice to members who wish to participate.

JANUARY 1991, VOLUME38, NUMBER 1 35 Invited Speakers and Special Sessions

Proposals for Special Sessions at the June 29-July I, 1992, meeting in by writing to: Electronic Abstracts, American Mathematical Cambridge, England, only should be sent to Professor Fossum at the Department Society, Publications Division, P.O. Box 6248, Providence, of Mathematics, University of Illinois, Urbana, IL 6180, Telephone: 217-244- 1741, Electronic mail: [email protected] RI 02940, USA. When requesting the abstracts package, users should be sure to specify whether they want the plain 1}3X, AM5'-1}3X, or the IDEX package. Information for Speakers A great many of the papers presented in Special Sessions at meetings of the Society are invited papers, but any member of the Society who wishes to do so may submit an abstract Number of Papers Presented for consideration for presentation in a Special Session, Joint Authorship provided it is received in Providence prior to the special Although an individual may present only one ten-minute early deadline announced above and in the announcements of contributed paper at a meeting, any combination of joint the meeting at which the Special Session has been scheduled. authorship may be accepted, provided no individual speaks Contributors should know that there is a limitation in size more than once. An author can speak by invitation in more of a single Special Session, so that it is sometimes true that than one Special Session at the same meeting. all places are filled by invitation. Papers not accepted for An individual may contribute only one abstract by title a Special Session are considered as ten-minute contributed in any one issue of Abstracts, but joint authors are treated papers. as a separate category. Thus, in addition to abstracts from Abstracts of papers submitted for consideration for pre­ two individual authors, one joint abstract by them may also sentation at a Special Session must be received by the be accepted for an issue. Providence office (Editorial Department, American Mathe­ matical Society, P. 0. Box 6248, Providence, RI 02940) by the special deadline for Special Sessions, which is usually Site Selection for Sectional Meetings three weeks earlier than the deadline for contributed papers Sectional Meeting sites are recommended by the Associate for the same meeting. The Council has decreed that no Secretary for the Section and approved by the Committee of paper, whether invited or contributed, may be listed in the Associate Secretaries and Secretary. Recommendations are program of a meeting of the Society unless an abstract of the usually made eighteen to twenty-four months in advance. paper has been received in Providence prior to the deadline. Host departments supply local information, ten to twelve Electronic submission of abstracts is available to those rooms with overhead projectors for contributed paper ses­ who use the 1}3X typesetting system. Requests to obtain sions and special sessions, an auditorium with twin overhead the package of files may be sent electronically via the projectors for invited addresses, and registration clerks. The Internet to [email protected]. Requesting the Society partially reimburses for the rental of facilities and files electronically will likely be the fastest and most equipment, and for staffing the registration desk. Most host convenient way, but users may also obtain the package departments volunteer; to do so, or for more information, on IBM or Macintosh diskettes, available free of charge contact the Associate Secretary for the Section.

held in May 1988to combinatorics and in the papers presented

36 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematics Sessions at the AAAS Annual Meeting Washington, DC, February 14-19, 1991

The annual meeting of the American Association for the Owens, David E. Rowe, and Sanford L. Segal), Monday, Advancement of Science (AAAS), February 14-19, 1991, in February 18, 8:30 a.m. Washington, DC, will feature many outstanding expository • Mathematics and mathematics education: Beyond reports, talks by prominent mathematicians. These talks include organized by RONALD G. DoUGLAS, SUNY at Stony the following symposia (three-hour sessions) and invited Brook. (William Bowen, Ernest L. Boyer, Edward E. address cosponsored by Section A (Mathematics) of the David, Jr., Ralph E. Gomory, Mary Good, Philip A. AAAS and the Society. In addition, there will be special Griffiths, William E. Kirwan, II, Frank Press and Alvin events during the meeting to celebrate the 20th anniversary W. Trivelpiece), Friday, February 15, 8:30a.m. and 2:30 of the Association for Women in Mathematics, including the p.m. symposium, "Mathematics in the public policy arena" listed below. • Calculus reforms: Some examples, organized by THOMAS The AMS helps to support mathematical activities at W. TUCKER, Colgate University. (James Callahan, Ed­ the AAAS meetings by contributing to the sponsorship of ward D. Gaughan, Deborah Hughes Hallet, David A. speakers in mathematical symposia it cosponsors with the Smith, and J. Jerry Uhl, Jr.), Saturday, February 16, 8:30 AAAS. In addition, the Society has a committee to act as a.m. a liaison with AAAS. The AMS believes that strengthening • Frontiers of physical sciences: A mathematics lecture by its ties with AAAS helps to create new opportunities for NEIL J. A. SLOANE, AT&T Bell Laboratories. Friday, mathematicians to interact with scientists from all disciplines. February 15, 8:30 a.m. and 2:30 p.m. The names and affiliations of the organizers follow (speakers' names are given in parentheses): In addition, Section A of the AAAS will sponsor various symposia that will especially interest mathematicians and • Robotics and mathematics, organized by BHUBANESWAR mathematics educators. These symposia include: MISHRA, New York. (Jerrold E. Marsden, Bhubaneswar Mishra, and Jacob T. Schwartz), Tuesday, February 19, • Science and mathematics education in the United States: 2:30p.m. A report from the Longitudinal Study of American Youth • The geometry and topology of DNA, organized by DE­ • Structuring the college environment for success in learn­ WITT L. SUMNERS, Florida State University. (Nicholas ing science and mathematics R. Cozzarelli, DeWitt L. Sumners, and James H. White), • Urban initiatives in precollege science and mathematics: Monday, February 18, 2:30p.m. A model program • Mathematics in the public policy arena, organized by • Minority mathematics and science education: Successful MARY W. GRAY, American University, JILL P. programs at community colleges MESIROV, Thinking Machines Corporation, and MARY BETH RusKAI, University of Lowell. (Ingrid Daubechies, • Implications ofmathematics curriculum reform for science Mary W. Gray, Barbara J. Grosz, Fern Y. Hunt, and Mary education Wheeler), Monday, February 18, 2:30 p.m. • Sophisticated uses of single computers • Voting: Mathematical foundations and political realities, • Global initiatives in high-pelformance computing and organized by ALAN D. TAYLOR, Union College. (Steven networking J. Brams, Samuel Merrill III, and William Zwicker), Monday, February 18, 8:30 a.m. The above symposia represent only a few of the ap­ proximately 150 AAAS program offerings that will broaden • Mathematics in the material sciences, organized by the perspectives of students and professionals alike. Indeed, DAVID S. KINDERLEHRER, Carnegie-Mellon Univer­ AAAS annual meetings showcase American science and sity. (Morton Gurkin, Richard James, Robert V. Kohn, deserve greater mathematical participation. The Section A and Mitchell B. Luskin), Sunday, February 17, 2:30 p.m. Committee seeks organizers and speakers who can present • Mathematics in times of social upheaval, organized by substantial new material in understandable ways. This task SANFORD L. SEGAL, University of Rochester. (Charles is not easy, but the outstanding success of the mathemat­ Edwin Ford, Charles Gillespie, Aleskey Levin, Larry ics symposia at last year's AAAS annual meeting in New

JANUARY 1991, VOLUME 38, NUMBER 1 37 ------··----··-··--······-···········------·AAAS Meeting

Orleans proved that effort and inspiration can accomplish For details about the symposia, see the September 7, wonders. That year's mathematics program demonstrated 1990, issue of Science. Participants are invited to attend that first-rate mathematical researchers can also effectively the Section A Committee meeting, 6:00 p.m. to 8:00 p.m., reach a broad and diverse scientific audience. February 16, 1991, in the Presidential Room of the Shoreham Section A of the AAAS knows that increasing the Hotel. The committee meeting is open to all who wish to representation and participation of mathematicians at AAAS stimulate interest in activities of the mathematical sciences annual meetings offers an important means for deepening within the AAAS. Symposia proposals for future AAAS public awareness and appreciation of the manifold ways meetings should be sent to: Warren Page, Secretary of that mathematics contributes to science and society. The Section A, AAAS, Department of Mathematics, New York Secretary of Section A welcomes suggestions for symposia City Technical College of the City University of New York, topics and individuals who might organize them. 300 Jay Street, Brooklyn, NY 11201.

PROCEEDINGS OF THE hand is still discernible in them. In addition to the historical and research oriented articles, the book contains other material that provides some colorful background on Gibbs and his world. Focusing on Gibbs and the teaching of science, the final article is a commentary, embellished GIBBS with personal reminiscences, on what to do and what to avoid in S Y MP 0 S I U M the education of prospective scientists. In the appendix, the editors have included a transcription of the Yale Physical Club (which YALE UNIVERSITY, MAY 15-17,1989 continues to this day as the Physics Club) for the meeting following D. G. Caldi and G. D. Mostow, Editors the death of Gibbs in 1903. The minutes provide a flavor of the esteem in which Gibbs was held by his colleagues and a vivid This volume, a joint publication with the American Insti­ glimpse of the Yale Physics Department at the time. The appendix tute of Physics, contains the proceedings of a symposium held May also has a section presenting a number of examples of various 15-17, 1989, at Yale University. The symposium was organized Gibbsian surfaces generated by computer graphics, for the graphi­ to honor the memory of Josiah Willard Gibbs, one of the giants of cal presentation of Gibbs's concepts dates back to Gibbs himself. theoretical physics, on the 150th anniversary of his birth. The Readers will appreciate the variety in this well-rounded range of the topics covered in the symposium reflects the extraor­ volume, and it would make an excellent addition to any library. It dinary versatility of Gibbs's ideas. Despite their widely separated is a fitting tribute to Josiah Williard Gibbs, a towering figure in expertises, the symposium speakers made an effort to present their American science and mathematics. lectures in a way that would be understandable to all the partici­ pants. The result was a genuine exchange of ideas across 1980 Mathematics Subject Classification: 01A55, 11009, 11E45, disciplines that is captured in this volume. 11F66, 11F67,11F70, 11G05, 11G40, 11R39, 22E50, 22E55, Three of the articles in the book provide perspectives on 60G15, 76N15, 80-02, 80-03 (01A55), 80A10, 80A50, 82A15, 82A25, 82A30, 82A97, 86A15, 90-02, 90-03 (01A99) Gibbs, the man, and on the place his work occupies in the history ISBN 0-8218-0157-0 (hardcover), September 1990 of science. There are also contributions from leading scientists who Individual member $41, List price $65, assess the state of the art in those areas of physics and mathematics Institutional member $52 in which Gibbs worked, primarily those having to do with statistical To order, please specify GIBBS/NA mechanics and thermodynamics. To underscore the great generality of Gibbs's methods and the broad applicability his work, contribu­ All prices subject to change. Free shipment by surface; for air delivery, tions were also solicited from distinguished investigators in a please add $6.50 per title. Prepayment required. Order from number of different fields, such as geophysics, number theory, American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-321-4AMS (321- general relativity, and economics. Some of these fields are far 4267) in the continental U.S. and Canada to charge with VISA or removed from those to which Gibbs contributed directly, but Gibbs's MasterCard.

38 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Summer Research Conferences in the Mathematical Sciences University of Washington, Seattle, June 22 to August 2, 1991

The 1991 Joint Summer Research Conferences in the Math­ Please type or print the following: ematical Sciences will be held at the University of Wash­ 1. Title and dates of conference desired ington, Seattle, from June 22 to August 2. It is anticipated 2. Full name that the series of conferences will be supported by grants from the National Science Foundation and other agencies. 3. Mailing address 4. Telephone number and area code for office, home and There will be eight conferences in eight different areas electronic-mail address of mathematics. The topics and organizers for the confer­ ences were selected by the AMS, Institute of Mathematical 5. Member of AMS, IMS, or SIAM? If AMS, please give Statistics (IMS), and the Society for Industrial and Applied member code Mathematics (SIAM) Committee on Joint Summer Research 6. Your scientific background relevant to the topic of the Conferences in the Mathematical Sciences. The selections conference were based on suggestions made by the members of the 7. Financial assistance requested; please estimate cost of committee and individuals submitting proposals. The com­ travel mittee considered it important that the conferences represent 8. Indicate if support is not required and if interested in diverse areas of mathematical activity, with emphasis on attending even if support is not offered. areas currently especially active, and paid careful attention The deadline for receipt of applications is March to subjects in which there is important interdisciplinary 1, 1991. Requests to attend will be forwarded to the activity at present. Organizing Committee for each conference for consideration The conferences emulate the scientific structure of those after the deadline of March 1. All applicants will receive held throughout the year at Oberwolfach. These conferences a formal invitation and notification of financial assistance are intended to complement the Society's program of annual from the AMS. Requests received past the deadline will be Summer Institutes and Summer Seminars, which have a returned. Funds available for these conferences are limited larger attendance and are substantially broader in scope. The and individuals who can obtain support from other sources conferences are research conferences and are not intended should do so. Women and members of minority groups are to provide an entree to a field in which a participant has not encouraged to apply and participate in these conferences. already worked. Any questions concerning the scientific portion of the It is expected that funding will be available for a limited conference should be directed to the chair or any member number of participants in each conference. Others, in addition of the Organizing Committee. to those funded, will be welcome, within the limitations of the facilities of the campus. In the spring a brochure of The Joint Summer Research Conferences in the Mathe­ information will be mailed to all who are requesting to attend matical Sciences are under the direction of the AMS-IMS­ the conferences. The brochure will include information on SIAM Committee on Joint Summer Research Conferences room and board rates, the residence and dining hall facilities, in the Mathematical Sciences. The following committee travel, local information, and a Residence Housing Form to members chose the topics for the 1991 conferences: John A. use to request on-campus accommodations. Information on Bums, Fan R. K. Chung, Leonard Evens, Martin Golubitsky, off-campus housing will also be included in the brochure. Anthony W. Knapp, Ingram Olkin, Emanuel Parzen, Stewart Participants will be responsible for making their own housing B. Priddy, Stephen Simpson and Gregg J. Zuckerman. and travel arrangements. Each participant will be required Descriptions of the subject matter of each of the 1991 to pay nominal registration and social fees. conferences appeared in the November issue of Notices, Those interested in attending one of the conferences pages 1278-1279; they were accompanied by lists of should send the following information to the Summer members of the respective Organizing Committees. Research Conference Coordinator, Meetings Department, American Mathematical Society, Post Office Box 6887, Prov­ N.B. Lectures begin on Sunday morning and run idence, RI 02940 or by E-Mail: [email protected] through Thursday. on the Internet.

JANUARY 1991, VOLUME 38, NUMBER 1 39 Joint Summer Research Conferences

Saturday, June 22 to Friday, June 28 Saturday, July 6 to Friday, July 12 Stochastic modeling and statistical inference for Biojluiddynamics selected problems in biology A.Y. CHEER (University of California, Davis), Chair CHARLES SMITH (North Carolina State University), C.P. VAN DAM (University of California, Davis), Co-Chair, Co-Chair GRACE L. YANG (University of Maryland, College Park), Co-Chair Saturday, July 13 to Friday, July 19 No conference scheduled Saturday, June 22 to Friday, July 5 Saturday, July 20 to Friday, August 2 Graph minors Motives NEIL ROBERTSON (Ohio State University), Co-Chair STEVEN KLEIMAN (Massachusetts Institute of P.D. SEYMOUR (Bell Communications Research), Technology), Co-Chair Co-Chair KARl VILONEN (Brandeis University), Co-Chair

Saturday, June 29 to Friday, July 5 Saturday, July 20 to Friday, July 26 Theory and applications of multivariate time series Mathematical aspects of classical field theory analysis MARK J. GOTAY (United States Naval Academy), ROBERT H. SHUMWAY (University of California, Davis), Co-Chair Co-Chair JERROLD E. MARSDEN (University of California, RUEY S. TSAY (University of Chicago), Co-Chair Berkeley), Co-Chair VINCENT E. MONCRIEF (Yale University), Co-Chair

Saturday, July 6 to Friday, July 12 Saturday, July 27 to Friday, August 2 Stochastic inequalities Systems of coupled oscillators MOSHE SHAKED (University of Arizona), Co-Chair D.G. ARONSON (University of Minnesota, Minneapolis) Y.L. TONG (Georgia Institute of Technology), Co-Chair Chair

Positive Definite Unimodular Lattices with Trivial Automorphism Groups Etsuko Bannai (Memoirs of the AMS, Number 429) In this book, the author proves that there exists a lattice with trivial automorphism group in every genus of positive definite unimodular Z-lattices of rank m (with m ~ 43 for the odd unimodular case and m ~ 144 for the even unimodular case). Siegel's mass formulas for lattices (for both orthogonal and hermitian cases) are used in the proof. In addition, the author shows that, for those positive definite unimodular Z-lattices in the given genus and of rank m, the ratio of the mass of classes with nontrivial automorphisms to the mass of all classes approaches 0 very rapidly as m increases. The book is intended for researchers and advanced graduate students in the areas of number theory and quadratic forms.

1980 Mathematics Subject Classification: 10 All prices subject to change. Free shipment by surface; for air ISBN 0-82 I 8-2491-0, LC 90-31824, ISSN 0065-9266 delivery, please add $6.50 per title. Prepayment required, 70 pages (softcover), May 1990 Order from American Mathematical Society, P.O. Box 1571, Individual member $10, List price $16. Annex Station, Providence, RI 02901-1571, or call toll free Institutional member $13 800-321-4AMS (321-4267) in the continental U.S. and Canada To order, please specify MEM0/429NA to charge with VISA or MasterCard.

40 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1991 Summer Research Institute Algebraic Groups and Their Generalizations Pennsylvania State University, University Park, July 8-28

The thirty-ninth Summer Research Institute sponsored by of functions on a Lie group. This has inspired the devel­ the American Mathematical Society will be devoted to Al­ opment of the theory of quantum groups particularly by gebraic groups and their generalizations and will take place Drinfel' d. Lusztig has formulated arithmetic quantizations at the Pennsylvania State University, University Park, Penn­ of the Kostant Z-forms of semi-simple Lie algebras which sylvania. Members of the Organizing Committee are: IGOR allow the formulation of statements concerning the represen­ FRANKEL, Yale University; ERIC FRIEDLANDER, North­ tation theory of semi-simple groups which have the theory western University; WILLIAM HABOUSH (chair), University over fields of positive characteristic as a specialization. of Illinois Urbana-Champaign; JENS JANTZEN, University Through these developments a major reformulation of of Oregon, Eugene; and BRIAN PARSHALL, University of the vocabulary of algebraic group theory has taken place. Virginia. Though conferences on various aspects of the theory of It is anticipated that the institute will be partially algebraic groups have taken place, no conference has focused supported by a grant from the National Science Foundation. on the general theory for some time. The summer institute Proceedings of the institute will be published in the AMS will attempt to present this new knowledge as a corpus series Proceedings of Symposia in Pure Mathematics. stressing overall structure, both common elements and This topic was selected by the 1989 AMS Committee on special features that mark off one area from another. Thus Summer Institutes and Special Symposia whose members at certain topics, such as Kazhdan-Lusztig theory and the idea the time were: STEVEN L. KLEIMAN (chair), HAYNES R. of induced representation as well as the higher derived MILLER, RAGHAVAN NARASIMHAN, BRIAN PARSHALL, functions of induction viewed as expressions of the structure and THOMAS C. SPENCER. of homogeneous spaces, are common threads while other While several recent conferences have been devoted to topics such as vertex operators and related matters are the theory of algebraic groups, it has been some time since based on unique aspects of special situations. Both types of there has been an extended conference devoted to the core ideas should be studied and juxtaposed. Similarly, certain subject itself. Meanwhile, the subject has undergone a most quantization theories couched in analytic terms can be remarkable expansion and transformation. compared to the Lusztig quantization. It is hoped that these juxtapositions can be organized to result in fertile exchanges The first of these developments is the one that be­ of ideas. gan with observations by Jantzen and Deodhar that certain There are plans for major lecture series on quantum composition factors in Verma modules occurred with mul­ groups, Kac-Moody Lie algebras and groups, Heeke alge­ tiplicity. This led to the work of Kazhdan and Lusztig bras, and on the representation theories associated to these relating these multiplicities to the representative theory of objects. In addition, a series of talks will be devoted to Weyl groups and Heeke algebras and the intersection ho­ induction in its various guises and to the geometry of ho­ mology of generalized Schubert cells, work culminating mogeneous spaces and their compactifications, especially as in the Kazhdan-Lusztig conjectures. The solutions to these they relate to representation theory. Directly related topics conjectures by Bernstein and Bielenson and by Kashiwara such as transformation spaces and quotients might also be have made algebraic analysis and the theory of the derived discussed particularly in so far as they can be applied to category part of the substance of representation theory which or viewed as applications of the main topics. For example, has led to a new way of understanding the subject as a transformation spaces can be related to orbit methods and to whole. questions concerning the intersection homology of homoge­ The second major development begins with the obser­ neous spaces which in tum might bear on the combinatoric vation by Kac and Moody that relaxation of the positivity aspects of representation theory. conditions on the Cartan matrix leads to a new class of A tentative list of the topics to be addressed follows. infinite dimensional simple Lie algebras and the subsequent Please note, however, that the program is subject to change. exploitation of this fact by Kac, Lepowsky, and others to develop a representation theory and a group theory for these Lie algebras. This has led to the development of a mean­ ingful infinite dimensional group theory by Kac, Peterson, Week One: Matthieu, and others. General theory of quantum groups and algebras, Kac­ The third major change begins with Woronowicz's dis­ Moody Lie algebras and root systems, basic Kac-Moody covery of a "non-commutative" deformation of the algebra group theory, finite dimensional representations in positive

JANUARY 1991, VOLUME 38, NUMBER 1 41 .._...... _.·-··-··---·--··-·····---··---···--·----- Summer Research Institute characteristic, infinitesimal structures, flag varieties, Bruhat available. All facilities will be accessible to the handicapped. decompostion and generalized Schubert cells in the finite and Information on housing, dining, travel, and the local infinite dimensional cases, standard bases for representations, area will be sent to invited participants in the spring. Each and loop groups. participant will pay a registration fee and a social fee to cover the costs of social events scheduled during the Week Two: institute. Theory of quantum groups and algebras continued, Those interested in receiving an invitation to participate Kac-Moody groups, the representation theory of quantum in the institute should send the following information to groups and of Kac-Moody groups and algebras, character Summer Institute Conference Coordinator, American Math­ formulae, Heeke algebras and Weyl groups, triangulated ematical Society, Post Office Box 6887, Providence, RI categories and derived categories in representation theory, 02940, prior to April1, 1991 or through electronic mail to D-modules induced representations, the derived functors [email protected]. of induction, homogeneous spaces, transformation spaces, almost homogeneous spaces, infinitesimal analogues, loop Please type or print the following: groups and affine Kac-Moody groups, and vertex operators. 1. Full name; 2. Mailing address; Week Three: 3. Telephone number and area code for office and home; 4. Which week or weeks you wish to attend; Arithmetic quantizations (the Lusztig quantization), quan­ 5. Your scientific background relevant to the institute topic; tum groups and representation theory in positive characteris­ 6. Financial assistance requested; tic, Kazhdan-Lusztig polynomials and their generalizations, 7. Indicate if support is not required, and if interested in the intersection homology of Schubert cells and its relation attending even if support is not offered. to Kazhdan-Lusztig theory, infinite dimensional analogues, D-modules and orbit methods, D-modules in positive char­ Requests for invitations will be forwarded to the Orga­ acteristic and other models of infinite dimensional theory nizing Committee for consideration up to the deadline of and quantum group theory. April 1, and applicants selected will receive formal invi­ Accommodations will be available in the campus res­ tations and notification of financial assistance beginning in idence halls for participants; cafeteria style meals will be mid-May.

CRYPTOLOGY AND COMPUTATIONAL NUMBER THEORY Carl Pomerance, Editor Proceedings of Symposia in Applied Mathematics, Volume 42

In the past dozen or so years, cryptology and computational number theory have become increasingly intertwined. Because the primary cryptologic application of number theory is the apparent intractability of certain computations, these two fields could part in the future and again go their separate ways. But for now, their union is continuing to bring ferment and rapid change in both subjects. This book contains the proceedings of an AMS Short Course in Cryptology and Computational Number Theory, held in August 1989 during the Joint Mathematics Meetings in Boulder, Colorado. These eight papers by six of the top experts in the field will provide readers with a thorough introduction to some of the principle advances in cryptology and computational' number theory over the past fifteen years. In addition to an extensive introductory article, the book contains articles on primality testing, discrete logarithms, integer factoring, knapsack cryptosystems, pseudo-random number generators, the theoretical underpinnings of cryptology, and other number theory-based cryptosystems. Requiring only background in elementary number theory, this book is aimed at non-experts, including graduate students and advanced undergraduates in mathematics and computer science.

All prices subject to change. Free shipment by surface; for 1980 Mathematics Subject Classification: 11, 94 air delivery, please add $6.50 per title. Prepayment ISBN 0-8218-0155-4, LC 90-1248, required. Order from American Mathematical Society, ISSN 0160-7634 P.O. Box 1571, Annex Station, Providence, RJ 171 pages (hardcover), December 1990 02901-1571, or call toll free 800-321-4AMS (321- Individual member $34, List price $57, 4267) in the continental U.S. and Canada to charge with Institutional member $46 VISA or MasterCard. To order, please specify PSAPM/42NA

42 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1991. IMACS Symposium on Parallel and Mathematical Sciences Distributed Computing in Engineering Sys­ tems, Athens, Greece. (Jul./Aug. 1990, p. 741) Meetings and Conferences Spring 1991. IMACS International Sympo­ sium on Iterative Methods in Linear Alge­ bra, Brussels Free Univ., Brussels, Belgium. (Mar. 1990, p. 334) * 1991-1992. Mittag-Leffler Institute Aca­ demic Program for 1991-1992: Combina­ torics, Djursholm, Sweden. PROGRAM: Emphasis will mainly be on algebraic and geometric aspects. CALL FOR PAPERS: Application dead­ line for postdoctoral fellowships: April 1, 1991. THIS SECTION contains announcements of meetings and conferences of interest to some INFORMATION: A. Bjorner, Dept. of Math­ segment of the mathematical public, including ad hoc, local, or regional meetings, and ematics, KTH, S-100 44 Stockholm, Swe­ meetings or symposia devoted to specialized topics, as well as announcements of regularly den, or D. Laksov, Institut Mittag-Leffler, scheduled meetings of national or international mathematical organizations. (Information on Auraviigen 17, S-182 62 Djursholm, Swe­ meetings of the Society, and on meetings sponsored by the Society, will be found inside the den. front cover.) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, and specifies the place, date, subject (when applicable), and the speakers; a second full announcement will be published only if there are changes or necessary additional information. Once an January 1991 announcement has appeared, the event will be briefly noted in each issue until it has been held and a reference will be given in parentheses to the month, year, and page of the issue in 14--15. AMS Short Course on "Probabilistic which the complete information appeared. Asterisks (*) mark those announcements containing Combinatorics and its Applications", San new or revised information. Francisco, CA. IN GENERAL, announcements of meetings and conferences held in North America carry only date, title of meeting, place of meeting, names of speakers (or sometimes a general INFORMATION: D. Plante, AMS, P.O. Box statement on the program), deadlines for abstracts or contributed papers, and source of 6248, Providence, RI 02940. further information. Meetings held outside the North American area may carry more detailed information. In any case, if there is any application deadline with respect to participation in 16-19. Joint Mathematics Meetings, San the meeting, this fact should be noted. All communications on meetings and conferences Francisco, CA. (including the annual meetings in the mathematical sciences should be sent to the Editor of Notices, care of the American of the AMS, AWM, MAA, and NAM) Mathematical Society in Providence. in this section are listed on the inside front cover of each issue. In P.O. Box DEADLINES for entries INFORMATION: H. Daly, AMS, order to allow participants to arrange their travel plans, organizers of meetings are urged to 6887, Providence, RI 02940. submit information for these listings early enough to allow them to appear in more than one to the meeting in question. To achieve this, listings should be received Teaching issue of Notices prior 20. Informal Workshop on the in Providence SIX MONTHS prior to the scheduled date of the meeting. of Calculus, San Francisco, CA. (Nov. 1990, EFFECTIVE with the 1990 volume of Notices, the complete list of Mathematical Sciences p. 1283) Meetings and Conferences will be published only in the September issue. In all other issues, 20--26. Spektraltheorie Singuliirer Ge­ only meetings and conferences for the twelve-month period following the month of that issue wohnlicher Differentialoperatoren, Oberwol­ will appear. As new information is received for meetings and conferences that will occur later fach, Federal Republic of Germany. (Apr. than the twelve-month period, it will be announced at the end of the listing in the next possible repeated until the date of the meeting or conference falls 1990, p. 499) issue. That information will not be within the twelve-month period. 21-25. IMA Workshop on Statistical Ther­ modynamics and Differential Geometry of Microstructured Material, University of Min­ nesota, Minneapolis, MN. (Nov. 1990, p. 1283) (Please note date change from Sep. 1990, 10--16. Affine Differentialgeometrie, Ober­ p. 934) wolfach, Federal Republic of Germany. (Apr. 27-February 2. Harmonische Analyse und 1990, p. 499) Darstellungstheorie Topologischer * 8-15. Discontinuous Solutions of the Navier­ Gruppen, Oberwolfach, Federal Republic of Stokes Equations for Compressible Flow, 11-15. The Twenty-Second Southeastern Germany. (Apr. 1990, p. 499) Mathematical Sciences Institute, Cornell Uni­ International Conference on Combinatorics, Graph Theory and Computing, Louisiana 28-30. Second ACM-SIAM Symposium versity, Ithaca, NY. State University, Baton Rouge, LA. (Oct. on Discrete Algorithms, San Francisco, CA. PROGRAM: A series of three lectures will 1990, p. 1136) (Jul./Aug. 1990, p. 741) David Hoff be given during this week by 17-23. Experimentelle, Insbesondere Com­ (Indiana Univ.) putergraphische Methoden in der Math­ INFORMATION: E.S. Titi, Mathematical ematik, Oberwolfach, Federal Republic of February 1991 Sciences Institute, Cornell University, 409 Germany. (Jul./Aug. 1990, p. 742) College Ave., Ithaca, NY 14850; 607-255- 17-23. Krein Spaces and Applications to 3-9. Konstruktive Methoden in der Kom­ 8005. plexen Analysis, Oberwolfach, Federal Re­ Differential Operators, Oberwolfach, Federal public of Germany. (Apr. 1990, p. 499) 10-16. Endlichdimensionale Lie-Algebren, Republic of Germany. (Nov. 1990, p. 1283) * 3-9. Winter School on Infinite Dimen­ Oberwolfach, Federal Republic of Germany. 18-23. Ninth International Seminar on sional Differential Geometry, Wien, Austria. (Apr. 1990, p. 499) Model Optimization in Exploration Geo-

JANUARY 1991, VOLUME 38, NUMBER 1 43 Meetings and Conferences

physics, with a Workshop on Geophysical cussed, including recent work of many 15-16. Central Section, Indiana University, Data Inversion in Archeological Site Inves­ authors on smoothness of horocyclic foli­ South Bend, IN. tigation, Berlin, Free University of Berlin, ations, marked length spectrum, entropy, INFORMATION: W. Drady, American Math· Mathematical Geophysics Group and Archeo­ and related topics. The titles of these h!c­ ematical Society, P.O. Box 6887, Provi­ logical Institute. (Oct. 1990, p. 1136) tures will be: I. Introduction and sketch of dence, RI 02940. 24-March 2. Medical Statistics: Statistical main results; 2. Geometry on the sphere at Models for Longitudinal Data, Oberwolfach, infinity; 3. Relationship between the fun­ * 16-23. Sixth Conference in Geometric Federal Republic of Germany. (Apr. 1990, damental group and geometry; 4. Rigidity Rigidity and Hyperbolic Dynamics, Penn p. 500) theorems I; 5. Rigidity theorems II and State Univ., State College, PA. 25-March I. IEEEComputerSocietyCOM­ open problems. INFORMATION: L. Conlon, Chairman, PROGRAM: The conference explores the PCON Spring '91, San Francisco, CA. (Jan. synthesis of several branches of dynam­ 1990, p. 62) Roever Lectures Committee, Washing­ ton University, Campus Box 1146, One ics (smooth dynamical systems, ergodic Brookings Dr., St. Louis, MO 63130-4899. theory, symplectic dynamics) with other mathematical disciplines (Lie groups and March 1991 * 13. The Emergence of Abstract Harmonic symmetric spaces, differential geometry, Analysis: 1930-1950, lnstitut Henri Poincare, group representations, number theory), March 1991. Computational Number The­ Paris. centered around the phenomenon of rigid­ ory, Rutgers University, New Brunswick, NJ. ity. (Oct. 1990, p. 1136) INVITED SPEAKERS: J.-P. Kahane (Paris ORGANIZERS: A. Katok, R. Spatzier, R. XI), W.T. Komer (Cambridge), G.W. 3-9. PartielleDifferentialgleichungen, Ober­ Zimmer. Mackey (Harvard), P. Malliavin (Paris wolfach, Federal Republic of Germany. (Apr. INFORl\iATION: A. Katok, Dept. of Math., VI), J.-P. Pier (Luxembourg). 1990, p. 500) Penn State Univ., University Park, PA 4-15. Workshop on Mathematical Physics INFORMATION: Association Henri Poin­ 16802; 814-865-2266; email: rigidity@ care pour l'Histoire et la Philosophie des and Geometry, Trieste, Italy. (Sep. 1990, math.psu.edu. p. 934) Math. et de la Physique Modemes, In­ stitut Henri-Poincare, 11, rue Pierre-et­ 17-23. Elementare und Analytische 5-7. Association for Computing Machinery Marie-Curie, F-7 5005 Paris (France) or Zahlentheorie, Oberwolfach, Federal Re­ 1991 Computer Science Conference, San Seminaire de Math., Centre Universitaire public of Germany. (Apr. 1990, p. 500) Antonio Convention Center, San Antonio, de Luxembourg, 162A, Avenue de la TX. (May/Jun. 1990, p. 611) 11-24. Sixth International Conference Faiencerle, L-1511 Luxembourg (Luxem­ on Geometry, University of Haifa, Israel. 7-8. Twenty-second ACM SIGCSE Tech­ bourg). (May/Jun. 1990, p. 612) nical Symposium on Education in the Com­ puting Sciences, San Antonio, TX. (May/Jun. 13-15. IMACS Workshop on Decision 21-28. Mathematical Aspects of Human 1990, p.612) Support Systems and Qualitative Reason­ Diseases, Erice (Trapani), Sicily, Italy. (Dec. 1990, p. 1453) 7-10. International Conference on Dif­ ing, LAAS-Toulouse, France. (May/Jun. 1990, ferential Equations, Cadi Ayyad University, p. 612) 22-23. Southeastern Section, University of Marrakech, Morocco. (May/Jun. 1990, p.612) 13-16. Twenty-Second Annual Iranian South Florida, Tampa, FL. 10-14. International Conference on In­ Mathematics Conference, Ferdowsi Univer­ INFORMATION: W. Drady, American Math· verse Problems: Computational Algorithms, sity of Mashhad, Iran. (Sep. 1990, p. 934) ematical Society, P.O. Box 6887, Provi­ Texas A&M University, College Station, TX. 14-16. Sixth S.E.A. Meeting, Southeastern dence, RI 02940. (Nov. 1990, p. 1284) Approximation Theorists Annual Meeting, 10-16. Mathematische Stochastik, Ober­ Memphis State Univ., Memphis, TN. (Sep. 22-24. Fifth SIAM Conference on Par­ allel Processing for Scientific Computing, wolfach, Federal Republic of Germany. (Apr. 1990, p. 934) 1990, p. 500) * 14-16. Bundles in Complex Differential Houston, TX. (Mar. 1990, p. 334) 11-15. NSF -CBMS Regional Research Con­ Geometry, Idaho State Univ., Pocatello, ID. 24-29. Mathematical Approaches to DNA II (The Genome: DNA to Protein Structure), ference on Nonlinear Dispersive Wave Sys­ PROGRAM: The objective of the confer­ Santa Fe, NM. (Dec. 1990, p. 1453) tems, University of Central Florida, Orlando, ence is to discuss a number of current FL. (Jul/Aug. 1990, p. 742) research topics in complex differential 24-30. Gewohnliche Differentialgleichun­ gen, Oberwolfach, Federal Republic of Ger­ 11-15. IMA Workshop on Free Boundaries geometry. in Viscous Flows, University of Minnesota, CONFERENCE TOPICS: Einstein-Hermi­ many. (Apr. 1990, p. 500) Minneapolis, MN. (Sep. 1990, p. 934) tian connections, the Yang-Mills Higgs 25-27. Fifth SIAM Conference on Par­ allel Processing for Scientific Computing, 11-15. William H. Roever Lectures in functional, harmonic metrics and flat bun­ * Houston, TX. (Jul./Aug. 1990, p. 742) Geometry, Washington Univ., St. Louis, MO. dles, invariant connections, the gauge group action on connections, Bianchi-type 25-28. International Conference on Math­ PROGRAM: P. Eberlein (Univ. of North identities for hermitian metrics, and the ematical Linguistics - ICML '91, Barce­ Carolina) will give the seventh series of use of twistor bundle in the study of lona, Spain. (Jul./Aug. 1990, p. 742) the W. H. Roever Lectures in Geometry. minimal surfaces. * 25-29. Forty-Third British Mathematical His topic will be The structure of non­ INFORMATION: R.J. Fisher, H.T. Laquer, Colloquium, Univ. of Bath, Claverton Down, positivity curved manifolds. There will and D. Stowe, Dept. of Math., Idaho State Bath, U.K. be five lectures, one each day, beginning Univ., Pocatello, ID 83209-8085; 208-236- with an overall introduction to the topic 3350; email: [email protected]. INVITED SPEAKERS: S.l. Adian (Steklov), that will be appropriate for a general H. Brezis (Paris), A.M. Odlyzko (AT&T mathematical audience. In the last two 14-20. Probability and Bayesian Statistics Bell Labs), G.R. Brightwell (LSE), C.J.B. lectures, the interplay between negative in Medicine and Biology, Erice (Trapani), Brookes (Cambridge), A.P. Carbery (Sus­ curvature and ergodic theory will be dis- Sicily, Italy. (Dec. 1990, p. 1452) sex), C.M. Goldie (QMW), F.C. Kirwan

44 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------Meetings and Conferences

(Oxford), W. Ledermann (Sussex), A.J. I 0-12. Fourth International Conference 2-4. International Conference on Poly­ Macintyre (Oxford), U. Martin (RHBNC), on Rewriting Techniques and Applications nomials with concentration at low degrees: M.J. Micallef (Warwick), R.W.K. Odoni (RTA-91), Como, Italy. (Jul./Aug. 1990, p. 743) From Analysis and Number Theory to Com­ (Glasgow), J.N. Ray (Manchester), R.S. 11-13. Twenty-Fifth Annual Spring Topol­ puter Science and Symbolic Computation, Ward (Durham). ogy Conference, California State University, Paris, France. (Nov. 1990, p. 1285) INFORMATION: G.R. Burton, School of Sacramento, CA. (Oct. 1990, p. 1137) 5-11. Darstellungstheorie Endlich-Di­ Math. Sci., Univ. of Bath, Claverton 11-16. Assessment in Mathematics Educa­ mensionaler Algebren, Oberwolfach, Fed­ Down, Bath BA2 7AY; tel: 0225 826218; tion and Its Effects, Calonge (Costa Brava), eral Republic of Germany. (Jul./Aug. 1990, email: [email protected]. Spain. (Sep. 1990, p. 935) p. 743) * 25-April 12. Linear and Nonlinear Disper­ 14-20. Brauer Groups and Representa­ 6-8. Fifth SIAM International Sympo­ sive Waves, Mathematical Sciences Institute, tion Theory of Finite Groups, Oberwolfach, sium on Domain Decomposition Methods Cornell University, Ithaca, NY. Federal Republic of Germany. (Apr. 1990, for Partial Differential Equations, Norfolk, p. 500) VA. (Jul./Aug. 1990, p. 743) PROGRAM: A series of nine lectures will 7-10. IMACS Symposium on Modelling be given by J.-C. Saut (Universire Paris­ 15-19. IMA Workshop on Variational Prob­ and Simulation of Control Systems, Casa­ Sud). lems, University of Minnesota, Minneapolis, blanca, Morocco. (Mar. 1990, p. 334) INFORMATION: E.S. Titi, Mathematical MN. (Sep. 1990, p. 935) Sciences Institute, Cornell Univ., 409 Col­ 18-20. Determinantal Ideals and Repre­ 7-14. Singapore Number Theory Work­ lege Ave., Ithaca, NY 14850; 607-255- sentation Theory, University of Arkansas, shop, National Univ. of Singapore, Kent 8005. Fayetteville, Arkansas. (Sep. 1990, p. 935) Ridge, Singapore. (Jul./Aug. 1990, p. 743) 20-21. Wabash Extramural Modern Anal­ 9-11. A Conference on History, Geometry, 29-30. 1991 Association for Symbolic Logic ysis Miniconference, Indiana University-Pur­ and Pedagogy in honor of the 80th birth­ Spring Meeting (in conjunction with a meet­ due University, Indianapolis, IN. (Dec. 1990, day of Howard Eves, University of Central ing of the American Philosophical Asso­ p. 1453) Florida, Orlando, FL. (Nov. 1990, p. 1285) ciation), San Francisco, CA. (Dec. 1990, 21-24. SUPER!: Supercomputing by Uni­ p. 1453) 12-18. Nichtlineare Evolutionsgleichungen, versity People for Education and Research, Oberwolfach, Federal Republic of Germany. 31-April 6. Arbeitsgemeinschaft mit Ak­ Park City, UT. (Nov. 1990, p. 1284) (Apr. 1990, p. 501) tuellum Thema, Oberwolfach, Federal Re­ 21-27. Numerical Linear Algebra, Oberwol­ public of Germany. (Apr. 1990, p. 500) 13-17. Conference in Harmonic Analysis fach, Federal Republic of Germany. (Jul./Aug. in Honor of E.M. Stein, Princeton University, 1990, p. 743) Princeton, NJ. (Mar. 1990, p. 334) April1991 21-May 4. NATO ASI Finite and Infinite 13-18. IMA Workshop on Degenerate Dif­ Combinatorics in Sets and Logic, Banff, fusions, University of Minnesota, Minneapo­ 1-4. Eighth International Conference on Canada. (Dec. 1990, p. 1453) lis, MN. (Sep. 1990, p. 935) Mathematical and Computer Modeling, Uni­ 23-26. Mathematical and Numerical As­ 15-17. Third IEEE Conference on Com­ versity of Maryland, College Park, MD. (Oct. pects of Wave Propagation Phenomena, puter Workstations: Accomplishments and 1990, p. 1137) Strasbourg, France. (Jul./Aug. 1990, p. 743) Challenges, Falmouth (Cape Cod), MA. (Sep. * 1-7. JAMI Workshop and Conference on 26-28. Similarity Solutions of Differential 1990, p. 936) Algebraic and Complex Geometry, Johns Equations, University of Pittsburgh, PA. (Oct. 15-18. International Conference on Theory Hopkins Univ., Baltimore, MD. 1990, p. 1137) and Applications of Differential Equations, PROGRAM: The conference will consist 26-28. First Eugene Lukacs Symposium, University of Texas-Pan American, Edinburg, of invited lectures on April 4-7 and will Bowling Green State University, Bowling TX. (Dec. 1990, p. 1454) follow a more informal workshop on April Green, OH. (Dec. 1990, p. 1453) 16-21. NSF-CBMS Regional Research 1-3. 28-May 4. Deductive Systems, Oberwolfach, Conferences in the Mathematical Sciences: ORGANIZING COMMITTEE: J.-1. lgusa, Federal Republic of Germany. (Apr. 1990, New Trends in Nonlinear Control Theory, Y. Kawamata, G. Kempf, S. Mori, B. p. 501) Louisiana State University, LA. (Dec. 1990, Shiffman, S. Zucker. 29-May 2. Joint U.S.-French Workshop on p. 1454) INFORMATION: Johns Hopkins Univ., Dept. Applied Stochastic Analysis, Rutgers Uni­ 17-18. Annual Regional Group Theory of Math., Baltimore, MD 21218. * versity, New Brunswick, NJ. (Nov. 1990, Conference, Bucknell Univ., Lewisburg, PA. p. 1285) 2-4. IMACS International Symposium on INFORMATION: H. Smith or M. Ward, Iterative Methods in Linear Algebra, Brus­ Dept. of Math., Bucknell Univ., Lewis­ sels Free Universities, Belgium. (May/Jun. May 1991 burg, PA 17837; email: howsmith@ 1990, p. 612) bucknell.edu, mward@ bucknell.edu. 7-13. Algebraische Gruppen, Oberwolfach, May/June 1991. Summer Workshop on Federal Republic of Germany. (Apr. 1990, Calculus, Computer, Concepts, and Coop­ 17-20. Conference/Workshop on Contin­ p. 500) erative Learning, Purdue University, West uum Theory and Dynamical Systems, Uni­ 8-12. Seventh International Conference on Lafayette, IN. (Nov. 1990, p. 1285) versity of Southwestern Louisianna, Lafayette, Data Engineering, Kobe, Japan. (Apr. 1990, May/June 1991. IMACS Workshop on Deci­ LA. (Dec. 1990, p. 1454) p. 500) sion Support Systems and Qualitative Rea­ 19-25. Differentialgeometrie im Grossen, 8-12. NASECODE VII, The Seventh In­ soning, Toulouse, France. (Mar. 1990, p. 334) Oberwolfach, Federal Republic of Germany. ternational Conference on the Numerical 2-3. Twenty-Second Annual Pittsburgh (Apr. 1990, p. 501) Analysis of Semiconductor Devices and Inte­ Conference on Modeling and Simulation, 20-24. Eleventh International Conference grated Circuits, Copper Mountain, Colorado. University of Pittsburgh, PA. (Sep. 1990, on Distributed Computing Systems, Arling­ (May/Jun. 1990, p. 612) p. 935) ton, TX. (Sep. 1990, p. 936)

------··--··----·.. ··--·-·---··-···--·-~·----··--·····----·--·-· ····-·-~·-···-~·-········-- ·······•···--·-·----····-.. ····--·-- JANUARY 1991, VOLUME 38, NUMBER 1 45 Meetings and Conferences

* 21-24. Quantization and Microlocal Anal- 3-7. NSF-CBMS Regional Research Con­ condition, including in particular: classi­ ysis, Reims, France. ferences in the Mathematical Sciences: Har­ fying spaces, loop space decompositions, monic Analysis and Partial Differential finite H -spaces and rational/algebraic ho­ PROGRAM: This international conference Equations, University of Missouri, St. Louis, motopy. Our hope is for a "workshop" is part of a special year on Semiclas­ MO. (Dec. 1990, p. 1455) atmosphere that will lead to an exchange sical methods sponsored by the French of ideas and techniques among these var­ C.N.R.S. and the D.R.E.D. (Ministry of 3-8. International Singularity Conference, ious subareas. Younger mathematicians, National Education). Its purpose is to Lille, France. (Nov. 1990, p. 1286) including graduate students, are particu­ bring together people interested in Partial 3-13. Fifth International Workshop in larly welcome. Differential Equations, Harmonic Analysis Analysis and its Applications, Kupari­ and Pseudodifferential analysis around the Dubrovnik, Yugoslavia. (Nov. 1990, p. 1286) INFORMATION: S. Halperin, Scarborough loose theme of quantization. Campus, Univ. of Toronto, 1265 Military *5-7. Conference in Honor of Moshe Zakai, Trail, Scarborough, Ontario M1C 1A4; INVITED SPEAKERS: D. Amal (Metz), N. Haifa, Israel. Berline (Ecole Polytechnique), J.M. Bony email: halper@ lake.scar.toronto.edu; 416- (Ecole Polytechnique), L. Coburn (Buf­ INFORMATION: Conference in Honor of 287-7265; Fax: 416-287-7013. Accomoda­ falo), A. Debiard (Paris), T. Fack (Lyon), Moshe Zakai, Dept. of Electrical Engi­ tion will be available from Sunday, June S. Helgason (M.I.T.), R. Howe (Yale), neering, Technion, Haifa 32000, Israel; tel: 9 to Saturday, June 16. 972-4-294676; email: [email protected]. B. Kostant (M.I.T.), Th. Paul (Paris), J. * 11-July 5. Miniworkshop on Nonlinearity: Peetre (Lund), V. Rivasseau (Ecole Poly­ * 5-15. A Normal Form for the Navier­ Fractals, Pattern Formation, Trieste, Italy. technique), B.W. Schultze (Berlin), and H. Stokes Equations and Its Connection to Upmeier (Kansas). Turbulence, Mathematical Sciences Institute, CHAIRMAN: H.A. Cerdeira, Trieste. INFORMATION: A. Unterberger, Dept. de Cornell University, Ithaca, NY. INFORMATION: International Centre for Math., Univ. de Reims, Moulin de Ia Theor. Physics, P.O. Box 586, Miramare, Housse, B.P. 347, 51062 Reims Cedex, PROGRAM: A series of four lectures will Strada Costiera 11, I-34100 Trieste. France; tel: (33) 26.05.32-16. be given by Ciprian Foias (Indiana Univ.). INFORMATION: Mathematical Sciences In­ 13-15. Western Sectional Meeting, Portland 22-24. Second International Conference on stitute, Cornell Univ., 409 College Ave., State University, Portland, Oregon. Algebraic Methodology and Software Tech­ Ithaca, NY 14850; 607-255-8005. nology, (AMAST), Iowa City, Iowa. (Apr. INFORMATION: W. Drady, American Math· 1990, p. 501) 9-12. International Workshop on Ele­ ematical Society, P.O. Box 6887, Provi­ 23-25. Sixth Annual Lehigh University mentary Operators and Applications, Hein­ dence, RI 02940. Geometry and Topology Conference, Beth­ rich Fabri-Institut der Universitiit Tiibingen, 14-17. Symposium on Lattice Theory and lehem, PA. (Dec. 1990, p. 1454) Blaubeuren/Ulm, Federal Republic of Ger­ many. (Nov. 1990, p. 1286) its Applications, in Honor of the 80th Birth­ 26-29. Twenty-first International Sym­ day of Garrett Birkhoff, Darmstadt, Federal 9-14. Second International Conference posium on Multi-Valued Logic, Victoria, Republic of Germany. (Oct. 1990, p. 1138) Canada. (Dec. 1990, p. 1454) on Fixed Point Theory and Applications, 16-19. Bar-IIan Symposium on the Foun­ 26-31. Signal Theory and Image Process­ Dalhousie University, Halifax, Nova Scotia, Canada. (Oct. 1990, p. 1138) dations of Artificial Intelligence, Ramat Gan, ing, Cetraro, Italy. (Sep. 1990, p. 936) Israel. (Nov. 1990, p. 1286) 26-June 1. Optimalsteuerung und Varia­ 9-15. Singulare Storungsrechnung, Ober­ * 16-22. Mathematische Methoden in der tionsrechnung-Optimal Control, Ober­ wolfach, Federal Republic of Germany. (Apr. Robotik, Oberwolfach, Federal Republic of wolfach, Federal Republic of Germany. (Apr. 1990, p. 501) Germany. 1990, p. 501) * 9-28. NSF Faculty Workshop on Computer­ 29-June 1. Eighth Biennial Conference of Aided Instruction in Linear Algebra and CHAIRMEN: H.G. Bock, Augsburg, F. the Association of Christians in the Mathe­ Differential Equations, University of New Pfeiffer, Miinchen. matical Sciences, Wheaton College, Wheaton, Hampshire, Durham, NH. INFORMATION: Mathematisches For­ IL. (Jul./Aug. 1990, p. 743) PROJECT DIRECTORS: L.L. Zia, H. schungsinstitut Oberwolfach Geschaft­ 29-June 1. Methods in Module Theory, Bechtell. sstelle: Alberstrasse 24 D-7800 Freiburg University of Colorado, Colorado Springs, INFORMATION: Applications should be im Breisgau. CO. (Sep. 1990, p. 936) postmarked no later than March 15, 1991. Participation will be limited to thirty fac­ * 17-19. Seventeenth International Work­ 30-31. Special Session on Polymer Config­ shop on Graph-Theoretic Concepts in Com­ urations: Nonlinear and Nonlocal Diffusion ulty. Direct preliminary inquiries to: CAl Workshop, Dept. of Math., Univ. of New puter Science, Fischbachau near Munich, Problems, University of Minnesota, Min­ Federal Republic of Germany. neapolis, MN. (Nov. 1990, p. 1286) Hampshire, Durham, NH 03824; 603-862- 2320; email: [email protected]. 31-June 2. CMS Summer Meeting 1991, INFORMATION: G. Schmidt, FB f. Infor­ Universire de Sherbrooke, Sherbrooke, Quebec. 10-14. Bernoulli Society Twentieth Con­ matik, UniBW Miinchen, Wemer-Heisen­ (Dec. 1990,p. 1454) ference on Stochastic Processes and their berg-Weg 39, D-8014 Neubiberg. Applications, Nahariya, Israel. (Nov. 1989, 17-21. 1991 International Symposium on p. 1254) the Mathematical Theory of Networks and June 1991 * 10-14. Trent Homotopy Theory Confer­ Systems (MTNS-91), International Confer­ 2-8. Diskrete Geometric, Oberwolfach, Fed­ ence, Trent Univ., Peterborough, Ontario, ence Center Kobe, Kobe, Japan. (Nov. 1989, eral Republic of Germany. (Apr. 1990, p. 501) Canada. p. 1254) 3-7. 1991 Annual Meeting of the Statistical PURPOSE: The theme of the conference 17-21. European Conference on Elliptic Society of Canada, Toronto, Ontario, Canada. will be the properties of spaces and loop and Parabolic Problems, Pont a Mousson, (Mar. 1990, p. 334) spaces in the presence of a finiteness France. (May/Jun. 1990, p. 613)

46 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

* 19-July 1. Nonsmooth Optimization-Methods INFORMATION: V. Cristante, Dipartimento research interests) in the area of focus and Applications, Brice (Trapani), Sicily. di Matematica Pura ed Applicata, Univ. di (e.g. minimal surfaces, calibrations, har­ Padova, Padova 35131, Italy; email (inter­ monic maps, isoparametric foliations) and LECTURERS: Israel: Ben-Tal; Italy: Di net): [email protected]. 2) an openness to educational activities Pillo, Gaudioso, Maugeri, Sutti, Zolezzi; and willingness to engage in discussion U.S.: Mifflin, Overton, Rockafellar, 24-28. NSF-CBMS Regional Research with members of our profession outside Schaible; USSR: Dem'yanov, Malozemov, Conferences in the Mathematical Sciences: of university mathematics departments. To Rubinov; Germany: Elster, Eschenauer, Multigrid and Multilevel Adaptive Methods apply send a letter of interest, a research Pallaschke, Zowe; France: Hiriart-Urruty, for Partial Differential Equations, George plan, and a CV listing two references Lemarechal; Poland: Kiwiel; Greece: Pana­ Washington University, Washington, DC. (Dec. to the address below. Preference will be giotopoulos; Vietnam: Sach; Belgique: 1990, p. 1455) given to individuals who can stay the Save; Romania: Zalinescu. 24-29. Geometry Conference in Honour entire month. Lodging, meals and trans­ INFORMATION: M. Pappalardo, Dept. of of Claude Godbillon and Jean Martinet, portation will be covered by the Institute Math., Univ. of Pisa, Via Buonarroti, 2, University of Strasbourg, France. (Dec. 1990, and participants not supported by regular 56100 Pisa, Italy. Fax: 0039-50-599524; p. 1455) NSF grants will receive a modest stipend. email: [email protected]. * 25-28. Eighth International Conference on The institute will help arrange suitable * 20-27. NP-Completeness: The First 20 Logic Programming, Paris, France. child care for accompanying children. INVITED SPEAKERS: Principle Lecturers: Years, Brice (Trapani), Sicily. INFORMATION: INRIA-Rocquencourt, Re­ M. Berger (IHES), R. Palais (Brandeis), lations Exterieures, Bureau des Col­ LECTURERS: Italy: Ausiello; U.S.: Hart­ C.-1. Terng (Northeastern). F. Almgren loques-ICLP '91, Domaine de Voluceau, manis, Johnson, Karp, Levin, Papadimi­ (Princeton), T. Banchoff(Brown), D. Hoff­ BP 105, F-78153 Le Chesnay Cedex. tiou, Shmoys, Sipser, Rabin; Canada: man (U. Mass.), F. Morgan (Williams). Cook, Edmonds; The Netherlands: van 26-28. Third IMACS International Sympo­ INFORMATION: D. O'Shea, NSF RGI Pro­ Emde-Boas, Lenstra; Germany: Groetschel; sium on Computational Acoustics, Harvard gram, Five Colleges, Inc., P.O. Box 740, Japan: Ibaraki; Hungary: Lovasz. University, Cambridge, MA. Amherst, MA 01004; email: PROGRAM COMMITTEE: Korte (Ger­ (Jul./Aug. 1990, p. 744) [email protected] or geometry@ many), Lawler (U.S.), Lucertini (Italy), math.umass.edu. Luccio (Italy), Rinnoy Kan (The Nether­ * 26-28. Local Communications Systems: lands), Toth (Italy), Welsh (U.K.). LAN and PBX, Palma, Balearic Islands, Spain. 2-5. European Control Conference, Greno­ INFORMATION: G. Gallo, Dept. of Comp. ble, France. (Jul./Aug. 1990, p. 744) Sci., Univ. of Pisa, Corso ltalia, 40 56100 INFORMATION: Univ. de les llles Balaers, * 2-5. International Conference on Com­ Pisa, Italy; Fax: 0039-50-510226. Dept. de Matematiques i Informatica, Cra. plexity: Fractals, Spin Glasses and Neural de Valldemossa, km. 7.6, 07071 Palma, Networks, Trieste, Italy. 23-29. Mathematische Methoden des VLSI­ Spain. Entwurfs und des Distributed Computing, ORGANIZERS: G. Parisi, L. Pietronero, Oberwolfach, Federal Republic of Germany. 30--July 3. Sixth Annual Conference on M. Virasoro, H.A. Cerdeira, S. Lundqvist. (Jul./Aug. 1990, p. 744) Structure in Complexity Theory, University INFORMATION: International Centre for of Chicago, Chicago, IL. (Nov. 1990, p. 1287) * 23-30. International Category Theory Meet- Theor. Physics, P.O. Box 586, Miramare, ing, Montreal, Quebec, Canada. 30--July 6. Elliptische Operatoren auf Strada Cc>>tiera 11, 1-34100 Trieste. Singuliiren und Nichtkompakten Mannig­ INVITED SPEAKERS: S. Abramsky, A. faltigkeiten, Oberwolfach, Federal Republic Carboni, J. Isbell, J. Jardine, F. Lamarche, 4-11. International Conference on Alge­ of Germany. (Apr. 1990, p. 501) G. Meloni, E. Moggi, J. Pelletier, A. Pitts, braic Topology, Oaxtepec, Mexico. (Nov. R. Street, V. Tmkova, R. Wood. 1990, p. 1287) CALL FOR PAPERS: Deadline for ab­ 7-12. Fifth Gregynog Symposium on Differ­ stracts: March 15, 1991. July 1991 ential Equations, University of Wales, UK. INFORMATION: Category Theory 1991, (Nov. 1990, p. 1287) 1-5. The Mathematics of Nonlinear Sys­ Math. Dept., McGill Univ., 805 Sher­ tems, University of Bath, United Kingdom. 7-13. Computational Number Theory, brooke St. W, Montreal, Quebec, Canada, (Dec. 1990, p. 1455) Oberwolfach, Federal Republic of Germany. H3A 2K6; email: [email protected]. (Jul./Aug. 1990, p. 744) * 1-26. NSF Geometry Institute - Geometry *24-27. Barsotti Memorial Symposium on in the Machine Age, Mount Holyoke College, * 7-20. Eighth International Conference on Algebraic Geometry, Abano Terme, Italy. South Hadley, MA. Probability in Banach Spaces, Bowdoin Col­ lege, Brunswick, ME. PROGRAM: A series of invited addresses PROGRAM: Amherst, Hampshire, Holy on algebraic geometry, most of which Cross, Mount Holyoke, Smith, and Wil­ PROGRAM: The first week will focus on will deal with areas of algebraic geometry liams Colleges and the University of Mas­ probability in separable Banach spaces enriched by the mathematical heritage of sachusetts at Amherst will host this NSF­ while the emphasis of the second week the late Iacopo Barsotti. Facilities for funded Institute. The first year will focus will be empirical processes. The meeting is supplementary informal gatherings will be on Optimization Problems in Geometry. intended to bring together analysts, prob­ provided. The institute will bring together geometry abilists, statisticians and theoretical com­ INVITED SPEAKERS: [As of Oct. 15, researchers, high school faculty, educa­ puter scientists who have been working 1990] F. Baldassarri, P. Berthelot, L. tion researchers, and undergraduate and on different aspects of related problems. Breen, S. Bosch, B. Dwork, G. Falt­ graduate students. Substantial interaction Two mini-courses have been arranged and ings, J.-M. Fontaine, L. lllusie, N. Katz, between the groups is expected. Forty ge­ five speakers have agreed to deliver hour W. Messing, L. Moret-Bailly, P. Norman, ometers are being sought who have 1) addresses. The remainder of the schedule A. Ogus. an established research program (or active will be filled by talks from the participants.

JANUARY 1991, VOLUME 38, NUMBER 1 47 ·-----~------.------·····-······-···-····----Meetings and Conferences

ORGANIZING COMMITTEE: K. Alexan­ tion; G. Benke (MITRE Corp.)- Random INFORMATION: ISSAC '91 Conference der, R.M. Dudley, M.G. Hahn, J. Kuelbs. trigonometric polynomials and their appli­ Office, C. Harms, GMD, SchloB Bir­ INVITED SPEAKERS: Mini-Courses: M. cations; G. Brown (Univ. of New South linghoven, P.O. Box 1240, D-5205 St. Talagrand-Majorizing Measures (first Wales and Prometheus Inc.) - Normal Augustin 1, Tel: 49-2241-142473; Tete­ week); E. Gine, J. Zion-Empirical Pro­ numbers and dynamical systems; P. Can­ fax: 49-2241-142618; email: gfl022@ cesses and the Bootstrap (second week). narsa (Univ. of Pisa and Prometheus Inc.) dbngmd21. bitnet. Hour Addresses: A. de Acosta, E. Bolthau­ - Stochastic optimal control; J.P. Kahane sen, M. Marcus, G. Pisier, G. Schechtman. (Univ. of Paris-Orsay) - Some continu­ 15-18. Sixth Annual IEEE Symposium on INFORMATION: M.G. Hahn, Dept. of ations of the work of Paley and Zyg­ Logic in Computer Science, Amsterdam, The Math., Tufts Univ., Medford, MA 02155; mund on random trigonometric series; G. Netherlands. (Sep. I 990, p. 937) 617-628-5000 x2363; email: mhahn@ Kallianpur (Univ. of North Carolina and * 15-18. The Fourth Interdisciplinary Con­ jade.cc. tufts.edu. Prometheus Inc.) - Stochastic differential ference on Natural Resource Modelling and equations in infinite dimensional spaces; Analysis, University of Barcelona, Spain. 8-12. Second International Conference on S. Mallat (Courant Institute) - Charac­ Industrial and Applied Mathematics, Wash­ terization of singularities from wavelet PURPOSE: The objective of the meeting ington, DC. (Apr. 1990, p. 501) transform maxima; Y. Meyer (Univ. of is to facilitate communication among biol­ 8-12. NATO Advanced Research Work­ Paris-Dauphine) - Wavelets and applica­ ogists, ecologists, economists, engineers, shop: Approximation by Solutions of Partial tions; D.J. Newman (Temple Univ. and mathematicians, physicists and other sci­ Differential Equations, Quadrature l<'ormu­ Prometheus Inc.) - Probability in logic; J. entists who share an interest in resource lae, and Related Topics, Hanstholm, Den­ Peyriere (Univ. of Paris-Orsay) - On the modelling. mark. (Please note changes from Oct. 1990, multifractal analysis of measures; A. Pa­ INVITED SPEAKERS: A. Laurec (IFRE­ p. 1139) poulis (Polytechnic Univ. of NY) - Topics MER, Paris, Fr.), Population dynamics in in sampling theory; B. Saffari (Univ. of fisheries; R. Margalef (Univ. of Barcelona, CONFERENCE TOPICS: Approximation Paris-Orsay and Prometheus Inc.) Appli­ Spain), Ecology; M. Sykes (Univ. of Up­ of solutions of partial differential equa­ cations of probability methods to some psala, Sweden), Management models in tions on closed subsets of N-dimensional extremal problems in Fourier analysis; W. forestry; M. Usher (Univ. of York, U.K.), Euclidean space or Riemann surfaces by Schempp (Univ. of Siegen) - Quantum Succession models in forestry; J. Wagens­ globally defined solutions; characteriz­ Holography. berg (Univ. of Barcelona, Spain), Theoret­ ing domains in N-dimensional Euclidean ical biology and nonequilibrium dynamics; space such as balls, annuli, strips, cylin­ CALL FOR PAPERS: February I, 1991: Deadline for receipt of request to partic­ and others pending. ders etc. by means of quadrature formulae; ipate, the title and abstract of the paper CALL FOR PAPERS: Abstracts deadline best L 1 and best L 00 approximation; and you would like to present (optional), and for contributed talks on any quantitative related topics. an indication if you will require financial aspects of fisheries, forests, soil, water, INVITED SPEAKERS: The list that was support. NOTE: Preference will be given wildlife or other natural resources: May mentioned in the Oct. issue was only a to people who communicate by electronic 31, 1991. partial list. mail and who agree to prepare their paper INFORMATION: P. Rubies, lnst. de Cien­ 8-12. Thirty-Fifth Annual Conference of (if presenting one) in 1}3X (any version). cias del mar, P. Nacional s/n, 08039 the Australian Mathematical Society, Mel­ Also, there is special support available for Barcelona, Spain; tel: 3-310 64 16; Fax: bourne, Australia. (Oct. 1990, p. 1139) U.S. citizens who are upper-level graduate 3-319 98 42; email: [email protected]. students or have recent Ph.Ds. 8-14. ICOR '91 International Conference INFORMATION: J. Byrnes, Prometheus * IS-August 2. Conference on Recent Devel­ on Radicals, Szekszard, Hungary. (Apr. 1990, opments in Differential Equations and Eco­ p. 502) Inc., 21 Arnold Ave., Newport, RI 02840; email: [email protected]; 401-849-5389 or logical Modeling, University of Wyoming, 14-20. Dynamische Systeme, Oberwolfach, 401-841-5048. Laramie, WY. Federal Republic of Germany. (Apr. 1990, p. 502) 15-17. Fifth IFACIIMACS Symposium on PROGRAM: Mornings will be devoted to * 14-20. International Conference on Near- Computer Aided Design in Control and lectures by the speakers which will ad­ rings and Near-fields, Linz, Austria. Engineering Systems, Swansea, UK. (Mar. dress selected important and recent devel­ 1990, p. 334) opments in differential equations and eco­ INFORMATION: G. Pilz, lnstitut fiir Math­ logical modeling. Afternoons will be de­ ematik, Universitiit Linz, A-4040 Linz, * 15-17. International Symposium on Sym­ voted to discussions, work sessions and/or Austria. bolic and Algebraic Computation (ISSAC talks which will assist in the incorporation '91), Bonn, Germany. of these ideas and concepts into college 14-27. 1991 NATO Advanced Study In­ * PROGRAM : The conference will feature courses at all levels. Funds to cover living stitute: Probabilistic and Stochastic Meth­ original research contributions, demonstra­ costs and a few small stipends are avail­ ods in Analysis, with Applications, Castel­ tions of hardware and software and invited able. See advertisement in this issue of vecchio Pascoli (Lucca), Italy. lectures. Notices. PROGRAM: The institute will be divided CONFERENCE TOPICS: Algorithms, lan­ INVITED SPEAKERS: The main speak­ into four sections: 1) Wavelets and frac­ guages and systems for symbolic and al­ ers will be H.l. Freedman, University of tals; 2) Applications in engineering; 3) gebraic computation; Automatic theorem Alberta and P.E. Waltman, Emory Univer­ Stochastic calculus; 4) Applications in proving and programming; Computational sity. Both will lecture for the entire three mathematics. The institute is supported by geometry, group theory and number the­ weeks. NATO, AFOSR, ONR, Prometheus Inc. ory; Interface/integration of symbolic, nu­ INFORMATION: A.D. Porter, Mathematics INVITED SPEAKERS: J.J. Benedetto meric, graphics computing; Applications Department, P.O. Box 3036, University (Univ. of Maryland and Prometheus Inc.) of computer algebra in science, engineer­ Station, University of Wyoming, Laramie, - Stationary frames and spectral estima- ing and education. WY 82071-3036.

48 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

15-August 9. IMA Summer Program in 19-23. The Seventh Prague Topological Semiconductors, University of Minnesota, Symposium. Prague, Czechoslovakia. (Dec. Minneapolis, MN. (Dec. 1990, p. 1456) August 1991 1990, p. 1456) * 21-26. SPIE's International Symposium on 3-7. Interamerican Conference on Math­ * 19-30. Course in Functional Integration Optical Applied Science and Engineering, ematics Education, Univ. of Miami. Coral and its Applications. Trieste. Italy. San Diego, CA. Gables, FL. (Apr. 1990, p. 502) ORGANIZERS: H.A. Cerdeira. Trieste; A. 4-10. Effiziente Algorithmen, Oberwol­ Ranfagni. L.S. Schulman. PROGRAM: The program on Mathemati­ fach, Federal Republic of Germany. (Jul./Aug. INFOR.:-.IATION: Intern. Centre for Thcor. cal Imaging is one of many. The major 1990, p. 744) Physics. P.O. Box 586, Miramare, Strada topics for this program are: geometric 5-8. ICMI-China Regional Conference Costiera II, I-34100 Trieste. methods in computer vision; image alge­ on Mathematics Education, Beijing, China. bra and morphological image processing (Jul./Aug. 1990, p. 744) 19-September 6. College on Singularity II: stochastic methods in signal processing, Theory, Trieste. Italy. (Sep. 1990. p. 938) 5-9. Fourteenth International Symposium image processing, and computer vision: 21-23. Thirteenth Boundary Element applications of digital image processing on Mathematical Programming, Amster­ dam. The Netherlands. (Jul./Aug. 1990, p. 745) Method International Conference. Tulsa. XIV. OK. (Nov. 1990. p. 1288) 5-10. NSF-CBMS Regional Research Con­ INFORMATION: SPIE, P.O. Box 10, Bel­ 21-24. Colloquium on Differential Equa­ ferences in the Mathematical Sciences: K­ lingham, WA 98227-0010; 206-676-3290; tions and Applications. Budapest. Hungary. Homology and Index Theory, University of Telex: 46-7053; telefax: 206-647-1445; (Dec. 1990, p. 1457) Colorado, CO. (Dec. 1990, p. 1456) OPTO-LINK 206-733-2998. 21-25. The International Conference on 7-14. 1991 ASL European Summer Meet­ the Theory of Rings, Algebras, and Modules ing (Logic Coloquium '91) in conjunction 21-27. Halbgruppentheorie, Oberwolfach, in Honor of A.I. Shirshov, Bamaul. U.S.S.R. with the Ninth International Congress of Federal Republic of Germany. (Jul./Aug. (Jul./Aug. 1990. p. 745) 1990, p. 744) Logic, Methodology and Philosophy of Sci­ ence, Uppsala, Sweden. (Dec. 1990, p. 1456) 25-31. Klassifikation Komplex-Aigebrai­ 22-26. Thirteenth IMACS World Congress scher Varietiiten, Oberwolfach. Federal Re­ on Computation and Applied Mathematics, 8-11. Joint Mathematics Meetings, Uni­ public of Germany. (Jul./Aug. 1990, p. 745) versity of Maine, Orono, ME. (including the Trinity College, Dublin University, Dublin, 25-31. Conference on Classifying Spaces Ireland. (Apr. 1990, p. 502) summer meetings of the AMS, AWM, MAA, and PME) of Compact Lie Groups and Finite Loop 28-August 2. Conference on Symbolic Dy­ Spaces, Gottingen University. (Nov. 1990. namics and its Applications, Yale University, INFORMATION: H. Daly, AMS, P.O. Box p. 1288) New Haven, CT. (Nov. 1990, p. 1287) 6887, Providence. RI 02940. 26-31. International Conference on Differ­ ential Equations: EQUADIFF 91. 11-17. European Young Statisticians Meet­ * 28-August 2. SIGGRAPH-Eighteenth In­ Barcelona, Spain. (Dec. 1990, p. 1457) ternational Conference on Computer Graph­ ing, Oberwolfach. Federal Republic of Ger­ ics and Interactive Techniques, Las Vegas, many. (Jul./Aug. 1990, p. 745) Nevada. 12-17. NSF-CBMS Regional Research September 1991 Conferences in the Mathematical Sciences: PROGRAM: The program includes: tech­ Higher Order Asymptotics with Applica­ 1-7. Topologie. Oberwolfach, Federal Re­ nical papers, panels, courses, workshops, tions to Statistical Inference. University of public of Germany. (Jul./Aug. 1990, p. 745) electronic theatre, art and design show, North Carolina, NC. (Dec. 1990, p. 1456) * 3-6. Seventeenth International Conference special interest groups, hypermedia ex­ 14-16. Short Conference on Uniform on Very Large Data Bases (VLDB '91). hibit, virtual reality demonstrations, educa­ Barcelona (Catalonia. Spain). tors' program, manufacturers' and devel­ Mathematics and Applications (Interna­ opers' exhibits. Because this conference is tional Conference on Quasi-Uniformities PROGRAl\1: VLDB conferences arc a truly the international forum for exploring the and Related Structures). Bern, Switzerland. international forum for identifying. en­ frontiers of computer graphics, it attracts (Sep. 1990, p. 937) couraging and exchanging ideas and ex­ engineers, scientists, artists. designers, per­ 18-24. The Navier-Stokes Equations: The­ periences on research. development and sonal computer users-everyone involved ory and Numerical Methods. Oberwolfach. novel applications of database manage­ with computer graphics-from novices to Federal Republic of Germany. (Jul./Aug. ment systems and techniques. Like its pre­ experts. It is the world's premier con­ 1990. p. 745) decessors, this conference aims at bringing ference for describing, discussing, and 18-24. The Third Conference of the Cana­ together researchers, developers and users displaying your work and the work of dian Number Theory Association, Queen's of database management systems from others with interests like yours. University, Kingston, Ontario. (Sep. 1990, academia and industry. to share this infor­ mation and explore new and challenging INFORMATION: SIGGRAPH '91, Confer­ p. 938) issues. ence Management Office, 401 N. Michi­ 18-September 4. Twenty-first Summer Ecole CONFERENCE TOPICS: Logic, deduc­ gan Ave., Chicago, JL 6061 I; 312-644- de Calcul des Probabilites. Saint Flour. tive, and knowledge base systems; exten­ 6610. France. (Jul./Aug. 1990, p. 745) sible, temporal and multi-media databases: 19-22. 1991 Joint Statistical Meetings. active and real-time database systems: 28-August 3. Gruppen und Geometrien, Atlanta, GA. (Mar. 1988. p. 466) advanced applications and requirements: Oberwolfach, Federal Republic of Germany. 19-23. NSF-CBMS Regional Research object-oriented and semantic databases: (Apr. 1990, p. 502) Conferences in the Mathematical Sciences: data models. languages. and user in­ 29-August 9. SMS-NATO ASI: Universal Qualitative and Structured Matrix Theory, terfaces; data structure. access methods. Algebra and Orders, Universire de Montreal, Georgia State University. GA. (Dec. 1990, and complex objects: database theory and Montreal, Canada. (Dec. 1990, p. 1456) p. 1456) algorithms: query optimization. database

JANUARY 1991, VOLUME 38, NUMBER 1 49 ------····------···----.. ·····-· Meetings and Conferences

design, and performance; storage manage­ CHAIRMAN: Jan de Lange. 12-13. Eastern Section, Temple University, ment, database machines, and parallelism; INFORMATION: J. de Lange, ICMTA 5, Philadelphia, PA. database integrity and security; concur­ OW&OC, Tiberdreef 4, 3561 GG Utrecht, rency control, transaction processing, and The Netherlands. INFORMATION: W. Drady, American Math­ recovery; distributed and heterogeneous ematical Society, P.O. Box 6887, Provi­ databases. 9-27. School on Dynamical Systems, Trieste, dence, Rl 02940. CALL FOR PAPERS: Original papers of Italy. (Sep. 1990, p. 938) 13-19. Geometrie, Oberwo1fach, Federal up to 5,000 words in length are invited on 10-13. IFAC/IMACS Symposium on Fault Republic of Germany. (Jul./Aug. 1990, p. 7 46) topics including, but not limited to, those Detection, Supervision and Safety for Tech­ listed above. Send five copies of double­ nical Processes-SAFEPROCESS '91, Baden­ 14-18. IMA Workshop on Sparse Matrix spaced manuscript, in English, including Baden, Federal Republic of Germany. (Apr. Computations: Graph Theory Issues and keywords, to one of the program chairs by 1990, p. 502) Algorithms, University of Minnesota, Min­ February 15, 1991: A. Sernadas, INESC, 11-13. IFAC!IFIPIIMACS Symposium on neapolis, MN. (Oct. 1990, p. 1140) Rua Alves Redol, 9, 7°. Apartado 10105, Robot Control (SYROCO '91), Vienna, Aus­ 16--18. SIAM Workshop on Micromechan­ P-1017 Lisboa Codex (Portugal), Internet tria. (Oct. 1990, p. 1140) ics, Leesburg, VA. (Nov. 1990, p. 1288) (US): inesc!acs%[email protected]; (Eu­ 11-14. Fourth SIAM Conference on Ap­ * 18-19. Differential and Delay Equations, rope) acs%[email protected] or acs@ plied Linear Algebra, Univ. of Minnesota, Iowa State University, Ames, Iowa. inesc.ctt.pt or G.M. Lohman, IBM Al­ Minneapolis, MN. (Nov. 1990, p. 1288) maden Research Center, Dept. K55, Bldg. 13-15. Representation Theory Conference, PROGRAM: Meeting on the occasion of 801, 650 Harry Rd., San Jose, CA 95120- University of Oregon, Eugene, OR. (Nov. the retirement of George Seifert. 6099 (U.S.A.); internet: [email protected] 1990, p. 1288) ORGANIZERS: A.M. Fink, R.K. Miller, or bitnet: lohman@almaden. · W. Kliemann. 15-20. DMV-Jahrestagung 1991, Biele­ INFORMATION: VLDB '91 - DIFINSA, INVITED SPEAKERS: K. Cooke, K. Deim­ Av. Republica Argentina, 63, Ent. 4a, E- feld, Federal Republic of Germany. (Jul./Aug. 1990, p. 746) ling, J. Hale, J. Nohel, K. Schmitt, T. 08023 Barcelona, Catalonia (Spain); tel: Yoshizawa. 34-3-418.80.67; Fax: 34-3-418.44.07. 15-21. Geometrie der Banachriiume, Ober­ wolfach, Federal Republic of Germany. INFORMATION: A.M. Fink, Iowa State * 3-6. Functional Integration and its Appli- (Jul./Aug. 1990, p. 746) University of Science and Technology, Dept. of Math., 400 Carver Hall, Ames, cations, Trieste, Italy. 22-28. Nonlinear and Random Vibrations, Iowa 50011; 515-294-1752; si.mth@ ORGANIZERS: H.A. Cerdeira, D. Mugnai, Oberwolfach, Federal Republic of Germany. isumvs. bitnet. A. Ranfagni. (Jul./Aug. 1990, p. 746) INFORMATION: Intern. Centre for Theor. 23-29. Sixth Symposium on Classical Anal­ * 20-26. C*-Algebren, Oberwolfach, Federal Physics, P.O. Box 586, Miramare, Strada ysis, Kazimierz Dolny, Poland. (Apr. 1990, Republic of Germany. Costiera 11, 1-34100 Trieste. p. 502) CHAIRMEN: J. Cuntz, Heidelberg; U. 24-27. International Conference on Theo­ Haagerup, Odense; L. Zsido, Stuttgart. * 3-10. Applied Mathematics in the Aerospace retical Aspects of Computer Software, To­ Field, Brice (Trapani), Sicily. hoku Univ., Sendai, Japan. (Sep. 1990, p. 938) INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschaft­ LECTURERS: Italy: Borri, Cercignani, Conti, 25-27. Ninth GAMM Conference on Nu­ sstelle: Alberstrasse 24 D-7800 Freiburg Quarteroni, Morino, Pandolfi, Santini; U.S.: merical Methods in Fluid Mechanics, Lau­ im Breisgau. Calise, Leitman, Miele, MacCormack, So­ sanne, Switzerland. (May/Jun. 1990, p. 613) biesky, Vander Velde, Van Dyke; U.K.: 29--0ctober 5. Kombinatorik Geordneter 21-26. Third International Workshop­ Crighton; Germany: Mengen, Oberwolfach, Federal Republic of Conference on Evolution Equations, Con­ Forsching; France: Lions. Germany. (Jul./Aug. 1990, p. 746) trol Theory, and Biomathematics, Han-sur­ INFORMATION: A. Salvetti, Dept. lngeg­ Lesse, Belgium. (Nov. 1990, p. 1288) neria Aerospaziale, Univ. di Pisa, Via Di­ otisalvi, Pisa, Italy; Fax: 0039-50-500987; * 27-November 2. Statistische Entscheidungs­ Tel: 0039-50-550200. theorie, Oberwolfach, Federal Republic of October 1991 Germany. 4-10. IMA Tutorial, University of Min­ CHAIRMEN: J.O. Berger, West Lafayette; nesota, Minneapolis, MN. (Oct. 1990, p. 1139) 6--12. Arbeitsgemeinschaft mit Aktuellem Thema (wird in den Mitteilungen der DMV J. Lehn, Darmstadt; D. Plachky, Miinster. 7-9. International Workshop on Software Heft 3/1991 bekanntgegeben), Oberwolfach, INFORMATION: Mathematisches For­ for Automatic Control Systems, Irkutsk, Federal Republic of Germany. (Jul./Aug. schungsinstitut Oberwolfach Geschiift­ USSR. (Oct. 1990, p. 1139) 1990, p. 746) sstelle: Alberstrasse 24 D-7800 Freiburg 8--14. Niedrigidimensionale Topologie, Ober­ 7-10. The Ninth International Symposium im Breisgau. wolfach, Federal Republic of Germany. on Applied Algebra, Algebraic Algorithms, (Jul./Aug. 1990, p. 745) and Error Correcting Codes, New Orleans, * 27-November 2. Convergence Structures in 8-14. Knoten und Verschlingungen, Ober­ LA._ (Dec. 1990, p. 1458) Topology and Analysis, Oberwolfach, Federal Republic of Germany. wo1fach, Federal Republic of Germany. 7-11. Workshop on Stochastic and Deter­ (Jul./Aug. 1990, p. 745) ministic Models, Trieste, Italy. (Sep. 1990, CHAIRMEN: E. Binz, Mannheim; H. Her­ 9-13. Journees Arithmetiques, Geneva, p. 938) rlich, Bremen; G. PreuB, Berlin. Switzerland. (Dec. 1990, p. 1457) 7-11. IMA-INRIA Workshop on Transfer INFORMATION: Mathematisches For­ *9--13. ICMTA 5 Teaching Mathematics by of Mathematics to Industry in the U.S. and schungsinstitut Oberwolfach Geschiift­ Applications, Noordwijkerhout, The Nether­ France, University of Minnesota, Minneapo­ sstelle: Alberstrasse 24 D-7800 Freiburg lands. lis, MN. (Dec. 1990, p. 1458) im Breisgau.

50 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -----·····-···-···------··--·--·------Meetings and Conferences

schungsinstitut Oberwolfach Geschiift­ sstelle: Alberstrasse 24 D-7800 Freiburg November 1991 January 1992 im Breisgau. 3-9. Mengenlehre, Oberwolfach, Federal * 1-11. Mathematische Optimierung, Ober- * 26-February 1. Applied and Computational Republic of Germany. (Jul./Aug. 1990, p. 746) wolfach, Federal Republic of Germany. Convexity, Oberwolfach, Federal Republic of 4-8. Second SIAM Conference on Geomet­ CHAIRMEN: B. Korte, Bonn; K. Ritter, Germany. ric Design, Tempe, AZ. (Nov. 1990, p. 1289) Miinchen. CHAIRMEN: P. Gritzmann, Augsburg; V. 9-10. Western Sectional Meeting, University INFORMATION: Mathematisches For­ Klee, Seattle; P. Kleinschmidt, Passau. of California, Santa Barbara. schungsinstitut Oberwolfach Geschiift­ INFORMATION: Mathematisches For­ sstelle: Alberstrasse 24 D-7800 Freiburg INFORMATION: W. Drady, American Math­ schungsinstitut Oberwolfach Geschiift­ im Breisgau. ematical Society, P.O. Box 6887, Provi­ sstelle: Alberstrasse 24 D-7800 Freiburg dence, RI 02940. *5-8. Second Caribbean Conference on im Breisgau. 11-15. IMA Workshop on Combinatorial the Fluid Dynamics, University of the West Indies, St. Augustine, Trinidad. and Graph-Theoretic Problems in Linear Algebra, University of Minnesota, Minneapo­ ORGANIZING COMMITTEE: B.S. Bhatt, The following new announcements will not lis, MN. (Oct. 1990, p. 1140) L. Kunar, D. McGaw, H.O. Phelps, H. be repeated until the criteria in the last Ramkissoon, G.S. Shrivastava. 17-23. Singularitaten der Kontinuums­ paragraph in the box at the beginning of mechanik: Numerische und Konstruktive INVITED SPEAKERS: J. Lighthill (U.K.), this section are met. Methoden zu Ihrer Behandlung, Oberwol­ T. Tezduyar (U.S.A.), A.G. Davenport fach, Federal Republic of Germany. (Jul./Aug. (Canada), J. Delery (France), J.P. Brill 1990, p. 746) (U.S.A.), A. Acrivos (U.S.A.), S.M.F. 18-22. Supercomputing '91, Albuquerque, Ali (Canada), T.E. Unny (Canada), G.A. NM. (Jan. 1990, p. 62) Barenblatt (Russia). CALL FOR PAPERS: Papers from all 20-26. C* -Aigebren, Oberwolfach, Federal February 1992 areas of Newtonian and non-Newtonian Republic of Germany. (Jul./Aug. 1990, p. 746) Fluid Dynamics are solicited. An award * 2-8. Thermodynamische Materialtheorien, 24-30. Numerische Methoden der Approx­ will be made to the authors of the best pa­ Oberwolfach, Federal Republic of Germany. imationstheorie, Oberwolfach, Federal Re­ per. Abstracts of about 500 words should CHAIRMEN: W. Biirger, Karlsruhe; I. public of Germany. (Jul./Aug. 1990, p. 746) be submitted in duplicate not later than Miiller, Berlin. 25-26. Central Section, North Dakota State March 31, 1991 to: Editorial Commit­ INFORMATION: Mathematisches For­ University, Fargo, ND. tee, CACOFD '92, Dept. of Math., The schungsinstitut Oberwolfach Geschiift­ INFORMATION: W. Drady, American Math­ Univ. of the West Indies, St. Augustine, sstelle: Alberstrasse 24 D-7800 Freiburg ematical Society, P.O. Box 6887, Provi­ Trinidad, W.l. im Breisgau. dence, RI 02940. INFORMATION: H. Ramkissoon, Chair, Organizing Committee, Dept. of Math., * 9-15. Numerical Methods for Parallel Com­ The Univ. of the West Indies, St. Augus­ puting, Oberwolfach, Federal Republic of tine, Trinidad; Fax: 809-662-4414. Germany. December 1991 8-11. Joint Mathematics Meetings, Balti­ CHAIRMEN: W. Hackbusch, Kiel; R. Ran­ 1-7. Statistik Stochastischer Prozesse, Ober­ more, MD. (including the annual meetings of nacher, Heidelberg; 0. Widlund, New wolfach, F.R.G. (Jul./Aug. 1990, p. 746) the AMS, AWM, MAA and NAM) York. 2-6. Workshop on Statistical Methods in INFORMATION: Mathematisches For­ INFORMATION: H. Daly, AMS, P.O. Box Imaging, Mathematical Sciences Research schungsinstitut Oberwolfach Geschiift­ 6248, Providence, RI 02940. Institute, Berkeley, CA. (Oct. 1990, p. 1140) sstelle: Alberstrasse 24 D-7800 Freiburg im Breisgau. 2-9. SIAM Conference on Combustion, St. * 12-18. Applied Dynamics and Bifurcation, Petersburg, FL. (Nov. 1990, p. 1289) Oberwolfach, Federal Republic of Germany. * 16-22. Funktiontheorie, Oberwolfach, Fed- 7-10. Canadian Mathematical Society Win­ CHAIRMEN: G. looss, Nice; H. KielhOfer, eral Republic of Germany. ter Meeting, Victoria, B.C., Canada. (Oct. Augsburg; J.E. Marsden, Berkeley; J. CHAIRMEN: G. Frank, Berlin; S. Rusch­ 1990, p. 1141) Scheuerle, Hamburg. eweyh, Wiirzburg; K. Strebel, Ziirich. 8-14. Stochastic Geometry, Geometric INFORMATION: Mathematisches For­ INFORMATION: Mathematisches For­ Statistics, Stereology, Oberwolfach, Federal schungsinstitut Oberwolfach Geschiift­ schungsinstitut Oberwolfach Geschiift­ Republic of Germany. (Jul./Aug. 1990, p. 746) sstelle: Alberstrasse 24 D-7800 Freiburg sstelle: Alberstrasse 24 D-7800 Freiburg 15-21. Quantenstochastik, Oberwolfach, im Breisgau. im Breisgau. Federal Republic of Germany. (Jul./Aug. 1990, p. 746) 13-17. IMA Workshop on Linear Algebra, * 23-29. p-Adische Analysis und Anwen­ Markov Chains, and Queuing Models, Uni­ 23-26. International Conference on Gen­ dungen, Oberwolfach, Federal Republic of versity of Minnesota, Minneapolis, MN. (Oct. eralized Functions and Their Applications, Germany. 1990, p. 1141) Banaras Hindu University, Varanasi, India. CHAIRMEN: S. Bosch, Munster; L. Ger­ * 19-25. Modelltheorie, Oberwolfach, Federal (Dec. 1990, p. 1458) ritzen, Bochum; A. Ogus, Berkeley. Republic of Germany. 27-31. Holiday Symposium on the Impact INFORMATION: Mathematisches For­ of Software Systems in Mathematical Re­ CHAIRMEN: D. Lascar, Paris; A. Prestel, schungsinstitut Oberwolfach Geschiift­ search, New Mexico State Univ., Las Cruces, Konstanz; M. Ziegler, Freiburg. sstelle: Alberstrasse 24 D-7800 Freiburg NM. (Jul./Aug. 1990, p. 746) INFORMATION: Mathematisches For- im Breisgau. ·-----·------··--·--·------· JANUARY 1991, VOLUME 38, NUMBER 1 51 --··········-·--··------~------Meetings and Conferences

INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ March 1992 sstelle: Alberstrasse 24 D-7800 Freiburg August 1992 * 1-7. Klassifizierende Raume und Anwen­ im Breisgau. * 22-28. Eighteenth International Congress dungen der Steenrod-Aigebra, Oberwolfach, of Theoretical and Applied Mechanics, Federal Republic of Germany. Technion-Israel Institute of Technology, Haifa, * 22-28. Teichmiiller-Theorie und Modul­ Israel. CHAIRMEN: H.-W. Henn, Heidelberg; H. raume Riemannscher Flachen, Oberwolfach, Miller, Cambridge; D. Puppe, Heidelberg. Federal Republic of Germany. CALL FOR PAPERS: Papers will be ac­ INFORMATION: Mathematisches For­ cepted in all areas of theoretical and ap­ schungsinstitut Oberwolfach Geschlift­ CHAIRMEN: G. Schumacher, Bochum; S. Wolpert, College Park. plied mechanics, but the following three sstelle: Alberstrasse 24 D-7800 Freiburg topics will receive special attention as im Breisgau. INFORMATION: Mathematisches For­ schungsinstitut Oberwolfach Geschiift­ subjects of mini-symposia: Instabilities in * 8-14. Mathematische Stochastik, Oberwol- sstelle: Alberstrasse 24 D-7800 Freiburg solid structural mechanics, sea surface fach, Federal Republic of Germany. im Breisgau. mechanics and air-sea interaction, biome­ chanics. The submitting author should CHAIRMEN: R. Griibel, Delft; G. Kerst­ prepare 6 copies of an Extended Sum­ ing, Frankfurt. mary of about 500 words and an Abstract 29-April 4. Topologische Methoden in der INFORMATION: Mathematisches For­ * of 100-150 words. The abstract must be Gruppentheorie, Oberwolfach, Federal Re­ schungsinstitut Oberwolfach Geschiift­ typed doubled-spaced on a single page. public of Germany. sstelle: Alberstrasse 24 D-7800 Freiburg The above material should be submitted im Breisgau. CHAIRMEN: R. Bieri, Frankfurt; K.S. to arrive before January 15, 1992 to the Brown, Ithaca. address below. * 15-21. Regelungstheorie, Oberwolfach, Fed­ INFORMATION: Mathematisches For­ INFORMATION: A. Solan, Secretary IC­ eral Republic of Germany. schungsinstitut Oberwolfach Geschiift­ TAM 1992, Faculty of Mechanical Engi­ CHAIRMEN: H.W. Knobloch, Wiirzburg; sstelle: Alberstrasse 24 D-7800 Freiburg neering, Technion-Israel Institute of Tech­ M. Thoma, Hannover. im Breisgau. nology, Haifa 32000, Israel.

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52 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

extension of the theory of affine group schemes. They establish a number of foundational results, including the theory of NOETHER-LEFSCHETZ THEORY AND THE induced representations and spectral sequences for quantum PICARD GROUP OF PROJECTIVE group cohomology. They then apply these results to give a SURFACES detailed study of the quantum general linear group and its Angelo Felice Lopez representation theory. Some of the central topics included are (Memoirs of the· AMS, Number 438) a development of quantum determinants, Frobenius kernels and their representation theory, high weight theory, and the This book deals with the study of curves lying on general generalization of various important theorems concerning the members of families of smooth projective surfaces over the cohomology of vector bundles on the flag manifold. Finally, the complex numbers. The guiding philosophy is that the set of authors use the theory to give a treatment of q-Schur algebras, curves on such surfaces is as small as it can possibly be; more proving, for example, that q-Schur algebras are quasi-hereditary. precisely, this means that the group of classes of Cartier divisors (or, equivalently, the group of line bundles called the Picard Contents group) of a general surface has the lowest possible rank given by the geometry of the family. Quantum Groups; Representation Theory of Quantum Groups; Quantum Matrix Spaces; Quantum Determinants; The Antipode and Quantum The focus of the book is Noether-Lefschetz theory, the study Linear Groups; Some Closed Subgroups; Frobenius Morphisms and of the locus of smooth surfaces in JP3 whose Picard group is Kernels; Global Representation Theory; Infinitesimal Representation not Z. The first part of the book presents a brief survey of basic Theory; The Generalization of Certain Important Theorems on the concepts and results, together with some natural questions Cohomology of Vector Bundles on the Flag Manifold; q-Schur Algebras. arising in the theory. In the second part, a deformation-theoretic technique introduced by Griffiths and Harris is used to determine 1980 Mathematics Subject Classifications: 20G05, 14L15 the Picard group of a general surface in JP3 containing a fixed ISBN 0-8218-2501-1, LC 90-19310, ISSN 0065-9266 curve. This idea is generalized in the third part to families 168 pages (softcover), January 1991 Individual member $14, List price $23, of surfaces in higher projective spaces, namely complete Institutional member $18 intersection surfaces in Jpm and projectively Cohan-Macauley To order, please specify MEM0/439N surfaces in JID4. Contents Part 1: A brief survey of Noether-Lefschetz problems: The Noether-Lefschetz theorem; Components of the Noether-Lefschetz locus; Higher dimensional problems; Part II: The Picard group of a general surface containing a space curve: Some classical facts; The results; Part Ill: The Picard group of some general surfaces in JP>n: The generalization of Theorem 11.3.1 in JP>n+2 ; The Picard group of general residual surfaces in JPl4; The Picard group of general projectively EXTRAPOLATION THEORY WITH Cohen-Macaulay surfaces in JID4. APPLICATIONS 1980 Mathematics Subject Classifications: 14J05; 14C22, 14J25, 14M12 Bjorn Jawerth and Mario Milman ISBN 0-8218-2500-3, LC 90-19299, ISSN 0065-9266 (Memoirs of the AMS, Number 440) 112 pages (softcover), January 1991 Individual member $11, List price $19, Institutional member $15 In the last few decades, interpolation theory has become an To order, please specify MEM0/438N established field with many interesting applications to classical and modern analysis. In this book, the authors develop a general theory of extrapolation spaces, which is a complement to the QUANTUM LINEAR GROUPS familiar theory of interpolation spaces. Their results allow an extension of the classical extrapolation theorem of Yano to Brian J. Parshall and Jian-pan Wang scales of Banach spaces. They give applications to classical and (Memoirs of the AMS, Number 439) modern analysis, including extreme forms of Sobolev imbedding This volume begins with a general discussion of the theory theorems, rearrangement inequalities for classical operators, and of quantum groups. The authors view the theory as a natural Nash-Moser implicit function theorems.

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Contents 272 pages (hardcover), December 1990 Individual member $73, List price $122, The -and -methods; Extrapolation of real interpolation spaces; Institutional member $98 Some extensions: quasi-Banach spaces and modulars; Examples and To order, please specify STEKL0/187N applications; Monotonicity and local factorization; A general extrapolation principle. The following publication originally appeared in the September 1990 issue of Notices. It is being reprinted here with the corrected Table of 1980 Mathematics Subject Classifications: 46M35; 46E30, 46E35, 42B20 Contents. ISBN 0-8218-2502-X, LC 90-23642, ISSN 0065-9266 82 pages (softcover), January 1991 Individual member $11, List price $18, Institutional member $14 To order, please specify MEM0/440N FESTSCHRIFTIN HONOR OF 1.1. PIATETSKI-SHAPIRO, PARTS 1-11 S. Gelbart, R. Howe, and P. Sarnak, Editors THEORY AND APPLICATIONS OF (Israel Mathematical Conference Proceedings, Volume 2-3) DIFFERENTIABLE FUNCTIONS OF SEVERAL Contents VARIABLES. XIII PERSONAL REMINISCENCES: L. N. Vaserstein, I. I. Piatetski-Shapiro, my advisor and friend; S. Gindikin, Siegel domains etc.; PAPERS IN S. M. Nikol'skii, Editor REPRESENTATION THEORY: Stephen S .. Gelbart and Jonathan (Proceedings of the Steklov Institute, Volume 187) D. Rogawski, Exceptional representations and Shimura's integral for This collection of papers deals with investigations into the local unitary group U(3); Guy Henniart, Quelques remarques sur various problems in the theory of differentiable functions of les theoremes reciproques; Roger Howe, Another look at the local several variables and the application of this theory to differential {}-correspondence for an unramified dual pair; Herve Jacquet and equations and numerical methods of solution. Among the topics Joseph Shalika, Rankin-Selberg convolutions: Archimedean theory; D Kazhdan and G. Savin, The smallest representation of simply laced covered are: embeddings of various spaces of differentiable groups; Marie-France Vigneras, On formal dimensions for reductive functions and their dependence on the domain of definition, p-adic groups; J.-L. Waldspurger, Demonstration d'une conjecture de multipliers and bases in weighted spaces, various approximations dualite de howe dans /e cas p-adique, pi 2; PAPERS IN ANALYSIS, of smooth functions and their representation with the use of series NUMBER THEORY AND AUTOMORPHIC £-FUNCTIONS; J. Bourgain, and integrals, spectral problems related to ordinary differential The Riesz-Raikov theorem for algebraic numbers; Daniel Bump and operators with singular coefficients, solutions of regular partial Solomon Friedberg, The exterior square automorphic £-functions on differential equations with emphasis on their behavior at infinity, GL(n); Jun-ichi lgusa, A problem on certain p-adic zeta-functions; and a block method for approximate solution of the Laplace Stephen S. Kudla and Stephen Rallis, Poles of Eisenstein series and equation. L-functions; Robert P. Langlands, Rank-one residues of Eisenstein series; G. A. Margulis, Orbits of group actions and values of quadratic Contents forms at integral points; V. Milman, Spectrum of a position of a 0. V. Besov, Application of integral representations of functions to convex body and linear duality relations; S .. J. Patterson, On Ruelle's interpolation of spaces of differentiable functions and Fourier multipliers; zeta-function; llya Piatetskl-Shapiro, The converse theorem for Va. S. Bugrov, Summability of Fourier transforms and absolute GL(n); Gilles Pisier, Factorization of operator valued analytic functions convergence of multiple Fourier series; V. I. Burenkov, On estimates and complex interpolation; Kenneth A. Ribet, Multiplicities of Galois of Fourier transforms and convolutions in Nikof skiT-Besov spaces; E. representations in Jacobians of Shimura cuNes; P. Sarnak, On cusp A. Volkov, Development of the block method for solving the Laplace forms II; Atle Selberg, Remarks on the distribution of poles of Eisenstein equation for finite and infinite circular polygons; M. L. Gol'dman, On series; Freydoon Shahidi, On multiplicity of local factors; David traces of functions with restrictions on the spectrum; V. P. II' in, On Soudry, Automorphic forms in GSp(4); N. R. Wallach and R. Miatello, imbedding theory for spaces of functions with power smoothness Kuznestsov formulas for products of groups of R-rank one; Don Zagier, in domains; K. S. Kazaryan and P. I. Lizorkin, Multipliers, bases, Heeke operators and periods of modular forms. and unconditional bases in the weighted spaces Band SB; G. A. Karapetyan, On stabilization to a polynomial at infinity of solutions of a 1980 Mathematics Subject Classification: 11 , 22 class of regular equations; L. D. Kudryavtsev, On some questions of Volume2 spectral theory for differential equations whose coefficients have singular 327 pages (softcover), September 1990 points; P. I. Lizorkin and S. M. Nikol'skii, Spaces of functions of mixed Individual member $36, List price $40 smoothness from the decomposition point of view; Yu. V. Netrusov, Sets Institutional member $36 of singularities of functions in spaces of Besov and Lizorkin-Triebel type; To order, please specify ISMC/2N V. D. Stepanov, On a weighted inequality of Hardy type for derivatives of higher order; V. N. Temlyakov, Bilinear approximation and applications; Volume3 A. P. Terekhin, Approximation in Lv by spherical polynomials, and 339 pages (softcover), September 1990 Individual member $36, List price $40 differentiability classes of functions on the sphere. Institutional member $36 1980 Mathematics Subject Classifications: 26010, 30C20, 34B10, To order, please specify ISMC/3N 34B25,35A35,35B40,35H05,35J05,41A10,41A27,41A46,42A10, 42B10,42B25,46E35,46F12,47B38;26A15,26B40,30C30,35A40, Set of Volumes 2 and 3 35G15,41A10,42A10,42B15,44A35,46B15,46E30,46E35,46M35, Individual member $68, List price $76 47B10,49G05,65E05 Institutional member $68 ISBN 0-8218-3135-6, LC 68-1677, ISSN 0081-5438 To order, please specify ISMSET/2/3N

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

ORDINARY MEMBERS Donald J Brown, Saint Albans Joan A Denhart, Champaign, IL Raghavendra Rao Gudipudi, Stanley E Adamski, Toledo, OH School, Washington, DC Anthony J DiMilo, Nashville, TN Columbia, SC John 0 Adeyeye, Johnson C Smith Edgar D Brown Jr, Las Vegas, NV Mirko Mirko Djuric, Kranj, Annette M Guertin, Pittsfield, MA Univ, Charlotte, NC Rafael Bru, Univ Politecnica of Yugoslavia Mahrnut Guner, Landenberg, PA Robert Aebi, Schonenwerd, Valencia, Spain Stuart H Doole, Saint Hughs Shun Sheng Guo, Hebei Normal Switzerland Jarolim Bures, Prague, College, Oxford, England Univ, People's Republic of Mosaad A Alabdullatif, Champaign, Czechoslovakia Olivier Dubuisson, Hallines, France China IL Leigh Byron, South Junior High Scott G Duncan, HBJ Holt College Rajendra K Gupta, Alloy, WV Douglas Cecil Alessi, Hayward, CA School, Newburgh, NY Publishers of Canada, Toronto, Molly Gustin, Ojai, CA Martins Ferry, OH Paul Amala, Livermore, CA Ronald Calinger, Catholic Univ of Ontario Cecil W Gwinn, 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Bowers, Mantua, NJ Peter E Crouch, Arizona State Univ, Ronald W Golland, Chicago, IL People's Republic of China Roger P Bowers, New Hartford, NY Tempe Rony Gouraige, Scarsdale, NY Phillip E Johnson, Univ of North S R Brandell, Alexandria, VA Alisa R Crowe, Brea, CA John Joseph Graham, Duryea, PA Carolina at Charlotte Michael F Brenner, New York, NY Bhaskar Dasgupta, State College, PA Anastasia Grandbois, Denver, CO Terri A Johnson, Clemson Univ, SC Jeffrey F Brock, New Haven, CT William J Decker, Univ of Virginia, Libing Gu, Alhambra, CA John B Johnston, Salt Lake City, UT Deborah S Brown, Iowa City, lA Charlottesville Stephen Guattery, Pittsburgh, PA Harry E Jones, Salt Lake City, UT

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Ray L Jones II, Marietta, GA Gordon W MacDonald, Univ of Takumi Oyane, New York, NY John 0 Stevenson Jr, Brooklyn, NY Robert M Jones, Wegberg, Federal California Berkeley Hector D Pacheco, Bayamon, PR Kevin P Sugrue, Jacksonville, FL Republic of Germany Raymond E MacDonald, Costa Young Bin Paik, Univ of California Katarina Surla, Institute of Paul Joyce, Univ of Southern Mesa, CA Irvine Mathematics, Novi Sad, California, Los Angeles Godfrey N Madukwe, Dover, DE Barry Richard Paine, Gloucester, MA Yugoslavia Brian J Jue, EI Cerrito, CA S Dolores Malecka, Chestnut Hill Antonio L Pastor, Sao Paulo, Brazil Herman Sutton, Detroit, MI John D Jure, Laguna Hills, CA College, Philadelphia, PA Pimpa Permpoon, Chulalongkom Timothy Carl Swanson, Silver Shulim Kaliman, Wayne State Univ, Srinivas B Mandalika, Indian Univ, Bangkok, Thailand Spring, MD Detroit, MI Institute of Science, Bangalore, Brian F Peters. Bentley Systems, Janet W Tarjan, Bakersfield College, Patricia A Kan, Parma. Oh India Exton, PA CA Beverly K Kaniecki, New Abraham S Mantell, State Univ of Debomh A Peterson, Elburn, IL Retha E Taylor, Florissant, MO Kensington, PA New York. Stony Brook Giao V Pharn. Denver, CO William Scott Taylor, Mountain Pin-Che Kao, Madison, WI Russell E Mardon, Tallahassee, FL Sherry L Pietch, Elyria, OH HomeAFB, 1D Andrzej J Karwowski, West Virginia Eric Matsuoka, Kaneohe, HI Barbara L Power, Meadville, PA Haroon 0 Tejumola, Lincoln Univ, Univ. Morgantown Robert M Mattheyses, General Robert E Quaker, South Portland, PA Andrew R Kavalov, Yerevan Physics Electric Research & ME Joshua A Tempkin, Virginia Institute, USSR Development Center, Earl J Quick. Florence, SC Polytech Institute & State Univ, Mbuyi N Kazadi, Naperville, IL Schenectady, NY Poovendran Raadhakrishnan, Univ of Blacksburg Sanza T Kazadi, Naperville, IL Liliana Maxim Raileanu, Univ AI Michigan, Ann Arbor Clayton F Tenney, Buckhannon, WV Paul Keller, Fergus Falls, MN Cuza Iasi, Romania Florin Radulescu. Institute of Jeffrey A Thomas, Univ of Charles L Kennedy, Carlsbad, NM Peter J McCabe, McMaster Univ, Mathematics, Bucharest, Rochester, NY Debra Kilmartin, Hickory Comers, Hamilton, Ontario, Canada Romania Robert S Thompson, Skiatook, OK MI John J McCall, Univ of California Stephen R Rasmussen, Tulsa, OK I Made Tirta, Univ of New England, Yoshifumi Kimura, Los Alamos Los Angeles Kenneth W Regan, SUNY at Armidale, Australia National Laboratory. NM Michael P McCarren, Pittsburgh, PA Buffalo, NY Denise Marie Tobias, San Luis Charles N Kirks, Brooklyn Center, Patrice McCaulley, Longport, NJ R Spencer Rhodes, Bozeman, MT Obispo, CA MN Richard Michael McDaniel, Yuma, John P Rickert, Nashville. TN Gustavo Adolfo Torres Fernandes da Charles Klabosh, Jacksonville, FL AZ Don Ridgeway. North Carolina State Costa, Univ of Michigan, Ann Omar M Knio, Massachusetts John McElligott. Jacksonville, FL Univ, Raleigh Arbor Institute of Technology, Boyd Jay McGee, Pine Island, MN Lewis H Robinson. San Francisco. Ann N Trenk, Johns Hopkins Univ, Cambridge Gary W McKenzie, Los Angeles, CA Baltimore, MD Philip G Kong, West Hempstead, CA Todd D Rockhold, Teradata Walter E Trzcienski Jr. Univ of NY Frank William McNolty, Santa Clara, Corporation, El Segundo, CA Montreal, Quebec, Canada Robert J Kosanovich, Ferris State CA Carlos J Rodriguez, Univ of National Ricky Tsang, Brooklyn, NY Univ, Big Rapids, MI Henry N McNutt, Birmingham, AL Agraria, Lima, Peru Theoharis Tsenoglou, Kingston, RI ,Alexander V Kosyak. Academy of Michael A Messer, Kennesaw, GA Deborah G Rogers. Huntsville, AL Irvin E Vance, Michigan State Univ, Science of the Ukrain, Kiev, Deanna M Metzger, Fairfax, VA Terry Lee Rooker. Oregon Graduate East Lansing. MI USSR Frank P Michielsen, Clarkson Univ, Institute, Beaverton Francis H Varino, Elmwood Park, NJ Roger P Kovach, Bolinas, CA Potsdam, NY Ermi Roos. Miami Lakes. FL Ramon Ventoso, Miami, FL Ralitza Kovacheva, Bulgarian Robert E Miller Jr, Weatherford, TX Jeffrey Rufinus, Madison, WI John M Verosky, Western Academy of Science, Sofia Jeanne A Moenk, South Euclid, OH James J Rutledge. Valrico, FL Washington Univ, Bellingham Roger A Kuhlman, Staten Island, F R Fred Monaco, Sunland, CA Alan J Saalfeld, Arlington, VA Joseph S Verret, Decatur, GA NY Joseph John Monaghan, Monash Scott F Saccone, Abington, MA Eryk Vershen, Menlo Park, CA Laura Elizabeth Kustiner. Pullman, Univ, Victoria, Australia Abbas Sable, Ferdosi Univ of Yu P Virchenko, Academy of WA Vicente Montesinos Santalucia. Mashhad, Iran Sciences of the Ukrain, Yue-Kuen Kwok, Hong Kong Univ Valencia, Spain Mohamed A Salim, Univ of Kharkov, USSR of Science & Technology. Edward Moore, Memorial Univ Manchester, England Bruce Alan Wagner, Yorba Linda, Kowloon of Newfoundland, StJohn's, Adil M Sanaulla, Windsor, CT CA Lawrence A LaJohn, Univ of Canada Enrico Jose Santana, San Juan, PR Stephanie Arnold Walborn, Oley, Western Ontario, London, Moshe Morgenstern, The Hebrew Freddie Santiago, Univ of Puerto PA Canada Univ of Jerusalem, Israel Rico, Mayaguez Gagan Walia, Deal, NJ Javad Laali, Teacher Training Univ, Kay E Morrissey, Bellingham, WA Eugene K Sargent, Vallejo, CA Jean Walrand, Univ of California Tehran, Iran Orville B Mott, Salisbury, MO Wieslaw Sasin, Technical Univ of Berkeley Kelly D Lane, Annandale, VA Michael P Murphy, Chevy Chase, Warsaw, Poland Ting Fu Wang, Harbin Univ of Nina A Langdon, St Charles, IL MD Joseph J Schonbok, Seattle, WA Science & Technology, People's Michael W Lanstrum. Chardon, OH Paula R Myers, Crystal Springs, MS Daniel D Scott, Warsaw, OH Republic of China Karen L Lassiter, Steek-Vaughn Michael I Nadler, Vero Beach, FL William T Sellers, Plano, TX Xiaoji Wang, Australian National Company, Austin, TX Scott Mitchell Nichols, St Michael J Seymour, Concord, NH Univ, Canberra Robert Gregory Lavender, Petersburg, FL Ricky L Shepherd, Chapel Hill, NC Yi Wang, SUNY at Stony Brook, Blacksburg, VA Judith L Nowalsky, New Orleans, Alexander N Shoshitaishvili, Institute NY Choon-Ho Lee, Seoul, Korea LA of Control Sciences, Moscow, Lee S Wayand, Columbus, OH George J Leibman, Mount Kisco, John T O'Bryan, Rose-Hulman USSR Elias Wegert, Bergakademie Freibert, NY Institute of Technology, Terre Christopher P Silva, Hawthorne, CA Freiberg, Federal Republic of Mark R Liberzon, Moscow Institute Haute, IN Jeffrey P Smith, Galloway, OH Germany of Aviation Technology, USSR Joseph O'Malley, Schenectady, NY Michael F Smith, Sunnyvale, CA Daniel J Weiner, Ann Arbor, MI Patricia M Lightfoot, Rockford, IL Lyle E O'Neal, Hico, TX Steve Speer, Tucson, AZ Mark Alan Wells. Camp Hill, PA Cynthia S Lowe, Dallas, TX John T O'Neil, Princeton, NJ Michael D Squirlock, Old Forge, PA Paul F West, Mountain View, CA Wei-Min Lu, California Institute of Irene E Ober, Huntington, NY Charles Gregory St Pierre, Norwich, Richard K White, Jacksonville, FL Technology, Pasadena Jon Ochs, Eureka Software, CT Jacques Wilhem, Cambridge, MA Jaywood Lukens, Coral Gables, FL Lacrosse, WA Peter E Staab, Pittsburgh, PA Linda Kay Williams, Toledo, OH Morris C Lumpkin, Columbia, SC Boris Petrovich Osilenker, Moscow, Albert G Stanger, St Louis, MO S Robert Wilson, Little Rock, AR Javier Luque, Univ of Puerto Rico, USSR Gunnar F Stefansson, Pennsylvania Robert B Wood, Colorado Springs, Rio Piedras Valerie D Owen, Rosemont, PA State Univ, Altoona co

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

William A Wood, Indiana Univ, Vincent J Zimmer, Houston. TX Sang Man Kim Sociedade Brasileira de Matematica Bloomington Russell Frank Zimmermann, Vienna, Sung Eun Koh Aplicada e Computacional Rita J Woodfill, San Antonio, TX VA London Mathematical Society Augusto C Gadelha Vieira Marie A Wright. Danbury. CT Richard E Zippel, Ithaca, NY Timothy S Harris Sociedade Brasileira de Matematica Jike Wu, Beijing Univ, People's Brian Zuernd01fer, Ann Arbor. MI Republic of China Leonard Christopher G Rogers Severino T Melo Jane M Wyman. Western New Ronald Shaw Unione Matematica Ita Iiana England College, Springfield, Malaysian Mathematical Society Vittorio Coti Zelati MA Mohamad Rashidi Razali Mario Salvetti Ganquan Xie, SUNY at Stony RECIPROCITY MEMBERS Mathematical Society of Japan Vijnana Parishad of India Brook, NY Australian Mathematical Society Akira Koyama Heman! Kumar Pathak Gune Yen. Notre Dame, IN C H J Johnson Shui-Cheung Yip, New York. NY Masataka Nakamura Wiskundig Genootschap Deutsche Mathematiker-Vereinigung Yonghyun Yoon, Starkville, MS Masako Takahashi G J Heckman Xiu Yuan Yu, Hangzhou Teacher's e. V. Kohhei Yamaguchi Franz J Delvos College, People's Republic of Nigerian Mathematical Society China Jorg F Donig Afonya-a R Bestman Jung Yueh, Flushing, NY Freidrich Sauvigny John David Yuskewich, Aurora, CO Joerg W Wildeshaus Norsk Matematisk Foreningros Haakon Waadeland Tomasz Zak, Technical Univ, Gesellschaft fiir Angewandte Wroclaw, Poland Mathematics und Mechanik Societe Mathematique de France Boris G Zaslavaskii, Leningrad, Frederic Nataf NOMINEE MEMBERS USSR Siegfried Helbig Ali Zave, Mashhad, Iran Iranian Mathematical Society Sociedad Colombiana de Matenuiticas Indiana University at South Bend Boguslaw Zegarlinski, Ruhr Univ Akbar Hassani Luis Edo Giraldo Robert Yoder Bochum. Federal Republic of Israel Mathematical Union Sociedad Matenuitica Mexicana University of Ari:::ona Germany Joseph A Thas Fernandez Anaya Guillermo Yixia Lu Xue Shan Zhang, Xian Institute, Sociedad de Matematica de Chile People's Republic of China Korean Mathematical Society University of Chicago Pamela J Zietlow, West Lafayette, IN Sung Kyu Choi Cecilia S Yarur Martin Heinz Mann

Miscellaneous

Personals age of 62. He was a member of the Robert R. Stoll, Professor Emeritus Arjun K. Gupta, Professor and former Society for 36 years. at Cleveland State University, died on Chair of the Department of Mathe­ November 4, 1990, at the age of 75. Edwin E. Floyd, of the University matics and Statistics, Bowling Green He was a member of the Society for 51 of Virginia, died on December 9, 1990, State University, has been awarded the years. at the age of 66. He was a member of Olscamp Research Award in recogni­ tion of his outstanding scholarly achieve­ the Society for 15 years. Liang Zhongchao, of the Oceano­ ments. Cletus 0. Oakley, Professor Emer­ graphic Institute of Qingdao, died on itus at Haverford College, died on October 17, 1990. He was a member Deaths November 12, 1990, at the age of of the Society for one year. James H. Case, of the University of 91. He was a member of the Society Utah, died on October 23, 1990, at the for 62 years.

JANUARY 1991, VOLUME 38, NUMBER 1 57 INSTITUTIONS NOT SUBJECT TO U.S. LAWS may be required to execute and submit a copy of this form with the text of recruitment advertisements for the Notices (see Policy Statement below). Publication of recruitment advertisements not accompanied by the completed form may be delayed or denied.

Em~oymentru ______(Name of Institution) (City) (Country)

is offered without discrimination on grounds of age, color, race, religion, sex, or national origin.

(Signature) (Date)

Name (please print) (Title)

Please return this form to: Advertising Department Notices of the American Mathematical Society P.O. Box 6248 Providence, Rl 02940, U.S.A.

AMS Policy on Recruitment Advertising

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

58 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

SUGGESTED USES for classified advertising are positions available, books or lecture notes for ics, The University of Alabama, Box 870350, sale, books being sought, exchange or rental of houses, and typing services. Tuscaloosa, AL 35487-0350. UA is an AAIEOE. THE 1990 RATE IS $55.00 per inch on a single column (one-inch minimum), calculated from the top of the type; $25 for each additional 1h inch or fraction thereof. No discounts for multiple ads or the same ad in consecutive issues. For an additional $1 0 charge, announcements can be placed anonymously. Correspondence will be forwarded. Advertisements in the "Positions Available" classified section will be set with a minimum UNIVERSITY OF SOUTH ALABAMA one-line headline, consisting of the institution name above body copy, unless additional headline Department of Mathematics and Statistics copy is specified by the advertiser. Advertisements in other sections of the classified pages will be set according to the advertisement insertion. Headlines will be centered in boldface at no extra Several tenure-track positions starting Septem­ charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, ber 1, 1991. Appointment will be made at the Assistant Professor or possibly Associate Pro­ including lines and spaces within. Any fractional text will be charged at the next 1h inch rate. Ads fessor level. Applicants must have a Ph.D. in will appear in the language in which they are submitted. . Mathematics (earned or anticipated by 9/1/91 ). Prepayment is required of individuals but not of institutions. There are n.~ member _d~scounts for classified ads. Dictation over the telephone will not be accepted for class1f1ed advert1s1ng. Strong research potential and a commitment DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising to excellence in teaching are required. The Department. successful candidate for appointments as As­ U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, sociate Professor must also demonstrate sig­ religion or national origin. "Positions Available" advertisements from institutions outside the U. nificant research accomplishments. Preference s. cannot be published unless they are accompanied by a statement that the institution does will be given to areas complementing existing not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific research specialties. Salaries will be competi­ wording may be found near the Classified Advertisements in the January and July/August issues tive. Applications will be accepted until positions of the Notices. are filled, but should be completed by 1/31/91 SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians to ensure consideration. Please send detailed are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) resume and arrange to have three letters of in the U.S. and Canada for further information. recommendation sent to Dr. Suzanne McGill, SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, Chair; Department of Math/Stat; University of Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street, South Alabama; Mobile, AL 36688. An Equal Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not Opportunity/Affirmative Action Employer. required to do so. AMS FAX 401-455-4004.

POSITIONS AVAILABLE ence will be given to strong candidates whose ARIZONA research interests are compatible with those of our current faculty; this includes numeri­ UNIVERSITY OF ARIZONA Department of Mathematics ALABAMA cal POE/Scientific computation, mathematical physics, partial differential equations, nonlinear Tucson, Arizona 85721 analysis, dynamical systems, including topolog­ AUBURN UNIVERSITY The Mathematics Department at the University ical dynamics, differential topology and differ­ Department of Algebra, of Arizona is happy to announce several po­ ential geometry. Faculty members have access Combinatorics and Analysis sitions which will be available beginning Fall to the Alabama Super Computer (using a Sun 1991. Station and a T-1 line to a Cray X-MP/24). Rank Applicants in combinatorics are sought for a Tenure-track positions. Excellent research and salary will be subject to qualifications. Send tenure-track appointment at the rank of assis­ record or potential, strong commitment to as soon as possible a curriculum vitae, selected tant professor expected to be made beginning teaching required. Fields should complement reprints, and three letters of reference to Search September 1991. Preference given to candi­ but not duplicate existing department research Committee, Department of Mathematics, Uni­ dates in discrete optimization, coding theory, strengths in algebra, arithmetic geometry, com­ versity of Alabama at Birmingham, Birmingham, cryptology, extremal set theory, or association putational science, differential equations, dy­ AL 35294. UAB is an Affirmative Action/Equal schemes. namical systems, fluid mechanics, differen­ Opportunity Employer. Some temporary one-year appointments at tial geometry, mathematical physics, nonlinear the rank of assistant professor are also expected analysis, nonlinear science, number theory, and beginning September 1991 . Preference given probability. to applicants in differential equations. Those in Postdoctoral Fellowships (Res·earch As­ algebra, analysis, combinatorics, linear algebra sociate). Applicants with strengths in all ar­ or probability considered. Research interests THE UNIVERSITY OF ALABAMA eas compatible with department interests, but compatible with current faculty. Math Faculty Positions specifically geometry and mathematical physics Excellence required in both teaching and are encouraged to respond. In addition, special research for all positions. Send resume and The department expects to fill two, or pos­ Center of Excellence Awards in nonlinear optics arrange for at least three letters of recommen­ sibly more, tenure-track positions at the rank and fluid mechanics are available. dation to be sent to James Wall, 120 Math of Assistant Professor or higher beginning Au­ The Mathematics Department will also have Annex, Auburn University, AL 36849-5307. Mi­ gust 16, 1991. Areas for specific consideration several visiting positions for next year. norities and women are encouraged to apply. include mathematical statistics and topology. We encourage early application. Deadline Auburn University is an Equal Opportunity/ Outstanding candidates in other areas may date will be February 1, 1991 or whenever posi­ Affirmative Action Employer. also be considered. Applicants for Assistant tions are filled. Women and minority applicants Professor should have or expect to have a are especially welcome. Send applications to: Ph.D. or the equivalent by August 16, 1991. Alan C. Newell, Head Excellence in both teaching and research is Department of Mathematics THE UNIVERSITY OF required. Applications for visiting positions may University of Arizona ALABAMA AT BIRMINGHAM also be considered. Women and minorities Tucson, Arizona 87521, USA Department of Mathematics are particularly encouraged to apply. Send a The University of Arizona is an Affirmative curriculum vitae, reprints and/or preprints, and Action/Equal Opportunity Employer. Applications are invited for one or more antic­ at least three letters of recommendation to: ipated tenure or tenure-track positions. Prefer- Search Committee, Department of Mathemat-

JANUARY 1991, VOLUME 38, NUMBER 1 59 -···-··············-···----·······--··········-······--·-·············-"" ··············································-·-···------Classified Advertisements

UNIVERSITY OF ARIZONA and state departments of educations is desir­ OCCIDENTAL COLLEGE Chairman able. The minimum requirement for appointment Los Angeles, California Program in Applied Mathematics to this position is a Ph.D. in Mathematics or in Mathematics Education with substantial gradu­ Applications are invited for a tenure-track posi­ The University of Arizona invites nominations ate work in Mathematics. tion in the Department of Mathematics at the and applications for the position of Chairman of For further information and inquiries: assistant professor or associate professor level. the Interdisciplinary Program in Applied Math­ Dr. Robert F. Arnold, Chair Preference will be given to applicants with expe­ ematics, effective July 1, 1991. The Chairman Department of Mathematics rience and expertise in an applied mathematical will be responsible for administering the Pro­ California State University science, including differential equations, numer­ gram, which offers degrees at the masters and Fresno, CA 93740-0108 ical analysis, applied statistics, and computer doctoral level, and for fostering interdisciplinary All materials for the tenure track positions must science. research involving applications of mathematics. be in by Feb. 4, 1991. Excellence in teaching and substantial pro­ The Chairman of the Program reports directly fessional achievement are the major expec­ to the Vice President for Research. He or she tations. The normal teaching schedule is two will also hold a faculty appointment in the De­ courses during each of three ten-week terms; partment of Mathematics and/or other relevant new faculty members are released from one Departments. course during the initial year. Each faculty CALIFORNIA STATE UNIVERSITY, The Program is extremely active with a member receives a sabbatical term every three strong international reputation. There are more NORTHRIDGE years; some institutional support for extended leaves is available. than 80 graduate students currently enrolled Applications are invited for two tenure-track Occidental College is a selective private and the Program has 85 participating faculty positions at the rank of Assistant Professor for college of the liberal arts and sciences with members drawn from departments throughout the Fall of 1991. We will consider candidates 1650 undergraduate students, a college faculty the University. The University of Arizona is a in the areas of algebra, analysis, topology, of 133, and a mathematics faculty of nine. major research and teaching university of more applied mathematics or mathematical physics. Occidental is located in northeast Los Angeles, than 35,000 students. It is located in Tucson, Requirements include receipt of a Ph.D. by the a fifteen minute drive from downtown Los which offers many recreational and cultural op­ Fall of 1991 , demonstrated record or poten­ Angeles and ten minutes from Pasadena. portunities. The University has demonstrated a tial in research, and a strong commitment to Salary is competitive. An excellent benefits strong commitment to inderdisciplinary research teaching. Responsibilities include teaching 9- package includes a choice of health care plans, and the Program in Applied Mathematics plays 12 hours, depending on research and/or other tuition grants for children of faculty, and a a leading role in this endeavor. contributions. Send vita and three letters of mortgage subsidy program. Desirable qualifications include: recommendation to Mary Rosen, Hiring Com­ Completed applications, including a current 1 .Strong intellectual leadership. mittee Chair, Dept. of Mathematics, California resume, a statement of professional goals, and 2. Academic experience related to mathe­ State University, ·Northridge, Northridge, CA three letters of reference (at least one evaluat­ matics and its applications. 91330 by February 15, 1991 for full consid­ ing teaching peformance and potential) should 3. Experience in, and commitment to, grad­ eration. Women and minorities are especially be received by February 16, 1991. Address all uate student education. encouraged to apply. CSUN is located in a materials to Faculty Search Committee, Depart­ 4. Management and organizational skills. Northwestern suburb of Los Angeles and is in ment of Mathematics, Occidental College, Los The deadline for applications is February proximity to Cal. Tech., USC, and UCLA. An Angeles, CA 90041. 1, 1991 or whenever the position is filled. Equ~l Opportunity/Affirmative Action, litle IX, Occidental College is an Equal Opportunity/ Nominations and applications should be sent to: Section 504 Employer. Professor Alan C. Newell Affirmative Action Employer and encourages! Department of Mathematics applications from women and ethnic minorities. University of Arizona Tucson, AZ 85721 The University is an Equal Opportunity/Affirma­ tive Action Employer and welcomes women and CALIFORNIA STATE UNIVERSITY minority applicants. SAN BERNARDINO Department of Mathematics OCCIDENTAL COLLEGE Applications are being accepted for the position Director, Academic Excellence Program in of Assistant Professor or Associate Professor Mathematics and Chemistry, Occidental Col­ CALIFORNIA (tenure-track); a Ph.D. in mathematics edu­ lege. Faculty position to direct a workshop based cation with at least a bachelor's degree in excellence program for the first year classes in CALIFORNIA STATE UNIVERSITY mathematics is required. Successful candidates mathematics and chemistry, work closely with will be expected to teach twelve hours per the faculty in the two departments in coordi­ The Department of Mathematics will have two week, participate in scholarly activities, and nating the program's operation, advise math tenure track positions (one in Mathematics Ed­ help implement a new MAT program. Current and science students particularly minority stu­ ucation) and several Lecture positions available salary range is $30,276-$52,896 dependent dents concerning opportunities in science. The Fall 1991. The teaching load is 12 hours per upon qualifications and experience. Applicants successful candidates must have an advanced semester. should submit a letter of application, vita, three degree in mathematics or chemistry, possess Mathematics Position. Candidates with letters of recommendation and all transcripts. strong communication and administrative skills, successful university teaching experience and Applications received after February 1, 1991, and experience working with student groups in with a demonstrable interest in other schol­ cannot be guaranteed consideration. Materials a multicultural environment. To apply, submit a arly activities are preferred. Familiarity with should be sent to: letter of application, a resume, transcripts, and micro-computer use is desirable. The minimum Dr. John Sarli three letters of reference by 20 January 1991 requirement for appointment to this position is a Chair, Department of Mathematics to: Dr. Chris Craney, Chemistry Department, Ph.D. in Mathematics or Statistics. All special­ California State University Occidental College, 1600 Campus Road, Los izations within Mathematics will be considered. University Parkway Angeles, CA 90041. Occidental College is an Mathematics Education Position. Candi­ 5500 San Bernardino, California 92407 Affirmative Action/Equal Opportunity Employer dates with a record of scholarly activity and AN EQUAL OPPORTUNITY/AFFIRMATIVE AC­ and especially invites applications from women excellent teaching, or strong indication of inter­ TION, SECTION 504, TITLE IX EMPLOYER and minorities. est in both, are preferred. Experience in grant writing, participation in local and state mathe­ matics associations and experience with local

60 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POMONA COLLEGE UNIVERSITY OF CALIFORNIA criteria of the University of California determine Claremont, CA LOS ANGELES salary. To assure full consideration, applicants Department of Mathematics should send their curriculum vita and list of Pomona College seeks to hire a tenure-track publications and have at least three letters of Assistant Professor of Mathematics, preferably TEMPORARY POSITIONS recommendation sent to: with postdoctoral experience. Excellent candi­ (1) Two E. R. Hedrick Assistant Profes­ Professor David Rush, Chair dates from all fields of mathematics will be sorships. Applicants must show very strong Analysis Hiring Committee seriously considered, but preference will be promise in research and teaching. Salary Department of Mathematics given to applied mathematicians. Pomona Col­ $38,500. Three year appointment. Teaching University of California lege, a highly selective liberal arts college with load: four quarter courses per year, which may Riverside, CA 92521-0135 intellectually gifted students, is one of the Clare­ include one advanced course in the candidate's by January 22, 1991 . UCR is an Affirmative mont Colleges, which together provide an active field. Preference will be given to applications Action/Equal Opportunity Employer. professional community of over 30 mathemati­ completed by January 1, 1991. cians, an excellent research library, weekly (2) Subject to administrative approval, sev­ Mathematics Colloquia, research seminars, and eral Research Assistant Professorships in Com­ clinics in applied mathematics. We are looking putational and Applied Mathematics. Applicants UNIVERSITY OF CALIFORNIA, RIVERSIDE for someone who can continue Pomona's tra­ must show very strong promise in research Position in Geometric Analysis dition of excellent and innovative teaching and and teaching. Salary $38,500. One year ap­ Applications and nominations are invited for a who will actively participate in the mathematical pointment, probably renewable up to two times. tenured or tenure-track position in Geometric life of the Claremont Colleges. Teaching load: at most four quarlJr courses per Analysis beginning July 1, 1991 or later. The Applications are to be sent to: The Search year, which may include one advanced course position is at the rank of Assistant or Associate Committee, Department of Mathematics, Po­ in the candidate's field. Preference will be given Professor; candidates in all areas of geomet­ mona College, Claremont, CA 91711-6348. to applications completed by January 1, 1991. ric analysis will be considered. Excellence in Applications received by January 31, 1991, will (3) Subject to administrative approval, one research and teaching is required. Established be given full consideration. Applications must or two Assistant Professorships in the Program criteria of the University of California determine include a vita and letters of recommendation, in Computing (PIC). Applicants must show salary and rank. To assure full consideration, including letters evaluating teaching, graduate very strong promise in teaching and research, applicants should send their curriculum vita and school transcripts, and a description, written for preferably in the general area of Logic and list of publications and have at least three letters the non-specialist, of research accomplishments Computation. Teaching load: four quarter pro­ of recommendation sent to: and plans. Please let us know if you will be gramming courses and an advanced quarter Professor Bun Wong, Chair attending the January AMS meeting in San course of the candidate's choice per year. Two­ Geometric Analysis Hiring Committee Francisco. year appointment, possibly renewable once. Department of Mathematics Pomona College is an Affirmative Ac­ Salary range: $38,500-$44,000. Preference will University of California tion/Equal Opportunity Employer and encour­ be given to applications completed by February Riverside, CA 92521-0135 ages applications from minority candidates and 1,1991. by January 22, 1991 . UCR is an Affirmative women. (4) Subject to administrative approval, one Action/Equal Opportunity Employer. or two Lectureships in the Program in Com­ puting (PIC). Applicants must show very strong promise in the teaching of programming. M.S. in Computer Science or equivalent degree pre­ UNIVERSITY OF CALIFORNIA, RIVERSIDE ferred. Teaching load: five quarter programming Position in Algebra or Comblnatorics courses per year. One-year appointment, possi­ UNIVERSITY OF CALIFORNIA Applications and nominations are invited for LOS ANGELES bly renewable up to five times, depending on the needs of the Program. Salary is based on ex­ a tenure-track position in Algebra or Combi­ Department of Mathematics perience and begins at $32,676. Preference will natorics beginning July 1, 1991 or later. The position is at the Assistant Professor level; REGULAR POSITIONS IN PURE AND AP­ be given to applications completed by February candidates in all areas of Algebra and "Com­ PLIED MATHEMATICS 1' 1991. binatorics will be considered. Excellence in Subject to administrative approval, two reg­ (5) Subject to administrative approval, a research and teaching is required. Established ular positions in pure and applied mathematics. few Adjunct Assistant Professorships. One year criteria of the University of California determine The six specific search areas are as follows: appointments, probably renewable once. Strong salary. To assure full consideration, applicants 1) logic and mathematical computer science; research and teaching background required. should send their curriculum vita and list of 2) algebra (including algebraic geometry and Salary $33,900-$38,200. Teaching load: five publications and have at least three letters of representation theory), number theory and com­ quarter courses per year. recommendation sent to: binatorics; 3) geometry and topology (including (6) Subject to administrative approval, sev­ Professor Richard Block, Chair dynamical systems and geometric partial dif­ eral positions for visitors and lecturers. Algebra/Combinatorics Hiring ferential equations); 4) analysis and differential To apply, write to Alfred W. Hales, Chair, Committee equations (including Lie groups and mathemati­ Department of Mathematics, University of Cal­ Department of Mathematics cal physics); 5) statistics, probability and game ifornia, Los Angeles, CA 90024-1555. Attn: University of California theory; 6) applied and computational mathe­ Staff Search. UCLA is an equal opportu­ Riverside, CA 92521-0135 matics. Very strong promise in research and nity/affirmative action employer. by January 22, 1991 . UCR is an Affirmative teaching required. Positions initially budgeted Action/Equal Opportunity Employer. at the assistant professor level. Sufficiently out­ standing candidates at higher levels will also be considered. Teaching load: averaging 1.5 UNIVERSITY OF CALIFORNIA, RIVERSIDE courses per quarter, or 4.5 quarter courses Position in Analysis UNIVERSITY OF CALIFORNIA, per year. To apply, write to Alfred W. Hales, SANTA CRUZ Chair, Department of Mathematics, University Applications and nominations are invited for a Department of Mathematics of California, Los Angeles, CA 90024-1555. tenure-track position in Analysis beginning July Attn: Staff Search. UCLA is an equal opportu­ 1 , 1991 or later. The position is at the Assis­ The Mathematics Department at the Univer­ nity/affirmative action employer. tant Professor level; candidates in all areas of sity of California, Santa Cruz, expects to have classical and modern analysis (including prob­ two J. W. T. Youngs Assistant Professorships ability theory) will be considered. Excellence in in Mathematics available beginning with the research and teaching is required. Established academic year 1991-92. These newly estab-

JANUARY 1991, VOLUME 38, NUMBER 1 61 ...... _...... -...... _...... _.. ,_ .. ______...... __ ,...... ,_ ...... Classified Advertisements

lished Assistant Professorships in Mathematics Ph.D. is required. The average weekly teach­ are named in honor of our founding chairman, COLORADO ing load is 7 1/2 hours. Generous support for J.W.T. Youngs. In addition, we also expect faculty development such as travel, teaching to have several other visiting positions. We COLORADO STATE UNIVERSITY off-loads, and summer research. Send resume invite applications from qualified mathemati­ Director and 3 letters of reference to K. M. Rangaswamy, cians in all fields. Appointees will be expected Center for Science, Mathematics Chairman. Screening will begin on Feb. 1, 1991 to teach, pursue their research, and perform and Technology Education and continue until filled. some department or university service. The J.W.T. Youngs Fellow positions are available Colorado State University, Colorado's land­ for a two-year period with the possibility of an grant university, invites nominations and appli­ extension for a third year. The other visiting cations for the position of Director of the newly positions are available for periods ranging from formed Center for Science, Mathematics and one quarter to the full academic year, with a Technology Education (CSMATE). The Center UNIVERSITYOF NORTHERN COLORADO possible extension to a second year. J.W.T. serves as a focal point for research aimed Department of Mathematics Youngs Fellows will be appointed at the Assis­ at improvement and innovations in science, & Applied Statistics tant Professor level only, while the other visiting mathematics and technology instruction at all Greeley, C0-80639 positions may be at either the Assistant, As­ levels-elementary through university. The Di­ sociate, or Full Professor level, as appropriate. rector is expected to obtain extramural funding Applicants are sought for the following positions Minimum Qualifications: Ph.D. in Mathematics through contracts and grants supporting the listed below for the 1991-92 academic year. and a demonstrated excellence in research initiation and enhancement of programs that The department is a broad-based one which and teaching or potential for excellence. Salary will address the needs and aspirations of K-16 includes components of Mathematics, Statistics, Range: $33,900 - 58,300 commensurate with science, mathematics and technology students, Computer Science, Computer Education, and qualifications and experience. Available: Fall teachers and administrators. The Director must Mathematics Education and consisting of 21 1991 . Application Deadline: January 15, 1991. have a strong interest in discipline-based sci­ full-time faculty. We offer advanced degrees in Please refer to position #T90-19. UCSC is an ence, mathematics and technology education mathematics (M.A. or M.A. with emphasis in affirmative action/equal opportunity employer. with teaching experience at the undergraduate teaching), Educational Mathematics (Ph.D.) and Applicants should send vitae, three letters of and graduate levels, evidence of successful Applied Statistics- (M.S. and Ph.D.). reference, and information about their teaching fund-raising for projects and experience in pro­ The University of Northern Colorado is a and research experience to: gram administration. The Director must provide senior public institution whose major role and leadership for and have the ability to work with mission is teacher training. The University Harold Widom, Chair diverse constituencies in the educational arena enrolls approximately 10,000 students and em­ Recruitment Committee and have experience in coordinating programs ploys about 450 faculty. Greeley is located 50 Mathematics Department across educational institutions and government miles north of Denver, 50 miles east of Rocky University of California agencies. An earned Doctorate is required. Mountain National Park, and has a population Santa Cruz, CA 95064 Interested parties should request a full job of 62,000. description. Applications should include a letter Position #21487 - Chair of Department. of interest, a current resume' and the names, The department of Mathematics and Applied addresses and telephone numbers of three Statistics at UNC is seeking a new chair for full­ references. The closing date for applications time, tenure-track position. We are accepting is January 31 , 1991 . The deadline may be applications from individuals in any of the above extended if a suitable candidate is not found. fields (Mathematics preferred) to serve as chair The position is available July 1, 1991 or sooner. beginning August 1991. The position carries a Applications and nominations should be sent to: three-credit hour teaching load in addition to Dr. Thomas A. Gorell, Chair the administrative duties. The candidate sold be CSMATE Director Search Committee willing to act as chair for at least three years. College of Natural Sciences, C-138 The successful candidate should have an Clark established research and teaching record and Colorado State University should qualify for an appointment at the Asso­ UNIVERSITY OF SOUTHERN CALIFORNIA Fort Collins, CO 80523 ciate or Full Professor level. Some administra­ Los Angeles, California Fax (303) 491-0528 tive experience and success in obtaining grants CSU is an EEO/AA employer. E.O. Office: 314 are desirable. The Department of Mathematics wishes to fill Student Services Bldg. Application deadline February 1, 1991. Send several tenure-track Assistant Professorships letter of application, curriculum vitae, and three and possibly tenured positions at Associate letters of recommendation to address below. Professor and Professor. Visiting positions (at Position #20938 - Senior Associate/Full Pro­ all levels) and postdoctoral appointments will UNIVERSITY OF COLORADO AT fessor Visiting Position. We are looking for es­ also be available. The department is particularly COLORADO SPRINGS tablished individuals with solid teaching record interested in applicants who work in the areas Department of Mathematics in any of the fields listed above who would like of: Algebraic Geometry, Analysis, Geometry, Colorado Springs, CO 80933-7150 the opportunity to share their ideas with us. Number Theory, Numerical Analysis, Partial For this position, the University is seeking a Differential Equations, and Statistics, but strong Applications are invited for a tenure-track Assis­ senior level person to collaborate with faculty candidates in all areas are encouraged to apply. tant Professor position for Fall 1991. Preferred projects that might lead to outside funding. The Applicants for assistant professorships must area of research interest: probability theory. position is for the full academic year with a show strong research promise. Applicants for However, consideration will also be given to salary commensurate with professional rank. senior positions must have an outstanding exceptionally strong candidates if their area There is a possibility of extension. The teaching record of research and scholastic achievement. of expertise is consistent with present re­ load is negotiable. Address inquiries to: Chair of Appointments search interests: harmonic analysis, computer Applicants should possess a Doctorate in Committee, Department of Mathematics-ORB vision and algebra. Current faculty expertise one of the fields represented in the department, 155, University of Southern California, Los in probability theory includes perculation the­ and a solid record of publication in area of . Angeles, CA 90089-1113. USC is an Equal Op­ ory, population genetics and theory of large specialization and educational mathematics. portunity/Affirmative Action Employer. Women deviations. Applicants should have significant Send a letter of application, curriculum vitae, and minorities are especially encouraged to research accomplishments or exceptional re­ and three letters of recommendation to address apply. search promise and evidence of good teaching. below. Initial screening will begin February 1,

62 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

1991. Applications will be considered until the we will be particularly interested in algebraists, applications is March 1 , 1991 . position is filled. logicians, and persons whose research inter­ The University of Delaware is an equal op­ Position #20953 - Assistant Professor of ests might intersect with current department portunity employer and invites and encourages Mathematics. Tenure-track position. Candidate members' areas: complex analysis, functional applications from women and minorities. will be expected to teach a variety of un­ analysis, geometry, graph theory, combinatorics, dergraduate and graduate level courses in and mathematical statistics. Requirements for mathematics. Additionally, the candidate will be the position: Ph.D. in mathematics, evidence of expected to take an active teaching/research teaching excellence at the undergraduate level, DISTRICT OF COLUMBIA role in the department's new Ph.D. program in indications of promise in research, and interest Educational Mathematics. Advising, committee in curriculum development. THE AMERICAN UNIVERSITY work, and continued scholarship is essential. Applicants should send a c.v., three letters Faculty Vacancies in Teaching load will be nine hours per week. of reference (at least one of which addresses Mathematics and Statistics Applicants should possess a Ph.D. in Math­ teaching) and a statement of teaching and Assistant Professor position ematics from accredited institution. Send a letter research interests to available for 1991-1992 of application, curriculum vitae, graduate tran­ Search Committee Chair scripts, and three letters of recommendation Dept. of Mathematics One tenure-track position in mathematics. Ad­ to address below. Initial screening will begin Trinity College ditional temporary positions in mathematics February 1, 1991. Applications will be consid­ Hartford, CT 061 06 and/or statistics may also become available. ered until the position is filled. No decision will be made prior to January Qualifications: Ph.D. in mathematics and Position #21341 - Assistant Professor of 21 after which the position may be filled at any evidence of strong teaching and scholarship Mathematics. This position can be held for one time. is required. Those with experience in actuarial to three years on mutually agreeable basis. Representatives of the Department will at­ science are especially invited to apply. Candidate is expected to teach a variety of tend the employment register at the joint Annual Responsibilities: Undergraduate and gradu­ undergraduate and graduate level courses in Meetings in San Francisco in January 1991. ate teaching, scholarship, student advising, and mathematics. Advising, committee work, and Trinity College is an Equal Opportunity/Affir­ university service. continued scholarship· is essential. Teaching mative Action Employer. Women and members Competitive salary, commensurate with qual­ load will be 12 hours per week. of minority groups are especially encouraged to ifications and experience. Position subject to Applicants should possess or expect to re­ apply. final budgetary approval. Send c.v. and names ceive a Ph.D. in Mathematics from accredited of three references. Preference given to appli­ institution by August 1991. Send a letter of ap­ cations received by March 1 , 1991 . plication, curriculum vitae, graduate transcripts, Professor Robert W. Jernigan and three letters of recommendation to address Chair, Department of Mathematics and below. DELAWARE Statistics Send all applications, etc. with position The American University number to: UNIVERSITY OF DELAWARE 4400 Massachusetts Avenue, N.W. Dr. Don Searls/Chair, Search Department of Mathematical Sciences Washington, D.C. 20016-8050 Committee Chairperson An EEO/AA University; minorities and women Dept. of Mathematics & Applied candidates are encouraged to apply. Statistics The University of Delaware invites applications University of Northern Colorado for the position of Chair of the Department of Greeley, CO 80639 Mathematical Sciences in the College of Arts THE GEORGE WASHINGTON UNIVERSITY and Science. Applicants for the position should have an outstanding record of research and Department of Mathematics scholarly activity and should have the skills Washington, D.C. 20052 UNIVERSITY OF SOUTHERN COLORADO to chair a department with major research, Tenure-track assistant professorships available Department of Mathematics teaching, and service responsibilities. Pueblo, CO 81001-4901 beginning August 1991, pending funding, for The Department has 40 regular faculty posi­ applicants in Geometry/Topology, Applied Math­ tions and an active graduate (Ph.D.) program. Applications are invited for at least one tenure­ ematics, Ergodic Theory & Dynamics, or Mathe­ Programs include pure mathematics, applied track assistant professor position for Fall 1991. matical Logic. Other outstanding candidates will mathematics, and statistics. The Department is Doctorate in Mathematics in numerical analysis, also be considered. Strong research potential unusual in its strength and commitment to ap­ optimization, modeling, or combinatorics is re­ and a commitment to excellence in teaching plied mathematics and related areas of analysis. quired. Evidence of commitment to teaching ex­ required. Send resume and three letters of The University has good computing and library cellence necessary. Active research desirable. recommendation to: Irving J. Katz, Chairman, facilities, and in addition, the Department has a Send letter of application, resume, graduate Department of Mathematics, The George Wash­ number of workstations and two Sun 3/180 file transcripts, and three letters of reference to ington University, Washington, D.C. 20052, by servers. The University of Delaware is located in Search and Screen Committee. Evaluation of February 1, 1991. The George Washington applications will begin 7 February 1991 and the pleasant university town of Newark midway University is an Equal Opportunity/Affirmative between Washington, DC and New York City. continue until position is filled. USC is an AAIEO Action Employer. employer. Applicants should submit a resume, the names and addresses of three references, and a letter of interest to (or contact) Prof. B.F. Caviness FLORIDA CONNECTICUT Chair: Search Committee for Mathematics FLORIDA ATLANTIC UNIVERSITY TRINITY COLLEGE Department of Computer and Information Sciences Florida Atlantic University invites applications The Department of Mathematics at Trinity Col­ 103 Smith Hall for three Assistant Professorships in the De­ lege invites applications for a tenure-track University of Delaware partment of Mathematics for August 1991. position, at the rank of assistant professor, Newark, DE 19716 Candidates are expected to show a strong beginning in the academic year '91-'92. The Phone: 302/451-8234 commitment to undergraduate teaching and normal teaching load is five semester-courses email: [email protected] promise in research. Candidates must have a per year ("3/2"). While we will be happy to re­ The position will be available beginning Septem­ Ph.D. in Mathematics or must complete a Ph.D. ceive applications from those with any specialty, ber 1, 1991. The deadline for the receipt of in Mathematics by August 1991 . Salary is com-

JANUARY 1991, VOLUME 38, NUMBER 1 63 Classified Advertisements

petitive. Areas of research in the department and transcript to Leonard J. Lipkin, Chairper­ science required; Ph.D. or Ed.D. in mathematics include Algebra, Analysis and Combinatorics. son, Department of Mathematics and Statistics, education preferred. Primary interest in math­ The department instituted a Ph.D. program in University of North Florida, 4567 St. Johns ematics education required. One Tenure- Track 1988 and has grown substantially over the last Bluff Road South, Jacksonville, Florida 32216. Position: M.A. or M.S. in computer science or a few years. Applicants from all research fields In order to receive full consideration, appli­ mathematical science required; Ph.D. or M.S. in are invited. cants are advised to have their files completed computer science preferred. One Tenure~ Track Applications, vita, list of publications and by February 15, 1991. The University is an Position: M.A. or M.S. in a mathematical science three letters of recommendation should be sent affirmative action/equal opportunity employer and experience required. Primary duties will in­ to: and encourages applications from women and clude teaching freshman-level mathematics. A Professor S.C. Locke, Chairman minorities. second position is possible. Several Temporary Hiring Committee Instructor positions may be added in the area of Department of Mathematics teaching freshman-level mathematics. Master's Florida Atlantic University degree in mathematics required. NEW COLLEGE OF USF Boca Raton, Florida 33431 MATHEMATICS/DEVELOPMENTAL STUD­ Telephone: (407) 367-3350 Tenure-track position in Mathematics starting IES: Three tenure-track (no time limit) posi­ Bitnet: LockeSC@servax Fall, 1991, pending budgetary approval. Duties tions. Master's degree required; two to three Application deadline is February 28, 1991. consist of two classes per semester, plus indi­ years' teaching experience preferred. Duties Florida Atlantic University is an Affirmative Ac­ vidual or group tutorials and supervising senior will include teaching developmental studies and tion/Equal Opportunity Employer. Women and theses (these are required for all students). New freshman/sophomore-level mathematics courses minorities are especially encouraged to apply. College is a small, highly selective liberal arts Send letter of application, vita, unofficial tran­ college with a studenVfaculty ratio of 10:1. We scripts of all college work, evidence of dedica­ have a system of contracts and written eval­ tion to outstanding teaching and three letters uations rather than grades. A report released of reference or placement file to: Prof. Susan FLORIDA INTERNATIONAL UNIVERSITY by the Independent Colleges Office ranks us Groover, Landrum Box 8093. Deadline: January The Department of Mathematics announces sixth in productivity of Ph.D.s for students who 14, 1991. tenure-track positions beginning August 1991. graduated between 1970 and 1982. Continuing Starting date is: September 1, 1991. The names of applicants and nominees, These positions are usually at the beginning faculty in Mathematics are an Analyst, an Al­ resumes, and other general non-evaluative in­ Assistant Professor level. Candidates must gebraisVComputer Scientist, and an Algebraic have a Ph.D. in Mathematics and a commitment Geometer. Women and minority candidates are formation are subject to public inspection under the Georgia Open Records Act. Georgia South­ to research and quality teaching. Qualified especially encouraged to apply. Submit appli­ ern is an Affirmative Action, Equal Opportunity candidates in all areas of Mathematics will be cation by January 31 with vita, three letters Institution. condisered. of recommendation, and a statement on your Teaching load consists of no more than teaching philosophy to Tony Horowitz, Division five 3-credit courses per academic year. Send of Natural Sciences, New College, 5700 N. Tamiami Trail, Sarasota, FL 34243-2197. New resume and arrange for 3 letters of recommen­ KENNESAW STATE COLLEGE dation to be sent to: Recruitment Committee, College of the University of South Florida is an AAEO employer. Mathematics Department Department of Mathematics, Florida Interna­ P.O. Box 444 tional University, Miami, FL 33199. Marietta, GA 30061 Florida International University is an Equal Opportunity/Affirmative Action Employer. It is At least one tenure-track position in Mathemat­ a member of the State University system of GEORGIA ics at the level of Assistant Professor beginning Florida, with approximately 22,000 students. GEORGIA INSTITUTE OF TECHNOLOGY in September 1991. A Ph.D. is required with a The department offers bachelor's and master's strong commitment to undergraduate education degrees. The Center for Dynamical Systems and Non­ as well as an interest in scholarly activities. Sta­ linear Studies expects to have some long and tistics preferred; other areas considered. Salary short-term visiting positions beginning Fall1991. and rank are competitive and commensurate These positions are in nonlinear differential with credentials and experience. The College UNIVERSITY OF NORTH FLORIDA equations, dynamical systems, computational is located in Northwest Metro Atlanta, and en­ Department of Mathematics and Statistics methods and related areas. In addition to a rolls over 10000 day and evening students in Applications are invited for anticipated tenure resume and at least three letters of reference, undergraduate and graduate programs. The de­ track and visiting positions beginning August candidates should send a summary of future partment of Mathematics has 19 full-time faculty research plans to Professor Jack K. Hale, Di­ and shares 6 others with the Department of 1991. Candidates must have the Ph.D. in Math­ ematics or Statistics, a record of excellence rector, CDSNS, Georgia Institute of Technology, Computer Science. Send resume and a list of in teaching and a commitment to continuing Atlanta, GA 30332-0190. Georgia Tech, a mem­ three references to Dr. Christopher Schaufele, Chair, Search Committee. Position will remain scholarly activity. A visiting teaching position ber of the University System of Georgia, is an may also be available for a person with the MS Equal Opportunity/Affirmative Action Employer. open until filled, but to ensure consideration, apply before Feb. 1, 1991. AA/EOE. in Mathematics or Statistics. The Department offers the BA and BS in Mathematics and in Statistics and the MA with tracks in Mathe­ GEORGIA SOUTHERN UNIVERSITY matics, Statistics, and Computing. The regular Department of UNIVERSITY OF GEORGIA faculty of 15 members is active in a variety of Mathematics/Computer Science Department of Mathematics areas of Mathematics and Statistics including Statesboro, GA 30460 Athens, GA 30602 functional analysis, probability, numerical analy­ sis, applied mathematics, differential equations, MATHEMATICS/COMPUTER SCIENCE: Send The department has tenure-track positions avail­ number theory, low-dimensional topology, ap­ letter of application, vita, unofficial transcripts able for the 1 991-92 academic year at the plied statistics, biostatistics, and use of technol­ of all college work, evidence of dedication assistant professor level. In addition there may ogy in the curriculum. Preference will be given to outstanding teaching and three letters of be some visiting positions available. The salary to applicants in these areas, though the field reference or placement file to: Prof. Elizabeth will be commensurate with the applicant's abil­ is open. The University, a growing institution Hardy, Landrum Box 8093. Deadline: February ities and experience. The principle requirement in the State University System of Florida, has 1, 1991. is excellence in teaching and research. Some more than 8000 students currently enrolled. One Tenure- Track Position: Assistant or As­ preference will be given to areas in which the Send resume, three letters of recommendation, sociate Professor, doctorate in a mathematical department is already well represented. Send

64 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... - ...... ------··········-···-- Classified Advertisements

curriculum vitae and four letters of recommen­ NORTHWESTERN UNIVERSITY sibilities may include introductory classes as dation to Richard E. Bouldin Head (address Department of Mathematics well as courses related to specialty area. Salary above) by January 15, 1991. UGA is an Equal 2033 Sheridan Road, negotiable. Send resume and three letters of Opportunity/Affirmative Action Employer. Evanston, Illinois 60208-2730 recommendation to Dr. Hubert J. Ludwig, Fac­ ulty Search Committee, Department of Mathe­ Applications are invited for one or more tenure­ matical Sciences, Ball State University, Muncie, track positions starting September 1991 . Al­ IN 47306. Review of applications will begin ILLINOIS though priority will be given to young, excep­ December 10, 1990 and continue until position tional research mathematicians (no more than is filled. DEPAUL UNIVERSITY several years after Ph.D.), more senior candi­ Ball State University Practices Equal Oppor­ Department of Mathematical Sciences dates with very exceptional credentials may be tunity in Education and Employment. considered for a tenured position. Fields of inter­ Applications are invited for a tenure-track posi­ est of the department include Algebra, Analysis, tion at the assistant professor level beginning Dynamical Systems, Probability, Partial Differ­ in September 1991. A Ph.D. in Mathematics is ential Equations, and Topology. Northwestern required. We will consider strong candidates in is an affirmative action, equal opportunity em­ any field of research. ployer committed to fostering a diverse faculty, DEPAUW UNIVERSITY DePaul University is primarily an undergrad­ so women and minority candidates are espe­ uate institution. The Department of Mathematics cially encouraged to apply. Candidates should Department of Mathematics has undergraduate and graduate programs in arrange that at least three letters of recommen­ and Computer Science Mathematics, Applied Mathematics, and Mathe­ dation be sent to Chair, Personnel Committee, Applications are being accepted for a tenure­ matics Education. Strong commitment to teach­ Department of Mathematics, Northwestern Uni­ ing is essential. The official teaching load is nine track position in mathematics. Requirements versity, Evanston, Illinois 60208. In order to include a Ph.D. in mathematics (any specialty), quarter courses/year, but a reduction to seven receive full consideration, applications should quarter courses/year for research is customary. excellence in teaching, achievement or promise be received by February 15, 1991. Hiring is in research, and commitment to the goals of Applicants should send a curriculum vitae contingent upon eligibility to work in the United a liberal arts college. Duties include teaching and 3-4 letters of recommendation, at least one States. of which pertains to teaching, to: Hiring Com­ twelve hours per week, maintaining scholarship mittee, Department of Mathematics, 2219 Noth or research, and service to the University Kenmore, Chicago, Illinois, 60614. Applications through advising, committee work, and the like. from women and members of minority groups NORTHWESTERN UNIVERSITY Applicants should send a letter indicating are encouraged. AFA/EOE. Mathematics Department interest in teaching in a liberal arts setting, 2033 Sheridan Road, transcripts, vita, and three letters of recom­ Evanston, Illinois 60208-2730 mendation with at least one addressing the applicant's demonstrated teaching ability to Un­ ILLINOIS STATE UNIVERSITY The Mathematics Department will sponsor an derwood Dudley, Mathematics Department, De­ Emphasis Year in algebraic topology, cohomol­ Pauw University, Greencastle, Indiana 46135. MATHEMATICS DEPARTMENT, ILLINOIS ogy of groups, and related topics. This program Women and minorities are encouraged to apply. STATE UNIVERSITY. Illinois State University will include 2-year Assistant Professorship po­ Applications will be accepted until the posi­ announces a tenure-track position in mathemat­ sitions starting September 1991 and possible tion is filled. DePauw is an Affirmative Action, ics at the assistant or associate professor level. visiting positions for more senior mathemati­ Equal Opportunity Employer. Applicants should have a Ph.D. by August 1991 ; cians for part or all of the academic year. a research interest in the areas of applied prob­ Applications should be sent to Prof. Mark ability, combinatorial optimization, graph theory, E. Mahowald at the department address and operations research, or statistics; and a strong include a curriculum vitae and three letters research record or potential. Candidates should of recommendation. In order to ensure full also have sufficient background to teach a consideration, an application must be received variety of undergraduate mathematics courses, by February 15, 1991. INDIANA STATE UNIVERSITY and be committed to quality teaching. To apply Northwestern University is an Affirmative Chairperson send vita, three letters of recommendation and Action/Equal Opportunity employer. Hiring is Department of Mathematics official transcripts by February 1 to: Dr. Jane 0. contingent upon eligibility to work in the United and Computer Science Swafford, Department of Mathematics, Illinois States. State University, Normal, IL 61761. AA/EEO The Department of Mathematics and Com­ Employer. puter Science, Indiana State University, invites applications for the position of Chairperson. Ap­ INDIANA plicants should have a doctorate in Mathematics or Computer Science, a record of successful NORTHERN ILLINOIS UNIVERSITY BALL STATE UNIVERSITY teaching and research, and a commitment to Department of Mathematical Sciences Muncie, Indiana promoting research, teaching, and other schol­ arly activities. Applicants should also possess Anticipated assistant professorship with a spe­ Mathematics the leadership skills necessary to chair a large cialization in differential or algebraic geometry Tenure-track positions anticipated August 1991. department which has diverse teaching and or topology. Ph.D. or equivalent and strong Ph.D. in pure or applied mathematics required. research responsibilities. The Computer Sci­ potential in research and teaching required. Specialty is open, though preference will be ence area is undergoing active development, Preference will be given to candidates who given to candidates whose research interests so familiarity with Computer Science curricular have two or three years experience and an are compatible with those of the present faculty. issues is desirable. ongoing research program. Application (vita) Present faculty research interests include differ­ The Department offers B.S. and B.A. de­ plus three letters of reference and description ential equations, numerical analysis, computa­ grees in Mathematics, Mathematics Education of rese~rch program should be sent to: Ge­ tion, combinatorics or combinatorial geometry, and Computer Science, as well as M.S. and ometry/Topology Position; c/o Professor William low-dimensional or general topology. Appoint­ M.A. degrees in Mathematics and Mathematics D. Blair, Chair, Department of Mathematical ment at assistant professor level. Successful Education. It is developing an M.S. degree in Sciences, Northern Illinois University, DeKalb, college or university level teaching level re­ Computer Science. IL 60115 by February 15, 1991. EO/AAE. quired. Publications and/or evidence of other Salary and rank are commensurate with scholarly productivity desired. Teaching respon- qualifications and experience. Please send a

JANUARY 1991, VOLUME 38, NUMBER 1 65 Classified Advertisements

letter of application and vita, and have three date: January 15, 1991. Late applications will letters of recommendation sent to: be considered until positions are filled. IOWA Chairperson Search Committee IUPUI is an Affirmative Action/Equal Oppor­ Department of Mathematics and tunity Employer. Women and minority candi­ IOWA STATE UNIVERSITY Computer Science dates are encouraged to apply. The Department of Mathematics of Iowa State Indiana State University University invites applications to fill three tenure­ Terre Haute, IN 47809 track positions for the 1991-92 academic year. The application deadline is February 1, 1991 . Start up funds will be available for the success­ Applications received after this date cannot be INDIANA UNIVERSITY-PURDUE ful applicant for each position. The areas of guaranteed consideration. U.S. citizenship or UNIVERSITY AT INDIANAPOLIS (IUPUI) interest and the level are (1) a senior position in eligibility for U.S. employment will be required. Department of Mathematical Sciences numerical analysis or computational mathemat­ Indiana State University is an Equal Opportunity/ at ics, (2) an entry level position in control theory Affirmative Action Employer. The Department of Mathematical Sciences IUPUI is seeking applicants for a tenure-track and (3) an entry level in mathematics education. position in Mathematics Education (at the Assis­ The successful candidate for each position is tant Professor level) to begin in August, 1991 . expected to have a strong interest in teaching Applicants must have an earned doctorate by at both the graduate and undergraduate level the starting date, a strong background in an and maintain an active research program in area of mathematics, and a serious commit­ his or her chosen area. In addition, candidates INDIANA STATE UNIVERSITY ment to research and teaching. Responsibilities for the senior position are expected to have Department of Mathematics include teaching undergraduate and graduate a strong research record, be willing to build and Computer Science level courses in mathematics and mathematics a strong research group in numerical analysis for or computational mathematics, to interact with Applications are invited for one or more tenure­ education, conducting inservice workshops in colleagues in related areas and to seek outside track positions starting in the fall semester of teachers in mathematics, and participating 9-12 funds for their research. 1991-92. The Department currently has twenty­ research and curriculum development in We will begin screening applications De­ five faculty. It has bachelor degree programs and post-secondary levels. growing comprehensive cember 15, 1990. However we shall continue to in Mathematics, Mathematics Education, and IUPUI is a rapidly The accept applications until the positions are filled. Computer Science. It also has master degree urban university with over 28,000 students. to Iowa State University is an Affirmative Ac­ programs in Mathematics and Mathematics Ed­ department offers programs of study leading de­ tion/Equal Opportunity Employer. Women and ucation. The Department is especially interested Purdue University B.S., M.S., and Ph.D. salaries minorities are encouraged to apply. in applicants with doctoral degrees in Statistics grees. The university offers competitive fringe benefits. Send Applications and three letters of recommen­ or Computer. Science, but all specialties are and provides excellent dation should be sent to Howard A. Levine, encouraged to apply. resume and three letters of recommendation Department of Chair, Department of Mathematics, Iowa State Please send a letter of application, vita, and to Prof. Bart S. Ng, Chair, 38th University, Ames, Iowa 50011 . have three letters of reference sent to: Mathematical Sciences, IUPUI, 1125 E. Chairperson Street, Indianapolis, IN 46205-2810. Closing applications will Department of Mathematics and date: January 15, 1991. Late be considered until positions are filled. Computer Science UNIVERSITY OF NORTHERN IOWA Indiana State University IUPUI is an Affirmative Action/Equal Oppor­ minority candi­ Assistant Professor of Mathematics Terre Haute, IN 47809 tunity Employer. Women and Interviews will begin in March 1991 . Indiana dates are encouraged to apply. We have a new tenure-track position for an State University is an Equal Opportunity/Affir­ assistant professor to aid in teaching our general mative Action Employer. education courses and to support our majors students. Applicants should have INDIANA UNIVERSITY AT SOUTH BEND and graduate a doctorate in a core area of mathematics and be Dept. of Mathematics committed to quality teaching and scholarship and Computer Science at a comprehensive university. Applications are invited for one or more tenure­ Appointment is for the academic year begin­ INDIANA UNIVERSITY-PURDUE track positions in mathematics at the assistant ning in August 1991. Salary is highly compet­ UNIVERSITY AT INDIANAPOLIS (IUPUI) professor level with a starting date of August, itive; fringe benefits are excellent. Application Department of Mathematical Sciences 1991. Applicants must have Ph.D. in math­ screening begins February 15, 1991. For more ematics or show substantial progress toward information contact Philip East, Mathematics The Department of Mathematical Sciences at completion and should have a commitment to and Computer Science, University of Northern IUPUI is seeking applicants for two tenure-track excellence in teaching and to continuing re­ Iowa, Cedar Falls, Iowa 50614 (319)273-2631 positions to begin in August 1991. Rank is open search. Specialization in any area of mathemat­ [email protected]. depending on qualifications. Applicants must ics will be considered, but we especially seek An affirmative action/equal opportunity edu­ have an earned doctorate by the starting date, candidates who have an interest in teaching cator and employer. a strong research record or excellent research applied mathematics courses. The department potential, and a commitment to quality graduate currently has 13 full-time faculty. Mathematics and undergraduate teaching. Some preference students may graduate with a B.A. in Math­ may be given to applicants in algebra. However, ematics or a B.S. in Applied Mathematics. KANSAS strong applicants from other areas of pure and The regular teaching load at IUSB is nine applied mathematics are encouraged to apply. credit hours. Salaries are competitive and the KANSAS STATE UNIVERSITY IUPUI is a rapidly growing comprehensive fringe benefits package is excellent. IUSB is an Department of Mathematics urban university with over 28,000 students. The Equal Opportunity/Affirmative Action employer; Subject to budgetary approval, applications are department offers programs of study leading to women and minority candidates are especially invited for several tenure track and visiting Purdue University B.S., M.S., and Ph.D. de­ encouraged to apply. Applications accepted un­ positions commencing August 18, 1991 ; rank grees. The university offers competitive salaries til January 30, 1991. Send vita to John P. and salary commensurate with qualifications. All and provides excellent fringe benefits. Send Russo, Chair, Department of Mathematics and fields will be considered, but for the tenure-track resume and three letters of recommendation Computer Science, Indiana University at South positions preference will be given to candidates to Prof. Bart S. Ng, Chair, Department of Bend, South Bend, IN 46634. Mathematical Sciences, IUPUI, 1125 E. 38th in Numerical Analysis, Partial Differential Equa­ Street, Indianapolis, IN 46205-281 0. Closing tions, Global Analysis, and Geometric Topology

66 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

(especially Low-Dimensional). Applicants must to quality instruction is expected. Preference will pate in the teaching program at graduate and have strong research credentials and a commit­ be given to those applicants with experience undergraduate levels. Applicants should submit ment to excellence in teaching. We require a and/or training in computing. Review of cre­ a detailed vita and a list of publications with at Ph.D. in mathematics or an accepted Ph.D. dis­ dentials begins January 10, 1991 ; applications least 3 letters of recommendation or the names sertation with only formalities to be completed. accepted until January 31, 1991. Submit letter of referees to Professor David Yang, Screening Letter of application, current vita, description of of application, resume, graduate transcripts and Committee, at the above address. The search research and three letters of recommendation three letters of recommendation, to: will remain open until the position is filled. Tu­ should be sent to: OFFICE OF PERSONNEL SERVICES lane is an Equal Opportunity/Affirmative Action Louis Pigno MOREHEAD STATE UNIVERSITY Employer. Department of Mathematics MM 101 Cardwell Hall137 MOREHEAD, KY 40351 Kansas State University MSU is an EEO/AA employer. Manhattan, KS 66506 Deadline: February 1, 1991. AA/EOE MARYLAND MORGAN STATE UNIVERSITY LOUISIANNA Department of Mathematics UNIVERSITYOF KANSAS LOUISIANA STATE UNIVERSITY and Computer Science Department of Mathematics Department of Mathematics Three tenure-track positions including depart­ Applications are invited for a visiting assis­ Baton Rouge, LA 70803; (504)388-1534 ment chair. Ph.D. in mathematics or computer tant professor position commencing August 16, 1243 science required. The normal teaching load is 1991 or as negotiated. (The availability of this The department anticipates openings for the 12 credit hours per semester (6 for the de­ position is contingent upon final administrative 91-92 academic year primarily at the Assis­ partment chair). The successful applicants will approval.) Preference will be given to can­ tant Professor level, but invites applications for be expected to maintain an active research didates whose research interests mesh well positions at all professorial-rank levels includ­ program and to participate in the usual faculty with those of present mathematics department ing visiting and tenure-track positions. Essen­ service activities. The closing date for applica­ faculty. Require Ph.D. or Ph.D. dissertation tial qualifications include competitive research, tions is January 31, 1991. Candidates should accepted with only formalities to be completed. good teaching and a Ph.D. or equivalent by send letters of application, resumes, and three Application, detailed resume with description August 1991. Preferred fields include areas of letters of recommendation to Nathaniel Knox, of research, and three recommendation letters combinatorics and graph theory and algebraic Acting Chairman, Department of Mathematics should be sent to C.J. Himmelberg, Chairman, number theory. Strong candidates in other areas and Computer Science, Morgan State Univer­ Department of Mathematics, 405 Snow, Univer­ are encouraged to apply. Application deadline is sity, Baltimore, MD 21239. AA/EOE. sity of Kansas, Lawrence, KS 66045-2142. March 1, 1991. To apply, specify your interests, Deadlines: February 1, 1991 for first consid­ enclose a full resume, and arrange for at least eration, then monthly until August 1, 1991. three persons to send letters of evaluation to Dr. The University of Kansas is an AA/EOE. Jimmie Lawson, Chairman (address above). UNITED STATES NAVAL ACADEMY LSU IS AN EQUAL OPPORTUNITY UNI­ Mathematics Department VERSITY. Annapolis, Maryland 21402-5002 KENTUCKY We anticipate one or two tenure-track ap­ LOUISIANA STATE UNIVERSITY pointments at the assistant professor level, CENTRE COLLEGE commencing August 1991. Ten month salary, Department of Mathematics commensurate with experience and qualifica­ Faculty Position, Computer Science/Math. A Baton Rouge, LA 70803; (504)388-1534 tions. Research opportunities exist for aug­ one-year full-time teaching (sabbatical replace­ We anticipate openings for full and part-time menting salary during summer. Applicants must ment) position starting September 1, 1991 . possess Ph.D., have a commitment to excel­ The successful candidate will teach traditional Instructors and Teaching Associates starting in August 1991, to teach freshman/sophomore lence in teaching and be capable of pursuing undergraduate courses in mathematics and independent research. Send inquiries and ap­ computer science, offer special topics courses courses, including developmental mathematics. plications to J. M. D'Archangelo. Required of in computer science in her/his area of exper­ The teaching load averages 12 hours of class per week. Applicants should have completed at each applicant are a resume, transcripts, and tise, and conduct student-faculty collaborative three letters of recommendation discussing ap­ research. Advanced degree in mathematics or least 18 graduate credit hours in mathematics plicant's teaching and research. The Naval computer science required, Ph.D. preferred. and hold a master's degree (in mathematics Academy is an EO/AA employer. Rank and salary dependent on qualification. for Instructor positions). Application deadline is Consideration of qualifications will begin Feb. April 1 , 1991 . To apply, specify your interest, 15, send inquires & vita to Dr. John Ward, Dean enclose a full resume, and arrange for at least three persons to send letters of evaluation to Dr. of the College, Centre College, Danville, KY UNIVERSITY OF MARYLAND 40422. EOE Jimmie Lawson, Chairman (address above). LSU IS AN EQUAL OPPORTUNITY UNI­ UNIVERSITY COLLEGE VERSITY. Teach in Asia or Europe MOREHEAD STATE UNIVERSITY The University of Maryland University Col­ Department of Mathematical Sciences lege seeks excellent teachers for openings on Assistant Professor of Mathematics TULANE UNIVERSITY U.S. military bases overseas. Appointments be­ Department of Mathematics gin August 1991. Requirements include M.A. Morehead State University invites applications New Orleans, LA 70118 or Ph.D., recent college teaching experience, and nominations for a tenure track position of and U.S. citizenship. Competence to teach in Assistant Professor of Mathematics beginning Applications are invited for a tenure-track posi­ another discipline desirable. Benefits include August 1991. Responsibilities: Teach twelve tion in Applied Analysis/POE at the Associate transportation and military base privileges (PX, hours per semester (reassigned time for re­ or Assistant Professor level, depending on commissary, etc.). Frequent travel and the cost search possible) of primarily undergraduate qualifications. Besides a Ph.D. degree in Math­ of schooling make these positions difficult for courses in mathematics together with scholarly ematics and teaching experience, candidates those with children. Send resume to Dr. Ralph production and service. Qualifications: Ph.D. in should have a demonstrated ability to carry out E. Millis, Assistant to the President, Overseas mathematics is required. A strong commitment high quality research and be willing to partici- Programs, The University of Maryland Univer-

JANUARY 1991, VOLUME 38, NUMBER 1 67 Classified Advertisements

sity College, College Park, MD 20742-1642. EXECUTIVE OFFICER and experience in undergraduate teaching of AA/EEO. COUNCIL ON mathematics will be important. Salary will be UNDERGRADUATE RESEARCH competitive and commensurate with qualifica­ tions. Send letter of application, resume, and Applications, nominations or inquiries are in­ three letters of reference to: Prof. Mark. J. Wat­ MASSACHUSETTS vited for the position of Executive Officer of the son, Chairman, at the above address by January Council on Undergraduate Research. CUR is 31, 1991, for full consideration. AAIEOE AMHERST COLLEGE a national society dedicated to the advance­ ment of scientific research by students and Applications are invited for a one-year visiting faculty at primarily undergraduate colleges and position in Mathematics, preferrably at the universities. Membership is available and open Assistant Professor level, beginning in August to anyone with such an interest. CUR is cur­ MICHIGAN TECHNOLOGICAL UNIVERSITY 1991. rently organized into biology, chemistry, geology, Department of Mathematical Sciences Amherst College is a private, undergraduate mathematical sciences, physics/astronomy and college which emphasizes both research and at-large sections governed by 122 Councilors Applications are invited for the following posi­ teaching. We attract bright students, possess a elected by the membership. CUR publishes a tions, starting Sep. 3, 1991. (1) At least two lively faculty, and have an administration com­ quarterly newsletter and directories of research tenure-track positions at the Assistant/Associate mitted to a vigorous program in mathematics. at undergraduate institutions, holds semi-annual level in Applied Mathematics. Areas of special The Department of Mathematics and Com­ conferences for science faculty, administrators, interest include fluid mechanics, mathematical puter Science consists of seven mathematicians and representatives of federal funding agencies modelling, computational mathematics and par­ and three computer scientists. We are located and private foundations, sponsors undergradu­ tial differential equations. (2) One tenure-track in the Seeley G. Mudd building, which also ate summer research fellowships, and provides position in Combinatorics. Areas of special in­ houses classrooms, seminar rooms, a library consultants to undergraduate science depart­ terest include pure and applied combinatorics, for mathematics and computer science, and the ments. The Executive Officer will coordinate the combinatorial optimization, coding theory, cryp­ academic computer center. Research facilities activities of the volunteer councilors, adminis­ tography and combinatorial designs. Appoint­ include computers in most faculty offices and a ter all CUR programs, and maintain liaisons ments at the non-entry level require substantial network of Sun workstations. with other scientific organizations. Candidates record of published research. Requirements Amherst College is part of a five college should have both organizational talent and ex­ include a Ph.D. in Mathematics, excellence in consortium that also includes the University of perience with scientific research at primarily research or potential for such, as well as a Massachusetts and Hampshire, Mount Holyoke undergraduate institutions. The initial appoint­ commitment to teaching at the undergraduate and Smith Colleges. There are numerous faculty ment is for a three year term, renewable and graduate level. (3) In addition, the depart­ seminars held at Amherst and the University, after review. The salary is competitive with ment expects to fill several Visiting Assistant and Boston is less than two hours away. academic salaries at professorial levels. For Professorship positions. Please send a letter If some anticipated leaves take place and further information, write to Professor Stuart B. of application, resume and three letters of rec­ if we receive authorization from the administra­ Crampton, President, Council on Undergradu­ ommendation to: Recruitment Committee, De­ tion, the position may be extended to a second ate Research, Department of Physics, Williams partment of Mathematical Sciences, Michigan (and possibly third) year given satisfactory per­ College, Williamstown, MA 01267. AA/EOE. Technological University, 1400 Townsend Drive, formance in the first year. Houghton, Ml 49931-1295. Applications will be Applicants should hold a Ph.D. in mathemat­ accepted until February 15, 1991. MTU is an ics. Please submit a vita, three references, and equal opportunity educational institution/equal transcripts from both your graduate and under­ TUFTS UNIVERSITY opportunity employer. graduate institutions. All applications received Department of Mathematics by February 15 are assured of consideration. Medford, MA 02155 Amherst College is an Affirmative Ac­ Assistant Professorship, tenure-track, beginning tion/Equal Opportunity Employer and encour­ Sept. 1, 1991. Ph.D., promise of strong research ages applications from minorities and women. and evidence of strong teaching ability required. MINNESOTA Reply to: Preferred areas: number theory, group theory, Professor David A. Cox, Chair numerical analysis, differential geometry, POE's CARLETON COLLEGE Department of Mathematics and and mathematical physics. Teaching load two Department of Mathematics Computer Science courses per semester. Send c.v. and have and Computer Science Amherst College three letters of recommendation sent to Richard Northfield, MN 55057-4025 Amherst, MA 01 002 Weiss, Search Committee Chair, by Feb. 12, send electronic mail to: [email protected] _r 1991. One, and possibly two, two-year non-tenure­ or [email protected] Tufts is an EO/AA employer. track positions beginning September 1991, with the possibility of renewal. Ph.D. required. Teach six courses per year in mathematics, computer science and/or statistics. Preference given to BOSTON UNIVERSITY MICHIGAN individuals who can teach in two of these Department of Mathematics areas. Excellent teaching skills essential. Dead­ The Department of Mathematics at Boston Uni­ HILLSDALE COLLEGE line February 15; applications accepted until versity invites applications for two anticipated Department of Mathematics positions are filled. Affirmative Action/Equal positions in the area of Dynamical Systems. Hillsdale, Ml 49242 Opportunity Employer; applications specifically One position is a permanent position at the As­ invited from women and minorities. Send letter sistant Professor level. The successful applicant An independent, coeducational, liberal arts col­ of application, resume, graduate transcript(s), should have a strong commitment to research lege of 1100 students, seeks a mathematician and three recent letters of reference to Jack and teaching. The Department also seeks appli­ for a tenure-track position as Assistant Profes­ Goldfeather, Chair. cations for a Visiting Assistant Professorship in sor of Mathematics to begin August 1991. A Carleton College is a highly selective, liberal this field. Applications and 3 letters of reference candidate should hold the Ph.D. in mathemat­ arts college 35 miles south of Minneapolis/St. should be sent to: Search Committee, Depart­ ics, and should expect to teach all levels of Paul. Department has 12 full-time members. ment of Mathematics, Boston University, 111 undergraduate mathematics. In addition to a Computing resources available to department Cummington St., Boston, MA 02215. AA/EOE. 12-hour teaching load per semester, duties will members include 12 NeXT's, 3 Mac ll's, a include academic advising and college service. DEC Micro VAX II running Ultrix, a Raster Tech A commitment to quality liberal arts education 3/85 graphics workstation, several Transputer

68 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

equipped parallel processing workstations, and varsity, with 21 00 majors and 140 faculty. It SOUTHWEST MISSOURI a variety of microcomputers. offers 15 different undergraduate majors and 17 STATE UNIVERSITY graduate degree programs (11 M.S., 6 Ph.D.) within 10 departments and the School of Engi­ Southwest Missouri State University Depart­ neering Technology. External funding for CY89 ment of Mathematics. One or more tenure­ exceeded $8 million. The University of Southern track and/or visiting positions in Mathematics Mississippi is one of the state's three compre­ and Statistics, beginning Fall 1991. Rank and THE UNIVERSITY OF MISSISSIPPI hensive universities and has an enrollment of salary will be commensurate with qualifications. Department of Mathematics more than 13,000. It is located in the pine­ Applicants must have a Ph.D. in Mathematics forested, rolling hills of South Mississippi, 70 or Statistics, evidence of excellence in teach­ The Department invites applications for a tenure miles from the Gulf Coast and is an easy 2-hour ing, and a commitment to continued research. track position at the Assistant or Associate drive from New Orleans. For all positions preference given to applicants Professor level beginning August 19, 1991. THE UNIVERSITY OF SOUTHERN MIS­ with research interests compatible with those Applicants should hold the Ph.D. degree, and SISSIPPI IS AN EQUAL OPPORTUNITY, AF­ of the current faculty. Duties include teaching, should be committed to excellence in teaching FIRMATIVE ACTION EMPLOYER. APPLICA­ research, and service. Applications will be re­ and a productive ongoing program of research. TIONS FROM WOMEN, MINORITIES, AND viewed as received and will be accepted until To ensure consideration, submit a letter of THE HANDICAPPED ARE ENCOURAGED. the positions are filled or until February 15, application, vita, and three letters or recommen­ 1991-the final deadline for all application ma­ dation by March 1, 1991, to: Search Committee, terials. Send vita and graduate transcripts, and Department of Mathematics, University of Mis­ have three letters of reference sent to: Clayton sissippi, University, MS 38677. Sherman, Acting Head, Department of Math­ The University of Mississippi is an Equal MISSOURI ematics, Southwest Missouri State University, Opportunity/Affirmative Action Employer. Springfield, MO 65804-0094. AA/EOE. NORTHEAST MISSOURI STATE UNIVERSITY COLLEGE OF Department of Mathematics SCIENCE AND TECHNOLOGY and Computer Science Kirksville, Missouri 63501 UNIVERSITY OF MISSOURI UNIVERSITY OF SOUTHERN MISSISSIPPI Department of Mathematics Director of the Program in Several tenure-track, assistant professorships Columbia, MO 65211 Scientific Computing available August 1991. Requirements include Ph.D., commitment to excellence in undergrad­ Applications are invited for two tenure-track Applications and nominations are invited for the uate teaching, and evidence of potential for positions at the rank of assistant professor be­ position of Director of the Program in Scientific research and other scholarly activity. Expertise ginning in August of 1991. The positions require Computing, which will begin not later than July in statistics is needed for at least one posi­ a Ph.D., quality teaching, and a commitment 1, 1991. The Director, who will report to the tion. Other preferred areas of expertise include to a distinguished research career. Selections Dean of the College of Science and Technol­ analysis, combinatorics, differential equations, for each position will be based primarily on ogy, will be responsible for administering the applied mathematics, logic, and computer sci­ demonstrated research achievement in an area new Ph.D. degree in Scientific Computing, with ence. Teaching loads average nine hours per complementary to areas of ongoing departmen­ emphasis areas in computational mathematics, week. Northeast is a selective, liberal arts and tal research. Send a curriculum vitae along with computational physics, and computer science. sciences university with an enrollment of almost a letter of application, and arrange for three It is an interdisciplinary program involving the 6,000. A complete application requires a letter letters of recommendation to be sent to Profes­ Departments of Computer Science & Statistics, of application, vita, transcripts of graduate and sor L. J. Lange, Chair, at the address above. Mathematics, and Physics & Astronomy, and undergraduate study, and at least three letters The application deadline is January 22, 1991, drawing faculty from among several other aca­ of reference. Send to Lanny Morley, Head, Di­ or until the positions are filled thereafter. Appli­ demic departments throughout the University. vision! of Mathematics and Computer Science. cations received after March 1 , 1991 , cannot be A major portion of the Director's time during Northeast is an Equal Opportunity Employer. guaranteed consideration. AAIEOE. the first year will involve program refinement, faculty and student recruitment, some teaching, and establishment of contacts with industry and funding agencies. The program will be initiated NORTHEAST MISSOURI at Stennis Space Center near Bay St. Louis, STATE UNIVERSITY NEBRASKA Miss., with implementation on the Hattiesburg Department of Mathematics campus the following year. UNIVERSITY OF NEBRASKA-LINCOLN The successful candidate will possess a and Computer Science Ph.D. in computer science, mathematics, or Kirksville, Missouri 63501 Applications are invited for a tenure-track posi­ physics, some administrative experience, ex­ Several temporary instructorships available Au­ tion at the Assistant Professor level beginning cellent communication skills, a distinguished gust 1991. Most positions renewable for one or in the fall of 1991 . Candidates must have a research record, and a proven ability to attract two additional years upon satisfactory perfor­ Ph.D. in mathematics or expect to receive their external funding for basic and/or applied re­ mance. Masters degree with demonstrated po­ degree by August of 1991. Candidates must search. The salary, dependent upon experience tential for excellence in undergraduate instruc­ have excellent teaching ability and outstand­ and qualifications, as well as the starting date tion essential. Degree or expertise in statistics ing research potential in an area which will is negotiable. The application package should required for at least one position. Teaching load complement the existing expertise in the de­ consist of a letter stating interest in the position; averages twelve hours per week. Northeast is partment. Applications accepted from qualified a curriculum vitae; and the names, addresses, a selective, liberal arts and sciences university candidates in all areas of mathematics, but and telephone numbers of three references; with an enrollment of almost 6,000. A complete candidates in numerical analysis, differential and should be send to: Chair, Scientific Com­ application consists of a letter of application, geometry, operations research, operator the­ puting Search Committee, College of Science & vita, transcripts of graduate and undergraduate ory and combinatorics are particularly urged Technology, University of Southern Mississippi, study, and at least three letters of reference. All to apply. Women and minority candidates are Hattiesburg, MS 39406-5165. The search will materials should be sent to Lanny Morley, Head, also encouraged to apply. Send vita and three remain open until the position is filled, and the Division of Mathematics and Computer Science. letters of recommendation to Search Committee review of applications will begin on February 15. Northeast is an Equal Opportunity Employer. Chair, Department of Mathematics and Statis­ The College of Science & Technology is tics, University of Nebraska-Lincoln, Lincoln, one of the largest academic units of the Uni- NE 68588-0323. The review of applications will

JANUARY 1991, VOLUME 38, NUMBER 1 69 ...... ·-·········------·-·······-··········-··························································································································-·······--········-····-······ Classified Advertisements

begin February 1, 1991, and continue until a results and interests. Also arrange for four let­ ematics. Ph.D. in mathematics or a closely candidate is selected. ters of reference to be sent, at least one of related discipline is required. Rank and salary which addresses teaching, and, if the applicant's are negotiable. Strong candidates in all areas native language is not English, the applicant's are encouraged to apply. We are especially ability to use English in a classroom. All appli­ interested in new colleagues with interests in NEW HAMPSHIRE cation material should be addressed to Phyllis differential and algebraic geometry, probability Bellmore, Recruiting Secretary, Department of and statistics, and computational mathematics. DARTMOUTH COLLEGE Mathematics and Computer Science, Dartmouth The university is located in upstate New York John Wesley Young College, Hanover, New Hampshire 03755. Ap­ close to the scenic Adirondack and Thousand Research Instructorship plications completed by February 1 will receive Island regions. The concentration of college first consideration. Dartmouth is committed to campuses in the vicinity creates a rich cultural The John Wesley Young Research Instructor­ Affirmative Action and encourages applications environment with a high quality of life without ship is a two year post-doctoral appointment from African Americans, Asian Americans, His­ the problems of major cities. for promising new or recent Ph.D.'s whose panics, Native Americans and women. Specific Applications including vita and names of research interests overlap a department mem­ questions on the selection process can be three references should be submitted to Pro­ ber's. Current departmental interests include directed to Richard E. Williamson, Recruiting fessor A. FOkas, Department of Mathematics areas in algebra, analysis, algebraic geometry, Chair. and Computer Science, Clarkson University, combinatorics, computer science, differential Potsdam, NY 13699. Clarkson University is an geometry, logic and set theory, number theory, equal opportunity/affirmative action employer probability and topology. Teaching duties of four and encourages applications from women and ten-week courses spread over two or three UNIVERSITY OF NEW HAMPSHIRE minorities. quarters typically include at least one course Department of Mathematics in the instructor's specialty and include ele­ Durham, NH 03824 mentary, advanced and (at instructor's option) graduate courses. Nine-month salary of $32,500 The Department of Mathematics expects to supplemented by summer (resident) research have tenure-track positions in applied math­ HOBART AND WILLIAM SMITH COLLEGES stipend of $7,150 (two-ninths). Send letter of ematics and statistics available in the Fall Department of Mathematics application, resume, graduate transcript, thesis Semester, 1991. While each position is at the and Computer Science abstract, description of other research activities assistant professor level, outstanding applicants Two Assistant Professor, tenure-track positions and interests if appropriate, and 3 or prefer­ at all ranks will be considered. We are partic­ starting in September 1991. Salary is competi­ ably 4 letters of recommendation (at least one ularly interested in candidates with a strong tive. should discuss teaching) to Phyllis A. Bell­ research potential in the applied mathemati­ For the first position applicants should have more, Department of Math and CS, Bradley cal areas of numerical analysis or dynamical a Ph.D. in computer science or a Ph.D. in Hall, Hanover, NH 03755. Applications received systems and an interest in interdisciplinary re­ mathematics and experience in computer sci­ by Jan. 15 receive first consideration; applica­ search. Successful applicants are expected to ence. Duties include teaching undergraduate tions will be accepted until position is filled. have a strong commitment to teaching and computer science, participating in the Colleges' Dartmouth College is committed to affirmative research. Preference will be given to those ap­ Interdisciplinary General Curriculum, and the action and strongly encourages applications plications received by February 1 , 1991 . Send possibility of teaching some mathematics (de­ from minorities and women. resume and names of three references to L. D. Meeker, Chairperson, Mathematics Depart­ pending on interests and qualifications). ment, University of New Hampshire, Durham, For the second position applicants should NH 03824. UNH is an AA/EO Employer. have a Ph.D. in mathematics; specialty open, DARTMOUTH COLLEGE but preference may be given to algebraists, Department of Mathematics applied mathematicians, or those with demon­ and Computer Science strated computer science expertise. Duties include teaching undergraduate mathematics, The Department of Mathematics and Computer NEW JERSEY participating in the Colleges' Interdisciplinary Science has an openng for a tenure-track General Curriculum, and the possibility of RUTGERS UNIVERSITY, CAMDEN Assistant Professor in Mathematics, with initial teaching some computer science (depending appointment in the 1991-1992 academic year. The Mathematical Sciences Department seeks on interests and qualifications). A candidate for the position must be committed highly qualified applicants for a research ori­ For both positions a strong commitment to to outstanding teaching at all levels of the ented assistant professorship. This is a tenure teaching and promise of continued scholarly ac­ undergraduate and graduate curriculum and track position at a competitive salary with a tivity is required_ Teaching load: two courses per must give evidence of a well-regarded research teaching load of one course for the first two trimester. Hobart College for men and William program that shows real promise for the future. years. At least one year beyond the Ph.D. and Smith College for women are coordinate, four Candidates with several years of experience one significant publication are necessary to be year, liberal arts colleges committed to teaching should in addition be ready to direct Ph.D. considered. Send C.V., a minimum of three let­ and interdisciplinary study with a combined en­ theses. ters of recommendation, and reprints/preprints rollment of 1900 students. Within an hour's drive To create an atmosphere supportive of re­ as soon as possible to: are three major universities: Cornell, Rochester, search, Dartmouth offers new faculty members Search Committee and Syracuse. grants for research-related expenses, a quarter Mathematical Sciences Department Send detailed resume, three letters of rec­ of sabbatical leave for each three academic Rutgers University ommendation (at least one including comments years in residence and flexible scheduling of Camden, NJ 08102 on teaching), and undergraduate and grad­ teaching responsibilities. The teaching responsi­ AA/EOE uate transcripts (photocopies acceptable) to: bility in mathematics is two courses per quarter Prof. Kevin Mitchell, Faculty Box 75, Depart­ for two ten-week quarters or one course for ment of Mathematics and Computer Science, two quarters and two courses for one quarter. Hobart and William Smith Colleges, Geneva, The department encourages good teaching with NEW YORK NY 14456. Evaluation of applications will be­ a combination of committed colleagues and gin December 15, 1990 and will continue until bright, responsive students. CLARKSON UNIVERSITY the position is filled. Women and minorities Applications are welcome in all fields of are strongly encouraged to apply. An Equal mathematics, including statistics. To apply for The Department of Mathematics and Com­ Opportunity/Affirmative Action Employer. the position, send a letter of application, cur­ puter Science at Clarkson University invites riculum vitae, and a brief statement of research applications for tenure track positions in math-

70 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

University, E. 24th & Euclid Ave., Cleveland, NORTH CAROLINA OHIO OH 44115. Equal Opportunity Employer, m/f/h. Women and minorities are encouraged to apply. UNIVERSITY OF NORTH CASE WESTERN RESERVE UNIVERSITY CAROLINA AT CHAPEL HILL Statistics Positions Department of Mathematics Tenure track positions, possibly Chapel Hill, NC 27599-3250 senior, in Ap­ plied Statistics will be available in the Summer OBERLIN COLLEGE Applications are invited for tenure-track ap­ of 1991. Outstanding research record or proven Department of Mathematics pointments effective Fall 1991. rank and salary research potential and teaching excellence is Oberlin, OH 44074 depend on qualifications and budget consid­ required. Initial appointments will be in the De­ Four-year, full-time, continuing erations. Ph.D., exceptionally strong research partment of Mathematics and Statistics. Since position at the level of Instructor, Assistant program and commitment to excellent teach­ the University has made the reestablishment of Professor, or higher, starting 1991-92. Ph.D. in hand ing required. Send curriculum vitae, abstract of Statistics a priority for future development it is or expected by September 1991. Background current research program and four letters of rec­ expected that these positions will eventually be in Operations Research and interest ommendation to Search Committee Chairman, in an independent Statistics Department. in applied mathematics essential. Excellence in Mathematics Department, CB #3250 Phillips Case Western Reserve University provides teaching and produc­ tive scholarship required. Five Hall, UNC at Chapel Hill, Chapel Hill, NC a wide scope to interact with researchers in courses per year, including a two-course 27599-3250. EO/AA Employer. Women and mi­ other Schools (Medicine, Engineering, Manage­ OR sequence. Salary commensurate with norities are encouraged to identify themselves ment, Nursing, Dentistry, Law and the Applied qualifications and expe­ rience. Vita, transcripts, voluntarily. Completed applications received by Social Sciences). There is ample opportunity and three letters of reference to be received February 1, 1991 are assured of full considera­ for cooperative ventures with members of the by November 9, 1990. tion. Faculties of Mathematics and Natural Sciences, Send to Michael Henle, Department of Mathe­ the Humanities and the Social Sciences. The matics, Oberlin College; Oberlin, Ohio 444074. University also has several established re­ Affirmative Action Equal Opportunity Employer. search Centers, including th CWRU Center Applications will continue to be accepted until for Stochastic and Chaotic Processes in Sci­ the position is filled. ence and Technology, whose efforts woul be UNIVERSITY OF NORTH enhanced by cooperation with applied statisti­ CAROLINA AT CHARLOTTE cians. Department of Mathematics Women and minority groups candidates are OBERLIN COLLEGE especially encouraged to apply. CWRU is an Department of Mathematics One tenure-track position at AssVAssoc. Prof. affirmative action and an equal opportunity Oberlin, OH 44074 level in Smooth Dynamical Systems, Functional employer. Send vita plus three letters of recom­ Analysis or Operator Algebras. Visiting or Post­ mendation to Four-year, full-time, continuing position at the doctoral appointment in Numerical Analysis. Dr. C. A. Cullis, Dean level of Instructor, Assistant Professor, or higher, Possible visiting positions in all areas at any Faculty of Mathematics and Natural starting 1991-92. Ph.D. in hand or expected level. Rank and salary depend on qualifications. Sciences by September 1991 . Background in modern ap­ Ph.D. and serious commitment to teaching and Crawford Hall, plied analysis essential. All specialties consid­ research are required. Also possible are lecturer Case Western University ered but preference given to chaotic dynamical positions (one or two year renewable; MAIMS Cleveland, OH 44106 systems, numerical analysis, and approximation required). Send vitae, list of 4 references to theory. Excellence in teaching and productive Prof. Alex S. Papadopoulos at the above scholarship required. Five courses per year, address. For full consideration, applications including at least one CLEVELAND STATE UNIVERSITY advanced course in mod­ should be submitted by Feb. 8, 1991 otherwise ern applied analysis. Salary commensurate with applications will be accepted until positions are MATHEMATICS/ASSISTANT PROFESSOR: Ap­ qualifications and experience. Vita, transcripts, filled. plications are invited for the anticipated posi­ and three letters of reference to be received UNCC IS AN EQUAL OPPORTUNITY/ tion of tenure-track Assistant Professor starting by November 9, 1990. Send to Michael Henle, AFFIRMATIVE ACTION EMPLOYER September 1991 . Candidate should have a Department of Mathematics, Oberlin College, strong research record and a commitment to Oberlin, Ohio 44074. Affirmative Action Equal excellent teaching. Research areas compatible Opportunity Employer. Applications will continue with those in the Department are preferred. to be accepted until the position is filled. Send vita, reprints/preprints and 3 letters of recommendation to: John Chao, Department WAKE FOREST UNIVERSITY of Mathematics, Cleveland State University, E. Department of Mathematics and 24th & Euclid Ave., Cleveland, OH 44115. OBERLIN COLLEGE Computer Science Equal Opportunity Employer, m/f/h. Women and Department of Mathematics minorities are encouraged to apply. Applications are invited for two tenure track Oberlin, OH 44074 positions in mathematics at the assistant pro­ fessor level beginning August 1991. Duties Two-year, full-time, continuing position at the include teaching mathematics at the under­ CLEVELAND STATE UNIVERSITY level of Assistant Professor starting 1991-92. graduate and graduate levels and continuing Ph.D. in hand or expected by September 1991. research. A Ph.D. is required. The department MATHEMATICS/DEPARTMENT CHAIR: Appli­ The encumbent will teach 5 courses in the has 22 members and offers a B.S. and M.A. cations and nominations are invited for the general area of mathematics and/or computer in mathematics and a B.S. in computer sci­ position of Department Chair starting Summer science. Excellence in teaching and productive ence. Send letter of application and resume to 1991. Candidates should have an outstand­ scholarship required. In addition the ability to Richard D. Carmichael, Chairman, Department ing research record and a commitment to teach computer science and/or statistics is of Mathematics and Computer Science, Wake excellent teaching. The Department has 27 highly desirable. Salary commensurate with Forest University, Box 7311, Winston-Salem, full time faculty and offers two baccalaureate quualifications and experience. Vita, transcripts, NC 271 09. AA/EO employer. and two masters degrees. Please send vita, and three letters of reference to be received reprints/preprints, and at least 4 letters of rec­ by February 1, 1991 . Send to Michael Henle, ommendation to the Chair Search Committee, Department of Mathematics, Oberlin College, Department of Mathematics, Cleveland State Oberlin, Ohio 44074. Affirmative Action/Equal

JANUARY 1991, VOLUME 38, NUMBER 1 71 ...... _ _...... - ...... •..•..... Classified Advertisements

Opportunity Employer. Applications will continue sent to: S. Hastings, Chairman, Department to be accepted until the position is filled. PENNSYLVANIA of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260. COMMUNITY COLLEGE OF PHILADELPHIA The University of Pittsburgh is an Equal Op­ portunity/Affirmative Action Employer. Mathematics Dept. at Community College of THE OHIO STATE UNIVERSITY AT Women and minorities are esp~cially encour­ Philadelphia invites applications for an expected aged to apply. NEWARK tenure-track Asst. Professorship position begin­ Department of Mathematics ning Fall 1991. The Dept. is actively engaged in course development. It has recently received ASSISTANT PROFESSOR, MATHEMATICS - grants from NSF and CASET. Teaching load is THE UNIVERSITY OF SCRANTON The Ohio State University at Newark is seeking 12 credit hours/semester. Outstanding benefits. Mathematics Department an Assistant Professor for a full-time, tenure Candidate must have a Ph.D. or master's + track position in the Mathematics Depart­ 3 years college teaching in mathematics and The University of Scranton is a Jesuit university ment. DUTIES INCLUDE: Teach undergraduate a commitment to quality teaching, both reme­ with over 3,500 undergraduates. The Mathe­ courses in Mathematics. Ability and willing­ dial and college level. Demonstrated strength m.atics Department has 15 full-time faculty and ness to teach elementary statistics course is in course development is essential. Candidate about 50 majors. desirable. Conduct research and render appro­ should provide clear evidence of strong back­ One (possibly two) tenure-track position is priate Campus, Departmental, and university ground in mathematics, together with ability to available for Fall 1991 for faculty interested in a service. QUALIFICATIONS INCLUDE: Ph.D. in bring to the first 2 years, mathematics topics teaching environment where research is encour­ Mathematics. Some experience at the college usually delayed until later. Send curriculum vitae aged and supported. Individuals with expertise or university level is preferred. TERMS: Full­ and 3 letters of recommendation by March 1 , in any area of mathematics will be considered. time, 9 month, tenure track position. START­ 1991 to J. Mason, Head, Dept. of Mathematics, Preferred areas include Applied Mathematics, ING DATE: Autumn Quarter, 1991. STARTING COMMUNITY COLLEGE OF PHILADELPHIA, Probability/Statistics, Actuarial Mathematics, Al­ SALARY: Negotiable; comprehensive benefits 1700 Spring Garden St., Phila., PA 19130. gebra, and Analysis. Rank and salary are open package. To assure consideration, send vita Women and minorities are encouraged to apply. and competitive. and three letters of reference written directly AA/EOE. Submit a vita, transcripts, and three refer­ to the search committee by 3/29/91 to Coordi­ ences to Mathematics Faculty Search Commit­ nator, Human Resources, Mathematics Search, tee, University of Scranton, Scranton, PA 18510 The Ohio State University, Drive, Newark, Ohio or phone (717) 941-6113. Screening will begin 43055. OSU at Newark is an Equal Opportu­ LAFAYETTE COLLEGE at once and applications will be considered nity/Affirmative Action Employer. Department of Mathematics until all positions have been filled. An AA/EO Easton, PA 18042 Employer and Educator. Tenure-track position at the rank of Assistant Professor beginning in late August 1991. Prefer­ OKLAHOMA ence for a candidate able to help with teaching WEST CHESTER UNIVERSITY statistics at all undergraduate levels. Women Mathematics and Computer THE UNIVERSITY OF OKLAHOMA and minorities are especially encouraged to Science Department Department of Mathematics . apply. West Chester, PA 19383 601 Elm Avenue, Room 423 Teach undergraduate mathematics, help to Norman, Oklahoma 73019-0315 develop our undergraduate mathematics pro­ Applications are invited for a tenure track posi­ gram, pursue scholarly development. Lafayette tion at the assistant or associate professor level Applications are invited for two anticipated offers liberal arts and engineering in a small starting September 1991. Candidates must pos­ tenured or tenure-track positiions in Mathemat­ (2000) highly selective private college close to sess a strong commitment to teaching and ics beginning Fall 1991. One position at the Philadelphia and New York City. research and have completed the Ph.D. in associate professor level, with preference given Send resume, 3 reference letters and tele­ mathematics by the starting date. Preference to applicants with research interests in the areas phone numbers (office and home) to Chair, will be given to candidates with specialties in of Geometry, Topology, or Analysis. One Assis­ Mathematics Search Committee. Review of ap­ combinatorics, algebraic groups, or functional tant Professor position at the entry level with plications will begin after January 20, 1991, and analysis. Salary and fringe benefits are com­ preference given to research interests compati­ will continue until the position is filled. petitive. Send resume, graduate transcript and ble with those of our current faculty. Candidates Lafayette is an Equal Opportunity Employer. three letters of recommendation to the Mathe­ must have a Ph.D. degree, demonstrated excel­ matics Search Committee at the above address. lence in research, and a strong commitment to Closing date March 15, 1991 . AAIEOE. Women high-quality teaching. Duties include research, and minorities are encouraged to apply. normally teaching six credit hours per semester, UNIVERSITY OF PITTSBURGH and Departmental and University service appro­ Department of Mathematics and Statistics priate to rank. Salary will be commensurate with qualifications and experience. There may also The department invites applications for the RHODE ISLAND be visiting positions. Applicants should send following positions, which will be available for their vita and have at least three letters of September 1991 if funding permits. PROVIDENCE COLLEGE reference sent to Dr. Ruediger Landes, Search 1 . Assistant Professor in the area of partial Assistant Professor of Mathematics Committee Chair, Department of Mathemat­ differential equations. ics, University of Oklahoma, 601 Elm Avenue, 2. Assistant Professor in some branch of A tenure-track position will be available in Room 423, Norman, Oklahoma 73019-0315. pure mathematics other than differential equa­ August 1991. Duties include teaching the full Initial screening begins December 15, 1990 tions. Applicants are especially encouraged in range of undergraduate Mathematics. Ph.D. in and every two weeks thereafter. Applications algebra and geometric or algebraic topology, Mathematics required. Send letter of application will be accepted until the positions are filled. but all areas will be considered. and resume to Mr. Frank Ford, Chair, at Math/CS The University of Oklahoma is an Equal Op­ Requirements include outstanding research Department, Providence College, Providence, portunity/Affirmative Action Employer. OU has accomplishment and potential commensurate R.I. 02918 by Mar. 1st and have transcripts and a policy of being responsive to the needs of with experience, and ability and interest in three letters of recommendation sent directly to dual-career couples. excellent teaching. the same address. At least one of the letters of Applicants should send resume and arrange recommendation must address teaching ability. to have at least three letters of recommendation Providence College is a Roman Catholic four-

72 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

year liberal arts college conducted under the sciences and an interest in innovative applica­ ics/Computer Science, The Citadel, Charleston, auspices of the Dominican Friars and is an tions. Candidates should have strong potential SC 29409. Email: [email protected]. Equal Opportunity Affirmative Action Employer. or demonstrated capability for effective re­ Review of applications will begin March 1. search and teaching. All of the above areas Women and minorities are encouraged to apply. of the mathematical sciences are integrated The Citadel is an equal opportunity/affirmative into degree programs at the B.S., M.S., and action employer. ROGER WILLIAMS COLLEGE Ph.D. levels. In addition, the department jointly Bristol, Rl 02809 administers a Ph.D. program in management School of Science and Mathematics science with the Department of Management. THE UNIVERSITY OF SOUTH CAROLINA Applications will be accepted until any approved The School of Science and Mathematics of Department of Mathematics Roger Williams College welcomes applications positions are filled. Applicants should indicate in for a full time faculty position, subject to funding the cover letter their research specialties. Vita Applications are invited for anticipated tenure­ approval, in mathematics beginning September and three reference letters should be sent to: track faculty positions at all ranks. Applications 1991 . The School offers majors in mathematics Professor R. D. Ringeisen, Head in all areas of mathematics will be considered. and computer science and provides support File M The department is building on existing research courses for College programs in science, en­ Department of Mathematical Sciences strengths and is increasing the scope of its gineering, business, architecture, psychology, Clemson University programs in applied mathematics. The Ph.D. and general education. The college enrolls Clemson, SC 29634-1907 degree or its equivalent is required, and all approximately 2100 full time and 1700 part Clemson University is an AAIEO Employer. appointments will be consistent with the depart­ time students in a variety of liberal arts and ment's commitment to excellence in research professional programs. It is situated in his­ and teaching at the graduate and undergradu­ toric Bristol, Rl on a bluff overlooking Mount ate levels. A resume, containing a summary of Hope Bay. We seek candidates who would research accomplishments and goals, and four COKER COLLEGE enjoy teaching undergraduates a variety of ma­ letters of recommendation should be sent to: Department of Science and Mathematics jor and service courses. The normal teaching Dr. Colin Bennett, Chairman load is 4 courses/12 contact hours. Doctorate Coker College invites applications for two Department of Mathematics and full time college teaching experience re­ tenure-track positions in mathematics. Can­ University of South Carolina quired. Salaries are competitive; fringe benefits didates must have a Ph.D. and demonstrate the Columbia, South Carolina 29208 excellent. potential for high quality teaching and continuing The closing date for applications is January Send a letter of application, curriculum scholarly activity. Duties begin August 1991 and 31, 1991. The University of South Carolina is an vita, and three letters of reference to: Faculty include teaching college algebra, all levels of Affirmative Action/Equal Opportunity Employer. Search Committee, School of Science and calculus and some combination of the following: Mathematics, Roger Williams College, Bristol, differential equations, probability and statistics, Rl 02809. Applications received by February discrete mathematics, and/or computer science WINTHROP COLLEGE 1, 1991 will be given first consideration. Roger courses. Total teaching load is 12 semester Mathematics Department Williams College is an affirmative action/equal hours per semester with approximately one­ Rock Hill, SC 29733 opportunity employer. quarter of the load to be taught in the evening program. Rank and salary commensurate with Winthrop College is seeking a tenure-track fac­ experience. Coker College is a private, four-year ulty member at the assistant level. Salary will THE UNIVERSITY OF RHODE ISLAND liberal arts college in Hartsville, SC. Heavily en­ be competitive and documentation of teach­ dowed, no courses have more than 20 students ing excellence will merit special consideration. Assistant Professor position (tenure track) pos­ and many upper level courses have only three Winthrop is a state supported comprehensive sibly available starting September 1991. Ph.D. or four. Independent study courses are encour­ college of South Carolina, located approxi­ in Mathematics required. Preference will be aged. Deadline for applications is February 4, mately 20 miles south of Charlotte, NC, with given to applicants in differential equations, 1991. Send a letter of application, curriculum an enrollment of 5000 students. An application, combinatorics, control theory and classical and vitae, and three references to Professor Kaye vita, and three letters of recommendation are functional analysis. Please submit, by 2/28/91, Crook, Chair, Mathematician Search Commit­ required. Deadline is March 8, 1991. Winthrop a letter of application indicating the title of the tee, Department of Science and Mathematics, College is an Equal Opportunity Institution and position applied for and a vita, and have three Coker College, Hartsville, SC 29550. AA/EOE an Affirmative Action Employer. Applications letters of reference sent to: L. Pakula, Search . are to be sent to: Dr. Ron C. Goolsby, Chair, Committee Chair, Assistant Prof., Mathemat­ Department of Mathematics, Winthrop College, ics (021098) Position, THE UNIVERSITY OF Rock Hill, SC 29733. RHODE ISLAND, P.O. Box G, Kingston, Rl 02881. An Affirmative Action/Equal Opportunity THE CITADEL Employer Employer. Applications are invited for a tenure track TENNESSEE position at the assistant or associate level. Qualifications include a Ph.D. in a mathematical MEMPHIS STATE UNIVERSITY SOUTH CAROLINA science or computer science, a firm commitment Department of Mathematical Sciences to undergraduate teaching, and a continuing CLEMSON UNIVERSITY program of research. Preference will be given The Department of Mathematical Sciences is Department of Mathematical Sciences to individuals with qualifications in the areas seeking applications for one tenure-track po­ of statistics, computing, or information science. sition each in DE/Applied Mathematics and Applications are inivited for anticipated tenure­ Salary is competitive. Statistics at the assistant/associate professor track positions at the assistant professor level, The Citadel is a state-supported liberal arts, level. Current areas of research in DE/Applied and possibly higher levels. The Department military college offering undergraduate degrees Mathematics include nonlinear boundary value of Mathematical Sciences includes the areas in the Arts, Sciences, Engineering, Education, problems, functional differential equations, dy­ of algebra/combinatorics, analysis, computa­ and Business Administration. The department namical systems and mathematical modeling. tional mathematics, operations research, and offers bachelor's degrees in mathematics and In Statistics, current areas of research include statistics. Applicants with specialties in any of computer science. Generous support for fac­ applied statistics, biostatistics, survival analy­ these areas are encouraged to apply. Desirable ulty research is available. Send a resume and sis, risk assessment, stochastic modelling and attributes for candidates include an interdisci­ three letters of reference to: Stephen D. Comer, statistical computing. The Department has ex­ plinary research orientation in the mathematical Search Committee, Department of Mathemat- cellent in-house library and computing facilities,

JANUARY 1991, VOLUME 38, NUMBER 1 73 ···············--····--······------·········-···-··········-········-································-···········································-·······-········-················-······························· Classified Advertisements

and offers degrees at all levels through the of applications will begin December 1 and will the nation which attracts outstanding students Ph.D. One additional faculty position is an­ continue until the position is filled. from throughout the world. ticipated. Applicants must have a Ph.D. by UTK is an EEO/AAmtle IX/Section 504 Angelo State University is an equal opportu­ September 1, 1991 and a strong potential for Employer. nity/affirmative action employer. excellence in teaching and research. Selection begins on January 31, 1991. Applications will continue to be accepted until LAMAR UNIVERSITY all positions are filled. Women and minorities are UNIVERSITY OF TENNESSEE strongly urged to apply. Successful candidates Beaumont, Texas Position Available. Assistant/Associate profes­ must meet Immigration Reform Act criteria of The Department of Mathematics seeks appli­ sor of Mathematics and Ecology, The University 1986. Applicants should submit a resume and cations for a tenure-track Assistant/Associate of Tennessee, Knoxville. A tenure-track joint direct three letters of reference to: Professor position beginning Fall 1991. Ap­ appointment in the Department of Mathematics Cecil C. Rousseau, Interim Chair must hold an earned Ph.D., should and the Graduate Program in Ecology is avail­ plicants Department of Mathematical Sciences be active researchers in Applied Mathematics able starting fall 1991. Appointee is expected Memphis State University and/or Numerical Analysis/Scientific Comput­ to interact with a large group of mathematical Memphis, TN 38152 ing, and have a strong commitment to teaching. and theoretical ecologists at UTK and Oak An Equal Opportunity/Affirmative Action Univer­ Lamar is a state supported educational and Ridge National Laboratory (Environmental Sci­ sity. institution of approximately 12,000 ences Division), have or establish an active research students. The Department, which is located research program, teach a variety of under­ within the College of Engineering, offers the graduate and graduate courses in mathematics, and M.S. degrees in Mathematics and lead graduate seminar courses in the Ecol­ B.A., B.S., and has 16 full-time faculty. ogy Program. A Ph.D. in mathematics, ecology, For the approximately 250,000 people in UNIVERSITY OF TENNESSEE or related area is required as well as previ­ the Beaumont area, there are eight muse­ AT CHATTANOOGA ous teaching experience. Area of expertise in ums, a symphony orchestra, ballet, opera, and mathematical ecology is open. Submit a c.v., Department Head other theatrical productions. Other facilities and transcripts, brief plan of future research, and events are found in Houston 85 miles west. The University of Tennessee at Chattanooga have three letters of recommendation sent to Nearby outdoor recreational opportunities in­ invites applications for Head of the Department Dr. Thomas G. Hallam, Chair, Math Ecology clude two of the largest freshwater lakes in of Mathematics. A Ph.D. in a mathematical Search Committee, Department of Mathemat­ Texas, the Big Thicket National Preserve, four science and at least five years of college ics, University of Tennessee, Knoxville, TN national forests, the Gulf of Mexico, and a large mathematics teaching experience are required. 37996-1300. Review of applications will begin inland saltwater lake. Applicants should provide evidence of leader­ December 31, 1990 and will continue until Salary and rank are commensurate with ship in curriculum development, teaching, public the position is filled. UTK is an EEO/AA Title and experience. Send a resume service and research/scholarly activities. In this IX/Section 504 Employer. qualifications primarily undergraduate institution, the faculty is and three letters of recommendation to: Dr. John expected to exhibit excellence in teaching while R. Canon, Chair; Department of Mathematics; maintaining a strong commitment to research Lamar University; P.O. Box 1 0047; Beaumont, and public service. The mathematics depart­ TX 77710. Full consideration will be given to ment has 21 faculty members including a Chair TEXAS completed applications received before March of Excellence in applied mathematics. Located 15, 1991. Lamar is an EEO/AA employer. in a very scenic metropolitan area of 400,000, ANGELO STATE UNIVERSITY UTC has a student enrollment of 7800. Send Department of Mathematics applications with current vita to: Dr. Paul L. Angelo State University is seeking applications RICE UNIVERSITY Gaston, Dean, College of Arts and Sciences, for a tenure track position at the Assistant Pro­ Department of Mathematics 119 Holt Hall, UTC, Chattanooga, TN 37403- fessor level for Fall1991. Candidates must hold 2598. Applications received by January 31, the Ph.D. degree in mathematics. Teaching load Applications are invited for a tenure-track assis­ 1991, will be assured full consideration. Women is twelve hours per semester at a nine-month tant professorship. There is a possibility of an and minorities are encouraged to apply. UTC is salary of $32,775 to $35,159, depending upon upgrade to associate or full professorship for an an Equal Opportunity Employment/Affirmative academic qualifications and college teaching exceptional senior candidate. Candidates must Actionmtle IX Section 504 Institution. experience, plus opportunity for summer teach­ have an extremely strong research background ing at the same monthly salary rate and other and good teaching skills. Preference will be University benefits. Job requirements include given to applicants in low-dimensional topology, ability to communicate effectively with under­ although outstanding candidates in analysis, graduate students, dedication to excellence geometry, and topology will also be considered. Please send a curriculum vitae and at least UNIVERSITY OF TENNESSEE in teaching, and strong commitment to high academic and professional standards. Inquiries 3 letters of recommendation to: Appointments The Mathematics Department of the Univer­ should be directed to: Committee, Department of Mathematics, Rice sity of Tennessee, in an effort to significantly Dr. J. M. Bailey, Head University, P.O. Box 1892, Houston, Texas improve its research position, seeks to fill a Department of Mathematics 77251. tenure-track assistant professorship or junior Angelo State University Rice University is an Equal Opportunity/ associate professorship. Employment begins San Angelo, Texas 76909 Affirmative Action Employer. August 1991. The Department's interests are in Angelo State University has one of the most the areas of algebra, analysis, applied mathe­ modern and attractive campuses in the nation matics, differential equations. geometry, mathe­ and is fully accredited by the Commission on TEXAS A&M UNIVERSITY matical ecology, numerical analysis, probability, Colleges of the Southern Association of Col­ Department of Mathematics and topology. Substantial research accomplish­ leges and Schools. The University student body ments and promise, as well as dedication to of 6,300 ranks first among regional universities The Department of Mathematics invites appli­ teaching are paramount. Interested applicants and third among all state universities in Texas in cations for one or more positions in the fields of should arrange to have a vita, three reference the high percentile ranking of entering freshmen algebra and topology. The department expects letters, and a research statement sent to Profes­ in their high school graduating classes. The to make several appointments in these fields sor John B. Conway, Mathematics, University of University offers one of the largest and most during the next 3 to 5 years in order to expand Tennessee, Knoxville, TN 37996-1300. Review distinctive academic scholarship programs in our algebra and topology group. Currently, we

74 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -········-·· .. ··········-············-·········-········-····-·············-··-·····-·-·-······-····--······-···------··-··········-··-··-··················- ·········-·········-- ...... ·-···---·······-····-······--··- Classified Advertisements

have active researchers in algebraic geometry, important asset in the economic development itive salaries and excellent medical, retirement combinatorics, algebraic K-theory and cyclic of the area. and professional benefits. homology, noncommutative ring theory, knot Applicants should submit a resume and Applications, including resume and three theory, and general topology. We are particu­ arrange to have at least three letters of recom­ letters of reference, should be submitted to: larly interested in modern algebraists who can mendation sent to Russell C. Thompson interact with the people presently at Texas A&M Professor Shair Ahmad, Director Search Committee and in algebraic topologists. Division of Mathematics, Computer Department of Mathematics and Texas A&M University is a major research Science, and Statistics Statistics institution with a total enrollment of 42,000. It The University of Texas at San Antonio Utah State University ranks in the top seven universities nationally San Antonio, Texas 78285-0664 Logan, UT 84322-3900 in extramural research funding and in the top E-mail: [email protected] Review of applications will begin February 1, five universities in the number of national merit The closing date for receipt of applications for 1991, and will continue until the position is filled. finalists currently enrolled. these positions is February 15, 1991 . UTSA is an Utah State University is an Equal Opportu­ To apply, please send a curriculum vitae and Equal Opportunity/Affirmative Action Employer. nity/Affirmative Action Employer. have at least three (3) letters of recommendation We encourage women and minorities to apply. sent to Prof. H. E. Lacey, Head, Department of Mathematics, Texas A&M University, College Station, TX 77843-3368. VERMONT Texas A&M University is an Equal Oppor­ tunity/Affirmative Action Employer. Women and LYNDON STATE COLLEGE minorities are encouraged to apply. UNIVERSITY OF TEXAS Lyndonville, Vermont AT ARLINGTON Tenure-track position in Department of Mathe­ Department of Mathematics matical Sciences, with concentration in Algebra. Applications are invited for several positions be­ Ph.D. for award of tenure; may consider for ginning Fall Semester 1991 . Salary and rank are employment candidates with A.B.D. and in ac­ commensurate with qualifications. The selected tive pursuit of doctorate. Teaching assignment TEXAS A&M UNIVERSITY candidates must have excellent credentials in will range from introductory service courses Department of Mathematics research and teaching. The desired area of to upper-division math major courses. Expe­ expertise are Differential or Algebraic Geome­ rience in mathematics education programs a The Department of Mathematics at Texas A&M try, Computational Geometry, Partial Differential plus. Salary is commensurate with experience; University hopes to fill several tenure-track Equations, Functional Analysis, Statistics and generous fringe benefits package is provided and visiting positions which begin in the fall Applied Mathematics. A resume with three without employee contribution. Academic year semester 1991. All areas will be considered. To letters of recommendation should be sent to: opens August 27, 1991. apply, please send a curriculum vitae and have Dr. Danny Dyer Lyndon State College is a vigorously growing at least three (3) letters of recommendation University of Texas at Arlington comprehensive institution with degrees through sent to Prof. H. E. Lacey, Head, Department Department of Mathematics the master's level. Nestled in the mountains of of Mathematics, Texas A&M University, College Box 19408 Vermont's Northeast Kingdom, Lyndon enrolls Station, TX 77843-3368. Arlington, Texas 76019 1150 undergraduates and 200 graduate and Texas A&M University is an Equal Oppor­ ATTN: RECRUITING CHAIRMAN non-degree students, and employs 60 full-time tunity/Affirmative Action Employer. Women and The University of Texas at Arlington does not and 50 adjunct faculty. minorities are encouraged to apply. discriminate on the basis of race, sex, color, re­ Lyndon's faculty are especially attentive to ligion, national origin, age, handicap, or veteran an academically diverse student body, including status in provision of educational opportunities a growing number of non-traditional students. or employment opportunities and benefits. The The College's mission emphasizes personal at­ University of Texas at Arlington is an Affirmative tention to individuals. Faculty are active in cam­ Action/Equal Opportunity Employer. pus governance and community service, while effective teaching is an important measure for THE UNIVERSITY OF TEXAS continued employment. Successful candidates AT SAN ANTONIO will also demonstrate ability to work harmo­ The Division of Mathematics, Computer Sci­ niously with colleagues in the department. Prior teaching experience is desirable unless noted. ence, and Statistics will have three tenure-track positions at the assistant professor level in Math­ Send letter of application and vita (listing UTAH at least three references) to Chair, Faculty ematics and Statistics, beginning August 1991 . Although applicants in all areas of mathematics Search Committee, c/o Associate Dean Hruska, UTAH STATE UNIVERSITY Lyndon State College, Lyndonville, VT 05851. an statistics will be considered, preference will Department of Mathematics and Statistics be given in one assistant professor position Closing date: February 1, 1991. Lyndon, as an equal opportunity employer, invites applications to those candidates whose research areas are Applications and nominations are invited for one from women and minorities and handicapped in applied or applicable mathematical analy­ or more tenure-track positions at the assistant sis, one to combinatorics and graph theory, or associate level beginning September 1991. persons. and one to mathematical physics. Applicants A Ph.D. (or its equivalent) in one of the math­ should have the Ph.D. degree in Mathematics ematical sciences is required. Preference. will or a related area by August 1991, and should be given to applicants with research interests demonstrate strong potential for excellence in in nonlinear partial differential equations, dy­ VIRGINIA research and teaching. Responsibilities include namical systems, numerical partial differential CHRISTOPHER NEWPORT COLLEGE research, teaching, direction of graduate stu­ equations or numerical optimization; however, dents, and contributing in program developent. highly qualified applicants in other areas will be Christopher Newport College Mathematics Ten­ San Antonio, Texas is a scenic, dynamic considered. ure Track Position at the assistant professor and fast growing city of rich cultural diversity. Excellence in research and a demonstrated or instructor rank for 1991-92 academic year. UTSA is the only public university in the city commitment to both graduate and undergradu­ Salary is competitive. Ability and potential in of San Antonio, and serves a metropolitan ate teaching are required. teaching and research. Should be interested in population of approximately one million people. Utah State University, located in the Wasatch being involved in the education of undergrad­ The univeristy is viewed by the community as an Range of the Rocky Mountains, offers compet- uates and in the other activities of a faculty

JANUARY 1991, VOLUME 38, NUMBER 1 75 ...... Classified Advertisements

member. Applicants must hold a Master's de­ be accepted until the position is filled. CNC hires subject to the continuing availability of funds. gree in mathematics. A Ph.D. is required for U. S. citizens and aliens lawfully authorized to The University is an EO/AA employer. appointment as assistant professor; candidates work in the U. S. AN EOE/AA!EMPLOYER. without Ph.D. but with realistic prospects of completing the Ph.D. in the near future will be considered for appointment at the rank of VIRGINIA POLYTECHNIC INSTITUTE instructor. All areas of Mathematics will be con­ sidered; areas of particular interest are P.D.E. AND STATE UNIVERSITY and nonlinear analysis. Department of Mathematics The Mathematics Department currently has Applications are invited for a tenure-track ap­ ten members only five of whom are tenured. In pointment, subject to budgetary approval, at the addition there are approximately twenty classes level of Assistant Professor beginning with the WEST VIRGINIA taught by adjuncts (many of whom work at 1991-92 academic year. A Ph.D. and strong NASA-Langley Research Center.) research potential are required. Preference will CNC is a growing, state-supported school WEST VIRGINIA UNIVERSITY be given to candidates with postdoctoral experi­ Department of Mathematics with small class sizes. The Mathematics Depart­ ence. Primary areas of interest are algebraic and ment currently grants the BA and BS degrees; differential geometry, discrete mathematics, dy­ The Department of Mathematics intends to an MAT degree will be initiated in 91-92. The namical systems, and computationally oriented make several faculty appointments that will usual teaching load is four three-credit courses mathematics. Applications will be accepted until commence August 1991. One appointment may in each of the two fifteen-week semesters. The March 15, 1991 or until position is filled. Appli­ be at the Associate rank; others will be at area contains CEBAF, NASA and many other cants should send a vita and arrange to have the Assistant rank. Candidates are expected technically oriented companies at which some three letters of reference submitted to Chair, to have a Ph.D. in mathematics or equivalent of the faculty members at CNC do consulting. Search Committee, Department of Mathemat­ with a strong record or demonstrated poten­ Please send applications including three let­ ics, Virginia Tech, Blacksburg, VA 24061-0123. tial in both research and teaching. Preference ters of recommendation, resume, and transcript Women and minorities are encouraged to apply. will be given to applicants whose research (or list of courses taken) to Prof. Martin Bartelt, Virginia Tech is Equal Opportunity/Affirmative interests complement those currently in the Mathematics Department, Christopher Newport Action Employer. Department in algebra, analysis, applied or College, 50 Shoe Lane, Newport News, VA numerical analysis, discrete mathematics. Nor­ 23606. Screening of applications will begin on mal responsibilities include research and a two or about February 18, 1991, but applications will course teaching assignment per semester at be accepted until the position is filled. Christo­ WASHINGTON the graduate or undergraduate level. Applica­ pher Newport College hires U. S. citizens and tions and inquiries should be directed to James aliens lawfully authorized to work in the U. S. WESTERN WASHINGTON UNIVERSITY Lightbourne, Department of Mathematics, West An EOE/AA/EMPLOYER. Virginia University, Morgantown, WV 26506. Applications are invited for tenure-track and Applicants should submit a vita and have three visiting positions to begin Fall 1991. Successful letters of reference sent (senior applicants may candidates will be expected to be active in choose to submit names of references). To research, to interact at the research level CHRISTOPHER NEWPORT COLLEGE insure consideration, application materials must with current department members, and to be Mathematics Education be received by January 15, 1991. WSU is an effective teachers with a commitment to both Tenure Track Opening Affirmative Action/Equal Opportunity Employer. undergraduate and graduate education. Qualified women and minorities are especially The Mathematics Department at Christopher Candidates in the following areas of math­ encouraged to apply. Newport College has a tenure track opening in ematics are especially sought: discrete math­ mathematics education for the 1991-92 school ematics (particularly graph theory), modeling, year. Salary is competitive. Evidence of ability optimization, and statistics. A Ph.D. is required. and potential in teaching and research with A demonstrated interest in the use of com­ credentials sufficient to contribute to the im­ puters for instructional purposes and in the plementation of a new M.A.T. degree program integration of applications of mathematics into in middle school mathematics. Should be in­ classroom material is desirable. terested in being involved in the education Rank and salary are open, but a substantial of undergraduates and graduate students and research record will be required for appoint­ in the other activities of a faculty member. ments above the Assistant Professor level. The The successful candidate must have either (1) normal teaching load for research faculty is two WISCONSIN a doctorate in mathematics education and a courses per quarter. bachelor's degree or its equivalent in mathe­ Western Washington University is located on UNIVERSITY OF WISCONSIN-RIVER FALLS matics; or (2) a Ph.D. in mathematics with a Bellingham Bay in an area of outstanding natu­ Mathematics Faculty Position distinguished record of achievement in mathe­ ral beauty within an hour's drive of the Seattle matics education. K-12 mathematics teaching and Vancouver, B.C., metropolitan areas and Applications are invited for two tenure-track po­ experience preferred. Duties include teaching the Cascade Mountains. The department has sitions at the assistant professor level beginning undergraduate and/or graduate courses, schol­ a strong undergraduate program with a some­ September 1, 1991. Ph.D. in mathematics or a arly activities, professional development and what applied flavor and a flourishing Master's closely related discipline is required. Applicants departmental duties. The department currently program with about twenty students. must have strong commitments to excellence in has ten members only five of whom are tenured. Applications should be sent to Professor undergraduate education and continuing schol­ In addition there are approximately twenty Thomas T. Read, Chairman, Department of arly activity. The current full-time teaching load classes taught by adjuncts (many of whom Mathematics, Western Washington University, averages 12 credit hrs./week; other responsibili­ work at the NASA-Langley Research Center). Bellingham, WA 98225-9063. ties include advising students and departmental, Please send applications including three !etters Interested candidates should submit a letter college, and university work. Salaries are com­ of recommendation, resume, and transcript (or of application, complete transcripts, a vita, and petitive. list of courses taken) to Stavroula K. Gail y, three letters of recommendation addressing The University of Wisconsin-River Falls is Mathematics Department, Christopher Newport the candidate's qualifications in teaching and located in west central Wisconsin, 30 miles College, 50 Shoe Lane, Newport News, VA research. Deadline for applications is February east of St. Paul and Minneapolis, Minnesota. 23606. Screening of application will begin on or 1, 1991; later applications will be considered Enrolling 5,200 students, the university offers about February 18, 1991, but applications will if positions remain available. Positions are bachelor's and master's degrees in the colleges

····························-·-···-· ·················-··················--·········----·········-········-... ··-·····-···········-············ ... ··-··--·········- ·······················-···--····- ····-···-·······-··············-········-····--··-···············-····-··············-·····-···-·····-····- 76 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

of Arts & Sciences, Agriculture, Education, and funding and research activities will be made holders. The salary will be commensurate with in the Graduate School. available. experience and research record. Applicants should submit resume, tran­ Screening will begin February 1 and continue Applications, including C.V. and names of scripts, and three letters of recommendation until the post is filled. ANEOE. references, should be sent to: The Head, De­ to: Send resume and three to five letters of partment of Mathematics, University of British Prof. Stephen E. List, Chair reference directly to: Columbia, Vancouver, B.C. Canada V6T 1Y4. Search and Screen Committee Dr. Mina Bayne, Chairperson Applications received after January 31, 1991 will Department of Mathematics/Computer Mathematics Education Search be considered only if vacancies remain to be Systems Committee filled. The University of British Columbia offers University of Wisconsin-River Falls Div. of Lifelong Learning & Instruction equal opportunity for employment to qualified River Falls, WI 54022 Box 337 4, University Station male and female candidates. In accordance Applications will be received until March 1, 1991 McWhinnie Hall with Canadian immigration requirements, pri­ or until position is filled. The University of Wyoming ority will be given to Canadian citizens and (UW-RF is an Equal Opportunity/Affirmative permanent residents of Canada. The University Action Employer. Women and minorities are of British Columbia is committed to the Fed­ encouraged to apply.) eral Government's employment equity program THE UNIVERSITY OF WYOMING and encourages applications from all qualified individuals. Department of Mathematics Junior Position in Pure Mathematics The Department of Mathematics invites appli­ UNIVERSITY OF TORONTO cations for a tenure-track assistant professor position in pure mathematics. Areas of inter­ Department of Mathematics est include Functional Analysis, Matrix The­ The Department solicits applications for a ory, Group Theory and Algebraic/Computational tenure-stream position in Mathematical Physics Combinatorics. The department has a strong at the downtown (St. George) campus to begin Applied Mathematics group with collateral inter­ on July 1, 1991 . The position is at the level of ests in scientific computation. Research areas Assistant Professor. In case of an exceptional overlapping these interests are particularly en­ candidate who has recently reached tenurable couraged. Excellence in teaching as well as level the appointment may be at Associate productive scholarship is required. Minorities Professor. and women are especially solicited. Duties include teaching and research, and WYOMING Salary is competitive and includes a startup candidates are expected to demonstrate excel­ travel/equipment package. Applicants should THE UNIVERSITY OF WYOMING lence at each. send a curriculum vitae, a description of re­ Applicants should send their complete C.V. A Senior Position in Mathematics search interests, and have three letters of together with a list of publications and arrange Education in the College of Education reference sent to: to have at least three letters of reference sent and The Department of Mathematics W. G. Bridges, Head directly to Professor J. Repka, Associate Chair­ of The College of Arts and Sciences Department of Mathematics man, Department of Mathematics, University of Box 3036, University Station Toronto, Toronto, Canada, M5S 1A 1. To insure The only four-year university in Wyoming, the Laramie, WY 82071 full consideration, this information should be University of Wyoming has an enrollment of Email inqUines should be sent to received by January 15, 1991 . approximately 12,000 students. If you are in­ [email protected]. Applications completed The University of Toronto encourages both terested in joining a faculty which is designing by January 15, 1991 will receive first con­ women and men to apply. In accordance with innovative teacher education programs includ­ sideration. The University of Wyoming is an Canadian immigration requirements, priority will ing elements of teaming and interdisciplinary Affirmative Action/Equal Opportunity Employer. be given to Canadian citizens and permanent approaches, your application is invited. residents. Candidates should have a doctorate in math­ ematics or mathematics education and have a demonstrated ability to interact in both the Math­ ematics Department and College of Education. CANADA UNIVERSITY OF WATERLOO Preference will be given to candidates who Pure Mathematics Department have had a minimum of three years teaching UNIVERSITY OF BRITISH COLUMBIA experience. Mathematics Department, Room 121 , The Department of Pure Mathematics at the The position will entail the development and 1984 Mathematics Road University of Waterloo invites applications for a teaching of methods courses in mathematics Vancouver, B.C., tenure-track position. This position is a bridg­ education for both elementary and secondary Canada, V6T, IY4 ing appointment in anticipation of retirements education majors. In addition, the successful in 1993. Subject to budgetary approval, the applicant will be expected to conduct graduate The Mathematics Department at the University appointment could be made as early as July 1, level seminars in mathematics education and of British Columbia expects to have a number 1991, to a candidate with very strong research to work with the mathematics department in of post-doctoral fellowships, sessional lecture­ and teaching qualifications. developing and teaching mathematics courses ships and visiting positions at the Assistant, The University is committed to increasing and training graduate teaching assistants. Associate and Full Professor level for the year the complement of female faculty members. The position also involves some undergrad­ starting July 1, 1991, subject to the availabil­ Applications from women mathematicians are uate advising as well as directing Masters and ity of funds. We also expect a number of particularly welcome. However, both female and Ph.D. students. Participation in outreach and summer session teaching positions during the male applicants in any area of pure mathematics coordination of the K-9 mathematics curriculum months of May through August 1991. A Ph.D. or will be considered. in our laboratory school will also be expected. equivalent and University teaching experience Duties will include research, and teaching Rank open. Salary to $60,000 depending and evidence of high potential for research in at all levels. Salary will depend on the can­ upon experience and qualifications. A personal Mathematics are required. Since some posi­ didate's qualifications. A Ph.D. is required for microcomputer, graduate assistance and an tions will be partially supported by research consideration. adequate travel budget will be provided. In addi­ grants, these positions will be filled by persons In order to be considered for an appointment tion, a reduced teaching load to accommodate having research interests relating to the grant in 1991, applications must arrive by February 11,

JANUARY 1991, VOLUME 38, NUMBER 1 77 ... ·····-·····-·-········ .. ·····•··················· ...... ------Classified Advertisements

1991. An application should contain a curriculum Both English and Chinese are used in teaching vitae of the candidate plus three letters of HONG KONG and administration. reference sent directly from the referees. Applications are invited for The University intends wherever possible HONG KONG BAPTIST COLLEGE Department of Mathematics Lecturer/Assist­ to fill its vacancies with assistant professors. Principal Lecturer/Senior Lecturer/Lecturer ant: Lecturer (2 posts) (Ref. no. 1081509/2/90) In accordance with Canadian immigration re­ in Mathematics Department Applicants should possess a Ph.D. degree quirements, this advertisement is directed at in Pure/Applied Mathematics. In addition to Canadian citizens and permanent residents. Highly-motivated applied mathematicians in­ participation in the activities of the Board of The University of Waterloo encourages applica­ terested in both research and teaching are Studies in Mathematics, tHe appointees are tions"from qualified women and men, members invited to apply for faculty positions com­ expected to undertake research in their fields of of visible minorities, native peoples, and persons mencing September 1991. Baptist College is specialization and be responsible for teaching at with disabilities. a government-funded institution with a stu­ the undergraduate (including Part-time Degree Please send applications to: dent body of 3000. Our congenial department Programme) and postgraduate levels. The posts Dr. F. A. Zorzitto, Chair of twelve lecturers offers a comprehensive are tenable from August 1991. Department of Pure Mathematics BSc(Honours) curriculum and MPhil by re­ Annual Salary-Lecturer: HK$279,900 - University of Waterloo search. We expect to launch a Ph.D. pro­ 317,580 by 2 increments BAR, HK$336,420 - Waterloo, Ontario N2L 3G1 gram in 1991. Typical teaching load is two 467,700 by 7 increments; Assistant Lecturer: subjects per semester. There is significant HK$203,940-260,940 by 3 increments (approx. micro/minicomputer support for teaching and exchange rate: US$1-HK$7.8; £1 =HK$15.3) research. The College and the government Grade and salary will be commensurate with GERMANY provide research funding support. qualifications and experience. Applicants should have a Ph.D. in math­ Conditions of Service: The University of­ ematics or a related discipline and expertise UNIVERSITAT BONN fers a competitive renumeration package. For in some area of applied mathematics (broadly superannuable appointment, benefits include Research Institute of Discrete Mathematics defined). Appointments to senior positions are leave with full-pay, contributory superannuation Director: Professor Bernhard Korte based on demonstrated teaching excellence, scheme (University 15%, appointee 5%), med­ Postdoctoral Fellowships on substantial research accomplishment, and the ical and dental care, education allowances for Discrete Mathematics ability to provide academic leadership. children, housing benefit for an appointee with Depending on qualification and experience, annual salary of HK$298,740 or above (with The Research Institute of Discrete Mathematics salary ranges from HK$192,420 to HK$333,300 appointee contributing 7,5% of salary towards announces the availability of two Postdoctoral p.a. for Lecturer (approx. 1US$=HK$7.78); the provision of housing benefits). Appointment Fellowships beginning with the academic year HK$348,660 to HK$463,500 p.a. for Senior may also be made on fixed term contract which 1991-1992. Lecturer and HK$413,940 to HK$534,060 p.a. carries equivalent benefits including, where ap­ These awards are intended for young math­ for Principal Lecturer. Benefits include hous­ plicable, contract-end gratuity (15% of basic ematicians and computer scientists with excep­ ing assistance for overseas appointees as well salary) in lieu of superannuable benefits. Fringe tional research promise in Discrete Mathematics as local appointees on a minimum salary of benefits will be packaged flexibly including cash and its applications. The postdoctoral fellows HK$290,700 p.a., medical/dental benefits, ed­ payment options subject to mutual agreement. are invited to take part in all research activities of ucation allowance for children, vacation leave Application Procedure: Send full resume in the Institute, however, teaching of one graduate and passage, baggage allowances for over­ duplicate, giving full particulars as well as names course per semester is expected. seas appointee only. Initial appointment will be and addresses of 3 referees, together with An award for a full academic year will range on 2-year contract with a gratuity of 15% to copies of certificates/diplomas, testimonials and between DM 36,000 and DM 39,600 depending Lecturer and 25% to Senior Lecturer & above recent publications to the Personnel Section, the upon qualifications and experience. The awards payable upon satisfactory completion of con­ Chinese University of Hong Kong, Shatin, Hong are not subject to German income tax. tract. Appointment may be renewed on contract Kong before January 31, 1991. Please quote Applications should include a vita, a bibliog­ or permanent terms. To apply send complete the reference number and mark "Recruitment" raphy, two letters of reference, and a research curriculum-vitae to the Personnel Section, Hong on cover. plan. To be eligible for the 1991-92 competition, Kong Baptist College, 224 Waterloo Road, a complete application should be on hand by Kowloon, Hong Kong [Fax: 852-338-8084). February 28, 1991. Candidates should also ask at least three Send application to: Prof. Hans Jiirgen referees to write to the College on their suit­ THE HONG KONG UNIVERSITY OF Promel, Research Institute of Discrete Math­ ability for the post without delay. Deadline for ematics, University of Bonn, Nassestrasse 2, SCIENCE AND TECHNOLOGY application is 15 February 1991. For more in­ Department of Mathematics D-5300 Bonn 1, W. Germany. formation about the Department contact Fred J. Hickernell, Head, E-mail:[email protected]. The Hong Kong University of Science and Technology is a new publicly funded research University. The first intake of students will UNIVERSITY OF BIELEFELD be in October 1991 at both undergraduate Department of Mathematics and graduate levels including the doctorate. Starting October 1st, 1990, a college for post­ Enrollment is expected to grow to 7,000 FTE graduate and postdoctoral studies in mathemat­ by 1996-1997. The medium of instruction is ics will be instituted at Universitiit Bielefeld. THE CHINESE UNIVERSITY OF English. Applications are invited for the following The main areas of research are: finite, HONG KONG positions: discrete and Lie groups, potential theory, rep­ Professor: Minimum US$79,600 p.a. resentation theory, topology, K-theory, combi­ The Chinese University of Hong Kong (founded Reader: US$58,200- US$77,300 p.a. natorics, numerical analysis, information theory 1963) offers comprehensive programmes up Senior Lecturer: US$55,800- US$74,900 p.a. and statistics. to Ph.D. level in the Humanities, Business Lecturer: US$35,900- US$40,700 Further information and application forms Administration, Science, Medicine, Social Sci­ BAR US$43, 100- US$60,000 p.a. may be obtained from: Prof. Dr. Andreas Dress, ence, Education, Engineering and Architecture. The Department will place major emphasis FakuiUit fiir Mathematik, Universitiit Bielefeld, Current student enrollment is 8,000 full-time on applications with an appropriate component Postfach 8640, 4800 Bielefeld 1, West-Germany equivalent, which will expand to 11,500 by of pure mathematics to preserve the integrity (Telefax: (0521) 106-4743). 1994-95. The University is very active in pro­ of the discipline. Research areas will be highly moting research and consultancies and liaising interdisciplinary and will include scientific com­ with industry and the business sector worldwide. putation, statistics, fluid and solid mechanics,

78 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·····························-·········-·························-······················-·······-···································-···-····------········-······················ ... ·· Classified Advertisements

mathematical physics, analysis, algebra, geom­ depending on qualifications. Specific fields of Geometry, Probability, and Computing Mathe­ etry, etc. interest include matics are especially wanted. Very good library Applicants should have a Ph.D. degree in the Numerical Analysis and computing facilities. Please send vita, and relevant fields. Appointees at the senior level Dynamical Systems letters of recommendation to Chairman. are expected to have a distinguished record Computational Geometry in research and have demonstrated an ability Nonlinear PDE to develop research programs; appointees at Parallel Computing Lecturer level are expected to have outstanding Computer Vision potential to develop research in his/her own and physics-oriented mathematics. fields. Responsibilities include undergraduate Applicants must have a Ph.D. and be able and postgraduate teaching not exceeding two to teach in Korean. Send a resume, three courses per semester. reference letters, academic records, and a Generous fringe benefits including medical description of planned research by the end of and dental benefits, annual leave, and chil­ March. We are in the process of establishing a world­ dren's education allowances are provided. Air LET THE GOVERNMENT FINANCE your new passages, housing or private tenancy allowance class research-oriented educational institution, or existing small business. Grants/loans to with 300 faculty members in eleven departments are also provided where applicable. Initial ap­ $500,000. Free recorded message: (707) 448- pointments will generally be on a three-year and 2000 students (800 graduate and 1200 0201. (SN9) contract which is renewable subject to mu­ undergraduate). tual agreement. A gratuity of an amount equal Our facilities such as computer systems and to 25% of the total basic salary drawn will· be library are already well-equipped for research payable upon successful completion of contract. and educational activities. Teaching loads are It is the intention of the University to introduce a low and salaries high, by both Korean and inter­ superannuation scheme and arrangements will national standards. We have the first graduates be made for eligible staff to join the scheme as this year. The undergraduates are drawn from appropriate. Approved sabbatical leave will be the top few percentiles of high school graduates at fu II salary. in Korea, and the graduates selected by a highly POSITION WAN:rED Applications/nominations should be sent competitive entrance exam. with a complete CV together with the names POSTECH currently has 180 faculty mem­ and addresses of at least three references to: bers, recruited from the best institutions and Research Mathematician, Ph.D. 1983. Spe­ Director of Personnel universities, mostly in the United States. cialization: control theory, differential games, The Hong Kong University of Science Our department has twenty faculty members robotics. Thirty publications. Fourteen years of and Technology both in applied and pure mathematics. academic and industrial research experience in 12/F, World Shipping Centre For further information, contact the Chair, the Academy of Science, USSR. References 7 Canton Road Professor C. N. Lee at the above address available upon request. Available immediately. Tsim Sha Tsui (Tel.: 0011-82-562-79-2041, Fax: 0011-82-562- Contact: Dr. V. Zak, c/o Prof. L. Charny, Boston Kowloon, Hong Kong 79-2799 from the USA) soon, and not later than University, 44 Cummington Street, Boston, MA Fax No.: (852) 735-7806 March 31,1991. 02215 Phone: (617) 353-5442. The search will continue until suitable appoint­ ments are made. TAIWAN KOREA POHANG INST OF SCIENCE NATIONAL CENTRAL UNIVERSITY Department of Mathematics & TECH (POSTECH) PUBLICATIONS WANTED Department of Mathematics Chungli, Taiwan, R.O.C. I Pohang, 790 Korea Positions in Applied & Positions of Professors, Associate Profes­ Wanted: Mathematical books, journals, reprints, Computational Mathematics sors, and visitors are available. Annual salary ephemera. Contact R. K. Dennis, Math. Dept., US$30,000 for new Ph.D. Reasonable teaching White Hall, Cornell U., Ithaca, NY 14853-7901. The Department invites applications for both load. Teaching in English is acceptable. Math­ Tel: 607-255-4027, FAX: 607-255-7149. email: junior and senior positions, with rank and salary ematicians with research interest of Algebra, [email protected]

JANUARY 1991, VOLUME 38, NUMBER 1 79 Modeling and Games Approximation Theory in the and Mathematical Sciences Economic Behavior Editor Ehud Kalai, Northwestern University, Evanston, lllinois Games and Economic Behavior publishes original and survey papers dealing with game-theoretic modeling in the social, biological, and mathematical sciences. Papers published are mathematically rigorous as well as accessible to readers in related fields. The purpose of the journal is to facilitate cross-fertilization between the theory and application of game-theoretic reasoning. Volume 3 (1991), 4 issues In the U.S.A. and Canada: $110.00 ISSN 0899-8256 All other countries: $133.00 IMPACT of Computing in Science and Engineering Managing Editor Peter Deuflhard, Konrad Zuse Center, Berlin, Germany IMPACT of Computing in Science and Engineering focuses on articles from the areas of mathematical and scien­ tific modeling, scientific computing, computer science, and scientific and engineering applications. The journal is interdisciplinary. Its papers touch upon a combination of at least two of the four main areas. Articles typically describe real-life problems attacked by a new or specifically adapted algorithm or by any other new computing technique. Volume 3 (1991 ), 4 issues In the U.S.A. and Canada: $86.00 ISSN 0899-8248 All other countries: $98.00

Under New Editorial Direction Journal of Approximation Theory Editors-in-Chief Paul Nevai, The Ohio State University, Columbus Allan Pinkus, Technion, Haifa, Israel The Journal of Approximation Theory is devoted to new advances in pure and applied approximation theory and related areas, such as classical and abstract approximation, constructive approximation, harmonic analysis and Fourier expansions, function spaces and interpolation of operators, real and complex function theory, orthogonal polynomials and special functions, general orthogonal systems, approximation theoretical aspects of difference and differential equations, multivariate approximation, and spline functions of one and several variables. Volumes 64-67 (1991 ), 12 issues In the U.S.A. and Canada: $452.00 ISSN 0021-9045 All other countries: $534.00 Submit manuscripts to: Journal of Approximation Theory Editorial Office Seventh Floor 1250 Sixth Avenue San Diego, California 92101, U.S.A.

All prices are in U.S. dollars and are sub;ect lo change without notice. 51169 New Releases for the Mathematical Professional

Functional Analysis Matrix Methods An Introduction for Physicists An Introduction Nino Boccara SECOND EDITION Based on a third-year course for French Richard Bronson students of physics, this book is a graduate This new edition emphasizes applications text in functional analysis emphasizing to Jordan-canonical forms, differential applications to physics. equations, and least squares, and includes September 1990, 344 pp., $44.50 a new chapter on inner products, addition­ ISBN: 0-12-108810-3 al material on elementary row applica­ tions, and hundreds of new exercises. Difference Equations February 1991, c. 528 pp., $44.50 (tentative) ISBN: 0-12-135251-X An Introduction with Applications Walter G. Kelley and Allan C. Peterson Representation Theory This book is intended for junior, senior, or beginning graduate courses. It is written and Automorphic as a modem introduction to the subject, Functions with an emphasis on computations and I.M. Gelfand, M.I. Graev, and applications rather than theory. Ilya Piatetski-Shapiro February 1991, c. 368 pp., $44.50 (tentative) This text touches on topics in the theory ISBN: 0-12-403325-3 of automorphic forms which have not yet reached their final form, and is ideal for C*-Aigebras and students and researchers alike. Operator Theory 1990,448 pp., $39.50/ISBN: 0-12-279506-7 Gerard J. Murphy This book constitutes a first- or second­ The Arithmetic and year graduate course in operator theory. It Ring Theory Spectral Properties of assumes a basic knowledge of functional STUDENT EDITION Poincare Series analysis but no prior acquaintance with operator theory is required. Louis Rowen James Cogdell and Ilya Piatetski·Shapiro August 1990,296 pp., $44.50 From a Review of the First Edition: These research-level notes deal with the ISBN: 0-12-511360-9 "As a textbook/or graduate students, spectral properties of Poincare series and Ring Theory joins the best." their relation with Kloosterman sums. Of special interest... -BULLETIN OF THE AMS 1990, 160pp., $24.95/ISBN: 0-12-178590-4 The Unreal Life January 1991, 688 pp., $55.00 ISBN: 0-12-599840-6 of Oscar Zariski Order from your local bookseller Carol Ann Parikh Pearls in Graph Theory or directly from This is the first biography of Oscar Nora Hartsfield and Gerhard Ringel Zariski-arguably one of the greatest mathematicians of the twentieth century. This is a text for an introductory course It includes a summary of his most pioneer­ in graph theory at the sophomore, junior, ACADEMIC PRESS ing work as well as his personal history, and senior levels. It covers the major Harcourt Brace •Jovanovich, Publishers which spans nearly eighty years and topics and theorems but is not unneces­ Book Marketing Department #19011 covers most of the globe. sarily rigorous. 1250 Sixth Avenue, San Diego, CA 92101 1990,256 pp., $29.95/ISBN: 0-12-328552-6 December 1990,264 pages, $29.95 CALL TOLL FREE ISBN: 0-12-545030-3 1-800-321-5068 FAX: 1-800·235·0256 Quote this reference number for free postage and handling on your prepaid order .. 19011 Prices subject to change without notice. '£'11991 by Academic Press, Inc. All Rights Reserved. TC/SS -19011. Muscle. It's the difference between negoti­ your changing cirrumstances. ating insurance for thousands and insurance for Take advantage of this benefit of member­ one. Your Sodety used it to obtain the best quality ship. Calll-800-424-9883 for further details (in coverage for members-at a very low price. Washington, D.C. call457-6820). We also used this group purchasing power to design insurance specifically for your profes­ AMS INSURANCE sional needs. Most plans cover the whole family and stay in effect even when you change jobs. Designed by Members. Your personal policy can also be tailored to suit For Members. Knots and Physics Advanced Series in Mathematical Physics - Vol. 9 by L H Kauffman ( Univ. of Illinois at Chicago) Braid Group, Knot Theory and Statistical This book is an introductory explication on the theme of knot and link Mechanics invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a edited by C N Yang (SUNY, Stony Brook) & M L Ge (Nankat) quasi-physical process. The demands of the knot theory, coupled with a quantum statistical framework create a context that naturally and powerfully "The theory of knots is a problem in topology which underwent in 1985 a includes an extraordinary range of interelated topics in topology and kind of phase transition with the discovery by Jones of his new famous mathematical physics. The author takes a primarily combinatorial stance invariant polynomials. Striking as this discovery was, it was even more toward the knot theory and its relations with these subjects. This has the striking that his work was related to some well known problems in advantage of providing very direct access to the algebra and to the statistical mechanics. There was thus ushered in a new era of cross combinatorial topology, as well as the physical ideas. This book is divided fertilization of ideas in physics and in mathematics. While the full extent into 2 parts: Part I of the book is a systematic course in knots and physics of this welcome development is not yet fathomable, we thought it starting from the ground up. Part II is a set of lectures on various topics worthwhile to collect in this single volume articles by workers in the field related with and sometimes based on Part I. Part II also explores some who have very different approaches. We believe the collection will be side-topics such as frictional properties of knots, relations with useful to many people." Foreword by C N Yang (SUNY, Stony Brook) & combinatorics, knots in dynamical systems. M L Ge (Nankai) 500pp (approx.)/Due: Feb 1991 336pp/Jun 198919971-50-828-1 US$6819971-50-833-8 (pbk) US$38 981-02-0343-8 US$541981-02-0344-6 (pbk) US$28

Advanced Series in Mathematical Physics- Vol.ll Advanced Series in Mathematical Physics - Vol. 10 New Developments in the Theory of Knots Yang-Baxter Equation in Integrable Systems edited by T Kohno (Nagoya Univ.) edited by M Jlmbo (Kyoto Univ.) This reprint volume focuses on recent developments in knot theory arising This volume will be the first reference book devo·ad specially to the Yang­ from mathematical physics, especially solvable lattice models, Yang­ Baxter equation. The subject relates to broad areas including solvable Baxter equation, quantum group and two dimensional conformal field models in statistical mechanics, factorized S matrices, quantum inverse theory. This volume is helpful to topologists and mathematical physicists scattering method, quantum groups, knot theory and conformal field because existing articles are scattered in journals of many different theory. The articles assembled here cover major works from the pioneering domains including Mathematics and Physics. This volume will give an papers to classical Yang-Baxter equation, its quantization, variety of excellent perspective of these new developments in Topology inspired by solutions, constructions and recent generalizations to higher genus mathematical physics. solutions 916pp/Aug 19901981-02-0162-1 US$861981-02-0163-X (pbk) US$48 728pp/Mar 19901981-02-0120-6 US$681981-02-0121-4 (pbk) US$36

Knots, Topology and Quantum Field Theory Integrable Systems Proceedings of the Johns Hopkins Workshop on Current Problems Hanks/ Lectures on Mathematical Physics In Particle Theory 13 Nsnkal/nstltute of Mathematics, Chins August 1987 Florence,ltaly 14-16June1989 edited by X C Song (Peking Univ.) edited by L Lusanna (lnst. Nazionale Fisica Nuc/eare) 264pp/Nov 198919971-50-856-7 US$53 664pp/Dec 19891981-02-0126-5 US$83 Yang-Baxter Equations, Conformal Invariance Non-Perturbative Quantum Field Theory Mathematical Aspects and Applications and Integrability in Statistical Mechanics and by J Frohlich (ETH-ZOrich) Field Theory 850pp (approx.)/Due: Mar 1991 Proceedings of 11 Conference ANU, 981-02-0432-9 US$861981-02-0433-7 (pbk) US$48 Canberra, Australis 10-14 July 1989 edited by M Barber & P Pearce (ANU) Nankai Lectures on Mathematical Physics (1989) 426pp/May 1990/981-02-0067-6 US$53 Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory Quantum Groups Spring Worlcshopon Quantum GroupsArgonneNstlonsl Laboratory Nsnksllnst of Mathematics, Chins 4 Msy-18 May 1989 edited by ML Ge (Nankai) & BH Zhao (Beijing) 16 Apr/1-11 May 1990 edited by T Curtright, D Fairlie & C Zachos 208pp/Sept 19901981-02-0207-5 US$48 250pp (approx.)/Due: Mar 19911981-02-0381-0 US$46 INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS University of Minnesota 514 Vincent Hall 206 Church Street S.E. Minneapolis, Minnesota 55455 FAX (612) 626-7370 telephone (612) 624-6066 ima-staff%csfsa.cs.umn.eduGumnacvx.bitnet ima-staff%csfsa.cs.umn.eduGcs.umn.edu

IMA Summer Program SEMICONDUCTORS July 15 - August 9, 1991

ORGANIZERS Farouk Odeh (chairman), Julian Cole, William M. Coughran, Jr., Peter Lloyd, Jacob White

The goal of the program is to foster interation in this interdisciplinary field which involves electrical engineers, computer scientists, semiconductor physicists and mathematicians, from both university and industry. The program will particularly encourage participation of numerical and mathematical analysts with backgrounds in ordinary and partial differ­ ential equations and help get them involved in the mathematical aspects of semiconductor models and circuits. Leading engineers in semiconductors will be invited to present the sig­ nificant industrial issues as well as to concentrate on those models which are most relevant to mathematicians. The main topics of the program are: Week 1, July 15-19 1991 ...... PROCESS MODELING Week 2, (1~ weeks), July 22-30, 1991 ...... DEVICE MODELING Week 3, (~ week), July 31-August 2, 1991 ...... QUANTUM EFFECTS Week 4, August 5-9, 1991 ...... CIRCUIT ANALYSIS *********************************** Partial list of confirmed speakers and participants (in addition to organizers): 0. Axelsson M. Giles H.C. Liu P. Poupaud M. Steer G. Baccarani M. Henderson P. Markowich E.J. Prendergast H. Steinrueck R. E. Bank K. Hess B. Meinerzhagen L. Reyna A. Strojwas H. Bennett J. W. Jerome R. Melville C. Ringhofer P. Szmolyan L. Borucki W. Juengling 0. Nevanlinna D. J. Rose H. Tang E. Buturla J. King J.-I. Nishizawa M. Rudan E. Thomann D. Cole K. Kundert R. R. O'Brien C. Schmeiser H. Vander Vorst P. Degond M. Law R. E. O'Malley T. Seidman J. Vlach C. Gardner Y. LeCoz 0. Palersinki M. Sever M. Ward C.W. Gear W. Liniger L. R Petzold K. Singhal P. Yang D. Gerber M. Zlamal

Some partial support is still available for researchers (including graduate students) who are, or wish to become, familiar with.the subject. Preference will be given to those who participate in the entire program. For details write to Avner Friedman, Director, at the above address. PARTICIPATING INSTITUTIONS:Georgia Institute of Technology, Indiana University, Iowa 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 Manitoba, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, Wayne State University PARTICIPATING CORPORATIONS:Bellcore, Cray Research, Eastman Kodak, General Motors, Hitachi, Honeywell, IBM, Motorola, 3M, UNISYS Titles i11 Applied Mathe111atics froJn SIAM Proceedings of the Second Annual ACM-SIAM Symposium on Discrete Mathematical Aspects of Numerical Grid Generation Algorithms Edited by Jose E. Castillo Contains papers presented at the symposium, Numerical grid generation plays a critical role in any scientific computing problem when the held in January 1991 in San Francisco and geometry of the underlying region is complex or when the solution has a complex structure. This jointlysponsoredbytheACMSpeciallnterest text discusses the mathematical aspects of grid generation in order to provide a deeper under­ Group on Automata Theory and the SIAM standing of the algorithms and their limitations. Variational methods are emphasized because Activity Group on Discrete Mathematics. they are more robust, but elliptic and transcendental algebraic methods are also considered. Although SODA is not intended to focus on any particular application area or algo­ Contents. Preface; Introduction, J.E. Castillo and S. Steinberg; Intrinsic Algebraic Grid Generation, P.M. Knupp; rithm type, it emphasizes a particular mode Elliptic Grid Generation and Conformal Mappmg, C.W. Mastin; Surface Grid Generation and Differential Geometry, of analysis. Areas of application Z.U.A. Warsi;Harmonic Maps in Grid Generation, A. Dvinsky;Mathematical Aspects of Harmonic Grid Generation, include com­ S.S. Sritharan; Harmonic Maps and Grid Generation, G. Liao; Continuum Variational Formulation, J.E. Castillo; binatorial optimization, geometry and graph­ Discrete Variational Grid Generation, J.E. Castillo; Bifurcation of Grids on Curves, S. Steinberg and P.J. Roache. ics, numerical and scientific computing, combinatorics and graph theory, algebra and March 1991/ Approximately 176 pages I Softcover /Frontiers in Applied Mathematics 8 number theory, symbolic computation, List Price: $24.50 I SIAM Member Price: $19.60 mathematical programming, artificial intelli­ Order Code FROB/ ISBN 0-89871-267-X gence, and data structures. January 1991/ Approx. 550 pages I Softcover Proceedings in Applied Mathematics 49 Large-Scale Numerical Optimization List Price: $45.00 I SIAM Member Price: $36.00 Thomas F. Coleman and Yuying U Order Code PR49/ ISBN 0-89871-271-8 This volume contains timely developments in large-scale optimization as well as practical developments in interior point methods. It discusses special techniques and new methods regarding parallel techniques for optimization and includes leading researchers among its Problems in Applied Mathematics contributors. Selections from SIAM Review Contents. Part 1: Applications; A Parallelized Algorithm for Image Reconstruction from Noisy Projections, G.T Edited by Murray S. Klamkln Herman, D. Odhner, K.D. Toennies, and S.A. Zenios; Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis, O.L. Mangasarian, R. Setiono, and W.H. Wolberg; On the Performance of People in all walks of life-and perhaps Algorithms for Large-Scale Bound Constrained Problems, J.J. More; Part II: Linear and Quadratic Problems; A mathematicians especially-delight in work­ Quadratically-Convergent Algorithm for Linear Programming Problem With Lower and Upper Bounds, T.F. Coleman ing on problems for the sheer pleasure of andY. U; Solving Multicommodity Network Flow Problems by an Interior Point Method, C. Choi and D. Goldfarb; meeting a challenge. The problem section of The Primal-Dual Interior Point Method On the Cray Supercomputer, I.J. Lustig, R.E. Marsten, and D.P. Shanno; The SIAM Review has always provided such a Effects of Degeneracy and Null and Unbounded Variables on Variants of Kilrmarkar' s Linear Programming Algorithm, challenge for mathematicians. The section M.J. Todd; Computational Aspects of an Interior Point Algorithm for Quadratic Programming Problems with Box was started Constraints, C-G Han, P.M. Pardalos, andY. Ye; Part III: Sparse and Nonlinear Problems; Direct Calculation to offer classroom instructors and of Newton Steps Without Accumulating Jacobians, A. Griewank; The Performance of Several Algorithms for Large their students, as well as other interested Scale Unconstrained Optimization, J. Nocedal; Sparse Jacobian Estimation and Factorization on a Multiprocessor, P .E. problemists, a set of problems-solved or Plassmann; Compact Clique Tree Data Structures in Sparse Matrix Factorizations, A. Pothen and C. Sun; Part IV: unsolved-illustrating various applications Parallel Approaches; Adaptive, Asynchronous Stochastic Global Optimization Algorithms for Sequential and of mathematics. In many cases the unsolved Parallel Computation, S.L. Smith, E. Eskow, and R.B. Schnabel; The k-Step Arnoldi Process, D.C. Sorensen; A problems were eventually solved. Problems in Comparative Study of Parallel Dual Coordinate Ascent Implementations for Nonlinear Network Optimization, S.A. Applied Mathematics is a compilation of 380 of Zenios, R. Qi, and E. D. Chajakis. SIAM Review's most interesting problems December 1990 / xii + 255 pages I Softcover I Proceedings in Applied Mathematics 46 dating back to the journal's inception in 1959. List Price: $38.50/ SIAM Member Price: $30.80 Contents. Mechanics; Electrical Resistance; Proba­ Order Code PR46/ ISBN 0-89871-268-8 bility; Combinatorics; Series; Special Functions; Ordinary Differential Equations; Partial Differential Equations; Definite Integrals; Integral Equations; Matrices and Determinants;Numerica!Approxima­ The Method of Equivalence and Its Applications tions and Asymptotic Expansions; Inequalities; Op­ timization; Graph Robert B. Gardner Theory; Geometry; Polynomials; Simultaneous Equations; Identities; Zeros; Func­ "The booklet provides a thorough, clear, and carefully written introduction into E. Cartan's method of tional Equations; Miscellaneous; Appendix. equivalence presented for the first time from the point of view both of geometry and of applied mathematical analysis. The stress is made on the algorithmical description conveniently illustrated by a number of examples October 1990 I xxvii + 588 pages/ Softcover selected from the calculus of variations, control theory, ordinary and partial differential equations, and List Price: $36.50/ Member Price: $29.20 Riemannian geometry. Only a modest background in calculus on manifolds and elements of Lie groups are Order Code 01'20 /ISBN 0-89871-259-9 assumed." -T. Chrastina, Zentralblatt fiir Mathematik -Mathematics Abstracts, 1990 The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description TO ORDER, PLEASE CONTACT: of this method, which finds invariants of geometric objects under infinite dimensional pseudo­ groups, is presented for the first time. SIAM Customer Services, BKAM91 As part of the algorithm, Gardner introduces several major new techniques. In particular, 3600 University City Science Center the use ofCartan's idea of principal components that appears in his theory ofRepere Mobile, and Philadelphia, PA 19104-2688 the use of Lie algebras instead of Lie groups, effectively a linear procedure, provide a tremendous simplification. One must, however, know how to convert from one to the other, and the author 215-382-9800 I Fax: 215-386-7999 provides the Rosetta stone to accomplish this. In complex problems, it is essential to be able to E-mail: [email protected] identify natural blocks in group actions and not just individual elements, and prior to this publication, there was no reference to block matrix techniques. Call Toll Free 1-800-447-SIAM Monday-Friday, 8:30-4:45 EST Contents. Equivalence Problems; Lifting of Equivalence Problems to G-Spaces; The Structure Equations; ReductionoftheStructureGroup;ThelnductiveStep;e-structures;GlobalResultsandlnvolutiveStructure;Ser­ Please have all ordering information endipity; Normal Forms and Generalized Geometries; Prolongation. ready when you call. 1989/ vii + 127 pages I Softcover ICBMS-NSF Regional Conference Series in Applied Mathematics 58 List Price: $21.75 I SIAM Member Price: $17.40 Order Code CB58/ ISBN 0-89871-240-8 • 5.1a.JTl. ® =r Professeur en mathematiques fondamentales Departement de mathematiques et d'informatique

Le departementde mathematiques etd'informatique sollicite des candidatures pour com bier un poste de professeurregulier ou invite familiarise avec tousles domaines des mathematiques mais ayant une preference pour Ia geometrie algebrique,les equations aux derivees partielles,la physique mathematique etla combinatoire enumerative.

Les domaines d'activite de recherche du departementsont Ia combinatoire enumerative, Ia geometrie differentielle et Ia topologie,les groupes et algebres de Lie et Ia logique. Sommaire de Ia fonction • Recherche • Direction d'etudiants au niveau du doctorat etde Ia maitrise • Enseignement aux trois cycles • Services i Ia communaute La charge norm ale d'enseignement est de six heures par semaine. L'enseignement se fait en franqais. Exigences Le candidat devra posseder un Ph.D. en mathematiques ou I' equivalent et une experience ou des capacites reconnues en recherche. En conformite avec /es exigences de /'immigration canadienne,/a preference sera donnee aux citoyens canadiens et aux residents permanents. L'UQAM souscrit aun programme d'acces a/'egalite des femmes en emploi. Faites parvenir avant le 15 fevrier 1991 un curriculum vitae, des tires apart de publications recentes ainsi que trois lettres de recommandation (directement des signataires) i M. Philippa Gabrini, diractaur, dipartamant de mathamatiquas at d'informatiqua, Univarsite du Quebec a Montreal, C.P. 880. succursala A, Montreal (Quebec) CANADA H3C 3P8. Tal.: (514)987-3239, t818copieur: (514) 987-8477

,,, Universite du Quebec a Montreal

MEMORIAL UNIVERSITY OF NEWFOUNDLAND St. John's, Newfoundland, Canada

HEAD, DEPARTMENT OF MATHEMATICS AND STATISTICS

Applications and nominations are invited for the position of Head of the Department of Mathematics and Statistics. The department, situated in the Faculty of Science, offers undergraduate and graduate programs in mathematics, applied mathematics, statistics and applied statistics up to the Ph.D. level. The department presently has 37 mathematicians, 11 statisticians and 11 support staff.

Applicants should have demonstrated excellence in research and teaching in mathematics and/or statistics, and be able to show leadership and administrative ability appropriate to the position of Head of a multidisciplinary department. The appointment will normally be made at the rank of Professor and qualifications in either mathematics or statistics commensurate with this rank are expected. The deadline for receipt of applications is 1 March 1991.

Memorial University has a student population of about 17,000 and is the only university in the province of Newfoundland and Labrador. St John's is the provincial capital with a population of over 150,000 in the metropolitan area, and one of the oldest cities in North America. It enjoys a moderate climate and offers numerous outdoor acitivities throughout the year.

Please address. enquiries, nominations, and applications, including a full Curriculum Vitae and the names of at least three references, to:

J. M. Foltz, Associate Dean of Science Chair, Search Committee for Head of Mathematics and Statistics Memorial University of Newfoundland St John's, Newfoundland, Canada AlB 3X7 [email protected] Telephone: (709) 737-8155, Fax: (709) 737-3316

Memorial University encourages both men and women to apply for this position. In accordance with Canadian Immigration requirments, priority will be given to Canadian citizens and permanent residents of Canada. ROBOTICS

R.W. Brockett, Editor THE AUSTRALIAN THE AUSTRALIAN NATIONAL UNIVERSITY NATIONAL UNIVERSITY Proceedings of Symposia School of Mathematical Sciences School of Mathematical Sciences in Applied Mathematics, Volume 41 Postdoctoral Postdoctoral The central problem of robotics is the analysis and replication of patterns of movement re­ Fellow Fellow quired to accomplish useful tasks. Physicists have found that deeper examination of the physical world often reveals inadequacies in the Reseach Fellow Research Fellow vocabulary and mathematics used to describe it; in much the same way, roboticists have found it quite awkward to give precise, succinct descrip­ Senior Senior tions of effective movements using the syntax and semantics in common use. What is needed Research Fellow Research Fellow to produce general purpose robots is a more ex­ Applications are invited from suitably qual­ pressive means for discussing movement. This Applications are invited from suitably qualified people for appointment to a full­ ified people for appointment to a full-time volume focuses on some of the ways that mathe­ research position as Postdoctoral Fellow, matics can be used to address problems in this time research position as Postdoctoral Fellow, Research Fellow or Senior Research Fellow or Senior Research Fellow area. in Pure Mathematics within the research Focusing on some of the important mathemati­ Research Fellow in Statistical Mechanics to work with Professor R.J. Baxter FAA, sections of the Institute of Advanced Studies cal questions arising in the field of robotics, this component of the School of Mathematical book conveys a sense for the effectiveness of FRS. Other sections of the School and the University are also active in research Sciences. The principal research groups are mathematics in capturing the essence of robot­ in algebra, functional analysis and geometry in related areas. The appointee will hold ics problems. In addition, the book will make and the senior researchers are: G. Huisken, a joint position within the Mathematics readers aware of the way in which computer L.G. Kovacs, M.F. Newman, R.W. Rich­ Research Section of the School of Math­ control interacts with geometry. The first four ardson and D.W. Robinson. Other sections ematical Sciences and the Department of papers deal with kinematics and control, relying of the School and the University are also on realistic models for kinematic processes. The Theoretical Physics of the Research active in research in related areas. No teach­ last two papers have more of the flavor of School of Physical Sciences. No teaching ing is required, but some participation in computer science and are concerned with the is required, but some participation in advanced undergraduate courses may be symbolic descriptions of motion, including the advanced undergraduate courses may be available. It may also be possible to combine treatment of uncertainty. available. Applications from those able to a part-time research position of this kind The book is directed toward mathematically take leave of absence from their own with a part-time teaching position in the literate readers interested in finding out about institutions will be welcomed. Department of Mathematics of the Faculty the questions that arise in robotics and how Enquiries may be addressed to Dr M.F. of Science. Applications from those able to mathematics can help answer them. A mathe­ Newman (Telephone 61 6 249 2955; Fac­ take leave of absence from their own insti­ matical background at the level of an under­ simile 61 6 249 0759; e-mail address tutions will be welcomed. graduate degree in mathematics and some knowl­ [email protected]). Enquiries may be addressed to Dr M.F. edge of basic mechanics is assumed. Closing date: 31 January 1991. Newman (Telephone 61 6 249 2955; Fac­ simile 61 6 249 0759; e-mail address Ref: SMS 26.11.1 [email protected]). SALARY: Closing date: 31 January 1991. Senior Research Fellow; Ref: SMS 26.11.2 $A45, 729-$A54,255 p.a. Research Fellow; SALARY: $A33,163-$A43,096 p.a. Senior Research Fellow; $A45,729-$A54,255 p.a. Postdoctoral Fellow Grade 1 All prices subject to change. Free shipment by (fixed point); Research Fellow; surface; for air delivery, please add $6.50 per $A28,792-$A32,762 p.a. $A33,163-$A43,096 p.a. title. Prepayment required. Order from Ameri­ Postdoctoral Fellow Grade 1 (fixed point); Appointment: Senior Research Fellow/ can Mathematical Society, P.O. Box 1571, $A28,792-$A32,762 p.a. Research Fellow up to three years, pos­ Annex Station, Providence, RI 02901-1571, or sibility of extension to five years; Post­ Appointment: Senior Research Fellow/ call toll free 800-321-4AMS (321-4267) in the doctoral Fellow normally two years, Research Fellow up to three years, possibility continental U.S. and Canada to charge with possibility of extension to three years. of extension to five years; Postdoctoral Visa or MasterCard. Fellow normally two years, possibility of Applications should be submitted in extension to t1!t'ee years. 1980Mathematics Subject Classifications: 70, duplicate to: The Registrar, The Aus­ Applications should be submitted in dupli­ 53,68,93 tralian National University, GPO cate to: The Registrar, The Australian ISBN 0-8218-0163-5, LC 90-1220, ISSN Box 4, Canberra ACT 2601 Australia, National University, GPO Box 4, 0160-7634 quoting reference number and including Canberra ACT 2601 Australia, quoting 196 pages (hardcover), November 1990 curriculum vitae. The University reserves Individual member $31, List price $51, reference number and including curriculum the right not to make an appointment or vitae. The University reserves the right not Institutional member $41 to appoint by invitation at any time. Fur­ to make an appointment or to appoint by To order, please specify PSAPM/41NA ther information is available from the invitation at any time. Further information Registrar. is available from the Registrar.

1111 l\1\IH\11\ I\\:'\ 1-l~l \1 OI'I'OHil:\11) 1\11'10\11{ University of Wyoming Rocky Mountain Mathematics Consortium Regional Summer School

RECENT DEVELOPMENTS IN DIFFERENTIAL EQUATIONS AND ECOLOGICAL MODELING

July 15 - August 2, 1991

The course will address certain topics of differential equations and dy­ namical systems with emphasis on persistence theory, and show how they may be applied to the analysis of models in population ecology. There are two main objectives in this course. The first is to introduce a new spectrum of applications into the undergraduate and graduate teaching of differential equations. The second is to create an awareness in both pure and applied mathematics of the many unsolved problems in mathematical PhD in Mathematics (or near completion) re­ ecology. Some of the topics to be included are dynamical systems, hyper­ quired; preference given to applicants with cycles, persistence theory, Lotka-Volterra systems, predator-prey models, research interests of department. Position competition, mutualism, food chains, functional differential equations. normally renewed for a second year upon PREREQUISITES: A familiarity with ordinary differential equations satisfactory performance of duties. Submit is required, and some knowledge of elementary linear algebra is desired. a letter of application and vita, and have SPEAKERS: The two lecturers are Herbert I. Freedman, University of Alberta and Paul E. Waltman, Emory University. Both will lecture for three reference letters sent by February three weeks. A few additional lectures will be presented by distinguished 20, 1991 to: Lewis Pakula, Search Commit­ experts in the subject. tee Chair, Lecturers, Mathematics ADMISSION AND SCHOLARSHIPS: Entry into the summer school (021094) Position. is restricted, but is without charge to those who are qualified and are admitted. National Science Foundation funding which consists of liv­ ing costs and a few stipends is available for selected faculty. A limited number of scholarships, covering living costs, are available for qualified The University of Rhode Island graduate students. For further information and application forms, please write to: P.O. Box G. Kingston, RI 02881 Professor A. Duane Porter - Mathematics Department An Affirmative Action/Equal Opportunity Employer Box 3036- University of Wyoming Laramie, WY 82071

FINITE GEOMETRIES NEW NOTICES CLASSIFIED RATES AND COMBINATORIAL DESIGNS TO BEGIN JANUARY 1991 Earl S. Kramer and Spyros S. Magliveras, Editors

Beginning in January 1991 classified advertising rates in the Notices Contemporary Mathematics, Volume Ill will be $55 per inch on a single column (one inch minimum), calculated from top of type; $25 for each additional 1/2 inch or More than eighty participants from all over the world attended an fraction thereof. AMS Special Session on Finite Geometries and Combinatorial De­ signs held in Lincoln, Nebraska in the fall of 1987. This volume Advertisements in the "Positions Available" classified section are set contains the proceedings of that Special Session, in addition to several with a minimum one-line headline, consisting of the institution name invited papers. Employing state-of-the-art combinatorial and geomet­ above body copy, unless additional headline copy is specified by the ric methods, the papers show significant advances in this area. Topics advertiser. Advertisements in other sections of the classified pages range over finite geometry, combinatorial designs, their automorphism groups, and related structures. will be set according to the advertisement insertion. Requiring graduate-level background, this book is intended primar­ ily for researchers in finite geometries and combinatorial designs. Headlines are centered in boldface at no extra charge. Classified However, the interested nonspecialist will find that the book provides rates are calculated from the top of the type in the headline to the an excellent overview of current activity in these areas. bottom of the type in the body copy, including lines and spaces within. Any fractional text will be charged at the next 1/2 inch rate. 1980 Mathematics Su/~ject All prices subject to change. Free Additional details may be found on the Classifications: 05, 51 shipment by surface; for air delivery, Advertising Rate Card. Any questions ISBN 0-8218-5118-7, LC 90-45302, please add $6.50 per title. Prepay­ should be directed to the AMS Adver­ ISSN 0065-9266 ment required. Order from 312 pages (softcover), October 1990 American Mathematical Society, tising Department, P.O. Box 6248, Individual member $32, P.O. Box 1571, Annex Station,. Providence, RI 02940; telephone 401- List price $53, Providence, RI 02901-1571. or call 455-4000 or 800-321-4AMS (321- Institutional member $42 toll free 800-321-4AMS (321-4267) 4267) in the continental U.S. and To order, please specify in the continental U.S. and Canada to Canada; FAX 401-455-4004. CONM/IIINA charge with Visa or MasterCard. Mathematical Impressions

Anatolii T. Fomenko

"/think of my drawings as if they were photographs of a strange but real world, and the nature of this world, one of infinite objects and processes, is not wed known. Clearly there is a connection beMeen the mathematical world and the real world .... This is the relationship I see between my drawings and mathematics."-Anatolil Fomenko, in the Introduction

Anatolil Fomenko is a Soviet mathematician with a talent for expressing abstract mathematical concepts through artwork. Some of his works echo those of M.C. Escher in their meticulous rendering of shapes and patterns, while other pieces seem to be more visceral expressions of mathematical ideas. Stimulating to the imagination and to the eye, his rich and evocative work can be interpreted and appreciated in various ways-mathematical, aesthetic, or emotional.

This book contains 84 reproductions of works by Fomenko (23 of them in color). In the accompa­ nying captions, Fomenko explains the mathematical motivations behind the illustrations as well as the emotional, historical, or mythical subtexts they evoke. The illustrations carry the viewer through a mathematical world consisting not of equations and dry logic, but of intuition and inspiration.

Since the mid-1970s, Fomenko has created more than 280 illustrations. Not only have his images filled pages of his own numerous books on geometry, but they have also been chosen to illustrate books on other subjects, such as statistics, probability, and number theory. In addition, his works have found their way into the Soviet scientific and popular press and have been displayed in more than 100 exhibits in the Soviet Union, Holland, India, and much ofEastem Europe.

Fomenko describes his images as "deep reflections about the essence of being and about the place of modem man-in particular, the learned man-in the stormy and unpredictable world surrounding him." His illustrations are the product of a sensitive, aesthetically attuned mind diving deep below the surface of modem mathematics and emerging with great stories to tell.

1980 Mathematics Subject Classification: 00 All prices subject to change. Free shipment by ISBN 0-8218-0162-7, LC 90-47514 surface; for air delivery, please add $6.50 per 194 pages (hardcover), December 1990; title. Prepayment required. Order from Amer­ Individual member $36, List price $45. icanMathematicalSociety,P.O.Box 1571, Anex To order, please specify MATIMP/NA Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS(321-4267)inthecontinental U.S. and Canada to charge with VISA or MasterCard. FIFTY YEARS OF EIGENVALUE NONWELLFOUNDED SETS I PERTURBATION THEORY AND THEIR APPLICATIONS Barry Simon I Jon Barwise Over the last fifty years, eigenvalue perturbation theory Nonwellfounded sets were originally a part of set has seen substantial progress. Some important open problems theory but were later banned because they were thought remain, but the connection between perturbation series and to be implicated in the paradoxes of set theory. (An eigenvalues is now fairly well understood. In this videotaped example of a non well founded set is a = ( 1,2, a), with the lecture, Barry Simon presents a historical overview of the usual definition of an ordered triple.) However, in recent developments of the past half-century, lecturing with clarity years, they have been finding their way back into set and insight on this area at the borderline of mathematics and theory as researchers have shown that nonwellfounded theoretical physics. The first half of the fifty years covered sets are far from incoherent and in fact have many useful in the lecture were marked by the development of abstract applications in computer science, artificial intelligence, theories by Kato and coworkers of such topics as analytic and cognitive science. This videotaped expository lec­ perturbations, asymptotic series, and stability. In the second ture presents a fascinating look at the use and theory of half of the period, when the emphasis shifted to a more nonwellfounded sets. Illuminating the subject with clarity detailed study of specific models, three themes have emerged: ofexposition and with carefully chosen examples, Barwise Bender-Wu asymptotic formulae, Borel summability, and first motivates the subject with a discussion of applica­ complex scaling. Among the topics covered are convergent tions, then moves on to the theory. This lecture would be perturbation theory, summability methods, double wells, accessible and appealing to anyone with a background in isoelectronic sequences, anharmonic oscillators, and the undergraduate mathematics. Zeeman and Stark effects. 1980 Mathematics Subject Classifications: 46, 81 1980 Mathematics Subject Classifications: 04, 03 ISBN 0-8218-8034-9 ISBN 0-8218-8033-0 NTSC format on 1/2 " VHS videotape; NTSC format on 1/2 " VHS videotape; approx. one hour, December 1990, Price $59 approx. one hour, December 1990, Price $59 To order, please specify VIDSIMON/NA To order, please specify VIDBARWISE/NA

FIFTY YEARS OF SOME APPLICATIONS OF MATHEMATICAL REVIEWS GROUP I Saunders Mac Lane REPRESENTATIONS its fiftieth anniversary I Mathematical Reviews celebrated Nolan Wallach at the Joint Mathematics Meetings in Louisville, Kentucky In this videotaped lecture, Nolan Wallach presents in January 1990. This historic event was highlighted by a examples of applications of Lie theory that show how the lecture by Saunders Mac Lane, whose broad knowledge, subject has gone beyond its original roots in an unex­ long memory, and caustic wit make this videotaped lecture pected way. Lie initially envisioned his theory as a way entertaining and insightful. Starting with the origins of MR, of solving differential equations by reducing the number Mac Lane tells a story peppered with many anecdotes. He of variables. As Wallach demonstrates, Lie theory is culled some of the amusingly scathing reviews that have often used today to set certain problems in a larger appeared in MR and even discovered a case of what might context by increasing the number of variables. Although be a record for getting the largest number of papers out of a the system then becomes larger, it often becomes simpler single theorem. In addition, he gives a sense for the way MR because one can use the power of abstraction in represen­ has expanded and changed over the years. The lecture is a tation theory and exploit symmetries in the new, larger fitting tribute from one great influence in mathematics to system. Using examples from differential equations and another. classical and quantum mechanics that demonstrate this principle, Wallach presents a lucid and engaging lecture. 1980 Mathematics Subject Classification: 01 The lecture should be accessible to advanced under­ ISBN 0-8218-8035-7 graduates or graduate students with strong backgrounds NTSC format on 1/2 " VHS videotape; in analysis. approx. one hour, December 1990, Price $59 To order, please specify VIDMAC/2NA 1980 Mathematics Subject Classification: 22 All prices subject to change. Free shipment by surface; for air delivery, please ISBN 0-8218-8036-5 Math­ add $6.50 per title. Prepayment required. Order from American format on 1/2 " VHS videotape; ematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901- NTSC 1571, or call toll free 800-321-4AMS (321-4267) in the continental U.S. approx. one hour, December 1990, Price $59 and Canada to charge with VISA or MasterCard To order, please specify VIDWALLACH/NA Application for Membership 1991 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ......

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Fold lwre The importance of submodular functions studied theoretically in connection with has been widely recognized in such equations have been the solitons, combinatorial optimization. This is the first shock waves and turbulence or chaotical Volume II: book devoted to the exposition of the processes. The latter two phenomena Finite Element theory of submodular functions, and deals lead to nonclassical or generalized edited by P.G. the subject from an elementary solutions for nonlinear partial differential ical level to an advanced one. equations. 1990 X+ 928 emphasis placed on the Price: US $11 aspects of the theory, which ISBN 0-444- to practical, efficient algorithms. Quasi homogeneous This is the second Distributions which will cover all Numerical ntum Physics, Relativity, by 0. von Grudzinski reference work on Complex Spacetime (North-Holland Mathematics Studies, 165) Contents: Finite 1991 viii + 450 pages Introduction (J. T Price: US $128.50/Dfl. 225.00 Estimates for ISBN 0-444-88670-2 Ciarlet). Local Methods (L.B. vvan1n,,. This is a systematic exposition of the Hybrid Methods (J.E. basics of the theory of Thomas). Eigenvalue quasihomogeneous functions and Babuska, J. Osborn). distributions. A major theme is the method (H. Fujita, T. Suzuki). of taking quasi homogeneous averages. It serves as a central tool for the study of the solvability of quasi homogeneous multiplication equations and of Latin Squares quasihomogeneous partial differential New Developments in equations with constant coefficients. Applications

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New, softcover edition available- M.H. Protter and C.B. Morrey, Jr., H.-D. Ebbinghaus and H. Hermes, Universitat Freiburg; University of California, Berkeley, CA F. Hirzebruch, Max-Planck-Institut fiir Mathematik, A First Course in Real Analysis Bonn; M. Koecher and R. Remmert, Universitat Second Edition Miinster; K. Mainzer, Universitat Augsburg; J. Neukirch, Universitat Regensburg; and A. Prestel, Designed for a first course in real analysis following the standard course in elementary calculus. Since many stu­ Universitat Konstanz, all FRG dents encounter rigorous mathematical theory for the trrst With an Introduction by K. Lamotke; English Edition time in this course, the authors have included such el­ edited by J. Ewing; Translated by H.L.S. Orde ementary topics as the axioms of algebra and their imme­ Numbers diate consequences as well as proofs of the basic theo­ This is a book about the system of numbers - all kinds rems on limits. 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It is a story that will give the reader the techniques of proofs and the standard tools of analysis. both a glimpse of the mystery surrounding imaginary Many changes have been made in this second edition. numbers in the 17th century and also a view of some The most notable is the addition of many problems and major developments in the 20th century. the inclusion of answers to most of the odd-numbered ex­ 1991/395 pp., 24 illus./Softcover/$39.00/ISBN 0·387·97497·0 ercises. The book's readability has also been improved Graduate Texts in Mathematics, Volume 123 by the further classification of many of the proofs. Readings in Mathematics 1991/app. 584 pp., 136 illus./Hardcover/$39.80 ISBN 0-387·97437-7 R. Remmert, Universitat Miinster, FRG Undergraduate Texts in Mathematics Theory of Complex Functions Translated from the German by R.B. Burckel, S. Gallot, Universite de Savoie, Chambery, France; Kansas State University D. Hulin, Ecole Polytechnique, Palaiseau, France; Material from function theory up to residue calculus is J. Lafontaine, Universite des Sciences et Techniques covered in a lively and vivid style. Also included is du Languedoc, Montpellier, France ample discussion of the historical evolution of the theory, Riemannian Geometry biographical sketches of important contributors, and cita­ Second Edition tions (original language together with English translation) In most textbooks about Riemannian geometry, the start­ from their classical works. Students making their way ing point is the local theory of embedded surfaces. Here, into a classical area of mathematics will find Theory of the authors begin directly with the so-called "abstract" Complex Functions useful. It includes many examples manifolds. To illustrate this point of view, a series of ex­ and practice exercises and offers quick access to essential amples is developed each time a new definition or theo­ results. 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Second Revised Edition Three Easy Ways to Order: This treatment of differential geometry combined with • Call: Toll-Free 1-800-SPRINGE(R): 1-800-777-4643. the mathematics required for general relativity makes the subject matter accessible for the first time to anyone fa­ In NJ call 201-348-4033 (8:30 AM-4:30PM EST). Your reference number is S726. miliar with elementary calculus in one variable and with some knowlepge of vector algebra. The emphasis • Write: Send payment plus $2.50 for postage throughout is on the geometry of the subject. Addresses and handling to: Springer-Verlag New York, Inc., mathematicians and physicists as well as students. This Attn: S. Klamkin - Dept. S726, new edition is typeset in TeX with numerous illustrations. 175 Fifth Avenue, New York, NY 10010. 1991/app. 598 pp./Hardcover/$52.00 (tent.) • Visit: Your local technical bookstore. ISBN 0-387·52018-X Graduate Texts in Mathematics, Volume 130 Instructors: Call or Write for information on textbook (1st edition published by Pitman & Sons Ltd.) examination copies! ®Springer-Verlag New York Berlin Heidelberg Vienna London Paris Tokyo Hong Kong Barcelona