Notices of the American Mathematical Society 0821801589

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OTICE S OF THE

AMERICAN MATHEMATICAL SOCIETY

Joint Meeting with the London Mathematical Society page 32

JANUARY 1992, VOLUME 39, NUMBER 1 · Providence, Rhode Island, USA ISSN 0002-9920

Calendar of AMS Meetings and Conferences is possible. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarters office of the Society. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. The abstract deadlines listed below should be carefully reviewed since an abstract deadline may expire before publication of a first announcement. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information, consult the meeting announcements and the list of special sessions.

This calendar lists all meetings and conferences approved prior to the date this issue went to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. Abstracts of papers presented at a meeting of the Society are published in the joumal Abstracts ofpapers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting, insofar as

Meetings Place

Date

Meeting#

Tuscaloosa, Alabama March 13-14, 1992 Springfield, Missouri March 20-21, 1992 Bethlehem, Pennsylvania April11-12, 1992 Cambridge, England June 29-July 1, 1992 (Joint Meeting with the London Mathematical Society) Dayton, Ohio • October 30-November 1, 1992 876 San Antonio, Texas January 13-16, 1993 (99th Annual Meeting) Knoxville, Tennessee March 26-27, 1993 Salt Lake City, Utah April9-10, 1993 Washington, D.C. April17-18, 1993 DeKalb, Illinois May 21-22, 1993 Vancouver, British Columbia August15-19, 1993 (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) College Station, Texas October 22-23, 1993 Cincinnati, Ohio January 12-15, 1994 (100th Annual Meeting) Lexington, Kentucky March 18-19, 1994 Manhattan, Kansas March 25-26, 1994 Denver, Colorado January 25-28, 1995 (101st Annual Meeting) Chicago, Illinois March 24-25, 1995 Orlando, Florida January 10-13, 1996 (1 02nd Annual Meeting) • Please refer to page 38 for listing of Special Sessions. 872 873 874 875

• • • •

Abstract Deadline

Program Issue

January 2 January 2 January30 February 28

March March April May-June

August 3

October

Conferences March 5-8, 1992: Joint Workshop on Changing the culture: education and the research community, Oakland/Berkeley, California. June 13-July 24, 1992: Joint Summer Research Conferences in the Mathematical Sciences, Mount Holyoke College, South Hadley, Massachusetts.

July 6-24, 1992: AMS Summer Research Institute on Quadratic forms and division algebras: Connections with algebraic K-theory and algebraic geometry, University of California, Santa Barbara. July 26-August 1, 1992: AMS-SIAM Summer Seminar in Applied Mathematics, Exploiting symmetry in applied and numerical analysis, Colorado State University, Fort Collins, Colorado.

Deadlines Classified Ads* News Items Meeting Announcements••

March Issue

April Issue

May/June Issue

July/August Issue

January 30, 1992 January 21, 1992 January 23, 1992

February 26, 1992 February 20, 1992 February 24, 1992

May 5, 1992 April 20, 1992 April 23, 1992

June 16, 1992 June 8, 1992 June 11, 1992

• Please contact AMS Advertising Department for an Advertising Rate Card for· display advertising deadlines. •• For material to appear in the Mathematical Sciences Meetings and Conferences section.

OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS 3 Letters to the Editor

FEATURE COLUMNS

5 Forum 8 Computers and Mathematics

Keith Devlin

Keith Devlin discusses the development of computer tools to support cooperative work by possibly large research and development teams. Also, Maurino Bautista reviews Models, Roger Pinkham takes a look at Calculus Calculator (CC), and Marvin Margolis reviews two programs, Derive 2.0 and ODE.

17 Inside the AMS Lenore Blum, Vice President of the AMS, reports on the Third Pan-African Congress of Mathematicians held in Nairobi last August and offers some suggestions for cooperative efforts between the American and African mathematical communities.

20 News and Announcements 24 1992 AMS Elections 27 Meetings and Conferences of the AMS Tuscaloosa, AL March 13-14, 27 Springfield, MO March 20-21, 29 Joint Workshop on Changing the Culture: Education and the Research Community, 31 Cambridge, England June 29-July 1, 32 Invited Speakers, 38 1992 Summer Seminar in Applied Mathematics, 41 1992 Summer Research Conferences in the Mathematical Sciences, 42 1992 Summer Research Institute, 44 46 Mathematical Sciences Meetings and Conferences 58 New AMS Publications 61 Miscellaneous Personal Items, 61 Deaths, 61 Visiting Mathematicians, 61 62 New Members of the AMS 63 AMS Policy on Recruitment Advertising 64 Classified Advertising 87 Forms

JANUARY 1992, VOLUME 39, NUMBER 1

From the Executive Director ... A WASHINGTON OFFICE AMERICAN MATHEMATICAL SOCIETY

EDITORIAL COMMITIEE Michael G. Crandall Amassa Fauntleroy Robert M. Fossum (Chairman) Carolyn S. Gordon (Forum Editor) D. J. Lewis L. Ridgway Scott Robert E. L. Turner (Letters Editor) MANAGING EDITOR John S. Bradley ASSOCIATE EDITORS

Ronald L. Graham, Special Articles Jeffrey C. Lagarias, Special Articles SUBSCRIPTION INFORMATION

Subscription prices for Volume 39 (1992) are $131 list; $105 institutional member; $79 individual member. (The subscription price for members is included in the annual dues.) A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Add for postage: Surface delivery outside the United States and lndia-$15; to lndia-$28; expedited delivery to destinations in North America-$32; elsewhere-$67. Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571. All orders must be prepaid. ADVERTISING

Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Copyright @ 1992 by the American Mathematical Society. All rights reserved. Printed in the United States of America. The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability. §Most of this publication was typeset using the TEX typesetting system. [Notices of the American Mathematical Society is published monthly except bimonthly in May, June, July, and August by the American Mathematical Society at 201 Charles Street, Providence, Rl 029042213. Second class postage paid at Providence, Rl and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Customer Service Department, American Mathematical Society, P. 0. Box 6248, Providence, Rl 02940-6248.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street address. Tel: 401-455-4000.

2

The AMS will open an office in Washington, DC in 1992. For many years, the Society has contemplated, with growing frequency and concern, its distance, physical and psychological, from the Washington, DC area. Benefits of having an AMS office in Washington have been discussed and weighed, generally with positive conclusions. In a recent consensus report involving the leadership, membership, and staff of the Society, the Strategic Planning Task Force (SPTF) clarified the Society's mission and set a strategic direction in response to numerous issues facing the mathematical sciences community. Most prominent among these are maintaining the health and vitality of mathematical research, reforming mathematics education at all levels, transferring mathematical knowledge to other disciplines and to industry, and making the public aware of the usefulness of mathematics and its connections to solving societal and economic problems. These overarching issues demand the Society's attention. However, the Society is faced with a significant barrier to its effectiveness in addressing such issues; more often than not, these issues are debated, shaped, and settled in the nation's capital. The SPTF concluded that the AMS must have an effective, proactive, and sustaining presence in the national decision-making process-a presence that can best be achieved by physically locating an AMS office and staff in Washington. The AMS Washington office will develop effective liaisons for the Society, providing early knowledge of what is happening in Washington, and conversely, communicating the Society's thinking and activities to Washington. It will coordinate AMS representation of numerous Washington functions and will provide on-the-spot availability and quick and informal personal contacts, both valuable for effectiveness within the Washington structure. Throughout the Society's recent strategic planning exercise, there was a constant and strong message that the AMS has important roles beyond its traditional activities. For the AMS to effectively respond to the needs of the community, it must find extraordinary funding and engage in sustaining programs and projects on behalf of mathematics. Some of these activities will be more effectively promoted by having the physical location and assistance of a Washington office. All Society efforts in government and public affairs will be communicated to, and coordinated closely with, the Washington office of the Joint Policy Board for Mathematics (JPBM), a partnership of the AMS, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. JPBM provides a forum in which the leadership of the three organizations may propose and discuss issues relating to the mathematical sciences and act in concert in areas where joint action is likely to be more effective than individual action. Many issues before the community are of common interest to the JPBM organizations and require concerted action. On the other hand, the AMS is in a special position to distinguish the health and vitality of mathematics as a science. The Society is supporting and building on the reform efforts for mathematics education and the importance of mathematics in solving science, engineering, and societal problems, while maintaining the Society's primary role of promoting and distinguishing the science of mathematics from its service components. The AMS is uniquely positioned to make the case for mathematics and for connections between research and mathematics education and the applications of mathematics. The current Associate Executive Director for programs and government and public affairs will head this office, with a small staff. It is anticipated that mathematicians from the community will be recruited to join the staff of the AMS Washington office, on a temporary basis, to assist on various Society projects and programs. In the near future, a formal announcement will be made about the opening of our Washington office. We invite members to visit our Washington office, as well as our Mathematical Reviews office-in Ann Arbor, Michigan, and the Society's headquarters in Providence, Rhode Island. William Jaco

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Letters to the Editor

Pipeline from Small Colleges

The September 1991 (Vol. 38, No. 7) issue of Notices presents a special section on Women in Mathematics. I applaud Notices for such a wellwritten and timely collection of articles. Among the articles was a piece by D. J. Lewis entitled "Mathematics and Women: The Undergraduate School and Pipeline." The main point of the Lewis article is that schools need to concentrate on retaining and encouraging women in the field of mathematics at the undergraduate level. The article only mentions the contribution at the baccalaureate level of research universities (Michigan, MIT, Berkeley, Chicago, and Texas), and despairs that only five Michigan women continued on to receive the Ph.D. in mathematics in the 1980s. However, D. J. Lewis has neglected to recognize the importance of the small college, and more specifically, the women's college pipeline to graduate programs in this country. In fact, the top 25 nationally ranked liberal arts colleges 1 produced a total of 44 women Ph.D.s in the mathematical sciences, while the top 25 nationally ranked research universities produced 133 women math Ph.D.s 2 , only three times that of the liberal arts colleges in this sample. These numbers are astounding considering that each year each of the liberal arts colleges produce between 200 and 800 graduates, while each of the research universities produce between 2000 and 5000 graduates (with few exceptions), resulting in far more than three times the alumnae. Actual Ph.D. productivity ratios are difficult to obtain, since 1College and university samples obtained from U.S. News & World Report, Oct. 15, 1990. 2 Data obtained from the Doctoral Records Files Office of Scientific and Engineering Personnel: National Research Council, April 1991.

the ratio of women to men students varies depending on the college or university. These numbers become even more important when it is pointed out that 43% of the women mathematics doctorates and 50% of the women engineering doctorates produced by the nationally ranked liberal arts colleges hold degrees from one of the five women's colleges on the list (Barnard, Bryn Mawr, Mount Holyoke, Smith, and Wellesley). In fact, after combining mathematics and engineering (M/E), the two schools which produced the most, Mount Holyoke and Bryn Mawr, each yielded ten women M/E doctorates in the '80s, more than any other liberal arts college, and more than seven of the top 25 research universities. It is also noteworthy that the two small colleges in the sample of the top 25 which produced the most women math Ph.D.s in the 1980s (Smith and Bryn Mawr) produced five, the same number as Michigan. There is additional evidence that small schools may have a better record of encouraging women in the sciences. For the coeducational schools in the top 25 liberal arts college sample, the average ratio of alumnae to alumni receiving physical science or engineering doctorates in the 1980s is 0.22, while the average ratio for the top 25 research universities is 0.15, approximately equal to the national average. Many of the other points made in the D. J. Lewis article are excellent and should be noted. For example, the discussion of academic environmental factors which influence women students is excellent and hopefully will be noted by many mathematics departments across the country. Given the above numbers, it is also hoped that more research universities will recognize the importance of the pipeline from small colleges, and specifically women's colleges, to graduate programs in the mathematical sciences. Norean Radke Sharpe Bowdoin College (Received November 13, 1991)

JANUARY 1992, VOLUME 39, NUMBER 1

Calculus Reform

I have heard too much recently about "Calculus Reform." I have also seen too often the trite phrase "A pump, not a filter." Why is it that we think there is something wrong with our Calculus courses, and why are we willing to spend millions of dollars on Curriculum Development programs? This is my third year as a Professor of Mathematics at a Liberal Arts college, and the third year that I have taught the Calculus sequence. I do not include f 8 definitions and only give proofs of theorems when they are elementary. I emphasize the deep ideas of Calculus rather than symbolic manipulation. And my classroom delivery has been described by many as "extremely animated." More than half of the class this Fall flunked the first midterm. For the most part they were the students who have not been doing homework and not attending class. Would "Calculus Reform" help? The answer is definitely "NO." What we need is Student Reform. The students cannot expect to learn Calculus through osmosis. The feeling I sense from many students is that they want to do the minimum work required to receive a passing grade. If these students are to be our future scientists and engineers I am very worried: I would not want to fly in a plane designed and built by individuals who strive for Letters to the Editor Letters submitted for publication in Notices are reviewed by the Editorial Committee. Notices does not ordinarily publish complaints about reviews of books or articles, although rebuttals and correspondence concerning reviews in Bulletin of the American Mathematical Society will be considered for publication. Letters should be typed and in legible form or they will be returned to the sender, possibly resulting in a delay of publication. All published letters must include the name of the author. Letters which have been, or may be, published elsewhere will be considered, but the Managing Editor of Notices should be informed of this fact when the letter is submitted. The committee reserves the right to edit let· ters. Letters should be mailed to the Editor of Notices, American Mathematical Society, P. 0. Box 6248, Providence, RI 02940, or sent by email to [email protected], and will be acknowledged on receipt.

3

Letters to the Editor

minimum passing acceptability. We certainly want as many students as possible to learn Calculus, but we cannot "pump" unwilling and uninterested students unless we want to pump gross impurities. Perhaps Calculus has served as a "filter" because

too many students have been "pumped through" their earlier classes without really learning. If we want a more accurate Calculus analogy, here is mine: Calculus is a catalyst. For those who have some interest and motivation (however small),

Calculus can blossom their thinking. But a catalyst cannot make a reaction occur if the necessary ingredients aren't there. David Sanker Holy Names College (Received October 21, 1991)

"This fascinating book is not of math, but of men" Jerome Stem

Tallahassee Democrat

Operations Analysis in the United States Army Eighth Air Force in World War II Charles W. McArthur Jerome Stem, a columnist for the Tallahassee Democrat, offers this summary of Operations Analysis in the

United States Army Eighth Air Force in World War II: "McArthur recounts all this amazingly well. His straightforward narrative lets the story tell itself and the chips fall where they may. The individual accounts let us hear the voices of the characters. Tragic anecdotes emerge. Personality conflicts over strategy resulted in lost lives. Errors in judgment are made. Politics sometimes prevailed over strategy. Inspirational stories are there too, of those whose contribution to the war was their intelligence, honesty and perseverence. Good ideas did not become strategy by themselves .... This fascinating book is not of math, but of men." McArthur's book offers a careful, readable study of an important slice of history on both World War II and operations analysis-one you won't find anywhere else! Call the AMS toll free at 800-321-4AMS (321-4267) and specify the code HMATH/4NA.

The History of Mathematics series is jointly published by the London Mathematical Society and the American Mathematical Society.

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1980 Mathematics Subject Classification: 01 ISBN 0-8218-0158-9, LC 90-829, ISSN 0899-2428 351 pages (hardcover), November 1990 Individual member $49, List price $81, Institutional member $65 To order, please specify HMATH/4NA

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Forum

The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between 1000 and 2500 words long. Readers are invited to submit articles for possible inclusion in Forum to: Notices Forum Editor American Mathematical Society P.O. Box 6248 Providence, Rl 02940 or electronically to [email protected]

Calculus Reform II Murray H. Protter University of California, Berkeley In a previous article on calculus reform [2], I discussed the influence textbook publishers have in restricting the choice of calculus texts and the ways in which this influence affects the syllabus and study habits of students. In addition, I described how the availability of sophisticated calculators as well as hand held computers increasingly influences the way calculus is taught. I now propose a change in the way calculus is taught in large universities and colleges, a change which I think will improve students' understanding and appreciation of mathematics. Most advanced undergraduate mathematics courses at both large and small colleges and universities are taught in small classes of between 15 and 35 students which meet either three times a week for one hour (read 50 minutes) or twice a week for 1 112 hours. These are usually conducted in an informal manner with the teacher developing a topic and allowing frequent questions and comments by students. Homework is assigned and discussed in class at regular intervals. At small institutions calculus is taught in similar fashion. However, the teaching of calculus at universities with large enrollments most often proceeds by the lectureTA system. Here a faculty member gives a formal lecture two or three times a week to several hundred students after which teaching assistants (TAs) meet with small groups of students (25 to 30) on the alternate days. The TAs discuss the homework, explain those parts of the faculty lectures which the students find difficult to understand, give quizzes, and answer miscellaneous questions about the course. Students

get to know theTA on a first-name basis but usually view the faculty lecturer as distant and remote. Many faculty members dislike giving large lectures to beginning students, while others enjoy the theatrics of performing before a large audience. At Berkeley more than half the faculty has never (or almost never) taught one of the calculus lecture sections; thus there is a sharp division of teaching duties between those who have contact with beginning students and those who don't. There is a reward in giving large calculus lectures in that teaching loads are reduced for the calculus faculty. Thus, we have a situation in which some professors try hard to avoid teaching the elementary courses, while others try just as hard to be successful at it and thereby get extra teaching credit. The technique for getting into either of the two categories is not difficult to describe. How to be a popular calculus lecturer.

Speak in a clear distinct voice, using a microphone if necessary. Always write large and fill the blackboard systematically. Work many illustrative examples, ones similar to those assigned for homework. Tell anecdotes, humorous if possible. Prove very few theorems and tell the students they don't have to know proofs for the tests. Complain often about the textbook (unless you wrote it). Smile a lot and encourage students to come to your office hours. How to be an unpopular calculus lecturer.

Be serious at all times. Write small and prove theorems in the lecture, sometimes giving a proof different from that in the text. Use Greek letters as often as possible. Tell students they are responsible on the tests for everything discussed in the lectures. Speak indistinctly or with a heavy accent (either real or simulated). Tell the class that the textbook is no better or worse than those being used elsewhere, the differences being insignificant. Discourage students from coming to your office hour. Whether or not a lecturer is popular, attendance at the lectures follows the same predictable path. At the beginning of the course the lectures are well attended with students taking notes and listening carefully. Then, empty seats in the room are noticeable here and there, and shortly thereafter exponential decay sets in. Lectures become sparsely attended with slight surges before midterm examinations. Of course,

JANUARY 1992, VOLUME 39, NUMBER 1

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Forum

students don't do this on the basis of the popularity or unpopularity of the lecturers. They divide lecturers into two types. First, there are those teachers who follow the text in detail and present the exact proofs that are in the book and who work examples in class that are only slight variations of those in the text. Students soon learn that going to class is a waste of time since they can just as well read the book more efficiently and get answers to their questions in the small TA section meetings. Students sleep through class or read or work on other courses. Second, there are those teachers who don't follow the text. They give alternate proofs to theorems and discuss auxiliary material that they think interested students might want to know about; they don't show students how to do homework problems. Students then reason that the lectures are irrelevant to the homework, the midterm tests, the final examination, and the final grade. They quickly learn to stay away from lectures. Thus, whatever the path the instructor of a large lecture course takes, exponential decay in attendance is the inevitable result. I firmly believe that when lecturers are honest with themselves they recognize the irrelevance with which most students view their performances. The lecture-TA system was developed over the last half century as a technique for reducing faculty teaching loads. If one were trying to devise a bad method for teaching elementary mathematics, it is hard to think of one worse than the lecture-TA system. Mathematics should always be taught in small classes with constant interaction between teacher and student. To eliminate the lecture-TA system, I propose that for one semester of each year every faculty member, in addition to his* regular teaching load, should be required to teach a small class of calculus, meeting three or four times a week. Since teaching loads for faculty members at most large universities are now two courses (or fewer) each semester, this calculus class would be a small addition to their regular teaching loads. Instead of 3 or 4 courses, faculty members would teach 4 or 5 courses a year. No exceptions should be allowed. There is no doubt that students would not only benefit but be delighted to have such ongoing contact with the regular faculty. These days paying special attention to the teaching of undergraduates has a high priority in university education. The extra time the faculty spends in this endeavor would reduce only marginally the time the faculty devotes to research. Teaching duties would be increased about 15 or 20 percent by the addition of this one course, since the work involved in teaching a calculus class is less than that required in teaching more advanced courses. If the typical faculty member devotes 30% of his time to teaching, 20% to departmental and administrative duties, and 50% to research, then adding this one course would reduce research time by less than 10 percent. What would happen to the TAs if the entire faculty were to teach calculus? I propose that the department insist that the University funds now earmarked for TAs be converted *I use the generic masculine throughout.

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to fellowships. This is a risky offer, since the University administrators will see an opportunity to snatch the funds for other purposes. However, the argument should be made that graduate programs must be maintained for the health of the department and the University; moreover, the willingness of the faculty to take on the extra duties must be matched by the willingness of the administration to keep the funds intact. By offering fellowships instead of teaching assistantships, the administration cannot help but make measurably higher the level of the incoming graduate students. If we eliminate the lecture-TA system, the benefits both to calculus teaching and to graduate programs are apparent. Note that incoming graduate students can now devote all their time to their courses and preparation for the Ph.D. qualifying examinations. Incoming foreign graduate students have ample opportunity to study English without concern about communicating with freshmen. Another feature of my proposal for elimination of the lecture-TA system involves giving additional teaching duties to graduate students once they complete their course work, have passed their qualifying exams, and are working on their theses. Unlike beginning graduate students, those at this later stage are committed to a career in mathematics. Since most of them will end up in academic positions it is important for them to have had teaching experience. Therefore, every advanced student should be required to teach, on his own, one small calculus course per semester. He would operate the course just as any faculty member might, but there should be a vice-chairman of instruction who supervises the work of all the graduate student teachers. In this way, by the time a student is working on his thesis, he is familiar with the workings of the institution, has mastered English if he is foreign, and is serious about being a mathematician. At this point he is either on a fellowship or is a Research Assistant. In either case he should be required to teach as a condition for getting his degree. Another alternative to the lecture-TA system is the self-paced method of teaching. I described that method as it has been used successfully at Berkeley for the last 20 years or so in the article "The Self-Paced Calculus Program at Berkeley" [3]. Since many students cannot adapt to the self-paced method of teaching, it is important to have it available only as an alternative to a more conventional program. I have observed through the years an important facet of self-paced programs: those students who stick with the self-paced program really enjoy learning calculus while those in the lecturer-TA system frequently dislike it. If the entire faculty becomes involved in teaching calculus, the method of choosing textbooks (always a problem) will improve substantially. Currently, publishers' representatives have an inordinately large influence in the way calculus texts are chosen. With the whole faculty required to live with these choices every year, the committee (or person) that chooses the text, who will now be much more subject to criticism, will reflect carefully on the selections available. However, it is still easy to be misled. In a recent article on the use of computers in teaching calculus, Halmos [1] raises

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Forum

doubts about the use of computers in elementary courses (with which I generally agree). However, he does mention approvingly that Courant's Calculus develops integration (which is done before differentiation) by showing that in simple cases one can actually add up the Riemann sums approximating the integral. My experience, in trying to do this using Courant's book, has been a complete failure. The trouble is that because Courant never taught a course in calculus, he wasn't aware of the background of the typical student. In fact, there are several calculus books written by eminent mathematicians who have never (or hardly ever) taught a regular undergraduate course in calculus. Errors in presentation occur more readily in these texts than in those written by faculty who have at least a modicum of experience in teaching calculus. With the whole faculty involved in lower division teaching, text selection should become a more rational process, and books with blunders such as that in Courant's book would be avoided. There are several difficulties in instituting a program such as the one I have outlined above. First of all, the faculty may not be willing to increase its teaching load voluntarily without additional compensation in some form

or other. If they say that the graduate program will benefit by attracting better graduate students, the argument may not suffice. Second, the administration may not be willing to agree to convert the teaching assistantships to fellowships. Even if there is agreement on this point, each year, in order to save money, the administration may attempt to whittle away the fellowship funds. It will be an ongoing struggle. Finally, we have the recruitment problem. It will be difficult to attract the best young researchers if other universities are offering them fewer teaching duties. This problem could be ameliorated somewhat if new faculty members are offered a period, say 3 to 10 years, free of calculus teaching. The length of time would depend, among other things, on the relative merits of the competing offers. References [1] Halmos, P.R., Is Computer Teaching Harmful?, Notices ofthe Amer. Math. Soc. vol. 38 (1991) pp. 420--423. [2] Protter, M. H., Calculus Reform, Math. lntelligencer, vol. 12 (1990) pp. 6-9. [3] Protter, M. H., The Self-Paced Calculus Program at Berkeley, Amer. Math. Monthly, vol. 98 (1991) pp. 245-249.

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Fixed Points

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JANUARY 1992, VOLUME 39, NUMBER 1

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Computers and Mathematics

Edited by Keith Devlin Editorial I just got back from a trip to Japan, where I took part in the International Symposium on New Models for Software Architecture (IMSA '91) held at Waseda University in Tokyo. The symposium marked the start of a major new 8-year project, established by Japan's Ministry of International Trade and Industry, to develop new models for software to support cooperative work by possibly large research and development teams, rather than the single-user models at which are aimed today's personal computers and desktop workstations, together with much of their software. The development of computer tools to support teamwork is not new. Probably the first purpose-built, distributed, office-support system was the Star System, developed by workers at Xerox PARC (the Palo Alto Research Center in Palo Alto, California). The networked system of Alto {later Star) computers, with the mouse-pointer-icon interface subsequently made popular by the Apple Macintosh, together with shared printers and information storage devices, used within PARC itself for almost the whole of the 1970s, was probably the first ever integrated office information system. "Personal distributed computing" was the name Xerox attached to this kind of integrated system. Following a conference held at the University of Texas at Austin in 1986, the concept developed at Xerox PARC developed into the field now known as "Computer Supported Cooperative Work" (CSCW). The rationale behind the CSCW paradigm is the same as the one that motivated the early Xerox PARC researchers and that made the Apple Macintosh such an incredibly successful personal computer. Namely, if you want to design a personal computer, or a computer system, to be used by certain kinds of people, start off by examining the way those people work and tailor the computer or computer system to match their needs. In other words, involve social scientists and cognitive psychologists in the design process right from the start, rather than letting technological or application-domain considerations dominate the whole development. Truly useful new developments in information support systems will depend on work that is not only international but also highly interdisciplinary. It will involve not just computer science and software engineering in the traditional sense, but many other disciplines as well. The successful computer scientist of tomorrow will be both mathematician and sociologist, engineer and philosopher, linguist and psychologist. That is what I, as a mathematician, was doing at the Tokyo symposium, alongside all the computer scientists, linguists, and what have you. New developments in technology have always required (and led to) new developments within mathematics. (As it happens, one of the few other fully-fledged mathematicians there was Jon Barwise, my predecessor as editor of this column!) But though my presence at IMSA '91 was as a mathematician whose research might help provide the mathematical underpinnings of information systems, I could not help but speculate on the effect the evolution of sophisticated cooperative support architectures might have

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on mathematics itself. At the moment, we are still adapting both our teaching and our research to take advantage of the ready availability of powerful personal computers and desktop workstations. Though we utilize email and electronic file transfer to communicate with our colleagues, for the most part we work alone, one person per machine, and it is with such usage in mind that present-day software systems are designed. When working at the computer we usually work individually and then communicate our results. This is largely true even in the case of instruction in an "electronic classroom." In order to do truly collaborative work, we walk along the corridor, or take to the roads or skies, and place ourselves face to face with our students or colleagues, be it in front of a sheet of paper, a blackboard, or a computer screen. Now, I doubt that there will ever be a technology that completely replaces actual face-to-face contact. But the development of mathematical software systems designed for team use, spread over a network, as opposed to individual users or even teams made up of individual users, such as we have today, will surely lead to a revolution in both research and teaching just as great as the one caused by the introduction of the personal computer. And just as we have had to learn, and are still learning, how to do and teach mathematics on a computer, so too we will have to adapt to yet another way to approach the subject. Doubtless there will be those who are not happy with such a development. But my guess is that regular readers of this column will find the prospect as exciting as I do. Editor's address: Professor Keith Devlin Department of Mathematics and Computer Science Colby College Waterville, Maine 04901 Correspondence by electronic mail is preferred, to: [email protected]

Software Reviews There are four software reviews this month. Maurino Bautista reviews Models. Following that, Roger Pinkham takes a look at Calculus Calculator, a program previously available as shareware (and reviewed as such in this column back in September 1989, pages 842-844) but now produced in commercial form. Then Marvin Margolis reviews two programs, Derive 2.0 and ODE.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

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Computers and Mathematics

Models 1.03 Reviewed by Maurino P. Bautista* Program Description Models is a spreadsheet-like program that provides a variety of graphics and computational tools to perform iterations of discrete mathematical systems (either discrete versions of differential equations, difference equations, discrete dynamical systems, or general mathematical models) and render the results visually. It was developed by Martin Lapidus who has produced other quite good programs for the Macintosh and MS-DOS machines. Two of these are Fields and Operators and f(z). In the context of this program, a model is any system of equations involving some variables and/or parameters whose current values describe the state of the system and whose succeeding values are computed from either the old values or the most currently known ones by applying a specified set of rules. The following diagram illustrates the concept:

require the numeric coprocessor. I would not recommend running complicated models without the floating point chip. Obviously, the faster the machine, the better the performance since the software performs intensive calculations. I conducted my evaluation using a Mac IT running System 6.0.7 and a 6-MHz IBM PC AT with VGA graphics, Microsoft mouse and running DOS 3.30. Installation is a breeze with either platform, and even the DOS version automatically selects the appropriate video driver for the highest screen resolution available on your system. I spent several sessions with both the Mac and the DOS version, although I preferred working with the Mac version. All the graphics included in this review were obtained from the Mac screen. I tested the program just like I have done with other programs that I have beta-tested before. Some of these are Matlab, Maple 4.2 and Maple V, Tools for Exploring Math, Calculus TIL, etc.

Basic Operation As an example, suppose one wants to study the classic predator-prey model involving rabbits and foxes, one of the models that come with the package. The phenomenon is described by the Volterra-Lotka differential equations:

I Parameters I

dx dt

T

f----.

_.(0)

y

Initial Conditions

Graphic or Table

--·-+--- -----' Feedback

Once the variables and parameters are identified, their initial values fixed, and the rules for generating new values specified on the spreadsheet, Models can perform the iterations and display the values on the spreadsheet itself, or better, graphically by creating (plotting) pens whose position in a 3-dimensional coordinate system is determined component-wise by a particular variable. These should become clear later.

~~ =cx(t)y(t) + dy(t) where x and y represent the number of foxes and rabbits, respectively, and a, b, c, d are parameters. The first step in entering the model is to create the spreadsheet description of this model through the Variables Table shown below:

0 t a

lb c d rabbitBirths rabbitDeaths foxBirths foxDeaths chan~InRabbits chan~InFoxes

Hardware Required The program runs on any Macintosh or DOS machine with at least 512 KB of memory and two floppy drives although a hard drive would provide a much better environment and more RAM would improve animations. I recommend a mouse for the MS-DOS version. Two versions of the program are provided with either platform: one that requires a numeric coprocessor (either a 6888x for the Mac or an 80x87 for DOS) and a much slower version that does not *Maurino P. Bautista is Associate Professor of Mathematics at Rochester Institute of Technology, Rochester, NY 14623. He received his Ph.D. in mathematics from Purdue University (1984) and has interests in inverse problems, partial differential equations and computer algebra systems. He is a beta-tester for a number of software companies. He can be reached at mpbsma @ritvax.isc.rit.edu.

=a x(t) + b x(t)y(t)

rabbits foxes

Predator and Prey 0 0.08 0.04 0.02 0.06 0 0 0 0 0 0 4 2









t+.Ot .08 .04 .02 .06

0 10

a*"rabbits ID*"rabbits*"roxes c*"rabbits*"foxes d*"foxes rabbitBirths-rabbitDeaths foxBirths-foxDeaths rabbits+chan~InRabbits/1 foxes+chan~InF oxes/1

0 ~

'21

The first column contains all the relevant quantities for tire model, the third column contains the initial values of these quantities, the second column contains the current value of the quantity, and the last column specifies how the new value is computed (the rules). Once the variable table is complete, the model can be run using menus that are fairly obvious. However, it does not automatically create any graphs. The basic mechanism for creating a plot in Models is called a pen. A pen is a locus of points in some 3-

JANUARY 1992, VOLUME 39, NUMBER 1

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Computers and Mathematics

dimensional coordinate system which Models always refers to as xyz-coordinates. Each of x, y or z can represent any quantity defined in the first column of the variable table or could be set to zero in order to obtain a 2-dimensional plot. Once a pen is defined, one can show its trail by showing all the points and/or connecting them with lines or not show its trail by only showing its current position. There are all sorts of controls on the size of the points, the thickness of connecting lines, which points to show, e.g. like every third point, etc. A more exciting feature is the ability to Link pens Goin 2 points from 2 plots with a line segment) or Project the point to any or to all of the coordinate planes and let the projection point trace another locus of points. All of the above are set-up in the Edit Pen window which looks like this: I

Select Pen Name H

elete Pen

ol

Rabbits&Time nbbits&foH foH time

13 D Graph

r

Irabbits

•••

11Il o~~n lo~llscrete Trail

y lfoHes z It

I[B

Pen diameter

IT:::]

..#

.Line color

Dk

l)

r-®Linear Trail

Project to planes

.Pen Color Line thickness ~

I

other curves are the projections of this plot to each of the 3 coordinate planes. There are other capabilities worth mentioning such as animation (which is not the same as iterating a model) and the ability to import an external data file created by another program like a word processor, a spreadsheet, or a programming language like Fortran. Once the data points are read in and assigned to specific iterates of different variables, the model can be played, and the program simply reads the next value from memory and assigns it to a variable or performs some computations before assigning it. The package comes with a sample model (Long Jump) obtained by digitizing successive images of an athlete as he performs a long jump. Only the x and y coordinates of certain parts of the body are needed, such as the left and right toe, left and right ankle, left and right knee, the middle hip, etc. Playing this model simply reads a succession of graphics frames from disk or memory and does not perform any computations. The computations are done in a previous stage and the resulting graphs are stored either in RAM or disk.

~y-z

z Link to: I

Good Features

OTrail

~H-Z

X

@No trail

~H-y

OTrail I[B®NoTrail

Wait ~ iterations before displaying, and then show euery li::::J'th iteration.

The result of running this model with the four pens defined above (3D Graph, Rabbits&Tzme, Rabbits&Fox, and Fox Time) showing the settings associated with the 3 D Graph pen is shown below: 3 D foHes - Rabbits -Time

foxes

One of the best features of this program is the ease with which one can plot parametric curves in 2- or 3-dimensions as well as define other points related to the curve and make them interact with each other. Thus, for example, you can start with the circle defined parametrically and plot all the trigonometric functions as you follow a point around the circle. Plotting numerical approximations to solutions of systems of differential equations is equally easy as soon as the discrete version of the system is obtained. I would consider it a sophisticated parametric curve plotter. Another good feature is the large collection of files that come with the program. These can be used as templates to create other models, making it much easier to use the package.

~!.L..............•.............................................__- r - -

I I The thick line represents the plot of the rabbit and fox population as functions of time (3D Graph pen) and the

10

Bad Features As with any new program, there are always a few bugs and design flaws. On a Mac, resizing the graphics window, zooming in or out, or rotating the axes will delete certain features of the current display, in particular links between points (or pens). On the IBM, the entire plot disappears! I could not print the graphics window on a Mac. I also ran the software on a Mac SE/30 with a color card hooked to a color monitor. In this setup, I could not get the color settings on the points, connecting lines, or the axes. There are also a number of design flaws that can cause frustration to the user. For example, there are no controls for the speed of an animation other than changing the number of iterations in the loop, and you cannot replay an animation without opening the file again. This means going through all the menus that you just performed in order to replay an animation. Double clicking items inside dialog boxes does not select the entire item. Some dialog boxes do not have cancel buttons. Hence, if you accidentally change a setting and you do not

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

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Computers and Mathematics

remember the previous value, there is no way to restore it. You cannot do multiple selection for deleting variables. Closing every window including the variables table does not close the model, and you cannot have more than one model open, making it difficult to compare 2 models. If your DOS system does not have a mouse, the operation of the menus is quite confusing. Menu selection is accomplished by pressing a letter corresponding to the capitalized letter in the item you want to select. For example, if you want to change screen characteristics, you have to select the sCreen menu by pressing the letter C. However, you can also navigate the menus using the Up-Down arrow keys. Models will highlight the chosen item with a box around it. For certain items, pressing the Enter or Return key will accomplish the selection, but for others one has to hit a letter as indicated above. This can be very frustrating to the unsuspecting user! At times, the mouse cursor would disappear while running a model, and it would take a few blind clicks before it showed up again. Hopefully, you have not selected an unwanted item during that time. Printing on a Laserjet II took forever and at 300 dpi resolution, the entire screen is reduced to a 2 inch by 3 inch image on paper! Printing at 75 dpi (ridiculous on a 300 dpi laser printer) produces what looks to me like a screen dump. Finally, there are some things that are inconsistent with our experience of mathematics. For example, one of the equations in the Lorenz model is dx dt

Documentation The documentation that comes with the package is really a collection of case studies involving various mathematical models. Some of these are Rectilinear Motion, Period Doubling, Spiders, etc., in addition tb those already mentioned earlier in the review. Each case study has associated files on the disk that essentially contain the variables table for the model. One can learn to use Models by simply browsing through a case study, modifying values and variables in order to experiment. Except for several typographical errors, the manual is well-written but assumes a certain amount of mathematical sophistication. The math though is rather informal. A reference section at the end collects all the information about the operation of menus and dialog boxes in one convenient place. I would say that it is not an easy task for a novice to use the software without the documentation. However, once the basic operations are learned, the manual is almost unnecessary.

Conclusion

= s(-x(t) + y(t))

which implies that dx

available on the Mac! (I hope the developers will read this.) The closest competitor on the Mac may be the Differential Equation routines written by John Hubbard and Beverly West of Cornell University (published by Springer-Verlag), but I have not seen the latest version of these routines.

= s(-x(t) + y(t)) dt.

Here, s is simply a parameter. The new value of x is then approximately x + dx. However, in the Lorenz Attractor file as well as in the documentation, dx is defined as B*(-x+y) and the new value of x is computed as x + dx * dt. This does not invalidate the model but I think it is sloppy mathematics!

I would recommend Models to anyone who needs to iterate discrete mathematical models. It is an excellent parametric curve plotter that allows you to make plane projections or graphical presentations of related points that cannot be easily done with other programs. It has the potential to become an extremely good program for running simulations of discrete mathematical systems. It would be nice if one can also enter continuous models, but this would require more mathematical sophistication on the part of the developer.

Obtaining the Program The Competition Other programs can be made to graph curves that Models plots but not as easily. It would take a much longer code in Mathematica to create a plot that shows the locus of several interrelated points with interconnecting lines, and would be impossible with current versions of other programs like Maple, Theorist, Analyzer 3.0, Tools for Exploring Mathematics, MathCad, etc. On the other hand, when it comes to handling systems of differential equations, the DOS packages Phaser and PhasePlane are much more versatile and powerful and provide more tools for studying systems without the need to discretize the equations. These excellent packages allow you to choose the numerical method for integrating the system and effectively write the iteration equations for you. I only wish that they were

The program costs $79.95 and can be obtained from Lascaux Graphics, 7601 N. Calle Sin Envidia #31, Thcson, AZ 85718. The Mac version comes with one diskette and a 126-page manual while the DOS version comes in two diskettes and a 118-page manual. For orders or additional information, you can also call 800-338-0993.

sf'

The Reviewer Dr. Maurino P. Bautista Department of Mathematics Rochester Institute of Technology One Lomb Memorial Drive Rochester, NY 14623 716-475-6122

JANUARY 1992, VOLUME 39, NUMBER 1

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Computers and Mathematics

Calculus Calculator (CC) Reviewed by Roger Pinkham* In these days of stupendous sales, massive heart attacks,

and incredible bargains, I am wary of describing anything as first class, but CC, the Calculus Calculator, is just that. At $25 for manual and diskette, it is one of the best buys in town. (The manual may be purchased separately for $15.) It was originally obtainable as shareware from David Meredith at San Francisco State University. It now exists in a commercial incarnation sold by Prentice Hall. The original review by Herbert Holden [1] is as applicable as ever. To that review I add a brief overview and some general comment. The original intent and structure have been preserved. Color has been used even more effectively-a command, once executed, changes color on the screen. The Table command with square brackets has been altered, again a plus, and the 40 pages of original help files have been incorporated into the text. The program enables doing a host of common tasks effortlessly. It (1) performs arithmetic calculations with both real and complex numbers, (2) provides evaluation of all standard mathematical functions, (3) differentiates symbolically, (4) integrates numerically and visually displays the function, the region, and the process, if so desired, (5) allows effortless function definition and variable assignment, (6) solves equations of the form f(x) = 0 numerically, (7) graphs in 2- and 3-D easily and with dispatch, (8) graphs lists, (9) makes histograms, (10) has vector operations, (11) allows defining functions implicitly and differentiation of implicitly defined functions, (12) allows writing on and printing graphs, (13) has its own very convenient programming language, which is recursive, and does not require variable typing. Perhaps the thing most noteworthy is the human-machine interface. The care and thoughtfulness which the result exhibits is a model other software designers would do well to emulate. There is a useful, informative demo and most features are illustrated by example. Finally, Chapter 6 of the manual entitled "Applications" is a delight. I noted only one trivial typo in the manual. On page 107, the result of differentiating x squared should be 2 * x. The only design flaw, in my opinion, is the way *Roger Pinkham is a Professor of Mathematics at Stevens Institute of Technology in Hoboken, New Jersey. He can be reached by email at the address [email protected].

12

in which histograms are displayed. Frequencies of 1,11, 17,23,24,12,8,3,1 are displayed by vertical bars having heights proportional to 1,0,11,0,17,0,23,0,24,0,12,... etc. This is disconcerting to one used to reading histograms or stemleaf plots, since visually you see zero frequencies between the actual counts. The program is so good and so inexpensive I am seriously considering having all my students in numerical analysis purchase CC the next time I teach the course. References [1] Herbert L. Holden, Notices of the AMS 36, September 1989, pages 842-844.

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Derive, Version 2 Reviewed by Marvin S. Margolis* Soft Warehouse, Inc., 3615 Harding Avenue, Suite 505, Honolulu, Hawaii 96816, produces Derive, Version 2, a Mathematical Assistant, list price $250.00. It is a menu driven symbolic manipulation program for doing mathematics on ffiM or compatible personal computers. Version 2 improves upon earlier versions without increasing hard disk requirements. Programs like Derive are significant because they (1) have potential use as educational tools and (2) enable practicing mathematicians to experimentally analyze mathematical problems by computer. Notices has previously published three reviews of Derive in this column. Eric L. Grinberg reviewed an earlier Derive version in the September 1989 (volume 36, number 7, page 838) issue. Although he does not mention which version he reviewed, Grinberg's comments comprise probably the most comprehensive description of the program except for the user manual. His comments still apply to program parts that Soft Warehouse did not update in Version 2. Phil Miles discussed Derive as a precalculus assistant in a second review in the March 1990 (Volume 37, number 3, pages 275-276) issue. In the third review, Barry Simon compared Derive with three other microcomputer environments in the September 1990 (Volume 37, number 7, pages 861-868) issue. To prepare a review article on four mathematical packages for PC Magazine, Simon developed 20 trial mathematical problems. He sent the problems to the package vendors requesting that each supply solutions. By showing the vendors' solutions to the trial problems, his Notices article allows the reader to compare the four programs, Mathematica, Maple, Macsyma, and Derive. Simon's article evaluating the four programs based on his analysis appears in the May 29, 1990 issue of PC Magazine (Volume 9, Number 10). He previously reviewed Derive separately in the September 26, 1989 issue *Marvin Margolis is an Associate Professor of Economics at Millersville University in Millersville, Pennsylvania.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

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Computers and Mathematics

of PC Magazine. I expect there are many other Derive reviews in the mathematical and technical literature. The Grinberg (Notices) and Simon (PC Magazine) reviews nicely summarize Derive's features. For readers unfamiliar with Derive, I will paraphrase a few favorable and unfavorable program features from Simon's review. "For only $250 and a small PC without a coprocessor, Derive does a significant subset of the symbolic manipulation of calculus functions offered by Mathematica and Maple. It also does numeric calculations to a user-prescribed degree of accuracy. The . . . graphics . . . are comparable to the best programs that run on XTs. The program uses a Microsoft Word-type menu. Derive does all this with executable code of less than 220K without overlays. This technically impressive feat allows the program to load quickly." However, Simon finds the following Derive limitations. "Derive lacks a programming language and does not directly support output of its graphs to a printer. It doesn't understand somewhat exotic functions like Bessel and hypergeometric functions. It cannot solve systems of nonlinear equations." But, when he weighs the pros against the cons, Simon concludes that " ... this powerful little package is an absolute joy to use." Version 2 retains the favorable features mentioned above and also corrects some limitations. It now understands Bessel and hypergeometric functions and has increased programming language features. Still, it lacks complete programming features and does not support output of its graphics to a printer. I believe the changes in Derive from the earlier to the latest 2.0 version are major. Soft Warehouse has attempted to respond to the many, e.g. Grinberg and Simon, criticisms of their previous versions. Version 2 offers improvements in many areas such as programming capability, equation solving, matrix operations, calculus, numerical methods, plotting, user interface, and documentation. Some improvements are minor but others are major changes. It is still true that Version 2 does not offer a complete programming language. However, to provide one may require an unacceptable change in the size of the program and/or the ease of use. The reason is Derive uses primarily an interpretive rather than a compile and execute approachanalogous to interpretive rather than compiled Basic. In an interpretive approach, the user issues one command at a time, receives an immediate feedback response to the command, and analyzes the response before issuing a second command. In the second approach, the user stores a series of commands in a program, compiles the program, and then executes it. For a beginning student, the interpretive approach is usually the fastest and easiest method to learn program commands. Therefore, Derive has exciting possibilities as an educational tool as I explain below. But, consider someone who already knows the commands and repeatedly wants to step or loop through a series of commands. He or she may desire to change one parameter at a time without seeing intermediate results. That person prefers a compile and execute approach. Barry Simon's comment that Derive

is probably unsuited for some high end scientific applications ... " still applies. But, the Version 2 programming capability improvements are significant if not complete. Version 2 provides an ifthen-else conditional construct with an indeterminate result clause option plus logical and relational operators for use as conditionals. Together the two new programming features greatly increase the users' ability to create sophisticated functions. Now Derive users can create functions that rival those in any advanced spreadsheet program. The Version 2 program floppy disk includes 20 utility files, some of which illustrate the power of the new programming commands. The utility files are collections of function definitions and variable assignments. The files cover major mathematical areas such as vectors, numerical differentiation and integration, ordinary differential equations, probability functions, and miscellaneous functions. The utility files also include examples of Hypergeometric and Bessel and Airy functions; Barry Simon noted the absence of the functions in earlier versions. Another utility file offers numerical solutions to systems of nonlinear algebraic equations using Newton's or the fixed-point method. Thus Version 2 fills another gap that Simon noted. In addition, the user manual describes the utility files. I expect that Soft Warehouse will in future versions expand the utility files to approach the long list of readymade specialized mathematical functions that characterize the larger competing programs. Derive's main program can still remain small; the user will simply fast load only the utility file that contains the particular mathematical function that he or she needs. The user can store the utility files on a floppy instead of a hard disk. Version 2 still cannot send graphics screen images to a printer. The user manual now includes a list of commercial screen capture programs which one can purchase. I have not purchased any of these programs and therefore have not tried to capture a Derive graphics screen on a printer. Soft Warehouse revised the user manual to include many improvements. Many sections now include more than one example of how to use a command. There is a bibliography, a list of screen capture programs, and the descriptions of the new utility programs. Soft Warehouse is probably strongly interested in the results of a recent MathCad competitive thrust. MathCad's latest update added symbolic manipulation capability which it obtained from Maple to a Windows framework. Soft Warehouse must consider whether to expand Derive in the Windows direction, that is, allow users to use a mouse and pull down windows. They obviously cannot retain all the benefits of their small program if they choose the Windows framework. Maybe Soft Warehouse should split Derive into two programs. One program would remain small like the current Derive and concentrate on the educational market. Fit into a palm sized computer as in one current use, it would enable traveling mathematicians to carry dedicated hardware and software. It also provides professors in class an alternative

JANUARY 1992, VOLUME 39, NUMBER 1

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Computers and Mathematics

to a regular PC or even a laptop. The other Derive program would be large and compete head on with the higher priced competition such as Mathematica, Maple, and Macsyma. Designed as a vehicle for research, it would be a Windows program with programmability, printer drives, and massive mathematical functions. For readers who are familiar with statistical software, 1 would compare Derive with the Minitab program. Derive does fall at the low end of the (symbolic manipulation) mathematical software spectrum just as Minitab tends to fall at the low end of the statistical spectrum. If Mathematica falls at the high end of the mathematical spectrum, then the large statistical program SAS falls at the statistical high end. The Minitab and Derive programs are similar in that they are easy for students to learn since they both use interpretive languages. Neither pr-ogram permits true (i.e., branching) programming. Derive is highly suitable for use in an academic computer laboratory for mathematical experiments just as Minitab is for statistical experiments. When I teach I always give class priority to mathematical or statistical theory and not to computer software. In teaching statistics, I have found that Minitab assignments do not require extensive class time to explain the program mechanics as the SAS program does. Although I have not personally used Derive in a class yet, I am convinced that it will also work well for mathematical courses for the same reasons that Minitab works well for statistical courses. In teaching statistics, I could choose from among several statistical textbooks that directly incorporated Minitab assignments. The Derive user manual lists four books in an annotated bibliography that illustrate applications of Derive. I have examined two of the four and I find those two unsuitable as a text because they give Derive examples more priority than the mathematical theory. I suggest authors get busy and write a text that gives mathematical theory first priority but does incorporate Derive examples. I am convinced it will sell well.

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ODE2.5 Reviewed by Marvin S. Margolis Keith Briggs, Box 75, Heidelberg West, Australia 3081, is the author of ODE 2.5-An Interactive Program for the Simulation of Discrete or Continuous Dynamical SystemsffiM PC Version, Price: public domain version $Al 0, Full version $A75. Briggs designed ODE to provide assistance in teaching ordinary differential equations. Teachers at several Australian and American universities tested earlier versions. As an interactive system, it allows students to experiment with solutions of differential equations using numerical methods. ODE includes 17 example files besides the main and help files. The public domain version, while fully functional, has some restrictions; the author intends that professors use it to evaluate ODE for possible class use.

14

Purpose ODE solves initial value problems numerically for systems

of ordinary differential or difference equations that arise in many scientific fields such as physics, chemistry, and biology. The program presents solution values either graphically or in numeric tables. The user specifies equations in natural notation and stores them in standard ASCII text files. A built-in text editor helps the user create and edit a file. The user can save files for later use. The author expects that users will apply ODE to teaching and small research problems. He assumes user familiarity with differential and difference equations and basic computer use. The author's disclaimer notes that users should not rely upon ODE output in a situation involving possible life or property danger. ODE features include the following. It solves systems of ordinary differential equations, even those coupled or nonlinear. It requires no numerical analysis knowledge and automatically graphs problem solutions. The user can plot any variable against any other variable and can produce phase-space plots and/or plot with dots, lines, or splines. A user can examine variable values at any time and only computer memory size limits the equation order. Users can solve equations applying numerical procedures such as the Euler, Runge-Kutta, or Bulirsch-Stoer methods and can choose fixed or automatic stepsizes. Several examples included with the program investigate chaotic equation systems. ODE also solves finite difference equations. The program extensively checks for errors and provides informative messages.

Hardware Requirements ODE requires an ffiM PC, XT, AT, PS/2 or compatible

computer with a PCDOS or MSDOS operating system and CGA, EGA, or VGA graphics. It supports a mouse. The author recommends a numeric coprocessor although it is not essential. He also supplies the program on either a 3.5 inch 720K, 5.25 inch 360K, or 5.25 inch 1.4M MSDOS floppy disk. The program prints graphs on a HP laser printer. An install file installs the main program, the help file, and the seventeen example ODE files on a hard disk.

The User Manual

The author printed the 47 page user manual using I5JEX. The manual includes a table of contents, a tutorial, a fifteen page reference manual, example file listings, references, and an index. ODE applies menus with explanatory messages and additional on-line help, so that for class use, students do not need multiple copies of the user guide.

The ODE User Manual Thtorial The user manual includes a tutorial chapter explaining how to use ODE. The user manual does not attempt to explain ordinary differential equation or numerical computation theory. For users who want that information, the manual lists references on differential equation theory and computer methods for numerical analysis.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

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The tutorial begins by explaining the user procedure for executing an existing example ODE file. A user first selects (1) the file menu from the main menu bar, (2) the "load a file" option from the file menu, and (3) a file from among a file list. After ODE loads the selected file, the program editor displays it. After a user examines or changes the file, she exits the editor and returns to the main menu. Then she selects the "solve the equation" menu option to obtain graphical (or numeric) results. When she finishes examining or printing the graph she returns to the main menu. The user need only press a function key to examine (a) current variable value(s) instead of a graph. To continue a solution, the user presses another function key. Experimenting with ODE is easy; the program design encourages user experimentation. With the program's extensive error checking, disasters rarely happen. The author discusses four example files in the tutorial. The first example illustrates exponential growth using the simplest possible differential equation. The second example examines a second-order differential equation and illustrates sinusoidal oscillation. ODE does not automatically provide a phase-space plot. Users must first choose the graph command, establish the vertical axis as a velocity variable, and the horizontal axis as a position variable. The author recommends that users experiment with the second example. Try increasing the initial position to see if the period changes. Set the initial position equal to 0, but the initial velocity nonzero. Does the phase-space picture change? When the experimenter adds damping, how does the phase-space picture change? The third example examines a standard chaotic system, the quadratic function of the plane first described by Henon. The example illustrates an orbit, a strange attractor, and some experiments to show the sensitive dependence on initial conditions. The fourth example is a continuous chaotic system, the famous Lorenz equations. After executing the four tutorial files, I felt qualified to study the other example files.

The User Manual Reference Manual Fifteen pages of chapter three comprise the reference manual of the user manual. The reference manual subsections refer to the main menu, text editor, ODE language rules, using the mouse, and difficulties. The main menu commands are help, file, edit, solve, method, graph, print, variables, and quit. The built-in text editor uses standard Wordstar commands but lacks text move cominands. When a user must move text to change a program file, she can save the file, quit ODE, and edit the file in any ASCII text editor or word processor. The ODE language rules involve lines of the form: ( 1) algebraic equations, of the form variable = expression, (2) differential or difference equations, of the form variable = expression, (3) comments, starting with the symbol #, (4) directives, starting with the symbol $, which control the method of solution.

An algebraic equation setting an initial value must precede each differential equation. A user must rewrite equations of order greater than one as a system of first -order equations by introducing new variables to represent the higher derivatives.

Solution Methods The author offers the user some solution methods such as difference equations solutions, Euler method, fixed step size, second-order midpoint method, fixed step size, third-order Runge-Kutta, fourth-order, fifth-order fixed or automatic step size, and the Bulirsch-Stoer method. An article by J. R. Dormand and P. J. Prince, Celestial Mechanics, 18, 23 (1978) describes the fifth-order Runge-Kutta algorithm the author uses.

Solving ODE solves problems to extended precision, corresponding

to 19 decimal places. Still, the user may face problems in solving a problem, for example, an unstable numerical solution method. Here the author recommends trying a higher-order method or smaller steps with a fixed step size. ODE will abort a solution if it calculates very slowly using an automatic step size. Then try a different order solution method. ODE also aborts a solution when dividing by zero or taking a log or square root of a negative number.

Example File Listings Seventeen example files accompany the ODE main program. Each contains brief comments that explain the file's purpose. The user manual also provides a printout of the files. The examples illustrate an Airy differential equation, a planetary orbit in a binary star system, two coupled oscillators, a Duffing oscillator-a driven nonlinear oscillator with chaotic solutions, an exponential growth model, a Henon attractor, a Lorenz chaotic attractor, a planetary orbit around a fixed star, a driven, damped oscillator, a real pendulum-a nonlinear oscillator, a quantumchromodynamics equation, Roessler's chaotic attractor, and stagnation point flow in fluid dynamics. The author's suggestions for which variables to plot on which axes are helpful for those unfamiliar with the models.

Limits Users may choose at most 50 parameters or variables, 150 constants, 80 program lines, 1000 solution steps, 18 differential equations, or 500 stored solution points. The bibliography refers to 12 listings in the literature.

Using the Mouse If users install a mouse and mouse driver on their computers,

they may point and click to select main menu items instead of using keys. The mouse cursor appears as a magenta female symbol. The right-hand side of the help and solution display screens provides scroll bars. The mouse is inactive

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when using the text editor. ODE provides an easy-to-use menu system with context-sensitive help.

Comparisons with Phaser Because of certain similarities, ODE invites a comparison with Huseyin Kocak's Phaser program*. Each program solves differential and difference equations and uses menus. Each runs on IBM and compatible personal computers. Each contains similar example files in their libraries, for example, the Henon and Lorenz equations. Each displays a problem solution graphically and uses numerical analysis solution methods. Still, both can optionally display numerical as well as graphical solutions. Both have many sample files that illustrate how to set up the solution to a differential equation problem. The main program (*.exe) files are approximately the same size. As primarily graphics programs, they require skill in formulating the equation files, choosing the solution method, using step sizes, specifying axes dimensions, and other considerations.

ODE's Advantages Because ODE is simpler and not as rigidly designed as Phaser, it is somewhat easier to learn to use. Unlike Phaser, it has an on-line help capability. The easier to understand ODE user manual is a model of clarity. Simpler and more logical ODE language rules more easily enable the user to create new example files. ODE does not assume the user automatically desires a phase port diagram. ODE allows limited mouse use. ODE mentions connections to chaos theory in it's tutorial more than Phaser does. I find ODE's use of a built-in text editor to generate new example files more logical and less rigid than Phaser's insistence on menus for every step. I found ODE more conducive to performing experiments than Phaser. Finally, ODE labels numbers on tick marks of its graphs. Phaser lists the endpoints only and not on the coordinate axes. ODE possesses a richer toolbox of methods for solving the differential equations. The ODE pull down menu method confuses less than does Phaser's.

Phaser's Advantages The Phaser program is more comprehensive than ODE. It offers more library (sample) files. The user manual contains more detail and references. Unlike ODE's manual, the Phaser manual tries to explain some differential and difference equation theory. Phaser's manual contains many geometrical figure screen dumps whereas ODE's manual has none. Unlike Phaser, ODE does not appear able to draw Planar Poincare Maps or stair step diagrams. Also, unlike ODE, a Phaser user can optionally graph a vector field or split a screen into two different Phaser graphs. Phaser provides more literature references for each library file of a differential or difference equation. *Huseyin Kocak, Differential and Difference Equations through Computer Experiments with a Supplementary Diskette Containing Phaser: An Animator/Simulator for Dynamical Systems for IBM Personal Computers, Second Edition, Springer-Verlag New York, 1989.

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Conclusions I had the same experience with ODE that I had with Phaser. In modeling a particular equation system, I obtained unexpected and/or puzzling results. I immediately began studying the references to understand the theory better. I doubt I would have been so motivated to delve into the theory without ODE. I liked ODE after only trying it for fifteen minutes. Specifically, I liked ODE's logical program design and how easily I learned to use it. Because the program is small and students can learn it quickly, educators teaching dynamical systems can potentially use the program as an auxiliary tool. Since ODE contains no theoretical discussions, educators will not want to teach with it alone. It can supplement a dynamical systems course by letting students do experiments. It can add more excitement to an already exciting mathematical area.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Inside the AMS

Report on the Third Pan-Mrican Congress of Mathematicians and Some Thoughts on Cooperation Between the American and Mrlcan Mathematical Communities Lenore Blum, Vice President American Mathematical Society Last August I attended the Third Pan-African Congress of Mathematicians in Nairobi as the official delegate of the American Mathematical Society at the invitation of the Mrican Mathematical Union (AMU). 1 Most African nations were represented2 at the Congress and a number of other international societies sent delegates, 3 as they have in the past. But this was the first time the AMS was officially represented. I went to Africa because I felt it important that the AMS be represented. Indeed, I had spent much time last year convincing the AMS to send an official delegate (and I am grateful to AMS President Michael Artin for his support). But in truth, I had not expected to become as involved as I did. Nor had I expected to find the high level of mathematical activity, nor the strong commitment to mathematics development that I found. Like many Americans, I was woefully ignorant and provincial with regards to most things African. And while I am hardly an expert at this stage, I have tried to educate myself during the past few months. Here I will briefly report on the Congress and my impressions, and then offer suggestions for cooperative efforts between the American and African mathematical communities. I hope this may lead to constructive discussions culminating in concrete programs. The Third Pan-African Congress was held under the auspices of the AMU, an association whose mandate-as underlined by Professor Aderemi Kuku of the University of lbadan in Nigeria in his presidential address at the opening ceremony-is to "propagate research and education in the Mathematical Sciences in their various ramifications all over the Continent of Africa." To fulfill this mandate, the AMU organizes or co-sponsors colloquia, symposia, and workshops in diverse mathematical areas, as well as

publishes a journal, Afrika Matematika, the main outlet for dissemination of mathematical research carried out on the Continent. In addition, there are four AMU Commissions: on Mathematics Education; on History of Mathematics in Africa; on Women in Mathematics in Africa; and on Pan-African Mathematics Olympiads.4 At the opening ceremonies, each of the foreign delegates was asked to say a few words. After remarking on the internationalism of our field (clearly reflected at the Congress) and our common values and shared ideals, I presented a bound citation to the AMU from the AMS which read: "The Council of the American Mathematical Society sends congratulations to the Third Pan-African Congress of the African Mathematical Union to be held in Nairobi in August 1991. The Council is pleased that an officer of the Society can deliver these greetings personally. It looks forward to future cooperation with the Union in furthering the Mathematical Sciences." The Academic Program of the Congress included: about fifteen one-hour plenary lectures intended to illustrate current directions and achievements in the mathematical sciences; about forty 45-minute invited lectures in parallel specialized sessions; contributed research papers; a Symposium on "Mathematical Education in Africa for the 21st Century;" a day of emphasis on "Industrial Mathematical and Computer Science;" and the Third Pan-African Olympiad. In addition to the academic part of the program, there were many discussions, both formal and informal, on the development of mathematics in Africa and the roles the African governments and the international mathematics community could play. I was much impressed with the level of mathematics presented at the Congress. The talks covered a broad spectrum of topics from pure and applied mathematics. The speakers also represented a broad spectrum from young researchers to established mathematicians, and visitors. This is all the more impressive given the incredibly harsh working conditions: few up-to-date books, lack of current international journals, virtually no access to preprints, poor telephone and postal communication, no electronic mail, scarce funds for travel even within the Continent, little opportunity for contact with the international mathematics community, and so on. (Harley Flanders had similar impressions when he attended an AMU symposium in 1988 in Arusha, Tanzania.

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Inside the AMS

See Notices, January 1990, p. 32.) I was also impressed with the commitment on the part of African mathematicians to strive for the highest levels. As an example, one of the main thrusts of the AMU in the direction of advancing research and high-level education in the mathematical sciences on the continent is the promotion and development of Centers of Excellence. Eighteen universities in Africa have been identified for this purpose. In addition, there is a desire to create non-university research centers such as the National Mathematical Centre in Nigeria (directed by Professor James Ezeilo of the University of Nigeria). Quoting Kuku: "These Centers would constitute a network that will complement those in the developed countries and hopefully, apart from maximizing the use of available resources in Africa through exchange of staff, student and facilities South-South, also promote North-South interaction through exchange of staff and students. Thus while our colleagues from the developed countries are encouraged to visit us and give lectures, seminars, etc., our students who are registered for degrees in Africa ... could spend some time ... at centers of excellence abroad to be better exposed and come back to write their theses. It is our considered view that this will help to retain the badly needed expertise for our universities and other institutions of higher learning and stem brain drain ... " AMS presence at the Congress was clearly appreciated; I was often called upon to be spokesperson for the foreign representatives. During the Congress, I met with members of the AMU Executive Committee, the Commission on Women, and the other foreign representatives. We discussed many possibilities for cooperative programs, mostly with the goal of increasing contact and communication. One of the most potentially important efforts here will be in establishing electronic communication linkages. I believe there is a great deal we, both as a society and as individuals, 5 could do to assist the AMU and the African mathematics community in its efforts. I also think there would be benefits for us, particularly coming from increased contacts with-and visibility of-African mathematicians. The question now is what are the priorities and how best to proceed. This question must be considered within the broader context of the Society's relationship to the international mathematical community. The AMS is being asked to become involved in such international issues as the health and preservation of mathematics in the Soviet Union and in Eastern Europe and the development of mathematics in Africa and Asia, and so forth. Given the current world situation, these requests for AMS assistance and involvement will undoubtedly increase. The usual response has been to set up committees to investigate and make reports and recommendations. However, these committees have no way to implement their recommendations. In my formal report to the AMS Executive Committee on my trip to Africa, I recommended that the AMS secure funds for a staff person to support

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and coordinate the work of these committees, help develop policy guidelines, raise funds, and oversee development and implementation of programs. This is essentially the recommendation presented by Raymond Ayoub in his report on the AMS Committee on Service to Mathematicians in Developing Countries. (See AMS Council Supplementary Agenda, August 1991, Attachment B, p. 14.) In that report, Ayoub also recommended setting up a Mathematical Sciences Book Foundation to "render aid to institutes in developing countries in need of library enhancements."6 (I would like to note here that the single most frequent request I received from African mathematicians was that the AMS provide CD-ROMs of Mathematical Reviews to be placed in strategically located mathematics centers in Africa: for example, one in each of the geographical areas, north, south, east, west.) I endorse Ayoub's recommendation but would expand the idea to a Book and Communications Foundation, which would also provide technical assistance for such facilities as electronic communication networks. From exploratory investigations during the past weeks, I have discovered that there are a number of government agencies and private foundations that have resources, programs, and possibly funds that could support development of electronic networks (using low cost and appropriate technology such as Fido-net) and such activities as exchange programs with Africa. Clearly, this would take a great deal of work. If we are to do anything at all, I think it would be appropriate to invite some of the key figures in the African mathematics community to visit and advise and work closely with us. Such visits could be sponsored jointly by the AMS as well as other mathematical societies, research centers, colleges, and universities, and the visitors could also participate in activities of the sponsoring institutions. I end my report by echoing Ayoub, "It is abundantly clear that the needs are great. How shall the AMS respond? It is happily a situation where virtue and expedience come together."

Footnotes 10ther

U.S. participants at the Congress were Jim Donaldson, Joshua Leslie, Walter Feit, and Bill Lawvere. 2 African nations represented at the Congress included: Kenya, Zimbabwe, Nigeria, Algeria, Senegal, Tunisia, Egypt, Cote D'Ivoire, Burundi, Sudan, Cameroon, Mozambique, Uganda, Tanzania, Ghana, Morocco, Sierra Leone, Burkina Paso, and (for the first time) South Africa. 3 International mathematical societies that sent delegates to the Congress included the European, German, London, French, Belgium, Japanese, Swedish, Moscow and Italian mathematical societies as well as the International Mathematical Union. In addition, there were representatives from UNESCO, the International Centre for Theoretical Physics (Trieste), the Third World Academy of Sciences, and the African Academy of Sciences. 4 In his presidential address, Professor Kuku described an impressive array of activities carried out by the AMU and its Commissions during the past four years. Some highlights: - During the past four years, the AMU has co-sponsored over a dozen workshops and conferences (in diverse mathematical areas such

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as: K-Theory, General Algebra, Algebraic Geometry, Computational Mathematics, Numerical Analysis in Computer Science, Mathematical Analysis and Applications, Mathematical Physics, Stochastic Analysis and Education). -The AMU Commissions on Pan-African Mathematics Olympiads (chaired by Professor Mohammed Akkar of Morocco) has organized three Olympiads with the aim of stimulating and encouraging African youths to study mathematics as well as to promote positive interactions and healthy competition. - The AMU Commission on History of Mathematics in Africa has published eight newsletters that are the authoritative source on research on history of mathematics in Africa. [For copies of the Newsletter, contact AMUCHMA chair, Professor Paulus Gerdes, Rector, Higher Pedagogical Institute (ISP), Maputo, Mozambique.] - Last year, the AMU Commission on Women (chaired by Professor Grace Alele-Williams of Nigeria) organized a symposium on the "Mathematics Education of Women in Africa" and is currently compiling a comprehensive list of women in mathematics in Africa. -AfrikaMatematika, in existence since 1978, has been invigorated with a new Editorial and international Advisory Boards. An appeal was made "to our colleagues from all over the world to patronize this journal." [The annual subscription is US$20.00 which can be mailed to the Editor-in-Chief, Professor S. 0. lyahen, Department of Mathematics, University of Benin, Benin City, Nigeria.]

For a complete text of the address contact Professor A. 0. Kuku. Department of Mathematics, University of lbadan, lbadan, Nigeria. 5 One way American mathematicians could assist their African colleagues would be to routinely send preprints of recent work to individuals in their field as well as to libraries of selected mathematics departments. To facilitate this, the AMU could provide the AMS with a list of African mathematicians and their specific mathematical interests as well as a list of mathematics departments and the specific areas of research of their members. 61n his report, Ayoub outlines how such a Book Foundation might work: "First a 503c foundation is created. All of the mathematical sciences organizations will be asked to be a part of this foundation .... They will be asked to provide a one time grant as 'seed' money .... The executive director [of the foundation], with the help of cooperating organizations, will solicit funds from private foundations. from U.S. government agencies and from individual citizens .... "These funds will be used initially for shipping costs and other collateral expenses .... Book publishers will be solicited for contributions of monographs and members of the mathematical sciences will be asked to contribute journals and monographs .... Specific projects might be proposed and funds solicited. E.g. Funds to purchase CDROM [Compact Disc-Read Only Memory] readers and the Math Reviews on CD-ROM."

Series in Discrete Mathematics and Theoretical Computer Science Discrete and Computational Geometry: Papers from the DIMACS Special Year

Volume 6

Jacob E. Goodman, Richard Pollack, and William Steiger, Editors Discrete and Computational Geometry presents some of the results growing out of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of significant recent progress in discrete and computational geometry. The diversity of the papers demonstrates how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and stimulation between the two disciplines.

1991 Mathematics Subject Classifications: 03, 05, 12, 13, 14, 15, 32, 51, 52, 57, 68, ISBN 0-8218-6595-1, 378 pages (hardcover), December 1991 Individual mem. $40, List price $66, Institutional mem. $53 Your ordering code is DIMACS/6NA

All prtces subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: Amertcan Mathematical Society, P.O. Box 1571. Annex Station, Providence, RI 02901-1571. or call toll free 800321-4AMS in the continental U.S. and Canada to charge with VlSA or MasterCard. Please add 7% GST to all orders totalling over $40 being shipped to Canada.

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News and Announcements

Calderon Receives National Medal of Science

Alberto P. Calder6n, University Professor Emeritus of Mathematics at the University of Chicago, received the National Medal of Science on September 16, 1991. The medal is the nation's highest award for scientific achievements. Calder6n was one of twenty medalists. A piece on Calder6n's background and mathematical achievements is being prepared for a future issue of Notices.

Lorenz Receives Kyoto Prize

Edward N. Lorenz, a meteorologist who was one of the first to explore the idea of chaos in dynamical systems, has received the 1991 Kyoto Prize in Basic Sciences. The prize consists of a gold medal and 45 million Japanese yen. Poincare showed at the turn of the century that certain types of deterministic dynamical systems could exhibit chaos, but this work went largely unnoticed. In his numerical research seventy years later, Lorenz demonstrated that even a system with a small number of variables could exhibit chaos, a result that implied that the important factor was the nonlinearity of the system. Very small changes in the initial conditions can have a major effect on the evolution of the system, a notion known as the "butterfly effect," for it implies that even the flapping of a butterfly's wings could change the state of the system dramatically. Lorenz's theoretical research established the basis for computer-aided atmospheric physics and meteorology and developed re-

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search methods for major environmental problems. Born May 23, 1917 in Connecticut, Lorenz received his A.B. in mathematics from Dartmouth College in 1938 and his Sc.D. in meteorology from the Massachusetts Institute of Technology in 1948. He spent his entire career at MIT, first as a member of the research staff (1946-1955), and then as an assistant professor (1955-1962) and professor (1962-1981) in the meteorology department. Currently, he is professor emeritus at MIT. His other awards and honors include the Rossby Research Medal of the American Meteorological Society (1969), the Symons Memorial Gold Medal of the Royal Meterological Society (1973), election to the National Academy of Sciences (1975), and the Crafoord Prize of the Royal Swedish Academy of Sciences (1983). McMullen Receives Salem Prize

Curt McMullen of the University of California at Berkeley has been awarded the 1991 Salem Prize for his work on iteration and algebraic numbers. The prize, established in 1968, is presented each year to a young mathematician judged to have done outstanding work in the field of Raphael Salemprimarily Fourier series and related topics. The committee to select the 1991 Salem Prize consisted of J. Bourgain, V. Ravin, Y. Katznelson, and E. M. Stein.

differential equations in mathematical physics. The $3000 prize is intended to recognize and reward talented young Canadian mathematicians. Karnran was born in Belgium on May 22, 1959 to parents of Iranian descent. He received his bachelor's degree in 1980 and his master's degree in 1981 from l'Universire Libre in Brussels. He came to Canada to continue his studies and received a Ph.D. in 1984 from the University of Waterloo, where his thesis won an award for excellence. He then took a postdoctoral position at the Centre des Recherches Mathematiques (CRM) in Montreal. In 1986, he visited the Institute for Advanced Study in Princeton and joined the mathematics department at Waterloo. Since 1989, he has been at McGill University, where he is an associate professor. The Aisenstadt Prize, which will be presented on January 29, 1992, is named for the philanthropist Andre Aisenstadt. The prizewinner was selected by a CRM steering committee consisting of twelve distinguished mathematicians. 1991 Autumn Prize of MSJ

The 1991 Autumn Prize of the Mathematical Society of Japan was awarded to Akihiro Tsuchiya of Nagoya University for his outstanding contribution to two-dimensional conformal field theory.

Kamran Receives Aisenstadt Prize

Graduate Student Fulbrights for 1991-1992

Niky Karnran of McGill University has received the first Andre Aisenstadt Prize for his research in the application of differential geometry to the study of

The J. William Fulbright Foreign Scholarship Board and the United States Information Agency have announced the names of U.S. graduate students who

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have received Fulbright awards for the academic year 1991-1992. The following lists the three recipients in the mathematical sciences, together with their home institution, the countries they will be visiting, and their research areas: MARGARET CONROY, University of Notre Dame, Germany, topology; JOSHUA FINKLER, Reed College, Hungary, applied mathematics; and ARTHUR WoERHEIDE, University of Illinois at Urbana-Champaign, Austria, number theory. AAUW Announces Fellowships and Grants

The American Association of University Women (AAUW) has announced fellowships and grants ranging from $1000 to $25,000 each to one hundred women recipients who will do postdoctoral research, complete doctoral dissertations, or enter the final year of study in a number of selected professions. None of the postdoctoral fellowships went to recipients in the mathematical sciences. Among the dissertation fellows is LYNN KIAER of the Florida Institute of Technology, who is studying discrete optimization strategies for timetabling; and SYLVIA WILLIAMSON of Emory University, who is studying fixed-point properties in ordered sets. Five women in the mathematical sciences received selected professions fellowships: CATHERINE AXTELL of Purdue University, in statistics; ELIZABETH BRADLEY of the Massachusetts Institute of Technology, in nonlinear dynamics; LINDA GARANT of Tufts University, in mathematics; and SuSAN ZARZECZNY of the University of California at Berkeley, in statistics. For information about applying for AAUW grants and fellowships, consult the "Stipends for Study and Travel" section of the October 1991 issue of Notices, pages 1021-1022. Richard Herman Appointed to JPBM Post

Richard Herman, dean of the College of Computer, Mathematical, and Physical Sciences at the University of Maryland, has agreed to serve also as chair of the Joint Policy Board for Mathematics

(JPBM). He will direct the JPBM Office of Governmental and Public Affairs, a joint effort of the three societies, AMS, the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM). In recent years, JPBM has served as an effective vehicle for heightening awareness of the mathematical sciences. Its main role has been to forge ties with government agencies and other entities that support mathematical sciences research, to increase public awareness of mathematics through print media and other avenues, and to act as a clearinghouse for general queries from the public and the government about the mathematical sciences. Herman sees his role as serving all segments of the mathematical sciences community. "I want to help the entire community-MAA, SIAM, and AMS-to set an effective strategy to get mathematics on the national agenda," he says. "This is an unparalleled opportunity in that mathematics has figured prominently in the public eye in recent years," particularly in the areas of improving precollege education, insuring a sufficient supply of mathematical expertise in the nation, and recognizing the impact of mathematics research on science and technology. "The priority is to clearly get mathematics on the table and keep it there." Herman sees JPBM as a route by which the mathematical sciences community can contribute to these kinds of national issues. "In comparison to what goes on in the physics and chemistry communities, we have a way to go," he remarks. "A great deal has been done through the efforts of my predecessors and Lisa Thompson [JPBM Assistant for Governmental Affairs], and I hope to build on what they have accomplished. We need to take advantage of present opportunities, map out a longterm agenda, and then stick to it." For example, in the area of coverage of mathematics, "thanks to Kathleen Hoimay [JPBM public information director], we have been successful in placing many more stories than in the past." But he would also like to encourage more mathematicians to write popular

JANUARY 1992, VOLUME 39, NUMBER 1

articles that would communicate some of the major developments of the day in mathematics research. He notes that breaking into business magazines and new media avenues could further raise the profile of mathematics and communicate the message that mathematics is having an impact on business and industry. Federal grant support for mathematical sciences research poses its own problems of communicating about mathematical sciences research. Herman intends to try to improve ties to the agencies and Congress to insure that the voice of mathematics is heard in the clamor for more funds. The job market in mathematics is another pressing concern. "Can we allay or mitigate difficulties of the job market?" he asks. Herman has not yet laid plans for specific JPBM projects. However, he says he would like to bring in mathematicians to serve as visiting scientists at the Washington office of JPBM to contribute their expertise to specific projects. Herman will share planning ideas on a regular basis with Society members through meetings, columns, and so on. He says he is looking forward to active, increased community involvement. Herman took his present position at the University of Maryland after being on the faculty of Pennsylvania State University for eighteen years, where he served as chair of the mathematics department from 1985 to 1990. He has also been on the faculties of the University of California at Los Angeles and the University of Rochester. Herman's contributions to mathematical literature have been largely in the area of operator algebras and mathematical physics, with much of his recent work focusing on classification of group actions on operator algebras and the modeling of dynamical systems. Congressional Staff Request Report from AMS

In July 1991, a task force of Congressional staff from the House Committee on Science, Space, and Technology asked the AMS to assist in a pilot project to assess goals and priorities in the mathematical sciences.

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News and Announcements

The objective of the task force, which has initiated several similar projects in a range of research and development programs, was "to extract general criteria which could be used to assess the success or failure of the wide variety of R&D programs which the Committee authorizes." In response to the task force request, the Society convened a panel of twelve mathematical scientists to produce a report. The starting point for the report was a list of fifteen questions framed by the task force. The questions fell into three broad categories: goals, existing assessment process, and attainment of goals. Here are some examples of the questions asked: What are the most important short- and long-term goals of the discipline? What specific criteria are used to measure progress toward goals? How successfully is the discipline achieving or making progress toward major goals? Because the mathematical sciences generally are not organized around clearly defined, predetermined goals, the questions were quite difficult for the panel to answer. However, the panel made every effort to provide clear and comprehensive answers within the framework the task force had laid out. The result is a thirteen-page report covering a range of issues, including mathematical sciences research, mathematics education, technology transfer, and human resources. The Society circulated drafts to a wide range of members of the mathematical sciences community. Their comments and criticisms contributed a great deal toward producing a focused, coherent report. On December 13, 1991, the report was delivered to the Congressional task force in Washington, DC. Presenting the report were panel members James G. Glimm of the State University of New York at Stony Brook, John C. Polking of Rice University, and AMS President Michael Artin of the Massachusetts Institute of Technology, in addition to Joint Policy Board for Mathematics (JPBM) Chair Richard H. Herman, AMS Executive Director William H. Jaco, and JPBM Assistant for Governmental Affairs Lisa A. Thompson.

22

The report received a positive response from the Congressional staff, who found it very thoughtfully prepared. After a general introduction by Artin and Glimm, the staff asked several specific questions about various points made in the report. Overall, the meeting was a successful exchange, with both sides indicating a willingness to continue the dialogue, which _would likely include a second iteration of the report. The House Committee on Science, Space, and Technology has authorization and oversight responsibility for the National Science Foundation, the National Aeronautics and Space Administration, the National Institute for Standards and Technology, and research and development at the Department of Energy and the Environmental Protection Agency. As a result, this Committee oversees a large percentage of federal funding for research in the mathematical sciences. The chair of the Committee is Representative George Brown, Democrat from California. The full text of the report will appear in the February 1992 issue of Notices. AMS Awards Grants to Four Universities

The AMS is pleased to announce the first group of schools selected to receive awards through the Society's Waldemar J. Trjitzinsky Memorial Fund. The awards of $2500 each will assist needy students in mathematics. The four institutions receiving the awards are: Duke University in Durham, North Carolina; the University of Scranton in Scranton, Pennsylvania; Montana State University in Bozeman, Montana; and Howard Payne University in Brownwood, Texas. The schools were selected randomly from the pool of nearly 500 AMS institutional members. Four awards will be made each year. The awards are to be used to assist students majoring in mathematics whose progress might be hindered by financial circumstances. Each school chooses one student to receive the $2500 award. The Society has encouraged each institution to also provide matching funds, if possible. In addi-

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

tion, the institutions are specifically asked to consider women and members of groups traditionally underrepresented in mathematics. This program is made possible through a bequest of $185,000 made to the Society. Barbara Trjitzinsky, wife of Waldemar Trjitzinsky, bequeathed one-third of her estate to the AMS "to be held, invested and maintained as a fund to be called the 'Waldemar J. Trjitzinsky Memorial Fund,' the income only to be used in its discretion for assistance to needy students studying in the field of mathematics." Waldemar Joseph Trjitzinsky was born in Russia in 1901 and received his doctorate in mathematics from the University of California at Berkeley. He taught at a number of different universities before taking a position on the faculty of the University of Illinois at Urbana-Champaign in 1934, where he remained for the rest of his professional life. He showed particular concern for students of mathematics and in some cases made personal efforts to insure that financial considerations would not hinder their studies. He served on the AMS Council from 1938 to 1940 and presented Invited Addresses at two AMS meetings. A member of the Society for forty-six years, he died on December 8, 1973 in Mattapoisett, Massachusetts, where he had lived since his retirement. Trjitzinsky wrote about sixty papers, primarily on quasi-analytic functions and differential equations. During a stay at Harvard early in his career, Trjitzinsky collaborated with George David Birkhoff on some work in linear difference equations. In a letter of recommendation dated November 1, 1931, Birkhoff wrote: "I am very fond of Trjitzinsky for his personal qualities. He is modest and even retiring, attractive in appearance and unusually charming in his general personality ... Trjitzinsky is heart and soul devoted to mathematics and a hard worker." The Society is honored to have the opportunity to offer these special awards and to help keep alive Trjitzinsky's commitment to mathematics and mathematics students.

News and Announcements

Regional Technology Centers Established at Ohio State University The increasing use of technology in teaching mathematics in secondary and middle schools provides new opportunities for mathematics faculty to become involved in precollege mathematics education. The Ohio State University received a grant from the National Science Foundation to establish regional technology centers to train technology specialists. Each center will consist of a college or university faculty member, a secondary teacher, and a middle school teacher. Ohio State, with support from the NSF grant, will provide team training through in-service summer sessions and academic year follow-up conferences. The regional teams will then help create and/or revise in-service training modules for technology specialists. Those interested in forming teams with middle and high school teachers and receiving team training should write TRANSIT, c/o Frank Demana and Bert Waits, The Ohio State University, De-

....

_ CoNTEMPORARY

'

MATHEMATICS

partment of Mathematics, 231 West 18th Avenue, Columbus, OH 43210. The deadline for applications is February 15, 1992. News from the Mathematical Sciences Research Institute Berkeley, California

The Mathematical Sciences Research Institute (MSRl) has scheduled eight workshops during 1992. The first three workshops are part of the 1991-1992 programs in Lie Groups and Ergodic Theory, and Statistics: February 10 -11, Workshop on Amenable Ergodic Theory, Committee: H. Furstenberg, D. Ornstein and B. Weiss; March 30 - April 3, Workshop on Statistical Methods in Molecular Biology, Organizer: M. Waterman; April 13 17, Workshop on Lie Groups, Ergodic Theory, and Geometry, Committee: A. Katok, R. Spatzier, and R. Zimmer (chairman). During the summer, MSRl will sponsor two special events: July 6

through August 14 there will be a program in Mathematical Physiology organized by Nancy Kopell and Mike Reed; August 10 through 21 are the dates of the summer program for students, this year devoted to Dynamical Systems. Because of the overlap with the Physiology program, the student program will be held this year at UCLA, one of MSRl's sponsoring institutions. During the fall, MSRl will be featuring programs in Algebraic Geometry, and Symbolic Dynamics. Five workshops are planned: September 21 - 23, Workshop on Algebraic Cycles, Committee: A. Beilinson, W. Fulto; October 12 - 16, Workshop on Visualization, Committee: A. Marden; November 2 - 6, Workshop on Symbolic Dynamics, Committee: R. Adler, J. Franks, D. Lind and S. William; November 16 - 18, Workshop on Higher Dimensional Geometry, Committee: J. Kollar, S. Mori; December 2 - 4, Workshop on Curves, Abelian Varieties, and their Moduli, Committee: E. Arbarello, A. Beauville and J. Harris.

Spinor Construction of Vertex Operator Algebras, Triality, and E8(l) Alex J. Feingold, Igor B. Frenkel, and John F. X. Ries

121

Directed at mathematicians and physicists, this book is accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Spinor Construction of Vertex Operator Algebras, Triality, and E~ 11 Alex J. Feingold Igor B. Frenkel John F. X. Ries

,

__ Amencan Mathematical Soc1ety

The reader will learn how the concepts and techniques of Lie theory can be generalized to give the algebraic structures associated with conformal field theory. The careful reader will gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras, and plays an important role in a spinor construction of vertex operator algebras, modules and intertwining operators with nontrivial monodromies. 1991 Mathematics Subject Classifications: 17,81 ISBN 0-8218-5128-4, 146 pp. (softcover), September 1991 lndiv. mem. $20, List $34, lnst. mem. $27 Your ordering code is CONM/121NA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per !Hie. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Please add 7% GST to all orders totalling over $40 being shipped to Canada.

JANUARY 1992, VOLUME 39, NUMBER 1

23

1992 AMS Elections Nominations by Petition

Vice-President or Member-at-Large One position of vice-president and member of the Council ex officio for a term of three years is to be filled in the election of 1992. The Council intends to nominate at least two candidates, among whom may be candidates nominated by petition as described in the rules and procedures. Five positions of member-at-large of the Council for a term of three years are to be filled in the same election. The Council intends to nominate at least ten candidates, among whom may be candidates nominated by petition in the manner described in the rules and procedures. Petitions are presented to the Council, which, according to Section 2 of Article VII of the bylaws, makes the nominations. The Council of 23 January 1979 stated the intent of the Council of nominating all persons on whose behalf there were valid petitions. Prior to presentation to the Council, petitions in support of a candidate for the position of vice-president or of member-at-large of the Council must have at least 50 valid signatures and must conform to several rules and operational considerations, which are described below.

Editorial Boards Committee Two places on the Editorial Boards Committee will be filled by election. There will be four continuing members of the Editorial Boards Committee. The new members will be elected in a preferential ballot. The President will name at least four candidates for these two places, among whom may be candidates nominated by petition in the manner described in the rules and procedures. The candidate's assent and petitions bearing at least 100 valid signatures are required for a name to be placed on the ballot. In addition, several other rules and operational considerations, described below, should be followed.

Nominating Committee Three places on the Nominating Committee will be filled by election. There will be six continuing members of the Nominating Committee.

24

The new members will be elected in a preferential ballot. The President will name at least six candidates for these three places, among whom may be candidates nominated by petition in the manner described in the rules and procedures. The candidate's assent and petitions bearing at least 100 valid signatures are required for a name to be placed on the ballot. In addition, several other rules and operational considerations, described below, should be followed.

Rules and Procedures Use separate copies of the form for each candidate for vicepresident, member-at-large, or member of the Nominating and Editorial Boards Committees. 1. To be considered, petitions must be addressed to Robert M. Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island 02940, and must arrive by 28 February 1992. 2. The name of the candidate must be given as it appears in the Combined Membership List. If the name does not appear in the list, as 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. 3. The petition for a single candidate may consist of several sheets each bearing the statement of the petition, including the name of the position, and signatures. The name of the candidate must be exactly the same on all sheets. 4. On the next page is a sample form for petitions. Copies may be obtained from the Secretary; however, petitioners may make and use photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that of the member whose name and address is given in the left-hand column. 6. The signature may be in the style chosen by the signer. However, the printed name and address will be checked against the Combined Membership List and the mailing lists. No attempt will be made to match 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 not to be.) 7. When a petition meeting these various requirements appears, the Secretary will ascertain whether the candidate agrees to stand for election to the position in question. Petitioners can facilitate this process by submitting a statement to this effect from the candidate along with the petition.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

NOMINATION PETITION FOR 1992 ELECTION The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one):

D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 1993. Name and Address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

JANUARY 1992, VOLUME 39, NUMBER 1

25

CALL FOR SUGGESTIONS There will be a number of contested seats in the 1992 AMS elections. Your suggestions are wanted by

THE NOMINATING COMMITTEE for vice-president, trustee, and five members-at-large of the council and by

THE PRESIDENT for three Nominating Committee members and two Editorial Boards Committee members In Addition

THE EDITORIAL BOARDS COMMITTEE requests suggestions for appointments to various editorial boards of Society publications. Send your suggestions for any of the above to: Robert M. Fossum, Secretary American Mathematical Society Department of Mathematics University of Illinois 1409 West Green Street Urbana, IL 61801

Tuscaloosa, Alabama University of Alabama March 13-14, 1992 First Announcement The eight-hundred-and-seventy-second meeting of the American Mathematical Society (AMS) will be held at the University of Alabama, Tuscaloosa, Alabama on Friday, March 13, and Saturday, March 14, 1992. All sessions will be held in the Paul W. Bryant Conference Center. Invited Addresses By invitation of the Southeastern Section Program Committee, there will be four invited one-hour addresses. The speakers, their affiliations, and the titles of their talks where available are: Jane M. Hawkins, University of North Carolina, Chapel Hill, title to be announced. Charles A. Micchelli, IBM, Pyramid schemes for the recursive computation of multivariate polynomials. Serge Ochanine, University of Kentucky, Lexington, What is elliptic cohomology. Peter M. Winkler, Bellcore, Linear extensions of partially ordered sets. Special Sessions By invitation of the same committee, there will be eight special sessions of selected twenty-minute papers. The topics of these sessions, and the names and affiliations of the organizers, are as follows: Spectral theory of ordinary and partial differential operators, Richard C. Brown, University of Alabama, Tuscaloosa. Infinite groups and group rings, Jon M. Corson, Martyn Russell Dixon, Martin J. Evans, Frank Roehl, University of Alabama, Tuscaloosa. Ergodic theory and dynamical systems, Karma Dajani, University of South Alabama, Jane M. Hawkins, Karl Petersen, and Mate Wierdl, University of North Carolina, Chapel Hill. Combinatorial problems or partially ordered sets, Peter M. Winkler, Bellcore. Operator algebras, Alan Hopenwasser, and Cecelia Laurie, University of Alabama, Tuscaloosa. Geometric topology, Vo Thanh Liem, and Bruce S. Trace, University of Alabama, Tuscaloosa. Harmonic analysis and related topics, Kai-ching Lin, Tavan T. Trent, James L. Wang, and Zhijian Wu, University of Alabama, Tuscaloosa.

Approximation theory: Modern methods, Charles A. Micchelli, and R. A. Zalik, Auburn University. Abstracts for consideration for these sessions should have been submitted by the December 12, 1991 deadline. This deadline was previously published in the Calendar of AMS Meetings and Conferences and in the Invited Speakers and Special Sessions section of Notices.

Contributed Papers There will also be sessions for contributed ten-minute papers. Abstracts for consideration of these sessions should have been submitted by the January 2, 1992 deadline previously published in the Calendar of AMS Meetings and Conferences. Late papers will not be accommodated. Registration The meeting registration desk will be located in the main lobby of the Paul W. Bryant Conference Center. The registration fees are $30 for members of the AMS, $45 for nonmembers, and $10 for students or unemployed mathematicians. Social Event A social event and cash bar will be held for conference participants at the University Club on Friday evening from 7:00p.m. to 9:00p.m. The University Club occupies a large antebellum home at the corner of University Boulevard and Queen City Avenue. Accommodations Rooms have been blocked for participants at the Holiday Inn, LaQuinta Inn, and the Quality Inn. These Inns are adjacent to the exit off of I-20 and 1-59 on McFarland Boulevard in Tuscaloosa. Morning and evening van transportation will be provided between these motels and the Bryant Conference Center. A block of rooms is also being held in Parker-Adams Hall, close to the President's Mansion on campus. This is a small, older residence hall that is now used only for conference participants and university visitors. In addition, a very limited number of rooms are available at Dill's Motor

JANUARY 1992, VOLUME 39, NUMBER 1

27

Meetings

Court. Participants should make their own arrangements with the hotel of their choice and ask for the AMS meeting rate. All rates are subject to an eight percent tax. The AMS is not responsible for rate changes or the quality of the accommodations offered by these hotels/motels. Holiday Inn (2.9 miles to Bryant Conference Center) 3920 McFarland Boulevard, Tuscaloosa, AL 35405 Telephone: 800-322-3489 or 205-553-1550 The deadline for reservations is February 11. Double $46

p.m.), and dinner (4:30p.m. - 6:30p.m.) on Friday and for lunch only on Saturday. The dining room offers all you can eat with a good selection of items at a reasonable price. The Oak Room in the Sheraton Capstone Inn, adjacent to the Bryant Center, serves moderately priced lunches as well as a lunch buffet. A list of off campus restaurants will be available at the registration desk. Parking

La Quinta Inn (3 miles to Bryant Conference Center) 4122 McFarland Boulevard, Tuscaloosa, AL 35405 Telephone: 800-531-5900 or 205-349-3270 The deadline for reservations is February 19. Double $44

Free parking for the Bryant Conference Center is available in the lot at the comer of Paul Bryant Drive and Second Avenue. Participants staying at Parker-Adams Hall may obtain visitor parking permits from the University Police Department in Gorgas Hall located at the comer of University Boulevard and Stadium Drive or may park in the lot adjacent to the College of Continuing Education.

Quality Inn 3801 McFarland Boulevard, Tuscaloosa, AL 35405 Telephone: 800-228-5151 or 205-556-9690 The deadline for reservations is February 11. Single $39 Double $112 Triple $49

Travel and Local Information

Dill's Motor Court (.6 miles to Bryant Conference Center) 521 University Boulevard, Tuscaloosa, AL 35405 Telephone: 205-758-7571 The deadline for reservations is March 10. Double $41.75 Triple $45.75 Parke-Adams Hall (.4 miles to Bryant Center) Reservations must be made by calling Sidney Hennessey at 205-348-2514. All rooms include linens. Advance payment is required and should be mailed to: Sidney Hennessey, Department of Housing, University of Alabama, P.O. Box 870399, Tuscaloosa, AL 35487. The deadline for reservations is March 2. Single $18 Double $26

Tuscaloosa is easily reached by car on Interstate 20/59. When arriving by car take exit 73 and follow McFarland Boulevard (U.S 82). The Tuscaloosa Airport is served by Atlantic Southeast Airlines (affiliated with Delta Airlines) from Atlanta and American Eagle (affiliated with American Airlines) from Nashville. Seats are limited and early reservations are recommended. The Birmingham Airport has more frequent service and is approximately a one hour drive from Tuscaloosa. AMTRAK provides daily passenger rail service to and from Tuscaloosa through Atlanta and New Orleans.

Weather The weather in Tuscaloosa in March is variable. In a recent year, daily lows averaged 43°F and daily highs averaged 67°F. Rainfall in March can be heavy.

Food Service Barna Dining, located in Mary Burke Hall, will be open for breakfast (7:00 a.m. - 9:30 a.m.), lunch (11:15 a.m. - 1:30

28

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Joseph A. Cima Associate Secretary Chapel Hill, North Carolina

Springfield, Missouri Southwest Missouri State University March 20-21, 1992 First Announcement The eight-hundred-and-seventy-third meeting of the American Mathematical Society (AMS) will be held at the Southwest Missouri State University (SMSU) on Friday, March 20, and Saturday, March 21, 1992. All sessions and addresses will be held in Glass Hall (John Q. Hammons Parkway). Invited Addresses

By invitation of the Central Section Program Committee, there will be four invited one-hour addresses. The speakers, their affiliations, and the titles of their talks where available are: Alexander Eremenko, Institute of Low Temperature Physics and Engineering, Recent progress in value distribution theory. Julia Knight, Notre Dame University, Algorithms based on guessing: nested priority arguments. Peter Olver, University of Minnesota, title to be announced. Ernst A. Rub, Ohio State University, Nilpotent structures on principal bundles. Special Sessions

By invitation of the same committee, there will be twelve special sessions of selected twenty-minute papers. The topics of these sessions, and the names and affiliations of the organizers, are as follows: Harmonic analysis, Nakhle Habib Asmar and Stephen John Montgomery-Smith, University of Missouri, Columbia. Combinatorics and discrete geometry, Margaret M. Bayer, University of Kansas, Lawrence. Partial differential equations, Wengxiang Chen and Shoo Chuan Hu, Southwest Missouri State University. Commutative algebra, William J. Heinzer and Craig Huneke, Purdue University, and Kishor M. Shah, Southwest Missouri State University. The geometry of connections, Louis Hernandez, University of Chicago, and Ernst Rub, Ohio State University. Lie algebras, cohomology, and new applications to quantum mechanics, Niky Kamran, McGill University, and Peter J. Olver, University of Minnesota. C*-algebras and algebraic topology, Ellen Maycock Parker, DePauw University.

Semigroups, Boris M. Schein, University of Arkansas. Fourier analysis, Vera B. Stanojevic, Southwest Missouri State University. Approximation theory, Xingping Sun and Xiang Min Yu, Southwest Missouri State University. Geometry of affine space, David Wright, Washington University. Classical complex analysis and related areas, Jang-Mei Wu, University of Illinois, Urbana, and David Drasin, Purdue University. Abstracts for consideration for these sessions should have been submitted by the December 12, 1991 deadline. This deadline was previously published in the Calendar of AMS Meetings and Conferences and in the Invited Speakers and Special Sessions section of Notices. Contributed Papers

There will also be sessions for contributed ten-minute papers. Abstracts for consideration of these sessions should have been submitted by the January 2, 1992 deadline previously published in the Calendar of AMS Meetings and Conferences. Late papers will not be accommodated. Registration

The meeting registration desk will be located in the eastern foyer of the second floor of Glass Hall. The registration fees are $30 for members of the AMS, $45 for nonmembers, and $10 for students or unemployed mathematicians. Accommodations

Rooms have been blocked for participants at the University Plaza Hotel, the Quality Inn North Motel, and the Park Inn Motel. Participants should make their own arrangements directly with the hotel of their choice and ask for the special AMS meeting rate. Other motels close to the Quality Inn are: Best Inns (417-866-6766), Best Western (417-8620701), Econo Lodge (417-864-3565), Holiday Inn North (417-865-8600), Markham Inn (417-866-3581), Motel 6 (417-869-4343), Ramada Inn (417-831-3131), Red Roof Inns (417-831-2100), Scottish Inns (417-865-6565), and Super 8 Motel (417-833-9218). Rates are subject to a room tax. The AMS is not responsible for rate changes or the quality of

JANUARY 1992, VOLUME 39, NUMBER 1

29

··~·.--~---····~---·~mnml••••mu•m•••m&mam· mm~••m:•r---

-------~-~--·----·-·

Meetings

the accommodations offered by these hotels/motels. Holiday Inn - University Plaza Hotel (one block from campus) 333 John Q. Hammons Parkway Springfield, MO 65806 Telephone: 417-864-7333 Plate rate: $62.50 Park Inn International (2 miles from campus) 1772 South Glenstone Avenue, Springfield, MO 65806 Telephone: 417-882-1113 Plate rate: $43 Quality Inn North (5 miles from campus) I-44 at Exit 80-B, Springfield, MO 65806 Telephone: 417-833-3108 Plate rate: $45 Food Service The Bears' Den has a salad bar, serves sandwiches, pizza, and a limited variety of other hot foods. It is located in the basement of the Campus Union. It will be open for lunch on Friday and Saturday. A complete list of local restaurants will be available at the meeting registration desk.

from the airport), then traveling south on National Avenue for about four miles. The other motels can be reached by turning from Kearney onto I-44, heading east. Arriving by car: Springfield is located on 1-44, roughly halfway between Oklahoma City and St. Louis on U.S. 65, which runs north and south, and on U.S. 60. Those arriving by car on I-44 should turn off at Exit 80 (Glenstone Avenue, also known as U.S. 65 Bus., where numerous motels, including the Quality Inn, are located. The Park Inn is located five miles south on Glenstone. To reach Glass Hall or the University Plaza Hotel, proceed south on Glenstone Avenue for four miles to Grand Avenue. Proceed west on Grand Avenue for one mile, continue past the corner of the campus at National Avenue, then turn right onto John Q. Hammons Parkway. Those arriving from the south on U.S. 65 should turn west onto U.S. 60 at the point where these two roads intersect southeast of Springfield. About one mile after this interchange, Glenstone Avenue (U.S. 65 Business) branches off heading north. This is also relevant to anyone coming in from the east on U.S. 60. Those arriving from the southwest on U.S. 60 will find that it becomes Sunshine Avenue, which eventually crosses National Avenue and then Glenstone Avenue.

Parking Free parking will be available to participants in a large lot on the south side of Glass Hall. Permits will not be required, as the university will be on spring break. Travel Arriving by air: Springfield Regional Airport is serviced by American Eagle, Northwest Airlink, TWA, USAir, and United Airlines. The airport is serviced by Avis, Budget, Hertz, and National car rental agencies. Transportation from the airport to the Park Plaza Hotel or the Quality Inn can be accomplished by hotel courtesy van. Transportation to other motels can be accomplished by taxi; relevant phone numbers are: Springfield City Cab 865-5787 and Yellow Cab Co. 862-5511. Participants renting a car at the airport may reach the university (and the Holiday Inn- University Plaza Hotel), by traveling east on Kearney Avenue (the only exit

30

Weather and Local Information The average high temperature in Springfield in March is 55°F and the average low is 32°F. Springfield is the hub of the Ozarks region, a scenic area of hills, forests, rivers, lakes, and limestone caverns. Spring is especially lovely, with the redbuds and dogwoods in bloom. Fans of country music may be interested in attending shows in Branson (about 40 miles south of Springfield), which has lately begun to attract some of the top entertainers in the field; those interested should contact the Branson Chamber of Commerce (417-334-4137) to find out who will be performing at the time of the meeting and to get phone numbers for reservations.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Andy R. Magid Associate Secretary Norman, Oklahoma

Joint Workshop on Education Reform Changing the culture: Education and the research community Oakland/Berkeley, California, March 5 -March 8, 1992 As part of the initiative to identify and cultivate educational leadership in the mathematics research community, the joint workshop is aimed at activating individual mathematicians to become involved in education reform as the first step in the process of making systematic changes. While highlighting opportunities to become involved in undergraduate education reform, the workshop will also present projects in precollege mathematics education with implications for undergraduate reform. To further the view that quality mathematics education is the collective commitment of the profession, the program will include discussions on policy issues relating to how departments, institutions and professional organizations can support education efforts and the individuals involved in these efforts. Presentations will feature mathematicians who are active in educational projects. Speakers include: Donald Bushaw, Washington State University; Joan Ferrini-Mundy, University of New Hampshire; Avner Friedman, Institute for Mathematics and its Applications; Harvey Keynes; University of Minnesota; D. J. Lewis, University of Michigan, Ann Arbor; Calvin Moore, University of California, Berkeley; Hugo Rossi, University of Utah; Paul Sally, University of Chicago; Uri Treisman, University of Texas at Austin; and Philip Wagreich, University of Illinois at Chicago. The workshop is co-sponsored by the American Mathematical Society (AMS), the Mathematical Association of America (MAA), the Mathematicians and Education Reform Network (MER), the Mathematical Sciences Research Institute (MSRI), the Society for Industrial and Applied Mathematics (SIAM), the Department of Mathematics, Uni-

versity of California, Berkeley, and the Office of Academic Affairs, University of California. The workshop is limited to sixty participants. Funding for the workshop, including funds to provide room (double occupancy) and board for participants, is being sought from the National Science Foundation. Participants will be housed at the Waterfront Plaza Hotel in Oakland, California. Sessions will be held at the Waterfront Plaza Hotel, the University of California, Berkeley campus, and MSRI. Those interested in attending the Workshop are invited to request an application and should send the following information to: Joint Workshop Coordinator, American Mathematical Society, P.O. Box 6887, Providence, R.I. 02940, email: [email protected], before January 10, 1992. Please type or print the following: 1. 2. 3. 4.

Full name; Mailing address; Telephone number and area code for office and home; email address if available;

A registration fee of $100 must accompany applications. When returning applications please enclose a check or money order (payable to the American Mathematical Society). Should you not be accepted, your fee will be refunded. Applications must be submitted by January 24, 1992. Notification of acceptance or refunds will be mailed by February 7, 1992. Applications received after January 24 will be considered until all spaces are filled. Full refunds will be granted if requested by February 21, 1992. After that time no refunds will be made for cancellations.

JANUARY 1992, VOLUME 39, NUMBER 1

31

J ({J)ilffit Mee1tilrilg J 1Ullffi® 2Sl = J uliy Jl ~ JL SJSJ2 Cam1briccllge~

Elffiglialril.) =I 0; Proof of irreducibility results; Proof of vanishing results outside the fair range; Proof of the inequivalence results. 1991 Mathematics Subject Classifications: 22E46; 43A85, 22E45, 22E47 ISBN 0-8218-2524-0, LC 91-36299, ISSN 0065-9266 106 pages (softcover), January 1992 Individual member $16, List price $26, Institutional member $21 To order, please specify MEM0/462N

60

(Asterisque, Number 66-67)

This book, an outgrowth of a seminar held in Orsay in

1976-1977, is the second edition of an exposition of Thurston's work on surfaces, as outlined in his research announcement. The entire theory is constructed using measured foliations rather than laminations. The main topics are: measured foliations on surfaces, compactification of Teichmuller spaces by projective space of measured foliations, classification in the mapping class group, and pseudo-Anosov diffeomorphisms.

Contents V. Poenaru, Presentation de /'ensemble des tMoremes de Thurston sur les surfaces; V. Poenaru, Quelques rappels sur les diffeomorphismes des surfaces; V. Poenaru, Rappels de geometrie hyperbolique en dimension 2 et generalites suri: s x s--> ~ +; V. Poenaru, L'espace des courbes simples fermees sur une surface; A. Fathi, Appendice-Double decomposition d'une surface en pantalons; A. Fathi and F. Laudenbach, Les feuilletages mesures; V. Poenaru, Appendice-Spines des varietes de dimension 2; A. Fathi, Les feuilletages mesures, suite; A. Fathi, Appendice-Formules explicites sur les feuilletages mesures; A. Douady, L'espace de Teichmiiller; A. Fathi and F. Laudenbach, Comment Thurston compactifie /'espace de Teichmiiller; A. Fathi, AppendiceEstimations de distances hyperboliques; V. Poenaru, Classification des diffeomorphismes des surfaces; A. Fathi and M. Shub, Some dynamics of pseudo-Anosov diffeomorphisms; F. Laudenbach, La tMorie de Poenaru, TMoremes Thurston sur les surfaces bord; A. Fathi and d'unicite des diffeomorphismes pseudo-Anosov; F. Laudenbach, Construction de diffeomorphismes pseudo-Anosov; D. Fried, Fibrations overS' with pseudo-Anosov monodromy; F. Laudenbach, Presentation du groupe de diffeotopies d'une surface compacte orientable.

a

v.

1991 Mathematics Subject Classifications: 57R30, 57R32, 57R50, 58F15, 57M99, 57N05, 57N10, 30F20 ISSN 0303-1179 296 (softcover), 1991 Individual AMS or SMF member $29, List price $41 To order, please specify AST/66/67N

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

Miscellaneous

Personals Gerald L. Alexanderson, chair of the mathematics department of Santa Clara University, has been elected senator of the Society of Phi Beta Kappa. Simon A. Levin, of Cornell University, has been appointed professor of ecology and evolutionary biology and has been named the George M. Moffett Professor of Biology at Princeton University. Lawrence E. Levine, of the Stevens Institute of Technology, has been appointed head of the department of pure and applied mathematics at that institution. Vladimir Pestov, of Tomsk State University, Russia, has accepted the position of lecturer at Victoria University of Wellington, New Zealand. Deaths Augusto Bobonis, of Santurce, Puerto Rico, died on September 26, 1990, at the age of 83. He was a member of the Society for 50 years. Lawrence F. Guseman, Jr., of Texas A&M University, died on November 5, 1991, at the age of 53. He was

a member of the Society for 24 years. Nicholas D. Kazarinoff, of Albuquerque, New Mexico, died on November 21, 1991, at the age of 72. He was a member of the Society for 38 years. Ellis R. Kolchin, Professor Emeritus of Columbia University, died on October 30, 1991, at the age of 75. He was a member of the Society for 53 years. Lawrence Kuipers, of Wassenaar, The Netherlands, died on September 30, 1991, at the age of 82. He was a member of the Society for 40 years. Christopher L. Thompson, of the University of Southampton, died on October 12, 1991, at the age of 50. He was a member of the Society for 12 years. MorrisYachter, of New York, New York, died on December 28, 1990, at the age of 78. He was a member of the Society for 33 years. Micha Yadin, of Technion-Israel Institute of Technology, died in April 1991, at the age of 58. He was a member of the Society for 7 years.

JANUARY 1992, VOLUME 39, NUMBER 1

Visiting Mathematicians Supplementary List

Mathematicians visiting other institutions during the 1990-1991 and 19911992 academic years have been listed in recent issues of Notices: December 1991, p. 1348; November 1991, p. 1192; October 1991, p. 1016; September 1991, p. 858; July/August 1991, p. 656; May/June 1991, p. 494; December 1990, p. 1466; November 1990, p. 1295; October 1990, p. 1148; September 1990, p. 959. Evgeni M. Chirka, (USSR), University of Washington, Several Complex Variables, 12/91-6/92. Maria Gonzalez, (Spain), University of Washington, Harmonic Measure Theory, 9/91-6/92. C. Robin Graham, (U.S.), University of Adelaide, Partial Differential Equations, 12/91-3/92. Salvador Perez-Esteva, (Mexico), University of Washington, Mathematical Analysis, 9/91-6/92. Boris Solomyak, (USSR), University of Washington, Classical Analysis, 9/91-6/92.

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New Members of the AMS

ORDINARY MEMBERS Allan R Adler, Kingston, RI David R M Allan, Sarnia, Ontario Canada Michael Gerald Austin, Benicia, CA Christoph Winfried Baxa, Moedling, Austria G Behforooz, Utica College, NY Peter Adam Beling, Richmond, CA Udayan B Darji, North Carolina State Univ, Raleigh William A Donnell, Graham, TX Oktay Metin Gokdemir, Tulsa, OK Ronald Alan Johns, Ohio Northern Univ, Ada Lawrence R Jones, Terre Haute, IN Martin Jurchescu, Bucharest, Romania Wayne Lee, Sugarland, TX William Joseph Long, Oakland, CA Yolanda Melendez, Univ of Extremadura, Badajoz, Spain

Ramon Melendez-Sierra, San Juan, PR Stanley Jay Nagler, Brooklyn, NY Pamela G Oden, Point Lorna College, San Diego, CA Solomon Peysakhov, Chicago, IL Suriani Pokta, Los Angeles, CA Aleksey Popelyukhin, Brooklyn, NY Thomas M Roberts, AL!OEDA, Brooks AFB, TX Leonardo Luca Rossi, Rochester, NY Michael Timothy Schwartz, Tallahassee, FL Pokta Suriani, Univ of California Los Angeles Peter Theron, Madison, WI Amir Uddin, Karachi, Pakistan John D Vedder, Houston, TX Cheng Wu Yang, East China Institute of Technology, Nanjing, People's Republic of China

ME~5)1RS American Mathematical Society

~wrr'it{es! Vol. 456

Combinatorial Patterns for Maps of the Interval

Jae-Nyun Yoo, Pohang Institute of Science and Technology, Korea Sixiang Zhang, Gannon Univ, Erie, PA

Sociedade Brasileira de Matenuitica Sebastiao Carneiro De Almeida Unione Matematica ltaliana Stefano Meda

RECIPROCITY MEMBERS

Osterreichische Mathematische Gesellschaft Hans Christian Reichel

London Mathematical Society James William Bruce Mathematical Society of Japan Kazuoki Ikeda Societe Mathematique Suisse Remo Moresi

NOMINEE MEMBERS City College (CUNY) Bing Huang

Societe Mathbnatique de France Pierre Moussa Sociedad Matemdtica Mexicana Guillermo Moreno Sociedad de Matemdtica de Chile Cesar Burgueno

c

Mississippi State University Wenyue Wang SUNY at Buffalo Ying Zhou University of New Orleans Qinqshun Hou

Vol. 457

Multiplicative Homology Operations and Transfer Norihiko Minami In Multiplicative Homology Operations and Transfer, Minami presents a completely new treatment of the homology operations QSO. 1991 Mathematics Subject Class!fi.cations: 55 ISBN 0-8218-2518-6, 80 pp. (softcover). November 1991 Indiv. mem. $11, List $18, Inst. mem. $14 Your ordering code is MEM0/457NA

Michal Misiurewicz and Zbigniew Nitecki This study investigates new features of the relation between cyclic permutations and its generalization to multicyclic permutations and combinatorial pattems. 1991 Mathematics Subject Classlftcations: 58, 54, 26 ISBN 0-8218-2513-5, 120 pp. (softcover), November 1991 Indiv. mem. $13, List $21. lnst. mern. $17 Your ordering code is MEM0/456NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from:American Mathematical Society, P.O. Box 1571. Annex Station. Providence. RI 02901-1571, or call toll free 800321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Please add 7% GST to all orders totalling over $40 being shipped to Canada.

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Vol. 458

Lyapunov Theorems for Operat.or Algebras Charles A. Akemann and Joel Anderson This book presents the result of a systematic generalization of Lyapunov's theorem to the setting of operator algebras. 1991 Mathematics Subject Class!fi.cations: 46; 28. 49, 52, 60, 93 ISBN 0-8218-2516-X, 96 pp. (softcover), November 1991 Indiv. mem. $11, List $19, Inst. mem. $15 Your ordering code is MEM0/458NA

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

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¢oyment~-------------------------------------------------------------

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

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Please return this form to:

Advertising Department Notices of the American Mathematical Society

P.O. Box 6248 Providence, RI 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 Vll of the Civil Rights Act of 1964, announcing a national policy of equal employment opportunity in private employment, without discrimination because of color, race, religion, sex, or national origin. All U.S.listings are accepted with the understanding that the employer complies with federal requirements. Advertisers not subject to U.S. laws may be required to sign a statement that they do not discriminate in employment on grounds of age, color, race, religion, sex, or national origin. Applicants should be aware that institutions outside the U.S. may not be legally bound to conform to these or similar requirements and the AMS cannot assume responsibility for enforcing compliance. Applicants are advised to inform themselves of conditions that may exist at the institutions to which they apply.

In particular, readers should note that the Equal Employment Opportunity Act (42 U.S.C., §§2000e et seq.), which prohibits discrimination in employment on the basis of race, religion, sex, or national origin, contains (in §2000e-1) 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.

JANUARY 1992, VOLUME 39, NUMBER 1

63

Classifi.ed Advertisements SUGGESTED USES for classified advertising are positions available, books or lecture notes tor sale, books being sought, exchange or rental of houses, and typing services. THE 1992 RATE IS $60.00 per inch on a single column (one-inch minimum), calculated from the top of the type; $30 for each additional 1/;. inch or fraction thereof. No discounts tor multiple ads or the same ad in consecutive issues. For an additional $10 charge, announcements can be placed anonymously. Correspondence will be forwarded. Advertisements in the "Positions Available" classified section will be set with a minimum one-line headline, consisting of the institution name above body copy, unless additional headline copy is specified by the advertiser. Advertisements in other sections of the classified pages will be set according to the advertisement insertion. Headlines will be centered in boldface at no extra charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, including lines and spaces within. Any fractional text will be charged at the next 11;. inch rate. Ads will appear in the language in which they are submitted. Prepayment is required of individuals but not of institutions. There are no member discounts for classified ads. Dictation over the telephone will not be accepted for classified advertising. DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising Department. . U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, religion or national origin. "Positions Available" advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution does not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific wording may be found near the Classified Advertisements in the January and July/August issues of the Notices. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians are accepted under certain conditions for tree publication. Call toll-free 800-321-4AMS (321-4267) in the U.S. and Canada for further information. SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, Rho~e Island 02940. AMS location tor express delivery packages is 201 Charles Street, Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not required to do so. AMS FAX 401-455-4004.

POSITIO

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AUBURN UNIVERSITY Department of Algebra, Combinatoric& and Analysis

Applicants in combinatorics are sought tor a tenure-track appointment at the rank of assistant professor expected to be made in beginning September 1992. Preference given to candidates in discrete optimization, coding theory, cryptology, extremal set theory, or association schemes. Some temporary one-year appointments at the rank of assistant professor are also expected beginning September 1992. Preference given to applicants in differential equations. Those in algebra, analysis, combinatorics, linear algebra or probability considered. Research interest compatible with current faculty. Ph.D. and excellence in both teaching and research required for all positions. Send resume and arrange for at least three letters of recommendation to be sent to James R. Wall, 120 Math Annex, Auburn University, AL 36849-5307. Minorities and Women are encouraged to apply. Auburn University is an Equal Opportunity Affirmative Action Employer.

THE UNIVERSITY OF ALABAMA AT BIRMINGHAM Department of Mathematics

Applications are invited tor tenure track positions at all levels to begin September 1992.

64

Applicants for a junior level position should have strong research potential as well as a commitment to teaching undergraduate and graduate students. Applicants with post-doctoral experience are especially welcome. Applicants tor senior level positions with tenure should have an exceptional record in research including research grants and a record of good teaching. Preference will be given to candidates whose research is compatible with that of our current faculty: this includes dynamical systems, differential geometry, mathematical physics, nonlinear analysis, partial differential equations including numerical p.d.e., and topological dynamics. To apply please send a curriculum vitae, selected reprints, and at least three letters of reference. Senior applicants may request that the Search Committee contact the referencesplease make that clear in the cover letter. Send applications to the following address: Search Committee Department of Mathematics University of Alabama at Birmingham Birmingham, AL 35294-2060 For full consideration applications should be received by February 15, 1992. UAB is an Affirmative Action/Equal Opportunity Employer.

CALIFORNIA CALIFORNIA STATE UNIVERSITY, SAN MARCOS Numerical Analyst

California State University, San Marcos, located thirty miles north of San Diego, is the newest campus in the California State University system. CSUSM seeks a Ph.D. mathematician in

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

numerical analysis for a tenure-track Assistant Professor position to begin in August 1992. CSUSM seeks an individual with strong academic and professional preparation and with interest in the development of the mathematical sciences at a new institution. Experience with machine computation is preferred. An application consists of a statement of interest in teaching, research and service, a complete resume, and at least three reference letters which should comment on the applicant's credentials in teaching, research, and service. Copies of scholarly work may be included. Opening pending authorization. Applicants should be U.S. citizens or individuals lawfully authorized to work in the U.S. Applications should be sent to: Mathematics Search Committee, California State University, San Marcos, 820 West Los Vallecitos Blvd., San Marcos, CA 920961477. Review of candidates will begin February 15, 1992, and continue until the position is tilled. Women and minorities are strongly encouraged to apply. CSUSM is an Affirmative Action/Equal Opportunity Institution.

UNIVERSITY OF CALIFORNIA, BERKELEY Department of Statistics

We invite applications for a faculty position at the non-tenure level, to begin 1 July 1992. We will consider strong candidates in any area of theoretical and applied statistics, probability and applied probability theory. Interdisciplinary interests are encouraged and joint appointments are a possibility. The department is particularly interested in hearing from suitably qualified women or members of minorities currently underrepresented in faculty positions. AA/EOE. Send inquiries and applications including a resume and three references to: David R. Brillinger, Personnel Committee, Department of Statistics, University of California, Berkeley, CA 94720, USA. We should receive this material no later than January 31, 1992.

UNIVERSITY OF CALIFORNIA, BERKELEY Fellowships in Mathematics and Molecular Biology

The Program in Mathematics and Molecular Biology has graduate and postdoctoral fellowship support available. Current topics in the Program include geometry, topology, and sequence analysis of DNA, molecular dynamics, and mapping functions and algorithms for DNA and protein structure prediction. Other areas will be considered. Fellowships can be held at any university or college in the United States. Deadline for Applications: February 1, 1992. Women and minorities are encouraged to apply. Apply to: Dr. S. J. Spengler/Dr. N. R. Cozzarelli, PMMB, 103 Donner Lab, University of California, Berkeley, CA 94720. Email: sylviaj @violet.berkeley.edu.

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UNIVERSITY OF CALIFORNIA, IRVINE Department of Mathematics Irvine, CA 92717

Applications are invited for up to five positions effective July 1, 1992 at the tenure-track level in the areas of algebra, analysis, applied mathematics, foundations, geometry, probability, statistics, or topology. Demonstrated leadership in research is expected of applicants at the tenure (Associate or Full Professor) levels. Applicants at these levels should send a curriculum vitae, list of publications, a few selected reprints or preprints, and the names of three references to Peter Li, Chair of the Recruitment Committee, at the above address. Applicants at the tenure-track level are expected to have demonstrated outstanding research potential, and should send a resume, reprints, preprints and dissertation abstract, and ask three people to send letters of recommendation to Peter Li. We should receive all these materials no later than March 1, 1992. The University of California is an Equal Opportunity/Affirmative Action employer. The Department of Mathematics welcomes applications from women and minority candidates.

UNIVERSITY OF CALIFORNIA, SAN DIEGO

A senior professorship (tenured) in statistics is expected to become available beginning July 1992 subject to administrative approval. Qualifications: Associate or Full Professor Level (Tenured), Ph.D. in Statistics, Mathematics, or related field, demonstrated research, and demonstrated teaching experience at the undergraduate and graduate levels. Interest in applications and computation will be given weight, however, all statistical areas of interest will be considered. To apply, send CV, publications, and the names and addresses of at least five references to "Statistics Appointments Committee," University of California, San Diego, Department of Mathematics, 0112, 9500 Gilman Drive, La Jolla, California 92093-0112. Applications received by January 31, 1992 will be given full consideration. Salary and level of appointment will be based on qualifications and UC pay scale. In compliance with the Immigration Reform and Control Act of 1986, individuals offered employment by the University of California will be required to show documentation to prove identity and authorization to work in the United States before hiring can occur. Immigration status and non-U.S. citizens should be stated on curriculum vitae. UCSD is an equal opportunity/affirmative action employer.

UNIVERSITY OF CALIFORNIA, SAN DIEGO

Expects a tenured position to become available at the associate professor or full professor level, subject to the availability of funds, in the field of mathematics or science education in the department of Biology, Chemistry, Mathematics, or Physics. The appointment begins July 1992. Qualifications include Ph.D. in Biology, Chemistry, Mathematics, or Physics,

demonstrated interest in issues of learning and teaching science or mathematics at the secondary or postsecondary levels, teaching experience at the undergraduate and graduate levels, and a record of scholarly achievement that will qualify for a tenured appointment. The successful candidate will be affiliated with the new Mathematics and Science Education Joint Ph.D. program with San Diego State University. To apply, send CV, publications, a short letter describing background and interests, and at least five letters of reference to "Math/Science Education Search Committee," University of California, San Diego, Mail Code 0112, 9500 Gilman Drive, La Jolla, California 92093-0112. Applications received by February 15, 1992 will be given full consideration. Salary and level of appointment will be based on qualifications and UC pay scale. In compliance with the Immigration Reform and Control Act of 1986, individuals offered employment by the University of California will be required to show documentation to prove identity and authorization to work in the United States before hiring can occur. Immigration status on non-U.S. citizens should be stated on curriculum vitae. UCSD is an equal opportunity/affirmative action employer.

UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Mathematics

Applications are invited for the KY FAN ASSISTANT PROFESSORSHIP. The Ky Fan assistant professorship is a special two-year nonrenewable position which carries a research stipend. Appointment is effective July 1, 1992. Candidates must possess a Ph.D by September 1992. Selection will be based primarily on demonstrated research achievement. Teaching experience is desirable. Teaching load will consist of four quarter courses per year. To apply send vita and publication list, and arrange to have 3 letters of recommendation sent to: Ky Fan Faculty Search Committee, Department of Mathematics, University of California, Santa Barbara, CA 93106. All applications received by January 10, 1992 will be given thorough consideration. UCSB is an Equal Opportunity/Affirmative Action employer. Proof of U.S. citizenship or eligibility for U.S. employment will be required prior to employment (Immigration Reform and Control Act of 1986).

UNIVERSITY OF SOUTHERN CALIFORNIA, LOS ANGELES

The Department of Mathematics has available several tenure-track or tenured positions at the Assistant and/or Associate Professor level. Applicants must show strong research promise and possess excellent communications skills for teaching undergraduate mathematics courses. Visiting positions (at all levels) and postdoctoral appointments will also be available. The Department of Mathematics also seeks to fill at least one tenured position at the senior level. Successful applicants will have an outstanding record of mathematical research and scholarship, and proven administrative skills for

JANUARY 1992, VOLUME 39, NUMBER 1

academic leadership. Applications should be mailed to: Chair of Appointments Committee, Department of Mathematics, DAB 155, University of Southern California, Los Angeles, CA 90089-1113. USC is an Equal Opportunity/Affirmative Action employer. Women and minorities are especially encouraged to apply.

UNIVERSITY OF NORTHERN COLORADO Greeley, Colorado

The Department of Mathematical Sciences at UNC is inviting applications for a one- or twoyear temporary position beginning August 1992. A Ph.D. in Mathematics is required along with a strong commitment to excellent teaching. In addition to a 12-hour teaching load at the undergraduate level, advising or committee work or continuing scholarly activities are expected. Send letter of application, resume, three letters of recommendation (and the names, addresses and phone numbers of the three references) and position number 21341 to: Professor Richard Grassl Chair, Department of Mathematical Sciences University of Northern Colorado Greeley, CO 80639 Applications received by January 15, 1992 will be given full consideration. AAEO

UNIVERSITY OF HARTFORD Mathematics and Computer Science Department West Hartford, CT 06117

Applications are invited for a full-time tenuretrack position beginning September 1992 at the rank of Associate or Assistant Professor of Mathematics depending upon qualifications and experience. A second position may become available pending funding. Candidates must have a Ph.D. in Mathematics and a strong commitment to excellence in undergraduate teaching and scholarship/professional development. Opportunity exists to teach in a nationally recognized inter-disciplinary general education curriculum. Review of applications will begin in January and continue until a decision is reached. Application package must include a resume, three letters of recommendation (at least one of which specifically addresses teaching), and a teaching statement that explains your interest and commitment to the teaching of undergraduate Mathematics. Send package to Dr. Joel Kagan, Chairman, Math/C.S. Dept., University of Hartford, W. Hartford, CT 06117. The University of Hartford is an Equal Opportunity Affirmative Action Employer and specifically invites and encourages applications from women, minorities and members of underrepresented groups.

65

Classified Advertisements

FLORIDA ROLLINS COLLEGE Department of Mathematical Sciences Winter Park, FL 32789

One tenure track position, involving both mathematics and computer science, preferably at the Assistant Professor level, is available for September 1992, pending approval. The Department offers majors in mathematics and computer science, and seeks a versatile, broadly educated mathematician who is willing to teach and participate in both programs. In addition to the usual range of undergraduate mathematics courses for majors and non-majors, the applicant must also be able to teach at least two upper-level ACM computer science courses; for example, database management systems, operating systems, or compiler construction. The area of mathematical specialization is open, but a Doctorate (or ABD with degree nearing completion), strong commitment to innovative teaching and continued professional development in a liberal arts environment is required. The teaching load is 8-10 hours per week. Winter Park, a delightful city of 40,000, is located in the greater Orlando area. To ensure full consideration, applications must be complete by 15 Feb 1992. Send resume, transcripts and three letters of recommendation (at least one of which must comment on teaching) to: David Kurtz, Chair. Rollins College assures equal employment opportunity through a continuing and effective affirmative action program.

GEORGIA EMORY UNIVERSITY ATLANTA, GA 30322 Department of Mathematics and Computer Science

The Department of Mathematics and Computer Science has three openings in mathematics to begin September 1, 1992. The positions are at the level of tenure-track assistant professor. Applicants must have a Ph.D. in mathematics and a strong record (or promise) of research. The areas of geometric analysis, algebra and combinatorics are of particular interest to us. The teaching load is 6 hrs./wk, including graduate and undergraduate courses. Please send vita and names of three references to the above address, and have reference letters forwarded to us. Screening of applications will begin Jan. 20, 1992. Emory University is an equal opportunity/affirmative action employer.

GEORGIA INSTITUTE OF TECHNOLOGY

The Center for Dynamical Systems and Nonlinear Studies expects to have some long and short-term visiting positions beginning Fall1992. These positions are in nonlinear differential equations, dynamical systems, computational methods and related areas. In addition to a resume and at least three letters of reference,

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candidates should send a summary of future research plans to Professor Jack K. Hale, Director, CDSNS, Georgia Institute of Technology, Atlanta, GA 30332-0190. Georgia Tech, a member of the University System of Georgia, is an Equal Opportunity/Affirmative Action Employer.

GEORGIA SOUTHERN UNIVERSITY Department of Mathematics and Computer Science

Applications are invited for two tenure-track positions starting September 1, 1992. 1. Assistant or Associate Professor, Ph.D. in Statistics required by September 1, 1992. Training or experience in applications of statistical methodology required. Three years experience in industrial applications preferred, experience with major statistical computer packages required. Duties include teaching graduate and undergraduate statistics for a variety of majors and supervision of research projects for M.S. degree candidates concentrating in statistics. Search #25365. 2. Assistant or Associate Professor, Ph.D. in Operations Research or closely related field required by September 1, 1992. Training or experience in applications of operations research in business and industry required, three years experience preferred. Duties include teaching graduate and undergraduate courses in operations research and mathematics, and supervision of research projects for M.S. degree candidates concentrating in operations research. Search #25364. In addition to the above positions, several temporary positions may be added at the instructor level in the area of teaching freshmanlevel mathematics. Experience preferred. Duties include teaching fifteen credit hours per quarter. M.A. or M.S. in mathematics required. Search #25379. Applicants are asked to send a letter of application indicating the search number of the position desired, curriculum vitae, unofficial transcripts of all college work, evidence of dedication to outstanding teaching, and three letters of recommendation by February 1, 1992 to Dr. Lila F. Roberts, Landrum Box 8093, Georgia Southern University, Statesboro, GA 30460.8093. The names of applicants and nominees, resumes, and other general non-evaluative information are subject to public inspection under the Georgia Open Records Act. Georgia Southern University is an Affirmative Action/Equal Opportunity Institution.

GEORGIA SOUTHWESTERN COLLEGE Department of Mathematics

Subject to budgetary approval, the Department of Mathematics expects to fill a tenure-track position at the assistant-professor level, starting September 1, 1992. The Department has bachelor degree programs in mathematics, mathematics education, and a masters degree program in mathematics education. The Ph.D. is required for promotion and tenure, but applicants with a clear prospect for comple-

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

tion of the degree in the near future will be considered. Strong commitment to teaching is essential. Candidates should send a letter of application, a resume, and arrange to have three letters of reference sent to: Dr. John Stroyls, Department of Mathematics, Georgia Southwestern College, Americus, GA 317094693, phone (912)928-1645 or (912)928-1251. The position will remain open until filled, but to ensure consideration, please apply by March 15, 1992. GSW is an Affirmative Action, Equal Opportunity Employer.

ILLINOIS ELMHURST COLLEGE

Tenure-track position beginning fall1992 (pending approval of the Board of Trustees). Qualifications desired: Ph.D. in mathematics, interest in continued scholarship, and a strong commitment to undergraduate teaching in a liberal arts college. Teaching load: 6 courses per year. Elmhurst College is a four-year private institution located in the western suburbs of Chicago. Applications should include a curriculum vitae and three letters of reference. Please send to Dr. Jon L. Johnson, Dept. of Mathematics, Elmhurst College, Elmhurst, IL 60126. Elmhurst College is an Equal Opportunity Employer.

LAKE FOREST COLLEGE

Mathematics. Lake Forest College invites applications for a continuing appointment in Mathematics at the Assistant Professor level, starting August 1992. We seek candidates with a Ph.D., a commitment to excellent teaching in a quality liberal arts environment, and an active interest in mathematical research. The teaching load is three courses per semester. Send a c.v. and arrange to have 3 letters of reference and a graduate transcript sent, by February 1, 1992, to Edward W. Packel, Chairperson, Mathematics & Computer Science Department, Lake Forest College, 555 N. Sheridan Rd., Lake Forest, IL 60045. Applications from women and minorities are actively encouraged. AA/EOE.

LOYOLA UNIVERSITY OF CHICAGO

The Department of Mathematical Sciences anticipates at least one tenure track position and some visiting positions beginning in August 1992. Requirements are the Ph.D., an active research program in any area, and a commitment to quality teaching. The department offers courses in mathematics, computer science, and statistics at the undergraduate and masters level. Interviews will begin in January and continue until all positions are filled. Send detailed C.V. and three letters of recommendation to Professor S.R. Doty, Department of Mathematical Sciences, Loyola University, Chicago, IL 60626. Loyola University of Chicago is an Equal Opportunity/Affirmative Action Employer.

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NORTHWESTERN UNIVERSITY Mathematics Department 2033 Sheridan Road, Evanston, Illinois 60208-2730

The Mathematics Department will sponsor an Emphasis Year in partial differential equations. This program will include 2-year Assistant Professorship positions starting September 1992, and possible visiting positions for more senior mathematicians for part or all of the academic year. Applications should be sent to Professor Neil S. Trudinger at the department address and include a curriculum vitae and three letters of recommendation. In order to ensure full consideration, an application must be received by February 15, 1992. Northwestern University is an affirmative action, equal opportunity employer committed to fostering a diverse faculty, so women and minority candidates are especially encouraged to apply. Hiring is contingent upon eligibility to work in the United States.

UNIVERSITY OF ILLINOIS AT CHICAGO Research/Teaching Fellow Office for Mathematics and Science Education and Department of Mathematics, Statistics, and Computer Science

Full-time fellow in mathematics and mathematics education. Responsibilities include teaching one mathematics or mathematics education course per semester and working on the Teaching Integrated Mathematics and Science (TIMS) Project, a major NSF-funded curriculum development project. One year renewable appointment. Qualifications: Master's degree in mathematics or mathematics education. Doctoral degree preferred. Strong mathematics background and pre-college teaching experience preferred. Review of applications will begin February 1, 1992 and will continue until the position is filled. Please send a curriculum vitae and three letters of reference to Dr. Philip Wagreich, co-Director, Office for Mathematics and Science Education (m/c 250), UIC Box 4348, Chicago, IL 60680. AAIEOE.

ill'/- - M : S i t :~-·~~-~·~------·---~·---··-····-"~·-·········· Classified Advertisements

is expected. Teaching at both the bachelor's and master's degree levels. Send curriculum vitae, photocopies of graduate transcripts and at least three letters of reference to: Mackinley Scott, Chairperson Department of Mathematics Western Illinois University Macomb, IL 61455 The selection process will begin February 17, 1992. WIU is an equal opportunity/affirmative action employer. Applications are especially invited from minorities, women and handicapped persons.

INDIANA UNIVERSITYPURDUE UNIVERSITY AT INDIANAPOLIS (IUPUI) Department of Mathematical Sciences

The Department of Mathematical Sciences at IUPUI is seeking applicants for three tenuretrack positions to begin in August 1992. Rank is open depending on qualifications. Applicants must have an earned doctorate by the starting date, either a strong research record or excellent research potential, and a commitment to quality graduate and undergraduate teaching. Some preference may be given to applicants in discrete mathematics, scientific computing and applied statistics. However, strong applicants from all areas of mathematical sciences are encouraged to apply. IUPUI is a comprehensive urban university with over 28,000 students. The department offers programs of study leading to Purdue University B.S., M.S., and Ph.D. degrees and we anticipate significant growth in our faculty during the next few years. The university offers competitive salaries and provides excellent fringe benefits. Send resume and three letters of recommendation to Prof. Bart S. Ng, Chair, Department of Mathematical Sciences, IUPUI, 1125 E. 38th Street, Indianapolis, IN 462052810. Closing date: January 15, 1992. Late applications will be considered until positions are filled. IUPUI is an Affirmative Action/Equal Opportunity Employer. Women and minority candidates are encouraged to apply.

MANCHESTER COLLEGE

WESTERN ILLINOIS UNIVERSITY Department of Mathematics

Applications are invited for a tenure-track position at the assistant professor level restricted to the areas of Applied and Computational Mathematics beginning Fall1992, subject to funding. A Ph.D., or equivalent, is required. Commitment to superior teaching and potential for research

Faculty Position: Math. Tenure-track appointment beginning Fall1992. Ph.D. with emphasis in applied mathematics. Expertise in computer science desirable. Teach undergraduate mathematics and possibly some computer science courses. Send letter of application, curriculum vitae, and three letters of recommendation to Dr. Stan Beery, Chair, Department of Mathematical Sciences, Manchester College, North Manchester, Indiana 46962. Review of applications will begin February 15, 1992. Manchester College is an AA/EOE.

JANUARY 1992, VOLUME 39, NUMBER 1

PURDUE UNIVERSITY CALUMET

The Department of Mathematics, Computer Science & Statistics will have one (1) tenuretrack mathematics position available for August 1992 at the rank of Assistant Professor. Requirements: a Ph.D. in Mathematics. Responsibilities will include undergraduate and graduate teaching, research, and curriculum development and oversight. Candidates with expertise in numerical analysis, combinatorics, or history of mathematics will be given preference. Submit a letter of application, a curriculum vitae, graduate and undergraduate school transcripts. Also, arrange for three (3) letters of recommendation, at least one (1) of which addresses your research potential and at least one (1) of which addresses your teaching ability. All material should be sent to: Professor Daniel J. Troy Department of Mathematics, Computer Science & Statistics Purdue University Calumet Hammond, IN 46323 Review of documents will begin on February 15, 1992 and will continue until position is filled. Minorities and Women are encouraged to apply. A representative of the Department will be interviewing at the Employment Register associated with the Annual Meeting of the American Mathematical Society, Baltimore, Maryland, January 1992. Purdue University Calumet is an Equal Opportunity/Affirmative Action Employer.

PURDUE UNIVERSITY CALUMET

The Department of Mathematics, Computer Science, and Statistics announces a tenure-track position in mathematics education available for August 1992. Duties and responsibilities include teaching a range of mathematics courses, including content and methods courses for prospective K-12 teachers, supervising field experience, and working collaboratively with public schools. Active involvement in research is expected. A doctorate in Mathematics, or in Mathematics Education with at least a masters degree in Mathematics, is required. Candidates should have a strong commitment to teacher education and to quality teaching at both the undergraduate and graduate levels. Submit a letter of application, a curriculum vitae, graduate and undergraduate transcripts. Also, arrange for three (3) letters of recommendation, at least one of which addresses your research potential and at least one of which addresses your teaching ability. Review of applications will begin February 1, 1992 and will continue until the position is filled. All materials should be sent to: Professor J. Paul McLaughlin, Department of Mathematics, Computer Science, & Statistics, Purdue University Calumet, Hammond, IN 46323. Minorities and women are encouraged to apply. Purdue University is an Equal Opportunity/Affirmative Action Employer.

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ROSE-HULMAN INSTITUTE OF TECHNOLOGY Department of Mathematics

We anticipate two or more tenure-track openings at the assistant professor or possibly higher rank in the fall of 1992. Applicants should have a Ph.D. in mathematics or statistics, and a strong commitment to teaching at the undergraduate level in addition to scholarly interests. Candidates with a background in statistics, operations research and/or applied mathematics are especially encouraged to apply. Letters of application, resume, copy of transcript, and three letters of recommendation (with at least one of them addressing the applicanfs teaching ability) should be sent to George Berzsenyi, Chairman, Department of Mathematics, RoseHulman Institute of Technology, Terre Haute, IN 47803. Rose-Hulman Institute of Technology is an equal opportunity employer.

IOWA IOWA STATE UNIVERSITY Department of Mathematics

Subject to the availability of funds, the Department of Mathematics of Iowa State University expects to fill one tenure track position at the assistant professor level in applied partial differential equations for the 1991-92 academic year. Start up funds will be av!iilable for the successful applicant. The successful candidate is expected to have a strong interest in teaching at both the graduate and undergraduate level and maintain an active research program. Iowa State is the closest member institution to the NSF Institute for Mathematics and its Applications in Minneapolis. The Department strongly encourages its faculty and graduate students to participate in the Institute's programs and provides direct and indirect support for them to do so. We will begin screening applications January 15, 1992. However we shall continue to accept applications until the positions are filled. A number of visiting positions in diverse areas of mathematics and applied mathematics are expected to be available and applications for them are also encouraged. Preference will be given to those applicants whose interests are similar to those of the current faculty. Iowa State University is an Affirmative Action/Equal Opportunity Employer. Women and minorities are encouraged to apply. Applications and three letters of recommendation should be sent to Howard A. Levine, Chair, Department of Mathematics, Iowa State University, Ames, Iowa 50011.

UNIVERSITY OF NORTHERN IOWA Assistant Professor of Mathematics

We have a tenure-track position for an assistant professor to aid in teaching our general education courses and to support our majors and graduate students. Applicants should have a doctorate in mathematics and be commit-

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ted to quality education and scholarship at a comprehensive university. Appointment is for the academic year beginning in August 1992. Salary is highly competitive; fringe benefits are excellent. Application screening begins February 14, 1992. For more information contact Joel Haack, Mathematics and Computer Science, University of Northern Iowa, Cedar Falls, lA 50614 (319)273-2631; [email protected]. An affirmative action/equal opportunity educator and employer.

KENTUCKY BELLARMINE COLLEGE Department of Mathematics

Tenure-track position in Analysis beginning Fall 1992. Ph.D. required. Should possess a dedication to quality teaching at a liberal arts college. Consideration will begin Feb. 1, 1992. Send letter of application, transcript and letter of recommendation along with vita to: Dr. Muzaffar Ali, Department of Math and Computer Science, Bellarmine College, 2001 Newburg Road, Louisville, KY 40205-Q671. AA/EOE

KANSAS EMPORIA STATE UNIVERSITY Division of Mathematics and Computer Sciences

Applications are invited for two tenure track Assistant Professor positions beginning August 18, 1992. For one of the positions a degree in computer science or a significant background in computer science is desirable. The other one is open to candidates from any area of mathematics. A Ph.D. is expected for either position. While ESU has an emphasis on teaching, the successful candidate should also have an interest in continuing scholarly activity. The Division of Mathematics and Computer Science offers undergraduate and graduate degrees in mathematics. Salary is commensurate with qualifications. Screening will begin on January 31 and continue until the positions are filled. Send letter of application, resume, transcripts, and three letters of recommendation to: Joe Yanik, Search Committee Chair, Emporia State University, Emporia, KS 66801-5087. ESU is an Affirmative Action/Equal Opportunity Employer. We encourage applications from members of protected classes.

LOUISIANA LOUISIANA STATE UNIVERSITY Department of Mathematics Baton Rouge, LA 70803; 504-388-1534

Applications are invited at the Assistant/Associate Professor level for two anticipated tenuretrack or visiting positions. Duties include teaching at the graduate and undergraduate level and maintenance of a strong research program. Selection is based on demonstration and promise of excellence in research and teaching; a Ph.D. or equivalent degree by August 1992 is also required. The department is primarily seeking to build on its strengths in probability, analysis and pde's, algebra, combinatorics, and topology. To apply, send a full resume and arrange for at least three letters of evaluation to be sent to Professor Jimmie Lawson, Chair (address above). LSU IS AN EQUAL OPPORTUNITY UNIVERSITY.

UNIVERSITY OF NEW ORLEANS Dean, College of Sciences KANSAS STATE UNIVERSITY Department of Mathematics

Subject to budetary approval, applications are invited for several tenure-track and visiting positions commencing August 18, 1992; rank and salary commensurate with qualifications. All fields will be considered, but for some of the tenure-track positions, preference will be given to candidates in Numerical Analysis, Differential Equations, and Global Analysis. Applicants must have strong research credentials and a commitment to excellence in teaching. A Ph.D. in mathematics or a Ph.D. dissertation accepted with only formalities to be completed is required. Letter of application, current vita, description of research and three letters of recommendation should be sent to: Louis Pigno Department of Mathematics Cardwell Hall 137 Kansas State University Manhattan, KS 66506 Deadline: February 1, 1992

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

The University of New Orleans, Louisiana's major urban public institution, is a comprehensive, selective-admissions university in the Louisiana State University System. Founded in 1958, it has 16,210 students, and 717 full and part-time faculty members. The College of Sciences consists of 7 departments: Biology, Chemistry, Computer Science, Geology & Geophysics, Mathematics, Physics and Psychology. All departments offer bachelor's and master's degrees, and Chemistry and Psychology offer the Ph.D. The screening committee is actively seeking applications and nominations. For more information, address correspondence to: Dr. George loup, Chair, Screening Committee for College of Sciences Dean, Office of Academic Affairs, Univ. of New Orleans, New Orleans, LA 70148. Applicants should include a cover letter, curriculum vitae, and the names, addresses, and phone numbers of three references. Review of applications will begin February 3, 1992. EEO/AA employer.

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UNIVERSITY OF SOUTHWESTERN LOUISIANA Department of Mathematics Lafayette, LA 70504-1010 The Department of Mathematics is actively seeking applications for research/teaching positions in applied partial differential equations. A Ph.D. degree in mathematics is required. We anticipate one tenure-track appointment at the Assistant Professor level, and one visiting position at the Assistant Professor level or above. Preference will be given to computational mathematics, including familiarity with local computer networking, computer languages and software. A formal letter of application along with a resume and at least three letters of recommendation should be sent to Bradd Clark, Chairman. EEO/AA.

plications will begin February 15 and continue until the position is filled. Amherst College is an Affirmative Action/Equal Opportunity Employer and encourages applications from minorities and women. Reply to: Professor Norton Starr Department of Mathematics and Computer Science Amherst College Box 2239 Amherst, MA 01002-5000 or send email to NSTARR@ Amherst.edu

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GUSTAVUS ADOLPHUS COLLEGE Tenure-track position beginning Sept. 19S2. Ph.D. in math stat., stat expected. Ability to build stat. track in math/cs program, commitment to excellence in teaching, continuing research interests in stats, operations research or modeling, some c.s. preferred. Women and minority candidates urged to apply. Send c.v., transcripts, 3 letters of reference by 31 January 1992 to: Dr. T. J. Morrison, Chair Math/C.S., Gustavus Adolphus College, St. Peter, MN 56082. Telephone: (507)933-7483 or 933-7009. Email: [email protected] or [email protected].

MICHIGAN TECHNOLOGICAL UNIVERSITY Mathematical Sciences Department The Department of Mathematical Sciences is seeking a director for the Fluids Research Oriented Group (F.R.O.G.). F.R.O.G. is an interdisciplinary group, involving Departments of Mathematical Sciences, Mechanical Engineering, Chemical Engineering, Geology, and Metallurgical & Materials Engineering, engaged in an active program of research in Fluid. Mechanics. This position will carry an appointment as Associate Professor or Professor. Candidates should have an active research record in Fluid Mechanics and Applied Mathematics. A good funding record and experience with Ph.D. students is required. The position starts in September 1992. Send a curriculum vitae and three letters of recommendation to Recruitment Committee, Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, Ml 49931-1295. Applications will be accepted until February 3, 1992. MTU is an equal opportunity educational institution/equal opportunity employer.

JANUARY 1992, VOLUME 39, NUMBER 1

HAMLINE UNIVERSITY Professor/Director of Science Development Hamline University seeks applications and nominations for a new senior-level interdisciplinary faculty position in the sciences. Departmental affiliation will be in Biology, Chemistry, Mathematics or Physics. We seek a person who has a broad scientific background, a distinguished research record and is committed to teaching, development of grant proposals, and fostering student-faculty research in a liberal arts college. Nominations or applications (including letter of interest with teaching philosophy and research interests, salary and support expectations, curriculum vitae and three letters of reference) should be sent to Jerry Greiner, CLA Dean's Office, Ham line University, 1536 Hewitt Avenue, St. Paul, MN 55104. Screening of applications will begin January 31, 1992 and continue until a successful candidate has been chosen.

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MISSISSIPPI MISSISSIPPI STATE UNIVERSITY Department of Mathematics and Statistics

Applications are invited for two or more anticipated tenure-track or visiting positions for 1992-93. Candidates should possess a doctoral degree, demonstrate a strong potential for research, and have a commitment to effective teaching. All areas are welcomed but preference will be given to the following: for the mathematics position(s), applied mathematics, computational mathematics, and partial differential equations; for the statistics position(s) multivariate analysis, nonparametric and robust inference, categorical analysis, and linear and nonlinear models. The Department offers graduate programs leading to the Master of Arts degree (M.A.) and the Master of Science degree (M.S.) in both mathematics and statistics and the Doctor of Philosophy degree (Ph.D.) in mathematical sciences. Facilities exist for applicants with interest in interdisciplinary research efforts and in particular for applicants with an interest in the computational aspects of the mathematical sciences. Applicants should send a curriculum vitae and arrange for three letters of recommendation to be sent to: C. Wayne Mastin, Chairman, Search Committee, Department of Mathematics and Statistics, P.O. Drawer MA, Mississippi State, MS 39762. The committee will begin to review applications on March 1, 1992, and continue until positions are filled. AA/EOE.

UNIVERSITY OF SOUTHERN MISSISSIPPI Department of Mathematics

Applications are invited for a tenure-track position at the assistant professor level. Candidates must have the Ph.D. in mathematics, the ability to establish a serious research program, and a sincere dedication to teaching. The successful candidate will be based at Gulf Park, the branch campus which fronts the scenic Gulf of Mexico in Long Beach, Mississippi. This campus is 75 miles south of the Hattiesburg main campus. As the sole full-time mathematician based at Gulf Park, the successful applicant will select and schedule mathematics courses on the Coast, and will be actively involved in advising students pursuing the baccalaureate degree and M. Ed. in mathematics. Ideally the candidate should possess a people-oriented personality, for an important part of the position is to sustain and nourish the mathematics program on the Coast. At present there are 25 majors working on degrees there. The teaching load is 9 credit hours per semester, including both undergraduate and graduate courses, with the possibility of a course release for research. Those candidates whose research interests complement those of the current faculty are especially urged to apply. These interests include algebra, combinatorics, differential equations, graph theory, mathematics education, matrix

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theory, linear algebra, mathematical physics, numerical analysis, and probability. In addition, the Department participates with Computer Science and Physics in a multidisciplinary Ph.D. program in Scientific Computing. It is expected that the successful applicant will interact with the Hattiesburg mathematics faculty through colloquia and faculty interchanges. The successful candidate may seek both promotion and tenure through the Mathematics Department in Hattiesburg or the Division of Arts and Sciences at USM Gulf Coast. The salary is negotiable and competitive, dependent upon qualifications. The starting date will be fall, 1992-93. While the application deadline is open, selection may begin as early as February 1st. Send resume and three letters of recommendation to: Chair, Search Committee, Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406-5045. The University of Southern Mississippi is an affirmative action, equal opportunity employer. Applications from women and minority group members are encouraged.

MISSOURI MARYVILLE UNIVERSITY-ST. LOUIS Mathematics Position Announcement

Maryville University invites applications for a tenure-track assistant professor position in mathematics beginning August 1992. Ph.D. in mathematics required. Background and interest must be compatible with the curricular needs of the mathematics undergraduate programs. In particular, qualified candidates should possess the ability to teach a wide range of courses, both core and upper division for our mathematics and/or actuarial science majors. Excellence in and strong commitment to teaching is expected. Maryville University-St. Louis, located in the Maryville Centre, along Highway 40 and Woodsmill Road in West St. Louis County, is an independent, comprehensive, coeducational university with an enrollment of 3,528 students. Maryville offers liberal arts and professional programs in more than 40 fields of study. Candidates should send a cover letter, detailed resume or vitae, as well as names, addresses and telephone numbers of three references to: Ms. Diana B. Dierberg Director of Human Resources MARYVILLE UNIVERSITY 13550 Conway Road St. Louis, Missouri 63141 AA/EOE Screening to begin February 15, 1992 and to continue until the position is filled.

SAINT LOUIS UNIVERSITY Department of Mathematics and Computer Science Saint Louis, MO 631 03

One or more tenure-track appointments, to begin in the Fall of 1992. Candidates should

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

have a Ph.D. in mathematics and be committed to teaching and research. Preference given to researchers in analysis, especially harmonic analysis, Lie group representations, and functional analysis. If more than one appointment is made, researchers in the area of group theory will also be given preference. The Department currently has 13 members, all of whom are active in research. Representatives of the Department will be present at the joint mathematics meetings in Baltimore. Deadline for full consideration is 2/1/92. Send vita (with email address if available) and three letters of reference to Bradley Currey, Chair, Faculty Search Committee, (email: curreybn@ sluvca.slu.edu). Saint Louis University is an equal opportunity employer; minorities and women are encouraged to apply.

SOUTHWEST MISSOURI STATE UNIVERSITY

Department of Mathematics. Applications are invited for an anticipated tenure-track position in Mathematics beginning Fall 1992 at the Assistant or beginning Associate Professor level. Applicants must have a Ph.D. by Fall 1992. Evidence of excellence in teaching, and a commitment to continued research are required. Preference given to applicants with research interests compatible with those of the current faculty. Of particular interest are analysis and probability/statistics. (If additional positions should become available, all compatible areas would be considered.) Duties include teaching, research, and service. Deadline for application is February 15, 1992. Credentials will be reviewed as they are received. Send vita and graduate transcripts, and have three letters of reference sent to: Dr. John Kubicek, Acting Head, Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804-0094. Women and minorities are encouraged to apply. AA/EOE.

MONTANA MONTANA STATE UNIVERSITY Department of Mathematical Sciences

Tenure-track position, assistant professor level, to begin August 1992. The position should complement the department's active Ph.D. programs in applied numerical analysis and dynamical systems, with particular emphasis on applied mathematics, control theory, and geometric analysis. Requirements include Ph.D. in Mathematics or related area, evidence of strong research potential and teaching skills. Send resume, name, address and phone number of three references to: K. J. Tiahrt, Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-0240. Further information about this position can be obtained by writing to Dr. Tiahrt or sending email to: SWANSON@ DEIMOS.OSCS.MONTANA.EDU. Screening will begin February 1, 1992 and continue until a

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suitable candidate is hired. AA/EO employer. Veterans preference.

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UNIVERSITY OF NEVADA, RENO Department of Mathematics Chair Wanted

Do you have what it takes to lead a Math Department boldly into the future? Would you welcome the opportunity to make an impact on an entire state? If you answered "yes" to these questions, then UNA invites your application! The Department of Mathematics is seeking a dynamic, well-rounded individual to be its Chair. Currently the department has 15 faculty. Among these are three recipients of distinguished teaching awards and one outstanding researcher award. More faculty members will be added in the near future, and the chair will play a key role in making those hires. We offer B.A., M.S., and M.A.T.M. degrees in mathematics. We are committed to excellence in teaching at all levels, especially in the university wide core curriculum math courses. We are also working to increase the quantity and quality of our research output. We intend that this position be filled by someone with the qualifications of a full professor, so an applicant must have a substantial and continuing record of scholarly achievement, research, and demonstrated interest in teaching. Salary will be competitive and commensurate with qualifications of the applicant. Applications should include biographical information and names, addresses (including email, if appropriate), and telephone numbers of five references. Please send to Don Pfaff, Department of Mathematics, University of Nevada, Reno, Reno, NV 89557, [(702) 784-6775; email address: [email protected]; FAX: 702-784-1478]. Review of applications will begin November 15, 1991; the search will continue until the position is filled. The University of Nevada, Reno is an Equal Opportunity, Affirmative Action employer and does not discriminate on the basis of race, creed, color, sex, age, national origin, veteran status or handicap in any program or activity it operates. The University of Nevada employs only United States citizens or aliens lawfully authorized to work in the United States.

DARTMOUTH COLLEGE John Wesley Young Research Instructorship in Mathematics. The John Wesley Young Research Instructorship is a two year postdoctoral appointment for promising new or recent Ph.D.s whose research interests overlap a department member's. Current departmental interests include areas in algebra, analysis, algebraic geometry, combinatorics, computer science, differential geometry, logic and set theory, number theory, probability and topology. Teaching duties of four ten-week courses spread over two or three quarters typically include at least one

course in the instructor's specialty and include elementary, advanced and (at instructor's option) graduate courses. Nine-month salary of $34,000 supplemented by summer (resident) research stipend of $7,556 (two-ninths). Send letter of application, resume, graduate transcript, thesis abstract, description of other research activities and interests if appropriate, and 3 or preferably 4 letters of recommendation (at least one should discuss teaching) to Phyllis A. Bellmore, Mathematics and Computer Science, 6188 Bradley Hall, Hanover, NH, 03755-3551. Applications received by Jan. 15 receive first consideration; applications will be accepted until position is filled. Dartmouth College is committed to affirmative action and strongly encourages applications from minorities and women.

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STEVENS INSTITUTE OF TECHNOLOGY

Applications are invited for a tenure-track position in applied mathematics at the Assistant or Associate Professor level beginning Fall 1992. Specialization in numerical analysis or probability or statistics is sought. Candidates must have demonstrated excellence in research or the potential for such. Evidence of teaching effectiveness is required (foreign applicants must provide evidence of ability to teach in English effectively). Applicants must have a Ph.D. in Mathematics earned or anticipated by 9/1/92. Send letter of application, resume, and 3 letters of recommendation to: Lawrence E. Levine, Head, Department of Pure & Applied Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030. Stevens is an EO/AA employer.

DARTMOUTH COLLEGE

The Department of Mathematics and Computer Science has an opening for a tenure-track Assistant Professor in Mathematics, with initial appointment in the 1992-1993 academic year. A candidate for the position must be committed to outstanding teaching at all levels of the undergraduate and graduate curriculum and must give evidence of a well-regarded research program that shows real promise for the future. Candidates with several years of experience should in addition be ready to direct Ph.D. theses. To create an atmosphere supportive of research, Dartmouth offers new faculty members grants for research-related expenses, a quarter of sabbatical leave for each three academic years in residence and flexible scheduling of teaching responsibilities. The teaching responsibility in mathematics is four courses spread over two or three quarters. The department encourages good teaching with a combination of committed colleagues and bright, responsive, students. Applications are welcome in all fields of mathematics and statistics; the department expects to be able to give applicants more information about departmental priorities after completion of an application, curriculum vitae, and a brief statement of research results and interests. Also arrange for four letters of reference to be sent, at least one of which addresses teaching, and, if the applicant's native language is not English, the applicant's ability to use English in a classroom. All application materials should be addressed to Phyllis Bellmore, Recruiting Secretary, Mathematics and Computer Science, 6188 Bradley Hall, Dartmouth College, Hanover, NH 03755-3551. Applications completed by February 1 will receive first consideration. Dartmouth is committed to Affirmative Action and encourages applications from African Americans, Asian Americans, Hispanics, Native Americans and women. Specific questions on the selection process can be directed to C. Dwight Lahr, Recruiting Chair.

JANUARY 1992, VOLUME 39, NUMBER 1

NEW MEXICO STATE UNIVERSITY Las Cruces, New Mexico Department of Mathematical Sciences

Possible visiting and tenure-track positions in pure and applied mathematics and statistics for 1992-93, primarily assistant professor level. Strong commitment to both research and teaching required. Applications from women and members of minority groups welcome. Applications kept on file through hiring period. Arrange for vita, short research description, and three reference letters to be sent to: Hiring Committee, Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003. Equal Opportunity/Affirmative Action Employer.

COLLEGE OF STATEN ISLAND (CUNY) Department of Mathematics

A tenure-track position in mathematics is available for Fall1992. Requirements: Ph.D., strong commitment to undergraduate teaching and to a productive research program. All mathematics research areas will be considered with special preference given to areas of strength within the department. These areas include probability, group theory and applied mathematics. The position is budgeted at the assistant professor level. The College of Staten Island is a senior college in CUNY. Send resume and three letters of reference to Dr. Jane Coffee, Chairperson, Mathematics Department, College of Staten Island, 130 Stuyvesant Place, Staten Island, N. Y. 10301, by January 15, 1992. AA/EOE Employer.

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DAEMEN COLLEGE Amherst, New York 14226

The Department of Mathematics invites applications for a tenure-track position in mathematics at the assistant professor level beginning September 1992. Candidate must have a Ph.D. in mathematics and must demonstrate a strong commitment to teaching. Send a curriculum vitae, three letters of recommendation and graduate transcripts by March 1, 1992 to: Chairperson, Math. Department Daemen College 4380 Main Street Amherst, New York 14226 Daemen College is an Equal Opportunity, Affirmative Action Employer.

ITHACA COLLEGE

The Department of Mathematics and Computer Science at Ithaca College invites applications for one tenure eligible position in mathematics beginning August 1992. Qualifications: Ph.D. in mathematics, applied mathematics or statistics in hand at time of application preferred; applicants with Ph.D.expected by August 1992 will also be considered. The successful candidate will be expected to demonstrate a strong commitment to undergraduate mathematics education. Screening begins December 16, 1991 . Send vitae to Dr. Diana D. Schwartz, Department of Mathematics and Computer Science, Ithaca College, Ithaca, New York 14850. An Affirmative Action/Equal Opportunity Employer.

three letters of reference sent, by April 1, 1992, to: Dr. Kenneth D. Magill Chair, Statistics Search Committee 174 CFS Addition State University of New York at Buffalo Buffalo, New York 14214 Email: mthmagil@ ubvms.bitnet

SUNY AT CORTLAND

Two Assistant Professors (Mathematics). These are tenure-track positions. These positions entail teaching a variety of mathematics courses each semester, from the elementary to the upper-division level, as well as taking part in departmental governance and student advisement. A doctorate in mathematics and evidence of strength in, and commitment to, undergraduate education is required. An interest in the preparation of secondary mathematics teachers will be valued, as well as research potential in mathematics or mathematics education. All areas of specialization in mathematics or mathematics education are encouraged to apply. Applications for the positions will be accepted untill January 31, 1992. AAIEEO Employer. Applicants should submit a letter of application, vita, three letters of recommendation and all transcripts to: Dr. Jalal Alemzadeh Chair, Search Committee of Mathematics Department State University of New York College at Cortland P.O. Box 2000 Cortland, NY 13045

SUNY PLATTSBURGH Math Faculty STATE UNIVERSITY OF NEW YORK AT BUFFALO Chairperson, Department of Statistics

The Department of Statistics invites applications for the position of Chairperson. Candidates should have a Ph.D. degree in Statistics, Biostatistics or a closely related field. They should have a strong commitment to both research and teaching and, preferably, some experience in administration. The Department of Statistics offers the B.A., M.A., and Ph.D. degrees in Statistics. The research areas of the faculty and the courses offered represent a wide variety of theoretical and applied areas in statistics and probability. The Department has recently affiliated with the School of Medicine and Biomedical Sciences. While it is not required that the research interests and professional background of candidates be exclusively, or even primarily, in biostatistics, candidates should have some experience in this area, as the Chairperson will be expected to provide leadership in the growth and development of such activities. SUNY/Buffalo is an Equal Opportunity/Affirmative Action Employer. Candidates should send a letter of interest, curriculum vitae, and arrange to have at least

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Send letter of application, current curriculum vitae, three letters of current recommendation, and other supporting evidence to: Chair, Search Committee c/o Office of Personnel SUNY Plattsburgh Box 1733-401 Plattsburgh, New York 12901 SUNY IS AN EQUAL OPPORTUNITY/AFFIRMATIVE ACTION EMPLOYER.

SUNY Plattsburgh invites applications for a tenure-track position in the Department of Mathematics beginning Fall 1992. Appointment at the level of Assistant Professor. Qualifications: Ph.D. in Mathematics, Mathematics Education or Statistics; evidence of teaching excellence and/or potential is of primary concern, and potential for continued scholarly growth is viewed as consistent with this concern. SUNY Plattsburgh is a four-year college with approximately 5,500 students including over 100 mathematics majors. A significant number of these students are secondary education majors; approximately half of all math majors are female. The college and department have as top priority the quality of undergraduate education, from service courses and general education as well as the upper level major courses. Plattsburgh is located in the northeast corner of New York State, in close proximity to Lake Champlain, the Adirondack Mountains and Montreal. WE ENCOURAGE CANDIDATES WHO CAN PROVIDE FEMALE OR MINORITY GROUP ROLE MODELS FOR OUR STUDENTS. Closing date is January 31 , 1992, but applications will be accepted until the position is filled.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

YORK COLLEGE Department of Mathematics & Computer Studies

Applications are invited for two tenure-track positions at the assistant or associate professor level starting Fall 1992. Ph.D. in Mathematics, Computer Science, or a closely related field required. Ability and interest in teaching excellence, scholarly research, and commitment to professional growth in developmental mathematics, mathematics, or computer science are expected. Areas of interest include: classical applied math, computational math, data structure & algorithms, database, computer graphics, networking, computer-based instructions: design, implementation & management of delivery systems. Salary ranges from $28,630 to $47,601 based on qualification and experience. The application deadline is February 21, 1992. Candidates should send a letter of application, curriculum vitae, and name, address, and phone number of three references directly to Personnel Director York College, CUNY Jamaica, NY 11451 AAIEOE.

NORTH CAROLINA UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL Department of Mathematics Chapel Hill, NC 27599-3250

Applications are invited for one faculty appointment effective Fall 1992. Rank and salary depend on qualifications and budget considerations. Ph.D. in mathematics highly preferred, exceptionally strong research program and commitment to excellent teaching required. Send curriculum vitae, abstract of current research program and four letters of recommendation to Search Committee Chairman, Math. Dept., CB #3250 Phillips Hall, UNC at Chapel Hill, Chapel Hill, NC 27599-3250. EO/AA Employer. Women and minorities are encouraged to identify themselves voluntarily. Completed applications received by February 15, 1992 are assured of full consideration.

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UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Mathematics Charlotte, NC 28223

Several tenure-track positions at Asst/Assoc/ Prof level. Areas of preference are Probability, Statistics, Mathematical Physics, PDEIODE, Dynamical Systems, Analysis, Commutative Algebra/Algebraic Geometry, Differential Geometry and Differential Topology. Strong candidates in other areas will also be considered. Possible visiting positions in all areas at any level or postdoctoral positions. Rank and salary depend on qualifications. Ph.D. and a serious commitment to teaching and research are required. Possible lecturer positions (non-tenure track, M.A. or M.S. required) also. Send vitae, list of 4 references, and abstracts of research to Alex Papadopoulos, Chair, Faculty Selection Committee, at the above address. Closing date: February 3, 1992, but all applications will be considered until the positions are filled. UNCC is an Affirmative Action/Equal Opportunity Employer and complies fully with the Immigration Reform and Control Act of 1986.

CASE WESTERN RESERVE UNIVERSITY Visiting Positions in Mathematics and Statistics

The Department of Mathematics and Statistics anticipates at least two one-year visiting appointments in Mathematics and Statistics, beginning July 1, 1992. Applications in all areas of mathematics are invited. Preferred areas include probability and statistics, global analysis and geometry, dynamical systems, control theory, functional analysis, partial differential equations, and numerical analysis. Women and minority group applicants are especially encouraged to apply. Send vita plus three letters of recommendation to Professor David Singer, Chairman, Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106-7058. CWRU is an Affirmative Action/Equal Opportunity employer.

KENYON COLLEGE Department of Mathematics

Applications are invited for a two year temporary position for the academic years 1992-1993 and 1993-1994. Applicants who have a Ph.D. in mathematics or computer science by the end of the summer of 1991 , or are in the final stages of their doctoral work, are preferred. The successful candidate will be expected to teach beginning programming in Pascal. It will be an advantage to a candidate to be able to teach intermediate computer science courses. Moreover, teaching responsibilities may include mathematics courses. This position is an entry level position, at the level of instructor or assistant professor, depending on qualifications. Applications will be reviewed beginning February 1, 1992. To apply, send vita, graduate transcript(s) and three letters of reference (at

least one about teaching) to Professor Robert M. McLeod, Chair, Search Committee, Department of Mathematics, Kenyon College, Gambier, OH 43022-9623. An Equal Opportunity Employer.

THE UNIVERSITY OF TOLEDO Department of Mathematics Toledo, OH 43606

The Department of Mathematics invites applications for a tenure-track position in statistics at the advanced assistant or associate level, beginning in the fall of 1992. The department currently offers bachelor's and master's degrees in statistics. Applicants are expected to have an established research record, be committed to excellence in teaching, and be willing to provide leadership for our statistics group. Applicants should send a curriculum vitae and three letters of recommendation to: Harvey Wolff, Chairman, Department of Mathematics, The University of Toledo, Toledo, Ohio 43606-3390. Screening will commence at the beginning of February, but applications will continue to be accepted until the position is filled. Applications from women and minorities are especially welcomed. The University of Toledo is an equal opportunity, affirmative action employer.

THE UNIVERSITY OF TOLEDO Department of Mathematics Toledo, OH 43606

Applications are invited for a visiting assistant professor position beginning in September 1992. Applicants should have a Ph.D. (or have completed all requirements for the Ph.D. by Fall 1992) and be committed to excellence in both teaching and research. Applicants should send a resume and arrange for three letters of reference to be sent to Harvey Wolff, Chairman, Department of Mathematics, The University of Toledo, Toledo, Ohio 43606-3390. The University of Toledo is an equal opportunity, affirmative action employer.

--OKLAHOMA

areas. However, outstanding candidates in other reated areas will also be considered. The mathematics faculty offers B.S. and B.A. degrees in Mathematics, an M.S. degree in Applied Mathematics, and collaborates in the Ph.D. program in Computer Science. In addition to campus and college computing facilities, the departmental research computing facilities include desktop computing for each faculty member, a network of 18 Sun servers and workstations, 2 DEC workstations, a BBN Butterfly, an Intel Hypercube, and a highresolution 24-bit color graphics system on an Alliant FX-40. The department is also a member of NSFnet. The department also has strong Computer Science research efforts in Artificial Intelligence and Knowledge Based Systems, Numerical Learning Systems, Parallel Computing, Scientific Computing, Databases, and Computer Graphics. The department is housed in the College of Engineering and Applied Mathematics, creating a strong opportunity for interdisciplinary collaborations. Applications will be evaluated beginning February 1, 1992. Late applications will be accepted until the position is filled. Send vitae, transcripts (for recent graduates), and three letters of reference to: Dr. Richard A. Redner Search Committee Chairman Mathematical and Computer Sciences University of Tulsa 600 S. College, Tulsa, OK 74104-3189 (email: [email protected]) The University of Tulsa, an equal opportunity/affirmative action employer, is committed to diversifying its faculty and staff. Members of underrepresented groups (people of color, people with disabilities, women, veterans, etc.) are strongly urged to apply.

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UNIVERSITY OF TULSA Department of Mathematical and Computer Sciences

The Department of Mathematical and Computer Sciences at the University of Tulsa invites applications for tenure-track positions in Mathematics beginning in Fall 1992. Salary is open and competitive. Responsibilities include teaching 6 hours per semester at the undergraduate and graduate levels and continuing scholarly activity. Minimum qualifications are a Ph.D. in Mathematical Sciences or a related discipline, and a strong commitment to teaching and research. The Department has research programs in Numerical Analysis, Statistics, and Scientific Computing and is seeking candidates in applied mathematics who will support these research

JANUARY 1992, VOLUME 39, NUMBER 1

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INDIANA UNIVERSITY OF PENNSYLVANIA College of Natural Science and Mathematics Department of Mathematics Notice of Vacancy Tenure-Track Position Beginning September 1992

Position: Assistant Professor of Mathematics in a department which places a high priority upon teaching excellence and expects faculty to be professionally active. Responsibilities: 1. To teach 12 semester hours of undergraduate and graduate courses per semester. No

73

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more than three different course preparations per semester will be required. 2. To advise students and to serve on faculty committees. 3. To participate in other academic and professional activities of the department, university, and the discipline. 4. To participate in continuing scholarly activity. Qualifications: 1. Doctorate (or degree nearing completion) required. 2. Teaching experience preferred. Review of applications will begin on January 15, 1992 and continue until position is filled. Applications must include a transcript, resume or curriculum vitae, the names, current addresses and telephone numbers of five referees, one of who must be your current employer/supervisor. Please send to: Search Committee B, Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA 15705, 412-357-2608. IUP is an affirmative action/equal opportunity employer.

MILLERSVILLE UNIVERSITY Department of Mathematics

Full-time tenure-track assistant professorship to begin August 1992, in a department of 20 faculty and over 225 math major-S. Primary duties: leadership in developmental mathematics, diagnostic techniques, remediation delivery packages, teaching and placement, teaching through calculus, advisement curriculum development, committees, and scholarly growth. Twelve-hour load per semester. Doctoral degree (or expected completion within one year) in mathematics, math education, or curriculum and instruction with a mathematics background at least through the master's level. Must exhibit evidence of strong commitment to excellence in teaching developmental mathematics, relate well with developmental students and the wider university community, and be an effective teacher of math through calculus. Experience in pre-university or urban teaching preferred. Excellent salary-benefits. Full consideration will be given to applications received by 2/1/92. Send letter of application, vita, copies of transcripts, and three letters of reference (at least two which attest to your teaching effectiveness) to: Prof. Marshall Anderson, Staff Search Committee Chair, Department of Mathematics AMS192, MILLERSVILLE UNIVERSITY, Millersville, PA 17551. AA/EOE.

Mathematics/Statistics, and Geology/Planetary Sciences in an AAU institution. It is a chance to direct, develop, and manage the services and collections for two libraries in a dynamic teaching and research environment. The required masters of library science may be waived at the time of appointment with the understanding that it will be acquired within three years of the initial appointment. The University of Pittsburgh has an ALA-accredited School of Library and Information Science. REQUIREMENTS: Degree in Physics, Mathematics, or related field. Familiarity with information sources and databases in these disciplines. Understanding of research process and ability to develop services needed by scientists; good communication and interpersonal skills; ability to work with and provide service to diverse populations. Candidates must demonstrate an interest in librarianship. Masters in library science must be acquired within three years of appointment. Rank of appointment as a faculty librarian would be commensurate with qualifications. Salary range: $25,00Q-$35,000. Applications must be received in writing, including a resume and three letters of recommendation. Your letters of recommendation should speak to your suitability as an applicant for this position. The position will remain open until filled. Address reply to: Secretary, Search Committee (Physics), 271 Hillman Library, University of Pittsburgh, Pittsburgh, PA 15260. The University of Pittsburgh is an Affirmative Action, Equal Opportunity Employer. Minorities are especially encouraged to apply.

74

UNIVERSITY OF SOUTH CAROLINA Department of Mathematics

The Department of Mathematics invites applications for expected tenure-track faculty positions for Fall 1992, at all ranks. Applications in all areas of mathematics will be considered. Research is supported by excellent inhouse library and computing facilities. The Ph.D. degree or its equivalent is required. Appointments will be consistent with the Department's commitment to excellence in research and in teaching at the undergraduate and graduate levels. A detailed resume, containing a summary of research accomplishments and goals, and four letters of recommendation should be sent to: Dr. George F. McNulty, Chairman Department of Mathematics University of South Carolina Columbia, SC 29208 The University of South Carolina is an Affirmative Action/Equal Opportunity Employer.

RHODE ISLAND THE UNIVERSITY OF RHODE ISLAND

Assistant Professor, Mathematics (two positions) Tenure-Track. Ph.D. in Mathematics required at the time of hiring. Strong commitment to excellent teaching as well as strong research accomplishments and/or research promise required. Applicants must have specialized in one of the following areas: combinatorics, differential equations, classical analysis, functional analysis, control theory, approximation theory. Submit a letter of application and vita, and have three letters of reference sent by January 31, 1992 to: E. Suryanarayan, Search Committee Chair, Assistant Professor, Mathematics (two positions), (021139) Position, THE UNIVERSITY OF RHODE ISLAND, P.O. Box G, Kingston, Rl 02881. An Affirmative Action/Equal Opportunity Employer.

UNIVERSITY OF PITTSBURGH

PHYSICS/MATHEMATICS LIBRARIES The University of Pittsburgh is offeril')g an opportunity for mathematicians/physicists/ geologists to give serious consideration to a career in information/libraries. We are seeking applications and nominations for a Faculty Librarian position as Physics/Mathematics Librarian. The Librarian will be providing information and research services for the departments of Physics/Astronomy,

teaching load is 9 hrs/wk, with possibilities for reductions through internal grants. The salary is competitive. Applicants should send a vita and have three letters of recommendation sent to William L Golightly, Chairman, Department of Mathematics, College of Charleston, Charleston, SC 29424. The process of evaluating applications will begin on January 13, 1992, but applications will be considered until the positions are filled. The College of Charleston is an Affirmative Action/Equal Opportunity Employer.

UNIVERSITY OF TENNESSEE, Mathematics Department Knoxville, TN 37996-1300

The Mathematics Department of the University of Tennessee, in an effort to significantly improve its research position, seeks to fill a tenure-track assistant professorship in harmonic analysis, several complex variables, function theoretic operator theory, differential geometry, numerical mathematics, theoretical probability and stochastic processes. Employment begins August 1992. Substantial research as well as dedication to teaching are paramount. Interested applicants should arrange to have a vita, three reference letters, and a research statement sent to Professor John B. Conway, Mathematics, University of Tennessee, TN 37996-1300. Review of applications will begin December 1 and will continue until the position is filled. UTK is an EEO/AA!Title IX Section 504/ADA Employer.

SOUTH CAROLINA COLLEGE OF CHARLESTON Department of Mathematics

Applications are invited for at least one tenuretrack position at the Assistant Professor level beginning August 1992. Candidates must have a Ph.D. in one of the mathematical sciences, a commitment to undergraduate teaching, and potential for continuing research. The normal

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

TEXAS ST. MARY'S UNIVERSITY San Antonio, Texas

The Department of Mathematics invites applications for a tenure-track position at the assistant or associate professor level beginning in the fall

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semester of 1992. Requirements include a doctorate in mathematics or mathematics education and a strong commitment to both teaching at the undergraduate level and to continued scholarly activity. In addition the candidate should have an interest and, preferably, experience in interaction with local school districts and in using technology in the teaching of mathematics. Send a letter of application including a statement of professional goals, resume, and three letters of reference to: Dr. S. Eugene Sims, Chair Department of Mathematics St. Mary's University San Antonio, TX 78228-8560 The closing date for applications is February 24, 1992. St. Mary's University is an Equal Opportunity Employer.

SOUTHERN METHODIST UNIVERSITY Department of Mathematics The Department of Mathematics at Southern Methodist University invites applications for a senior level and a junior level tenure-track position, with employment beginning in Fall 1992. The applicants must be active researchers, must have a strong commitment to undergraduate teaching and must be ready to teach advanced courses in the doctoral program in applied mathematics, numerical analysis and scientific computation. The senior applicants must have research interests in applied mathematics and must be able to supervise doctoral dissertations. A strong grant record is also desirable. The junior applicants must be active in research in numerical analysis. The standard teaching load is two courses (six hours) per semester. Departmental research interests include fluid mechanics, numerical analysis of differential equations, mathematical software, asymptotic and perturbation methods, nonlinear waves, bifurcation theory, combustion theory, dynamical systems, and mathematical biology. Thirteen of the sixteen faculty are applied or numerical mathematicians. Senior faculty include W. E. Ferguson (numerical partial differential equations), I. Gladwell (mathematical software), R. Haberman (nonlinear waves), G. W. Reddien (numerical bifurcation theory), D. A. Reinelt (fluid mechanics), and L. F. Shampine (numerical ordinary differential equations). Southern Methodist University has a 20 processor Sequent Symmetry for research use. The application deadline is February 11 , 1992. Send a letter of application and a vita to: Professor I. Gladwell, Chairman, Department of Mathematics, Southern Methodist University, Dallas, Texas 75275. (Tel: 214/692-2506). Junior applicants should arrange for three letters of recommendation to be sent to Professor Gladwell. SMU is an equal opportunity/affirmative action/Title IX employer.

THE UNIVERSITY OF TEXAS AT SAN ANTONIO

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The Division of Mathematics, Computer Science, and Statistics will have one tenure-track position at the assistant professor level in Mathematics, beginning August 1992. Although applicants in all areas of mathematics will be considered, preference will be given to those candidates whose research areas are in applied or applicable analysis. Applicants should have a Ph.D. degree in Mathematics by August 1992, and should demonstrate strong potential for excellence in research and teaching. Responsibilities include research, teaching, direction of graduate students, and contributing to program development. San Antonio, Texas is a scenic, dynamic and fast growing city of rich cultural diversity. UTSA is the only public university in the city of San Antonio, and serves a metropolitan community of approximately one million people. The university is viewed by the community as an important asset in the economic development of the area. Applicants should submit a resume and arrange to have at least three letters of recommendation sent to Professor Shair Ahmad, Director Division of Mathematics, Computer Science and Statistics The University of Texas at San Antonio San Antonio, TX 78285-0664 Email: [email protected] The closing date for receipt of applications for this position is January 31, 1992. UTSA is an Equal Opportunity/Affirmative Action Employer. Women and minorities are encouraged to apply.

UNIVERSITY OF TEXAS AT ARLINGTON Department of Mathematics The Department invites applications for two to three anticipated tenure-track positions beginning with the Fall Semester, 1992. We seek candidates in areas of Mathematics which are complementary to those of the current faculty and would enhance and support the goals of the Department. Salary and rank are commensurate with qualifications which must include the Ph.D. degree or its equivalent (in hand or received by September 1992). Assistant Professor candidates must show strong potential for excellence in teaching and research. For an Associate or Full Professorial appointment the candidate must have excellent teaching credentials and a nationally established research record; some success in attracting outside funding is preferred. A resume with three letters of recommendation should bb sent to: Dr. Danny Dyer University of Texas at Arlington Department of Mathematics Box 19408 Arlington, Texas 76019-0408 ATTN: RECRUITING CHAIRMAN The University of Texas at Arlington is an Affirmative Action/Equal Opportunity Employer.

JANUARY 1992, VOLUME 39, NUMBER 1

UNIVERSITY OF UTAH Department of Mathematics Invites applications for the following positions: 1. At least two full time tenure track appointments on the professorial levels. The Department is primarily interested in applicants who work in the research areas represented in the Department and who received their Ph.D. degrees prior to 1991 . Selection will be based on research and teaching ability. 2. Two or more nonrenewable three-year Instructorships. Persons of any age receiving Ph.D. degrees in 1991 or 1992 are eligible. Applicants will be selected on the basis of ability and potential in teaching and research. Starting salary will be $32,000; future cost of living increases are contingent on action by the State Legislature. Duties consist of teaching five courses during the three quarter academic year. 3. One C. R. Wylie Instructorship. The term of this instructorship is one year, but it may be renewed for up to three years. It will be awarded either to an incoming Instructor or to one of the Instructors already in residence on the basis of ability and potential in teaching and research. The stipend in $36,200. Duties consist of teaching four courses during the three quarter academic year. 4. One or more visiting faculty positions of one year or less in any of the professorial ranks. Selection will be based on potential contributions to the department's research program, and on teaching ability. It is expected that offers of Instructorships will begin on January 1, 1992, but applications for all positions will be accepted until January 31, 1992, or until all positions are filled. Applications for any of these positions should include curriculum vitae, bibliography and three letters of reference. (Instructorship applications should also include an abstract of the thesis and either a list of graduate courses completed or a transcript of graduate work.) Visiting faculty applications should indicate the portion of the three-quarter academic year during which the applicant wishes to visit. Please send your application to Committee on Staffing, Department of Mathematics, University of Utah, Salt Lake City, Utah 84112. The University of Utah is an Equal Opportunity, Affirmative Action Employer and encourages nominations and applications from women and minorities.

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UNIVERSITY OF VERMONT Position in Mathematics The Department of Mathematics and Statistics solicits nominations and applications to fill a 2-year Visiting Assistant Professor position in mathematics. Applicants should have a Ph.D. in Mathematics or a related discipline and demonstrated excellence in research and teaching. Research interests must be compatible with existing groups in the department, including algebra, number theory, and combina-

75

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torics. Preference will be given to researchers in combinatorics and to those who have received their Ph.D. in the last three years. Duties include teaching two courses per semester and conducting research. Applicants should send a vitae, description of research and three letters of reference to: Personnel Committee, Department of Mathematics and Statistics, University of Vermont, Burlington, VT 05401-1455. The deadline for applications is February 1, 1992; duties begin in the Fall Semester 1992. UVM is an Equal Opportunity/Affirmative Action Employer. Minorities and women are strongly encouraged to apply.

apply send curriculum vitae, copies of research papers and names of three referees. Applications close February 15, 1992 but late applicants will be considered until the position is filled. Send all inquiries to: Chair, High Performance Computing Search Committee c/o Dean of College of Sciences Old Dominion University Norfolk, VA 23529-0162 or [email protected] Old Dominion University is an affirmative action, equal opportunity employer and requires compliance with the Immigration Reform and Control Act of 1986.

VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY Department of Mathematics

VIRGINIA OLD DOMINION UNIVERSITY Senior Faculty Position

The Department of Computer Science and the Department of Mathematics and Statistics have an opening for a joint appointment in a senior position. We are seeking a research faculty member to enhance our existing strong program in High Performance Computing. The successful applicant must have a proven research and grant record in some combination of Applied Mathematics and High Performance Computing. The Computer Science Department has a High Performance Computing Lab, which includes DAP and N-Cube machines, an innovative minor in High Performance Computing at the undergraduate level, and a highly successful graduate research group working in parallel computation and parallel architecture. The Department of Mathematics and Statistics has very active research groups in Continuum Mechanics, Mathematical Biology and Numerical Analysis/Approximation Theory. Research projects to develop computational models and algorithms for parallel computers involve faculty from both departments. In addition, there are joint research efforts using computational and asymptotic methods in the areas of fluid dynamics and combustion. These research groups are complemented by a strong network research group which concentrates on developing gigabit networks to support the distribution of remote supercomputing services to local clients. Both departments have established programs at the Bachelor, Master's and the Ph.D. levels. Standard equipment for faculty and student offices includes a Sun workstation connected via ethernet and FDDI to other computing resources and Internet. Special equipment needs can be supported. Salary competitive. Ph.D. in Applied Mathematics, Computer Science or Computational Science preferred. To

76

The Department of Mathematics at Virginia Tech is seeking qualified applicants for a tenure-track position at the rank of Assistant Professor in the area of Computational Mathematics/Numerical Analysis. The position should be available beginning with the 1992-1993 academic year. A Ph.D. and strong research potential are required. The Department currently includes a large group of Applied Mathematicians including a number of numerical analysts and computational scientists. Also, through the Interdisciplinary Center for Applied Mathematics, members of the Department have developed close collaborations with numerous scientists and engineers throughout the University. We seek applicants who will be able to interact with the present staff and aid in the further development of the Computational Mathematics/Numerical Analysis program in the Department. The position involves teaching duties of approximately six hours per week; thus, there should be strong indications that an applicant is or will become an effective teacher. The deadline for applications is March 15, 1992; after that date, applications will be entertained only if the position remains unfilled. A curriculum vitae, description of research interests, including a synopsis of the dissertation, three letters of recommendation and any other supporting materials should be sent to Max D. Gunzburger, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123. Virginia Tech is an Equal Opportunity, Affirmative Action Employer. In keeping with Virginia Tech's commitment to providing equal opportunity for all, women, minorities, and the disabled are especially encouraged to apply.

VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY Department of Mathematics

Applications are invited for a tenure-track appointment at the level of Assistant Professor in the general area of Dynamical Systems beginning with the 1992-93 academic year. A Ph.D. and strong research potential are required. A likelihood of productive interaction with current senior faculty members, such as the group

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY

in partial differential equations and continuum mechanics, would be helpful. Since the position involves teaching duties of approximately six hours per week, there should be strong indications that the candidate is or will become an effective teacher. Applicants should send a vita and arrange to have three letters of reference submitted to Kenneth B. Hannsgen, Chair, Dynamical Systems Search Committee, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123. Applications will be accepted for as long as a position remains available but no later than May 1, 1992. Virginia Tech is an Equal Opportunity, Affirmative Action Employer. In keeping with Virginia Tech's commitment to providing equal opportunity for all, women, minorities, and the disabled are especially encouraged to apply.

VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY Department of Mathematics

The Department of Mathematics is actively seeking applications for a tenure-track position in the area of discrete mathematics, combinatorics, and graph theory beginning with the 1992-93 academic year. Candidates with an interest in computing are especially encouraged to apply. A Ph.D. and strong research potential are required. Preference will be given to candidates with postdoctoral experience. Applications will be accepted until March 15, 1992 or until the position is filled. Applicants should send a curriculum vitae and arrange to have three letters of reference submitted to Chair, Discrete Math Search Committee, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123. Women and minorities are encouraged to apply. Virginia Tech is an Equal Opportunity/Affirmative Action Employer.

VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY Department of Mathematics

Applications are invited for a tenure-track position in Geometry (differential or algebraic, or related areas) beginning Fall 1992. Because we seek applicants who will be able to develop a strong case for eventual promotion and tenure, preference will be given to those with postdoctoral or instructorship experience and established research programs. Please send vita and brief description of research and have three letters of reference sent to Prof. Frank Quinn, Chair, Geometry Search Committee, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123. Applications will be accepted until March 15, or until position is filled. Virginia Tech is an Equal Opportunity/Affirmative Action Employer. The University takes its affirmative action mission seriously and is especially interested in receiving applications from women and people of color.

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VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY Department of Mathematics

The department invites applications in the area of partial differential equations. Applicants should have a strong theoretical background in partial differential equations and a demonstrated interest in applications. We are particularly interested in applicants at the assistant professor level. Applicants should submit a curriculum vitae and list of publications and arrange three letters of recommendation to be sent to Michael Renardy, Chair, Applied POE Search Committee, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123. Applications accepted until March 15, 1992 or until position is filled. Virginia Tech is an Equal Opportunity/Affirmative Action Employer. The University takes its affirmative action mission seriously and is especially interested in receiving applications from women and people of color.

WEST VIRGINIA.··---~ WEST VIRGINIA UNIVERSITY Department of Mathematics

The Department of Mathematics intends to make two faculty appointments at the Assistant Professor rank that will commence August 1992. Candidates are expected to have a Ph.D. in mathematics or equivalent with a strong record or demonstrated potential in both research and teaching. Preference will be given to applicants whose research interests complement those currently in the Department. One appointment will be in analysis, applied analysis, or numerical analysis. The other, pending funding, will be in algebra or discrete mathematics. Normal responsibilities include research and a two course teaching assignment per semester at the graduate or undergraduate level. Applications and inquiries should be directed to Michael Mays, Department of Mathematics, West Virginia University, Morgantown, WV 26506. Applicants should submit a vita and have three letters of reference sent. To insure consideration, application materials must be received by January 15, 1992. WVU is an affirmative action/equal opportunity employer. Qualified women and minorities are especially encouraged to apply.

expanding Mathematics Department. The College seeks candidates who wish to participate in the building of a strong mathematics program and who would also look forward to developing interdisciplinary ties in a college-wide setting. Applications, consisting of transcripts and three letters of reference, should be submitted to: Dr. Thomas A. Brawner, Chairperson of the Division of Natural Sciences, Carthage College, Kenosha, Wl53140. Review of applications will begin on December 1, 1991. A representative from the department will attend the joint AMSMAA January 1992 meetings in Baltimore and meet with interested candidates. Strong candidates not able to attend the meetings will also be considered. Carthage College is an equal opportunity employer and specifically invites and encourages applications from women and minorities.

THE UNIVERSITY OF WYOMING Department of Mathematics Position in Mathematics

Applications are invited for a tenure-track position in Applied Mathematics or Analysis at the rank of assistant professor. Strong consideration will be given to, but not limited to, the following areas: partial differential equations, numerical linear algebra, applied functional analysis, and numerical analysis. Salary is competitive and commensurate with experience and qualifications. Candidates should demonstrate accomplishment and potential in research and teaching. Applicants should send vita, three letters of recommendation, and brief description of his/her research plans to: Dr. John George, Chairman, Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071. Email inquiries should be sent to [email protected]. Applications completed by January 15, 1992 will receive first consideration. The University of Wyoming is an AA/EOE.

lattice gas cellular automata techniques in the context of geological, biological, atmospheric, oceanic, etc., phenomena. Experts who have already expressed an interest in participating in the development of this sub-theme with the program directors (J. Chadam, L. Glass and W. Langford) include B. Matkowsky (Northwestern), G. Doolen, (Los Alamos), M. Golubitsky (Houston), R. Kapral (Toronto), A. Lawniczak (Guelph), W. R. Peltier (Toronto), P. Ortoleva (Indiana), G. Oster (Berkeley) and J. Tyson (Virginia Polytechnic Institute). Other sub-themes will be integrated into the Dynamical Systems and Bifurcation Theory program. Applications, including curriculum vitae, should be sent to: Dr. J. E. Marsden Director The Fields Institute for Research in Mathematical Sciences 6095 Mathematics and Computer Building 200 University Avenue West Waterloo, Ontario N2L 3G1 Please arrange for three letters of reference to be sent directly from the referees. The Institute, funded by the Ministry of Colleges and Universities of Ontario and the Natural Sciences and Engineering Research Council of Canada, is a collaboration involving McMaster University, the University of Toronto and the University of Waterloo. Universities from across Canada are being invited to join as affiliate members. The successful applicants will join a group of about 50 researchers and postdoctoral fellows brought together for collaborative research in the mathematical sciences, as well as providing graduate training for students from across Canada. All Institute Fellows will have access to library facilities, computing facilities; a wide spectrum of mainframe and microcomputer software and electronic mail. In addition, Junior Fellows will be eligible for a small research grant. The Fields Institute for Research in Mathematical Sciences is supported by The Ministry of Colleges and Universities of Ontario and the Natural Sciences and Engineering Research Council of Canada.

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

WISCONSIN CARTHAGE COLLEGE Kenosha, Wisconsin

Applications are invited for two tenure-track Assistant Professor positions, to begin Fall 1992. A strong general mathematical background, including a Ph.D. is expected. One of the positions requires an interest in probability and/or statistics. Commitment to excellence in undergraduate instruction, continued mathematical scholarship and development of independent student mathematical work is required. Carthage College is a liberal arts college located on Lake Michigan between Chicago and Milwaukee, with a growing enrollment and an

The Fields Institute for Research in Mathematical Sciences invites applications for Institute Junior Fellowships for the 1992-93 program year. Candidates should possess a Ph.D. degree in mathematical sciences and have a strong research record. Partial support may also be available for a limited number of more senior Institute Fellows working in the program area. For the 1992-93 academic year the topics of concentration will be Dynamical Systems add Bifurcation Theory. Part of the program will be devoted to the study of Pattern Formation in Dynamical Systems from several viewpoints including partial differential equations, symmetry/group theoretic methods and

JANUARY 1992, VOLUME 39, NUMBER 1

NATIONAL CENTRAL UNIVERSITY Department of Mathematics Chungli, Taiwan, R.O.C.

Positions of Professors, Associate Professors, and visitors are available. Annual salary US$30,000 for new Ph.D. Reasonable teaching load. Teaching in English is acceptable. Mathematicians with research interest of Algebra, Geometry, Probability, Statistics, and Computing Mathematics are especially wanted. Very good library and computing facilities. Please send vita, letters of recommendation, and copies of research work to Chairman.

77

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NATIONAL CHUNG CHENG UNIVERSITY Institution of Applied Mathematics Taiwan, R.O.C. Applicants are invited for Visiting Professors or Assistant Professors in the area of Partial Differential Equations, Statistics and Numerical Analysis from 1 August of 1992. A degree of Ph.D. in Math. is required. Applicants should send a curriculum vitae, reprints of published paper (or accepted for publication), and three letters of recommendation to Professor C. S. Lin, Chairman, Department of Mathematics, National Chung Cheng University, Ming-Hsiung, Chia-Yi, Taiwan, Republic of China. Fax number: 011-8865-272-0497. The teaching duty is at least 6 hours per week and the deadline for receipt of complete applications is 15 March of 1992.

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UNIVERSITAT BONN Research Institute of Discrete Mathematics Director: Professor Bernhard Korte Postdoctoral Fellowships in Discrete Mathematics The Research Institute of Discrete Mathematics announces three Postdoctoral Fellowships for the academic year 1992-1993. These awards are intended for young mathematicians and computer scientists with exceptional research promise in Discrete Mathematics and its applications. The postdoctoral fellows will be able to take part in all research activities of the Institute, but the teaching of one graduate course per semester is expected. The award will range between DM 36,000 and DM 39,600 for the academic year depending upon qualifications and experience, and is not subject to German income tax. Applications should include a curriculum vitae, a bibliography, two letters of reference, and a research plan. To be eligible for one of the 1992-1993 fellowships, please send a complete application at your earliest convenience, but not later than February 28, 1992, to: Professor B. Korte, Research Institute of Discrete Mathematics, University of Bonn, Nassestrasse 2, D-5300 Bonn 1, Germany.

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SISSAIISAS, TRIESTE Postdoctoral Positions The International School for Advanced Studies (SISSA/ISAS) in Trieste expects to offer a number of postdoctoral positions in the following fields: Nonlinear analysis Geometry Mathematical Physics Theoretical Particle Physics Theory of Condensed Matter Theoretical Astrophysics and Cosmology Neurophysiology or Molecular Neurobiology These positions will be available from the Fall of 1992 for one year and renewable for a second year. Candidates should submit their applications by 31 January 1992 with their Curriculum Vitae, list of published works and their research programme. They should arrange for 3 letters of reference to be sent by the same date. Applications and correspondence should be sent to: Postdoc programme International School for Advanced Studies Via Beirut 2-4 34014 TRIESTE

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Aegean Park Press, P.O. Box 2837, Laguna Hills, CA 92654 is publisher of books concerning coding, shift register sequences, data encryption standard, statistics and probability pertaining to cryptology. Write or call for list of all books. (714)586-8811. In U.S. toll free (800)736-3587.

MATH SCI PRESS, 53 Jordan Rd., Brookline, MA 02146, 617-738-0307. GEOMETRIC STRUCTURES AND NONLINEAR PHYSICS, $95. GEOMETRIC COMPUTING SCIENCE, $85, both by R. Hermann. Under development: DEFORMATION THEORY IN PHYSICS AND COMPUTING SCIENCE. Lecturing and Consulting available.

Zentralblatt fiir Mathematik Band 1 (1931) through Band 23 (1941) plus Index (Band 24 and Band 25). Mathematical Reviews (194o1991 ). Mint condition. Cal.l 203-633-3798.

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