Calendar of AMS Meetings and Conferences

This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe­ January 1993 issue of the Notices on page 46. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island, on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings

Abstract Program Meeting# Date Place Deadline Issue 890 t March 18-19, 1994 Lexington, Kentucky Expired March 891 t March 25-26, 1994 Manhattan, Kansas Expired March 892 • April8-10, 1994 Brooklyn, New York January 28 April 893 • June 16-18, 1994 Eugene, Oregon April4 May-June 894 • August 15-17, 1994 (96th Summer Meeting) Minneapolis, Minnesota May 17 July-August 895 • October 28-29, 1994 Stillwater, Oklahoma August3 October 896 • November 11-13, 1994 Richmond, Virginia August3 October 897 • January 4-7, 1995 (101st Annual Meeting) San Francisco, California October 1 December March 4-5, 1995 Hartford, Connecticut March 17-18, 1995 Orlando, Florida March 24-25, 1995 Chicago, Illinois November 3-4, 1995 Kent, Ohio November 17-18, 1995 Greensboro, North Carolina January 10-13, 1996 (102nd Annual Meeting) Orlando, Florida March 22-23, 1996 Iowa City, Iowa April19-21, 1996 Baton Rouge, Louisiana January 8-11, 1997 (103rd Annual Meeting) San Diego,California * Please refer to page 41 for listing of Special Sessions. t Please refer to the Table of Contents for further information.

Conferences

June 7-11, 1994: AMS Symposium in Research Mathematics on Quantization and Nonlinear Wave Equations, Massachusetts Institute of Tecnology, Cambridge, Massachusetts. June 11-July 6, 1994: Joint Summer Research Conferences in the Mathematical Sciences, Mt. Holyoke College, South Hadley, Massachusetts June 20-July 1, 1994: AMS-SIAM Summer Seminar in Applied Mathematics on Dynamical Systems and Probabilistic Methods for Nonlinear Waves, Mathematical Sciences Research Institute, Berkeley, California.

Other Events Cosponsored by the Society

February 18-23, 1994: Section A (Mathematics) Sessions at the AAAS Annual Meeting, San Francisco, California.

Deadlines

March Issue April Issue May-June Issue Classified Ads* January 26, 1994 February 22, 1994 April 25, 1994 News Items January 17, 1994 February 13, 1994 April11, 1994 Meeting Announcements** January 20, 1994 February 17, 1994 April 18, 1994 * Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. ** For material to appear in the Mathematical Sciences Meetings and Conferences section. OTICES OF THE AMERICAN MATHEMATICAL SOCIETY

DEPARTMENTS ARTICLES 3 Letters to the Editor 10 Forum 5 Cultural Aspects of Mathematics Education Reform Michael Fellows, 29 News and Announcements Ann Hibner Koblitz, and Neal Koblitz 34 Funding Information for the How can we reform mathematics education so as to make the subject Mathematical Sciences accessible to students with diverse cultural backgrounds? How do we promote depth of understanding instead of the gimmickry of our high-tech, 37 1994 AMS Election instant-gratification culture? Based on the authors' work with young people 39 Meetings and Conferences of of diverse cultural backgrounds, this article provides insights on these the AMS important issues. Lexington, KY March 18-19, 39 Manhattan, KS FEATURE COLUMNS March 25-26, 40 Invited Addresses, Special Sessions, and Contributed Papers, 14 Computers and Mathematics Keith Devlin 41 Three software reviews make up the first column of 1994. First, Larry Joint Summer Research Lambe looks at AXIOM. Then, Suzanne Molnar reports her experiences Conferences in the Mathematical with the Student Edition of Object Logo. Finally, Jim Northrup reviews Sciences, 44 Fields& Operators. 1993 Summer Seminar in Applied Mathematics, 46 25 Inside the AMS Symposium on Quantization and Nonlinear Wave Equations, 48 This month's column contains reports about the Society's Program Development Fund and about the 1993 Trjitzinsky Awards, presented to four 50 Mathematical Sciences Meetings deserving mathematics undergraduates. and Conferences 60 New Publications Offered by the 27 Washington Outlook AMS This month's column, written by Lisa Thompson, reports on the 64 AMS Reports and establishment of the National Science and Technology Council (NSTC) to Communications coordinate federal R&D. 1993 Election Results, 64 Reports of Past Meetings, 64 66 Miscellaneous Personal Items, 66 Deaths, 66 67 New Members of the AMS 68 AMS Policy on Recruitment Advertising 69 Classified Advertising 87 Forms

JANUARY 1994, VOLUME 41, NUMBER 1 ...... ------····- ...... _.. ,_ .... ,...... _____ ...... _......

From the Executive Director ...

ADDRESSING PUBLISHING ISSUES In the March 1993 Notices this column discussed the publishing role of the AMS. There it was observed that most of the programs and services of the Society AMERICAN MATHEMATICAL SOCIETY relate to publishing and the communication of mathematics. It was also pointed EDITORIAL COMMITTEE out that the Society is undertaking a major effort to broaden and enhance its role Sheldon Alder as a publisher, positioning itself to respond to change and to be the publisher of Amassa C. Fauntleroy choice for mathematics. Robert M. Fossum (Chairman) Susan J. Friedlander (Forum Editor) The issues facing the Society as a publisher are quite challenging. Many of Carolyn S. Gordon these issues face all publishers, but they take on a different twist when combined Carl R. Riehm with the Society being a professional, membership organization. The mission and L. Ridgway Scott (Letters Editor) goals of the Society require the consent of the membership. For the Society to MANAGING EDITOR achieve the goals of its publication program, it is necessary for the membership of John S. Bradley the Society to accept, in principle, the general philosophy of the publication pro­ ASSOCIATE EDITORS gram and support the various activities and services of this program. Therefore, Jeffrey C. Lagarias, Special Articles it is important that the members of the AMS be informed of the issues related to ASSOCIATE MANAGING EDITOR the publication program and that there be a synergy between the volunteers and Allyn Jackson the staff who work in the Publication Division. SUBSCRIPTION INFORMATION A way of interpreting the AMS publication goal is for the Society to become Subscription prices for Volume 41 (1994) are a discipline-based leader in information services. This philosophy has been em­ $146 list; $117 institutional member; $88 individ­ braced by the Society's governing bodies and in the Society's strategic planning. ual member. (The subscription price for members However, there is a need for broader communication of this philosophy to the is included in the annual dues.) A late charge of membership, as well as a need to adjust current thinking and practice to make 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 the AMS "publisher of choice for mathematics". In particular the AMS must ad­ of the subscription year. Add for postage: Surface vance electronic delivery of information; improve its book acquisition program; delivery outside the United States and lndia-$15; increase economies of production; and develop effective worldwide marketing, to lndia-$28; expedited delivery to destinations in promotion, and distribution of its products and information. Under the general North America-$32; elsewhere-$67. Subscrip­ umbrella of this AMS philosophy are particular issues like: tions and orders for AMS publications should be addressed to the American Mathematical Society, • publication cost recovery and the use of publication income to support P.O. Box 5904, Boston, MA 02206-5904. All orders non-income-producing activities of the AMS, must be prepaid. • quality of production and the extent to which the AMS switches to author- ADVERTISING prepared materials and away from fully in-house edited and typeset materials, Notices publishes situations wanted and classified • ownership of materials and copyright, advertising, and display advertising for publishers • electronic preprint and reprint services, and and academic or scientific organizations. • proactive acquisitions and a broader list of AMS publication products and @ Copyright 1994 by the American Mathematical services. Society. All rights reserved. There are other important issues of publication related to Mathematical Re­ Printed in the United States of America. views and the Society's Russian translation program. This column addressed the § The paper used in this journal is acid-free and publication of Mathematic at Reviews in the November 1993 issue of theNotices. falls within the guidelines established to ensure per­ The Society is currently engaged in negotiations with the Russian Academy of manence and durability. Sciences for continuation of AMS rights to translate into English and publish 0 Printed on recycled paper. Russian language mathematics journals. Most of this publication was typeset using the TE;X In an effort to address these issues in publication and the delivery of informa­ typesetting system. tion, a policy Committee on Publications has been established, and an individual [Notices of the American Mathematical Society is is being sought to fill the newly created position of Publisher of the AMS. The published monthly except bimonthly in May, June, policy Committee on Publications is the mechanism for volunteer guidance and July, and August by the American Mathematical So­ ciety at 201 Charles Street, Providence, Rl 02904- formulation of policy to be considered by the governing bodies and is expected 2213. Second class postage paid at Providence, to take the long-range view and advise the Society on policy related to publica­ Rl and additional mailing offices. POSTMASTER: tion. The Publisher of the AMS is expected to bring vision and leadership to the Send address change notices to Notices of the Publication Division and will lead a division of nearly one hundred employees American Mathematical Society, Customer Service and will have responsibility for book and journal acquisition, publication pro­ Department, American Mathematical Society, P. 0. Box 6248, Providence, Rl 02940-6248.] Publica­ duction, electronic products and services, marketing, promotions and sales, and tion here of the Society's street address, and the warehousing and distribution. other information in brackets above, is a technical The new policy Committee on Publications will hold its first meeting at the requirement ofthe U. S. Postal Service. All corre­ Annual Joint Meetings in Cincinnati. It is expected that the publisher will join spondence should be mailed to the Post Office Box, the staff of the Society about this same time. NOT the street address. Tel: 401 -455-4000. e-mail: ams@math. ams . org. William Jaco

2 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY On February 7, 1993, Andy Rooney joining a boycott as a political statement, Letters rendered a priceless service to mathe­ as Smith claims, but were acting in the matics. Before a large national audience, best interests of the entire membership to the Editor he exposed the junk books, the idiotic by avoiding a meeting place which had games, and the bogus methods that are expressed hostility against a significant being used to teach arithmetic in some number of members, including officers. elementary schools. Transcripts of this I wish to respond to Smith's as­ "60 Minutes" broadcast may be obtained sertion that the AMS decision involves Biting the Bullet from Burrelles Transcripts, Box 7, Liv­ "enforcing political correctness". He of­ Why on Earth did the Forum edi­ ingston, NJ 07039. fers no hint as to what he means by tor reprint Solomon A. Garfunkel's It is absolutely appalling that the pro­ this oft-used phrase. But I have learned rambling editorial (Notices, July/August moters of the "Standards" are receiving to be suspicious of arguments or con­ 1993)? Saunders Mac Lane provided such extensive funding from the Na­ clusions decorated with this buzzword; an intelligent response to Garfunkel's tional Science Foundation (NSF). The such reasoning is often unsupported by gibberish concerning graduate studies. NSF has awarded $100 million to or­ evidence or logic. I'll just point out However, Mac Lane failed to expose ganizations in twenty-eight states. This that within the lifetime of most AMS the fanciful claims about the current money is being used in a massive pro­ members it was politically acceptable, revamping of the K-12 curriculum. paganda campaign for "Statewide Sys­ and sometimes required, at many Amer­ Garfunkel would have us believe temic Initiative". If the so-called Con­ ican institutions of higher education to that the current fads, which are being necticut Academy for Education is any exclude persons of African heritage as promoted under the NCTM "Standards", indication, these funds are being shame­ students or faculty members, to limit the will finally "get it right". The rubbish lessly wasted. number of Jews by rigid quotas, to pay that is being promoted under the guise Although more and more mathemati­ women far less than the salary earned by of "implementing the Standards" is doc­ cians are speaking up, the vast majority men in the same position, and to fire any umented clearly in The Mathematics are ignoring the current scams in mathe­ gay men or lesbians unfortunate enough Teacher, and I urge all members of the matics education. No mathematician can to be "found out". While the road to a AMS to read the deplorable articles that remain silent when so much flimflam is more equitable society may not always have been published since September being promoted as "mathematics". be a smooth one, I'd prefer to strive for 1992. Domenico Rosa inclusion and fairness than to return to John Saxon has done an outstand­ Teikyo Post University the "correct" behavior of the past. ing job at exposing the self-professed (Received September 21, 1993) Mr. Smith claims that Colorado's "mathematics educators" who are un­ Amendment 2 involves prohibiting "a able to teach arithmetic and algebra, special status" for lesbians and gay men. much less the "real-world problem solv­ Moving the Joint Meetings The simple truth is that we are only ing" that they claim to be teaching. On from Denver interested in the equal status enjoyed by December 2, 1992, Saxon was featured I am writing in response to the letter most Americans to work, to live, and to on WTIC-AM Radio in Hartford, CT. in the October 1993 Notices from Ken participate in society free of harassment. He presented a very accurate analysis W. Smith decrying the decision by the of the deplorable state of mathemat­ Boards of the AMS and the MAA to ics education in the United States and relocate the 1995 joint meetings from Letters to the Editor Letters submitted for publication in the Notices stated: Denver in response to the passage in are reviewed by the Editorial Committee. "The National Council of Teachers Colorado of the antigay Amendment 2. The Notices does not ordinarily publish com­ of Mathematics, unfortunately, is over­ When I first heard of the decision, I plaints about reviews of books or articles, al­ though rebuttals and correspondence concerning run by college professors of mathematics was pleased that the boards of my pro­ reviews in Bulletin ofthe American Mathematical education. These people are people who fessional organizations were addressing Society will be considered for publication. couldn't cut it in math. So they ran down my concerns as an openly gay mathe­ u;tters should be typed and in legible form or to the School of Education, took sixty matician. When I read the resolutions they will be returned to the sender, possibly re­ sulting in a delay of publication. All published let­ hours of show-and-tell, and call them­ themselves, I was especially proud to be ters must include the name of the author. Letters selves doctors. And all of a sudden they a mathematician, a long-time member of which have been, or may be, published elsewhere are experts in math education, and they both organizations, and a former MAA will be considered, but the Managing Editor of the Notices should be informed of this fact when the control the National Council of Teach­ Section officer, because of the precision letter is submitted. ers of Mathematics. Now this is not of the boards' rationale for the decision The committee reserves the right to edit let­ all of them; this is not a broad-brushed to relocate the meetings: that as a result ters. treatment. But the ones who are joiners, of the passage of Amendment 2, not all Letters should be mailed to the Editor of the Notices, American Mathematical Society, P. 0. who have big egos, they are the ones members of the MAA and AMS would Box 6248, Providence, RI 02940, or sent by e­ who control the philosophy of math. feel welcome in the convention city. It mail to notices@math. ams. org, and will be education in America." seemed to me that the boards were not acknowledged on receipt.

JANUARY 1994, VOLUME 41. NUMBER 1 3 Letters to the Editor

At present, because of long-standing seeking employment, housing, or public I am troubled by the AMS Denver de­ prejudices against gay men and lesbians accommodations. cision. During my long-standing mem­ and a coordinated national campaign to An employer, landlord, or busi­ bership, I had always assumed that the deny us our rights, dignity, and even our ness who discriminates against African AMS was there to look after only my safety, we do not enjoy such equality. Americans or against women can be mathematical interests. I never imagined Amendment 2, if implemented, forced to answer to the law, but under that the AMS would someday aspire to would provide the protection of the law Amendment 2, discriminators against form my conscience for me and take to an employer, an apartment manager, lesbians and gay men would be pro­ the liberty of representing me in purely or a business owner who fires someone tected from any legal sanction. So it is political, social, or moral matters. The from her or his job, evicts a person not gays and lesbians, but those who are Denver action signals the emergence of from a rental, or bars a person from a prejudiced against us, who are demand­ a new dimension to AMS membership restaurant or store for the sole reason ing "special rights" to act out their that goes beyond acceptability. that the person is perceived to be lesbian prejudice to the detriment ofothers. Instead of drifting out any further, I or gay. In some jurisdictions, this sort of I commend the MAA and AMS for hope that the Society will adopt a pol­ discrimination is specifically prohibited their principled response to the climate icy of refraining from involvement in by statute or court rulings, so that vic­ of intolerance in Colorado and urge the purely political, social, or moral issues. tims may have a redress to the law. The boards of the two organizations not to My intention is to not renew my mem­ proposed Amendment 2 to the Colorado retreat from their position on meetings bership unless and until such a course is State Constitution would forbid the state in that state. It should also be noted affirmed. legislature, the governor, the courts, and that opinions such as those expressed J. R. Senft every local government within the state by Smith will be firmly and publicly University of Wisconsin to prohibit such discrimination. Amend­ challenged. (Received October 27, 1993) ment 2 can be viewed as the assertion of a triple negation: No law may say Donald Y. Goldberg "no" to those who, because of preju­ Occidental College dice, say "no" to gay men and lesbians (Received October 27, 1993)

Mathematics and Sports L. E. Sadovskii and A. L. Sadovskii

This unique book presents simple mathematical models of various aspects of sports, with applications to sports training and competitions. Requiring only a background in precalculus, it would be suitable as a textbook for courses in mathematical modeling and operations research at the high school or college level. Coaches and those who participate in sports will find it interesting as well. The lively writing style and wide range of topics make this book especially appealing.

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AI! prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: ~!(y'S~ ~ \ (") American Mathematical Society, P.O. Box 5904, Boston MA 02206-5904, or call toll free 800-321-4AMS (321-4267) in the U.S. and

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4 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Cultural Aspects of Mathematics Education Reform

Michael Fellows, Ann Hibner Koblitz, and Neal Koblitz

Our Project Michael Fellows is in the Department of Computer Science at the In order to gain a broad experience in presenting mathematical University of Victoria in Canada; Ann Hibner Koblitz is in the De­ ideas to children, the authors have worked with groups of partment of History at Hartwick College in Oneonta, New York; and children in a variety of settings. These have included: second Neal Koblitz is in the Department of Mathematics at the University to seventh graders from middle-class families in Victoria, of Washington, Seattle. Canada; a diverse group of children and parents in a city park in Victoria; sixth grade classes in Seattle which are In discussions of reform of precollege mathematics education, 70%-80% Black and Hispanic; two seventh grade classes cultural aspects are often overlooked. Here we shall use in rural Washington state; third and fifth grade classes in the word culture in several senses: the culture of different Lima, Peru; an informal group of 7- to 12-year-olds in Cuzco, countries and ethnic communities, American popular culture, patriarchal culture. Our purpose is to stimulate consideration Peru; sixth and seventh graders in two different schools (one of such questions as: private, one public) in San Salvador, El Salvador; a group • To what extent do the currently proposed ideas for math of rural schoolgirls brought together in the provincial city of education reform carry across cultural boundaries (to other San Vicente, El Salvador; a group of 7- to 13-year-olds in countries and to minority communities in the U.S.)? a low-income barrio in San Juan, Puerto Rico; and a class • How might girls' study of science and math be affected by of thirty seventh graders in a poor neighborhood of Harare, education reform? How does the reform of math education Zimbabwe. relate to current discussions of gender and science? The topics we have presented are radically different from • What distortions of the education reform process can occur the usual type of material in school curricula. They have as a result of the peculiarities of American culture? included: Mathematics is arguably the most international and inter­ 1. Finding a minimum weight spanning tree for a graph. cultural of all academic professions. Just as the basic ideas For example, at minimum cost you want to pave enough and techniques of the mathematical sciences can develop in streets of Muddy Town so that one can find a paved any part of the world, so also one would expect that the best route from any vertex (street intersection) to any other methods and materials for teaching math would be ones that vertex. can be readily adapted for use in any cultural context. 2. Finding a minimum dominating set of vertices in a graph. Lately, more mathematicians than ever before have be­ Stories told to motivate this topic concern the problem come interested in precollege education and have started of facilities location. Two examples will be mentioned visiting classrooms in an attempt to improve children's im­ later. Children usually get an intuitive feeling that this pressions of mathematics. One hopes that this activity will problem is harder than the spanning tree problem (in eventually produce far-reaching benefits. However, these con­ fact, it is NP-complete). tacts with the school system have often been limited to the 3. Constructing a graph in which we know a "hidden" relatively privileged schools which the mathematicians' own perfect code that would be very hard for anyone else to children attend or else the advanced tracks and the special find. Such a construction can be used for a type of public programs for selected youngsters. key cryptography that is accessible to children. To broaden one's perspective, it is worthwhile to try out 4. Using Boolean circuits to construct a "long distance coin one's ideas for teaching math to children in nonprivileged flip" protocol. classrooms as well-for example, in the nonadvanced tracks 5. Breaking a Caesar or Vigenere encryption by analyzing of urban public schools. This gives a fairer test of how well the frequency of letters. ideas work, and in some ways it can be especially rewarding. 6. Playing a card game based on generating certain classes These children, after all, are not nearly so accustomed to of prime numbers. It is an unsolved problem of num­ enrichment presentations as are the children in the upper ber theory whether or not the card game can go on tracks and the wealthier schools. indefinitely.

JANUARY 1994, VOLUME 41, NUMBER 1 5 ····~···· .. ·-----·-··-.. ·.. -···--··--"-"~ ...... ~ .. ~ ...... -...... ~·····-···"""""~"-""""""""""""• ... ·-·· ... ~·-.. -·-·-···-·•""•"""""""""" ...... ~~~-·Qj )ji&QJJ;..-j;~~-.. -·-·-·-.. ···-...... Math Education Reform

7. Using the different types of averages (mean, median, teaching, and alternative assessment methods, are beginning mode). When are they nearly the same, and when do to change the face of math education in the U.S. they give very different impressions of the data? This change is welcome and overdue. However, some of After posing a problem such as Muddy Town, we typically these efforts have gone astray because of certain political find that the classroom explodes with activity, and there is pressures and the peculiarities of American popular culture. a tremendous range of response. The children's immediate In the first place, in order to make a good impression on objective is to find the best possible solution. After a child has a the funding agencies, coordinators of pilot projects must solution, her or his name is posted on the blackboard along with demonstrate rapid success. This creates pressure to set one's the cost of the solution. Students are asked to describe their sights very low and present material that the students will strategies and ideas. Some are able to discover a systematic almost certainly find easy. As a result, many of the units procedure (perhaps a variant of Kruskal's algorithm) and can that have been developed are conceptually trivial and are offer arguments supporting it. One fascinating aspect of the not challenging for the target grade level. For instance, in classroom experience has been the reports of the teachers the otherwise excellent booklet Assessment Alternatives in that their expectations concerning student performance are Mathematics, we found that most of the concrete examples often turned topsy-turvy; the children who do well on these have too little mathematical content for the intended age problems are not always those who have done well at the group. Interestingly, the booklet's only illustrative problems usual arithmetic drill. that contain challenging mathematics were taken from the There is something in these problems for the whole Shell Centre for Mathematical Education in Great Britain, range of students, from the slowest to the brightest. Some where educational standards have not yet fallen to American students only manage to understand the mechanics of finding levels. a correct solution. Others make progress toward an algorithm The anti-intellectual nature of U.S. popular culture is well for obtaining an optimal solution. The most inventive students known. Children are accustomed to rapid-fire visual imagery, want to design their own Muddy Towns and to ask further passive entertainment, and instant gratification. The schools questions, for example: How can one determine if a given then have an uphill struggle if they want to teach intellectual solution can be improved upon? What is the minimum number discipline, delayed gratification, problem-solving techniques of streets paved in an optimal solution? How many different to handle difficult challenges, and the non-oral forms of optimal solutions can there be? communication (reading and writing). Unfortunately, there is These topics are fun and exciting for the students. Once, no easy way out of this dilemma. But it would be a tragic after we presented some of the topics to a 5th grade class in mistake to throw in the towel, stripping science and math of Peru, the students insisted on continuing through the recess their content in order to make education easy and entertaining. period despite the appeals of the school's headmaster telling There is a real danger in the level of hype in the education them it was time to go. The teacher observers later commented reform movement. An extreme example of this tendency is to us that they were astounded to see youngsters refusing to the public television program "Square One". Listening to the leave math class to go to recess! songs about math, seeing the animation and special effects, Beyond their entertainment and motivational value, the and watching the guessing games, one might not notice that the topics listed above provide an excellent vehicle for imple­ program has virtually no mathematical content. Moreover, the menting the NCTM standards, which place an emphasis on program gives a misleading impression of what mathematics problem-solving, communication of mathematical ideas, and is and how it is used. real applications. Because of their intrinsic interest, problems such as these tend to elicit sustained periods of concentration. Computermania Besides providing opportunities for children to practice "the American youngsters-and, in fact, most teachers and ed­ basics", they lead naturally to discussions of sophisticated ucation reformers as well-have grown up in a culture and challenging ideas of contemporary mathematics and com­ that emphasizes gimmickry, easy technological fixes, and puter science (complexity of algorithms, one-way functions, 15-second sound bites on TV. In addition, the computer interactive protocols, prime number generation, interpretation industry-one of the few industries in which the U.S. is the of statistics). They convey some of the spirit and excitement undisputed leader-has a vested interest in promoting the of mathematics as it is known by those who do mathematical adoption of technology in the schoolroom. science. Amidst all the hype about computers in the classroom, few have stopped to consider certain basic questions. Do the results justify the vast amounts of resources-money, The Influence of U.S. Culture time, and human energy-that have been invested? Are other The educational reform movement has taken a strong stance needs (school libraries, released time for teachers, low-tech against the traditional characterizations of math as difficult, forms of math enrichment) being neglected? Students have a dreary, and accessible only to a small number of people. common perception of mathematics as something formalistic Slogans such as "math for everyone", "math for girls", "math and mechanical. Won't computers make matters worse? for the family", and "math is fun", along with new concepts Of course, it is reasonable to think that there might be some of cooperative learning, integrated (i.e., interdisciplinary) appropriate uses for computers-just as earlier for television

6 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··:::-:J ...... Math Education Reform and movies-in the classroom. But from our observations it (Muddy Town) by a story about deciding which streets to plow seems that most of the time computers serve as little more after a snowstorm. The first author has found that Canadian than an expensive distraction. They foster a Golly-Gee-Whiz youngsters relate especially well to the Snowy Town story. attitude that sees science and math as a magical black box, In our zeal to replace dreary traditional math with en­ rather than as an area of critical thinking. That is, fetishizing tertaining practical examples, we can easily let our own computers serves to reinforce the fascination with gadgetry background and biases affect the problems selected. As a (as opposed to intellect) that is endemic in American popular result, children with different backgrounds have difficulty culture. comprehending and relating to the unfamiliar material. From what we have seen, most educational software is Sometimes people who have the best intentions are guilty based on immediate gratification and very little creativity. of this. For example, the Interactive Mathematics Project Generally, the pupil is programmed to follow a path already (IMP)-supported by the NSF and a consortium of Bay laid out in detail by others. The child is physically active Area educational institutions-has developed fifteen units for but intellectually passive. The computer controls the student, eventual use in California high schools. Of these units, four rather than vice-versa. It seems to us that what children appear to be flawed because of cultural biases: need in order to become mathematically literate citizens in 1. Pennant Fever. "The Good Guys have a three-game lead the computer age is not early exposure to manipulating a over the Bad Guys for the baseball pennant . . . . The keyboard but, rather, wide-ranging experience working in a central problem of the unit is to find the probability that creative and exciting way with algorithms, problem-solving the Good Guys will win the pennant." techniques, and logical modes of thought. This baseball setting is designed to motivate the study Finally, the notion that computers must be at the heart of of probabilities. But clearly boys are more likely than educational reform necessarily implies that most people in girls to be inspired by this example. the world are excluded from the reform. The vast majority of 2. The Overland Trail. "This unit looks at the western schools do not have anything like the resources that would be migration of the 1840s and 1850s in terms of the many needed to incorporate computers into classroom learning. linear relationships involved. These relationships grow out of the study of planning what to take on the 2400- Cultural Appropriateness mile trek, estimating the cost of the move, studying rates When designing problems that relate to real life, it is easy, of consumption and of travel, and estimating the time to despite our good intentions, to be insensitive to cultural reach the final goal." differences. For example, the first author initially constructed The perspective is that of the white colonists. Would a story about "Tourist Town" in order to present the minimum Native American and Chicano children, many of whose dominating set problem of graph theory to children in the ancestors were displaced or killed in the conquest of U.S. and Canada. The merchants of Tourist Town (of which North America, identify with this point of view? a map has been passed out to the class) are preparing for the 3. The Dawning of the Age of Aquarius. "This unit uses a summer season. They decide to construct ice cream stands on question based on astronomy as a way of having students some of the street comers. What is the minimum number of feel a need for using scientific notation . . . . The sixties ice cream stands they'll have to build so that anyone standing song 'Aquarius' talks about 'the Age of Aquarius' as an at a street comer without an ice cream stand will have to walk era of harmony and liberation, and students are asked to only one block to find one? consider the question of when, astonomically speaking, But when the three of us tried this in Peru, we quickly this age should actually begin." realized that this story made little sense to the children. The The song "Aquarius" might motivate mathematics reason is that, in the first place, ice cream sellers use movable for the offspring of a certain number of Californians of carts, not fixed stands. Moreover, in any country with large the generation of the 1960s. But this would include very unemployment, where much of the population depends on the few children from the large Black, Hispanic, or Asian so-called "informal economy" for their livelihood, there is communities of the state. Nor would most rural and always an overabundance of people available to sell ice cream blue-collar white children feel included. to tourists. The children saw no purpose in trying to minimize 4. Leave Room for Me! "This unit opens with a table the number of ice cream vendors. of world population data over the last thousand years So we changed the setting for the dominating set problem, and asks the following rather facetious question: 'If presenting it by means of a story about minimizing the number population growth continues to follow this pattern, how of wells in order to achieve an efficient water supply for a long will it be until people are squashed up against each village or barrio. In most Third World contexts such a story other?' ... [students] discover that exponential functions is more appropriate than the one about ice cream stands, and have the special property that their derivative is pro­ it has led to a more enthusiastic response both by the children portional to the value of the function and see that ... an and the teacher observers. exponential function is a reasonable choice to use to Similarly, when working with children in the industrialized approximate their population data." countries of the northern latitudes, one might want to replace Of course, the exponential model is extremely dubi­ the street-paving story for minimum weight spanning trees ous for human populations. But more importantly, the

JANUARY 1994, VOLUME 41, NUMBER 1 7 Math Education Refonn

point of view of this unit suggests a certain political Turkle here is propagating a fundamental misconception judgment that is popular in the U.S. and Europe: that of mathematical and scientific thought processes in that she population growth must somehow be decreased among divorces the artistic and creative elements from the rigor and the fastest growing segments of the world's people and intellectual discipline. What Turkle dichotomizes as "hard" that otherwise these people will overrun us. At its worst, versus "soft" mastery are actually two necessary components the alarmism implicit in the cry "Leave room for me!" of innovative thinking in science. The attempt to categorize leads to racist paranoia. In any case, none of the IMP people as being one or the other therefore misses a crucial units provide alternative, less elitist viewpoints-for ex­ point and reinforces certain sexist stereotypes and notions of ample, that the more fundamental causes of the world's gender polarity which are already far too powerful in our problems are the extreme inequities in distribution of culture. wealth and in consumption. Turkle herself inserts some caveats in her generalizations. We wish to reiterate that the Interactive Math Project But what has usually been picked up by the media is may very well be making important positive contributions to the rather simplistic idea that girls cannot be attracted to the curriculum. Cultural insensitivity can be a problem even the computer-or to anything math-related-unless it can be among the most experienced and well-intentioned people. portrayed as artistic, relational, and "soft", and unless it has been purged of everything complex, systematic, and mathe­ Gender Questions matically challenging. Unfortunately, too often the result is Given the different socialization of girls and boys in the pedagogical material that is scientifically and mathematically U.S., it seems clear why traditional methods of teaching trivial. mathematics would yield better results with boys than with One of the most common manifestations of sexism and girls. When taught in a formalistic, mechanical manner-as racism in the classroom is a refusal to intellectually challenge something boring and lifeless-math can be perceived as girls and members of minority groups. They are condescended akin to a fraternity _hazing. That is, the student might view to and patronized, and do not receive adequate exposure to the math class as an unpleasant and pointless ritual that one must more rigorous and thought-provoking aspects of mathematics. go through in order to join an elite of successful people. Their understanding thus rarely attains the level of the Under those circumstances it is outside pressure and societal systematic and the structural; they seldom arrive at the stage expectations that determine who is likely to do well. where they can see much point in doing mathematics. Boys might be more willing to put up with the torment In our experience, though, once young women have of poorly taught math courses because they have confidence become intrigued by a problem, they relate well to all aspects that eventually they will be rewarded by society. Girls, on the of mathematical creativity-the formal and systematic as well other hand, tend to have fewer role models, fewer external as the intuitive. For example, as often as not, the optimal incentives to do well at math, and more peer pressure not to do solutions to the discrete math problems we have presented­ well. For instance, it is more common for parents to tell their and rigorous arguments to support these solutions-are offered sons that they must get good grades in math so as to become first by girls. This is in spite of the fact that the boys tend engineers like their fathers than to tell their daughters that to push themselves forward more and tend to receive more they must get good grades in math so as to become engineers encouragement for this aggressive behavior from their teachers like their mothers. (and often from the girls themselves). Because of the different pressures on girls in our society, they are unlikely to become interested in mathematics unless Conclusion it is intrinsically motivated-in other words, unless it is taught In the course of our travels we have been struck by the in an absorbing, lively, thought-provoking manner. While extent to which the crisis in math education is international. obviously all students can benefit from reform of mathematics Educational reform is a topic that is likely to provoke intense education, there can be particular gains for girls. interest and animated debate in a mathematical gathering At the same time, there are also special pitfalls against almost anywhere in the world. Invariably, in our meetings which reformers, we believe, have not been sufficiently with math educators we are asked to share any materials vigilant. One of these pitfalls relates to the use of computers that we have. Consequently, when we in. the U.S. develop and the notions of so-called "soft" and "hard" mastery, made new curricular material, we should adopt a multicultural popular by Sherry Turkle in her book The Second Self perspective and be sensitive to the diversity of people who For Turkle, "hard mastery is the imposition of will over may want to use it. the machine through the implementation of a plan ... the hard We need to resist the pressures of fads and hype and be masters tend to see the world as something to be brought aware of the inevitable tension that exists between American under control." Soft mastery, on the other hand, is more popular culture and the study of mathematics. We should not interactive-"the soft masters are more likely to see the world let those who have money-the foundations and government as something they need to accommodate to, something beyond agencies, the computer companies and textbook publishers­ their direct control." Though Turkle gives examples of soft dictate the agenda for reform. The math education reform masters of both sexes, she says, "Girls tend to be soft masters, movement should be open to input from many sources: while the hard masters are overn;helmingly male." educators who do not have foundation support as well as those

8 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Math Education Reform

who do, laypeople as well as professionals, people from the 4. N. Koblitz, The profit motive: the bane of mathematics education, impoverished schools and universities of the Third World as Humanistic Mathematics Network Journal, no. 7 (1992). 89-92. well as those from the centers of prestige and power in the 5. J. Kozol, Savage inequalities: Children in America's schools, Crown Publishers, 1991. u.s. 6. National Council of Teachers of Mathematics, Curriculum and evaluation standards for school mathematics, 1989. References 7. National Council of Teachers of Mathematics, Professional stan­ 1. M. R. Fellows and N. Koblitz, Combinatorially based Cl)ptog­ dards for teaching mathematics, 1991. raphy for children (and adults), to appear in Proc. 24th Southeastern 8. M. B. Ruskai, "Dear Colleague" Letter, Newsletter of the Asso­ Intern. Conf. Combinatorics, Graph Theory and Computing. (Boca Ra­ ciation for Women in Mathematics, 16, no. 3 (1986). ton, Florida, February 1993). 9. J. K. Stenmark, ed., Assessment altematives in mathematics: an 2. Interactive Mathematics Project, Information about IMP: A brief oven·iew of assessment techniques that promote teaming. University of description of the first, second, and third year's curriculum, preprint. California Regents, 1989. 3. A. H. Koblitz, A historian looks at gender and science, Intern. J. 10. S. Turkle, The second self: computers and the human spirit, Science Education 9 (1987), 399-407. Simon and Schuster, 1984.

HISTORY OF MATHEMATICS Golden Years of Moscow Mathematics Smilka Zdravkovska and Peter L. Duren, Editors Volume 6

This volume contains articles on Soviet mathematical history, many of which are personal accounts by mathematicians who witnessed and contributed to the turbulent years of Moscow mathematics. In today's climate of glasnost, the stories can be told freely for the first time, with a candor uncharacteristic of the "historical" accounts published under the Soviet regime. The articles focus on mathematical developments in that era. the personal lives of Russian mathematicians, and political events that shaped the course of scientific work in the Soviet Union. An important feature is the inclusion of two articles on Kolrnogorov, perhaps the greatest Russian mathematician of the twentieth century. The volume concludes with an annotated English bibliography and a Russian bibliography for further reading. This book appeals to mathematicians, historians, and anyone else interested in Soviet mathematical history. The History of Mathematics series is published jointly with the London Mathematical Society (LMS).*

1991 Mathematics Subject Classification: 01 ISBN 0-8218-9003-4, 269 pages (hardcover), October 1993 Individual member $56, List price $94. Institutional member $75 To order, please specify HMATH/6NA

* Members of the LMS are entitled to member prices. The LMS is incorporated under Royal Charter and is registered by the Charity Commissioners.

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

JANUARY 1994, VOLUME 41, NUMBER 1 9 Forum

or showing, a la Babai, that certain statements are "probably true"? The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between 1000 and In the uproar that has followed hard upon the Scientific 2500 words long. Readers are invited to submit articles for possible American article, it has been pretty well established that the inclusion in Forum to: theme of the article is a figment of the author's imagination. Notice$ Forum Editor Nobody can find a mathematician who is willing to state in American Mathematical Society public that the proof is dead (anyone care to volunteer?). P.O. Box 6248 Evidently John Horgan (the author) only partially understood Providence, Rl 02940 his interviews with a number of mathematicians. He fashioned or electronically to notices@math. ams. org a chimera! picture of what he thought he heard, weaving pieces of various interviews into a bizarre tapestry with no basis in reality. No matter what the genesis of the article that actually appeared in print, I think that the ideas presented there are The Immortality of Proof dangerous-dangerous to you, to me, and to our profession Steven G. Krantz and our subject. A number of good people have stood up and Washington University formulated their own answers to the article. This is mine. This is a response to the cover story, "The Death of Proof," in Here is the truth: Andrew Wiles's proof of the Fermat theorem is not an "anachronism", as the article asserts. It is a the October 1993 issue of Scientific American. More generally, it is a commentary on the circle of ideas touched on in that triumph of the human intellect. Understanding it is not beyond article. our collective ken, as the article suggests. Gauss claimed to The article suggests that the fashion of mathematicians have been the first to discover non-Euclidean geometry. He stating theorems and proving them is passe. Various reasons did not publish because he did not think that anyone would have been offered for this transition: that mathematics has understand what he was talking about. By contrast, students become so complicated that most mathematicians cannot un­ today learn about non-Euclidean geometry in high school. derstand other mathematicians' proofs; moreover, the proofs New ideas take time to become part of the infrastructure. are too long and complicated. Wiles's proof of Fermat's Last All over the world, in hundreds of seminars, people will Theorem is 200 pages; it would be 1000 pages if all the go through Wiles's proof of Fermat's Last Theorem. It will details were provided. W. Y. Hsiang's resolution of Kepler's finally be validated, or it will not. A good role model here is sphere-packing problem is still, after three or more years, Louis de Branges's book on Hilbert spaces of holomorphic in doubt. (In fact some experts have told me recently that functions, which (purportedly) gave a proof of the Bieberbach they believe Hsiang's proof to be incorrect-but at least these conjecture. After a lot of thought and analysis by many experts understood the material that Hsiang offers as a proof!) mathematicians, there is now a two-page proof by Lenard This time delay is also offered as tribute to the idea that things Weinstein-based on de Branges's ideas, to be sure, but are so complicated that we don't know what we are doing. involving little more than calculus. Lennart Carleson's proof Some have suggested that the logical foundations of of the Lusin conjecture was also quite obscure. But, after a mathematics are little more than a polite agreement. They time, a great deal of study by many mathematicians, and an are riddled with inconsistencies that are virtually insoluble. independent proof by Charles Fefferman, we now know that it This is offered, it seems, as evidence that those dinosaurs is correct. That proofs evolve and are validated in this way is (such as myself) who cling to mathematical tradition are being a tribute to the robustness of mathematics and to the process unreasonably stodgy. After all, what is the sense of defending of mathematics. It is quite likely, if Wiles's proof is right, that something that isn't quite right? Why not allow that there simplified proofs of Fermat's theorem will evolve. are other ways to do mathematics besides proving theorems? It is worth developing this last idea. Mathematics is not Can we not establish truths by analyzing computer graphics simply an endeavor carried out by certain individuals or small

10 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum groups. It is in fact a process. Certain "point men" often come nor Egorov's work on canonical transformations. Computers up with the final step-the proof-of a great theorem, but were used in one of the technical steps of de Branges's proof a close analysis shows the workings of the infrastructure to of the Bieberbach conjecture, but it is ludicrous to think of generate many of the ideas in the proof and to validate it de Brangcs using the computer to generate power series of afterward. This is part of what is so beautiful about the way various Schlicht functions and staring at the coefficients to get that mathematics works-one person puts the final words on ideas. paper, but the entire community carries the ball (and makes It is my understanding that the movie Not Knot has sure that the ball has air in it). been used to great effect in getting high school students It is true that Hsiang's proof is still in doubt. This is because excited about mathematics. Many of those students have very few people have read it or thought hard about it. In the gone on to become math majors and then on to careers in three hundred-odd years since the problem was formulated, mathematics. Any device that will generate talented American mathematics has evolved and dispersed in many directions. mathematicians, that will draw students back to math from Until recently sphere packing has not been considered to business school, law school, computer science, and so forth is be a central issue. (The recent book of Conway and Sloan a godsend. But let us not, in our enthusiasm (with a pied piper will probably change that.) But the purported solution of the like John Horgan), trick ourselves into thinking that the movie Kepler problem is just not the sort of problem-today-that is a "computer proof" of anything. The movie Not Knot is a will make mathematicians drop what they are doing to read device for popularizing mathematics, something that needs to the 150-page solution. Eventually we will know whether be done a lot more in this country. Most Americans are not Hsiang is right, but most of us have had our attention diverted even aware that there is a profession called "mathematician". elsewhere. There is nobody to blame for this but ourselves. Finally, about the foundations of mathematics: everyone In many respects this is a golden age for mathematics­ knows about Russell's paradox and the problems with con­ and I mean classical, rigorous mathematics done in the structing the integers. But logicians have determined how to traditional way. There are fantastic collaborations taking place deal with these things. Morris Kline to the contrary, math­ between geometers and PDE people, between geometers and ematics is not built on a foundation of sand. There is no physicists, between geometers and analysts (to name just a area of human inquiry that is more robust or more solid than few). The rate at which enormous breakthroughs are being mathematics. One of the reasons that mathematics is oflasting made is incredible. Yet the mathematics that often grabs the value is that it is logically consistent. New generations do not headlines is some new form of computer graphics. This is shoot down old mathematics in favor of the new. For good understandable, for the public is much more ready to consume mathematicians to claim otherwise is counterproductive and computer graphics than pseudodifferential operators. irresponsible. Yet this puts the onus on us, the dinosaurs, to figure out how Another point of view worth considering is this: while to get the public to appreciate what we are up to. Don't forget the foundations of mathematics are interesting and important, that "the public" includes (1) potential graduate students, (2) they have little to do with the everyday workings of mathemat­ senators and congressmen, and (3) the American voters. Also, ics. Waving Godel's incompleteness theorem and Russell's program officers at the National Science Foundation (NSF) paradox in my face is not going to stop me from thinking about and other agencies read Scientific American. I wouldn't doubt complex analysis, and it should not stop you from thinking that their ideas about funding are influenced in part by what about geometric topology or whatever your chosen field may they read. If you work in a field, such as I do, that does not be. The Hilbert/Bourbaki view of mathematics as growing lend itself to computer graphics in any obvious way, then you logically from solid foundations is a bit like Newton's view should think about how to let your graduate students, your of physics: philosophically sound, but not the whole picture. undergraduates, and (if possible) a broader base of people One of the themes of the Scientific American article is that know what it is that you do and why it is worthwhile. proofs will soon be replaced by computer experimentation. Doing mathematics is hard. Programming computers (at Invoking recent ideas of Babai, it is suggested that computers least at the level of creating videos of a theorem that some can suggest to us that assertions are "probably true". Computer smart guy proved ten years ago) is relatively easy. While the graphics can show us things that we cannot see unaided. It latter can be important in popularizing and communicating our is important to sort out here the differences among computer subject, I hope that we will not commit the same error as John simulation, graphical experimentation, numerical experimen­ Horgan and think that it is the same as doing mathematics. tation, "computer proof'' (whatever that is), and the use of Looking at this in a different way, let me point out that doing computers to graphically illustrate the meaning of a theorem graphic or numerical experimentation to generate ideas for a that has already been proved by classical means (such as the proof or to provide enough examples to give one the courage computer graphics movie Not Knot). Let me point out that to go on is a valuable exercise. But it is not a goal in itself. It computer experiments could never have informed Yau's proof has no intrinsic value. of the Calabi conjecture, nor the Calder6n-Zygmund theorem At the risk of beating a dead horse, let me observe that about singular integrals, nor the work of Nirenbergffreves and dynamical systems is a vital, well-rooted, vigorous area of Beals/Fefferman on local solvability of PDE's, nor the work modem mathematics. Drawing pictures of fractals, giving of Kohn on the inhomogeneous Cauchy-Riemann equations, them names like "XP-43", and printing them on picture

JANUARY 1994, VOLUME 41, NUMBER 1 11 Forum postcards that sell for $1 a throw is not. areas that can be informed by computer experiment (and also I was quoted in the Scientific American article to the more visceral experiment-like dipping wire frames into soap effect that mathematicians are a bunch of "spineless slobs", solution). Mter they have done their experimentation, they unwilling to stand up and defend their subject. I regret this. I then prove theorems. That way we know what is true. One don't recall making the statement; in fact it is not expressed in of the triumphs of mathematics is that it transcends anecdotal my usual argot. But it is up to us to define what our subject is information. The traditional definition of theorem is something and to defend it. If I had in fact made this statement, I would like this: "the establishing of immutable quantitative or now have to withdraw it; I have been pleased to see the great geometric truths by means of tried and exact reasoning". numbers of mathematicians responding to Horgan in defense To replace this definition with "the offering of uninformed of what we do. I'd like to think of Horgan's misquotation of speculation after staring at computer graphics" would be both me as a catalyst. Now let's consider it used up and dead. wrong headed and tragic. Tragic because it abrogates, without As the Scientific American article reported, high school careful thought, everything that we've learned in the last teachers in Berkeley are now minimizing proofs in Euclidean 3000 years. Wrong headed because the value of traditional geometry. One argument in support of this change is that a mathematics is well established while the value of the new computer can quickly test 5000 cases of an assertion so that stuff is not. proofs are no longer necessary. Well meaning though these To use the work of Hoffman and Taylor to justify changes may be (the teachers may have in mind students from discarding proofs and replacing them with "probable proofs" disadvantaged backgrounds or students who have watched too and "graphical analysis" is like using the work of John much television and are permanently in the passive mode), Stuart Mill to justify anarchy. William Jennings Bryan was they fly in the face of fundamental mathematical values. The a great public speaker and so was Adolph Hitler. Therefore article itself claims that students no longer appreciate the what? Again, the Scientific American article is using classical value of proofs. So we have to find another way to teach them. propagandistic techniques, such as confusing the converse Students do not appreciate the value of reading unless with the contrapositive, to support the case that mathematical they are taught. They do not appreciate the value of good proof is being replaced with computer experiment. We all music unless they are taught. (Is anyone advocating that we know that this is fallacious but will the readership of Scientific replace Beethoven's Fifth Symphony by "da da da dum" and American know this? a video because it is too complicated?) And students will not I have used computer algebra to inform calculations appreciate the value and importance of mathematical thinking that had become too complicated to handle by hand. I unless they are taught. It is our job to teach them, not to bend imagine that someday I will use graphics to help me to see like reeds in the breeze. We should work with high school something that I cannot see in my mind or with a pencil teachers to inculcate strong intellectual values in students, not and paper. I advocate strongly that other traditionally trained to pander to their uninformed whimsy. I fear that the low mathematicians consider becoming conversant with these new salaries and lack of respect that high school teachers find tools. But the tools are not an end in themselves. Drawing a to be their lot these days has given us a group of not very picture of a simply connected domain in the plane is not the well trained high school teachers who are uncomfortable with same as proving the Riemann mapping theorem (RMT), even proofs in Euclidean geometry. I recently asked a group of high if it is a computer that drew the picture. I've been thinking school teachers in my city how they treat Euclidean geometry about the RMT for over twenty years, and I've never used in school, and they didn't know what Euclidean geometry any kind of picture to aid my thoughts. Thurston, Rodin, and was. Sullivan have given us interesting new ways to think about the Another interesting aspect of life is that bureaucracies like RMT that are very geometrical and do lend themselves to nice hardware. When parents come to a university to get an impres­ computer pictures. But the pictures do not prove anything. sion of whether they should send little Sally there for her four And let us not misunderstand each other: pictures are formative years, the leading lights in the administration do valuable. They are particularly valuable in communicating not trot out their rather shabby-looking Nobel Laureates and mathematical ideas, but they are also valuable when you Fields Medalists. Instead, they show off their genetic engi­ are in private, trying to solve a problem. The availability of neering labs and supercomputer centers. Likewise, taxpayers wonderful graphics software now makes drawing complex understand money that is spent to buy PCs and software. They pictures easy and offers us an exciting new tool. But if Gauss, do not understand money that is spent to increase teachers' smart as he was, had had a computer available to him, it would salaries so that we can get better teachers. Remember that not have enabled him to prove the Riemann mapping theorem we, the mathematicians in this country, are the caretakers of years before Riemann. mathematical knowledge. It's not the books, and it's not the I hope that other mathematicians will discuss these matters software; it's us. It is up to us to define what mathematics is and perhaps disagree strongly with what I say. The wolves are and to defend it. Now that NSF grants are going the way of in our midst, and it is time for us to decide what we believe the dodo, maybe we will have more time to do so. and what we value. One of the upshots of the discussions I am happy that the work of Jean Taylor and of David that have taken place since the Scientific American article Hoffman and his group were given prominent mention in the appeared is that it seems unlikely that many of the wolves are article in Scientific American. These scientists are working in mathematicians. But the wolves are still a danger. They have

12 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ·················-·- ...... ·-··-··-·--·---·-·---·····-···· -··--·-·- ...... ~·:::··,: ;;·· ...... ······-··-··-·· .... -··. ,...... ------~·-···· .\...... :...•. :"'--'-··---·-···--~---·-·--·-·---·~·-···-·-·'-· Forum influence in the media and influence with funding agencies. will have abandoned proofs and will be letting computers tell We must be aware of the dangers that lie outside our cloister. us what is probably true. But in ten or fifteen years it will be It may or may not be true that in ten or fifteen years we too late to decide what we want. We have to decide today.

TOPOLOGICAL METHODS IN NONUNEAR ANALYSIS Kazimierz G~ba, Lech G6rniewicz, and Andrzej Granas, Editors

This new international journal is published Editorial Committee quarterly by the Juliusz Schauder Center for Nonlinear Studies of the Nicolas Copernicus University in Torun, Poland. It contains T. B. Benjamin 0. Ladyzhenskaja high-quality research papers on a wide range H. Brezis M. Lassonde of topics in nonlinear analysis. Alongside the M. Burnat J. Leray central classical subjects of nonlinear PDEs A. Dold A. Marino ~- and ODEs, specific areas include (among • others) the following: S. Eilenberg J.Mawhin • Nonlinear problems offluid and gas E.Fadell L. Nirenberg dynamics; KyFan C. Olech *Topological Methods in • Global solutions of evolution equations; Nonlinear Analysis is a • Qualitative properties of solutions of Boju Jiang S. Takahashi elliptic equations; promising young journal • Nonlinear problems arising in liquid * * * with a very distinguished crystals; Sobolev maps editorial board. In order to • Topological and variational methods in encourage circulation, presence of symmetries; ISSN 1230-3429 we're making a special of­ • Hamiltonian systems; Conley index Individual $100; List Price $200 • Topics in equivariant topology related to fer to new subscribers. If To order, please specify: 94TMNA/NA nonlinear problems. you subscribe for 1994 be­ foreMay31, 1994,youwill With the current-day interest in nonlinear science, this journal makes an important addition to individual and institutional libraries. TMNA is distributed worldwide by the American also get the 1993 subscrip­ Mathematical Society. tion year free! Discounts for libraries in developing countries are possible; to see if you are eligible, write to: Editorial Office of the TMNA, Juliusz Schauder Center, ul. Chopina 12/18, 87-100 Torun, Poland. Internet: [email protected]; FAX number 48 56 28979 $1:REMA7'.t.

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JANUARY 1994, VOLUME 41, NUMBER 1 13 Computers and Mathematics

Edited by Keith Devlin

This month's column taken verbatim in connection with AXIOM. Some of the new Three software reviews make up the first column of 1994. First, Larry things are a user interface that rivals anything that can be Lambe looks at AXIOM. Then, Suzanne Molnar reports her experiences found in the market these days, a flexible graphics interface with the Student Edition of Object Logo. Finally, Jim Northrup reviews that can provide both insight and enjoyment, and a new book Fields&Operators. All three reviewers have contributed to the column in the past, and [JS] that covers the system quite nicely. it is good to see them back. But I am always on the lookout for new Specifically, AXIOM is a "mathematically object-oriented" reviewers. In particular, my list of volunteers willing to review Macintosh environment consisting of five major components and a sixth software is starting to run down. If you use a Macintosh and would like that is under development and soon to be released. They are to make your own contribution to the column, please send me a message 1. an interactive computational environment, at the address below (e-mail or snail-mail), mentioning any particular 2. a "hypertext" interactive documentation system that is preferences as to the kind of software you would like to review. user programmable, Editor's address: 3. a graphics package that manipulates and displays objects Professor Keith Devlin in two and three dimensions, School of Science 4. an object-oriented language, Saint Mary's College of California 5. an extensive mathematical library compiled into ma­ P.O. Box 3517 chine code for efficiency with complete access to the Moraga, California 94575 source code for all users, and Correspondence by electronic mail is preferred, to: 6. a link to external libraries written in other languages. The thrust of the 1989 article was the object-oriented [email protected]. nature of the system and, in particular, its inclination towards mathematics. This is an important and distinguishing feature of AXIOM. Issues such as "code reusability" have been around in computer science for some thirty years. The notion Reviews of Mathematical Software of parameterized types in the formal theory of computer languages goes back quite a way as well. These days more and more of such concepts are finding their way into other areas of science that use computer aids. We are still in a time when there are different terminologies AXIOM System in use for exactly the same concepts in dlfferent object­ Reviewed by Larry Lambe* oriented languages. Because of this, it will be useful to set up a dictionary, through the use of analogy, to define some terms. I'm pretty sure that you've all heard phrases like "object­ A little more than four years ago, I wrote about "Scratchpad oriented thinking" from other sources. I will not attempt a II as a tool for mathematical research" in this column [Ll]. definition here, but since I am addressing mathematicians, Scratchpad has grown into what is now called the AXIOM I can safely say that you should be familiar with it, since system, and there is a lot to say about this evolution. I think most of you do it. In object-oriented programming, however, of it more as a maturation, although neither term is quite right there are also some important ideas needed that fall outside for what has happened. In fact, as you will see, my original of traditional mathematical experience. The best way to remarks about the mathematical nature of Scratchpad can be proceed is to think about the foundations for some of the usual structures we encounter in mathematics, for example, *Larry Lambe is at Rutgers University in New Jersey. He can be reached polynomials. by e-mail at: llambe

14 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ~ ...... ,...... ·-·~-~ ...... ' ·············-··-··-' ········-·····::::.. ~...... Computers and Mathematics trouble in realizing a functor such as "FreeModule", whose None of the major computer algebra systems today have parameters (arguments) are a ring Rand a set X and whose parameterized types built into the language except AXIOM. value is a module over R, as a concrete object. On the other hand, all of the major computer algebra systems Given the functor above, we can easily define all sorts have some form of dynamic allocation and automatic garbage of mathematical structures. For example, if we are given a collection built in. It is fair to say that these latter concepts monoid M, i.e., a set M with a binary operation *: MxM---+M are what make symbolic computation systems so attractive to which is associative and has an identity element, we can form most researchers. Without them a user is not free to spend all the monoid ring of Mover a ring R by defining an operation on of his time concentrating on mathematical concepts. Instead, FreeModule (R, M) as follows. First define a function he or she must, for example, constantly make sure that there Mx M---+ FreeModule (R, M) is enough memory available for a process which may be growing in a way that is not measurable before execution and by simply "coextending" the given operation on M. Now also come up with some scheme for reclaiming memory that extend this function bilinearly to has been used, but which will not be used again unless steps are taken to make it so. Let me now go on to say some specific FreeModule(R,M)xFreeModule(R,M)---+FreeModule(R,M). things about the six components of the AXIOM system given This gives a mathematical structure which we will denote above. by MonoidRing(R,M). Let's agree to call these functors First, there is the interactive environment. Among com­ "constructors" to emphasize the point that they produce new puter algebra systems, AXIOM is unique in the way that it mathematical objects out of collections of others. It is now dynamically builds datatypes based on user input. If you easy to see that we can get an object isomorphic to the enter x * *2 + 1/3, it will build polynomials with rational usual polynomial ring in one indeterminant over a ring R by coefficients. If you enter x * *2 + 0.333 * %i, it will create simply forming MonoidRing (R, IN), where IN is the monoid polynomials with complex coefficients. Type inferencing also of natural numbers with addition. If we agree to write a linear applies to function definitions. You can define a function f by combination rt n1 + · · · + rknk where ri E R and ni E IN f(x) == x * *2. Iff is applied to an integer, the type off is as r 1tnr + · · · + rktnk, we obtain the usual representation of chosen to be Integer---+ integer. Iff is applied to a rational polynomials as well. function such as 1/(x + 1), the type off is chosen to be It might surprise you to find out that the polynomial ring in one indeterminant over an arbitrary ring R may be Fraction Polynomial Integer ---+ Fraction Polynomial defined in AXIOM in exactly the above way. Furthermore, Integer, there are facilities for providing a wide range of display forms etc. automatically (so elements of MonoidRing (R, IN) can indeed be made to display as polynomials in "t"). Occasionally, type declarations are necessary. AXIOM Two important components of object-oriented paradigms provides for that. For example, to declare x to be a polynomial are encapsulation and inheritance. In AXIOM, an abstract with integer coefficients you may use the syntax x: POLY INT. datatype has the properties of encapsulation (private and In fact, all of the choices AXIOM makes can be made instead public parts, etc.). Datatypes in AXIOM are typically param­ by the user, if desired. eterized and represent mathematical structures. An important The hypertext facility is called "HyperDoc~· in AXIOM. consequence of the object-oriented paradigm (in the above A sequence of windows is displayed on the next page. sense) is polymorphism, i.e., objects (programs and mathe­ The windows should be read from left to right and top to matical structures) can be reused in a variety of contexts. bottom. Beginning with the "HyperDoc" window, the next The abstract type FreeModule (R, X) is parameterized by the window was obtained by clicking on "Basic Commands". abstract types Ring (the R parameter) and Set (the X parame­ The "Series" field was clicked on to give the third window, ter). Furthermore, note that the addition in Monoid.Ring(R,M) "Series Basic Command", and in that window the choice for comes from its "parent" FreeModule(R,M) upon which it is "Formula" was chosen. This produced the fourth window, built. This is an example of inheritance. In this light it is clear "Power Series Basic Command", in which "Puiseux Series" that these aspects of object orientation have been present in was chosen. That produced the fifth window. At this point mathematics for quite some time. Concepts falling outside of the traditional mathematical some other choices can be made. It is possible to overwrite experience, but relevant in a discussion of object-oriented the data which automatically come up in the "Puiseux Series methods, are the notions of dynamic binding and dynamic Basic Command" window and enter other data. This makes it dispatch as well as dynamic memory allocation and automatic convenient to experiment with AXIOM. The given data were garbage collection. We will not go into detail concerning chosen. By clicking on the "Continue" button, those data were these concepts here, but the interested reader will find more used to create a valid AXIOM statement displayed in a new information in the references [C], [MW]. Object-oriented window labelled "Basic Command". Some other HyperDoc languages do not have to have built-in memory management. pages cause collections of statements to be generated. If the C++ is an example. "Do It" button is clicked, the statement is executed in the

JANUARY 1994, VOLUME 41, NUMBER 1 15 ...... ~~h1l!ilililiil!iir··-··-··-········-····-··-····-·-·-········-··-··-··-· .. -···-·-······-·-.. ········-·· .. -·-·······-··-·········-··-········-·-·-·-·-·-·-·-···········-··-· ...... Computers and Mathematics

~~~~~M·AII.ul~l~~·M·.______~H~y~p~e~r~D~o~c~------~~~~~~~~~~~ Basic Commands This is the top level of HyperDoc. To select an item, move the •calwlua Compute integrals, derivatives, or limits cursor with the mouse to a word in thia font then click a mouse •Matrix Create a matrix button. For an introduction to HyperDoc, click on HELP. •Dl'llll Create 2D or 3D plots. •Seriea Create a power series What would you like to do? •Solve Solve an equation or system of equations. • Baaic Command& Solve problems by filling in templates. • Topica Learn how to use Axiom, by topic. • Brow1e Browse through the Axiom library. •Examplu See examples of use of the library. •Rererenee Scan on-line documentation on Axiom. •s.ttinp Axiom system commands and variables. •HyperDoc: Write your own HyperDoc.

Series Basic Command Power Series Basic Command

Create a series by: Select the kind of power series you ~o~ant to create: • ExpaJIIion Expand a function in a series around a point • Taylor Seriu • FOl'IIIUla Give a formula for the i'th coefficient Series where the exponent ranges over the integers from a non-negative integer value to plus infinity by an arbitrary positive integer step size • Lauront Seriu Series where the exponent ranges from an arbitrary integer value to plus infinity by an arbitrary positi-ve integer step size • Puiaeux Seriu Series where the exponent ranges from an arbitrary rational value to plus infinity by an arbitrary positive rational n'WI!ber step size

Puiseux Series Basic Command Basic Comnumd

• Enter the forrtiUla for the general coefficient of the series Here is the AxiOII! co~ (-1l**((3*n - 41/61/factorial(n - 1/31_ you could ha:ve issued to co~t?pute this result:

• Enter the index variable for your formula series(n +-> ( -1l**((3*n- 41/6)/factorial(n- 1/3} ,x = • Enter the pmJer series variable 0,4/3 •• ,21 • Enter the point about which you want to expand 0

For Puiseux Series, the exponent of the power series variable ranges from an initial va.lv..e, an arbitary rati6nal number, to Select Exit to l>!ake th.is ~.tindOIJ go aua.y. pl~ infinity; the step size is an any positive rational number.

• Enter the initial value of index (a rational number) 4/3 • Enter the step size (a positive rational number) 2

!Continue!

16 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics original AXIOM interpreter automatically. Here is the result: sphere(r,a,b,c) == (1) ->series(n +->(-1)**((3*n - 4)/6)/ x EXPR INT := r * cos(u) * cos(t) + a factorial(n- 1/3),x = 0,4/3 .. ,2) y : EXPR INT := r * cos(u) * sin(t) + b z : EXPR INT := r * sin(u) + c [x,y ,z] 4 10

3 1 3 5 xx ruled(t,t**2,1,cos(t),sin(t),t) (1) X - - X + O(x ) 6 sp ·= make0bject(surface(xx.1,xx.2,xx.3), Type: t=-%pi/2 .. %pi/2,s=-2 .. 2,_ UnivariatePuiseuxSeries(Expression Integer,x,O). var1Steps==35,var2Steps==35) xx := ruled(t/2,t**2,1,cos(t)/2,sin(t)/2,t/4) There are also facilities for causing new interpreter windows to pop up and execute AXIOM commands automatically (e.g., make0bject(surface(xx.1,xx.2,xx.3+1.2), using the "Examples" field of the HyperDoc window). Also, t=-%pi .. %pi,s=-2 .. 2,space==sp,_ by clicking on the "HyperDoc" field of the HyperDoc window, var1Steps==35,var2Steps==35) you can learn how to write your own HyperDoc lessons on any subject you like along the lines of what has been explained (and more). The system has a convenient browser that lets you find Modern Art (?) out about a domain's operations, attributes, ancestors in the hierarchy, and cross references. All of this is HyperDoc oriented. There are tutorials in HyperDoc that cover the basic graphics. The first procedure that I will describe is the "draw" function. This function can be used quite naturally and simply, as in the command draw(x**2,x=-1 .. 1) • which causes a window to pop up with the graph of the • given parabola in the given range. It can, however, also be embellished somewhat, as in the command draw(tan x,x=-2*%pi .. 2*%pi, clip==true,curveColor==blue()). There is a wide range of draw options, and they are accessed by the syntax indicated above. The "Clip" option as written turns clipping on, i.e., large values are shut off (the user can adjust the maximal value, if desired). Many more examples of this sort of thing are given in the book [JS], and complete information is available through hyperdoc. The user can graph parametric equations and surfaces The first call to makeObject creates the object sp, and through the use of the draw procedure as well. In fact graphs the next one given above has the draw option space==sp may be manipulated as objects in AXIOM. For a bit of which causes the graph argument to be added to the space sp. whimsey, the built-in procedure "makeObject" was used to Following the lines indicated above, more scaling was done, produce the picture given on this page. The AXIOM code is more graphs were added to the space, and then spheres of quite straightforward, and the first part of it is given here. various radii and locations were added. A more mathematical use of AXIOM's graphical facilities can be found in [LL]. Moving on to AXIOM's object-oriented compiler, let me ruled(y1,y2,y3,g1,g2,g3) == refer the reader to the 1989 article [Ll], where the basic -- create expressions for the parameterization concepts are discussed, and the book [JS]. Version 2.0 of x EXPR INT := y1 + s * g1 AXIOM will provide a compiler for the A# programming y : EXPR INT := y2 + s * g2 language which has a syntax similiar to the current compiler z : EXPR INT := y3 + s * g3 for AXIOM but which generalizes many concepts and produces -- return the three coordinates more efficient code. In addition, with A# in place, the user will [x,y ,z] be able to take advantage of interlanguage communications.

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The compiler is used to produce the AXIOM library and Programming: Systems, Languages and Applications, ACM Press, New can also be used by any user to produce new library files (or Orleans, LA, 1989, pp. 23-35. even replace system files). It would be impossible to list all of the mathematical expertise built into AXIOM in this space. The 742-page book [JS] is a good but brief introduction to what is present. To get an idea of the level of abstraction and Object Logo™ extensibility possible, the reader might want to take advantage Student Edition of the (p )reprint series at NAG, Inc. Send e-mail to Dr. Richard Luczak (rl@nag. com) for more information. Reviewed by Suzanne M. Molnar* For an application of the full power of AXIOM's compiler and the interactive mathematical environment, let me point to [L2] and [L3], where it was used to set up categories Object Logo™ Student Edition is an implementation of the programming language Logo for the Macintosh. It is available and domains of computation in order to derive formulas in from Paradigm Software Inc. (P.O. Box 2995, Cambridge, a complex area of algebra, and [AB], where it was used to discover an unexpected theorem enabling the authors to give MA 02238; 617-576-7675) for $49.95. System requirements simpler proofs of results in [A]. (It is due to a large backlog include a Macintosh Plus computer or greater with at least 1 megabyte of RAM (2 are recommended) and System 6.0.4 or that [AB] has appeared before [A]!) The reference [L2] also later. The software is compatible with System 7 with 24-bit contains general information about the system. addressing. For the purpose of this review it was run on a Finally, release 2.0 of AXIOM will also have the "NAG­ Macintosh II with 5 megabytes of RAM and System 6.0.7. Link" in place. This is a facility which uses AXIOM and Object Logo™ Student Edition provides the functionality HyperDoc to link to the NAG FORTRAN library software of the mathematics and list processing of Logo and turtle over a network so that AXIOM's environment can be used geometry. In addition it supports an object-oriented pro­ to manage accurate numerical calculations involving root gramming environment. The full version of Object Logo™ finding, interpolation, optimization, integration, ODEs, PDEs, ~ncludes and statistical applications. ($195.00) a file compiler, application generator, MIDI (mustc) and robotics modules, and a complete 465-page For general information contact John Zurawski at NAG INC., 1400 Opus Place, Suite 200, Downers Grove, IL 6051S Object Logo™ Reference Manual. At the time of this writing the full version was available for $135.00 for owners of the (j ohnz@nag. com). For questions about AXIOM and technical support you Student Edition. The Student Edition comes with the 186-page book Logo may contact: Tom Ryan (ryan@nag. com) for the academic en­ vironment; Sheila Caswell ( caswell@nag. com) or Tony Nilles for the Macintosh: An Introduction through Object Logo™ by Harold Abelson and Amanda Abelson [1]. After working (nilles@nag. com) for the industrial or government environ­ through the first few chapters, the user has the groundwork ments; and axiom@watson. ibm. com for technical support. for further exploration into turtle geometry, recursion, and list Outside the Unites States contact infodesk@nag. co. uk. processing even if one has not programmed. This is a primary advantage if Object Logo™ is to be used by students with little or no programming background. If you have familiarity References with the programming language LISP, from which Logo's use [A] G.B. Andrews, Plane partitions V: The TSSCPP conjecture, J. Combin. Theory, Ser. A (to appear). of lists is adapted, the learning curve is a straight line with [AB] G.B. Andrews and W.H. Burge, Determinant identities, Pacific small slope! J. Math. 158 (1993), 1-14. There are three windows available to the user of Object [C] L. Cardelli, Basic polymorphic type checking, Science of Com­ Logo™, illustrated in Figures 1 and 2 on pages 19 and puter Programming, vol. 8, (1987), pp. 147-172. 20, respectively. When Object Logo™ begins, the Listener [JS] Richard D. Jenks and Robert S. Sutor, AXIOM, The scientific window appears with the ?-prompt. This is the window where computation system, Springer-Verlag, New York (1992). interactive sessions occur. The Graphics window (or turtle [Ll] Larry Lambe, Scratchpad II as a tool for mathematical re­ search, Computers and Mathematics colunm, Notices Amer. Math. Soc. window) also appears upon start-up, provided the Object (February 1989). Logo™ Elementary file-the program which controls turtles [L2] Larry Lambe, Next generation computer algebra systems, from the keyboard, mouse, and menu-is placed in the Startup AXIOM and the Scratchpad concept: Applications to research in al- . Folder. One turtle appears at the center of this window. The gebra, Plenary talk, 21st Nordic Congress of Mathematicians, Lulea, third window is the file window for creating, editing, and Sweden, summer 1992 (to appear). saving programs. [L3] Larry Lambe, Resolutions that split off of the bar construction, Journal of Pure & Applied Algebra, voL 84, (1993), pp. 311-329. Since Object Logo™ is interactive, procedures may be [LL] Larry Lambe and Richard Luczak, Object-oriented mathemat­ written in the Listener window without using the file window. ical programming and symbolic and numeric inteJface, 3rd International The transcript of the Listener session can be saved but will Conference on Expert Systems for Numerical Computing, May 1993 (to not run, as it has responses interspersed with commands. appear) . . ~] Thomas G. Moher and Paul R. Wilson, Design of the oppor­ *Suzanne Molnar teaches mathematics and computer science at the College tunzstzc garbage collector, Proc. 1989 Conference on Object Oriented of St. Catherine, St. Paul, MN. e-mail: smmolnar@alex. stkate. edu.

18 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ,.. • File Edit Logo Windows Colors Fonts Turtle 11:14:18 • .,

c.... >z $: ~ ~ ID ~ C§ I E [ :: m :!:: z c :: Ill m iiD Listener Object Logo:pythagoras tree-lop :II r ~ Welcome to Object Logo 101 to pythag :size : rs i ze :I eve I Student Edition if :level = 0 [stop] version 2. 6 1 ! house :size :rsize ; draw stem returns to bottom corner where started Tools loaded. forward :size ; position for left house Welcome to Object Logoll!!!iilleft arccos <:rsize/:size) Elementary 1.0! pythag :rsize (:rsize * :rsize)/:size : level-1 ; draw left tree SQUARE defined. right 90 , position for right house ROOF defined. forward :rsize ; up the roof HOUSE defined. ; draw rt PYTHAG defined. make. "s i de sqr t ( : s i ze * :s i ze - : rs i ze * :rs i ze ) ? penup pythag :side <:rsize * :side)/:size : level-1 ; draw right tree ? back 80 back :rsize ; down the roof ? pendo•n right 90 +arccos <:rsize/:size) ; back home ? pythag 50 25 12 forward :size ? ht rt 180 ? I I;J"Jiend

Figure 1

... CD ~

,... File Edit Logo Windows Colors Fonts Turtle 9:30:44 .... • Object Logo:Conuert/Trace EHample [I; from Logo for Macintosh, p. 126 with comments added ~ to convert :n :b , convert n to base b less than 10 if :n = 0 [output OJ ; if n = 0 output 0 output butfirst (base :n :b) ; else strip leading zero end to base :n :b , where work goes on :n 0 [output OJ ; n 0 0 z if = if = output 0 output word , else concatenate remainders a·-i; _(base (intquotient :n :b) :b) ; cal I base with quotient m CIJ _ (remainder :n :b) ,0 end n ~ m ~ ~ =o Listener '8 1!:m :D Welcome to Object Logo Student Edition version 2.61! ~ Tools loaded. ~ Welcome to Object Logo Elementary 1.0! l 3: !i CONVERT defined. :I:m BASE defined. ~ 3: ? convert 121 2 ~ !i You don't say what to do with 1111001. ::t. ? print convert 121 2 &l ~ 1111001 g ? trace [convert basel ? print convert 121 8 ~ Entering CONVERT with inputs: 121 8 Entering BASE with inputs: 121 8 Entering BASE w i th inputs: 15 8 Entering BASE with inputs: 1 8 Entering BASE with inputs: 0 8 Ill Exiting BASE with output: 0 Exiting BASE with output: 01 I Exiting BASE with output: 017 Exiting BASE with output: 0171 Exiting CONVERT with output: 171 17 1 ? untrace [convert basel ! ?l I~] Figure 2 Computers and Mathematics

In developing the procedures to draw the Pythagorean tree specifying the turtle's position which could have been used (Figure 1), the Listener window is invaluable for guiding instead. the turtle through its moves, one elementary instruction at Ease of use and turtle graphics should not detract from a time. The file window is where the final procedures were the fact that Object Logo™ has the capabilities of list developed. As with most LISP editors, the Object Logo™ processing languages like LISP and supports object-oriented editor has the advantage of alerting the user visually to the programming. The latter paradigm allows one to create matching left bracket (or left parenthesis) when its mate is objects, and by means of inheritance, create new objects keyed. If only Mathematica [2] would do this! One minor from other objects. It is therefore possible to use Object annoyance: if several new files are created, all are given the Logo™ to design versions of two "classic" programs: one name "Untitled", with no numeric designation. If Window is which recognizes animals and another which carries on a chosen from the Menu bar, several "Untitled" files are listed. conversation with a therapist [1]. In a development environment, it is unnecessary to save every Object Logo™ has the flexibility to be used in a variety attempt. Thus, having temporary "Untitled" files followed by of settings, namely, as an introduction to programming or as a number is a feature most Macintosh applications allow. a painless way for students at various levels of mathematical Once a set of procedures is saved, double-clicking on maturity to acquaint themselves with recursion and fractals. I the file icon starts Object Logo™, loading the procedures intend to make use of Object Logo™ to introduce symmetry of contained in that file. The Listener window in Figure 1 shows scale and fractals in a liberal arts mathematics course for non­ the four drawing procedures being loaded. To position the majors [5]. Although binary tree variants, Koch snowflakes, turtle to allow the entire tree to appear on the screen, three and Sierpinski triangles can be drawn using Mathematica turtle commands are keyed, followed by the call to "pythag", [2,6,7], students should find initial experimentation with such which draws the tree. The original square is size 50, one designs more appealing and intuitive in Object Logo™. side of the original triangle is size 25, and the depth of the Paradigm Software has available additional books and recursion is 12. The ht (or hideturtle) command is used disks for using Logo with a college audience. They are for the screen save; there is no need for the command if included in the references below [8-11]. Investigations in the Graphics window is being printed directly from Object Algebra is for exploring combinatorics, number theory, and Logo™. Output of the graphic directly from Object Logo™ discrete functions; Turtle Geometry: The Computer as a is far superior to that of the screen dump in Figure 1. Medium for Exploring Mathematics is an invaluable reference. While developing procedures in the file window, one can try them out by selecting them, then choosing Run Selection References from the Logo menu. If the syntax is correct, the procedure [1] Abelson, Harold, and Abelson, Amanda, Logo for the macintosh: names will appear in the Listener window. If the code is An Introduction through Object Logo™. Paradigm Software Inc .. 1992. incorrect, appropriate error messages appear. The similarity [2] Mathematica, Wolfram Research, Inc. to a LISP programming environment is evident in debugging [3] Lauwerier, Hans, Fractals: Endlessly repeated geometrical fig­ support through step and trace commands (Figure 2). There ures, Princeton Univ. Press, 1991. is also a Watch window for viewing how specified variable [4] Papert, Seymour, Mindstorms: Children. computers, and poll'er­ values change. The Student Edition does not allow files to be ful ideas, Basic Books, 1980. [5] Tannenbaum, Peter, and Arnold, Robert, Excursions in modem compiled; the full version of Object Logo™ does. mathematics, Prentice Hall, 1992. One of the beauties of Object Logo™ is that recursion [6] Gray, Theodore W., and Glynn, Jerry, Exploring mathematics comes easily and visually, too. Not only can a binary tree be with Mathematica: Dialogs concerning computers and mathematics, defined recursively, but one can see it grow. If you compare the Addison-Wesley, 1991. Object Logo™ code which produced Figure 1 to Lauwerier's [7] Wagon, Stan, Mathematica in action, W. H. Freeman, 1991. BASIC code [3] for a similar diagram, there is no question [8] Lewis, Philip, Approaching precalculus mathematics discretely, The MIT Press, 1989. that computer languages influence the thinking process. This [9] Harvey, Brian, Computer science Logo style, The MIT Press, is why Logo has a long tradition of use by children [4]. Like 1985-1987. programming in LISP, procedures can be built incrementally [10] Cuoco, Albert A., Investigations in algebra, The MIT Press, from the bottom up, as seen by the procedures defined in 1990. Figure 1. "Square" draws a generic square; "Roof'' draws [11] Abelson, Harold, and diSessa, Andrea, Turtle geometry: The a right triangle with a given hypotenuse; "House" draws a computer as a medium for exploring mathematics, The MIT Press, 1981. single house; "Pythag" is a variation on drawing a binary tree, except it draws "Houses" instead of branches. Object Logo™ supports arithmetic operations and the usual functions such as "sqrt" and "arccos" used in Figure 1. Arithmetic operations are entered in infix notation, unlike LISP which uses prefix notation. The tree was drawn with no need to know any coordinate system or coordinate values. The turtle merely had to be moved back a bit so the entire tree would fit in the Graphics window. There is a setxy turtle command for

JANUARY 1994, VOLUME 41, NUMBER 1 21 ------_ . Computers and Mathematics

features of Fields&Operators is its ability to obtain function values from a text file; for example, a numerical analyst might Fields&Operators use this software to present data graphically generated by Reviewed by Jim Northrup* some external C or FORTRAN code. Each graphics layer in a drawing has associated with it a window which determines what will be presented in that Fields&Operators is an interactive Macintosh graphics pro­ layer (e.g., the graph of a function or the graph of an operator gram for viewing curves, surfaces, and fields in either two or applied to a function). Normally these auxiliary windows are three dimensions. Its ability to calculate closed-form deriva­ hidden behind the main graphics window and are pulled to the tives makes it more than just another plotting package but front by means of the Layers menu item. Figure 1 (see next less than a full-blown symbolic computation package such page) shows such an auxiliary window, one associated with a as Maple or Mathematica. Accordingly, Fields&Operators tangent plane layer. fills a specialized niche in the spectrum of plotting packages. Although I found a few minor bugs in the software, I believe its overall facility would make it a welcome tool in many Graphics & Animation vector calculus classes. Fields&Operators can draw either wireframe or shaded im­ ages. Shaded images can be either solidly shaded or dithered, though I found the dithering option presented a less useful Basic Layout 3-D effect than solid shading. The user has explicit control The basic layout of Fields&Operators is a single graphics over the domain of the drawing (though the domain must window composed of layers of images, similar to the layers always be a rectangle) and the display of axes. Singularities concept commonly encountered in Macintosh drawing pro­ are detected by determining when the function exceeds some grams. A single layer contains an image of just one surface, set value, rather than by any algebraic means, but the user curve, or field. More complex drawings can be built by piling does have explicit control of the cutoff value. layers on top of each other. For example, a user could draw a One of the nicest features of Fields&Operators is its surface on one layer, its level sets on a second layer, a tangent ability to generate animations. Animation files are stored to plane on a third layer, etc. All of these layers are visible to disk as they are generated, so disk space can get used up the viewer simultaneously, as if each layer were drawn on quickly. While other user interfaces in this software seemed transparent viewgraphs. A single document can contain up to unduly cumbersome, the interface used to design animations ten layers total, depending on available memory. is excellent. In a rotation storyboard the user is presented What many users will be unfamiliar with is the fact with a sequence of frames from the animation (up to twelve that only one document at a time can be opened by the frames being presented on-screen at anyone time). The object Fields&Operators application. For instance, it would be to be viewed is represented in each frame as a cube. Clicking cumbersome to copy an image from one document and on one of the frames and then clicking on either a zoom paste it into another, since both documents could not be or rotate button causes that action (zoom or rotate) to be open at the same time. The point is moot, however, since performed on all subsequent frames. The cube presented in Fields&Operators does not even allow pasting ofimages. Both each frame changes its orientation so as to reflect the selected ofthese shortcomings run counter to the typicallook-and-feel transformation. The user does not have any control over the associated with Macintosh applications and are accompanied target ofthe observer's view, but since there is only one object by other "un-Macintosh-like" features. For example, opening in the view space, this seems like a reasonable concession to a document does not immediately render the document"s make in return for an easy-to-use animation interface. Figure graphics image on the screen; rather, the user must explicitly 2 (see page 24) shows the animation storyboard as well as render the image by selecting the Draw item from the Draw some vector field graphics. menu. Given the software's sluggish rendering speed, I would rather tell the software when to render an image than let it decide. Thus, one could consider this last aspect of the Bugs & Problems Overall I like Fields&Operators, but there are some problems software a feature rather than a bug. that ought to be addressed. There are some outright bugs. Interface issues aside, Fields&Operators does offer an For instance, opening a Fields&Operators document from the excellent array of drawing capabilities. It can render curves, surfaces, or vector fields in either rectangular, spherical, or Macintosh Finder while the Fields&Operators application is running will cause the application to hang. The floppy disk on cylindrical coordinates. FieIds& Operators can compute gra­ dients, divergences, curls, Laplacians, and partial derivatives which Fields&Operators is distributed contains two folders: "Mac II (Color)" and "Mac Plus. SE (Black & White)". in closed form. It can generate tangent planes automatically Each folder contains a different version ofFields& Operators, and compute flow diagrams numerically. One of my favorite but these have nothing to do with color versus black & white; rather, the "color" version of the software assumes *Dr. Northrup is a principal research scientist at Sterling Software's Information Technology Division in Rome, NY He can be reached bye-mail at a floating point coprocessor, and either version will run in [email protected]. color. (Apparently the folders were named before Classics,

22 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ,:...... :.. : ..•.. ·...... ·········~······ ; Computers and Mathematics

LCs, Performas, Quadras, Centrises, and Powerbooks became small interface problems and minor bugs. Still, I would like to popular.) see an improved version of the interface, especially if I were I ran the black & white version of Fields&Operators on going to tum it over to students. a Macintosh LC II (with 256 colors) and on a Powerbook 160 (with sixteen shades of gray). On both of these machines Summary Fields& Operators rendered images frustratingly slow. (It took Fields&Operators is a good graphics program that fills a thirty seconds to render the "Hom with Tangent" shown in unique and specialized niche. If used as course software, Figure 1 on an LC II.) It is understandable that the initial it might not provide all of the functionality I would want rendering might be slow, but subsequent rendering when an for a first-year calculus course, but it would be very useful image was "exposed" by window movement was also slow, in a vector calculus course. Additionally, its ability to read as if the Macintosh were recomputing some of the image function data from text files makes it useful for visualizing data rather than refreshing an already rendered bitmap. The data obtained from other software, and the package may be shading of objects seemed to take advantage of very few useful as a research or presentation tool as well. Though colors, and the dithered shading added no depth cues at all to Fields& Operators does perform closed-form calculation three-dimensional images. As shown in Figure 2, the vector of derivatives, it does not (nor is it intended to) provide fields graphics tend to look jagged (however, one can request all of the graphics or computation capabilities of a large thinner arrows from a vector parameters dialog box). symbolic computation package. Still, at only 185K of disk In general, the interface is somewhat cumbersome (with space and 384K of RAM, it provides much more capability the notable exception of the rotation storyboard) and "un­ than many other small graphics packages. The interface is Macintosh-like". All in all, this package gives the impression a bit cumbersome, and the quality of the graphics could be that the authors concentrated on mathematics rather than on improved; but all in all it is a good, useful package. the interface. Certainly this is the proper priority; and given Fields&Operators is available from Lascaux Graphics, the packages wide array of capabilities, I can tolerate some 3771 E. Guthrie Mt. Place, Tucson, Arizona 85718.

Draw

as: !Surface

-Side 1 II Side 2

Hide @Show Operator: [angent Plane I Display as: ._IP_Ia_n_e______. lt Tangent to:l1) EHponential horn Tangent at ... II Side 1 II Side 2 f H = (H*(eHp(0.5)*-sin( t))+y*(cos(t)*eHp(0.5)))+eHp(0.5)*cos(t)

f = (H*(eHp(0.5)*cos(t))+y*(sin(t)*eHp(0.5)))+eHp(0.5)*sin(t) y

f 2 = 0.5+y

Figure 1. Two layers: a surface and its tangent plane; also, the tangent planes defining window.

JANUARY 1994, VOLUME 41, NUMBER 1 23 ...... _.. ,. .______.. ,,.. ,_ ...... _,...... ,_. __ ,,...... _...... -...... -...... ______,,,... _ Computers aud Mathematics

,.. • File Edit Options Definitions Layers Draw

Preuiew

Rotat~ by I o.os 8¢[1] ( Reset (Radians) ,______. ( Cancel ) Zoom byj,_ 0_.0_1 ______. cC>[I){P

Local scalej,_ 1_0 __ __. 0¢JGJ n Ok J ( Remoue ) [ Ok

Figure 2. Rotation storyboard and vector field graphics.

24 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Trjitzinsky Awards Announced Waldemar J. Trjitzinsky award now makes it possible." The Society has announced the names of four undergraduate The University of Virginia made its award to MIKHAIL mathematics majors who have received awards through the KRICHMAN. Mr. Krichman was born in Tashkent, Uzbekistan. Waldemar J. Trjitzinsky Memorial Fund. The fund is made He studied mathematics at the University of Tashkent until his possible by a bequest from the estate of Waldemar J., Barbara family emigrated to the United States in 1988. He is currently G., and Juliette Trjitzinsky. The will of Barbara Trjitzinsky a fourth-year mathematics major at Virginia. "I think that stipulates that the income from the bequest should be used to my early fascination with mathematics can be linked with establish a fund in honor of the memory of her husband to my interest in music, which I also displayed when I was assist needy students in mathematics. still very young," wrote Mr. Krichman in an autobiographical Each year the Society selects four geographically dis­ statement he prepared for receiving the award. "Now I find a tributed schools which in turn make one-time awards of lot of similarities between mathematics and music, probably roughly $2,500 each to mathematics undergraduates to assist because both of them are the attempts to find some kind them in their pursuit of careers in mathematics. The schools of harmony in our dissonant and contradictious world." He are selected in a random drawing from the pool of AMS insti­ intends to pursue a Ph.D. in mathematics and become a tutional members. This year the four institutions receiving the mathematics professor. award funds were the University of California at Los Angeles, For more information about the Trjitzinsky Fund contact the State University of New York at Geneseo, Eastern New Timothy J. Goggins, Development Officer, AMS, P.O. Box Mexico University, and the University of Virginia. 6248, Providence, RI 02940-6248. UCLA presented its award to MICHELLE L. LANIR, a junior in mathematics/applied science. She is specializing in operations research and is considering further study in the Graduate School of Management and in computer science. AMS Program Development Fund Ms. Lanir has been on the Dean's Honor List twice and was Timothy J. Goggins, an Alexander-Bee Scholar three times. She is a member of AMS Development Officer the UCLA College Honors Program and the UCLA Actuarial and Assistant to the Executive Director Club. In addition to her studies she works twenty hours a week for International Affairs at a credit union and as a mathematics tutor for the UCLA The Executive Committee and Board of Trustees (ECBT) Athletics Department. recently voted to establish a Program Development Fund and SUNY Geneseo selected Jom C. WRIGHT for its award. to ask members to make contributions to it as part of the Ms. Wright has attended SUNY Geneseo since 1991. A student membership dues billing. In doing so the ECBT recognized with an excellent high school record, Ms. Wright is continuing the varied and substantial challenges confronting the Society's to do very well in her college work, maintaining a grade point mission to promote mathematical scholarship and research average of 3.8. In addition to majoring in mathematics Ms. and the need to set aside General Fund monies to specifically Wright is pursuing course work in secondary education. address these challenges. Eastern New Mexico University presented its award to The ECBT also recognized an opportunity for the Society REBECCA K. MooRE, a single parent with a four-year-old to invest its unrestricted member support in mission·-related daughter. Currently a mathematics major, Ms. Moore intends programmatic initiatives. For example, the new publication to earn a Ph.D. in mathematics and teach at the university What's Happening in the Mathematical Sciences used this level. Thurman Elder, chair of the mathematics department, concept to attract broader outside support from the Exxon said, "Ms. Moore is very deserving of this award. She is Education Foundation and the Alfred P. Sloan Foundation. bright and has a genuine interest in mathematics. She has In the June 1994 membership dues notifications the check­ been concerned about being able to continue school in the fall off box for the General Fund will be replaced by a check-off because her student loan has not been awarded. However, the box for the Program Development Fund.

JANUARY 1994, VOLUME 41, NUMBER 1 25 -·------·--- ·------"1!111111ii liii!UIIIIII " '!Pf" I !!!!!! ..------·------Inside the AMS

Traditionally the Society has supported mathematical to $50,000 for each fund. Revenue to support the match will scholarship and research through its Centennial Fellowship be taken from the income earned each year on the Society's and prize funds. This emphasis will continue and expand. At endowment. the time the Board established this new fund, it also voted to Finally, each year a report on the disbursement of Program match all gifts to both the Centennial Fellowship Fund and Development Funds will be published in the Notices so that the Program Developrp.ent Fund on a dollar-for-dollar basis up members can follow closely the use of their donations.

CONTEMPORARY MATHEMATICS

Martin C. Tangora, Editor Volume 746 This book consists of twenty-nine articles contributed by participants of the International Conference in Algebraic Topology held in July 1991 in Oaxtepec, Mexico. In addition to papers on current research, there are several surveys and expositions on the work of Mark Mahowald, whose sixtieth birthday was celebrated during the conference. The conference was truly international, with over 130 mathematicians from fifteen countries. The papers range over much of algebraic topology and cross over into related areas, such as K-theory, representation theory, and Lie groups. Also included is a chart of the Adams spectral sequence and a bibliography of Mahowald's publications.

1991 Mathematics Subject Classification: 55; 00 ISBN 0-8218-5162-4, 481 pages (sottcover}, June 1993 Individual member $43, List price $71, Institutional member $57 To order, please specify CONM/146NA

Neil Robertson and Paul Seymour, Editors Volume 747

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, held at the University of Washington in Seattle in the summer of 1991. Among the topics covered are: algorithms on tree-structured graphs, well-quasiordering, logic, infinite graphs, disjoint path problems, surface embeddings, knot theory, graph polynomials, matroid theory, and combinatorial optimization.

1991 Mathematics Subject Classification: 05; 57, 06, 68 ISBN 0-8218-5160-8, 688 pages (softcover}, June 1993 Individual member $49, List price $81, Institutional member $65 ~ To order, please specify CONM/147NA 'R -~ All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll-free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

26 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook

• Civilian Industrial Technology R&D • Education and Training R&D This month's column is written by Lisa A. Thompson, • Transportation R&D who is the Assistant for Governmental Affairs of the Joint • National Security R&D Policy Board for Mathematics (JPBM). • International Science, Engineering, and Technology The FY 1995 budget proposal, which the administration must release soon, will bear some marks of enhanced priority President Clinton setting and interagency coordination, a process pioneered by Establishes National Science FCCSET over the past several years. White House sources and Technology Council say the full review is expected to be completed in time for incorporation into the FY 1996 budget proposal a year from to Coordinate Federal R&D now. During his campaign for president, Bill Clinton expressed The president also established at the same time a Pres­ faith in science and technology as engines of economic ident's Committee of Advisors on Science and Technology growth and hinted he would elevate science and technology (PCAST), a private-sector advisory group for the president policy to a level of highest concern in his administration. Late last year, President Clinton fulfilled many expectations when and the NSTC. PCAST will consist of fifteen distinguished he issued an executive order establishing the National Science individuals in industry, education, and research and will be and Technology Council (NSTC). co-chaired by John Gibbons, the assistant to the president for According to a White House news release, "The principle science and technology and director of the Office of Science purposes of the NSTC will be to establish clear national goals and Technology Policy (OSTP). for federal science and technology investments and to ensure The president envisions PCAST as a forum for seeking that science, space, and technology policies and programs advice from the private sector on orienting federal investments are developed and implemented to effectively contribute to in science and technology toward national goals and as a those national goals." The president himself will chair this mechanism to encourage public-private partnerships, such as cabinet-level body, which is intended to function as do the the Clean Car Initiative the administration developed last year National Security Council and the Economic Policy Council. with U.S. auto makers. The NSTC was originally proposed by the National Congressman Rick Boucher (D-VA), chair of the House Performance Review, a set of recommendations to improve Science Subcommittee, has introduced legislation to codify the workings of nearly every federal entity formulated under Clinton's plans for the NSTC and PCAST, and thereby insti­ the leadership of Vice-President Al Gore. The new council tutionalize the increased visibility of science and technology will assume the responsibilities of the Federal Coordinating within the White House policy-making apparatus. Council for Science, Engineering, and Technology (FCCSET), His bill would amend the National Science and Technology as well as two other White House panels on space and Policy, Organization, and Priorities Act of 1976-which es­ materials. tablished OSTP and FCCSET-to require annual submission The president has asked the NSTC Council to conduct of a consolidated R&D budget that identifies the president's an across-the-board review of the federal R&D budget to priorities for science and technology and the societal goals align spending priorities with national goals. The NSTC those priorities are designed to address. will establish nine committees to prepare coordinated R&D The bill would go even further than Clinton with a strategies and budget recommendations in the following areas: proposal to establish a National Sciences and Technologies • Health, Safety, and Food R&D Assessment Panel to assess the nation's performance in critical • Fundamental Science and Engineering Research technologies and major fields of research. Such a panel would • Information and Communication R&D be in keeping with recommendations made in a recent report • Environment and Natural Resources Research from the Committee on Science, Engineering, and Public

JANUARY 1994, VOLUME 41, NUMBER 1 27 Washington Outlook

Policy of the National Academy of Science called, "Science, would be based on how it contributes to the national goals Technology, and the Federal Government: National Goals for identified by the NSTC. aNew Era." With or without the Boucher bill, the Clinton admin­ Boucher's bill also adopts the primary recommendation istration clearly intends to reshape the federal science and of that report by declaring as policy that the U.S. "should be technology policy process in order to maximize the contribu­ among the world leaders in all major areas of science and tions of federal research and development to the health and should maintain clear leadership in selected major areas of prosperity of the nation. science." The decision to select a field for clear leadership

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science Groups and Computation Larry Finkelstein and William M. Kantor, Editors Volume 11

This volume contains papers presented at the Workshop on Groups and Computation, held in October 1991. The workshop explored interactions among four areas: symbolic algebra and computer algebra, theoretical computer science, group theory, and applications of group computation. The papers also discuss such topics as parallel algorithms for groups, computation in associative algebras, asymptotic behavior of permutation groups, the study of finite groups using infinite reflection groups, combinatorial searching, computing with representations, and ' Cayley graphs as models for interconnection networks.

1991 Mathematics Subject Classification: 20 ISBN 0-8218-6599-4, 313 pages (hardcover), September 1993 Individual member $41, List price $69, Institutional member $55 To order, please specify DIMACS/11NA

Network Flows and Matching First DIMACS Implementation Challenge David S. Johnson and Catherine C. McGeoch, Editors Volume 12

The DIMACS Implementation Challenge was organized to encourage experimental work in the area of network flows and matchings. Participants at sites in the U.S., Europe, and Japan undertook projects between November 1990 and August 1991 to test and evaluate algorithms for these problems. The Challenge culminated in a three-day workshop held in October 1991 at DIMACS. This volume contains the revised and refereed versions of twenty-two of the papers presented at the workshop, along with supplemental material about the Challenge and the Workshop.

1991 Mathematics Subject Classification: 68, 90 ISBN 0-8218-6598-6, 592 pages (hardcover), October 1993 Individual member $58, List price $96, Institutional member $77 To order, please specify DIMACS/12NA

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

28 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

James Wallace Givens, Jr. show that, contrary to current beliefs, of applied mathematicians, computer 191Q-1993 floating-point computation was easier to scientists, and computer engineers to James Wallace Givens, Jr., died on analyze than fixed-point computation." pursue research in support of the divi­ March 5, 1993, in El Cerrito, California. Givens developed an interest in and sion's computing service activities. The He had moved to California in 1979 on ability for mathematics early in life. group's interests included, for example, his retirement from Northwestern Uni­ Born in Alberene, Virginia, he gradu­ reactor mathematics, the mathematical versity. He is survived by his former ated from high school at the age of foundations of quantum physics, auto­ wife, Virginia Shelton Givens (Berke­ fourteen and from Lynchburg College mated theorem proving, computer lan­ ley, California); their three sons, James cum laude at the age of seventeen. His guages, image processing, and computer Wallace Givens ill (Berkeley), Brian graduate career began at the University performance monitoring. Givens had a Hughes Givens (Richmond, California), of Kentucky, continued at the Univer­ remarkable skill for finding talented in­ and Barry Shelton Givens (Davis, Cali­ sity of Virginia, and was completed at dividuals and stimulating their interests fornia); and four grandchildren. Princeton University, where he received in applied mathematics and computer The name of Givens is known to nu­ a Ph.D. in 1936 under the direction of science. Many of the early Argonne merical analysts mainly because of the Oswald Veblen. From 1935 to 1937, AMD staff members moved on to very Givens rotations-plane rotation ma­ as Veblen's assistant at the Institute for successful careers at other academic, trices that arise in eigenvalue compu­ Advanced Study, Givens developed an industrial, and government institutions, tations. This approach to computing intense interest in projective geome­ extending Givens's legacy far beyond eigenvalues by reducing a symmetric try that was to continue throughout his Argonne. matrix to a tridiagonal form was devel­ career. Later, in the 1940s, after attend­ At Argonne Givens maintained his oped by Givens during the 1950s. It is ing a series of lectures at Princeton in interest in numerical linear algebra and indicative of his love for the elegance of which von Neumann described his plans continued a tradition he had initiated mathematics that this fundamental con­ for a stored-program digital computer, in 1957 while chair of the mathematics tribution was motivated by a paper on Givens's interests expanded to include department at Wayne State. In that year matrices over finite fields. Gene Golub numerical computation. This new focus, he had organized a workshop on dense and Beresford Parlett, in the January together with his background in projec­ matrix computations that is sometimes 1991 issue of the SIAM Journal on Ma­ tive geometry, led to the development of referred to as "Gatlinburg 0", because trix Analysis and Applications which his method for computing eigenvalues. it was the inspiration for the Gatlinburg is dedicated to Givens, point out that Givens held appointments in math­ meetings subsequently organized by Al­ Givens's method was "the first round­ ematics at Cornell University (1937- ston Householder. In the three following off error analysis of matrix computa­ 1941), Northwestern (1941-1946), the years, Givens was a lecturer at another tions that was deliberately made in the University of Tennessee (1947-1956), set of remarkable gatherings of numer­ 'backward' mode". Givens's analysis, Wayne State University (1956-1960), ical mathematicians-the University of published as an Oak Ridge National and Northwestern again (1960) before Michigan summer sessions on numeri­ Laboratory technical report, is entitled becoming director of the Applied Math­ cal analysis. The roster of participants "A Method of Computing Eigenvalues ematics Division (AMD) of Argonne in the summer programs he organized at and Eigenvectors Suggested by Clas­ National Laboratory in 1964. He was Argonne was a similar "Who's Who" of sical Results on Symmetric Matrices". already familiar with the national lab­ numerical mathematics, especially nu­ Although never published in an archival oratories, having served on the Oak merical linear algebra and the numerical journal, the paper "did fall into the Ridge National Laboratory Mathemat­ solution of partial differential equations. right hands", Golub and Parlett relate. ics Panel for more than a decade. At Before the term "mathematical soft­ "Wilkinson saw the great potential in Argonne he built on this experience, re­ ware" was invented, Givens advocated backward error analysis and went on to cruiting and nurturing an eclectic group implementing state-of-the-art algorithms

JANUARY 1994, VOLUME 41, NUMBER 1 29 News and Announcements and making them readily available for in which Raphael Salem worked, pri­ Lewis Award Presented use by scientists and engineers. He rec­ marily Fourier series and related topics. The John Frederick Lewis Award of the ognized the importance of the numerical The selection committee for the 1993 American Philosophical Society (APS) linear algebra algorithms in the com­ prize consisted of J. Bourgain, V. Ravin, has been presented to DAVID GILMAN puter language ALGOL that appeared in Y. Katznelson, and E. M. Stein. RoMANO, Keeper of the Collection, Numerische Mathematik and, with the Mediterranean Section, at the University assistance of J. H. Wilkinson, initiated a Humboldt Foundation Awards Museum of the University of Pennsyl­ project for translating these algorithms The Alexander von Humboldt Founda­ vania. into FORTRAN programs. He supported tion in Bonn, Germany, recently pre­ The award recognized Romano's their distribution via AMDLffi, an early sented a number of awards and fellow­ book Athletics and Mathematics in Ar­ mathematical software library. Thus, he ships to distinguished mathematicians. chaic Corinth as the best book published was instrumental in creating the en­ The Foundation presented the Hum­ by the APS in 1993. This book deals with vironment for, and the forerunner of, boldt Award for Senior American Scien­ literary, historical, epigraphical, and ar­ EISPACK, the first of the ANL mathe­ tists to the following mathematicians: chaeological evidence which reveals the matical software PACKs. JOHN CHIPMAN, University of Min­ origins of the Greek Stadium in the sixth In 1969, while at Argonne, Givens nesota; R. KEITH DENNIS, Cornell Uni­ century B.C. In order to establish a start­ began a two-year term as president of versity; Jurus HARTMANIS, Cornell Uni­ ing line which gave each runner an equal SIAM. He also served on the SIAM versity; CHRISTOPHER JONES, Brown Uni­ chance to win, Greek architects had to be Council for seven years from 1965 to versity; CHARLES ANTHONY MICCHELI, familiar with plane geometry, including 1971. In 1970, after retiring as division ffiM T.J. Watson Research Center; and the basic properties of the circle and pi. director and resuming his role as a senior JosEPH WEIZENBAUM, Massachusetts In­ Romano is the first to demonstrate that scientist at Argonne, Givens returned to stitute of Technology. sixth and fifth century B.C. Greek math­ the study of Lyapunov mapping that he The following outstanding young ematicians knew of pi, even though the had partially completed and reported in a mathematicians were selected for Re­ relationship is well known from second 1961 ANL paper, "Elementary Divisors search Fellowships for long-term col­ millenium sources in both Mesopotamia and Some Properties of the Lyapunov laborative research projects in Ger­ and Egypt. Mapping X -+ AX +X A*." He contin­ many: THOMAS BRIDGES, Rijksuniver­ The American Philosophical So­ ued to be interested in the development siteit Utrecht; PETER CLOTE, Boston ciety is an international organization and implementation of numerical lin­ College; JAMES DAVIS, Indiana Univer­ which promotes excellence and useful ear algebra algorithms, however, and sity; DAVID GRABLE, Clemson Univer­ knowledge in the sciences and human­ especially enjoyed J.H. Wilkinson's an­ sity; TAILEN HsiNG, Texas A&M Uni­ ities through scholarly research, pro­ nual summer visits to Argonne. In 197 4 versity; KEITH KEARNES, Harvey Mudd fessional meetings, publications, library Givens received the prestigious Alexan­ College; ALBERT MILANI, University of resources, and community service. der von Humboldt Stiftung Award and Wisconsin; FRANK NIJHOFF, Clarkson visited Bonn; in the following year, he University; and JoN GORDON WOLFSON, Luc Vinet Named Director of CRM retired from Argonne and returned to Michigan State University. In July 1993 Luc Vinet was appointed Northwestern as a professor of mathe­ The following mathematicians have director of the Centre des Recherches matics. Wallace Givens will be remem­ been selected for postdoctoral research Mathematiques (CRM) at the Univer­ bered as one of the small group of in Germany under the Humboldt Foun­ site de Montreal. He succeeds Francis pioneers who created the field of matrix dation's Feodor-Lynen program. Clarke, who served as director of CRM computations, as a creative adminis­ Through this program, German schol­ for nine years and who remains as pro­ trator who advocated support of basic ars holding a doctorate carry out re..: fessor of mathematics at the Universite research, and as a friend who helped search at institutes of former Humboldt de Montreal. many individuals launch their careers. guest researchers. Listed below are the Vinet is currently a member of the James C.T. Pool names of the postdoctoral researchers, Mathematical Physics Group at CRM Drexel University followed by the names and institutions of and of the Department of Physics of (Reprinted with permission from SIAM their U.S. hosts: SUSANN HENSEL, Wolf­ the Universite de Montreal. He did his News, July 1993.) gang H. Fuchs and Ronald Kline, Cor­ undergraduate and graduate studies at nell University; MARIO BoNK, Frederick the Universite de Montreal, obtaining a Treil Awarded 1993 Salem Prize W. Gehring, University of Michigan; Ph.D. in 1980. A year earlier he had The Salem Prize for 1993 has been HANS-PETER KRusE, Jerrold E. Mars­ received a doctorate at the Universite awarded to SERGEI TREIL of Michigan den, University of California, Berke­ Pierre et Marie Curie (Paris VI). He State University for his work on operator ley; and ANDREAS RIEDER, Raymond J. did postdoctoral studies at the Mas­ theory and complex analysis. The prize, O'Neil Wells, Jr., Rice University. sachusetts Institute of Technology be­ established in 1968, is given each year to See the Funding News section of this fore returning to his alma mater in a young mathematician who is judged to issue of the Notices for information on 1982 as University Research Fellow, have done outstanding work in the area Humboldt Foundation programs. sponsored by the National Science and

30 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Engineering Research Council of Canada. title of his lectures is "Isoperimetric In­ a yearlong program in Several Complex In 1987 he became an assistant professor equalities and Concentration of Measure Variables, and other programs that are in the Department of Physics at Montreal in Product Spaces". still to be determined. and reached the rank of full professor in The lectures are open to the public In addition to its scientific programs 1992. He has served as visiting professor and are held in honor of Everett Pitcher, MSRI has been working vigorously in at the Universite Catholique de Louvain, former secretary of the AMS. Pitcher new directions aimed at reaching out MIT, and the Universty of California at served in the mathematics department toward wider groups of people. A video­ Los Angeles. His research in physics at Lehigh from 1938 until 1978, when tape based on our celebrated Fermat Fest centers on the study of symmetry and its he retired as Distinguished Professor of will ship near the end of December. A related mathematical structures. Mathematics. Further information can toll free number is now available to order be obtained by writing to Pitcher Lec­ the videotape: 1-800-677-7001 (ask for Appointments to NSF ture Series, Department of Mathemat­ part #3009a). This one-of-a-kind pro­ Advisory Board ics, Lehigh University, Bethlehem, PA duction begins with Andrew Wiles and A number of mathematical scientists 18105; or by calling 215-758-3753. ends with a song written and sung by have been appointed to the Mathemati­ Tom Lehrer. cal and Physical Sciences (MPS) Advi­ News from the This year we launched a human sory Committee for theNational Science Mathematical Sciences resources project, aimed at achieving Foundation (NSF). The NSF's Advisory Research Institute substantially greater participation of un­ Committee for the Mathematical Sci­ Berkeley, California derrepresented minorities at MSRI than ences was disbanded as part of a federal The fall semester of 1993 has been very is typical in the U.S. mathematical re­ effort to reduce the number of advisory active at the Mathematical Sciences Re­ search community. Our top-level human committees in the government; it met search Institute (MSRI) ("Emissary"). resources advisory committee had a very for the last time in the spring of 1993. Our Differential Geometry program has productive first meeting in November, The MPS Committee will provide ad­ been quite energetic, with a schedule alongside our existing Scientific Advi­ vice to the NSF for all of the disciplines that included four intensive workshops sory Council and Steering Committee, under the MPS Directorate, which in­ during the fall: Riemannian Metrics Sat­ to make plans for changing the face of cludes mathematics, physics, chemistry, isfying Curvature Equations, Spaces of MSRI. astronomy, and materials science. Negative Curvature, Comparison Ge­ The mathematical scientists on the ometry, and Spectral Geometry. The New sculpture MPS Advisory Committee are Nancy spring semester of 1994 promises to be MSRI unveiled its first sculpture, "The Kopell of Boston University, Ettore In­ even busier, as a second program on Eightfold Way" by Helaman Ferguson, fante of the University of Minnesota, and Probabilistic Methods and Dynamical on November 14. The sculpture is a Richard H. Herman of the University of Systems for Partial Differential Equa­ depiction of the Klein quartic, a famous Maryland at College Park. Also on the tions joins the continuing Differential object of mathematical study for more Committee is Edward E. David, who Geometry Program. In conjunction with than a century. The abstract surface is a chaired the committees that produced this program, MSRI will host an AMS­ 3-holed torus that incredibly has a group the two "David Reports". SIAM Summer Program in Probabilistic of symmetries of order 336. This group The MPS Advisory Committee also Methods for PDE's, described elsewhere cannot act isometrically in 3-space. The has "disciplinary subcommittees" to fo­ in this issue. sculpture shows the symmetry topolog­ cus on the individual areas that come un­ In spring of 1994 MSRI will hold five ically, using a pattern of twenty-four der the MPS directorate. On the mathe­ workshops: Waves in the Ocean (Febru­ heptagons. Abstractly, each heptagon is matical sciences subcommittee are Mary ary 7-11), Exterior Differential Sys­ equivalent to each other heptagon and Ellen Bock of Purdue University, Ronald tems, Submanifolds, and Control Theory each heptagon can be rotated and re­ G. Douglas of the State University of (March 1--4 ), Dynamical Systems Meth­ flected on itself in fourteen ways. The New York at Stony Brook, F. Alberto ods Designed for PDE's (March 14- sculpture is made of white marble, and it Grunbaum of the University of Cali­ 18), Harmonic Maps, Minimal Subman­ rests on a 7 -sided black column that rises fornia at Berkeley, D. J. Lewis of the ifolds, and Rigidity Questions (April out of a model of the hyperbolic plane, University of Michigan, and Margaret 20-22), and Mesoscopic Modeling of tiled by regular heptagons meeting three Wright of AT&T Bell Laboratories. Nonequilibrium Systems (May 23-27). to a vertex. The surface itself is a quo­ For further information write c/o any tient space of the hyperbolic plane by a Talagrand to Give Pitcher Lectures of the workshop titles to MSRI, 1000 subgroup of index 336 in the group of The next series of Everett Pitcher Lec­ Centennial Drive, Berkeley, CA 94720. isometries that preserves the heptagonal tures will be held February 7, 8, and Next year (1994-1995), MSRI will tiling. 9, 1994, on the campus of Lehigh Uni­ host a yearlong program in Automorphic The sculpture makes a beautiful cen­ versity in Bethlehem, Pennsylvania. The Forms and a spring semester program in terpiece for our newly remodeled pa­ speaker will be Professor Michel Tala­ Complex Dynamics and Hyperbolic Ge­ tio, which now serves as much-needed grand of the Ohio State University. The ometry. For 1995-1996 we are planning expansion space during our crowded

JANUARY 1994, VOLUME 41, NUMBER 1 31 News and Announcements periods (particularly workshops) and an graduate students, and postdoctoral and contribution; and (5) a short biogra­ inspiring spot to contemplate mathemat­ senior researchers. phy of the student. Submissions will be ics. This year's three-week institute will judged on originality, significance, and be held in Park City, Utah, July 10- quality of exposition. Workshop on Combinatorial Games 30, 1993 (contingent upon funding from Submissions must reach SIAM on This summer MSRI will host a spe­ the National Science Foundation). High or before March 15, 1994. The win­ cial2-week workshop on Combinatorial school teachers, in partnership with uni­ ners will be notified by June 1, 1994. Games from July 11-21, 1994. versity mathematicians and students, For more information contact: Allison The mathematical study of 2-player will explore the evolution of classi­ Bogardo, SIAM, 3600 University City perfect-information games seeks pre­ cal geometry to modern geometry on Science Center, Philadelphia, PA 19104- cise, provable assertions about vari­ curved spaces and will discuss issues 2688; tel.: 215-382-9800; fax: 215-386- ous positions and strategies-rather than of education reform. Undergraduate and 7999; e-mail: bogardo@siam. org. heuristics-which hope to be good graduate students will be offered an in­ enough to compete with strong human tense yet accessible introduction to areas players in real time. Conway's theory of current research and application. The Graph Theory Newsletter of partisan games has provided a frame­ Research and Graduate Summer School The Graph Theory Newsletter (GTNL), work for analyzing games whose po­ topic is "Gauge Theory and the Topol­ published since 1971 at Western Michi­ sitions split into disjoint sums. This ogy of Four-Manifolds". gan University, is now being published theory and its variations have been The deadline to apply to partici­ by the Department of Mathematics of very successful in analyzing intricate pate in the Institute is March 1, 1994. B. V. Bhoomaraddi College in Bidar, endgame problems in a wide range of For further information and applica­ Karnataka, India. The newsletter has games, including such popular games tion forms contact: PC/IAS Mathemat­ several purposes: to help researchers as Go and Dots-and-Boxes as well as a ics Institute, 18C DeTrobriand Street, locate publications in graph theory; to much longer list of mathematical games Salt Lake City, UT 84113; telephone: allow authors to publish abstracts of such as Domineering and Hackenbush. 801-585-3488; fax: 801-585-5793; elec­ recent research; to pose unsolved prob­ Combinatorial game theory now encom­ tronic mail: pcmi@math. utah. edu. lems and conjectures; and to announce passes a substantial collection of general newly conferred degrees, upcoming con­ theorems, constructive algorithms, com­ Student Paper Competition ferences, new publications, and changes plexity proofs, and extensive databases The Society for Industrial and Applied of address. of endgame solutions for classical games Mathematics (SIAM) is sponsoring a For further information write to: such as chess. Engineers are also begin­ program of awards for outstanding stu­ D. G. Akka, Editor, GTNL, Rampure ning to show some interest in this subject dent papers. The authors of the three Colony, BIDAR-585403, Karnataka, In­ because the problem of decomposing a best papers will each receive an award dia. game position into simpler games can be of $750, and their registration fees will somewhat analogous to the problem of be waived for the SIAM Annual Meet­ decomposing a large hardware-software ing in San Diego, July 25-29, 1994. New Journal system into tractable modules. Winners must present their papers at the from Academia Sinica The organizing committee for the meeting. The Institute of Mathematics of the workshop consists of E. Berlekamp Papers must be singly authored and Academia Sinica in the People's Repub­ (chair), J. Conway, N. Elkies, A. Fraen­ not previously published or submitted lic of China has launched a new journal kel, R. Guy, R. Nowakowski, J. Propp, for publication. To qualify, authors must entitled Algebra Colloquium. The first and K. Thompson. be students in good standing who have issue will appear in March 1994. The aim For more information write to Com­ not yet received their doctorates at the of the journal is to introduce the latest binatorial Games Workshop, MSRI, time of submission. developments in algebra and to promote 1000 Centennial Drive, Berkeley, CA Submissions, which must be in En­ international scholarly exchanges. The 94720; or combinatorial_games@ glish, can be sent by regular mail or journal will publish research articles in msri.org. fax. Each submission must include (1) pure and applied algebra. an extended abstract not longer than The Editorial Board for Algebra Col­ Park City/lAS Mathematics five pages (including bibliography); (2) loquium includes B. H. Neumann, S. Institute the complete paper, which will be used Amitsur, A. Bak, P. M. Cohn, Paul The Park City/Institute for Advanced solely for clarification of any questions; Pong, Y. Pong, P. Hilton, N.D. Gupta, Study Mathematics Institute, formerly (3) a statement by the student's faculty J. I Lepowsky, M. L. Liu, M. Nagata, I. known as the Regional Geometry Insti­ advisor that the paper has been prepared R. Shafarevich, K. P. Shum, and H. F. tute, incorporates learning, teaching, and by the author indicated and that the au­ Tuan. For further information write to research activities in a unique, four-level thor is a student in good standing; (4) the Managing Editor, Fu-an Li, Institute integrated format. Participants include a letter by the student's faculty advisor of Mathematics, Chinese Academy of high school teachers, undergraduates, describing and evaluating the paper's Sciences, Beijing 100080, China.

32 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Mathematics Awareness Week Awareness Week, in future issues of the yama's Conjecture; Fermat's Last The­ "Mathematics and Medicine" Notices. orem Follows" (Notices, July/August April 24-30, 1994 1993), Kenneth Ribet chose the name Mark your calendars now and plan to Erratum "Taniyama Conjecture" for economy of observe Mathematics Awareness Week Two recent articles in the Notices re­ expression, but now regrets his decision. (MAW) in your area, institution, or or­ ferred to the conjecture that all ellip­ He believes it would have been prefer­ ganization. With the theme of "Mathe­ tic curves over Q are modular as the able to use the term "Taniyama-Shimura matics and Medicine", MAW provides "Taniyama Conjecture". The attribution Conjecture", as that has become the an excellent opportunity to celebrate the of this conjecture has been the sub­ standard name for it. In addition, the beauty and power of the mathematical ject of debate within the mathemati­ October 1993 issue of the Notices car­ sciences. Please do your part to promote cal community. Some believe that the ried an article entitled "Fermat Fest public awareness of mathematics from name "Taniyama-Shimura Conjecture", Draws a Crowd", which also referred to Sunday, April 24, to Saturday, April or sometimes "Taniyama-Shimura-Weil the conjecture as the "Taniyama Conjec­ 30, 1994. Look for further information Conjecture", more accurately reflects the ture". This article also should have used from the Joint Policy Board for Mathe­ history of the conjecture. the standard name, "Taniyama-Shimura matics, national sponsor of Mathematics In his article "Wiles Proves Tani- Conjecture".

Topology and Its Applications S. P. Novikov, Editor

This book contains the proceedings of an international topology conference held in the town of Zagulba. near . Baku in the former Soviet Union, in October 1987. Sponsored by the Institute of Mathematics and Mechanics of Azerbaijan and the Steklov Mathematical Institute, the conference was organized by F. G. Maksudov and S. P. Novikov. About 400 mathematicians, including about 100 foreigners, attended the conference. ·This book covers aspects of general, algebraic, and low-dimensional topology.

1991 Mathematics Subject Classification: 58, 55, 57, 54 ISBN 0-8218-3151-8, 250 pages (softcover), November 1993 Individual member $108. List price $180, Institutional member $144 To order, please specify STEKL0/193NA

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

JANUARY 1994, VOLUME 41, NUMBER 1 33 Funding Information for the Mathematical Sciences

NSF-CBMS Regional Conference meals and some travel support but do two major goals: to encourage the de­ Series not receive stipends. CBMS pays the lec­ sign and implementation of innovative, TheNational Science Foundation (NSF), turer a stipend of $2000 for the delivery short-term activities and to demonstrate with the sponsorship of the Conference of the lectures and an additional stipend the effectiveness of existing activities Board of the Mathematical Sciences of $3000 when the lecturer completes through evaluation, refinement, expan­ (CBMS), intends to support six NSF­ the manuscript. sion, or replication to a different popula­ CBMS Regional Conferences in 1995. Conferences proposed for 1995 tion or setting. There is a yearly deadline Each five-day conference features a should normally be scheduled to oc­ of January 15. distinguished lecturer who delivers ten cur sometime after the end of classes in Experimental Projects for Women lectures on a topic of important cur­ May 1995 and before the beginning of and Girls are intended to produce long­ rent research in one sharply focused classes in September 1995 but may also term infrastructure changes through com­ area of the mathematical sciences. The be scheduled during December 1995 or prehensive projects bringing permanent lecturer subsequently prepares an expos­ January 1996, when most colleges and results. The program has two major itory monograph based on the lectures universities are in recess. goals: to create positive and perma­ to be published by the AMS, the Society The NSF-CBMS Regional Confer­ nent changes in academic, social, and for Industrial and Applied Mathematics, ences for 1994 may be found in the scientific climates to stimulate the in­ or jointly by the American Statistical December 1993 issue of the Notices, terest and develop the aptitude of girls Association and the Institute for Mathe­ page 1370. and women in science, engineering, and matical Statistics. Proposals, which are submitted to mathematics and to add to knowledge One of the purposes of the program the NSF, must be received by April 4, about interactions between gender and is to stimulate local research activity 1994. For further information on how the infrastructure of science, mathemat­ in each regional conference area. Par­ to submit proposals contact: Conference ics, and engineering that can provide ticipants include not only established Board of the Mathematical Sciences, directions for future efforts. There is a researchers but also newcomers to the 1529 Eighteenth Street, NW, Washing­ yearly target date of May 15 for infor­ field, such as interested faculty and grad­ ton, DC 20036; telephone: 202-293- mal preliminary proposals and a yearly uate students from nearby institutions. 1170. deadline of September 1 for formal Colleges or universities with at least proposals. some research competence in the field of NSF Programs Information Dissemination Activi­ the proposal are eligible to apply. Since for Girls and Women ties are designed to provide mechanisms a major goal of these conferences is to The National Science Foundation has for interactions among individuals to attract new researchers to the research a number of programs designed to disseminate successful strategies for en­ area and to stimulate new research activ­ promote the participation of girls and couraging participation of women and ity, institutions interested in upgrading women in science, mathematics, and girls in science, mathematics, and en­ or improving their research efforts are engineering. These programs are coor­ gineering. The program also supports especially encouraged to apply. dinated by the Directorate for Education dissemination of information about the Support is provided for about thirty and Human Resources (EHR). interest, retention, and advancement of participants at each conference, and Model Projects for Women and Girls women and girls in these areas to teach­ the conference organizer invites both are designed to produce significant and ers, faculty, administrators and/or the established researchers and interested immediate changes. These projects fo­ general public. There is no deadline, but newcomers, including postdoctoral re­ cus on critical stages which can facilitate informal preliminary proposals must be searchers, graduate students, and mem­ or hinder the successful participation of submitted at least twelve months prior bers of underrepresented groups. Par­ women and girls in science, mathemat­ to the planned date of a conference or ticipants are provided with lodging and ics, and engineering. The program has activity.

34 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information

In addition, existing programs in enabling them to carry out research at An applicant should be nominated by EHR offer significant opportunities for institutes in Germany. Applications may the dean of students or another eminent projects to improve the participation of be submitted at any time by scholars person in his or her field, must be under females in science, mathematics, and from any nation and in any academic thirty years of age, and should have at engineering. discipline. The fellowships initially run least a B.A. degree. Graduates, post­ The program announcement "EHR six to twelve months, and extensions graduates, and young professionals are Activities for Women and Girls in Sci­ of up to twenty-four months may be eligible. The program includes language ence, Engineering, and Mathematics" granted. Up to four months of this period classes, which begin in Germany in Au­ contains more information about these may be spent at research institutes in gust, and the stay ends mid-September programs. These announcements may other European countries. of the following year. be obtained from: Education and Hu­ Feodor Lynen Research Fellowships The Humboldt Foundation also spon­ man Resources, National Science Foun­ are granted annually to German scholars, sors Research Awards that enable promi­ dation, 4201 Wilson Boulevard, Arling­ who have doctorates and who are at most nent scholars in the natural sciences to ton, VA 22230. Program announcements thirty-eight years old, to carry out re­ spend four to twelve months carrying out may also be requested by sending elec­ search at institutes of former Humboldt resarch in Germany. For these awards, tronic mail to pubs@nsf. gov (Internet) guest researchers abroad. Applications nominations must be made by eminent or pubs@nsf (Bitnet); request publica­ may be made at any time for all dis­ German scholars; direct applications are tion number 93-126 and be sure to in­ ciplines and countries. The sponsorship not accepted. clude the title of the program announce­ period is for one to three years. Each The Foundation maintains contact ment, your name, your complete mailing applicant must secure a formal invitation with the scholars it supports by invit­ address, and the number of copies you from a former Humboldt fellow or award ing them to spend further short periods need. winner and have a specific research plan doing research in Germany, by donat­ and a good command of English or the ing academic literature and scientific language of the host country. equipment (in the U.S. this applies only Programs of the Bzmdeskanzler Scholarships for Fu­ to exceptional cases), and by awarding Humboldt Foundation ture American Leaders are awarded an­ grants toward printing costs and toward The Alexander von Humboldt Founda­ nually to ten eminent young Americans the cost of attending academic confer­ tion has a number of programs designed to spend a year in Germany in academic ences in Germany. to promote international scientific ex­ or other public institutions. The aim is For more information and applica­ changes. Between 1953 and 1990, nearly to maintain and foster the close relation­ tions contact: Dr. Jan Keppler, Alexan­ 14,000 scholars from 100 nations were ship between the U.S. and Germany by der von Humboldt Foundation, North sponsored by the Humboldt Foundation. sponsoring individuals who could play American Office, 1350 Connecticut Av­ Humboldt Research Fellowships for a pivotal role in the future of this re­ enue, NW, Suite 390, Washington, DC Foreign Scholars are granted annually to lationship. Applications are reviewed in 20036; tel.: 202-296-2990; fax: 202- up to 600 researchers who have doctor­ February each year and must be received 833-8514; electronic mail: humboldt@ ates and who are under the age of forty, by October 31 of the preceding year. umail. umd. edu.

Conference Proceedings, Canadian Mathematical Society

Representations of Algebras Vlastimil Dlab and Helmut Lenzing, Editors

The Sixth International Conference on Representations of Algebras was held at Carleton University in Ottawa, Canada, in August 1992. This refereed volume contains papers pre­ sented at the conference, as well as papers submitted after the conference. Describing developments at the forefront of the field, this book will interest algebraists working in the field of representation theory.

1991 Mathematics Subject Classification: 16; 20 ISBN 0·8218·6019-4, 478 pages (softcover), December 1993 Individual member $49, List price $81, Institutional member $65 CMS members may order at the AMS member prices. To order, please specify CMSAMS/14NA

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

JANUARY 1994, VOLUME 41, NUMBER 1 35 CALL FOR SUGGESTIONS

There will be a number of contested seats in the 1994 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, Illinois 61801 e-mail: [email protected] 1994 AMS Election Nominations by Petition

Vice-President or Member-at-Large The President will name at least six candidates for these One position of vice-president and member of the Council ex three places, among whom may be candidates nominated by officio for a term of three years is to be filled in the election of petition in the manner described in the rules and procedures. 1994. The Council intends to nominate at least two candidates, The candidate's assent and petitions bearing at least 100 among whom may be candidates nominated by petition as valid signatures are required for a name to be placed on described in the rules and procedures. the ballot. In addition, several other rules and operational Five positions of member-at-large of the Council for a considerations, described below, should be followed. 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 Rules and Procedures described in the rules and procedures. Use separate copies of the form for each candidate for vice­ Petitions are presented to the Council, which, according to president, member-at-large, or member of the Nominating and · Section 2 of Article Vll of the bylaws, makes the nominations. Editorial Boards Committees. The Council of23 January 1979 stated the intent of the Council 1. To be considered, petitions must be addressed to Robert M. Fossum, Secretary, P. 0. Box 6248, Providence, Rhode Island of nominating all persons on whose behalf there were valid 02940, and must arrive by 28 February 1994. petitions. 2. The name of the candidate must be given as it appears Prior to presentation to the Council, petitions in support of in the Combined Membership List (CML) . If the name does not a candidate for the position of vice-president or of member-at­ appear in the list, as in the case of a new member or by error, large of the Council must have at least fifty valid signatures and it must be as it appears in the mailing lists, for example on the must conform to several rules and operational considerations, mailing label of the Notices. If the name does not identify the which are described below. candidate uniquely, append the member code, which may be obtained from the candidate's mailing label or the Providence office. 3. The petition for a single candidate may consist of several Editorial Boards Committee sheets each bearing the statement of the petition, including the Two places on the Editorial Boards Committee will be filled name of the position, and signatures. The name of the candidate must be exactly the same on all sheets. by election. There will be four continuing members of the 4. On the next page is a sample form for petitions. Copies Editorial Boards Committee. may be obtained from the secretary; however, petitioners may The President will name at least four candidates for these make and use photocopies or reasonable facsimiles. two places, among whom may be candidates nominated by 5. A signature is valid when it is clearly that of the member petition in the manner described in the rules and procedures. whose name and address is given in the left-hand column. The candidate's assent and petitions bearing at least 100 6. The signature may be in the style chosen by the signer. valid signatures are required for a name to be placed on However, the printed name and address will be checked against the Combined Membership List and the mailing lists. No attempt the ballot. In addition, several other rules and operational will be made to match variants of names with the form of name in considerations, described below, should be followed. the CML. A name neither in the CML nor on the mailing lists is not that of a member. (Example: The name Robert M. Fossum is that of a member. The name R. Fossum appears not to be.) 7. When a petition meeting these various requirements ap­ Nominating Committee pears, the secretary will ask the candidate to indicate willingness Three places on the Nominating Committee will be filled to be included on the ballot. Petitioners can facilitate the proce­ by election. There will be six continuing members of the dure by accompanying the petitions with a signed statement from N aminating Committee. the candidate giving consent.

JANUARY 1994, VOLUME 41, NUMBER 1 37 ...... · .iJ._•..· .11· .

NOMINATION PETITION FOR 1994 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 Metnber-at-Large ofthe Councll D Metnber ofthe Notninating Conunittee D Metnber ofthe Editorial Boards Conunittee of the American Mathematical Society for a term beginning 1 February, 1995.

Narne and Address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

38 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY University of Kentucky, Lexington, Kentucky March 18-19, 1994 First Announcement

The eight hundred and ninetieth meeting of the American Accommodations Mathematical Society (AMS) will be held at the University Rooms have been blocked in the following hotels. An of Kentucky, Lexington, Kentucky, on Friday and Saturday, NCAA Regional Men's Basketball Tournament is scheduled March 18-19, 1994. in Lexington for the weekend of March 18, so participants are advised to make reservations early. Participants should make Invited Addresses their own arrangements with the hotel of their choice. The Jack Dongarra, Oak Ridge National Laboratory and Uni­ AMS is not responsible for rate changes or the quality of versity of Tennesee, Recent work in parallel algorithms for the accommodations offered by these hotels/motels. linear algebra. David R. Morrison, Institute for Advanced Study, Mirror Campbell House: 1375 Harrodsburg Road, Lexington, KY symmetry and the quantum moduli space of Calabi-Yau 40504. Telephone: 606-255-4281. Single $55 and Double $60. manifolds. Deadline for reservations is March 3, 1994. James E. McClure, Purdue University, Applications of Hochschild andAndre-Quillen homology to homotopy theory. Hyatt Regency Lexington: 400 West Vine Street, Lexington, George F. McNulty, University of South Carolina, Avoid­ KY 40507. Telephone: 606-253-1234. Single or Double $78. ing combinatorial patterns in strings of symbols. Deadline for reservations is February 24, 1994. Special Sessions Infinite groups and group rings, James C. Beidleman and Kentucky Inn: 525 Waller Avenue, Lexington, KY 40504. Donald B. Coleman, University of Kentucky. Telephone: 800-221-6652 or 606-254-1177. Single $30 and Geometric group theory and metric geometry, Philip L. Double $40. Deadline for reservations is March 3, 1994. Bowers, Florida State University. Partial differential equations and minimal smoothness Springs Inn: 2020 Harrodsburg Road, Lexington, KY 40503. conditions, Russell M. Brown and John L. Lewis, University Telephone: 800-354-9503 or 606-277-5751. Single $35 and of Kentucky, and Zhongwei Shen, Purdue University. Double $44. Deadline for reservations is February 17, Graph theory, Karen L. Collins, Wesleyan University, 1994. and Ewa M. Kubicka, University of Louisville. Collaborative learning in calculus and precalculus, Registration Michael B. Freeman, University of Kentucky. The meeting registration desk will be located in the main Inverse spectral problems: theory and computation, Peter foyer on the ground floor of the Business and Economics D. Hislop and Peter Perry, University of Kentucky. Building, which is near the main gate on South Limestone H omtopy theory, Mark A. Hovey, University of Kentucky, Street, and will be open from 7:30a.m. to 5:00p.m. on Friday, and James E. McClure. March 18, and 7:30 a.m. to noon on Saturday, March 19. Combinatorics of words and equations in algebra, logic, The registration fees are $30 for members of the AMS, $45 and computer science, George F. McNulty. for nonmembers, and $10 for emeritus members, students, or Quantum algebraic geometry, David R. Morrison, Insti­ unemployed mathematicians. tute for Advanced Study. Elliptic genera and elliptic cohomology, Serge Ochanine, University of Kentucky. Travel Large-scale matrix computations with applications, Charles Delta has been selected as the official airline for this meeting. H. Romine, Oak Ridge National Laboratory. The following benefits are available exclusively to mathe­ Mathematics of many-body quantum theory, M. Beth maticians and their families attending the meeting: a savings Ruskai, University of Massachusetts at Lowell. of up to 10% off any published domestic fare (includes U.S., Canada, Bermuda, the Bahamas, Puerto Rico, and the The deadline for submission of abstracts for consideration in any of these sessions has expired. U.S. Virgin Islands), subject to applicable fare restrictions, There will also be sessions for contributed ten-minute is available. Seats are limited. Call 1-800-241-6760 between papers. The deadline for submission of abstracts for these 8:00a.m. and 11:00 p.m. EST to contact Delta directly or call any licensed travel agent. Instruct the ticket agent to refer to sessions has expired. Unfortunately, late papers cannot be file M0456 in order to qualify for the applicable discount. accommodated.

JANUARY 1994, VOLUME 41, NUMBER 1 39 Kansas State University, Manhattan, Kansas March 25-26, 1994 First Announcement

The eight hundred and ninety-first meeting of the American Accommodations Mathematical Society will be held at Kansas State University Rooms have been blocked for participants at the Ramada in Manhattan, Kansas, on Friday, March 25, and Saturday, Inn, Best Western Continental Inn, and Days Inn. Participants March 26, 1994. All sessions will be held in Cardwell Hall should make their own arrangements directly with the hotel and Waters Hall. of their choice and request the AMS conference rate to obtain the rate listed. All rooms will be on a space-available basis Invited Addresses after March 8, 1994. Marilyn Breen, University of Oklahoma, Krasnosel'skii-type theorems in orthogonal polygons. Ramada Inn (0.2 mile to Cardwell Hall): 17th and Anderson Michael C. Cranston, University of Rochester, On cou­ Avenue, Manhattan, KS 66502. Telephone: 913-539-7531. pling in applications ofprobability to analysis. Single $57 and Double $63. The Ramada Inn is next to David M. Goss, Ohio State University, Zeta functions of the San Bernardino Freeway (Interstate 10). The Ramada characteristic p arithmetic. will furnish complimentary shuttle service to the campus and Mei-Chi Shaw, University of Notre Dame, Solvability complimentary continental breakfast. and estimates for the tangential Cauchy-Riemann operators. to Cardwell Hall): 100 Bluemont Special Sessions Best Western (1.2 miles Avenue, Manhattan, KS 66502. Telephone: 800-452-5111 or Harmonic analysis and probability, Andrew G. Bennett and 913-776-4771. Single or Double $54 ($4 each additional Charles N. Moore, Kansas State University. person). · Groups and geometries, Andrew L. Chermak and Albert L. Delgado, Kansas State University. Days Inn (1.7 miles to Cardwell Hall): 1501 Tuttle Creek Quantum topology, Louis Crane and David Yetter, Boulevard, Manhattan, KS 66502. Telephone: 800-325-2525 Kansas State University. or 913-539-5391. Rooms are $50 (2 double beds, 1-4 people). Global fields, David M. Goss, Ohio State University; Michael I. Rosen, Brown University; and Dinesh Thaker, Other hotels/motels in the area are the Holiday Inn (1.8 University of Arizona. miles to Cardwell Hall), tel: 913-539-5311; Super 8 Motel (1.6 Special functions, Robert A. Gustafson, Texas A&M miles to Cardwell Hall), tel: 913-537-8468 or (800) 800-8000; University. and Motel6 (1.3 mile to Cardwell Hall), tel: 913-537-1022. Several complex variables and partial differential equa­ Registration tions, A. Alexandrou Himonas, Institute of Advanced Study, The registration desk will be located inside the main entrance and Mei-Chi Shaw. to Cardwell Hall and will be open from 8:00a.m. to 5:00p.m. Nonlinear topics and critical phenomena in partial dif­ on Friday, March 25, and from 8:00 a.m. to noon on Saturday, ferential equations, Lev Kapitanski, Brown University, and March 26. The registration fees are $30 for members of the Lige Li, Kansas State University. AMS, $45 for nonmembers, and $10 for emeritus members, Representations of algebraic groups and quantum groups, students, or unemployed mathematicians. State Univer­ Zongzhu Lin and David B. Surowski, Kansas Social Events sity. A cash bar reception will be held on Friday evening from 8:00 Operator theory, Gabriel Nagy, Kansas State University, p.m. to 11:00 p.m. at the Ramada Inn located just south of the and Vladimir V. Peller, University of Hawaii. Kansas State campus. Convergence problems in ergodic theory, Joseph M. Rosenblatt, Ohio State University. Travel Dynamical systems and fluid dynamics, Misha Vishik, USAir is the official airline for this meeting. The following University of Texas at Austin. benefits are available exclusively to mathematicians and Computational mathematics and numerical analysis, Hu­ their families attending the meeting: 10% discount off any nan Yang and Qisu Zou, Kansas State University. published domestic fare with a seven-day advance purchase. The deadline for submission of abstracts for consideration Call USAir's Meetings and Convention Reservation Office at in any ofthese·sessions has expired. 1-800-334-8644 between 8:00a.m. and 9:00p.m. EST or call There will also be sessions for contributed ten-minute any licensed travel agent. Instruct the agent to refer to gold papers. This deadline has also expired. file #16950015 in order to qualify for the applicable discount.

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

Invited Addresses at AMS Meetings April1994 Meeting in Brooklyn, New York The individuals listed below have accepted invitations to Eastern Section address the Society at the times and places indicated. For Associate Secretary: Lesley M. Sibner Deadline for organizers: Expired some meetings the list of speakers is incomplete. For full Deadline for consideration: Expired announcements or programs of meetings occurring prior Boris Aronov, Computational geometry to the first meeting listed below see the table of contents Craig J. Benham, Mathematical problems in molecular biology in this issue. Invited addresses at Sectional Meetings are Joan S. Birman, Sylvain E. Cappell, and Edward Y. Miller, selected by the Section Program Committee, usually twelve to Invariants of low dimensional manifolds eighteen months in advance of a meeting. Members wishing Jozef Dodziuk and Edgar A. Feldman, Geometric analysis to nominate candidates for invited addresses should send Benjamin Fine, Anthony M. Gaglione, and Kathryn Kuiken, relevant information to the associate secretary for the section Combinatorial group theory and related topics who will forward it to the Section Program Committee. Frederick P. Gardiner and Yunping Jiang, Teichmiiller theory and dynamical systems Dorian Goldfeld, Analytic number theory Brooklyn, NY, April1994 Jacob E. Goodman and Erwin Lutwak, Geometric convexity David Bayer Debasis Mitra Pao-sheng Hsu and L. Narisi, Topological methods; topologi- Peter B. Kronheimer Nicholai Reshetikhin cal measure the01y Yanyan Li, Partial differential equations Eugene, OR, June 1994 Janos Pach and William Steiger, Discrete geometry Stephen A. Mitchell Gustavo A. Ponce Robert J. Sibner, Gauge the01y and applications Alan A. Weiss, Models in telecommunications

Minneapolis, MN, August 1994 June 1994 Meeting in Eugene, Oregon Todd J. Arbogast Carole B. Lacampagne Western Section (AMS-MAA) (AMS-MAA) Associate Secretary: Lance W. Small Deadline for organizers: Expired Cameron Gordon Pierre Louis Lions Deadline for consideration: March 14, 1994 (AMS-MAA) (Progress Lecturer) Frank W. Anderson and Kent R. Fuller, Rings and their representations Stillwater, OK, October 1994 Steven A. Bleiler, 3-manifolds Frank R. Demeyer and Thomas M. McKenzie, Commutative V. Lakshmibai David J. Wright algebra and probability groups David E. Marker Joel Zinn Paul G. Goerss and Stephen A. Mitchell, Algebraic K-the01y and homotopy Richmond, VA, November 1994 Chris Phillips, Simple C*-algebras Loren D. Pitt Doron Zeilberger Robby Robson, Undergraduate research Cora S. Sadosky August 1994 Meeting in Minneapolis, Minnesota Associate Secretary: Lesley M. Sibner Hartford, CT, March 1995 Deadline for organizers: Expired Ben F. Logan Kari Vilonen Deadline for consideration: April 26, 1994 Nina N. Uraltseva Shouwu Zhang October 1994 Meeting in Stillwater, Oklahoma Central Section Associate Secretary: Andy R. Magid Organizers and Topics of Special Sessions Deadline for organizers: January 28, 1994 The list below contains all the information about special Deadline for consideration: July 13, 1994 sessions at meetings of the Society available at the time this Ara S. Basmajian and Robert R. Miner, Complex hyperbolic issue of the Notices went to the printer. geometry and discrete groups

JANUARY 1994, VOLUME 41, NUMBER 1 41 ...... ______.... _...... Meetings

Edward T. Cline, Representations of algebraic groups January 1996 Meeting in Orlando, Florida Brian Conrey and William D. Duke, Number theory Associate Secretary: Lance W. Small Bruce C. Crauder and Zhenbo Qin, Algebraic geometry Deadline for organizers: April 12, 1995 Deadline for consideration: To be announced Edward G. Dunne and Roger C. Zierau, Geometry and representations of Lie groups Benny D. Evans, The evolving undergraduate mathematics March 1996 Meeting in Iowa City, Iowa curriculum Central Section Associate Secretary: Andy R. Magid Vladimir Ezhov and Alan V. Noell, Several complex variables Deadline for organizers: June 22, 1995 Jerry A. Johnson, Technology in the classroom Deadline for consideration: To be announced Daniel D. Anderson, Commutative ring theory November 1994 Meeting in Richmond, Virginia Southeastern Section April1996 Meeting in Baton Rouge, Louisiana Associate Secretary: Robert J. Daverman Southeastern Section Deadline for organizers: February 11, 1994 Associate Secretary: Robert J. Daverman Deadline for consideration: July 13, 1994 Deadline for organizers: July 19, 1995 Paul S. Bourdon and William T. Ross, Operator on Banach Deadline for consideration: To be announced spaces of analytic functions January 1997 Meeting in San Diego, California January 1995 Meeting in San Francisco, California Associate Secretary: Lesley M. Sibner Deadline for organizers: April 8, 1996 Associate Secretary: Andy R. Magid Deadline for consideration: To be announced Deadline for organizers: April 2, 1994 Deadline for consideration: September 9, 1994 Information for Organizers March 1995 Meeting in Hartford, Connecticut Special sessions at Annual and Summer Meetings are held Eastern Section under the supervision of the Program Committee for National Associate Secretary: Lesley M. Sibner Meetings (PCNM). They are administered by the associate Deadline for organizers: June 3, 1994 secretary in charge of that meeting with staff assistance from Deadline for consideration: To be announced the meetings department in the Society office in Providence. Special sessions are selected by the PCNM from a March 1995 Meeting in Orlando, Florida list of proposed special sessions in essentially the same Southeastern Section manner as individuals are selected to give invited addresses. Associate Secretary: Robert J. Daverman The number of special sessions at a Summer or Annual Deadline for organizers: June 17, 1994 Deadline for consideration: To be announced Meeting is limited. Precise details concerning proposals for Robert C. Brigham and Richard P. Vitray, Combinatorics and and organization of special sessions are contained in the graph theory "Rules for Special Sessions", available upon request from the John R. Cannon, Inverse and ill-posed problems meetings department or any associate secretary. S. Roy Choudhury, Nonlinear dynamical systems, chaos, and Each person selected to give an invited address is invited turbulence to generate a special session, either by personally organizing S. Roy Choudhury and Lokenath Debnath, Solitons and one or by having a organized by others. Proposals to organize nonlinear waves a special session are sometimes requested either by the Xin Li and Ram N. Mohapatra, Approximation theory and PCNM or by the associate secretary. Other proposals should special functions be submitted to the associate secretary in charge of that Piotr Mikusinski, New trends in generalized functions meeting (who is an ex officio member of the committee). Ahmed I. Zayed, Sampling theory, wavelets, and signal These proposals must be in the hands of the PCNM at least processing nine months prior to the meeting at which the special session is to be held in order that the committee may consider all the proposals for special sessions simultaneously. March 1995 Meeting in Chicago, Illinois It should be noted that special sessions must be announced Central Section in the Notices in such a timely fashion that any Society member Associate Secretary: Andy R. Magid Deadline for organizers: June 24, 1994 who so wishes may submit an abstract for consideration for Deadline for consideration: To be announced presentation in the special session. The consideration deadline is usually three weeks before the usual deadline for abstracts for the meeting. November 1995 Meeting in Kent, Ohio The processing of proposals for special sessions for Central Section Associate Secretary: Andy R. Magid Sectional Meetings is handled in essentially the same manner Deadline for organizers: February 4, 1995 as for Annual and Summer Meetings by the Section Program Deadline for consideration: To be announced Committee. Again, no special session at a Sectional Meeting

42 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings may be approved so late that its announcement appears past office (Abstracts Coordinator, AMS Meetings Department, the deadline after which members can no longer send abstracts P.O. Box 6887, Providence, RI 02940) by the special deadline for consideration for presentation in that special session. for special sessions, which is usually three weeks earlier than The Society reserves the right of first refusal for the the deadline for contributed papers for the same meeting. publication of proceedings of any special session. These The Council has decreed that no paper, whether invited or proceedings appear in the book series Contemporary Mathe­ contributed, may be listed in the program of a meeting of the matics. Society unless an abstract of the paper has been received in Western Section Providence prior to the deadline. Lance W. Small, Associate Secretary Electronic submission of abstracts is available to those Department of Mathematics who use the 1FX typesetting system. The electronic package of University of California, San Diego files may be requested from e-MATH via e-mail by following La Jolla, CA 92093 E-mail: [email protected]. ams. org this procedure: Telephone: 619-534-3590 1. Type telnet e-math@math. ams. org. Central Section 2. When asked for login, type e-math. Andy R. Magid, Associate Secretary 3. When asked for password, type e-math. Department of Mathematics 4. Type Q to bypass welcome information and go directly University of Oklahoma to the Main Menu. 601 Elm PHSC 423 5. In the Main Menu, select #12 for Gopher. Norman, OK 73019 6. In Gopher, select #11 for Meetings and Conferences. E-mail: [email protected]. ams. org 7. In Meetings and Conferences, select #3 for Abstracts Telephone: 405-325-6711 and follow the instructions for the type of 1FX macro Eastern Section package needed. Lesley M. Sibner, Associate Secretary Users may also obtain the package on illM or Macintosh Department of Mathematics Polytechnic University diskettes, available free of charge by writing to Electronic Brooklyn, NY 11201-2990 Abstracts, AMS Meetings Department, P.O. Box 6887, Prov­ E-mail: [email protected]. ams. org idence, RI 02940. When requesting the abstracts package, Telephone: 718-260-3505 be sure to specify either the plain '!FX, A,MS-'IFX, or the Southeastern Section h'IFX package. Requests for general information concerning Robert J. Daverman, Associate Secretary abstracts may be sent to abs-misc@math. ams. org. Department of Mathematics University of Tennessee Number of Papers Presented Knoxville, TN 37996-1300 E-mail: g_daverman@math. ams. org Joint Authorship Telephone: 615-974-6577 Although an individual may present only one ten-minute As a general rule, members who anticipate organizing special contributed paper at a meeting, any combination of joint sessions at AMS meetings are advised to seek approval at least nine authorship may be accepted, provided no individual speaks months prior to the scheduled date of the meeting. more than once. An author can speak by invitation in more than one special session at the same meeting. Information for Speakers An individual may contribute only one abstract by title A great many of the papers presented in special sessions at in any one issue of Abstracts, but joint authors are treated as meetings of the Society are invited papers, but any member a separate category. Thus, in addition to abstracts from two of the Society who wishes to do so may submit an abstract for individual authors, one joint abstract by them may also be consideration for presentation in a special session, provided it accepted for an issue. is received in Providence prior to the special early deadline announced above and in the announcements of the meeting. Site Selection for Sectional Meetings Contributors should know that there is a limitation in size of Sectional Meeting sites are recommended by the associate a single special session, so that it is sometimes true that all secretary for the Section and approved by the Secretariat. places are filled by invitation. Recommendations are usually made eighteen to twenty-four Papers submitted for consideration for inclusion in special months in advance. Host departments supply local infor­ sessions but not accepted will receive consideration for a ten­ mation, ten to twelve rooms with overhead projectors for minute contributed paper session, unless specific instructions contributed paper sessions and special sessions, an auditorium to the contrary are given. Contributed papers will be grouped with twin overhead projectors for invited addresses, and reg­ by related Mathematical Reviews subject classifications into istration clerks. The Society partially reimburses for the rental sessions, insofar as possible. The title of each paper accepted of facilities and equipment, and for staffing the registration and the time of presentation will be listed in the program of desk. Most host departments volunteer; to do so, or for more the meeting. information, contact the associate secretary for the Section. Abstracts of papers submitted for consideration for presen­ tation at a special session must be received by the Providence

JANUARY 1994, VOLUME 41, NUMBER 1 43 Joint Summer Research Conferences in the Mathematical Sciences Mount Holyoke College, South Hadley, Massachusetts, June 11 to July 15, 1994

The 1994 Joint Summer Research Conferences in the Math­ Please type or print the following: ematical Sciences will be held at Mount Holyoke College, 1. Title and dates of conference desired. South Hadley, Massachusetts, from June 11 to July 15. It is 2. Full name. anticipated that the series of conferences will be supported 3. Mailing address. by grants from the National Science Foundation and other 4. Telephone number and area code for office and home, agencies. e-mail address, fax number. There will be six conferences in six different areas of 5. A short paragraph describing your scientific background mathematics. The topics and organizers for the conferences relevant to the topic of the conference. Also indicate if were selected by the AMS, the Institute of Mathematical you are a graduate or undergraduate student, or if you Statistics (IMS), and the Society for Industrial and Applied received your Ph.D. on or after 7/1188. Mathematics (SIAM) Committee on Joint Summer Research 6. Financial assistance requested; please estimate cost of Conferences in the Mathematical Sciences. The selections travel. were based on suggestions made by the members of the 7. Indicate if support is not required and if interested in committee and individuals submitting proposals. The com­ attending even if support is not offered. mittee considered it important that the conferences represent diverse areas of mathematical activity, with emphasis on The deadline for receipt of requests for information is areas currently especially active, and paid careful attention to March 4, 1994. Requests to attend will be forwarded to the subjects in which there is important interdisciplinary activity Organizing Committee for each conference for consideration at present. after the deadline of March 4. All applicants will receive The Joint Summer Research Conferences are intended to a formal invitation, Brochure of Information, notification of complement the Society's program of annual Summer Insti­ financial assistance, and a tentative scientific program (if tutes and Summer Seminars, which have a larger attendance the chair has prepared one in advance; otherwise, programs and are substantially broader in scope. The conferences are will be distributed at on-site registration) from the AMS by research conferences and are not intended to provide an entree May 1. Funds available for these conferences are limited and to a field in which a participant has not already worked. individuals who can obtain support from other sources should It is expected that funding will be available for a limited do so. The allocation of grant funds is administered by the number of participants in each conference. Others, in addition AMS office, and the logistical planning for the conferences to those funded, will be welcome, within the limitations is also done by the AMS. However, it is the responsibility of of the facilities of the campus. In the spring a brochure the chair of the Organizing Committee of each conference to of information will be mailed to all who are requesting to determine the amount of support participants will be awarded. attend the conferences. The brochure will include information This decision is not made by the AMS. Women and minorities on room and board rates, the residence and dining hall are encouraged to apply and participate in these conferences. facilities, travel, local information, and a Residence Housing Any questions concerning the scientific portion of the Form to request on-campus accommodations. Information on conference should be directed to the chair or any member of off-campus housing will also be included in the brochure. the Organizing Committee. Participants will be responsible for making their own housing The Joint Summer Research Conferences in the Mathemat­ and travel arrangements. Each participant will be required to ical Sciences are under the direction of the AMS-IMS-SIAM pay a conference fee. Committee on Joint Summer Research Conferences in the Those interested in attending one of the conferences should Mathematical Sciences. The following committee members send the following information to the Summer Research chose the topics for the 1994 conferences: Fan R. K. Chung, Conference Coordinator, Conferences Department, American Leonard Evens, Alan F. Karr, Peter W. K. Li, Bart Ng, Stew­ Mathematical Society, Post Office Box 6887, Providence, RI art B. Priddy, Robert J. Serfling, Michael Shub, William E. 02940; fax: 401-455-4004; e-mail: chh@math. ams. org. Strawderman, and Sue Whitesides.

N.B. Lectures begin on Sunday morning and run through Thursday. Check in for housing begins on Saturday. No lectures are held on Saturday.

44 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

Please refer to the November issue of the Notices for complete Saturday, June 25, to Friday, July 1 descriptions. Markov chain Monte Carlo methods ALAN GELFAND (University of Connecticut), chair Saturday, June 11, to Friday, June 17 Continuous algorithms and complexity Saturday, July 2, to Friday, July 8 J. F. TRAUB (Columbia University), co-chair Periodicity and structured homology theories in homotopy J. RENEGAR (Cornell University), co-chair the my PAUL G. GoERSS (University of Washington), co-chair Saturday, June 18, to Friday, June 24 HAL SADOFSKY (Johns Hopkins University), co-chair PAUL L. SHICK (John Carroll University), co-chair Moonshine, the monste1~ and related topics GEOFFREY MASON (University of California, Santa Cruz), chair Saturday, July 9, to Friday, July 15 CHONGYING DoNG (University of California, Santa Cruz), Bergman spaces and the operators that act on them co-chair STEPHEN D. FISHER (Northwestern University), co-chair JoHN McKAY (Concordia University), co-chair SHELDON AXLER (Michigan State University), co-chair PETER L. DuREN (University of Michigan), co-chair Saturday, June 25, to Friday, July 1 Multidimensional complex dynamics ERic D. BEDFORD (Indiana University), co-chair JoHN-ERIK FoRNJESS (University of Michigan, Ann Arbor), co-chair

UNIVERSI1Y LECTURE SERIES Group Characters, Symmetric Functions, and the Heeke Algebra David Goldschmidt Volume 4

The book is made up of lecture notes from a course taught by Goldschmidt at the University of California at Berkeley in 1989. The course was organized in three parts. Part I covers, among other things, Burnside's Theorem that groups of order p"qb are solvable, Frobenius's Theorem on the existence of Frobenius kernels, and Brauer's characterization of characters. Part II covers the classical character theory of the symmetric group and includes an algorithm for computing the character table of S"; a construction of the Specht modules; the "determinant form" for the irreducible characters; the hook-length formula of Frame, Robinson, and Thrall; and the Murnaghan-Nakayama formula. Part III covers the ordinary representation theory of the Heeke algebra. the construction of the two-variable Jones polynomial. and a derivation of Ocneanu's "weights" due to T. A. Springer.

1991 Mathematics Subject Classification: 20. 57 ISBN 0-8218-7003-3, 73 pages (softcover). June 1993 Individual member $42. List price $70, Institutional member $56 To order, please specify ULECT/4NA

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

JANUARY 1994, VOLUME 41, NUMBER 1 45 1994 Summer Seminar in Applied Mathematics

Dynamical systems and probabilistic methods for nonlinear waves Mathematical Sciences Research Institute, Berkeley, California, June 20-July 1

The twenty-fourth AMS-SIAM Summer Seminar in Applied results in the equilibrium statistical mechanics of solitons, in Mathematics will be held June 20-July 1, 1994, at the Math­ the advection of a passive scalar via a random velocity field, ematical Sciences Research Institute in Berkeley, California. in nonequilibrium statistical theories of both weak and strong The seminar will be sponsored by the American Mathematical turbulence, and in stochastic pde's such as the randomly forced Society, the Mathematical Sciences Research Institute, and Burgers and nonlinear Schroedinger equations. Controlled the Society for Industrial and Applied Mathematics. It is numerical studies are beginning to appear which investigate anticipated that the seminar will be partially supported by the coexistence of random and nonlinear effects in waves, and grants from federal agencies. The proceedings of the seminar which test the predictions of the more heuristic turbulence will be published by the American Mathematical Society in theories. These theories and numerical studies directly impact the Lectures in Applied Mathematics series. our knowledge of wind-driven waves in the ocean, of chaotic Nonlinear waves provide a rich source of phenomena and turbulent behavior in plasmas, of the long-distance which are important to both mathematics and science. Sci­ propagation of laser pulses in nonlinear fibers, and of idealized entifically, these include disturbances in the atmosphere and models of proteins and DNA, for example. the oceans, the propagation of laser light in nonlinear optics, This research area, bringing probabilistic and dynamical and waves in plasmas and fluids. Mathematically, nonlinear systems methods to bear on pde's, is very broad. Advances wave theory has unveiled the soliton: one of the most im­ require that modem mathematical theories, together with portant discoveries in nonlinear partial differential equations computational and visualization methods, be developed and (pde's) during the last twenty-five years. In addition, results applied to appropriate and relevant scientific problems. Prob­ in nonlinear wave theory include rigorous descriptions of the abilistic and dynamical methods pose important technical scattering of localized solitary waves, detailed descriptions of problems in pde theory and unveil fascinating new phenom­ the development of singularities for nonlinear pde's, a thor­ ena. They constitute an important general area to expose to ough understanding of dissipative and dispersive mechanisms researchers who are just initiating their own programs. for the regularization of these singularities, and numerical The organizing committee consists of Percy Deift, observations (with theoretical interpretation) of temporally Courant Institute for the Mathematical Sciences, New York chaotic behavior in nonlinear dissipative waves. University; Philip Holmes (co-chair), Cornell University; From a mathematical perspective, many recent results James M. Hyman, Los Alamos National Laboratories; about nonlinear waves belong to a relatively new area­ C. David Levermore, University of Arizona; David W. infinite dimensional dynamical systems theory for pde's. McLaughlin (co-chair), Princeton University; Y. Sinai, Princeton University; and C. Eugene Wayne, Pennsylva­ Soliton equations are completely integrable Hamiltonian sys­ nia State University. tems in infinite dimensions. The stability and scattering of Expository series of lectures will be given by senior solitary waves naturally admit dynamical systems interpreta­ researchers including Peter S. Constantin, Walter L. Craig, tions which play a central role in their resolution. The same Percy Deift, Charles Doering, Hermann Flaschka, Nancy J. can be said of the description of the development and be­ Kopell, Dave Levermore, David W. McLaughlin, Alexander havior of singularities for nonlinear Schroedinger equations. Mielke, Gene Wayne, and Steve Wiggins. Dynamical systems theory is central to any study of chaotic dispersive waves. Those interested in attending the seminar should send However, from a scientific perspective, these successes the following information before March 15, 1994, to AMS­ have been restricted to relatively simple situations involving SIAM Summer Seminar Conference Coordinator, American one, a very few, or a regular array of solitary waves. To Mathematical Society, P.O. Box 6887, Providence, R.I. 02940; address issues of greater scientific relevance and complexity, e-mail: dls@math. ams . org. Please type or print the following: it is likely that probabilistic methods for nonlinear pde's 1. Full name and mailing address; are required. Nonlinear waves are beginning to provide an 2. Telephone number and area code for office and home; excellent testing ground for these methods. Natural questions 3. E-mail address if available; concern the interaction of many solitary waves (coherent 4. Anticipated arrival and departure dates; structures) with each other and with a random environment 5. Your scientific background relevant to the topic of the which itself could be fixed or evolving. seminar; please indicate if you are a student or if you More specifically, the organizers note recent mathematical received your Ph.D. on or after 7/1188;

46 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

6. Financial assistance requested (please estimate cost of to apply for a grant-in-aid should so indicate; however, funds travel); indicate if support is not required and if interested available for the seminar are very limited, and individuals who in attending even if support is not offered. can obtain support from other sources should do so. Graduate students who have completed at least one year of graduate Special encouragement is extended to junior scientists to school are encouraged to participate. apply. A special pool of funds expected from federal agencies has been earmarked for this group. Other participants who wish

American Mathematical Society Translations, Series 2

Ordered Sets and Lattices II Volume 152

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativny{ Zhurnal Matematika from mid-1982 to the end of 1985. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

1991 Mathematics Subject Classification: 06; 03, 08 ISBN 0-8218-7501-9, 247 pages (hardcover), November 1992 Individual member $77, List price $128, Institutional member $102 To order, please specify TRANS2/152NA Singularity Theory and Some Problems of Functional Analysis Volume 153 S. G. Gindikin, Editor

The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians-as well as physicists, engineers, and other consumers of singularity theory-to the world of ideas and methods in this burgeoning area.

1991 Mathematics Subject Classification: 40, 51, 57, 58, 92; 12, 19, 28, 32, 35, 49, 60 ISBN 0-8218-7502-7, 199 pages (hardcover), November 1992 Individual member $61, List price $101, Institutional member $81 To order, please specify TRANS2/153NA ~~~-·~,,~ All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: l~~~g 9, American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS (321-4267) ~ ~ ~ ~ in tbe U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

·~l.?JDED \'l:.'b'b•

JANUARY 1994, VOLUME 41, NUMBER 1 47 Symposium on Quantization and Nonlinear Wave Equations Massachusetts Institute of Technology, Cambridge, Massachusetts June 7-11, 1994

With the support of a fund established by Dr. and Mrs. Carroll University of Pennsylvania; Richard Schoen, Stanford Uni­ V. Newsom in honor of the memory of John von Neumann and versity; Irving Segal, Massachusetts Institute of Technology; anticipated support from the National Science Foundation, a Walter Strauss, Brown University; Michelle Vergne, Cen­ symposium on Quantization and nonlinear wave equations tre de Recherche Scientifique; Arthur Wightman, Princeton will take place at the Massachusetts Institute of Technology, University; and Zhengfang Zhou, Michigan State University. Cambridge, Massachusetts, from Tuesday through Saturday, A list of prospective panel discussion leaders includes June 7-11, 1994. Victor Guillemin, Massachusetts Institute of Technology; The topic was selected by the AMS Committee on Summer Cathleen S. Morawetz, Courant Institute of Mathematical Institutes and Special Symposia, whose members at the time Sciences; P. L. Lions, University of Paris; and David Vogan, of selection were William Browder, Princeton University; Massachusetts Institute of Technology. Dotiald L. Burkholder, University of lllinois; Lawrence Craig One afternoon will be free of scheduled talks in order Evans, University of California, Berkeley; Melvin Hochster, to facilitate ad hoc scientific discussions or visits to sites of University of Michigan; Nicholas Katz, Princeton University; general interest in the greater Boston area. Brian Parshall (chair), University of Virginia; Jean-Francois Accommodations will be in MIT dormitories located on Treves, Rutgers University; and Edward Witten, Institute the Charles River a short walk from the meeting area. Rooms for Advanced Study. Proceedings will be published by the of several sizes and types will be available, both with and American Mathematical Society. without a meal plan. MIT is conveniently reached by subway The Organizing Committee for the symposium includes or taxi from the rail terminus, South Station, or Logan Airport William Arveson, University of California, Berkeley; Robert in a matter of minutes. MIT adjoins Kendall Square, which Blattner, University of California, Los Angeles; Haim is well supplied with hotels and restaurants. The meeting Brezis, Rutgers University and University of Paris (co-chair); area will be close to the Institute Science Library and nearby Thomas Branson, University of Iowa; and Irving Segal, discussion/seminar rooms will be available. Massachusetts Institute of Technology (co-chair). In the spring a brochure of information will be mailed to The symposium will review, report recent progress in, all who are requesting to attend the symposium. The brochure and survey possible future directions in the field of physical will include information on room and board rates, the res­ mathematics that was at the heart of von Neumann's moti­ idence and dining hall facilities, travel, local information, vation and some of his most seminal contributions. Session and a Residence Housing Form to request on-campus ac­ topics include the global theory of classical nonlinear wave commodations. Information on off-campus housing will also equations and its differential geometric and general relativistic be included in the brochure. Participants will be responsible aspects; the mathematical theory of quantum fields and its for making their own housing and travel arrangements. It is algebraic and constructive aspects; operator algebra, groups expected that funding will be available for a limited number of automorphisms, and new directions in quantum mechanics; of participants. Limited support is expected to be available for and symplectic quantization and group representations. graduate students. A social fee of $15 will be required. A list of prospective speakers includes William Arveson, Those interested in attending the symposium should send University of California, Berkeley; Robert Blattner, Univer­ the following information to the Symposium Conference Co­ sity of California, Los Angeles; Thomas Branson, University ordinator, Meetings and Conferences Department, American of Iowa; Haim Brezis, Rutgers University and University Mathematical Society, Post Office Box 6887, Providence, RI of Paris; Yvonne Choquet-Bruhat, University of Paris; Alain 02940; fax: 40 1-455-4004; e-mail: wsd@math. ams . org. Connes, College de France and Institute des Hautes Etudes Please type or print the following: Scientifiques; Ludwig Faddeev, Steklov Mathematical Insti­ 1. Full name. tute; Charles Fefferman, Princeton University; Jurg Frohlich, 2. Mailing address. Eidgenosse Technische Hochschule; Izrail Gelfand, Rutgers 3. Telephone number and area code for office and home, University; Leonard Gross, Cornell University; Roger Howe, e-mail address, fax number. Yale University; Arthur Jaffe, Harvard University; Palle Jor­ 4. A short paragraph describing your scientific background gensen, University of Iowa; Sergio Klainerman, Princeton relevant to the topic of the conference. University; David Kazhdan, Harvard University; Peter Lax, 5. Financial assistance requested; please estimate cost of Courant Institute of Mathematical Sciences; Robert Power, travel.

48 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ·-········ . ···-··:~:···T·····---.. -·--·-··-··-·-·-··-·-····-·- Meetings

6. Indicate if support is not required and if interested in available for the symposium are limited, and individuals who attending even if support is not offered. can obtain support from other sources should do so. The 7. Indicate if graduate student, undergraduate student, or allocation of grant funds is administered by the AMS office, Ph.D. received on or after 7/1188. and the logistical planning for the conferences is also done The deadline for receipt of requests for information by the AMS. However, it is the responsibility of the co-chairs is March 1, 1994. Requests to attend will be forwarded of the Organizing Committee to determine the am,ount of to the Organizing Committee for consideration after the support participants will be awarded. Women and minorities deadline of March 1. All applicants will receive a formal are encouraged to apply and participate in this symposium. invitation, Brochure of Information, notification of financial Any questions concerning the scientific portion of the assistance, and a tentative scientific program (if the co-chairs symposium should be directed to Irving Segal, MIT, Room have prepared one in advance; otherwise, programs will be 2-244, Cambridge, MA 02139; telephone: 617-253-4985; distributed on-site) from the AMS by May 1, 1994. Funds e-mail: ies@math. mit. edu.

TRANSLATIONS OF MATHEMATICAL MONOGRAPHS

Functions on Manifolds Algebraic and Topological Aspects V. V. Sharko Volume 131

This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.

1991 Mathematics Subject Classification: 57, 58 ISBN 0-8218-4578-0, 193 pages (hardcover), November 1993 Individual member $59, List price $98, Institutional member $78 To order, please specify MMON0/131NA ...... All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-32l-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.

JANUARY 1994, VOLUME 41, NUMBER 1 49 Mathematical Sciences Meetings and Conferences February 1994 February 1994. WorkshoponDynamicaiDis­ ease, Laurentian Mountains north of Montreal. (Jan. 1992, p. 64) February-mid-May. Linear Operators, Ste­ fan Banach International Mathematical Center, THIS SECTION contains announcements of meetings and conferences of interest to some segment of the mathematical public, including ad hoc, local, or regional meetings, and Warsaw, Poland. (Nov. 1993, p. 1253) meetings or symposia devoted to specialized topics, as well as announcements of regularly 2-4. IMACS Symposium on Mathematical scheduled meetings of national or international mathematical organizations. A complete listing Modelling, Vienna, Austria. (Jul./Aug. 1993, of meetings of the Society, and of meetings sponsored by the Society, will be found inside the p. 711)) front cover. 4-5. Conference on Applied Mathemat­ AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers and specifies the place, date, subject (when applicable), and the speakers; a second ics (CAM), University of Central Oklahoma, announcement will be published only if there are changes or necessary additional information. Edmond, OK. (Dec. 1993, p. 1445) Once an announcement has appeared, the event will be briefly noted in each issue until it has 6-10. AMC 94: The Thirtieth Australian been held and a reference will be given in parentheses to the month, year, and page of the Applied Mathematics Conference, Pokolbin, issue in which the complete information appeared. Asterisks (*) mark those announcements Hunter Valley, N.S.W. (Nov. 1993, p. 1253) containing new or revised information. IN GENERAL, announcements of meetings and conferences held in North America carry 6-12. C*-Aigebren, Oberwolfach, Federal only date, title of meeting, place of meeting, names of speakers (or sometimes a general Republic of Germany. (Mar. 1993, p. 285) statement on the program), deadlines for abstracts or contributed papers, and source of 7-11. Differential Geometry, Hamiltonian further information. Meetings held outside the North American area may carry more detailed Systems, and Operator Theory, University information. In any case, if there is any application deadline with respect to participation in of the West Indies, Mona, Jamaica. (Jul./Aug. the meeting, this fact should be noted. All communications on meetings and conferences in 1993, p. 711) the mathematical sciences should be sent to the Editor of the Notices, care of the American Mathematical Society in Providence, or electronically to notices@math. ams. org. 10-11. IMACS Workshop on Theoretical DEADLINES for entries in this section are listed on the inside front cover of each issue. In and Computational Aspects of 'furbulence, order to allow participants to arrange their travel plans, organizers of meetings are urged Rutgers University, New Brunswick, NJ. (Dec. to submit information for these listings early enough to allow them to appear in more than 1993, p. 1445) one issue of the Notices prior to the meeting in question. To achieve this, listings should be * 12-13. Third Southern California Geomet­ received in Providence SIX MONTHS prior to the scheduled date of the meeting. ric Analysis Seminar, University of Califor­ EFFECTIVE with the 1990 volume of the Notices, the complete list of Mathematical Sciences Meetings and Conferences will be published only in the September issue. In all other issues, nia, Irvine, CA. only meetings and conferences for the twelve-month period following the month of that issue INVITED SPEAKERS: J.P. Bourguignon, Ecole will appear. As new information is received for meetings and conferences that will occur later Polytechnique; T. Lyons, Imperial College; than the twelve-month period, it will be announced at the end of the listing in the next possible W. Muller, Bonn; L. Simon, Stanford; R. issue. That information will not be repeated until the date of the meeting or conference falls Stem, UC Irvine; T. Wolff, UC Berkeley. within the twelve-month period. INFORMATION: P. Li, Dept. of Math., Univ. of California, Irvine, CA 92717; e-mail: pli@oac. uci. edu; tel.: 714-856-5510; (Jul./Aug. 1993, p. 710) fax: 714-856-7993. 1994 23-25. Fifth Annual ACM-SIAM Sympo­ 13-19. Funktionentheorie, Oberwolfach, sium on Discrete Algorithms, Arlington, VA. Federal Republic of Germany. (Mar. 1993, 1994-1995. Mittag-Leffler Institute's Aca­ (May/Jun. 1993, p. 513) demic Program for 1994-1995: Statistical p. 285) Mechanics and Stochastic Analysis, Mittag­ 23-29. Singulare Integral- und Pseudo­ 14-18. Workshop on Galois Module Struc­ Leffler Institute, Djursho1m, Sweden. (Dec. Differentiai-Operatoren und Ihre Anwen­ ture, The Fields Institute, Waterloo, Ontario. 1993, p. 1444) dungen, Oberwolfach, Federal Republic of (No~ 1993,p. 1253) Germany. (Mar. 1993, p. 285) 14-March 4. Winter College on Quantum 24-28. IMA Workshop on Mathematical Optics, Trieste, Italy. (Dec. 1993, p. 1445) Population Genetics, Institute for Mathemat­ 18-23. Section A (Mathematics) Sessions at January 1994 ics and its Applications, University of Min­ the AAAS Annual Meeting, San Francisco, 12-15. Joint Mathematics Meetings, Cincin­ nesota, Minneapolis, MN. (Jan. 1993, p. 64) CA. (Sep. 1993, p. 924) nati, OH (including the annual meetings of the 24-28. Complex Analysis on Hyperbolic 20-26. Barmonische Analyse und Darstel­ AMS, AWM, MAA, and NAM). 3-manifolds, Research Institute for Mathemat­ lungstheorie Topologischer Gruppen, Ober­ wolfach, Federal Republic of Germany. (Mar. INFORMATION: H. Daly, AMS, P.O. Box ical Sciences, Kyoto University, Kyoto, Japan. 1993, p. 286) 6887, Providence, RI 02940. (Jul./Aug. 1993, p. 711) 27-March 5. Mathematical Economics, 16-22. Gruppentheorie (Permutationsgrup­ 25-29. Sixth Benin International Confer­ Oberwolfach, Federal Republic of Germany. pen), Oberwo1fach, Federal Republic of Ger­ ence on Scientific Computing, University of (Mar. 1993, p. 286) Benin City, Nigeria. (Sep. 1993, p. 924) many. (Jul./Aug. 1993, p. 710) 28-March 4. IMA Workshop on Stochastic 17-19. Structure and Statistical Law of 30-February 5. Nichtstandardanalysis und Networks, Institute for Mathematics and its Turbulence, Research Institute for Mathemat­ Anwendungen, Oberwolfach, Federal Repub­ Applications, University of Minnesota, Min­ ical Sciences, Kyoto University, Kyoto, Japan. lic of Germany. (Mar. 1993, p. 285) neapolis, MN. (Jan. 1993, p. 64)

50 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

28-March 4. Workshop on Algebraic K­ NJ. (Dec. 1993, p. 1445) 27-April 2. Endliche Modelltheorie, Ober­ theory and Arithmetic, The Fields Institute, 18-19. Southeastern Section, University of wolfach, Federal Republic of Germany. (Mar. Waterloo, Ontario. (Nov. 1993, p. 1253) Kentucky, Lexington, Kentucky. 1993,p.286) 28-30. Moduli Spaces, Galois Represen­ INFORMATION: W. Drady, AMS, P.O. Box tations, and L-functions, Research Institute 6887, Providence, RI 02940. March 1994 for Mathematical Sciences, Kyoto University, 20-26. Regelungstheorie, Oberwolfach, Fed­ Kyoto, Japan. (Jul./Aug. 1993, p. 711) 4-5. First Permian Basin Conference in eral Republic of Germany. (Mar. 1993, p. 286) 28-30. Conference on Semigroup Theory Algebra and Number Theory, The University 21-24. IMA Period of Concentration: and Its Applications in Memory of Alfred of Texas of the Permian Basin, Odessa, TX. H. Clifford, Tulane University, New Orleans, QDec. 1993,p. 1445) Stochastic Problems for Nonlinear Partial Differential Equations, Institute for Mathe­ LA. (Dec. 1993, p. 1446) *5--6. A Celebration of Women in Mathemat- matics and its Applications, University of Min­ 28-31. Twenty-fifth Annual Iranian Mathe­ ics, MIT, Cambridge, MA. nesota, Minneapolis, MN. (Dec. 1993, p. 1446) matics Conference, Sharif University of Tech­ PROGRAM: This conference is intended 21-25. Symplectic Geometry of Moduli nology, Tehran, Iran. (Jul./Aug. 1993, p. 711) to illustrate the impressive contributions Spaces, CIRM, Marseille/Lurniny. (Sep. 1993, 29-31. Data Compression Conference (DCC that women have made in mathematics. p. 925) '94), Snowbird, Utah. QDec. 1993, p. 1446) Colloquium-style lectures will be given by 21-25. L-functions Conference, Fields Insti­ 31-April2. Mathematical Approaches to the distinguished women mathematicians on a tute, Waterloo, Ontario. (Nov. 1993, p. 1254) Study of Nonlinear Materials, Fayetteville, wide range of topics which will include 21-25. International Conference on Com­ Arkansas. (Sep. 1993, p. 925) analysis, differential geometry, dynamical putational Methods and Function Theory systems, knot theory, minimal surfaces, '94, Penang, Malaysia. (Dec. 1993, p. 1446) mathematical physics, symplectic geome­ try, applied mathematics, and computing. * 21-25. Fourth Workshop and Miniconfer­ April1994 This workshop is funded by the NSF Vis­ ence on Operator Theory and Evolution 3-9. Arbeitsgemeinschaft Mit Aktuellem iting Professorship for Women Program Equations, Louisiana State University, Baton Thema (wird in den. Mitteilungen der DMV and supported by Brown Univ. and MIT. Rouge, LA. Heft 1/1994 Bekanntgegeben), Oberwolfach, All mathematicians are cordially invited to INVITED SPEAKERS: W. Arendt, Ph. Clement, Federal Republic of Germany. (Mar. 1993, attend. I. Cioranescu, R. deLaubenfels, M. De­ p. 286) LECTURERS: J. Birman, Columbia; D. Mc­ muth, K.H. Forster, M. Hieber, V. Keyan­ 4-10. Colorado Conference on Iterative Duff, SUNY, Stony Brook; J. Mesirov, tuo, C. Lizama, G. Lumer, M. Neumann, Methods, Breckenridge, CO. (Nov. 1993, Thinking Machines; C. Morawetz, Courant; M. Pang, D. Pascali, V.Q. Phong, A. Venni, p. 1254) J. Pipher, Brown; J. Taylor, Rutgers; C. Lian P. Vieten, V. Wrobel. Terng, Northeastern; K. Uhlenbeck, U. of INFORMATION: G.R. Goldstein, F. Neubran­ * 5-7. First Annual Meeting of the Saudi Texas; L. Sang Young, U. of Arizona. der, Dept. of Math., LSU, Baton Rouge, LA Association for Mathematical Sciences, King INFORMATION: Susan Friedlander, e-mail: 70803; [email protected] Saud University, Riyadh, Saudi Arabia. [email protected]. or neubrand@marais. math .lsu. edu; CONFERENCE TOPICS: Pure and applied and L. Weis, Math. lnst., Univ. Kiel, 6-12. Mathematische Stochastik, Oberwol­ mathematics, mathematical physics, statis­ 24118 Kiel 1, Germany; e-mail: nms29@ fach, Federal Republic of Germany. (Mar. tics & O.R., mathematical education. rz.uni-kiel.d400.de. 1993,p.286) INFORMATION: Annual Meeting Commit­ tee, Dept. of Math., College of Science, 7-11. Twenty-fifth Southeastern Interna­ 22-24. The Rhine Workshop on Computer King Saud Univ.. P.O. Box 2455, Riyadh tional Conference on Combinatorics, Graph Algebra, Karlsruhe, Germany. (Sep. 1993, 11451, Saudi Arabia. · Theory, and Computing, Florida Atlantic p. 925) University, Boca Raton, FL. (Sep. 1993, p. 924) 24--26. Fourth Eugene Lukacs Symposium, 5-9. MEGA-94, The Third International 7-25. Workshop on Fluid Mechanics, Inter­ Bowling Green State University, Bowling Symposium on Effective Methods in national Centre for Theoretical Physics, Trieste, Green, OH. (Oct. 1993, p. 1085) Algebraic Geometry, Santander, Spain. (Jul./ Italy. (Jul./Aug. 1993, p. 711) 24--27. Joint 1994 Annual Spring Topology Aug. 1993, p. 711) 13-17. The DAB-Georgia Tech Interna­ Conference and Southeast Dynamical Sys­ 5-11. Effective Methods in Algebraic Ge­ tional Conference on Differential Equations tems Conference, Auburn University, Auburn, ometry (MEGA '93), Santander, Spain. (Mar. and Mathematical Physics, Birmingham, AL. AL. (Nov. 1993, p. 1254) 1993, p. 286) (Oct. 1993, p. 1085) 25-26. Central Section, Kansas State Univer­ 5-15. Instructional Conference on Har­ 13-19. Elementare und Analytische Zahlen­ sity, Manhattan, KS. monic Analysis and Partial Differential theorie, Oberwolfach, Federal Republic of Equations, International Centre for Mathemat­ INFORMATION: W. Drady. AMS, P.O. Box Germany. (Mar. 1993, p. 286) ical Sciences, Edinburgh, Scotland. (Jul./Aug. 6887, Providence, RI 02940. 16-19. Prospects in Topology: A Conference 1993, p. 711) on the Occasion of William Browder's 60th 25-26. Southeastern-Atlantic Section of 7-9. 1994 John H. Barrett Memorial Lec­ Birthday, Princeton University, Princeton, NJ. SIAM, Wake Forest University, Winston­ tures on Zero-Dimensional Commutative (Dec. 1993, p. 1445) Salem, NC. (Dec. 1993, p. 1446) Rings, University of Tennessee, Knoxville, 17-19. Seminar on Stochastic Processes 25-27. Third Annual Boise Extravaganza in TN. (Nov. 1993, p. 1254) 1994, Texas A&M University, College Station, Set Theory (BEST) Conference, Boise State 8-9. Mathematical Breakthroughs in the TX. (Sep. 1993, p. 925) University, Boise, Idaho. (Dec. 1993, p. 1446) Twentieth Century, The State University of 17-20. Joint Workshop on Computational 27-April 2. Algebraische Gruppen, Ober­ New York at Farmingdale, NY. (Jul./Aug. 1993, Aspects of Geometric Group Theory II, DI­ wolfach, Federal Republic of Germany. (Mar. p. 712) MACS, Rutgers University, New Brunswick, 1993,p.286) 8-9. lllinois Number Theory Conference,

JANUARY 1994, VOLUME 41, NUMBER 1 51 Meetings and Conferences

University of lllinois, Urbana, IL. (Dec. 1993, cations: A Conference in Honor of Harold and Algebra Dedicated to Roberto Magari p. 1447) J. Kushner, Newport, RI. on his 60th Birthday, Pontignano (Siena), Italy. 8-10. Eastern Section, Polytechnic Univer­ ORGANIZERS: P. Dupuis, A. Shwartz, G. sity, Brooklyn, NY. Yin. PRoGRAM: The program will consist of long INFORMATION: W. Drady, AMS, P.O. Box INVITED SPEAKERS: I. Karatzas, R.Z. Khas­ talks by invited speakers and short talks. 6887, Providence, RI 02940. minskii, P.R. Kumar, T.G. Kurtz, L. Ljung, The main topics will be logic, universal D. Mitra, M.l. Reiman, A.D. Wentzell, M. algebra, and algebraic proof theory. * 9-10. Ninth Union College Conference Zakai. SciENTIFIC CoMMITTEE: E. Fried, G. Gratze: on Category Theory, Algebraic Topology, INFORMATION: J. D'Amico, The Lefschetz D. Mundici, F. Montagna, D. Pigozzi. and Set-theoretic Topology, Union College, Center for Dynamical Systems, Brown Uni­ INVITED SPEAKERS: Teiztative S. Artemov, Schenectady, NY. versity, Providence, RI 02912; 401-863- E. De Giorgi, D. De Jong, E. Kiss, R. Mckenzie, A. Pixley, G. Zappa. PROGRAM: Hour-long invited talks in cat­ 2358; e-mail: jmd@brownvm. brown. edu. FEE AND SUPPORT: The conference fee egory theory, algebraic topology, and set­ 17-22. International Conference on New is expected to range between $130-$180 theoretic topology, along with parallel ses­ Trends in Computer Science I (NETCOMS depending on outside support. A limited sions of contributed talks. 1), University of lbadan, Nigeria. (Please note amount of support is available. Priority CALL FOR PAPERS: Abstract deadline: March date change from Nov. 1992, p. 1121) will be given to the participants corning I, 1994. from the former Eastern Block countries INFORMATION: S. Niefield, niefiels@ 17-23. Designs and Codes, Oberwolfach, and, among them, to those contributing gar.union.edu;B.Johnson,johnsonb@ Federal Republic of Germany. (Mar. 1993, with a paper. gar.union.edu; T.LaBerge,laberget@ p. 286) 18-20. Conference on Emerging Issues in INFORMATION: MAGCONF, Dipartimento gar. union. edu. di Matematica, Via del Capitano, 53100 Mathematics and Computation from the Siena, Italy; fax: (577)-270581; e-mail: 10-16. Numerical Linear Algebra with Materials Sciences, Pittsburgh, PA. (Sep. [email protected]. Applications, Oberwolfach, Federal Republic 1993, p. 925) of Germany. (Mar. 1993, p. 286) 22-24. North East Dynamics Meeting, State * 29-May 1. Fourth Midwest Geometry Con- 11-15. Simulation for Emergency Manage­ University of New York, Stony Brook, NY. ference, University of Iowa, Iowa City, lA. ment, La Jolla, CA. (Dec. 1993, p. 1447) (Dec. 1993,p. 1447) PLENARY SPEAKERS: M.T. Anderson, M. * 11-15. Workshop on L-functions and Auto­ * 24-27. The Second Annual Object-Oriented Gursky, A. Uribe, Z. Zhou. morphic Forms, The Fields Institute, Water­ Numerics Conference, OON-SKI '94, Sun­ INFORMATION: T. Branson, Dept. of Math., loo, Ontario, Canada. river, Oregon. U. of Iowa, Iowa City, lA 52242; 319- ORGANIZER: K. Murty (U. of Toronto). PROGRAM: OON-SKI provides a forum 335-0744; fax: 319-335-0627; branson@ INVITED SPEAKERS: (*tentative) J. Arthur where computer scientists and scientific math. uiowa. edu. (U. of Toronto), D. Bump (Stanford U.), J. programmers can discuss how to use object­ Cogdell (Oklahoma State U.), H. Darmon oriented programming techniques to more (Princeton U.), C. Deninger (U. of Mun­ effectively write complex scientific codes. ster), W. Duke (Rutgers U.)*, E. Fouvry (U. There will be four separate areas of fo­ May 1994 of Orsay)*, J. Friedlander (U. of Toronto), cus: object-oriented environments: design, R. Gupta (U. of British Columbia)*, M. development, and debugging tools; object­ 1-7. Gmppentheorie, Oberwolfach, Federal Harris (U. of Brandeis)*, H. Iwaniec (Rut­ oriented analysis and design methodolo­ Republic of Germany. (Mar. 1993. p. 286) gers U.), H. Jacquet (Columbia U.), S. gies; object-oriented software components 1-7. Linear Operators and Application, Kudla (U. of Maryland), R. Murty (McGill and class libraries; applications. Oberwolfach, Federal Republic of Germany. U.), S. Rallis (Ohio State U.)*, D. Rohrlich INFORMATION: M. Chapman, Program Co­ (Jul./Aug. 1993, p. 712) (U. of Maryland)*, P. Sarnak (Princeton ordinator, Rogue Wave Software, P.O. 2-4. Hard Problems in Mathematical Physics: U.), R. Schulze-Pillot (U. of Cologne), F. Box 2328, Corvallis, OR 97339; e-mail: A Meeting to Celebrate the Sixtieth Birth­ Shahidi (Purdue U.), C. Stewart (U. of amc@roguewave. com; tel: 503-754-3010; day of Paul Federbush, Ann Arbor, MI. (Dec. Waterloo), B. Sury (Tata Institute and U. of fax:503-757-6650. 1993, p. 1447) Toronto). 2-6. IMA Workshop on Image Models (and INFORMATION: For registration informa­ 24-28. First World Congress on Compu­ Their Speech Model Cousins), Institute for tion contact J. Motts, The Fields Insti­ tational Medicine and Public Health, Uni­ Mathematics and its Applications, University tute, 185 Columbia Street West, Waterloo, versity of Texas Center for High Performance of Miunesota, Minneapolis, MN. (Jan. 1993, Ontario, Canada N2L 5Z5; automorp@ Computing, Austin, TX. (Nov. 1993, p. 1255) p. 64) fields. uwaterloo. ca, fax: 519-725- 24-30. Geschichte der Mathematik, Ober­ 2-6. International Conference on Topolog­ 0704,phone:519-725-0096. wolfach, Federal Republic of Germany. (Mar. ical Vector Spaces, Algebras, and Related 1993,p.286) * 11-22. Spring School and Workshop on Areas, McMaster University, Hamilton, On­ String Theory, Gauge Theory, and Quantum 25-29. Third International Conference on p­ tario, Canada. (Mar. 1993, p. 286) Gravity, Trieste, Italy. adic Functional Analysis, Clermont-Ferrand, 2-6. Wavelet Analysis as a Tool for Ge­ France. (Sep. 1993, p. 925) ometric Synthesis and Analysis, University CHAIRMEN: R. Dijkgraff, R. lengo, I. Kle­ 26. Second Annual Workshop on 110 Paral­ of Minnesota, Minneapolis, MN. (Nov. 1993, banov, K.S. Narain, S. Randjbar-Daerni. lel Computer Systems (to be held in conjunc­ p. 1255) INFORMATION: International Centre for The­ tion with the International Parallel Process­ oretical Physics, P.O. Box 586, 1-34100 * 2-6. Conference on Massively Parallel Com­ ing Symposium-IPPS '94), Cancun, Mexico. Trieste. puting Systems (MPCS): the Challenges (Dec. 1993,p. 1447) of General-Purpose and Special-Purpose * 15-16. Stochastic Systems and Their Appli- * 26-30. International Conference on Logic Computing, Ischia, Italy.

52 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

PROGRAM: This conference has been con­ INFORMATION: CIRM, Luminy Case 916, 25-28. Second Conference on Function ceived to gather experts from research, F-13288 Marseille Cedex 9. Spaces, Southern lllinois University at Ed­ academia, and industry who are interested wardsville, Illinois. (Sep. 1993, p. 926) in all problems related to the definition 14-18. International Congress Henri Poin­ care, Archives-Centre d'Etudes et de Re­ * 26-27. Sixteenth Symposium on Mathemat­ and implementation of massively parallel ical Programming with Data Perturbations, computing systems. A major goal of the cherche Henri-Poincare, Nancy, France. (Jul./Aug. 1993, p. 712) George Washington University, Washington, conference is to foster communication and DC. cooperation between communities study­ 15-21. Critical Phenomena in Spatial Sto­ ing general- and special-purpose massively chastic Models, Oberwolfach, Federal Repub­ PRoGRAM: This symposium is designed to parallel systems. The conference is or­ lic of Germany. (Mar. 1993, p. 286) bring together practitioners who use mathe­ ganized in different sessions: 1) Keynote 16-20. IMA Workshop on Stochastic Mod­ matical programming optimization models sessions by outstanding experts; 2) Regular els in Geosystems, Institute for Mathematics and deal with questions of sensitivity anal­ and special sessions; and 3) Short-note and and its Applications, University of Minnesota, ysis with researchers who are developing late paper sessions. Minneapolis, MN. (Jan. 1993, p. 64) techniques applicable to these problems. CoNFERENCE TOPics: Architecture of CONFERENCE TOPICS: Contributed papers in 16-20. Geometrie Algebrique, CIRM, Mar­ MPCS: processors and communication net­ seille, France. (Jan. 1993, p. 64) mathematical programming are solicited in works; design methods for MPCS, with par­ the following areas: Sensitivity and stabil­ ticular reference to prototyping, validation, 16-27. Workshop on Commutative Alge­ ity analysis results and their applications; diagnosis, and quality ensurance; general­ bra and its Relation to Combinatorics and solution methods for problems involving purpose vs. special-purpose MPCS; in­ Computer Algebra, International Centre for implicitly defined problem functions; solu­ teractions among programming languages, Theoretical Physics, Trieste, Italy. (Jul./Aug. tion methods for problems involving deter­ programming environments, and parallel 1993, p. 712) ministic or stochastic parameter changes; architectures; impact of MPCS on effec­ 20-22. Wavelets and Fractals, University of solution approximation techniques and er­ tiveness and efficiency of applications; pro­ Pittsburgh, Pittsburgh, PA. (Dec. 1993, p. 1448) ror analysis. Clinical presentations that gramming environments for MPCS with 22-24. Conference in Honor of E. Dynkin, describe problems in sensitivity or stabil­ reference to program transformation, load MSI, Ithaca, NY. (Jul./Aug. 1993, p. 712) ity analysis encountered in applications are balancing high-level scheduling, and mes­ also invited. 22-27. Nonlinear Analysis, Function Spaces, sage routing; implementation of massively CALL FOR PAPERS: Abstracts of papers in­ parallel UO subsystems; tools for perfor­ and Applications, V, Prague, Czech Republic. (Sep. 1993, p. 926) tended for presentation at the symposium mance prediction and evaluation; abstract should be sent in triplicate to the address machines for MPCS; and fine-grain paral­ 22-28. Diskrete Geometrie, Oberwolfach, below by March 15, 1994. Abstracts should lelism and parallel computer arithmetics. Federal Republic of Germany. (Mar. 1993, provide a good technical summary of key SPECIAL SESSIONS: Communicating in p. 287) results, avoid the use of mathematical sym­ MPCP systems; architecture of massively 23-25. Twenty-sixth Symposium on Theory bols and references, not exceed 500 words, parallel computers for comp. vision/image of Computing (STOC), Montreal, Canada. and include a title and the name and full processing; application specific massively (September 1993, p. 926) mailing address of each author. Approx­ parallel architecture implementation; and 23-25. The 1994 Scalable High Perfor­ imately 30 minutes will be allocated for MPCS prototypes in European universities. mance Computing Conference, SHPCC94, each paper. INFORMATION: G.R. Sechi, Program Chair, Knoxville, TN. (Nov. 1993, p. 1255) INFORMATION: A.V. Fiacco, Organizer, via Bassini, 15, 20133 Milano, Italy; tel: School of Engineering and Applied Sci­ +39 2 2363747; fax: +39 2 2362946; e­ 23-27. Elliptic and Parabolic Methods in Geometry, University of Minnesota, Min­ ence, The George Washington University, mail: [email protected]; or E. Washington, DC 20052; 202-994-7511. Attanasio or D. Nardo, viaP. Castelino, 111, neapolis, MN. (Nov. 1993, p. 1255) Napoli, Italy; tel: +39 81 5452419; fax: +39 * 23-27. Geometrie Algebrique, Marseille, 26-28. Spatial Stochastic Models in Biol­ 815454330;[email protected]. France. ogy, The University of Colorado at Colorado Springs. (Nov. 1993, p. 1256) 3-10. Spring College on Quantum Phases, CHAIRMEN: L. Szpiro; R. Elkik, Paris; A.N. Trieste, Italy. Pershin, Moscow. 26-29. ICANN '94-International Confer­ INFORMATION: CIRM, Luminy Case 916, ence on Artificial Neural Networks, Sorrento CHAIRMAN: Solid State Advisory Commit­ F-13288 Marseille Cedex 9. Congress Center, near Naples, Italy. (Jul./Aug. tee. 1993, p. 712) INFORMATION: International Centre for The­ 24-27. Conference on Hermann G. GraB­ oretical Physics, P.O. Box 586, 1-34100 mann (1809-1877), Isle of Rtigen, Germany. 29-June 3. International Conference on Trieste. (September 1992, p. 775) Real and Complex Algebraic Geometry, Soesterberg, The Netherlands. (Jul./Aug. 1993, 3-14. The Fourth International School * 24-28. International Workshop on Math­ p. 712) on Differential Equations: Bifurcations and ematical Methods and Tools in Computer Simulation, St. Petersburg State University, 29-June 4. Singulare Storungsrechnung, Chaos, Katsiveli, Crimea, Ukraine. (Sep. 1993; Oberwolfach, Federal Republic of Germany. p. 926) St. Petersburg, Russia. (Please note corrected information to Sep. 1993, p. 926) (Mar. 1993, p. 287) 8-14. Variationsrechnung, Oberwolfach, 29-June 4. Spring School on Potential The­ Federal Republic of Germany. (Mar. 1993, INFORMATION: The correct e-mail address ory and Analysis, Paseky, Czech Republic. p. 286) is statmod@hq. math .lgu. spb. su. (Dec. 1993,p. 1448) '9-13. Algorithme et PrograiUIDation, Mar­ 24-28. First International Conference on 30--June 3. On the Interaction between Func­ seille, France. Difference Equations and Applications, Trin­ tional Analysis, Harmonic Analysis, and CHAIRMEN: D. Monasse, Paris; R. Roland, ity University, San Antonio, TX. (Dec. 1993, Probability, University of Missouri -Columbia, Aix-Marseille. p. 1448) Columbia, MO. (Jul./Aug. 1993, p. 713)

JANUARY 1994, VOLUME 41, NUMBER 1 53 ...... ~-···-···-·-···-·······-··-··-···-····-·····-·-·-······-·-·······················-·-·-··········-·-·····-·-··· ...... Meetings and Conferences

* 30-June 3. International Congress on Women nitz; D. Simson, Torun; A. Skowronski, sachusetts. (Dec. 1993, p. 1449) Mathematicians, Moscow, Russia. Torun; J. Trlifaj, Charles; L. Unger, Pader­ 12-18. Nichtlinearitaten vom Hysteresis­ bom. PRoGRAM: The work of the congress will typ, Oberwolfach, Federal Republic of Ger­ INFORMATION: E. Novakova, katedra Al­ be divided into four sections: 1. differential many. (Mar. 1993, p. 287) gebry MFF UK, Sokolovska 83, 18600 equations; 2. topology, algebra; 3. math­ * 13-14. The 1994 IEEE Workshop on Fault­ Praha 8-Karlin, Czech Republic; e-mail: ematical simulation; and 4. mathematical Tolerant Parallel and Distributed Systems, [email protected]. education. College Station, TX. CALL FOR PAPERS: The titles of the reports 5-11. The Navier-Stokes Equations: The­ PROGRAM: The goal of this workshop is to and abstracts are to be received before ory and Numerical Methods, Oberwolfach, provide a forum for researchers to present March l, 1994. Germany. (Jul./Aug. 1993, p. 713) and exchange research results and advances INFORMATION: I. Yaroshevskaya, Center of * 5-11. Workshop on Harmonic Analysis, Os­ in the field of fault-tolerant parallel and Visiting Programs, Arch. Vlasova st., 51 cillatory Integrals, and Partial Differential distributed systems. Both hardware and Moscow, 117393, Russia; tel./fax: (095) Equations, International Centre for Mathe­ system issues are of interest. 120-11-20; yarosh

54 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

matrices: Can the next century Top This 20--25. Third World Congress of the Bernoulli INFORMATION: E. Goodman, John Wiley One?; R.S. Schreiber, RIACS-NASAAmes Society for Mathematical Statistics and and Sons Publishers, 605 Third Avenue, Res. Ctr., Parallel matrix computations; Probability and the 57th Annual Meeting New York, NY 10158; 212-850-6711. L.E. Trotter, Cornell U., Linear algebraic of the Institute of Mathematical Statistics, duality for discrete optimization. Chapel Hill, NC. (Dec. 1993, p. 1449) 25-July 2. Symposium on Diophantine Prob­ lems in Honor of Wolfgang Schmidt's 60th INVITED MINISYMPOSIA: A. Bunse-Gerstner, 20--July 1. AMS-SIAM Summer Seminar U. of Bremen, Numerical methods for Birthday, Boulder, Colorado. (May/Jun. 1993, in Applied Mathematics on Dynamical Sys­ p. 514) structured matrices; T.F. Coleman, Cornell tems and Probabilistic Methods for Nonlin­ U., Linear algebra in optimization; I. Duff, ear Waves, Mathematical Sciences Research 26-July 2. Graphentheorie, Oberwolfach, Rutherford Appleton Labs. and CERFACS, Institute, Berkeley, CA. Federal Republic of Germany. (Mar. 1993, Direct methods for large sparse systems; R. p.287) Freund, AT&T Bell Labs., Iterative meth­ INFORMATION: Donna Salter, American 26-July 2. Inverse Problems, Lake St. Wolf­ ods for large sparse systems; P. Lancaster, Mathematical Society, P.O. Box 6887, gang, Austria. (May/Jun. 1993, p. 514) U. of Calgary, The algebraic Riccati equa­ Providence, RI 02940. 27-July 2. Convex and Discrete Geometry, tion and applications; A. Pothen, U. of Bydgoszcz, Poland. (Dec. 1993, p. 1450) Waterloo, Graph theory and linear algebra; * 20--July 1. Miniworkshop on Submicron Dynamics, Trieste, Italy. 28-July 1. Structure in Complexity Theory, G. Strang, MIT, Teaching of linear algebra. Ninth Annual IEEE Conference, Amsterdam, CHAIRMEN: H. Cerdeira, B. Kramer, G. 15-24. Canadian Mathematical Society An­ The Netherlands. (Nov. 1993, p. 1256) SchOn. nual Seminar. Representations of Groups: Finite, Algebraic, Lie, and Quantum, Banff, INFORMATION: International Centre for The­ Alberta, Canada. (Dec. 1993, p. 1449) oretical Physics, P.O. Box 586, 1-34100 Trieste. July 1994 16-18. Western Section, University of Ore­ 2-8. Fourth Conference of the Canadian gon, Eugene, Oregon. 21-24. NASECODE X: The Tenth Interna­ * Number Theory Association, Dalhousie Uni­ tional Conference on the Numerical Analy­ INFORMATION: W. Drady, AMS, P.O. Box versity, Halifax, Nova Scotia, Canada. (Sep. sis of Semiconductor Devices and Integrated 6887, Providence, RI 02940. 1993, p. 927) Circuits, Dublin, Ireland. 3-9. Analysis und Geometrie Singularer * 18-19. IMS Workshop on Directions in CONFERENCE TOPICS: Analysis, code vali­ Riiume, Oberwolfach, Federal Republic of Sequential Analysis, Chapel Hill, NC. dation against real devices and processes, Germany. (Apr. 1993, p. 415) PRoGRAM: The workshop precedes the joint computational techniques, device model­ 4-7. International Conference on Nonlin­ meetings of the lnst. of Math. Stats. and ing, electrothermal effects, energy transport ear Dynamics and Pattern Formation in the Bernoulli Society. The purpose is to models, manufacturing equipment model­ the Natural Environment, Amsterdam, The provide an international forum for sharing ing, mathematical analysis, Monte Carlo Netherlands. (Dec. 1993, p. 1450) simulations, physical aspects, process mod­ and promoting research in theoretical and 4-7. Ninth Annual IEEE Symposium on els, process simulation, quantum dot, quan­ applied aspects of sequential methodology Logic in Computer Science, Paris, France. tum well and quantum effects, quantum in statistics and probability. Formal pre­ (Oct. 1993, p. 1087) sentations will be made by forty invited tunneling, simulation of integrated cir­ 4-8. International Conference on Computer speakers. cuits and VLSI interconnections, TCAD frameworks, TCAD industrial applications, Aided Geometric Design (CAGD), Penang, ORGANIZING COMMITTEE: M. Woodroofe, Malaysia. (Jul./Aug. 1993, p. 713) G. Simons, A.N. Shiryaev, P.K. Sen, T.L. transcircuit and interconnection analysis Lai, and B.K. Ghosh. and simulation. 4-8. Thirty-eighth Annual Meeting of the Australian Mathematical Society, University INFORMATION: B.K. Ghosh, Dept. of Math., CALL FOR PAPERS: Potential authors should of New England in Arrnidale, Australia. (Oct. Lehigh U., Bethlehem, PA 18015; e-mail: submit three copies of a camera ready 1993, p. 1087) bkgO

JANUARY 1994, VOLUME 41, NUMBER 1 55 ...... lUI!.IIUUI!ii!UUII_II_ --~~-~~-~~--~~,l!!fli!l!llll!lllllll!··-~~--~~- ...... Meetings and Conferences

fach, Federal Republic of Germany. (Apr. 1993, (Jul./Aug. 1993, p. 714) zur Gathen, Dept. of Comp. Sci., Univ. p. 415) 17-23. Conference Internationale de Topolo­ of Toronto, Toronto, Ontario M5S 1A4, * 10-16. Euroconference: Combinatorial Ge- gie,CIRM,Marseille,France. (Jan.1993,p. 64) Canada; issac@cs. toronto. edu; or S. Hague, NAG Ltd., Wilkinson House, ometry, Anogeia, Crete, Greece. 17-23. Algebraische Zahlentheorie, Ober­ Jordan Hill Rd., Oxford OX2 8DR, UK wolfach, Federal Republic of Germany. (Apr. ORGANIZERS: P. Mani, Bern; J. Wills, steve@nag. co. uk. Siegen; G. Ziegler, Berlin. 1993, p. 415) SUPPORT: Full financial support for travel 17-23. Workshop on Harmonic Analysis 20-30. Third Souslin Conference, Saratov, and expenses for a number of young re­ and Elliptic Partial Differential Equations, Russia. (Jul./Aug. 1993, p. 714) searchers from B.C. countries (possibly International Centre for Mathematical Sci­ 24--30. Complex Geometry: Moduli Prob­ also from some Central and East European ences, Edinburgh, Scotland. (Jul./Aug. 1993, lems, Oberwolfach, Federal Republic of Ger­ countries). p. 714) many. (Apr. 1993, p. 415) INFORMATION: S. Papadopoulou, Dept. of * 17-23. Euroconference: Actions of Lie 25-29. Representation des Groupes Reduc­ Math., University of Crete, P.O. Box 1470, Groups and Discrete Subgroups on Man­ tifs p-adiques, CIRM, Marseille, France. (Nov. Iraklion, Crete, Greece; e-mail: suzana@ ifolds, Anogeia, Crete, Greece. 1992, p. 1122) talos.cc.uch.gr; fax: 81-234516. ORGANIZERS: G. Margoulis, Yale; R. Zim­ 25-29. 1994 SIAM Annual Meeting, San * 10-30. The Park City/Institute for Ad­ mer, Chicago. Diego, CA. (Sep. 1993, p. 927) vanced Study Mathematics Institute, Park SUPPORT: Full financial support for travel 25-29. Conference on Evolution Equations, City, Utah. and expenses for a number of young re­ University of Strathclyde, Glasgow, Scotland. searchers from B.C. countries (possibly PRoGRAM: High school teachers, in part­ QDec. 1993,p. 1451) also from some Central and East European nership with university mathematicians and * 25-29. European Colloquium of Category countries). students, will explore the evolution of clas­ Theory (ECCT), Tours, France. INFORMATION: S. Papadopoulou, Dept. of sical geometry to modem geometry on Math., University of Crete, P.O. Box 1470, SCIENTIFIC COMMITTEE: Saunders Mac curved spaces, and will discuss issues of Iraklion, Crete, Greece; e-mail: suzana@ Lane, Chicago; J. Adamek, Prague; J. geometry education and reform. Under­ talos.cc.uch.gr; fax: 81-234516. Benabou, Paris; F. Borceux, Louvain; A. graduates and graduate students will be Carboni, Milano; P. Damphousse, Tours; offered an intense, yet accessible, introduc­ 18-22. Sixth International Conference on Y. Diers, Valenciennes; R. Gnitart, Paris; tion to areas of research and application by Fibonacci Numbers and Their Applications, J. Gray, Urbana; H. Herrlich, Bremen; P. nationally respected leaders in mathemat­ Washington State University, Pullman, WA. Johnstone, Cambridge; M. Kelly, Sidney; ics. The Research and Graduate Summer (Jul./Aug. 1993, p. 714) I. Moerdijk, Utrecht; G. Reyes, Montreal. School topic for the 1994 summer session is 18-22. Conference Internationale de Topolo- PREREGISTRATION: Send a one-line e-majl "Gauge Theory and the Topology of Four­ * gie, Marseille, France. to ecct-request@univ-tours. fr with Manifolds". Active researchers will have a the one line subscribe. stimulating but informal working environ­ CHAIRMEN: Y. Mathieu, Marseille. CALL FOR PAPERS: Deadline for submitting ment. A range of computer activities and INFORMATION: CIRM, Luminy Case 916, papers is April1, 1994. problems in geometry can be explored by F-13288 Marseille Cedex 9. INFORMATION: Contact via e-mail: participants in a fully networked computer damphous@uni v-tours. fr or gui tart@ 18-29. Fifth Workshop of Stochastic Anal­ lab. univ-tours . fr or write to ECCT, c/o P. APPLICATION DEADLINE: March 1, 1994. ysis of Oslo-Silivri, Silivri, Istanbul, Turkey. (Oct. 1993, p. 1087) Damphousse, Dept. de Math., Faculte des INFORMATION: PC/lAS Mathematics Insti­ Sciences, Pare de Grandmont, Tours 37200, tute, 18C DeTrobriand St., Salt Lake City, * 20-22. International Symposium on Sym­ France. UT 84113; tel.: 801-585-3488; fax: 801- bolic and Algebraic Computation, ISSAC 585-5793; e-mail: pcmi@math. utah. edu. '94, St. Catherine's College, Oxford, UK. 26--30. Seventh International Colloquium on Differential Geometry, Universidade de CONFERENCE TOPICS: Algorithms for prob­ 11-15. Fourteenth IMACS World Congress Santiago de Compostela, · Santiago de Com­ lems in algebra, number theory, group on Computational and Applied Mathemat­ postela, Spain. (Dec. 1993, p. 1451) ics, Georgia Institute of Technology, Atlanta, theory, algebraic geometry, differential al­ GA. (Oct. 1992, p. 951) gebra and differential equations; combined * 26-30. Algebraic K-Theory, Universite Paris VII, Paris, France. 11-15. The First International Derive Con­ symbolic/numeric methods; languages and ference, Plymouth, UK. (Dec. 1993, p. 1450) systems for symbolic computation; parallel ORGANIZERS: M. Karoubi, B. Kahn, R. symbolic computation; automatic theorem Thomason. 11-22. SMS-NATO ASI: Topological Meth­ proving and programming; applications of ods in Differential Equations and Inclusions, INVITED SPEAKERS: G. Carlsson, H. Gillet, symbolic computation to mathematics, sci­ U. Janssen, K. Kato, M. Levine, I. Panin, J. Universite de Montreal, Montreal, Canada. ence, engineering, and education. (Dec. 1993,p. 1451) Rogues, M. Rost, C. Soule, A. Suslin. CALL FOR TOPICS: Papers may be submitted REGISTRATION: Deadline for regsitration is 12-15. Theoretical Models in Biological * either electronically in P.'l.EX form using AprilS, 1994. Systems, Trieste, Italy. a standard article style or (preferred) as INFORMATION: E-mail to kthconf@ CHAIRMAN: J.A. Krumhans. Postscript files, or in hard copy form. The frmap711.mathp7 .jussieu.fr or fax: INFORMATION: International Centre for The­ preferred format is 12pt., with a maximum (33-1)-44276366 or write to Algebraic K­ oretical Physics, P.O. Box 586, 1-34100 of 10 pages. Papers must be received by theory Conference, L. Barenghi, UFR de Trieste. January 15, 1994. Math., Univ. de Paris VII, Case 7012, INFORMATION: M. MacCallum, School of 75251 Paris Cedex 05, France. 14--18. LFCS'94: Logic at St. Petersburg, Math. Sci., Queen Mary and Westfield Col­ a Symposium on Logical Foundations of lege, Mile End Road, London El 4NS, 27-August 1. International Conference on Computer Science, St. Petersburg, Russia. UK; mm@maths . qmw. ac. uk; or J. von Commutative Algebra (A Satellite Confer-

56 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY L~-- ...... ····-·-·-······-·······-···-·- ... Meetings and Conferences

ence of ICM 94, Zurich), Universitiit Os­ mus University, Rotterdam, The Netherlands. Stanford; M. Gromov, IRES; I. Hamble­ nabrtick, Standort Vechta, Germany. (Dec. (Dec. 1993, p. 1452) ton, McMaster; N.J. Hitchin, Warwick; J. 1993, p. 1451) * 15-19. 1994 International Conference on Hurtubise, McGill; N. Karnran, McGill; F. 28-August 1. Workshop on Harmonic Maps Parallel Processing, The Pennsylvania State Lalonde, UQAM; M. Min-oo, McMaster, and Curvature Properties of Submanifolds, University, University Park, PA. D. Rolfsen, UBC; M. Troyanov, UQAM. University of Leeds, England. (Dec. 1993, WORKSHOP TOPICS: Exterior differential INFORMATION: T. Feng, The Pennsylvania p. 1451) systems; Cartan's equivalence problem; ap­ State University, 220 Pond Lab., University plications to the calculus of variations, to 31-August 6. Mechanics of Materials, Ober­ Park, PA 16802-6106. wolfach, Federal Republic of Germany. (Apr. Riemannian geometry, and to the study of 1993,p.415) 15-26. Advanced Workshop on Algebraic pdes. Geometry, International Centre for Theoretical INFORMATION: M. Louise Pelletier, CRM, Physics, Trieste, Italy. (Jul./Aug. 1993, p. 714) Universite de Montreal, C.P. 6128, Suc­ cursale A, Montreal, Quebec H3C 3J7, 16--20. ICMI-China Regional Conference August 1994 Canada;[email protected]. on Mathematics Education, Shanghai, China. 1-5. Third World Congress on Computa­ (Jul./Aug. 1993, p. 714) tional Mechanics (WCCM Im, Chiba, Japan. *Fall 1994. Workshop on Geometry of Non­ (May/Jun. 1992, p. 497) 18-23. Fifth Colloquium on Differential compact Manifolds, Centre de Recherches Eqnations, Plovdiv, Bulgaria. (Apr. 1993, Mathematiques. Universite de Montreal. l-19. IMA Course on Mathematical Mod­ p. 416) eling for Teachers, Institute for Mathematics PRoGRAM: See the preceding listing for and its Applications, University of Minnesota, 18-25. Third International Conference on the program and a list of the scientific Minneapolis, MN. (Dec. 1993, p. 1451) Group Theory, Pusan. Republic of Korea. committee. (Nov. 1993, p. 1258) 3-11. The International Congress of Mathe­ WoRKSHOP TOPICs: Asymptotic invariants, maticans 1994, ZUrich, Switzerland. (Jul./Aug. 20-26. International Conference on Rings harmonic functions, spectra of Laplacians, 1993, p. 714) and Radicals, Shijiazhuang, China. (Mar. invariants of quasi-isometry. 1993, p. 287) 7-13. Effiziente Algorithmen, Oberwolfach, INFORMATION: M. Louise Pelletier, CRM, Federal Republic of Germany. (Apr. 1993, 21-27. Mathematical Models in Phase Tran­ Universite de Montreal, C.P. 6128, Suc­ p. 416) sitions, Oberwolfach, Federal Republic of Ger­ cursale A, Montreal, Quebec H3C 3J7, many. (Apr. 1993, p. 416) Canada; pelletl@ere. umontreal. ca. 12-20. 1994 Summer Workshop-Conference 22-26. Sixth Conference on Numerical on Classical and Quantum Geometry of 4-10. Topologie, Oberwolfach, Federal Re­ Methods in Hungary, Miskolc University, Homogeneous Spaces, International Sophus public of Germany. (Apr. 1993, p. 416) Miskolc, Hungary. (Sep. 1993, p. 928) Lie Centre, Moscow. (Oct. 1993, p. 1087) 5-8. ECCOMAS-Second European Compu­ 13-17. Third Colloquium on Numeri­ 27-28. Conference on the History of Math­ ematics in Honor of Boris Rosenfeld, Penn­ tational Fluid Dynamics Conference, Stutt­ cal Analysis, Plovdiv, Bulgaria. (Apr. 1993, gart, Germany. (Dec. 1993, p. 1452) p. 416) sylvania State University, University Park, PA. (Dec. 1993, p. 1452) *5-9. IX Brazilian Meeting of Topology, 13-19. International Conference on Po­ 28-September 3. Komplexe Analysis, Ober­ Universidade Federal Flurninense, Instituto de tential Theory (ICPT '94), Kouty, Czech Matematica, Niteroi, Rio de Janeiro, Brazil. Republic. (Dec. 1993, p. 1452) wo1fach, Federal Republic of Germany. (Apr. l993,p.416) 14-20. Nonlinear Evolution Equations, PuRPOSE: To promote interchange among Oberwolfach, Federal Republic of Germany. the Brazilian topologists throughout the (Apr. 1993, p. 416) country and abroad. September 1994 CONFERENCE TOPICS: Foliations, locally 14-21. International Conference on Func­ free actions of groups, bounded coho­ tional Differential Equations and Applica­ September 1994. Suslin Jubilee International mology, characteristic classes, K-theory, tions, Moscow, Russia. (Nov. 1993, p. 1257) Conferences, Suslin Foundation, Russia. (Oct. bordism, and others. 14-27. NATO Advanced Study Institute on 1993, p. 1088) INVITED SPEAKERS: Partial list: E. Ghys, "Finite and Locally Finite Groups", Bospho­ * Fall 1994. Workshop on Exterior Dif­ ENS Lyon; U. Koschorke, U. Gesamthoch­ rous University, Istanbul, Turkey. (Nov. 1993, ferential Systems and Applications, Centre schule; W. Mio, U. Florida; J. Palis, IMPA; p. 1257) de Recherches Mathematiques, Universite de P. Schweitzer, PUC/RJ; T. Tsuboi, U. 15-17. Mathfest, University of Minnesota, Montreal. Tokyo; B. Williams, U. of Notre Dame. Minneapolis, MN (including the summer meet­ INFORMATION: S. Firmo, IX Encontro Brasi­ PROGRAM: There will be a program of ings of the AMS, AWM, MAA, and PME). leiro de Topologia, Rua Sao Paulo s/n- Va­ visitors, both short- and long-term, with longuinho, 24020-005, Niteroi-RJ-Brazil; INFORMATION: H. Daly, AMS, P.O. Box more informal activities organized in con­ fax: 55 21 717 4553; e-mail: ebtuff@ 6887, Providence, RI 02940. sequence. Special emphasis will be placed brlncc. bitnet. on the integration of graduate students into 15-18. Tenth Summer Conference on Gen­ the year's activities. In particular, each 6--8. International Conference on Parallel eral Topology and Applications, Free Univer­ workshop will be preceded by a minicourse sity, Amsterdam, The Netherlands. (Nov. 1993, Processing: CONPAR 94-VAPP VI, Linz, of one or two weeks to prepare students Austria. (Oct. 1993, p. 1088) p. 1258) for the workshop. There will also be a full * 7-9. IEEE European Workshop on Computer­ 15-19. Fifteenth International Symposium program of term-length graduate courses Intensive Methods in Control and Signal on Mathematical Programming, University given both by local faculty and by visitors Processing: Can We Beat the Cnrse of Di­ of Michigan, Ann Arbor, MI. (May/Jun. 1993, on topics covered by the program. mensionality?, Prague, Czech Republic. p. 515) SCIENTIFIC COMMITTEE: L. Vinet, director 15-19. Fourth Conference of the Interna­ of CRM; S. Boyer, UQAM; R. Bryant, PROGRAM: The aim of this workshop is to tional Linear Algebra Society (ILAS), Eras- Duke; A. Casson. Berkeley; Y. Eliashberg, bring together researchers and practitioners

JANUARY 1994, VOLUME 41, NUMBER 1 57 ...... ______, ...... Meetings and Conferences

working in academia, government, and in­ of database research are especially invited. dustry. Particular emphasis will be placed Submissions are solicited in all aspects of on "The curse of dimensionality", i.e., the information systems that deal with paral­ November 1994 extreme dimensionality of computations lelism and/or distribution. 11-13. Southeastern Section, University of connected with the implementation of the­ CALL FOR PAPERS: Original papers on the Richmond, Richmond, VA. oretically optimal mathematical procedures above topics are invited. These should be of inference and decision making. no longer than twenty-five double-spaced INFORMATION: W. Drady, AMS, P.O. Box CONFERENCE TOPICS: Parallel algorithms pages with no smaller than 11 point type. 6887, Providence, RI 02940. and architectures; neural nets; model re­ Please submit six copies to a program chair 13-17. 1994 International Symposium on duction; finite-dimensional estimation, fil­ at one of the addresses below to arrive no Logic Programming, MSI, Ithaca, NY. (Jul./Aug. tering, and control; complexity; multivari­ later than March 28, 1994. 1993 p. 715) ate integration and optimization; nontradi­ INFORMATION: H. Korth, MITL, Pana­ 13-19. Komplexitiitstheorie, Oberwolfach, tional approaches. sonic Technologies, Inc., 2 Research Way, Federal Republic of Germany. (Apr. 1993, INFORMATION: M. Karny, IEEE Workshop Princeton, NJ 08540-6628; e-mail: hfk@ p. 417) "CMP", Institute of Information Theory mitl.research.panasonic.com; or A. and Automation, P.O. Box 18, 182 08 Sheth, Bellcore, RRC-1J210, 444 Hoes 20-26. Mathematical Aspects of Computa­ Prague, Czech Republic; tel: +(42)(2)6641 Lane, Piscataway, NJ 08854; ami t@ tional Fluid Dynamics, Oberwolfach, Federal 3421; fax: +(42)(2)6641 4903; e-mail: ctt.bellcore.com. Republic of Germany. (Apr. 1993, p. 417) kulhava@utia. cas. cz (Internet). 27-December 3. Mathematical Models for Infectious Diseases, Oberwolfach, Federal Re­ 11-17. Homotopietheorie, Oberwolfach, Fed­ public of Germany. (Jul./Aug. 1993, p. 715) eral Republic of Germany. (Apr. 1993, p. 416) October 1994 15-19. Fifteenth International Symposium on Mathematical Programming, University 2-8. Randelementmethoden: Anwendungen of Michigan, Ann Arbor, MI. (Apr. 1993, und Fehleranalysis, Oberwolfach, Federal Re­ December 1994 p. 416) public of Germany. (Apr. 1993, p. 416) 4-10. Applied Probability, Oberwolfach, 18-20. Teaching of Mathematics for Indus­ 9-15. Arbeitsgemeinschaft mit Aktuellem Federal Republic of Germany. (Jul./Aug. 1993, try, Prague. (Jul./Aug. 1993, p. 715) Thema (Wird in den Mitteilungen der DMV p. 715) 18-24. Risk Theory, Oberwolfach, Federal Heft 3/1994 Bekanntgegeben), Oberwolfach, 12-14. SIAM Conference on Inverse Prob­ Republic of Germany. (Apr. 1993, p. 416) Federal Republic of Germany. (Apr. 1993, lems, Fish Camp, CA. (Dec. 1993, p. 1453) p. 416) 18-24. DMV-Jahrestagung 1994 (Annual 18-23. Asymptotik Hochdimensionaler Statis­ Meeting of the German Mathematical Soci­ 10-28. School/Workshop on Variational and tischer Modelle, Oberwolfach, Federal Repub­ ety), Duisberg, Federal Republic of Germany. Local Methods in the Study of Hamiltonian lic of Germany. (Apr. 1993, p. 417) Systems, International Centre for Theoretical ~ov. 1993,p. 1258) Second International Conference on Nu­ Physics, Trieste, Italy. (Jul./Aug. 1993, p. 715) 19-23. 3eme Atelier International de Theorie merical Methods for Volterra and Delay des Ensembles, CIRM, Marseille, France. 12-18. CARl '94: Second African Confer­ Equations (A conference to celebrate the (Apr. 1993, p. 416) ence on Research in Computer Science, Oua­ 100th anniversary of Volterra's birth.), Italy. gadougou (Burkina-Faso). ~ov. 1993, p. 1259) 21-22. International Symposium on Object­ (Mar. 1992, p. 251) Re­ Oriented Methodologies and Systems, Paler­ 16-22. Geometrie, Oberwolfach, Federal mo, Italy. (Nov. 1993, p. 1258) public of Germany. (Apr. 1993, p. 416) 23-29. Wabrscheinlicbkeitsmafie aufGrup­ 21-23. Meeting on Matrix Analysis and January 1995 Its Applications, Vitoria-Gasteiz, Spain. (Oct. pen und Verwandten Strukturen, Oberwol­ 1993, p. 1088) fach, Federal Republic of Germany. (Jul./Aug. 4-7. Joint Mathematics Meetings, San Fran­ 1993, p. 715) cisco, CA (including the annual meetings of 25-0ctober 1. Mathematical Methods in 11. Fourth Autumn Course the AMS, AWM, MAA, and NAM). Tomography, Oberwolfach, Federal Republic *24-November of Germany. (Apr. 1993, p. 416) on Mathematical Ecology, Trieste, Italy. INFORMATioN: H. Daly, AMS, P.O. Box 26-0ctober 1. First International Workshop CHAIRMEN: L. Gross, T. Hallam, S. Levin. 6887, Providence, RI 02940. on Functional Analysis, Trier University, near INFORMATION: International Centre for The­ * 16-19. First Asian Computational Fluid Luxembourg, Germany. (Oct. 1993, p. 1088) oretical Physics, P.O. Box 586, 1-34100 Trieste. Dynamics Conference, Hong Kong University * 26-30. Journees de Probabilites, Marseille, of Science and Technology, Clear Water Bay, France. 28-29. Central Section, Oklahoma State Hong Kong. CHAIRMEN: J. Azema, M. Yor, Paris. University, Stillwater, Oklahoma. CONFERENCE TOPICS: Newly developed INFORMATION: CIRM, Luminy Case 916, INFORMATION: W. Drady, AMS, P.O. Box schemes and algorithms; incompressible F-13288 Marseille Cedex 9. 6887, Providence, RI 02940. flows; compressible flows, hypersonic flows, and rarefied gas flows; turbulent flow com­ * 28-30. Third International Conference on 30-November 5. Finite Volume Methods, putation; transition and modelling; reacting Parallel and Distributed Information Sys­ Oberwolfach, Federal Republic of Germany. flows; multiphase flows; meteorology and tems, Austin, Texas. (Apr. 1993, p. 416) oceanography; applications to aeronautics CONFERENCE TOPICS: While the scope of 31-November 4. Orthogonality, Moment and astronautics; applications to structural, this conference includes all aspects of paral­ Problems, and Continued Fractions: An In­ civil, and environmental engineering; fi­ lelism and distribution in database systems, ternational Conference in Honor of T.J. nite element methods; unstructured grid submissions presenting results and expe­ Stieltjes, Jr. (1856-1894), Delft, Holland. scheme; parallel computation in computa­ rience in these and other emerging areas (Dec. 1993,p. 1453) tional fluid dynamics.

58 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

INFORMATION: Conference Secretary, Dept. Theory and Applications to Low-dimensional vax1.rz.uni-regensburg.d400.de. of Math., Hong Kong University of Sci­ Topology, Centre de Recherches Mathematiques, ence and Technology, Clear Water Bay, Universite de Montreal. * 10-12. Conference on Linear Algebra and Hong Kong; fax: 852-358-1643; e-mail: its Applications, University of Manchester, PROGRAM: See the preceding listing for the [email protected]. England. program and the scientific committee. WORKSHOP TOPICS: Yang-Mills moduli and ORGANIZING COMMITTEE: N.J. Higham, applications to four-dimensional topology; chair, U. of Manchester; I.S. Duff, Ruther­ The following new announcements will not applications of ideas from theoretical ford Appleton Labs.; R. Fletcher, U. of be repeated until the criteria in the last physics to geometry and topology. Dundee; T.L. Freeman, U. of Manchester; paragraph in the box at the beginning of this INFORMATION: M. Louis Pelletier, CRM, S.J. Harnmarling, NAG Ltd.; N.K. Nichols, section are met. Universite de Montreal, C.P. 6128, Suc­ U. of Reading. cursale A, Montreal, Quebec H3C 317, INFORMATION: P. Irving, The Conference Canada;[email protected]. Officer, The Institute of Mathematics and March 1995 its Applications, 16 Nelson St., Southend­ *Spring-Summer 1995. Workshop on Sym­ on-Sea, Essex, SS1 1EF, UK; tel: 0702 4-5. Eastern Section, Hartford, Connecticut. plectic Geometry and Topology, Centre de 354020; fax: 0702 354111. INFORMATION: W.S. Drady, American Math­ Recherches Mathematiques, Universite de Montreal. ematical Society, P.O. Box 6887, Provi­ November 1995 dence, RI 02940. PRoGRAM: See the preceding listing for the program and a list of the scientific 3-4. Central Section, Kent State University. 17-18. Southeastern Section, Orlando. Florida. committee. Kent, Ohio. INFORMATION: W.S. Drady, American Math­ WORKSHOP TOPICS: Geometry of symplec­ INFORMATION: W. Drady, AMS, P.O. Box ematical Society, P.O. Box 6887, Provi­ tic manifolds and of Lagrangian manifolds, 6887, Providence, RI 02940. dence, RI 02940. elliptic techniques, and variational tech­ niques. 17-18. Southeastern Section, University of 24-25. Central Section, DePaul University, INFORMATION: M. Louis Pelletier, CRM, North Carolina, Greensboro, NC. Chicago, IL. Universite de Montreal, C.P. 6128, Suc­ cursale A, Montreal, Quebec H3C 317. INFORMATION: W.S. Drady, AMS P.O. Box INFORMATION: W. Drady, AMS, P.O. Box 6887, Providence, RI 02940. 6887, Providence, RI 02940. Canada;[email protected]. 23-26. KdV '95, Amsterdam, The Nether­ lands. (Dec. 1993, p. 1453) January 1996 April1995 10-13. Joint Mathematics Meetings, Or­ ~Spring 1995. Workshop on Groups and lando, Florida (including the annual meetings Three-Manifolds, Centre de Recherches July 1995 of the AMS, AWM, MAA, and NAM). Mathematiques, Universite de Montreal. * 3-7. The Third International Congress on INFORMATION: H. Daly, AMS. P.O. Box PRoGRAM: There will be a program of Industrial and Applied Mathematics, CCH 6887, Providence, RI 02940. visitors. both short- and long-term, with Congress Centrum, Hamburg, Germany. more informal activities organized in con­ sequence. Special emphasis will be placed PRoGRAM: The program will focus world­ March 1996 on the integration of graduate students into wide attention on the importance of math­ the year's activities. In particular, each ematical and computational methods in the 22-23. Central Section, University of Iowa, workshop will be preceded by a minicourse solution of real world problems. The pro­ Iowa City, Iowa. of one or two weeks to prepare students gram consists of invited and contributed INFORMATION: W. Drady, AMS, P.O. Box for the workshop. There will also be a full lectures, minisymposia, poster presenta­ 6887, Providence, RI 02940. program of term-length graduate courses tions, and an exhibition. given both by local faculty and by visitors CONFERENCE TOPICS: Presentations are SO­ on topics covered by the program. licited in all areas of applied mathematics, April1996 SCIENTIF1C COMMITTEE: L. Vinet, director computer science, applied probability and 19-21. Southeastern Section, Baton Rouge, of CRM; S. Boyer, UQAM; R. Bryant, statistics, scientific computing, and appli­ Louisiana. Duke; A. Casson, Berkeley; Y. Eliashberg, cations in science, medicine, engineering, Stanford; M. Gromov, IHES; I. Hamble­ economics, and other related fields. INFORMATION: W.S. Drady, American Math­ ton, McMaster; N.J. Hitchin, Warwick; J. CALL FOR PAPERS: Participants are invited ematical Society, P.O. Box 6887, Provi­ Hurtubise, McGill; N. Kamran, McGill; F. to submit a paper, which may be presented dence, RI 02940. Lalonde, UQAM; M. Min-oo, McMaster, in lecture or poster format. Authors will D. Rolfsen, UBC; M. Troyanov, UQAM. have approximately 15 minutes for the lec­ WORKSHOP TOPICS: Progress on Thurston's ture, with an additional five minutes for January 1997 Geometrization conjectures, group actions discussion. Alternatively, poster presenta­ 10-13. Joint Mathematics Meetings, San on trees, properties of three-manifold groups. tions will allow interactive discussions with individuals interested in their work. Dead­ Diego, California (including the annual meet­ INFORMATION: M. Louis Pelletier CRM ings of the AMS, AWM, MAA, and NAM). Universite de Montreal, C.P. 6128, Sue~ line for papers is August 31, 1994. cursale A, Montreal, Quebec H3C 317, INFORMATION: GAMM-Office, Univ. Re­ INFORMATION: H. Daly, AMS, P.O. Box Canada; pelletl@ere. umontreal. ca. gensburg, NWF !-Mathematik, D-93053 6887, Providence, RI 02940. Regensburg, Germany; tel: +49-941-943- ~Spring-Summer 1995. Workshop on Gauge 4918; fax: +49-941-943-4005; iciam95@

JANUARY 1994, VOLUME 41, NUMBER 1 59 New Publications Offered by the AMS

CONTEMPORARY MATHEMATICS R. Parimala and R. Sridharan, Reduced norms and pfaffians via Brauer-Severi schemes; R. Perlis, K. Szymiczek, P. E. Conner, and R. Litherland, Matching Witts with global fields; J. Shick, On Witt-kernels offunction fields of curves; V. Suresh, On the canonical class of hyperelliptic curves. · Recent Advances in Real 1991 Mathematics Subject Classification: OOB25, llExx, 14Pxx ISBN 0-8218-5154-3, LC 93-6377, ISSN 0271-4132 Algebraic Geometry and 405 pages (softcover), January 1994 Quadratic Forms Individual member $34, List price $57, Institutional member $46 To order, please specify CONM/155N William B. Jacob, Tsit-Yuen Lam, and Robert 0. Robson, Editors The Structure of Relation Volume 155 Algebras Generated by The papers in this volume grew out Relativizations of a year-long program in "Real Algebraic Steven R. Givant Geometry and Quadratic Forms", held at the Volume 156 University of California at Berkeley during the 1990-1991 academic -·- year. This valuable collection of research articles by top workers serves The foundation for an algebraic theory as a record of current developments in these areas and as a tribute to of binary relations was laid by De Morgan, the fruitful interaction between them. Students and researchers alike Peirce, and Schroder during the second will find this book a useful reference, with articles ranging from the half of the nineteenth century. Modern technical to the expository. Also included are summaries of the current development of the subject as a theory of developments in several subdisciplines and indications of new research abstract algebras, called "relation algebras", was undertaken by Tarski and his students. This book aims to analyze directions. the structure of relation algebras that are generated by relativized Contents subalgebras. As examples of their potential for applications, the main T. Recio and C. Andradas, D. W. Dubois and the pioneer days of real algebraic results are used to establish representation theorems for classes of geometry; Papers on real algebraic geometry: S. Akbulut, On algebraic relation algebras and to prove existence and uniqueness theorems for structures of manifolds; C. Andradas and J. M. Ruiz, On local uniformization simple closures (i.e., for minimal simple algebras containing a given of orderings; R. Berr, Real algebraic geometry over p-real closed fields; family of relation algebras as relativized subalgebras). This book is L. Brocker, On the reduction of semialgebraic sets by real valuations; T. C. well-written and accessible to those who are not specialists in this area. Craven, Orderings for noncommutative rings; C. N. Delzell, Nonexistence of In particular, it contains two introductory chapters on the arithmetic and analytically varying solutions to Hilbert's 11th problem; M. A. Dickmann, the algebraic theory of relation algebras. This book is suitable for use in A combinatorial geometric structure on the space of orders of a field IT; graduate courses on algebras of binary relations or algebraic logic. M. J. Gonz8lez-Lopez and T. Recio, Formal determination of polynomial Contents consequences of real ortlwgonal matrices; R. Huber and M. Knebusch, On valuation spectra; M. Marshall, Minimal generation of basic sets in the real Basic definitions and laws; Algebraic notions; The characteristic of an equivalence element; The arithmetic ofrectangles; Structure theorems; Existence, spectrum of a commutative ring; A. Pfister, A new proof of the homogeneous uniqueness, and representation theorems; Relation algebras generated by nullstellensatz for p-fields, and applications to topology; M. J. de Ia Puente, The equivalence elements; Bibliography; Index of symbols; Index of names and compatible valuation rings of the coordinate ring of the real plane; G. Stengle, subjects. Estimates for parametric nonuniformity in representations of a definite polynomial as a sum offourth powers; Papers on quadratic forms: J. Kr. 1991 Mathematics Subject Classification: 03G15; 08A05, 08A30 Arason, R. Elman, and B. Jacob, On generators for the Witt ring; E. Becker ISBN 0-8218-5177-2, LC 93-36607, ISSN 0271-4132 134 pages (softcover), January 1994 and T. Wiiermann, On the trace formula for quadratic forms; W. Bichsel and Individual member $20, List price $34, Institutional member $27 M.-A. Knus, Quadratic forms with values in line bundles; M. Kriiskemper, On To order, please specify CONM/156N annhilators in graded Witt rings and in Milnor's K-theory; K. H. Leung, An application of the theory of order completions; D. B. Leep and A. S. Merkurjev, Growth of the u-invariant under algebraic extensions; J. Mimic, Remarks on Merkurjev's investigations of the u-invariant; R. Parimala and W. Scharlau, On the canonical class of a curve and the extension property for quadratic forms;

Three easy ways to order: 1) call800-321-4AMS (321-4267) in the U.S. and Canada to use VISA or MasterCard; 2) use the order form in the back of this issue; or 3) use e-mail via the Internet: cust-serv@math. ams. org.

60 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Publications Offered by the AMS

TRANSLATIONS OF MATHEMATICAL MEMOIRS OF THE AMS MONOGRAPHS

MEMOIRS (16, 6) Configurations and of the Complements of \"'o

JANUARY 1994, VOLUME 41, NUMBER 1 61 New Publications Offered by the AMS

foliate the energy levels of the unperturbed system as a consequence of some questions about topological seruigroups of real functions are KAMtheory. answered. Contents Contents Introduction and statement of the results; Bifurcations; Separatrix surfaces and The ordinary density topology; Category analogues of the density topology; foliations of the energy levels; The perturbed Hamiltonian; References. I-density continuous functions; Semi groups; Appendix A. Notation; References; 1991 Mathematics Subject Classification: 70H05 Index. ISBN 0-8218-2581-X, LC 93-39026, ISSN 0065-9266 1991 Mathematics Subject Classification: 26A21; 28A05 191 pages (softcover), January 1994 ISBN 0-8218-2579-1, LC 93-39028, ISSN 0065-9266 Individual member $22, List price $36, Institutional member $29 133 pages (softcover). January 1994 To order, please specify MEM0/107/513N Individual member $19, List price $32, Institutional member $26 To order, please specify MEM0/107/515N Associated Graded Algebra of a Gorenstein ADVANCED STUDIES IN Artin Algebra PURE MATHEMATICS Associated Graded Algebra Anthony A. larrobino of a Gorenstein Artln Algebra Volume 107, Number 514 In 1904, Macaulay described the Hilbert function of the intersection of two Progress in Differential plane curve branches: It is the sum of a Geometry sequence of functions of simple form. This monograph describes the structure Katsuhiro Shiohama, Editor of the tangent cone of the intersection Volume22 underlying this symmetry. Iarrobino generalizes Macaulay's result This volume brings together twenty-five beyond complete intersections in two variables to Gorenstein Artin research papers and two survey articles on algebras in an arbitrary number of variables. He shows that the tangent differential geometry and global analysis, cone of a Gorenstein singularity contains a sequence of ideals whose areas in which Japanese differential successive quotients are reflexive modules. Applications are given to geometers have recently made great determining the multiplicity and orders of generators of Gorenstein progress. Urakawa's paper is a deep and ideals and to problems of deforming singular mapping germs. Also comprehensive survey on recent results and included are a survey of results concerning the Hilbert function of open problems in differential geometry, including Green functions and Gorenstein Artin algebras and an extensive bibliography. Liouville type theorems. Yamaguchi's survey deals with the Lie algebra Contents of all infinitesimal automorphisms of a differential system on a manifold Gorenstein Artin algebras and duality; The intersection of two plane curves; and presents basic material on the geometry of differential systems Extremal decompositions; Components of the Hilbert scheme strata; What and simple graded Lie algebras over the real or complex numbers. The decompositions D and subquotients Q(a) can occur?; Relatively compressed research articles cover such topics as minimal surfaces, submanifold Artin algebras; Bibliography; List of theorems, definitions, and examples; Index. theory, analysis on manifolds, L 2-cohomology theory, and Riemannian 1991 Mathematics Subject Classification: 13H10; 13A30, 13010, 13040, geometry. This book will appeal to mathematicians interested in modern 13E10, 14B05,58C27 differential geometry, as well as to graduate students who are looking ISBN 0-8218-2576-3, LC 93-39027, ISSN 0065-9266 for a good overview of some of the main trends in this field. 115 pages (softcover), January 1994 Advanced Studies in Pure Mathematics is published for the Individual member $18, List price $30, Institutional member $24 Mathematical Society of Japan by Kinokuniya, Tokyo, and is distributed To order, please specify MEM0/107/514N worldwide, except in Japan, by the American Mathematical Society. Contents K. Enomoto, Compactification of submanifolds in Euclidean space by the MEMOIRS I-Density Continuous of the \ooec1cn Matbou•otocn\Soc otv inversion; H. Fujimoto, Gauss maps of complete minimal surfaces; N. Innami, Functions Applications of Jacobi and Riccati equations along flows to Riemannian Krzysztof Ciesielski, geometry; G. Ishikawa, Maslov class of an isotropic map-germ arising from one-dimensional symplectic reduction; T. lwai andY. Uwano, On symmetry .;tDensity Continuous Functions Lee Larson, and

KJzya:to!CI~Iclskl groups of the MIC-Kepler problem and their unitary irreducible representations; kct.araon Krzysztof Ostaszewski KrzyutofO~~tan~:wakl S. lzumiya, Geometric singularities for Hamilton-Jacobi equation; T. Kakehi Volume 107, Number 515 and C. Tsukamoto, Characterization of images ofRadon transforms; M. Koiso, ~ The classical approach to showing A uniqueness result for minimal surfaces in 8 3 ; T. Koda and K. Sekigawa, . the parallel between theorems concerning Self-dual Einstein Hermitian surfaces; H. Omori, Y. Maeda and A. Yoshioka, Lebesgue measure and theorems concerning Non-commutative complex projective space; Y. Matsushita, Some remarks on Baire category on the real line is restricted fields of2·planes on compact smooth 4-manifolds; R. Miyaoka, A note on Lie to sets of measure zero and sets of first contact manifolds; K. Nagatomo, Rational solutions of the Ernst equation; category. This is because classical Baire category theory does not have H. Naitoh, Submanifolds of symmetric spaces and Gauss maps; Y. Nakamura, an analogue for the Lebesgue density theorem. By using I-density, this Lax equations associated with a least squares problem and compact Lie algebras; deficiency is removed, and much of the structure of measurable sets and M. Okada, Green function on self-similar trees; K. Ono, On a theorem of functions can be shown to exist in the sense of category as well. This Edmonds; T. Ohsawa, On the L 2 cohomology groups of isolated singularities; monograph explores category analogues to such things as the density Y. Se-ashi, A geometric construction of Laguerre-Forsyth's canonical forms of topology, approximate continuity, and density continuity. In addition, linear ordinary differential equations; K. Shiohama and M. Tanaka, The length

62 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Publications Offered by the AMS

function of geodesic parallel circles; T. Shioya, Diameter and area estimates simple graded Lie algebras; T. Yamaguchi, Tits metric and visibility axiom. for 8 2 and P 2 with nonnegatively curved metrics; K. Sugahara, On the poles 1991 Mathematics Subject Classification: 53 ofRiemannian manifolds of nonnegative curvature; S. Takakuwa, Bubbling of ISBN 4-314-10105-9 minimizing sequences for prescribed scalar curvature problem; H. Urakawa, 505 pages (hardcover), 1993 Geometry of Laplace-Beltrami operator on a complete Riemannian manifold; Individual member $58, List price $97, Institutional member $78 K. Yagi, Super Lie groups; K. Yamaguchi, Differential systems associated with To order, please specify ASPM/22N

CONTEMPORARY MATHEMATICS The Reconstruction of Trees from Their Automorphism Groups Matatyahu Rubin The Reconstruction Volume 151 of Trees from Their Automorphism Groups This book focuses on automorphism groups of trees, providing a nearly complete Matatyohu Rubin analysis of when two trees have isomorphic automorphism groups. Special attention is paid to the class of N0-categorical trees, and for this class the analysis is complete. Various open problems, mostly in permutation group theory and in model theory, are discussed, and a number of research directions are indicated. Aimed at graduate students and researchers in model theory and permutation group theory, this self-contained book will bring readers to the forefront of research on this topic.

1991 Mathematics Subject Classification: 03; 20, 06 Nielsen iheorv and ISBN Q-8218-5187-X, 274 pages (softcover), September 1993 DynomicOI Systems Individual member $34, List price $56, Institutional member $45 e>Ph6':1(.McCOrd To order, please specify CONM/151NA cnrtsl' Ectttor Nielsen Theory and Dynamical Systems Christopher K. McCord, Editor Volume 152

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Nielsen Theory and Dynamical Systems, held in June 1992 at Mount Holyoke College. Focusing on the interface between Nielsen fixed point theory and dynamical systems, this book provides an almost complete survey of the state of the art of Nielsen theory. Most of the articles are expository and provide references to more technical works, making them accessible to both graduate students and researchers in algebraic topology, fixed point theory, and dynamical systems.

1991 Mathematics Subject Classification: 54, 55; 34, 58 ISBN 0-8218-5181-0, 350 pages (softcover), September 1993 Individual member $31, List price $52, Institutional member $42 To order, please specify CONM/152NA

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JANUARY 1994, VOLUME 41, NUMBER 1 63 AMS Reports and Communications

Election Results of 1993 266 registrants, including 171 members M. RENEGAR, Cornell University. In the election of 1993, 4806 valid of the Society. Lie Theoretic Methods in Mathemat­ ballots were returned and counted. Invited Addresses. By invitation ical Physics, ALVANY ROCHA, Graduate Cathleen S. Morawetz was elected of the Northeastern Section Program School and University Center (CUNY). president-elect. She will serve one-year Committee, there were four invited Contributed Papers. There were in this position after which she will serve speakers. The speakers, their affilia­ four sessions of contributed papers. for two years as president and one year tions, and their titles were as follows: Local Arrangements. These were as ex-president. TADEUSZ lWANIEC, Syracuse University, most ably handled by Dan Waterman Jean E. Taylor was elected to a three­ Nonlinear PDEs and harmonic integrals of Syracuse University, assisted by Patti year term as vice-president. in quasiconformal analysis; CHARLES Ford, both of whom did a superb job There are five newly elected A. McGIBBON, Wayne State Univer­ of coordinating all the details of such a members-at-large of the Council: Robert sity, The rational homology of the p­ large sectional meeting. K. Lazarsfeld, Frank Morgan, Norberto adic completion of a sphere; JAMES Salinas, Sylvia M. Wiegand, and Robert M. RENEGAR, Cornell University, Com­ Lesley M. Sibner J. Zimmer. Each will serve a three-year plexity theory, round-off errors and lin­ Associate Secretary Brooklyn, New York term. ear programming; and ALVANY RocHA, Donald J. Lewis was elected to a Graduate School and University Cen­ five-year term as a trustee. ter (CUNY), Minimal series representa­ The October Meeting Elected to three-year terms on the tions and conformal symmetry. in College Station Council's Nominating Committee were Special Sessions. By invitation The 886th meeting of the Society was Morris W. Hirsch, Hugh L. Montgomery, of the same committee, there were ten held on the campus of Texas A&M University, College Station, Texas, on and Linda Preiss Rothschild. special sessions. The topics and names Friday, October 22, and Saturday, Octo­ Members elected to the Council's and affiliations of the organizers follow: Editorial Boards Committee for three­ ber 23, 1993. There were 320 registrants, Geometric Topology, DouGLAS R. year terms were Carolyn S. Gordon and including 251 members of the Society. ANDERSON, Syracuse University. Martin Golubitsky. There were 36 student registrants. Algebraic Topology, ROBERT The proposed amendment to the By­ Invited Adresses. By invitation of BRUNER and CHARLES A. McGIBBON, laws passed. the Central Section Program Committee, Wayne State University. All terms begin on 1 February 1994 there were four invited one-hour ad­ Commutative Algebra and Algebraic except those for the Nominating Com­ dresses. The speakers, their affiliations, Geometry, STEVEN P. DIAZ, Syracuse mittee, which begin on 1 January 1994. and the titles of their talks were as fol­ University, and ANTHONY V. GERAMITA, The report of the tellers may be lows: GILLES PISIER, University of Paris Queen's University. obtained by contacting the secretary of VI and Texas A&M University, Hilber­ the Society. The full list of members of Harmonic Analysis, ALLAN GREEN­ tian operator spaces; STEVEN P. LALLY, the Council, the Board of Trustees, and LEAF, University of Rochester, and RoB­ Purdue University, Symbolic dynamics, the members of the Executive Commit­ ERT S. STRICHARTZ, Cornell University. probability, and counting problems in tee will appear in a future issue of the Differential Geomet1y and Global geometly; THEODORE A. SLAMAN, Uni­ Notices. Analysis, Wu-ThH HsiANG, Syracuse versity of Chicago, The structure of de­ University. finability; and STEPHEN A. STOLZ, Uni­ Robert M. Fossum Representations of Finite Dimen­ versity of Notre Dame, Nonconnected Secretary sional Algebras, MARK KLEINER and moduli spaces of positive sectional cur­ Urbana, Illinois DAN ZACHARIA, Syracuse University. vature metrics. Nonlinear Potential Theory, JUAN J. The speakers were introduced by The September Meeting MANFREDI, University of Pittsburgh. David Larson, Carl Cowan, Neil Sloane, in Syracuse Topics in Probability, TERRY R. Mc­ and Phillip Yasskin, respectively. The 884th meeting of the Society was CoNNELL, Syracuse University. Special Sessions. By invitation held in Syracuse, New York, on the cam­ Computational Problems Involving of the same committee, there were thir­ pus of Syracuse University. There were Polynomials,PAULPEDERSENandJAMES teen special sessions of selected twenty-

64 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

minute papers. The topics of these ses­ Reaction Diffusion Systems, WILLIAM The sessions on Several complex sions and the names and affiliations of E. FITZGIBBON, University of Houston, variables, Control systems governed by the organizers were as follow: and J. J. MoRGAN, Texas A&M Univer­ partial differential equations, Texas ge­ Harmonic Analysis and its Applica­ sity, College Station. ometry and topology, Reaction diffusion tions, JOSEFINA ALVAREZ, New Mexico Nonselfadjoint Operator Algebras, systems, Nonselfadjoint operator alge­ State University. DAVID R. LARSON, Texas A&M Univer­ bras, Representation theory and geom­ Several Complex Variables, HAROLD sity, College Station. etry of noncommutative algebras, and P. BOAS, AL BOGGESS, and EMIL J. Representation Theory and Geom­ The geometry of Banach spaces and STRAUBE, Texas A&M University, Col­ etry of Noncommutative Algebras, Eo­ operator spaces were dedicated to the lege Station. WARD S. LETZTER, Texas A&M Univer­ memory of Ilya Bakelman, professor of Composition Operators on Spaces sity, College Station. mathematics at Texas A&M University of Analytic Functions, RANDALL K. Identities and Varieties of Algebraic and formerly chair professor and head CAMPBELL-WRIGHT, University of Structures, JoHN C. MEAKIN, University of the geometry section at Leningrad Tampa; CARL C. COWEN, Purdue Uni­ of Nebraska-Lincoln; AMITAI REGEV, Pedagogical University, who died unex­ versity; and BARBARA D. MACCLUER, Pennsylvania State University, Univer­ pectedly in 1992. University of Richmond. sity Park; MARK V. SAPIR, University Contributed Papers. There was Nonlinear Partial Differential Equa­ of Nebraska-Lincoln; and SAMUEL M. one session for contributed ten-minute tions, ALFONSO CASTRO, JosEPH A.lAIA, Vovsi, Trenton State College. papers chaired by Susan Geller of Texas JOHN W. NEUBERGER, and HENRY A. Noncommutative Differential Geom­ A&M University. WARCHALL, University of North Texas. etry, EFTON L. PARK, Texas Christian Committee. Local arrangements Control Systems Governed by Par­ University. were made by Ms. Karola Pletz, Edi­ tial Differential Equations, GooNG CHEN The Geometry of Banach Spaces torial Assistant and Administrative As­ and JIANXIN ZHou, Texas A&M Uni­ and Operator Spaces, GILLES PISIER and sistant (ret.) of the Department of Math­ versity, College Station. THOMAS ScHLUMPRECHT, Texas A&M ematics of Texas A&M University, with Texas Geometry and Topology, TIM University, College Station. the assistance of her staff. D. COCHRAN, Rice University; LORENZO Algebraic Combinatorics, SuNG A. SADUN, University of Texas at Austin; YELL SoNG, Iowa State University, and Andy R. Magid and PHILIP B. YASSKIN, Texas A&M PAUL M. TERWILLIGER, University of Associate Secretary University, College Station. Wisconsin, Madison. Norman, Oklahoma

History of Mathematics Lectures in the History of Mathematics Henk J. M. Bos Volume 7

This volume contains eleven lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. Those who teach mathematics, as well as mathematics historians, will appreciate this insightful, wide-ranging book.

1991 Mathematics Subject Classification: 00, 01 ISBN 0-8218-9001-8, 197 pages (hardcover), December 1993 Individual member $52, List price $86, Institutional member $69 To order, please specify HMATH7/NA Members of the London Mathematical Society may order at the AMS member price. The LMS is incorporated under Royal Charter and is registered by the Charity Commissioners.

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

JANUARY 1994, VOLUME 41, NUMBER 1 65 Miscellaneous

Personals Massachusetts, Amherst, has been pro­ of the Society for 56 years. Kazimierz Goebel, of Marie-Curie moted to professor at that institution. Eldon Dyer, professor emeritus of Sklodowska University, was named Andrew J, Woldar, of Villanova the Graduate School and University rector of that university and was elected University, will be visiting the Institute Center of the City University of New president of the Polish Mathematical for Advanced Study in Princeton, New York, died on October 26, 1993. He Society. Jersey, January-April 1994. was born on June 19, 1929, and was a Leon Henkin, professor emeritus member of the Society for 45 years. of the University of California, Berke­ Charles G. Lange, of the University ley, has been named a Phi Beta Kappa Deaths of California, Los Angeles, died on June Visiting Scholar for 1993-1994, during Robert 0. Abernathy, of Orangeburg, 25, 1993. He was born on March 30, which he will visit nine institutions. South Carolina, died on July 19, 1993. 1942, and was a member of the Society Gerald A. Heuer, of Concordia Col­ He was born on April16, 1927, and was for 25 years. lege, has been awarded an MAA Cer­ a member of the Society for 36 years. Henrik H. Martens, of the Univer­ tificate of Meritorious Service for 1993 Maurice J, Bresson, of Divonne­ sity of Trondheim, died on October 10, and will be a visiting professor at Graz Les-Bains, France, died on March 6, 1993. He was born on March 16, 1927, University (Austria) from January-May 1993. He was born on May 13, 1921, and was a member of the Society for 39 1994. and was a member of the Society for 27 years. Charles W. Peck, of the California years. Bertram Ross, retired professor of Institute of Technology, was named chair R. P. Dilworth, professor emeritus mathematics from the University of New of the Division of Physics, Mathematics, of the California Institute of Technology, Haven, died on October 27, 1993. He and Astronomy at that institution. died on October 29, 1993. He was born was born on October 17, 1918, and was Jon L. Sicks, of the University of in December 1914, and was a member a member of the Society for 29 years.

LECTURES ON MATHEMATICS IN THE LIFE SCIENCES Some Mathematical Questions in Biology: Predicting Spatial Effects in Ecological Systems Robert H. Gardner, Editor Volume 23

The central themes of these papers are the characterization of effects, exploration of mechanisms, and understanding of consequences of spatial heterogeneity on ecological systems. The new mathematical approaches presented here will be especially useful for identifying the effect of landscape change on ecosystem productivity and sustainability. Mathematicians and ecologists interested in these issues will find this book useful, and individual chapters will be of interest to physicists, econometricians, landscape ecologists, and human ecologists.

1991 Mathematics Subject Classification: 92; 93, 90 ISBN 0-8218-1174-6, 168 pages (softcover), October 1993 Individual member $20, List price $33, Institutional member $26 To order, please specify LLSCI/23NA

.,w'ttui~,.,{' ~~,p,""'S All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. ~ 1 S, ,; g Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toll free 800-321-4AMS ·"8 ' - ,_."' (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. "N'DE.D \"&

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

ORDINARY MEMBERS Luis Arbey Gomez, Duitama­ Daniel Segalen, Univ of Bangui, Norsk Matematisk Foreningros Juan Jose Abad, Univ of Texas at Boyaca, Colombia Central African Republic Johannes Mykkeltveit Juan M Hernandez-Guerra, Las A A Shkalikov. Moscow State Univ, Austin Sociedad Matematica Mexicana Palrnas, Spain Russia Ruben Agin, Massachusetts Institute Gerna Mercado Sanchez of Technology, Cambridge Jun Irnai, NTT Communication Maciej J Smuga-Otto, Edmonton, Elizabeth Ann Arnold, Sumerduck, Science Laboratory, Kyoto, Alberta Canada Southeast Asian Mathematical Society VA Japan Cinque S Soto, Union, NJ Nurul Muchlisah Ahmadsarido Danold Charles Bacon Jr, Lancaster, Carlos Jose Jimenez, Univ San Craig S Stevenson, Socorro, NM Svenska Matematikersamfundet Francisco de Quito, Ecuador Michael Stillman, Cornell Univ, CA Bjorn Sture Lennart Gustafsson Earl R Barnes, Georgia Institute of Janet B Jones-Oliveira, Pleasanton, Ithaca, NY Technology, Atlanta CA Hans Thunberg, Royal Institute of Thomas Albert Beiter, Bath, IN Kenneth Lewis Judd, Hoover Technology, Stockholm, Sweden Alan Jon Boertjens, Indian Harbour Institute, Stanford, CA R K Tuteja, Haryana, India NOMINEE MEMBERS Beach, FL Arman H Karapetyan, Armenian Lars Falck Villemoes, Stockholm, Case Western Reserve University Srisakdi Charrnonrnan, Assumption Academy of Science, Erevan Sweden College, Bangkok, Thailand Armin Kargol, Virginia l'olytech Edward Williams, Univ of Notre Xia Chen Xiaoan Chen, SUNY at Stony Institute & State Univ, Dame, IN Central Missouri State University Brook, NY Blacksburg Soodabeh R Zamani, Hayward, CA Paul J Plummer Chee-Whye Chin, Berkeley, CA Alexandre A Kirillov, Moscow State Rafal Waclaw Zbikowski, Univ of North Carolina State University David Lee DeWester, Ft Drum, NY Univ, Russia Glasgow, Scotland Bharat Madhusudan Deshpande, Christopher R Lee, John Carroll Hiroshi Ishikawa Indian Institute of Technology, Univ, Cleveland, OH Southern lllinois University, Bombay, India Frederic Lehobey, Rennes, France Edwardsville Mkhitar Djrbashian, Armenian Robert E Mahony, Australian RECIPROCITY MEMBERS Youhong Gong National Univ, Canberra Academy of Sciences, Yerevan Australian Mathematical Society Carol J Graham Jeannine A Epps, Yonkers, NY Claudia Malvenuto, Univ of Quebec at Montreal, Canada David A Pask University of Delmmre Todd Frederick Fennimore, Chicago, Jacqui Rarnagge IL L G Mikhailov, Dushanbe, Tajikistan Lynn Ann Firestine Abesolom Abby Fidel, Portland, OR Sandor Molnar, Budapest, Hungary Deutsche Mathematiker-Vereinigung University of Idaho Kelly Gaddis, Cornell Univ, Ithaca, Luiza A Moraes, Rio de Janeiro, e. V. Allen Terral Bailey Brazil NY Peter Draexler Jayathi Sundar Raghavan Mora Alpizar Gerardo, Sede de Kuniaki Nakamitsu, Tokyo Denki Detlef Frank Univ, Saitama, Japan Marilyn S Stein Occidente UCR San, Alajuela, Klaus Josef Spitzmueller Costa Rica Byeong Kweon Oh, Seoul National University of Southern Mississippi Eldar Y Giladi, Stanford Univ, CA Univ, Korea Gesellschaft fiir Angewandte Jichun Li Valery Borisovich Giner, Melbourne, Christine Potier, Ecole Norrnale Mathematics und Mechanik Elizabeth Pierson Riggs Superieure, Paris, France Australia Michael Dellnitz Vanderbilt University Snezhana Gocheva-Ilieva, Plovdiv, Bruce Thomas Prendergast, Cypress, London Mathematical Society CA Artur Ryszard Andrzejak Bulgaria Bernard L D Thorp Alcaraz Guillermo Gomez, Univ Bobby Quan, Brooklyn, NY Washington University National Autonoma de Mexico, Nancy M Rodgers, Hanover College, Mathematical Society of Japan Benjamin P Nicholson Mexico, Mexico IN Masaaki Homma David Birdsong Weiland Atsushi Katsuda

JANUARY 1994, VOLUME 41, NUMBER 1 67 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.

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No listing for a position will be printed if it expresses or implies any preference, limitation, specification, or discrimination based on age, color, race, religion, sex, or national origin in contravention of any federal or state statute prohibiting discrimination in employment on the basis of these criteria. The publisher reserves the right to edit any listing prior to publication which does not conform with federal or state law on discrimination in employment. All employers in the United States are required to abide by the requirements of Title VII of the Civil Rights Act of 1964, announcing a national policy of equal employment opportunity in private employment, without discrimination because of color, race, religion, sex, or national origin. All U.S. listings are accepted with the understanding that the employer complies with federal requirements. Advertisers not subject to U.S. laws may be required to sign a statement that they do not discriminate in employment on grounds of age, color, race, religion, sex, or national origin. Applicants should be aware that institutions outside the U.S. may not be legally bound to conform to these or similar requirements and the AMS cannot assume responsibility for eriforcing 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.

NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

SUGGESTED USES for classified advertising are positions available books or lecture notes for s~rvices. to the development of an interactive research sale, books being sought, exchange or rental of houses, and typing group in statistics. In addition, qualifications THE 1994 RATE IS $70 per inch on a single column (one-inch minimum), calculated from the include substantial evidence of high quality top of the type; $40 for each additional 16_ inch or fraction thereof. No discounts for multiple ads or teaching and demonstrated potential for a pro­ the same ad in consecutive issues. For an additional $10 charge, announcements can be placed ductive, quality research program. At present, anonymously. Correspondence will be forwarded. there are three statisticians and two probabilists Advertisements in the "Positions Available" classified section will be set with a minimum in the Department. The starting date is August one-line headline, consisting of the institution name above body copy, unless additional headline 22, 1994. speci~ied copy is by the advertiser. Advertisements in other sections of the classified pages will Northern Arizona University has an on­ be set according to the advertisement insertion. Headlines will be centered in boldface at no extra campus enrollment of 16,000. The Department ?harg~. Cl~ssified c.al~ulated rates are from top of type in headline to bottom of type in body copy, of 28 tenure-track faculty offers Bachelor's and 1ncludmg lines and spaces w1th1n. Any fractional text will be charged at the next Ih_ inch rate. Ads Master's degrees with emphases in mathe­ will appear in the language in which they are submitted. matics, mathematics education, statistics, and Prepayment is required of individuals but not of institutions. There are no member discounts actuarial science. for classified ads. Dictation over the telephone will not be accepted for classified advertising. To apply, send letter of application with vita DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising and direct three letters of reference to: Screen­ Department. ing Committee, Department of Mathematics, ~· LA~S PR~H.IBI,! di~~riminati~n ~mploy'!lent . S. in on the basis of color, age, sex, race, P. 0. Box 5717, Northern Arizona University, relig1on or nat1onal ongm. Pos1t1ons Available' advertisements from institutions outside the U. s. Flagstaff, Arizona 86011. The search will remain cannot be published unless they are accompanied by a statement that the institution does not open until the position is filled. The Screening discr~minate on these grounds whether or not it is subject to U. S. laws. Details and specific Committee will begin reviewing applications wording may be found near the Classified Advertisements in the January and July/August issues January 17, 1994. The University is an equal of the Notices. employment opportunity/affirmative action insti­ SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians tution; women and underrepresented minorities ~reaccepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) are encouraged to apply. 1n the U.S. and Canada, or 401-455-4084 worldwide, for further information. SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street Prov!dence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not requ1red to do so. AMS FAX 401-455-4004. ·cALIFORNIA. CALIFORNIA STATE POLYTECHNIC UNIVERSITY, POMONA POSITIONS AVAILABLE considered but those in the following areas are particularly encouraged: functional analysis, Subject to the availability of funding, one tenure numerical analysis, number theory, differential track teaching position in mathematics at the as­ sistant professor level, salary dependent upon ALABAMA geometry, and partial differential equations. We seek a candidate with a Ph.D. in qualifications. Doctorate in Mathematics or re­ mathematics who shows strong potential in lated field and expertise in ordinary, partial, THE UNIVERSITY OF ALABAMA and/or stochastic differential equations and their Department of Mathematics teaching and research, who has the promise to strengthen our undergraduate and graduate applications to modeling required. Evidence of The department hopes to have available, begin­ programs, and who will appreciate the unique potential for excellent teaching and scholarly ning August 16, 1994, a tenure-track position geography and climate of interior Alaska. research required. Closing date 3/30/94; posi­ at the rank of assistant professor. Applicants Please send a curriculum vitae, with a tion starting 9/94. Cal Poly Pomona is actively whose research interests are in group the­ description of professional interests and as­ seeking to maintain its heritage and identity ory, ring theory, or homological algebra are pirations, and arrange that three letters of as a comprehensive center of education that preferred. Applicants in other areas may be recommendation be sent directly to: serves a dynamic, multicultural region (with considered. The Search Committee 58% ethnic minorities). For additional informa­ The successful candidate shall have com­ Department of Mathematical Sciences tion or to apply, contact: Search Committee, pleted the Ph.D. degree or equivalent by August University of Alaska Fairbanks Mathematics Dept., California State Polytechnic 15, 1994. Excellence in research and a strong P.O. Box 756660 University, 3801 W. Temple Avenue, Pomona, commitment to teaching are required. Fairbanks, AK 99775-6660 CA 91758-4033. 909-869-3467. EOEIAA Applicants should send curriculum vitae, Application files will be reviewed starting reprints and/or preprints, and at least three February 24, 1994. We welcome applications letters of recommendation to: Search Com­ from traditionally underrepresented groups. UAF CALIFORNIA STATE UNIVERSITY, is an AA/EO employer and educational institu­ mittee, Department of Mathematics, The Uni­ HAYWARD versity of Alabama, Box 870350, Tuscaloosa, tion. Department of Mathematics AL 35487-0350. Preliminary enquiries may be addressed to Martyn Dixon (205-348-5154; and Computer Science e-mail: mdixonll!mathdept. as. ua. edu). UA The department seeks applicants for a tenure­ is an affirmative action/equal opportunity em­ track appointment, effective Fall 1994, at the ployer. Women and minorities are particularly Assistant Professor rank. Applicants should encouraged to apply. NORTHERN ARIZONA UNIVERSITY hold a Ph.D. in mathematics. The successful Department of Mathematics candidate will be expected to teach a variety Position in Statistics of mathematics courses ranging from service courses for the Business School to graduate ALA!)KA The Department of Mathematics of Northern courses in analysis and differential equations. Arizona University invites applications for a The teaching load is 3 courses per quarter, UNIVERSITY OF ALASKA, FAIRBANKS tenure-track position for an assistant professor with classes meeting both day and evening. in statistics. Preference will be given to those Beyond a commitment to excellent teaching, Applications are invited for an anticipated tenure with a doctorate in statistics, strong theoretical candidates should exhibit the competence and track position at the assistant professor level. background, interest in applied statistics and in­ potential to engage in significant professional Applicants in all areas of mathematics will be tramural consulting, and the ability to contribute activities, including research and publication.

JANUARY 1994, VOLUME 41. NUMBER 1 69 Classified Advertisements

Send resume and names of 3 references tunity/Affirmative Action employer committed to the Department of Mathematics, beginning fall to Mathematics Faculty Search Committee by excellence through diversity. 1994. January 15, 1994. CSUH (AA/EOE), with an (1) Ky Fan Assistant Professorship: Candi­ ethnically diverse student body, encourages dates will be considered in the following math­ applications from women and men of all ethnic ematical areas: linear and nonlinear functional backgrounds and physical abilities. Position UNIVERSITY OF CALIFORNIA, analysis, harmonic analysis, and computational #94-95 MATH-TT. LOS ANGELES complexity. The Ky Fan assistant professorship Department of Mathematics is a special two-year nonrenewable position Regular Positions in Pure and which carries a research stipend. Appointment is effective July and candidates must Applied Mathematics 1, 1994, CALIFORNIA STATE UNIVERSITY, possess a Ph.D. by September 1994. Selection NORTHRIDGE Subject to availability of resources and ad­ will be based primarily on research achieve­ Faculty Positions ministrative approval, one regular position in ment, but evidence of satisfactory teaching is Department of Mathematics pure and applied mathematics. The six specific necessary. Teaching load will consist of 4 one quarter courses per year. California State University, Northridge, seeks search areas are as follows: 1) statistics; 2) ap­ (2) Tenure track position: Applications are one tenure-track assistant professor and, de­ plied and computational mathematics; 3) logic invited for a tenure-track appointment at the pending on qualifications, one assistant or and mathematical computer science; 4) geom­ assistant professor level, effective July 1, 1994, associate professor beginning Fall The etry and topology (including dynamical systems 1994. in the area of numerical analysis of nonlinear availability of these positions is subject to final and geometric partial differential equations); partial differential equations. Candidates should approval of funding. A Ph.D. in Mathematics 5) analysis and differential equations (includ­ have a command of the field of the numerical or equivalent completed by August is ing mathematical physics); 6) algebra, number 1994 analysis of nonlinear partial differential equa­ required and excellent accomplishments or po­ theory, and combinatorics (including represen­ tions, demonstrated excellence in research in tential in one of the following areas: algebra, tations). Very strong promise in research and associated numerical applied mathematics, and analysis, geometry, applied mathematics, or teaching required. Positions initially budgeted have a command of and interest In the de­ topology. In addition the successful applicant at the assistant professor level. Sufficiently out­ velopment of associated rigorous mathematical must have a strong commitment to teaching and standing candidates at higher levels will also theories. A demonstrated excellence in the de­ a willingness to interact and collaborate with be considered. Teaching load: averaging 1.5 sign, analysis, and implementation of algorithms colleagues. courses per quarter, or 4.5 quarter courses for the computation of solutions of nonlinear par­ Responsibilities include teaching a maximum per year. To apply, send electronic mail to tial differential equations is highly desirable as of 12 units per semester with possible reductions search@math. ucla. edu OR write to Thomas is the ability and desire to interact with sci­ in the teaching load to carry out research or M. Liggett, Chair, Department of Mathemat­ entists in applied areas such as engineering to make other professional contributions. Upper ics, University of California, Los Angeles, CA and physics. The appointee will also have the division and graduate classes are often held in 90024-1555. Attn: Staff Search. UCLA is an potential to provide leadership in the acquisition the evening. equal opportunity/affirmative action employer. of new computational facilities, demonstrated CSUN is located in the Los Angeles area the potential to become an effective teacher, and is in close proximity to Caltech, UCLA, and and completed the Ph.D. degree by September usc. 1994. To apply submit a letter describing your UNIVERSITY OF CALIFORNIA, RIVERSIDE (3) Special visiting positions: Subject to specific qualifications, vita, and three letters of Department of Mathematics availability of funds, one or more special one­ recommendation to Department of Mathematics, Position in Topology year visiting assistant professorships in the Hiring Committee, CSUN, 18111 Nordhoff St., Applications and nominations are invited for a research areas mentioned under (1) and (2) Northridge, CA 91330-8313. tenured or tenure track position in Topology above, with possibility of a second year, carrying Application deadline: February 1, 1994. beginning July 1, 1994, or later. The position is a teaching load of approximately 5 one quarter California State University, Northridge, is at the Assistant or Associate Professor level. A courses per year. Applicants for the Ky Fan and an Equal Opportunity/Affirmative Action, Title Ph.D. in Mathematics or related specialization the tenure track positions will automatically be IX, Section 504, Employer. Applications from area is required. Demonstrated excellence in considered for the visiting positions. Excellence women, minorities, and persons with disability research and teaching is essential. Respon­ in research, potential for interaction with other are particularly encouraged. sibilities include teaching undergraduate and 94/96 faculty and evidence of good teaching graduate level courses and seminars, con­ required. Candidates must possess a Ph.D. by ducting scholarly research, and participating in September 1994. UNIVERSITY OF CALIFORNIA, IRVINE service activities. Established criteria of the Uni­ Applicants should send a vita, a publication Department of Mathematics versity of California determine salary and rank. list, a one-page statement of research interests, Irvine, CA 92715-3875 To assure full consideration, applicants should and arrange to have three letters of recom­ send their curriculum vita, including a list of mendation sent to: the Ky Fan Committee for Applications are invited for several one or two publications, and have at least three letters of the Ky Fan position, to the Numerical Analysis year Visiting Assistant Professor positions in recommendation sent to: Committee for the tenure track position, and the following areas of research: 1) applied Professor David Rush to the Visiting Appointment Committee for the and computational mathematics; 2) geometry Topology Hiring Committee special visiting positions (but only if not oth­ and topology (includes geometric analysis); Department of Mathematics erwise applying) at the address: Department 3) analysis and POE (includes mathematical University of California of Mathematics, University of California, Santa physics); 4) algebra and number theory (in­ Riverside, CA 92521-0135 Barbara, CA 93106. Include an e-mail address cludes algebraic and arithmetic geometry); 5) by January 24, 1994. UCR is an Affirmative if available. Applications which are complete by logic and set theory; 6) probability. Strong Action/Equal Opportunity Employer. January 15, 1994, will be given full considera­ promise in research and teaching is required. tion. Salary $30,500-$38,800. Teaching load: 5 to UCSB is an affirmative action/equal oppor­ 6 quarter courses per year. Applicants should tunity employer. send a resume, preprints, reprints, dissertation UNIVERSITY OF CALIFORNIA, abstract and ask three people to send letters of SANTA BARBARA recommendation to: Recruitment Committee, at Department of Mathematics the above address. The deadline for application is January 31, 1994, or until the position is filled. The University of California, Santa Barbara The University of California is an Equal Oppor- invites applications for the following positions in

70 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

UNIVERSITY OF SOUTHERN CALIFORNIA applicant must have held an academic position Los Angeles, California for at least five years, and show evidence of demonstrable administrative ability, including The Department of Mathematics anticipates visionary leadership, communication skills, and FLORIDA INTERNATIONAL UNIVERSITY several tenure-track or possible tenured posi­ effective interaction and evaluation of person­ tions at the Assistant and/or Associate Profes­ nel. The Head is expected to manage and direct The Department of Mathematics announces sor level. Applicants must show strong research the department's efforts in instruction and in tenure track positions beginning August 1994. promise and possess excellent communications scholarship, to continue and enhance its excel­ These positions are usually at the beginning skills for teaching undergraduate mathemat­ lence in teaching and in research, to plan and Assistant Professor level. Candidates must ics courses. Visiting positions (at all levels) and oversee the development of its research activi­ have a Ph.D. in Mathematics and a commitment postdoctoral appointments will also be available. ties and academic programs, and to represent to research and quality teaching. Qualified To apply, please submit the following mate­ the department on campus and externally. candidates in all areas of Mathematics will be rials in a single package: letter of application The Colorado School of Mines is a state considered. (including your e-mail address and fax number), university, internationally renowned in the en­ Teaching load consists of no more than and a curriculum vitae. Candidates for junior ergy, materials, and resource fields, attracting five 3-credit courses per academic year. Send positions should also provide at least three outstanding students in a broad range of sci­ resume and arrange for 3 letters of recommen­ letters of recommendation. Mail application to: ence and engineering disciplines. The School dation to be sent to: Recruitment Committee, Chair of Appointments Committee, Department of Mines is strongly committed to quality teach­ Department of Mathematics, Florida Interna­ of Mathematics-ORB 155, University of South­ ing and research. CSM provides an attractive tional University, Miami, FL 33199. ern California, Los Angeles, CA 90089-1113. campus environment, a collegial atmosphere, Florida International University is an equal USC is an Equal Opportunity/Affirmative Action relatively small size (3000 student, about 30% opportunity/equal access employer. It is a mem­ Employer. Women and minorities are especially in graduate programs), and an ideal location in ber of the State University system of Florida, with encouraged to apply. the foothills of the Rocky Mountains 13 miles approximately 24,000 students. The department from downtown Denver. offers bachelor's and master's degrees. Applications will be considered beginning February 15, 1994, and thereafter until the WHITTIER COLLEGE position is filled. The applicant should provide Whittier, CA 90608 a statement giving administrative, pedagogical, GEORGIA The Department of Mathematics invites appli­ and scholarly philosophy which should include cations for an anticipated tenure-track position a discussion of advantages and disadvan­ DEKALB COLLEGE at the assistant professor level to teach under­ tages of programs combining both Computer A Two-Year Unit of the graduate mathematics courses beginning fall of Science and Mathematics, and how to recon­ University System of Georgia 1994, pending final budgetary approval. cile research vs. teaching conflicts. This letter Dean Mathematics Qualifications: Ph.D. (completed or to be and a vita should be sent by postal mail to (Position Ref. 95-14) completed by the summer of 1994) in Math­ the Colorado School of Mines, Department ematics, evidence of quality teaching, and Head Search #94-01-31, 1500 Illinois Street, Located on four campuses in suburban Atlanta, potential for scholarly growth. Expertise in Ap­ Golden, CO 80401. The applicant should also DeKalb College provides an attractive environ­ plied Mathematics preferred. Most faculty at arrange for five letters of reference to be mailed ment of learning for a motivated student body the college participate in teaching College-wide to the above address or sent by e-mail to of 16,000 representing a wide range of cultures. courses such as Freshman Writing Seminars [email protected]. The College has earned an exceptional reputa­ and other interdepartmental courses. CSM is an AAIEEO. Women and minorities tion among two-year institutions for the quality Candidates should send a curriculum vitae, are encouraged to apply. of its teaching of liberal arts and sciences as a statement of teaching philosophy, and three well as professional career preparation. letters of recommendation to Chairperson, De­ The division dean serves in a college-wide partment of Mathematics, Whittier College, P.O. capacity to ensure the effectiveness of the Box 634, Whittier, California 90608. Mathematics curriculum in achieving the stated outcomes of the institutions's mission. She/he is Review of completed applications will begin .. ·······························-······ ...... ······················-······· on Feb. 15, 1994. responsible to the Vice-President for Academic Whittier College is an Equal Opportu­ _ '········ ...... CONNI;CTICUT Affairs and supervises all department heads in nity/Affirmative Action Employer. SOUTHERN CONNECTICUT the Mathematics area. Candidate must possess strong interper­ STATE UNIVERSITY sonal and communication skills; knowledge of Mathematics Department current trends in higher education; ability to Tenure-track position at Assistant Professor initiate/manage a wide variety of activities with rank beginning 8/22/94 to teach undergradu­ minimal direction; ability to work with a variety COLORADO SCHOOL OF MINES ate/graduate mathematics education and math­ of groups, both inside and outside the college, ematics, and supervise secondary school stu­ to promote the college and its programs; ability The Colorado School of Mines is seeking candi­ dent teachers. Teaching load: 12 hours/sem. to manage change and to negotiate resolutions dates for the position of Head of the Department Salary range: $32,677 to $45,786. Qualifica­ to problems among groups with competing in­ of Mathematical and Computer Sciences. This tions: doctorate (or near completion) in mathe­ terests. A doctorate is required with a minimum department offers B.S., M.S., and Ph.D. de­ matics or mathematics education with a strong of 18 semester (30 quarter) graduate hours in grees under the department title. With a faculty mathematics background, evidence of quality mathematics. of 18 tenured and tenure track members, the teaching, potential for scholarly growth. Sec­ A minimum of three years administrative department receives annually approximately a ondary school teaching experience preferred. experience at the department head level or million dollars in grants; 116 undergraduate stu­ Send letter of application, vita, transcripts (unof­ above is essential plus five years of full­ dents and 70 graduate students are currently ficial ok), three letters of reference to Dr. Robert time college teaching experience (preferably at enrolled in our degree program. Washburn, Chair, Search 93-269, Southern the two-year college level). Salary: $50,000+ The position requires a Ph.D. in a math­ Connecticut State University, 501 Crescent St., (placement is commensurate with education ematical or computer science. The applicant New Haven, CT 06515. Full consideration given and experience); excellent benefits. This is a should have a sufficiently outstanding record to applications received by 1/15/94. AA/EOE. twelve month, tenure track position with faculty of scholarly achievement and teaching expe­ rank beginning July 1, 1994. rience to justify a tenured appointment at the Applications and nominations for the DEAN Full Professor level. In addition, the successful MATHEMATICS will be accepted until 1/28/94.

JANUARY 1994, VOLUME 41, NUMBER 1 71 Classified Advertisements

To be considered, please provide the following: THE UNIVERSITY OF ILLINOIS "z'z"·-=~="·"""~=-~1Ni5'iANJr=~~=,~­ (1) letter of application referencing position AT CHICAGO ~,:==::::::-=:·~~::.:."SY~~:rr~l==-~=-.=.."ll?"~:tw.:====:-=~=lli number (#95-14); (2) resume; (3) unofficial Department Head copies of graduate transcript(s); (4) names, Department of Mathematics, Statistics, INDIANA UNIVERSITY-PURDUE addresses, and telephone numbers of three and Computer Science UNIVERSITY references. AT INDIANAPOLIS (IUPUI) Please submit requested documents in a The Department of Mathematics, Statistics, and Department of Mathematical Sciences single packet to: Judy Chastonay, DeKalb Col­ Computer Science at the University of Illinois lege, Personnel Dept., 3251 Panthersville Rd., at Chicago seeks applicants for the position of The Department of Mathematical Sciences at Decatur, GA 30034. DeKalb College is an Head. The Department enjoys an AMS Group IUPUI is seeking applicants for two or more Equal Opportunity, Affirmative Action Employer I classification, and has 68 faculty and over tenure-track positions to begin in August 1994. which invites and encourages applications from 200 graduate students. Major research pro­ Rank is open depending on qualifications. Ap­ minorities. Georgia is an Open Records State. grams include applied mathematics, mathemat­ plicants must have an earned doctorate by the ical computer science, mathematics education, starting date. A strong research record or excel­ probability and statistics, and pure mathemat­ lent research potential as well as a commitment ics. Located in the heart of Chicago, UIC is to quality graduate and undergraduate teaching a research university with 16,000 undergrad­ are required. Some preference may be given to uate, 5,000 graduate, and 3,000 professional applicants in scientific computing and applied students. statistics. However, strong applicants from all ILLINOIS INSTITUTE OF TECHNOLOGY The Head is the chief administrative officer areas of mathematical sciences are encouraged Mathematics Department Chair of the Department, with responsibility for in­ to apply. structional programs, administrative, budgetary, IUPUI is a comprehensive urban university Applications are invited for a senior-level fac­ promotion, and recruitment matters. The Head with over 28,000 students. The department ulty appointment as department chair, starting is expected to provide leadership in the further offers programs of study leading to Purdue August 1994. The department has 14 full-time development of research, teaching, and public University B.S., M.S., and Ph.D. degrees. The faculty, and offers masters and doctoral de­ service. The successful candidate will have an university offers competitive salaries and pro­ grees in mathematics, applied mathematics, earned doctorate and be eligible for appointment vides excellent fringe benefits. Send resume and applied statistics. at the rank of full professor. A strong record and three letters of recommendation to Prof. C. The candidate should have a vital research in research and university teaching, a demon­ D. Aliprantis, Acting Chair, Department of Math­ program in an area that complements current strated commitment to equality of opportunity, ematical Sciences, IUPUI, 402 N. Blackford departmental strengths. The chair is responsible and substantial leadership and organizational Street, Indianapolis, Indiana 46202-3216. Clos­ for leading the development of all research and skills are required. Women and minority candi­ ing date: January 15, 1994. Late applications educational activities in the department. dates are especially encouraged to apply. The will be considered until positions are filled. Review of applications will begin in January desired appointment date is August 21, 1994. IUPUI is an Affirmative Action/Equal Oppor­ 1994 and will continue until the position _is Applications should be received by February tunity Employer. Women and minority candi­ filled. Candidates must be U.S. citizens or meet 1 , 1994, to receive full consideration, although dates are encouraged to apply. Immigration Reform Act criteria. the search will proceed until the position is Send letter of application, curriculum vitae, filled. Materials, including a full curriculum vitae and names of references to: and names and addresses of four references, Search Committee r::s::~.~~:;:z~7z:r.::tn:::Vera Pless ~m:?.?.;.:~=-,:;.-=;-r.:~:c3~w.:ru:~~ Illinois Institute of Technology Search Committee for Department 10 West 32nd Street KANSAS STATE UNIVERSITY Head Chicago, IL 60616 Department of Mathematics c/o College of Liberal Arts and Phone: 312-567-3162; Fax: 312-567-3155 Sciences, m/c 228 Illinois Institute of Technology is an Equal Subject to budgetary approval, applications The University of Illinois at Chicago Opportunity/Affirmative Action University. are invited for tenure-track and visiting posi­ 601 South Morgan Street tions commencing August 18, 1994; rank and Chicago, Illinois 60607-7104 salary commensurate with qualifications. The UIC is an Affirmative Action/Equal Opportunity Department seeks candidates whose research Employer interests mesh well with current faculty. The NORTHWESTERN UNIVERSITY Department has research groups in the area Mathematics Department of analysis, algebra, geometry/topology, and 2033 Sheridan Road differential equations. Although all fields will be Evanston, Illinois 60208-2730 WOLFRAM RESEARCH, INC. seriously considered, some preference will be Mathematics Development given to candidates in differential equations. Ap­ The Mathematics Department will sponsor an plicants must have strong research credentials Emphasis Year in dynamical systems. This We are looking for more top quality mathe­ and a commitment to excellence in teaching. program will include two-year assistant pro­ maticians to join the Mathematica research and A Ph.D. in mathematics or a Ph.D. dissertation fessorship positions starting September 1994 development team. We anticipate openings in accepted with only formalities to be completed and possible visiting positions for more senior several areas. Applicants should be able to work is required. Letter of application, current vita, mathematicians for part or all of the academic in a fast-paced environment and be capable of description of research, and three letters of year. Applications should be sent to Professor interacting well with mathematicians and others. recommendation should be sent to: Clark Robinson at the department address and Applicants should have a broad knowledge of Louis Pigno include a curriculum vitae and three letters of mathematics. Applicants should have consid­ Department of Mathematics recommendation. In order to ensure full con­ erable programming experience: knowledge of Cardwell Hall 137 sideration, an application should be received Mathematica is required; experience with C is Kansas State University by January 15, 1994. Northwestern University preferred. A Ph.D in mathematics (or equiva­ Manhattan, KS 66506 is an affirmative action, equal opportunity em­ lent experience) is required. Send resumes to: It is expected that offers will begin on De­ ployer committed to fostering a diverse faculty; Attn: Personnel, Wolfram Research, Inc., 100 cember 14, 1993, but applications for positions women and minority candidates are especially Trade Center Drive, Champaign, IL 61820 or will be reviewed until February 1, 1994, or until encouraged to apply. resumes@wri. comm. AA/EOE positions are closed. AA/EOE

72 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

THE WICHITA STATE UNIVERSITY productive research. Preference will be given to sume, undergraduate and graduate transcripts candidates with expertise in Algebra, Numerical and three letters of recommendation evaluating The Department of Mathematics and Statistics Analysis, Mathematical Modelling, or a related teaching and scholarship should be sent to invites applications for a tenure-eligible position field. We seek applicants with a strong commit­ David B. Damiano, Chair. Deadline for Applica­ starting August 1994. Special consideration ment to teaching at both the undergraduate and tions: February 1 , 1994. Representatives of the will be given to persons having expertise in graduate levels and an interest in innovative Department will attend the Joint Mathematics numerical analysis or geometric analysis. We approaches to the teaching of mathematics. Meeting in Cincinnati and will participate in seek someone whose research interests are Women and minorities are encouraged to ap­ the Employment Register. We expect to invite consonant with those of our faculty. Senior ply. Send letter of application, curriculum vitae, candidates to campus for interviews beginning candidates should have distinguished research graduate transcripts, and three letters of rec­ in early February 1994. records. Junior candidates are expected to ommendation to: Joel Irish, Chair, Department have excellent research potential. All candidates of Mathematics and Statistics, RE: 102, Uni­ should have a strong commitment to excellence versity of Southern Maine, 37 College Avenue, in teaching and the ability to participate in and Gorham, ME 04038. USM is an EEO/AA em­ contribute to our doctoral program in Applied ployer. Review of applications will begin January TUFTS UNIVERSITY Mathematics. Salary and rank negotiable. Ph.D. 20, 1994, and continue until the position is filled. Department: Mathematics in Mathematics is required. Women and minority Contact Person: Todd Quinto, candidates are especially urged to apply. Send Search Committee Chair application letter, detailed resume, and arrange Address: Medford, MA 02155 to have three reference letters sent by January MARYLAND 20, 1994 (or monthly until the position is filled) Application Deadline: February 15, 1994 to: - TEACH IN ASIA OR EUROPE Applications are invited for one tenure-track po­ The Wichita State University University of Maryland University College seeks sition at the rank of Assistant Professor starting Professor Stephen W. Brady, Search September 1, 1994. A Ph.D. in mathematics Committee Chair excellent teachers for openings on U.S. military bases overseas. Appointments begin August with specialization in numerical analysis is re­ Department of Mathematics and quired. Applicants must show promise of strong - Statistics 1994. Requirements include M.A. or Ph.D., recent college teaching experience, and U.S. research and will be expected to excel in teach­ Wichita, Kansas 67260-0033 ing, especially at the introductory level. The e-mail: brady@twsuvm. uc. twsu. edu citizenship. Competence to teach in another dis­ cipline desirable. Benefits include transportation teaching load will be two courses per semester. fax: 316-689-3748 Please send a c.v. and have three letters of AAIEOE and military base privileges (PX, commissary, etc.). Frequent travel and the cost of schooling recommendation sent by February 15, 1994. make these positions difficult for those with As an Affirmative Action/Equal Opportunity Em­ children. Send resume to: Dr. Ralph E. Millis, ployer, Tufts encourages women and minority Assistant to the President, Overseas Programs, candidates to apply. University of Maryland University College, Col­ BOWDOIN COLLEGE lege Park, MD 20742-1642. AAIEEO. Brunswick, Maine 04011 ...... -······ ··············- Mathematics Department: Tenure-track Assisant .. M1$$QI..IRI Professorship in applied mathematics starting ______1\iiAssAcHus~n$ Fall 1994. Initial appointment for three years NORTHEAST MISSOURI with renewal possible. Possibility of second, BOSTON UNIVERSITY STATE UNIVERSITY non-tenure-track position-field open. Ph.D. re­ The Department of Mathematics at Boston Uni­ The following positions are expected to be quired and strong research record or potential versity invites applications for a regular faculty available in August 1994: Tenure-track Assis­ expected. Normal teaching load is two courses position in the area of Algebra/Number Theory. tant or Associate Professor of Mathematics per semester. Candidates with record of effec­ The successful applicant should have a strong Education, Tenure-track Assistant Professor of tive undergraduate teaching preferred. Review commitment to both research and teaching. Statistics, Tenure-track Assistant Professor of of candidates begins 1 January, but applica­ Applications and at least three letters of recom­ Mathematics, and two or more temporary In­ tions will be considered until position is filled. mendation should be sent to: Search Committee structor positions. Tenure-track positions require Send resume and 3 letters of recommenda­ (Algebra and Number Theory), Department of appropriate doctoral degree; Instructor positions tion to James E. Ward, Chair, Department of Mathematics, Boston University, 111 Cumming­ require at least the Master's degree. Candidates Mathematics, Bowdoin College, Brunswick, ME ton St., Boston, MA 02215. AAIEOE. for the Mathematics Education position should 04011. Include e-mail address. Bowdoin College have teaching experience in secondary edu­ is committed to equal opportunity through affir­ cation and be qualified to supervise teaching mative action. Women and members of minority interns. Substantial driving to internship sites groups are urged to apply and invited to identify COLLEGE OF THE HOLY CROSS required. themselves as such. Worcester, Massachusetts One tenure-track position and at least one Tenure track appointment beginning in Septem­ temporary instructorship will involve teaching ber 1994 is available for a Ph.D. mathematician some or all statistics courses. Teaching loads UNIVERSITY OF SOUTHERN MAINE interested in teaching at an undergraduate lib­ are nine hours per semester for tenure-track po­ Assistant Professor eral arts college. Strong commitment to teach­ sitions, twelve for instructors. Candidates should Department of Mathematics and Statistics ing and research is required. Preference will be supply evidence of potential for excellence in given to candidates in the fields of global analy­ teaching, advising, research, and service ap­ The University of Southern Maine invites appli­ sis, mathematical physics, differential topology, propriate for the position they seek. Experience cations for a tenure-track position at the rank and geometry. Teaching load is three courses with the use of technology in teaching desirable. of Assistant Professor starting in the Fall of each semester. Salary is competitive. Fringe Complete applications consist of a letter of 1994. Candidates without the Ph.D. completed benefits include TIAA-CREF, medical, dental, application, a statement of teaching philoso­ at the time of application must accompany the and life insurance plans and generous sabbati­ phy, transcripts of undergraduate and graduate application with a statement from the institution cal and faculty fellowship programs. study, and three letters of reference. These in which enrolled for doctoral studies confirming Holy Cross is an affirmative action/equal op­ should be sent to Dr. Lanny Morley, Division that the degree will be completed by August portunity employer. Women and minorities are Head, Mathematics and Computer Science, 1, 1994. Candidates must show potential for encouraged to apply. Applications, including re- Northeast Missouri State University, Kirksville,

JANUARY 1994, VOLUME 41, NUMBER 1 73 ...... -...... ----···········-...... _. ______...... _...... Illllllllll.lllllllll!lllllll...L&&ili2! li!llllllll______.... ~·--·~-~-~--~·~·~-·~·~·~ ...... ~-~-~~---...... Classified Advertisements

MO 63501. NMSU is an Equal Opportunity Nevada, Reno, Reno, NV 89557. Please include TRENTON STATE COLLEGE Employer. the AMS classification number(s) of your field of Department of Mathematics and Statistics specialization, if possible. Anticipated Faculty Vacancies for Fall1994 =:~:~=:~i-::::::::::: Tenure track positions at the Assistant Professor level: Req'd: Doctorate in Mathematics Educa­ UNIVERSITY OF NEBRASKA AT KEARNEY tion, Statistics, or Mathematics; demonstrated commitment to quality teaching; strong research Statistics: Tenure track position, Assistant or As­ DARTMOUTH COLLEGE potential. All fields will be considered; openings sociate Professor beginning Aug. to teach 1994 John Wesley Young Research are anticipated in Mathematics Education as undergraduate and graduate courses, advise Instructorship in Mathematics well as in Statistics and Mathematics. students, service/consulting. Ph.D. in statistics Send vita and three letters of recommenda- or a closely related area. Prefer applicants The John Wesley Young Research Instructor­ tion to: with emphasis in applied statistics, stat comput­ ship is a two year postdoctoral appointment Aigli Papantonopoulou, Chair ing, and actuarial science. Strong commitment for promising new or recent Ph.D.s whose Search Committee to excellence in teaching and scholarship es­ research interests overlap a department mem­ Dept. of Mathematics and Statistics sential. Productive research potential, strong ber's. Current departmental interests include CN 4700 Hillwood Lakes interpersonal and communication skills. Inter­ areas in algebra, analysis, combinatorics, com­ Trenton, NJ 08650-4700. est in coordinating, integrating, and developing puter science, differential geometry, logic and The review process will begin February 1, 1994, the statistics and actuarial science programs set theory, number theory, probability and topol­ and will continue until all the positions are filled. preferred. Salary commensurate with experi­ ogy. Teaching duties of four ten-week courses Non-U.S. citizens must include a statement of ence and education. The University provides spread over two or three quarters typically in­ current visa status. Retirement Plan options and a flexible benefits clude at least one course in the instructor's The department currently enrolls over two program at a minimal cost to the employee. speciality and include elementary, advanced, hundred and fifty majors in Mathematics, Math­ Review of applicants will begin February 14, and (at instructor's option) graduate courses. ematics Education, and Statistics. A graduate Send letter of application describing expe­ 1994. Nine-month salary of $34,000 supplemented by program offers a master's degree in mathemat­ rience and qualifications, transcripts, vita, and summer (resident) research stipend of $7,556 ics and in mathematics education. three letters of recommendation to Dr. Richard (two-ninths). Send letter of application, resume, To enrich education through diversity, TSC Barlow, Statistics Search Committee Chair, L. graduate transcript, thesis abstract, description is an AA/EOE. Dept. of Mathematics and Statistics, Univ. of of other research activities and intersects if Nebraska at Kearney, 68849-5360. EEO/AA. appropriate, and 3 or preferably 4 letters of recommendation (at least one should discuss teaching) to Phyllis A. Bellmore, Mathemat­ ::~:=:1mm[ciFfC?~ ics and Computer Science, 6188 Bradley Hall, Hanover, NH 03755-3551. Applications received UNIVERSITY OF NORTH by Jan. 15 receive first consideration; applica­ CAROLINA-CHARLOTTE UNIVERSITY OF NEVADA, RENO tions will be accepted until position is filled. Mathematics Department The Department of Mathematics of the Univer­ Dartmouth College is committed to affirmative Charlotte, NC 28223 sity of Nevada, Reno, has openings for t~o action and strongly encourages applications tenure-track positions "A:' and "0" at the assis­ from minorities and women. Two tenure-track positions at the Assistant Pro­ tant professor level. Minimum qualifications for fessor level-one in Mathematics Education both positions are: a Ph.D. in a mathematical and one in any area of Mathematics. The science; strong potential for significant resear~h Department's major strengths are in the areas accomplishments; demonstrated excellence 1n -=~-=-'Niw'JE'RSEv'~=='"~=~~, of Statistics, Applied Mathematics, Probability, PDEs, Numerical Analysis, Operator Theory, Al­ teaching, including interest in incorporating in­ ~'%)\,.l~":{'~~:.;n.~;r~~=~~~~~""""'~~.MJ===: structional innovation and technology in the gebra. Visiting positions and Postdoc Positions RUTGERS UNIVERSITY-NEWARK are also available. Ph.D. and serious commit­ classroom; leadership potential and demon­ Assistant Professor of Mathematics strated interest in curricular and programmatic ment to teaching and research required for all development at both the undergraduate and The Department of Mathematics and Computer positions. The applicant should send vita and graduate level; ability to communicate and work Science invites applications for an anticipated a short abstract of current research interest effectively with students and faculty; and com­ tenure-track Assistant Professor position begin­ and should indicate which position and at what patibility with the programmatic and research ning ·September 1994. Candidates must have rank for which she/he wishes to be consid­ needs of the department. a Ph.D., have a strong research record, and ered. Females are especially encouraged to For position "A:' the department has particular be able to demonstrate outstanding promise, apply. Address to Professor R. F. Anderson at needs in several areas of Applied Mathematics as well as a commitment to effective teaching. the above address. The applicant should also including Applied Logic, Computational Math­ Preference will be given to candidates with arrange. for 4 letters of reference, addressed ematics, Differential Equations, and Statistics; research interests in one or more of the follow­ to Professor Anderson. For full consideration, for position "0" the department has particular ing areas: algebraic geometry, representation applications should be submitted by January 28, needs in the areas of Differential Geometry, theory, automorphic forms, and number theory. 1994; otherwise, applications will be accepted Dynamical Systems, Harmonic Analysis, and Applicants should arrange for a curriculum until positions are filled. Low-Dimensional Topology. Candidates with vitae and at least four letters of recommen­ UNCC IS AN AFFIRMATIVE ACTION/EQUAL expertise in one or more of these areas are es­ dation, including one which addresses teach­ OPPORTUNITY EMPLOYER. pecially encouraged to apply. For both positions, ing, to be sent to Mark Feighn, Associate excellence of qualifications will be given greater Chair, Department of Mathematics and Com­ weight than field of specialization. AA/EEO. puter Science, Rutgers University, Newark, NJ WAKE FOREST UNIVERSITY Women and Minorities are especially encour­ 071 02. Responses may also be a-mailed to Department of Mathematics aged to apply. math@andromeda. rutgers. edu. Processing and Computer Science Send application specifying the position(s) of applications will begin January 15, 1993. applied for by the application deadline of Febru­ Rutgers University is an equal opportu­ Applications are invited for a position as In­ ary 15, 1994, with your vita and three letters nity/affirmative action employer. structor or Visiting Assistant Professor in Math­ of recommendation to: Dr. Chaitan Gupta, ematics. The term is one year, renewable for Chair, Department of Mathematics, University of up to three years. Rank is dependent upon

74 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

qualifications, and a Master's or Ph.D. degree Bowling Green State University essential. The successful candidate will hold in Mathematics or Statistics is required. Du­ Bowling Green, OH 43403-0221 USA rank in the Ohio State University's Department ties consist only of teaching three courses per Equal Opportunity Employer: Women and of Mathematics. To apply, send letter, vita, and semester. A strong interest and preparation minorities are encouraged to apply. 3 letters of reference to Dr. Gary Kennedy, OSU for teaching calculus and introductory statistics Mansfield, 1680 University Drive, Mansfield OH is desirable. The department has 22 mem­ 44906. To ensure full consideration, arrange for bers, offers a B.S. and M.A. in mathematics, all materials to arrive by February 15, 1994. and a B.S. and M.S. in computer science. CLEVELAND STATE UNIVERSITY The Ohio State University is an equal opportu­ Send a letter of application and resume to Assistant Professor in Mathematics nity/affirmative action employer. OSU Mansfield Richard D. Carmichael, Chairman, Department The Mathematics Department invites applica­ has identified diversity of its faculty, staff, and of Mathematics and Computer Science, Wake tions for a tenure track position at the Assistant students to be a very important goal. Qualified Forest University, Box 7388, Winston-Salem, Professor level. Candidates must have com­ women, minorities, Vietnam-era veterans, and NC 27109. AA/EO employer. pleted a Ph.D. in a mathematical science by individuals with disabilities are encouraged to the starting date and must have demonstrated apply. a commitment to excellence in both teaching WAKE FOREST UNIVERSITY and research. Applicants must have research Department of Mathematics specialization in one of the following areas: and Computer Science applied statistics, applied probability, stochastic processes, numerical analysis, wavelet the­ ..... QKI,AHQMA. Applications are invited for a position as In­ ory. Applicants should arrange to have a vita structor or Visiting Assistant Professor in Math­ and three letters of recommendation sent to SOUTHEASTERN OKLAHOMA ematics. The term is one year, renewable for Professor John J. Walsh, Department of Math­ STATE UNIVERSITY up to three years. Rank is dependent upon ematics, Cleveland State University, Cleveland, Faculty Position Announcement qualifications, and a Master's or Ph.D. degree OH 44115. (Funding for this position is pend­ in Statistics or Mathematics is required with ing.) Starting Date: September 19, 1994. Salary: DEPARTMENT CHAIR OF MATHEMATICS: preference being given to holders of a statistics competitive. Deadline for applications: Febru­ Ph.D. required. Administrative skills necessary. degree for this position. Duties consist only of ary 4, 1994. Minorities, women, and handi­ Rank is negotiable. Teaching load is six hours teaching three courses per semester. A strong capped are particularly encouraged to apply. per semester. Applicants must have demon­ interest and preparation for teaching introduc­ Cleveland State University is an Equal Oppor­ strated scholarship and at least five years tory statistics and calculus is desirable. The tunity/Affirmative Action Employer. teaching and/or administrative responsibilities. department has 22 members, offers a B.S. and ASSISTANT PROFESSOR/INSTRUCTOR: M.A. in mathematics, and a B.S. and M.S. in Applicant must possess either Ph.D. in Mathe­ computer science. Send a letter of application matics (Assistant Professor rank, tenure track) and resume to Richard D. Carmichael, Chair­ DENISON UNIVERSITY or must be an ABD (Instructor rank). Duties include teaching undergraduate mathematics at man, Department of Mathematics and Computer The Department of Mathematical Sciences an­ all levels, student advising, scholarly activities, Science, Wake Forest University, Box 7388, ticipates a two-year position with the possibility and committee service. Winston-Salem, NC 27109. AA/EO employer. for renewal at the level of Assistant Professor To apply, submit a letter of application, starting in Fall 1994. Eventual conversion to resume, official transcripts, statement of ad­ tenure-track is likely. A doctorate (or ABD) in ...... ministrative/academic philosophy or teaching ...... ····oHIO mathematics is required. Ability to teach sta­ philosophy, and three letters of recommenda­ tistics or "computer literacy" courses a plus, tion to Southeastern Oklahoma State University, but not required. A commitment to quality BOWLING GREEN STATE UNIVERSITY Personnel Office, Station A, Durant, OK 74701. undergraduate instruction is essential. Duties Department of Mathematics Minorities and women are especially encour­ include teaching three courses per semester aged to apply. Application deadline is February and Statistics and continued scholarship. 7, 1994. EOEIAA Bowling Green, OH 43403-0221 Denison is a liberal arts college of about Assistant Professor, Tenure-Track 1900 students located in a village of about The Department anticipates two tenure-track 4000, twenty-five miles east of Columbus. The positions and encourages applications in: Math­ department offers B.A. and B.S. degrees in ematics Education, Functional/Applied Analysis mathematics and in computer science. The ...... PENNSYLVANIA (Approximation Theory, Banach Spaces, Oper­ department consists of nine full-time members. Send resume, transcripts of graduate work, ator Theory, Optimization, PDEs and Scientific BIOSTATISTICIAN Computation) and Probability and Stochastic and three letters of recommendation (at least Processes. We have 31 faculty, 70 full-time one should address your teaching) to Professor Seeking an individual to work in Spring House, graduate students, and a growing doctoral Todd Feil, Chair, Department of Mathematical PA, to be involved in the development and program (23 Ph.D.s awarded in the last five Sciences, Denison University, Granville, Ohio implementation of statistical analysis plans for years). The selected candidate, who must have 43023. preclinical and clinical research, analyzing re­ a Ph.D., will be expected to pursue research, Applications should be made by February 1, sults and writing statistical reports according teach two courses per semester, work with 1994; applications beyond this date will be con­ to the Standard Operating Procedures of the graduate students, and eventually have the sidered until the position is filled. Denison is an employer. Individual will work closely with pre­ opportunity to direct Ph.D. dissertations. Those Affirmative Action/Equal Opportunity Employer; clinical and clinical staff on the design of studies with postdoctoral experience are encouraged women and minorities are encouraged to apply. for projects in different therapeutic areas. Quali­ to apply. Candidates are expected to have a fied applicants must possess a Ph.D in Statistics strong research record (or potential) in an area and three years experience as a Statistician, at compatible with current faculty. Salary Compet­ THE OHIO STATE UNIVERSITY least two of which must be in the field of Bio­ itive. Please provide vita, publication list, official Mansfield Campus statistics. Applicants must possess a knowledge transcript, and have three letters of recom­ of pharmacokinetic/pharmacodynamic analysis, mendation (one concerning teaching) sent by Tenure-track assistant professorship in math­ SAS and FORTRAN Programming, familiarity February 1, 1994, to: ematics. Ph.D. required. Preference for can­ with VAX and PC. Applicants must have the Professor A.M.W. Glass, Chair didates specializing in algebraic geometry or ability to design statistical protocols. Annual Department of Mathematics and Lie algebras. Strong commitment both to un­ salary $58,500. Submit resume or C.V. to the Statistics dergraduate teaching and to math research is Philadelphia Job Bank, 444 N. 3rd St., 3rd Fl.,

JANUARY 1994, VOLUME 41, NUMBER 1 75 Classified Advertisements

Philadelphia, PA 19123. Job2 Order Number beginning with the Fall Semester 1994. We 4542207. seek candidates in various areas of Mathemat­ ics which are complementary to those of the VANDERBILT UNIVERSITY current faculty and would enhance and support Department of Mathematics the goals of the Department. Application dead­ CARNEGIE MELLON UNIVERSITY Nashville, TN 37240 line is February 15, 1994, or until positions filled. Salary and rank are commensurate with quali­ Department of Mathematics We invite applications for a Distinguished or fications which must include the Ph.D. degree The Department of Mathematics anticipates the Named Professor position beginning Fall 1994. (in hand or expected by Sept. 1994). Assistant appointment of tenured or tenure-track fac­ This is a tenured position and we are seeking a Professor candidates must show strong poten­ ulty members beginning Sept~mber ~, 199~. specialist in algebra with outstanding research tial for excellence in teaching and research. For We are particularly interested In applicants In credentials. The interests of our algebra group an Associate or Full Professorial appointment the areas of applied analysis and numerical include universal algebra and lattice theory, set­ the candidate must have excellent teaching cre­ analysis. Some visiting positions may ~Iso ~e theoretic algebra, abelian groups, semigroups, dentials and a nationally established research available. Applicants should send a vlta~ .lIst ring theory, and logic with applic~tions to .co":'­ record; some success in attracting outside fund­ of publications, and a statement descnblng puter science. Evidence of effectIve teachIng IS ing is preferred. Please send a resume and current and planned research, and arrange to required. To apply, send the following materi~ls three letters of recommendation to: have three letters of recommendation sent to: in a single mailing to Professor ConstantIne Chairman Appointments Committee, Department of Math­ Tsinakis, Chair, at the address above: letter Recruiting Committee ematics, Carnegie Mellon University, Pittsburgh, of application (with e-mail address if availa~le) University of Texas at Arlington PA 15213. Carnegie Mellon University is an Af­ and a curriculum vitae with a list of publIca­ Department of Mathematics firmative Action/Equal Opportunity Employer. tions. Additional information, including letters Box 19408 of recommendation, will be requested from se­ Arlington, TX 76019-0408 lected candidates after the initial screening. The University of Texas at Arlington is an Only solicited letters of recommendation will be Affirmative Action/Equal Opportunity Employer. considered. SAINT JOSEPHS UNIVERSITY VANDERBILT UNIVERSITY IS AN EQUAL Philadelphia, PA 19131 OPPORTUNITY/AFFIRMATIVE ACTION EM­ PLOYER. The Department of Mathematics and Computer Science seeks applicants for a one year re­ placement of a faculty member on le.a~e for UNIVERSITY OF UTAH 1994-1995. Candidates should be WIllIng to Mat~e­ teach courses at all levels of the undergraduate University of Utah, Department of curriculum. Applications with three letters of matics invites applications for the follOWIng TEXAS A&M UNIVERSITY-KINGSVILLE positio~s. recommendation should be sent to Dr. J.P.E. Availability of positions is contingent upon funding. . Hodgson at the above address. A~plications Subject to availability of resources and admin­ 1. One full-time tenure track appoIntment on should be received by February 15th In order to istrative approval, at least one tenure track the professorial level in mathematics applica­ guarantee consideration. position at the Assistant Professor level will be ble to materials science. Applicants must have available beginning with the Fall Semester 1994. received their Ph.D. degrees prior to 1993. Se­ Applicants must have a Ph.D. in M~them8:t~cs lection will be based on research and teaching and show evidence of good teachIng abIlIty, ability. excellent communication skills, and tangible 2. One C. R. Wylie Instructorship. The evidence of scholarly activity. We are seeking term of this instructorship is one year, but it persons who can take an active role in teaching may be renewed for up to three years. It will and curriculum development in support of our be awarded either to an incoming Instructor or THE UNIVERSITY OF PUERTO RICO undergraduate and graduate programs in Math­ to one of the Instructors already in residence AT MAYAGUEZ ematics, Statistics, and the training of teachers on the basis of ability and potential in teaching Department of Mathematics of Mathematics. Candidates with strong back­ and research. The stipend is $38,000. Duties grounds in applied mathematics and/or Complex consist of teaching four courses during the three [Please note: The previous version of this Analysis will be given first consideration. Te~~h­ ad ran with an error. The sentence "Fluency quarteracadem~yea~ ing assignments will include lower le~el servlc~ Englis~ 3. One or more visiting faculty positions of in spoken and written Spanish or ..." courses. Salary is commensurate WIth expen­ one year or less in any of the pr~fessori~1 ra~ks. should have said "Fluency in spoken and wntten ence. Send resume, transcript, and three letters Selection will be based on potentIal contnbutlons Spanish AND English ..."] The DeP8:rtment of of recommendation to: to the department's research program and on Mathematics has a tenure-track opening for an Faculty Search Committee teaching ability. Instructor in the area of applied mathematics Department of Mathematics Applications for all positions will be accepted (with emphasis in optimal contro!), with a salary Campus Box 172 until January 31, 1994, or until all positions are of $21,000 per year. Fluency in spoken and Texas A&M University-Kingsville degr~e filled. written Spanish or English, a Master's Kingsville, TX 78363-8201 Applications for any of these positions should in mathematics, and one year of academIC Completed applications received by Febru­ include curriculum vitae, bibliography, and three experience are required. The appointee will be ary 1, 1994, will be given first consideration. letters of reference. (Instructorship applications expected to teach undergraduate courses and Texas A&M University-Kingsville is part of the should also include an abstract of the thesis do research. Texas A&M University System and is an equal and either a list of graduate courses completed Send resume and three letters of recom- opportunity/affirmative action employer. mendation to: or a transcript of graduate work.) Visiting faculty Prof. Yuri Rojas-Ramirez applications should indicate the portion. of the Acting Chairperson three-quarter academic year dunng whIch the Department of Mathematics-UPR UNIVERSITY OF TEXAS applicant wishes to visit. Please send your ap­ P.O. Box 5000 AT ARLINGTON plication to Committee on Staff!ng, ~epartment Mayaguez, Puerto Rico 00681-5000 Department of Mathematics of Mathematics, 233 JWB, UniversIty of Utah, EEO/AA Salt Lake City, Utah 84112. The University of The Department invites applications for po~~ibly Utah is an Equal Opportunity, Affirmative Action two to three anticipated tenure-track posItIons Employer and encourages applications from

76 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

women and minorities, and provides reason­ professor. The candidate should have a Ph.D. least three years experience in teaching and able accommodation to the known disabilities of and an established research record in the rep­ research after the Ph.D. and to be able to applicants and employees. resentation theory of finite groups and algebras, demonstrate excellence in each. In particular, including Lie algebras, and must have strong a candidate's research should show clearly the teaching credentials. The candidate must also ability to make significant original and inde­ demonstrate an interest in working with our ex­ pendent contributions to Mathematics. Salary ...... VI:RI\IIQNI isting research group in algebraic combinatorics . commensurate with qualifications. The Department also has active researchers in Applicants should send their complete C.V. UNIVERSITY OF VERMONT analysis, applied mathematics, and mathemat­ including a list of publications,a short statement Position in Mathematics ics education. The availability of this position is describing their research programme, and all subject to administrative approval. appropriate material about their teaching. They The Department of Mathematics and Statistics Complete applications consist of a vita, a should also arrange to have at least four letters solicits nominations and applications to fill a list of publications, a summary of research of reference sent directly to Professor K. Murty, 2-year Visiting Assistant Professor position in interests, and three letters of recommenda­ Associate Chair, Department of Mathematics, mathematics for the academic years 1994-95 tion sent directly to Professor Myron B. Allen, University of Toronto, Toronto, Canada M5S and 1995-96. Applicants should have a Ph.D. Chair, Department of Mathematics, University 1A 1. At least one letter should be primarily in Mathematics and demonstrated excellence in of Wyoming, Laramie, WY 82071-3036. Com­ concerned with the candidate's teaching. To research and teaching. Strong preference will pleted applications received by 1 January 1994 insure full consideration, this information should be given to researchers in algebraic number receive first consideration. Women and minori­ be received by January 31, 1994. theory, arithmetic algebraic geometry, and com­ ties are encouraged to apply. The University In accordance with its Employment Equity putational number theory who will contribute to of Wyoming is an affirmative action/equal­ Policy, the University of Toronto encourages ap­ the activities of the ongoing Quebec-Vermont opportunity employer. plications from qualified women or men, mem­ Number Theory Seminar. Duties include teach­ bers of visible minorities, aboriginal peoples, ing two courses per semester and conducting and persons with disabilities. research. Applicants should send a vitae, de­ scription of research, and three letters of refer­ UNIVERSITY OF WYOMING ence to: David Dummit, Personnel Committee, Department of Mathematics Department of Mathematics and Statistics, Uni­ Tenure-Track Position in Analysis UNIVERSITY OF WATERLOO versity of Vermont, Burlington, VT 05401-1455. Department of Pure Mathematics Applications will be processed starting February The University of Wyoming Mathematics De­ 1, 1994; duties begin in the fall semester 1994. partment invites applications for a tenure-track The Department of Pure Mathematics at the UVM is an Equal Opportunity/Affirmative Ac­ position in Analysis at the rank of assistant University of Waterloo invites applications for a tion Employer. Members of underrepresented professor starting August 1994. Applicants must tenure-track position at the Assistant Professor groups are strongly encouraged to apply. demonstrate strong ability in research, breadth level starting July 1, 1994. The Department of mathematical knowledge, interest in collab­ is particularly interested in candidates whose oration with mathematicians in other areas, research interests are related to Algebraic Topol­ strong commitment to high quality undergrad­ ogy, Differential Geometry, Functional Analysis, ...... ··············· WiscoNsiN .. uate and graduate teaching, and willingness or Number Theory. In order to be considered to supervise masters and doctoral students. for the position, a Ph.D. is required. An ap­ UNIVERSITY OF WISCONSIN-PARKSIDE Preference will be given to researchers with pointment will be offered only to someone with strength in the areas of nonlinear functional very strong research and teaching qualifica­ The Department of Mathematics invites appli­ analysis and PDE. Outstanding candidates in tions. The University of Waterloo is committed cations for an anticipated tenure-track assistant other areas of analysis are also encouraged to to increasing the number of its female faculty, professorship to begin in fall 1994. Excellence apply. The availability of the position is subject and therefore applications from women mathe­ in mathematical research is required, as well to administrative approval. The Mathematics maticians are particularly welcome. Duties will as a serious commitment to excellent teach­ Department has 25 full-time faculty in applied include research, and teaching at all levels. ing of undergraduate mathematics, including mathematics, algebra/combinatorics, analysis, Salary will depend on the candidates's quali­ elementary algebra, to an increasingly diverse and mathematics education. fications. The closing date for applications is student population. The ability to interact with Complete applications consist of a vita, a January 15, 1994. An application should contain research of current faculty will be positively list of publications, a summary of research the curriculum vitae of the candidate plus three considered; these areas include infinite and interests, and three letters of recommenda­ letters of reference sent directly from the refer­ combinatorial group theory, ring theory and tion sent directly to Professor Myron B. Allen, ees. In accordance with Canadian immigration enveloping algebras, low-dimensional topology Chair, Department of Mathematics, University requirements, this advertisement is directed to and set theory. Teaching duties are 9-1 0 hrs/wk. of Wyoming, Laramie, WY 82071-3036. Com­ Canadian citizens and permanent residents. Women and minorities are encouraged to apply. pleted applications received by 1 January 1994 The University of Waterloo encourages applica­ Applications, including at least three letters of receive first consideration. Women and minori­ tions from qualified women and men, members reference, should be sent to Professor A. M. ties are encouraged to apply. The University of visible minorities, native peoples and persons Brunner, Department of Mathematics, University of Wyoming is an affirmative action/equal­ with disabilities. The availability of this posi­ of Wisconsin-Parkside, Box 2000, Konosha, WI opportunity employer. tion is subject to budgetary approval. Please 53141-2000. Review of applications will com­ send applications to: Dr. J. W. Lawrence, mence February 12, 1994. UW-Parkside is an Chair, Department of Pure Mathematics, Uni­ Equal Opportunity/Affirmative Action Employer. versity of Waterloo, Waterloo, Ontario, Canada C~NADA .. N2L3G1. UNIVERSITY OF TORONTO \IVYQMIN~·· Department of Mathematics YORK UNIVERSITY UNIVERSITY OF WYOMING The Department solicits applications for a Faculty Position in Discrete Mathematics Department of Mathematics tenure-stream appointment in Analysis. Pref­ Tenure-Track Position in Algebra erence will be given to researchers in the areas Subject to budgetary approval, applications are of nonlinear analysis and geometric analysis. invited for a tenure-track appointment at the The Department of Mathematics at the univer­ The appointment is at the Erindale campus Assistant Professor level in the Department sity of Wyoming seeks to hire an algebraist in at the level of Assistant Profesor to begin July of Mathematics and Statistics, to commence a tenure-track position at the rank of assistant 1, 1994. Candidates are expected to have at July 1, 1994. The successful candidate will be

JANUARY 1994, VOLUME 41, NUMBER 1 77 ...... ______Classified Advertisements

expected to have a strong established research his/her research plan to: Professor Hai-Chau record in Discrete Mathematics. Preference will SWITZERLAND Chang, Chairman, Department of Mathemat­ be given to Combinatorics or Graph Theory. ics, National Taiwan University, Taipei, Taiwan, Applicants must have a completed Ph.D. and SWISS FEDERAL INSTITUTE R.O.C .. FAX: 886-2-391-4439. E-mail inquiries proven teaching abilities. OF TECHNOLOGY (ETHZ) should be sent to Professor 1-Liang Chern at Applicants should send resumes and ar­ chern@math. ntu. edu. tw. Applications com­ range for at least three letters of recommenda­ The Swiss Federal Institute of Technology in pleted by February 15, 1994, will receive first tion to be sent so that they arrive before January Zurich (ETHZ) invites applications for the posi­ consideration. The National Taiwan University 24, 1994, directly to: Georges Monette, Chair, tion of an Assistant Professor of Mathematics. is an equal opportunity employer. Department of Mathematics and Statistics, York Duties of the new professor include research University, 4700 Keele Street, North York, On­ as well as an active participation in under­ tario, M3J 1P3, Canada, FAX: 416-736-5757; graduate and graduate courses for students of e-mail: mathstat@mathstat. yorku. ca. York mathematics, natural sciences, and engineer­ POSITION WANTED is implementing a policy of employment equity, ing. Candidates should have a university degree including affirmative action for women faculty. In and successfully completed own research work. accordance with Canadian immigration require­ Willingness to teach at all university levels and Research Mathematician. Ph.D. 1984. Full ments, priority will be given to Canadian citizens to cooperate with colleagues is expected. The Prof. 1992 Institute of Mathematics, Ukrainian and permanent residents of Canada. positions of assistant professors have been Academy of Sciences. Specialty: Approxima­ established to promote the career of younger tions and Expansions, Theoretical Computer scientists. They are available for three years Sciences, Functional Analysis. Other interests: in the first instance, with the possibility of a Fournier Analysis. Available now. Alexander renewal for an additional three years. Kushpel, c/o 7131 - 136 Avenue Edmonton, AB. Applicants with curriculum vitae and a list of T5C 2K3 CANADA. publications should be submitted no later than UNIVERSITY OF WARWICK February 15, 1994, to the President of the ETH Mathematics Institute Zurich, Prof. Dr. J. Nuesch, ETH Zentrum, CH- E. C. Zeeman Research Fellowship 8092 Zurich. The ETHZ specifically encourages PUBLICATIONS FOR SA in Mathematics female candidates to apply with a view towards increasing the proportion of female professors. Applications are invited for the first E. C. MATH SCI PRESS, 53 Jordan Rd., Brook­ Zeeman Research Fellowship in Mathematics. line, MA 02146; 617-738-0307. Lie-Cartan­ The position is available from October 1, 1994, Ehresmann Theory; Constrained Mechanics and is tenable for three years. UNIVERSITY OF ZURICH and Lie Theory; Geometric Structures in Applicants may have research interests in Professor of Mathematics Nonlinear Physics, by R. Hermann, $95 each. any branch of mathematics. They must be within two years of completing their Ph.D. thesis on Applications are invited for two positions as October 1, 1994; apart from this there are no Professor of Mathematics at the University of other restrictions on potential applicants. Zurich, one in Analysis and on in Numerical The salary will be on the Research Assistant Analysis. Applicants are expected to be active PUBLICATIONS WANTED Scale £12,828, to £20,442 at age-for-wage in research and to be willing to participate in plus three additional increments (to reflect the teaching at all levels. Wanted: Mathematical books, journals, reprints, prestigious nature of the Fellowship). Applications, including CV and list of publi­ ephemera. Contact R. K. Dennis, Math. Dept., The successful applicant will be expected to cations, should be sent to Professor G. Rasche, White Hall, Cornell U., Ithaca, NY 14853-7901. do no more than three hours teaching per week, Dekan der Philosophischen Fakultiit II, Uni­ Tel: 607-255-4027, FAX: 607-255-7149. e-mail: and this may be entirely at postgraduate level. versitiit Zurich-lrchel, Winterthurerstrasse 190, [email protected] Applicants must submit a summary of their CH-8057 Zurich, to arrive before 15th February research interests, a research plan (one side 1994. of A4 maximum), and a curriculum vitae. They must arrange for two letters of recommendation to be sent directly to the address below. Applicants are invited to submit in addition one TAIWAN or more pieces of recent work (for example, Ph.D. thesis, preprints, papers). NATIONAL TAIWAN UNIVERSITY The closing date for applications is: 31 Department of Mathematics March 1994. Address for correspondence: The Department of Mathematics invites applica­ E. C. Zeeman Fellowship in tions for a tenure-stream appointment in Applied Mathematics Mathematics. Strong consideration will be given Mathematics Institute to, but not limited to, the following areas: University of Warwick large-scale scientific computing, partial differen­ Coventry CV 4 7 AL tial equations, numerical analysis, mathematical U.K. biology, fluid mechanics. Applicants should send vita, three letters of recommendation, and brief description of

78 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ElMS subscribers: New Information for 1993-1994! Are you looking for a job? Do you have an open position to fill?

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Send Orders to: Prepaid orders: American Mathematical Society, P.O. Box 5904. Boston, MA 02206-5904 Charge orders: American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248 ' To qualify for the Student or Unemployed rate, one of the following statements must accompany the order: "I am currently unemployed and actively seeking employment. My unemployed status is not the result of voluntary resignation or retirement from my last position. I am not enrolled in a graduate study program." OR "I am a full-time student enrolled in a program leading to a degree or diploma at: " University of Minnesota The Geometry Center The National Science & Technology Research Center for Computation and VIsualization of Geometric Structures

The Geometry Center is the NSF demonstrate a high level of research Research Professorships Science and Technology Research accomplishment in mathematics or Center for Computation and computer science, and to be at home A very limited number of positions to Visualization of Geometric in a computing environment. supplement sabbatical support may Structures. The Center has created be available to those with substantial a unified computing environment Postdocs are expected to maintain a research accomplishments for all or centered on math and supporting: vigorous program of independent · part of the academic year 1994-95. research. They are also expected to The salary will be at the rate of - math and computer science participate fully in the life of the $30,00019 months or that which research, Center, that is, to participate in brings the sabbatical salary up to the - mathematical visualization, ongoing or to initiate new activities in full salary, whichever is less. To - software and tool development, a combination of technology apply please send by February 28, - application development, development, education, and 1994 a resume, and proposed - video animation production, and outreach. research directions for the period of - K-16 math education and residence, including a detailed outreach. Center postdocs may participate in statement of how they will involve the scientific activities of the the computational and graphics The Center supports an active University's Computer Science and resources of the Center. One or research visitor program, a postdoc Mathematics departments, as well as more letters sent on your behaH are program, an expertly staffed the IMA and other institutes and also invited but not required. technology development program centers at the University. and sponsors a variety of education Please send the application and outreach activities. Additional To apply please send 1) your vita, 2) materials preferably by email to a summary of your research [email protected], or to information about the Center can be Professor A. Marden at the address found in the anonymous ftp directory accomplishments, 3) information concerning your computing experience, below. at geom.umn.edu. in particular details of major programs you have written, and 4) a research plan, indicating how you plan to make The Geometry Center Postdoctoral Research use of computing and graphics University of Minnesota Fellowships resourses. In addition, 5) please list at Suite 500 least three references who are familiar 1300 South Second Street Up to three fellowships will be with your work and whom you have Minneapolis, MN 55454 awarded for the academic year asked to send separately letters of 1994-95 to individuals who have recommendation. Applications from those with full or received their Ph.D. within five years partial external support are strongly The University of Minnesota is an equal of their starting date. They are for encouraged. opportunity educator and employer. one year with the possibility of a one Application materials should be sent year renewal by mutual agreement. by February 28, 1994 preferably by email to [email protected], or by Remuneration will be $40,000/12 surface mail to Postdoc Applications at months if there is no other support. the address below. Applicants are expected to COMPUTATIONAL MECHANICS, INC., publisher ofbooks in engineering and numerical methods, is pleased to offer the members of the American Mathematical Society a 25% discount on all titles. Below are descriptions of a small sampling.

Boundary Elements: Computational Stochastic Applied Differential Equations An Introductory Course (2nd ed.) Mechanics for Scientists and Engineers C.A. Brebbia and J. Dominguez M. Ralunan AH-D. Cheng, C.Y. Yang (eds.) Titis best selling textbook has been written to provide These two volumes present a clear and well organized a simple and up-to-date introduction to the Boundary Tilis book discusses the computational aspects ofthe treatment ofthe concepts behind the development of Element Method. It is based on the authors' long application of stochastic teclmiques in the analysis of mathematics. The tex't material is presented in a highly experience teaching this numerical analysis method. engineering mechanics problems. It covers research in readable, mathematically solid fonnat. Many practical The book has been written in a form enabling it to be fields where computational stochastic teclmiques have problen!S have been illustrated displaying a wide used as a text book at undergraduate or graduate level reached a level of considerable sophistication, and variety of solution teclmiques Tite volumes are as well as by the engineer in practice who wants to those of an ell:ploratory and pioneering nature. intended for undergraduate mathematics courses for leam the fundamentals ofthe technique. Of particular engineering students. Graduate students in math.:mati­ interest is the way in which boundary element The book is divided into two parts: Titeory and cal and physical sciences can also use them towards concepts are introduced and applied in simple - but Computational Methodology, and Engineering their degree programs. useful - computer codes. Titese codes (four for Application. It includes applications in structural ISBN: 1562520563 potential and two for elasticity) facilitate comprehen­ dynamics and reliability, fatigue and fracture November, 199I 2 vols. SlW:OO $157.50 sion ofboundary elements. An introductory chapter mechanics, water waves, soil dynamics, earthquake and wind engineering, geoacoustics, composite Ordinary Differential Equations explains why boundary elements are needed, and their Volume 1 advantages compared with finite elements in the materials, shape design and identification, reliability design of dam-reservoir systelllS, groundwater flow, ISBN: I56252057I solution ofmany engineering problems. Other November, I99I 656pp _$.lA(t;6(T $105.00 chapters deal with potential problen!S, elastostatics, contaminant transport, among others. It also covers a combination with fmite elements and other topics of few unconventional topics such as chaotic d)1tamics Partial Differential Equations interest. and fuzzy sets. Volume2 DISKETTE ISBN: I562521748 ISBN: 156252058X A diskette with a complete listing ofprogram codes is October, 1993 750pp _!304:00 $228.00 November, 1991 356pp ~ $54.75 included. ISBN: I562520873 Advanced Formulations in Adaptive Finite and Boundary January, I992 322 pp book ~ $44.93 Methods Element Methods disk ..$481)(} $36.00 Boundary Element M.H. Aliabadi, C.A. Brebbia (eds.) C.A. Brebbia, M.H. Aliabadi (eds.) Tite boundary element method is now being increas­ In recent years increasing attention has been paid to ingly applied to new topics in engineering. Titis has led adaptive meshing and analysis teclmiques in order to researchers to investigate and develop new fonuula­ improve the reliability of numerical analysis tech­ tioJIS of the method which lend themselves better to niques such as the finite and boundary element problems such as fracture mechanics, coupling with method. Tltis book presents a comprehensive review of finite elements, moving boundary applicatiOJIS and the current state of adaptive analysis in engineering non-linear problems. This book presents new boundary computation. As such the topics are wide ranging and element fonuulations which are now emerging as include algoritluus for automatic meshing, adaptive viable altematives for a wide range of complex improvements, error analysis and adaptive solution problems. procedures. ISBN: 156252111X ISBN: 1562521144

Special Discount Yes, please send me ...... copy(ies)of: Order Form Send this form or copy to: 0 Payment enclosed: (check, money order) Please add $3 per book for shipping & Computational Mechanics, Inc. D Charge my credit card D Visa 0 Mastercard handling or $5 per book for UPS. 25 Bridge Street Card number ______Exp. date. ______Billerica, MA 01821 Name: ______Make check payable to: Address: Computational Mechanics, Inc. ------Tel: THE UNIVERSITY OF ARIZONA Department of Mathematics and Program in Applied Mathematics

The Department of Mathematics at the University of Arizona offers a broad spectrum of graduate courses and seminars in algebra, analysis, applied mathematics, geometry, mathematical physics, probability, and mathematics education that lead to the degrees of Master of Arts, Master of Science, and Doctor of Philosophy with majors in mathematics. Some course work outside the Department of Mathematics is required for each of these degrees. Both master's degrees require a thesis and can serve as a basis for further study toward a Ph.D. degree. Highly flexible programs in pure, and applications-oriented mathematics and mathematics education are offered in the Ph.D. program in mathematics. Completion of course work in major and minor fields and a dissertation presenting the student's original research are required.

In addition, the interdisciplinary Program in Applied Mathematics offers courses of study leading to the degrees of Master of Science and Doctor of Philosophy with majors in applied mathematics. Students entering the Program in Applied Mathematics take a one-year sequence of mathematics courses tailored to the needs of applied mathematics. Beyond this, the program offers great flexibility. Both M.S. and Ph.D. candidates are required to complete a certain number of courses outside the mathematics department. Ph.D. students complete a dissertation embodying original research under the direction of a member of the Program faculty. These faculty are 43 in number and have appointments in more than twenty departments of the University. The highly interdisciplinary faculty membership is a distinguishing feature of the Program in Applied Mathematics.

Applicants of superior quality will be among the students invited to the Eighth Annual Workshop for Advanced Undergraduates on Current Ideas in Nonlinear Science, March 5-8, 1994. Limited support is available for attendees. The workshop is designed to communicate topics in current active research in three areas: (i) Geometry and Physics, (ii) Geophysical Modeling, and (iii) Patterns.

Teaching assistantships are available for qualified graduate students. The stipend in 1993-1994 is $9678 and up for teaching four class hours. Associate teaching assistantships are available to students with a master's degree or the equivalent; the stipend ranges upward from $10,448. Out-of-state tuition is waived, but a registration fee of $889 is required each semester. Fellowships of $10,000 for the academic year are available on a highly competitive basis. In total, about 175 students are enrolled in the mathematics and applied mathematics graduate programs.

Application should be made to one of the two programs only at any one time. Forms are available from the addresses below. GRE scores should be submitted to the appropriate program. Application review will begin February 15; therefore all students must ensure that their complete applications for admission and financial aid are received by February 1.

Graduate Committee Graduate Committee Department of Mathematics Program in Applied Mathematics University of Arizona University of Arizona Tucson, AZ 85721 Tucson, AZ 85721 Telephone: (602) 621-2068 Telephone: (602) 621-2016 or 4664 The University of Arizona is an Equal Opportunity/Affirmative Action Employer ESSENTIAL MATHEMATICS FROM CAMBRIDGE Statistical Analysis of Circular Data Partial Differential Equations in N.l. Fisher Classical Mathematical Physics Provides a unified and up-to-date account of techniques Isaak Rubinstein and Lev Rubinstein for handling circular data. Considers the important theory of partial differential equa­ 1993 295 pp. 35018-2 Hardcover $59.95 tions in mathematical physics as an interdisciplinary science that treats the hierarchy of mathematical phenomena as Computation with Finitely reflections of their physical counterparts. Presented Groups 1993 600 pp. 41058-4 Hardcover $94.95 Charles C. Sims Describes methods for working with elements, sub­ Phyllotaxis groups, and quotient groups of a finitely presented group. A Systemic Study in Plant Morphogenesis Encyclopedia ofMathematics and its Roger \1. Jean Applications 48 Describes a unified concept of phyllotaxis and presents a 1994 500 pp. 43213-8 Hardcover $99.95 mathematical model of plant growth based on experimental, anatomical, cellular, physiological, and paleontological observations. Available in bookstores or from 1994 574 pp. 40482-7 Hardcover $74.95 CAMBRIDGE Arithmetic of Blowup Algebras UNIVERSITY PRESS Walmer \1. Vasconcelos Provides an introduction to the theory of blowup algebras­ Rees algebras, associated graded rings, Hilbert functions, and 40 West 20th Street, New York, NY 10011-4211 birational morphisms-and its period of rapid development. Call toll-free 800-872-7423 London Mathematical Society Lecture Note Series 195 MasterCard/VISA accepted. Prices subject to change. 1994 400 pp. 45484-0 Paper $34.95

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN 31261, SAUDI ARABIA DEPARTMENT OF MATHEMATICAL SCIENCES NEEDS

Faculty members for teaching graduate and undergraduate courses in all areas of mathematical sciences. Ph.D. in mathematics is required. Candidates must have strong research potential or accomplishments and demon­ strated excellence in teaching. Preferred areas of research are applied mathematics and numerical analysis.

KFUPM offers attractive salaries, benefits that include free furnished air-conditioned accommodation on campus, yearly repatriation tickets, two months paid vacation and two years renewable contract.

Interested applicants are requested to send their Curriculum Vitae with supporting documents no later than one month from the date of this publication, to: Dean of Faculty & Personnel Affairs King Fahd University of Petroleum & Minerals Dept. No. 9414 Dhahran 31261, Saudi Arabia UNIVERSITY OF VIRGINIA DEPARTMENT OF APPLIED MATHEMATICS

CHAIR

The University of Virginia invites applications and nominations for the position of Chair, Deparlment of Applied Mathematics. The Department, which is in the School of Engineering and Applied Science, has a full-time faculty of eleven, and has numerous active research programs grouped in three major areas: continuum mechanics, conlrol theory, and numerical analysis/scientific computing. The Department offers B.S., M.S., and PhD. degrees in Applied Mathematics and is responsible for all liDdergraduate and graduate education in Applied Mathematics within the School of Engineering and Applied Science. Candidates for the position must have a PhD. degree and an outstanding record of research and scholarship in Applied Mathematics. Also, they must have a firm knowledge of the best programs in Applied Mathematics nationally and internationally. A clear commibnent to academic leadership, teaching, and administration within an environment dedicated to engineering and applied science is expected. Women and ethnic minority candidates are encouraged to apply. Priority will be given to applications received by March 1, 1994. Applications should be sent to: Professor Paul Allaire Chair, Search Committee c/o Department of Applied Mathematics Thornton Hall University of Virginia Charlottesville, VA 22903-2422 The University of Virginia is an equal opportliDity/affirmative action employer.

N MODERN LOGIC PUBLISHING W

Modern Logic (ISSN 1047-5982). A journal for publication of historical studies of nineteenth- and twentieth- century mathematical logic, set theory, and foundations of mathematics and of expository surveys of contemporary work in these and closely allied fields. Contributors to volumes 1- 3 included M. BORGA & D. PALLADINO, Jacqueline BRUNNING, John W. DAWSON, Jr., J.C.E. DEKKER, Randall R. DIPERT, Anita Burdman FEFERMAN & Solomon FEFERMAN, Maria J. FRAPoLU, Gottfried GABRIEL, Jean-Yves GIRARD, Warren GOLDFARB, Theodore HAILPERIN, Benjamin S. HAWKINS, Jr., Nathan HOUSER, Philip E. B. JOURDAINt, B.A. KUSHNER, Z.A. KUZICHEVA, Gregory H. MOORE, Roman MURAWSKI, Josep PLA I CARRERA, W.V. QUINE, Wim RUITENBURG, Jonathan SELDIN, Craig SMORYNSKJ; Christian THIEL, Jean VAN HEDENOORTt, George WEAVER and many more. - Individual subscriptions: US$ 36.00; library/institutional subscriptions: US$ 100.00. History of Logic Newsletter (ISSN 1069-2878).- US$ 15 per year; 6 issues per year. Free to individual subscribers to Modern Logic as part of their current subscription. 1994 Modern Logic Calendar. Find the dates in the lives of those who have contributed to modem logic and its history. Each month features a brief biography or sketch of the work of a logician born in that month. - US$ 6.00 MLP BOOKS PROGRAM begins 1994 with the publication of Irving H. Anellis, Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort - Pre-publication comments: "A thorough and impressive job on vm Heijenoort. I am much informed."- W.V. QUINE (Harvard University). "Anellis is certainly not only qualified for writing it but also a natural choice to do so."- Michael RESNIK (University of North Carolina)- Price: paper: US$ 39.95; hardcover: US$59.95.

Inquiries concerning subscriptions should be sent to: Order & Subscription Department, Modem Logic Publishing, Box 1036, Welch Avenue Station, Ames, lA 50014-1036, USA. Orders postmarked within 30 days of the AMS Meeting in Cincinnati and mentioning the AMS receive a 20% convention discount. VISA and MasterCard accepted. The University of Edinburgh is seeking to fill two Chairs in the .-. :fi:*~m~I¥1S1c Department of Mathe·natics and Statistics to enhance further ~I the teaching and research reputations of this Department. r City Polytechnic of Hong Kong COLIN MacLAURIN CHAIR OF .r Expected to be granted university statue by the Hong Kong Government in 1114 MATHEMATICS The City Polytechnic of Hong Kong Is a well-established degree-granting Institute Applications are invited for the Colin MacLaurin Chair of in Hong Kong directly funded by the government through the University and Mathematics. The University seeks to appoint a distinguished Polytechnic Grants Commmee ·(Hong Kong). Its current student population is mathematician with a considerable international reputation in a 14,000 and the number is expected to grow to 16,000 by the mid-1990's. The central area of mathematics. The successful candidate will play Polytechnic is committed to excellence In teaching and research and to maintaining an important role in leading the research of the Department. close relationships with the community and industry. The medium of Instruction Is Please quote REF. AMS 930490. English. Applications are invited for the following posts:

CHAIR OF STATISTICS University Lecturers (Ref.A/136/41] The University seeks to appoint to the Chair of Statistics a distinguished statistician with a substantial international in the Department of Mathematics reputation in research. The successful candidate will play an important role in leading the research and teaching in statistics The appointees will be required to teach Computing Mathematics Including in the Department and fostering collaborative research both Computational Geometry, Scientific Computing and Parallel Computation at within and beyond the University. undergraduate level; and to undertake research activities In related areas. Applicants should have a PhD In Mathematics with teaching experience at university Please quote REF: AMS 930491. level. Preference will be given to candidates with a record of publications in refereed Each position is available from I October, 1994, or an journals In Mathematics. alternative date by mutual agreement. Informal enquiries about either Chair may be made to Professor Monthly Salary and Conditions of Service D F Parker (Telephone: 031-650 5062 or Fax: 031-650 6521). HK$31,435- $52,515 per month (Exchange rate : US$1 = HK$7.8 approximately) Appointment will be on superannuable terms with provision for retirement benefits. Further information may be obtained from: Generous fringe benefits Include medical and dental schemes and long leave. THE SECRETARY m THE UNIVERSITY, Passages and housing benefits may be provided, where appropriate. THE UNIVERSITY OF EDINBURGH, I ROXBURGH STREET, EDINBURGH EHS 9TB, Further Information and Application with whom applications (I 4 copies, except for candidates from Further information concerning the posts can be obtained from the Personnel overseas who need submit only one copy) including a Office, City Polytechnic of Hong Kong, Tat Chee Avenue, Kowloon (Fax: 852- curriculum vitae and giving the names and addresses of three 7881154 or 852-7889334; E-mail: [email protected] HK). Please send referees should be lodged. your application with a current curriculum vitae and the names and addresses of three academic or professional referees to the same Office by 31 January 1994. Closing date: 28 Fel:iruary, 1994. Please quote the post reference In your application.

NATIONAL SCIENCE FOUNDATION* ARK CITY I INSTITUTE FOR ADVANCED STUDY MATHEMATICS INSTITUTE July 10-July 30, 1994 Columbia Unlver~ly • DU9)'of Four-Manlfolele. Lecturere will include: John Morean (Columbia University), Bob Friedman (Columbia University), Ron Stern tUG 1991 Mathematics Subject Classification : 34 Irvine), Tom Mrowka (Caltech), and CliffTaubee {Harvard University). ISBN 0-8218-4569-1, 375 pages (hardcover), Dec. 1992 Indiv. member $121, List price $201, Inst. member $161 APPLICATIONS: Fully funded elote are limited. Apply early! Application forme To order, please specify MMON0/112NA are available by phone, mail, or e-mail. Recommendation lettere are r~uireel forundereraduatee and eraduate etudente. Deadline to applyie 3/1/94. No new All prices subject to change. Free shipment by surface; for air delivery, please add teacher applications will accepted for the 1994 program. $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904, or call toO free II00-321-4AMS in the U.S. and REQUEST APPLICATIONS AND/OR INFORMATION FROM: Canada to cbarge with VISA or MasterCard. Residents of Canada, please add 7%GST. PC/lAS Mathematics lnetitute,18C DeT robriand St., Salt Lake City, UT, 84113 {801) 585-3488 fax: {801) 585-5793 e-mail: [email protected] Funding has been roquoslod CONTEMPORARY MATHEMATICS

Index Theory and Operator Algebras Jeffrey Fox and Peter Haskell, Editors Volume 748

Index Theory and This collection of papers by leading researchers provides a broad picture of current Operator Algebras research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Jeffrey Fox Peter Haskell Conference on K -Homology and Index Theory, held in August 1991 at the University of Editors Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

1991 Mathematics Subject Classification: 58, 46, 19 ISBN 0-8218-5152-7, 190 pages (softcover), July 1993 Individual member $25, List price $41, Institutional member $33 To order, please specify CONM/148NA

Doeblin and Modern Probability Harry Cohn, Editor Volume 749

Doeblin and This book is based on papers presented at the conference, "Fifty Years after Modern Probability Doeblin: Developments in the Theory of Markov Chains, Markov Processes, and Harry Cohn Editor Sums of Random Variables," held at Blaubeuren, Germany, in November 1991. With contributions by top probabilists from sixteen countries, this book will interest both researchers in probability and science historians.

1991 Mathematics Subject Classification: 60 ISBN 0-8218-5149-7, 347 pages (softcover), July 1993 Individual member $29, List price $49, Institutional member $39 To order, please specify CONM/149NA

Mapping Class Groups and Moduli Spaces of Riemann Surfaces Carl-Friedrich Bodigheimer and Richard M. Hain, Editors Mapping Class Groups Volume 750 and Moduli Spaces of Riemann Surfaces

Cori-Frledr1ch B6dlghelmer Richard M. Haln This book contains proceedings from two workshops held in the summer Editor& of 1991, one at the University of Gottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.

1991 Mathematics Subject Classification: 14, 30; 20, 55 ISBN 0-8218-5167-5, 372 pages (softcover), August 1993 Individual member $31, List price $51, Institutional member $41 To order, please specify CONM/150NA

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Fields Institute Communications series features proceedings and lecture notes growing out of the various activities at the Fields Institute for Research in Mathematical Sciences located in Water­ loo, Ontario. The publications evolve from each year's main program. For 1993, the program focused on dynamical systems. For 1994, the main program is L-functions. Interdisciplinary titles are featured in areas of mechanical, civil, and aerospace engineer­ ing, control theory, and physics.

Dynamics and Control of Mechanical Systems The Falling Cat and Related Problems Michael J. Enos, Editor Volume 1 This book contains a collection of papers presented at the Fields Institute workshop, 'The Falling Cat and Related Problems," held in March 1992. The theme of the workshop was the application of methods from geometric mechanics and mathematical control theory to problems in the dynamics and control of freely rotating systems of coupled rigid bodies and related nonholonomic mechanical systems. This book will prove useful in providing insight into this new and exciting area of research.

199 I Mathematics Subject Classification: 70. 58, 93. 49 ISBN 0-8218-9200-2, 280 pages (hardcover), July 1993 Individual member $52, List price $87, Institutional member $70 To order, please specify FIC/!NA

Control of Flexible Structures K. A. Morris, Editor Volume 2 This volume contains papers presented at the workshop "Problems in Sensing, Identification, and Control of Flexible Structures". Topics range from theoretical research on the well-posedness of systems to experi­ mental implementations of various controllers. A number of controller design techniques are discussed and compared, and there are several papers on modelling the complex dynamics of flexible structures. This book is a useful resource to control theorists, engineers, and mathematicians interested in this important field of research.

1991 Mathematics Subject Classification: 93, 70 ISBN 0-8218-9201-0, 243 pages (hardcover), July 1993 Individual member $49, List price $82, Institutional member $66 To order. please specify FIC/2NA

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

Theory of Commutative Fields Masayoshi Nagata Volume 125

This book is a translation of the 1985 updated edition of Nagata's 1966 book; both editions originally appeared in Japanese. Nagata aimed to provide an introduction to com­ mutative fields that would be useful to those studying the topic for the first time as well as to those wishing a reference book. The book presents, with as few prerequisites as possible, all of the important and fundamental results on commutative fields. Each chapter ends with exercises, making the book suitable as a textbook for graduate courses or for independent study.

1991 Mathematics Subject Classification: 12 ISBN 0-8218-4572-1, 249 pages (hardcover), July 1993 Individual member $75, List price $125, Institutional member $100 To order, please specify MMON0/125NA

Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications M. L. Agranovskil Volume 126

This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains.

1991 Mathematics Subject Classification: 43; 22 ISBN 0-8218-4604-3, 131 pages (hardcover), July 1993 Individual member $43, List price $71, Institutional member $57 To order, please specify MMON0/126NA

$'"EM.

Volumes 45 & 46

New Scientific Applications of Geometry and Topology De Witt L. Sumners, Editor Based on an AMS Short Course held in January 1992, this book contains articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science. All are exposi­ tory and require no specific knowledge of the science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course. 1991 Mathematics Subject Classification: 53, 57; 82, 92 ISBN 0-8218-5502-6, 250 pages (hardcover), November 1992 List price $49, Individual member $29, Institutional member $39 To order, please specify PSAPM/ 45NA

The Unreasonable Effectiveness of Number Theory Stefan A. Burr, Editor This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This short course provided some views into the great breadth of applications of number theory outside cryptology and highlighted the power and applicability of number theoretic ideas. This book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provide excellent introductions to various applications. 1991 Mathematics Subject Classification: 11 ISBN 0-8218-5501-8, 125 pages (hardcover), November 1992 List price $37, Individual member $22, Institutional member $30 To order, please specify PSAPM/ 46NA

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

Translations of Mathematical Monographs

An Introduction to Sato's Hyperfunctions Mitsuo Morimoto Volume 129

This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research. 1991 Mathematics Subject Classification: 46; 32, 58 ISBN 0-8218-4571-3, 273 pages (hardcover), October 1993 Individual member $52, List price $87, Institutional member $70 To order, please specify MMON0/129NA

Cobordisms and Spectral Sequences V. V. Vershinin Volume 130

Cobordism is one of the most basic notions of algebraic topology. This book is devoted to spectral sequences related to cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and applications of these and other sequences to the investigation of cobordism rings. 1991 Mathematics Subject Classification: 55 ISBN 0-8218-4582-9, 97 pages (hardcover), October 1993 Individual member $37, List price $62, Institutional member $50 To order, please specify MMON0/130NA

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

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DISCRIMINANTS, Special Pr:· INTEGRABLE SYSTEMS ASYMPTOTIC ANALYSIS: =LTANTS $49.50*tce: The Verdier Memorial Conference: A DISTRIBUTIONAL Actes du Colloque International de Luminy APPROACH MULTIDIMENSIONAL 0. Babelon, Universite Paris VI; P. Cartier, Ecole Normale Superieure de Paris & Y. Kosmann­ R. Estrada, University of Costa Rica & DETERMINANTS Schwarzbach, Ecole Polytechnique (Eds.) R.P. Kanwal, The Pennsylvania State University I.M. Gelfand, Rutgers University, NJ; This book contains fifteen articles by the most Asymptotic analysis is an old subject that has M.M. Kapranov, Northwestern University, IL & found applications for many years in various fields A.V. Zelevinsky, Northeastern University, MA eminent specialists in the theory of completely integrable systems, bringing together the diverse of pure and applied mathematics, both classical approaches to classical and quantum integrable and modem. The authors present here a simplified The study of discriminants and resultants was approach to asymptotic techniques for solving the focus of many remarkable mathematicians in systems and covering the principal current research developments. In the first part of the problems of mathematics, physics and engineer­ the 19th and early 20th centuries: Cayley, ing. They also provide an interplay between the Sylvester, Brill, Macaulay, among others. book, the emphasis is on the algebro-geometric methods and the tau-functions. Essential use of underlying theories of asymptotic analysis and Amazingly, in an 1848 note by Cayley on the resul­ generalized functions, one enriching the other in tant, the foundations of modem homological alge­ Riemann surfaces and their theta functions is made in order to construct classes of solutions of the process. The book is self-contained in both bra were developed, only to be forgotten for almost these subjects. a century. More recent interest in discriminants integrable systems. The five articles in the second part of the book are mainly based on Hamiltonian The purpose of the book is to provide for stu­ and resultants is motivated by their applications to dents a firm grasp of the mathematical theory the study of singularities, real algebraic geometry, methods, illustrating their interplay with the methods of algebraic geometry, the study of while demonstrating applications. The authors first and computational algebra. derive the basic results and theorems of the theory This book presents a systematic study of dis­ Hamiltonian actions, and the role of the biharnil­ tonian formalism in the theory of soliton equa­ of asymptotics and then follow up with numerous criminants and resultants in the general context of applications in various scientific fields such as dif­ projective algebraic geometry. Cayley's classical tions. The third part deals with the theory of two­ dimensional lattice models, in particular with the ferential equations and quantum mechanics. method is investigated by using such tools as The book is aimed primarily at senior under­ coherent sheaves, perverse sheaves, microlocal symmetries of the quantum Yang-Baxter equation. In the fourth and final part, the integrability of the graduate or graduate students in departments of geometry, and D-modules. The authors also pre­ mathematical and physical sciences. As a research sent their original results relating discriminants hierarchies of Hamiltonian systems and topological field theory are shown to be strongly interrelated. monograph, it will will also be useful to many and resultants with general hypergeometric func­ research workers in the above fields. Indeed, the tions and discrete geometry. In fact, this volume In the overview that introduces the articles Bennequin surveys the evolution of the subject most important feature of the book is to stimulate may be considered as a first step in constructing a application of these methods of asymptotic analy­ general theory of hyper geometric functions. from Abel to the most recent developments, and analyzes the important contributions of J.-1. sis in both study and research. This book has many novel features. One of 1994 Approx. 500 pp., 76 illus. Hardcover Verdier to whose memory the book is dedicated. them is the ingenious use of generalized functions ~ISBN 0-8176-3660-9 1994 372 pp., 35 illus. Hardcover in asymptotic analysis of certain seril\S in number Mathematics: Theory & Applications $89.50 ISBN 0-8176-3653-6 theory. In this study, the authors introduce the *Special Price Expires Feb. 15, 1994 Progress in Mathematics, Volume 115 notion of distributional smallness and relate it to corresponding classical results. The chapter on this subject will open up many new vistas in applica. THE COLLECTED PAPERS SEMINAIRE DE THEORIE tions of generalized functions in number theory OFRAOULBOTT DES NOMBRES, PARIS, and related topics. Volume 1: Topology and Lie Groups 1991-1992 1994 268 pp. Hardcover $49.50 R.D. MacPherson, MIT, Cambridge, MA (Ed.) ISBN 0-8176-3716-8 S. David, Universite de Paris- Sud, France (Ed.) The four volumes of the collected works of Raoul Bott attest to the -extraordinary breadth of This is the thirteenth annual volume of papers contributions to mathematics made by this world­ based on the lectures given at Seminaire de Theorie renowned mathematician from Harvard. His work des Nombres de Paris in 1991-1992, including some is especially significant in that it has brought additional papers of widespread interest. The topology to bear on so many different fields - lie results presented here by an international group of groups, differential geometry, foliations, analysis mathematicians reUect recent works in many areas Three Easy Ways to Order! of partial differential equations, and mathematical of number theory and should form a basis for fur­ physics. Each time he courageously embarked ther discussion of these topics. Contributors eCALL: Toll-Free 1-800-777-4643. upon a new field, he left it significantly changed include: 1. Denis, M. Flach. M. Kolster, In .NI please call 201-348-4033. Your reference number is Y759. and deepened. Forthcoming volumes include: B.E. Kunyavskii, M. Langevin. 0. Lecacheux. F. Leprevost, M.C.liu, K.M. Tsang, s. Louboutin. • WRITE: Birkhlluser, Dept. Y759, Volume 2: Differential Operators (the 1960's); 44 Hartz Way, Secaucus, NJ 07096-2491. Volume 3: Foliations (the 1970's); Volume 4: D.W. Masser, B.H. Matzat, Y. Nesterenko, E. Saias, eVISIT: Your local technical bookstore or urge Mathematics related to Physics (the 1980's). P. Salberger, A.J. Scholl & D. Solomon. your librarian to order for your department. In addition to his collected works, the author Payment can be made by check, money order or has written some "Autobiographical Fragments", 1994 320 pp. Hardcover credit card. Please enclose $2.50 for shipping & reflecting his personal charm, his forceful spirit, $89.50 ISBN 0-8176-3741-9 handling for the first book ($1.00 for each addi­ and his buoyant enthusiasm for life and for math­ Progress in Mathematics, Volume 116 tional ~ook) and NY, NJ, MA, VT, PA, VA, TX & CA restdents, please add sales tax. Canadian resi­ ematics. dents please add 7% GST. Prices are valid in North America only, are payable in U.S. CWTency 1994 Approx. 600 pp., 71 illus. Hardcover or its equivalent, and are subject to change with­ $95.00 ISBN 0-8176-,613-'1 out notice. For price and ordering infonnation out­ side North America, please contact Birkhlluser Contemporary Mathematicians Verlag AG, Klosterberg 23, CH-4010, Basel Birkhauser Switzerland. Fax 061 271 7666. ' Boston • Basel. Berlin SPRINGER FOR MATHEMATICS

Y.A. Drozd and V.V. Klrichenko, both of Kiev Taras Shevchenko Announcing a new series ... University, Kiev, Ukraina LECTURE NOTES IN LOGIC FINITE-DIMENSIONAL ALGEBRAS The Lecture Notes in Logic series, provides a unique This book presents both the basic classical theory and forum for the discussion of topics in which logic plays recent results closely related to current research, i.e. some a critical role. The series will draw topics from areas category theory including Morita's theorem, schemes of within which logic has a traditional place, i.e. within quivers and tensor algebras, duality, quasi-Frobenius, mathematics and philosophy, together with topics hereditary, and serial algebras. The only prior knowledge from within areas in which logic has an emerging assumed of the reader is linear algebra and, in places, a importance, i.e. within computer science and linguis­ little group theory. Each chapter includes a series of tics. Fmthermore, the series will provide for exercises, illustrating the content and introducing more the timely and rapid publication needed in these areas. refined results. For the complicated exercises, hints for the solution are given, thus the book can be used as a classroom text or for self-study or as an up-to-date refer­ J.R. Shoenfleld ence to the field. RECURSION THEORY 1993/ APP . 256 PP.jHARDCOVERj $49.00/ ISBN 0.387-53380-X An introduction to recursive functions intended for grad­ UNIVERSITEXT uate students with some mathematical maturity, and some know ledge of group theory and topology. This book introduces the main topics of recursion theory, such as Y.N. Moschovakis, University of California, Los Angeles, CA hierarchy theory, RE sets, and undecidable theories. NOTES ON SET THEORY 1993/84 PP.jSOFTCOVER/$29.50/ISBN 0.387-57093-4 This book gives a rigorous introduction to the axiomatic LECTURE NOTES IN LOGIC, VOLUME 1 theory of sets and an explanation of its role as a foundation of mathematics and computer science. Aimed at advanced undergraduates in mathematics, computer science, and J. Olkkonen and J. Viininen (Eds.) philosophy, it may be used as a textbook or for individual LOGIC COLLOQUIUM '90 study. It does not assume knowledge of formal logic, but ASL Summer Meeting in Helsinki introduces ideas and techniques of logic as they are needed. Many exercises are interspersed throughout the The Proceedings of an Association for Symbolic Logic text, with somewhat harder problems at the end of each Meeting held in Helsinki, July 1990. It contains 13 chapter- some of them introducing new material. research papers written mainly by the invited speakers 1994/ APP . 296 PP., 50 ILLUS./HARDCOVER/ $39.00/ ISBN 0.387-94180.0 of the congress. They represent all fields of mathemat­ UNDERGRADUATE TEXTS IN MATHEMATICS icallogic from the philosophy of mathematics through model theory, proof theory, recursion theory and set theory, to connections of logic to computer science. Nicolas Bourbaki, Paris, France 1993/APP. 314 PP./SOFTCOVER/$54.00/ISBN 0.387-57094-:2 ELEMENTS OF THE HISTORY LECTURE NOTES IN LOGIC, VOLUME 2 OF MATHEMATICS In each volume of Bourbaki's The Elements of G.B. Pedrick, California State University at Hayward, CA Mathematics, there is a section devoted to the history of the subject. This book collects these historical segments A FIRST COURSE IN ANALYSIS with an emphasis on the emergence, development and This is a new text covering advanced calculus. It discuss­ interaction of the leading ideas of mathematical theories es such topics as number systems, the extreme value presented in the "Elements." In particular, the book problem, continuous functions, differentiation, integration provides a highly readable account of the evolution of and infinite series. It provides many examples which are algebra, geometry, infinitesimal calculus, of the concepts important to students in a first analysis course, and the of number and structure, from the Babylonian era focus of attention is on careful reasoning from hypothesis through to the 20th Century. to conclusion. The book is intended both for a terminal 1993/ APP. 304 PP./HARDCOVERj $49.95/ISBN 0-387-19376-6 course and as preparation for more advanced studies in 0 mathematics, science, engineering and computation. 0 ~~~~ 1994/APP. 280 PP., 621LLUS./HARDCOVERj $39.50/ ISBN 0.387-94108-8 UNDERGRADUATE TEXTS IN MATHEMATICS 3 Easy Ways to Order: -:o ~~~~ CALL Toi~Free 1-800-SPRINGER (NJ call 201-348-4033) or FAX 201-348-4505. Please mention 5202 when ordering by phone...... WRITE to Springer-Verlag New York. Inc., Dept. #S202. PO Box 2485, Secaucus, NJ, 07096-2491. VISIT your local technical bookstore. Payment can be made by check, purchase order, or credit card . Please enclose $2.50 for shipping ($1.00 each additional book) & add appropriate sales tax if you reside in CA, IL, MA, NJ, NY, PA, !...... II TX, VA, or VT. Canadian residents please add 7% GST...... Remember ... your 30-day return privilege is always guaranteed! :!>~~

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