OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

Scientific Issues in Manufacturing page 404

Three Reports on Graduate Education: National Research Council page 390 Conference Board of the Mathematical Sciences page 398 AMS-MAA-SIAM Committee on Preparation for College Teaching page 412

Cambri ge Meeting (June 29-July 1) page 460

MAY/JUNE 1992, VOLUME 39, NUMBER 5 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences

This calendar lists all meetings and conferences approved prior to the date this insofar as is possible. Abstracts should be submitted on special forms which are issue went to press. The summer and annual meetings are joint meetings of the available in many departments of mathematics and from the headquarters office of Mathematical Association of America and the American Mathematical Society. the Society. Abstracts of papers to be presented at the meeting must be received The meeting dates which fall rather far in the future are subject to change; this is at the headquarters of the Society in Providence, Rhode Island, on or before the particularly true of meetings to which no numbers have been assigned. Programs deadline given below for the meeting. The abstract deadlines listed below should of the meetings will appear in the issues indicated below. First and supplementary be carefully reviewed since an abstract deadline may expire before publication of announcements of the meetings will have appeared in earlier issues. Abstracts a first announcement. Note that the deadline for abstracts for consideration for of papers presented at a meeting of the Society are published in the journal Ab· presentation at special sessions is usually three weeks earlier than that specified stracts of papers presented to the American Mathematical Society in the issue below. For additional information, consult the meeting announcements and the corresponding to that of the Notices which contains the program of the meeting, list of special sessions. Meetings

Abstract Program Meeting# Date Place Deadline Issue 875 June 29-July 1, 1992 Cambridge, England Expired May..June (Joint Meeting with the London Mathematical Society) 876 • October 30-November 1, 1992 Dayton, Ohio August 3 October 877 • November 7-November 8, 1992 Los Angeles,Califomia August 3 October 878 • January 13-16, 1993 San Antonio, Texas October 8 December (99th Annual Meeting) 879 • March 26-27, 1993 Knoxville, Tennessee January 5 March 880 * April 9-10, 1993 Salt Lake City, Utah January 29 April 881 • April17-18, 1993 Washington, D.C. January 29 April 882 • May 21-22, 1993 DeKalb, Illinois February 26 May-June 883 * August 15-19, 1993 Vancouver, British Columbia May 18 July-August (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) October 22-23, 1993 College Station, Texas January 12-15, 1994 Cincinnati, Ohio (1 OOth Annual Meeting) March 18-19, 1994 Lexington, Kentucky March 25-26, 1994 Manhattan, Kansas October 28-29, 1994 Stillwater, Oklahoma January 25-28, 1995 Denver, Colorado (101st Annual Meeting) March 24-25, 1995 Chicago, Illinois January 10-13, 1996 Orlando, Florida (1 02nd Annual Meeting) *Please refer to page 476 for listing of Special Sessions.

Conferences

July 6-24, 1992: AMS Summer Research Institute on Quadratic January 11-12, 1993: AMS Short Course on Wavelets and forms and division algebras: Connections with algebraic K-theory Applications, San Antonio, Texas. and algebraic geometry, University of California, Santa Barbara. July 26-August 1, 1992: AMS-SIAM Summer Seminar in Applied Mathematics, Exploiting symmetry in applied and numerical analysis, Colorado State University, Fort Collins, Colorado. Deadlines

September Issue October Issue November Issue December Issue Classified Ads* July 30, 1992 August 27, 1992 October 1, 1992 November 13, 1992 News Items July 16, 1992 August 13, 1992 September 21 , 1992 October 29, 1992 Meeting Announcements** July 16, 1992 August 17, 1992 September 21 , 1992 October 29, 1992 * Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. •• For material to appear in the Mathematical Sciences Meetings and Conferences section. ••mmm- OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

ARTICLES DEPARTMENTS 390 Educating Mathematical Scientists: The Doctoral and Postdoctoral 387 Letters to the Editor Experience in the United States Reprinted here are the executive summary and introduction of this important 424 Forum new report from the Board on Mathematical Sciences. In addition, five 447 News and Announcements members of the mathematical sciences community present their reactions to Funding Information for the the report. 457 Mathematical Sciences 398 Graduate Education in Transition This report by the Conference Board on the Mathematical Sciences 458 For Your Information discusses some of the major issues in graduate education in the 459 1992 AMS Elections for improvements. mathematical sciences and makes recommendations 460 Meetings and Conferences of 404 Scientific Issues in Manufacturing the AMS Manufacturing poses many intriguing scientific problems, some of which Cambridge, England were discussed at a recent workshop on intelligent manufacturing. Allyn June 29-July 1, 460 Jackson reports on the workshop. San Antonio, TX 408 The Agency that Came in from the Cold Richard Shaker January 6-9, 482 Invited Speakers, 476 These excerpts from a speech presented at the Joint Mathematics Meetings Call for Topics, 480 in Baltimore in January describe recent efforts by the National Security Symposium on Some Agency to "come in from the cold" and contribut!'l to mathematics research and education. Mathematical Questions in Biology, 485 412 The Graduate Student Cohort, Doctoral Department Expectations, and Teaching Preparation Bettye Anne Case and M. Annette Blackwelder 486 Mathematical Sciences Meetings This article reports the results of the first phase of a survey of the graduate and Conferences student population and aspects of graduate training and contains interesting 498 New Publications Offered by the new data that has not been collected elsewhere. AMS 419 Support for Mathematics Departments and Federal Funding 506 AMS Warehouse Sale Allyn Jackson reports on lively discussions at a recent meeting of the AMS 512 AMS Reports and Committee on Science Policy. Communications 422 Annual AMS-MAA Survey: Doctoral Degrees Conferred 1990-1991 Recent Appointments, 512 (Supplementary List) Reports of Council Meetings, 512, A list of names and thesis titles for the 1990-1991 Ph.D. class is featured. 516 The second report of the AMS-MAA Survey will appear in the next issue of Reports of Business Meetings, the Notices. 512,516 FEATURE COLUMNS 518 Miscellaneous Personal Items, 518 427 Computers and Mathematics Keith Devlin Deaths, 518 An article by M. C. Nucci precedes two reviews of the new version 2.0 of Visiting Mathematicians the Mathematica system. (Supplementary List), 519 438 Inside the AMS 522 New Members of the AMS This month's column includes: reports from the AMS Secretary, Robert M. Fossum, and Treasurer, Franklin P. Peterson; a report on the JPBM 525 Classified Advertising Committee on Professional Recognition and Rewards; a note on a 545 Forms temporary policy change for Transactions of the AMS; and a brief look at the Trjitzinsky awards made to students. 445 Washington Outlook Richard Herman, chair of the Joint Policy Board for Mathematics, discusses the FY 1993 budget for the National Science Foundation.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 385 From the Executive Director ...

MATHEMATICS INFRASTRUCTURE: POSTDOCS This column (November 1989 Notices) addressed postdoctoral programs in the AMERICAN MATHEMATICAL SOCIETY mathematical sciences with particular attention on the need to have a strong compo­ nent of mentorship in any such program and asked the question should postdoctoral positions in mathematics be less-the-exception and more-the-rule. Discussions taking place at that time in the AMS Committee on Science Policy were a major impetus for the National Research Council (NRC) study on doctoral and postdoctoral experiences in the mathematical sciences reported on in this issue of the Notices. The NRC report EDITORIAL COMMITTEE and a related report on a workshop "Graduate Education in Transition" published by Michael G. Crandall the Conference Board on Mathematical Sciences (1992) has heightened discussion of Amassa Fauntleroy position in mathematics Robert M. Fossum (Chairman) the mathematics postdoctoral experience. Should a postdoc Carolyn S. Gordon (Forum Editor) be a logical next-step after the doctorate? Is it an important step in continuing lifelong D. J. Lewis professional development? L. Ridgway Scott (Letters Editor) There is statistical information available that provides some perspective. For the Robert E. L. Turner year 1988 (last year of complete figures), there were 752 new Ph.D.s in mathematics MANAGING EDITOR from U.S. doctoral granting institutions, 280 individuals being counted as postdocs, John S. Bradley and 188 postdocs receiving some federal support. During the same period, physics had 1093 and chemistry had 1990 new Ph.D.s, 1578 physicists and 3429 chemists ASSOCIATE EDITORS were counted as postdocs, and 1280 physics postdocs and 2587 chemistry postdocs Ronald L. Graham, Special Articles were receiving some federal support. It is often pointed out that the differences are Jeffrey C. Lagarias, Special Articles easily explained because both physics and chemistry can be viewed as laboratory sciences. It is also true that one must be careful in using such comparisons-if for INFORMATION SUBSCRIPTION no other reason than parity is not going to be a successful argument for increasing Subscription prices for Volume 39 (1992) are the availability of postdoctoral experiences in mathematics. The issue, however, is $131 list; $105 institutional member; $79 individ­ ual member. (The subscription price for members on the importance of a postdoctoral experience in the professional development of a is included in the annual dues.) A late charge of mathematician and whether it is an element of the mathematics infrastructure that has 10% of the subscription price will be imposed upon been greatly neglected and under-supported. orders received from nonmembers after January 1 The prevalent model for a postdoctoral experience in the mathematical sciences of the subscription year. Add for postage: Surface is one in which an individual has exhibited outstanding research potential while a delivery outside the United States and lndia-$15; to lndia-$28; expedited delivery to destinations in graduate student and has successfully competed for a limited number of prestigious North America-$32; elsewhere-$67. Subscrip­ postdoctoral positions. What happens to the large number of individuals who have tions and orders for AMS publications should be shown great promise, who have made their first important independent discovery, addressed to the American Mathematical Society, which becomes a dissertation, and spend the latter part of their graduate program P.O. Box 1571, Annex Station, Providence, Rl polishing this dissertation and applying for a position? Many of these individuals end 02901-1571. All orders must be prepaid. up in environments that not only do not provide continuing professional development but have duties and expectations for which the recent Ph.D. was never prepared. Many ADVERTISING survive; but are we risking the loss of valuable talent? Are we risking stagnation of publishes situations wanted and classified Notices careers and the loss of the investment made toward attainment of the doctoral degree? advertising, and display advertising for publishers and academic or scientific organizations. These issues are currently being debated within the Society concerning a pro­ Copyright @ 1992 by the American Mathematical posal for a broad, national, postdoctoral program, one that introduces new elements Society. All rights reserved. Printed in the United into the community's view of a postdoctoral experience. Such a program would have States of America. the goal of increasing the number of academic postdoctoral research opportunities The paper used in this journal is acid-free and falls available and increasing the number of nonacademic postdoctoral positions available within the guidelines established to ensure perma­ in mathematics institutes, government facilities, and in business and industry; it would nence and durability. @Most of this publication introduce postdoctoral experiences for mathematics Ph.D.s interested in mathematics was typeset using the TE;X typesetting system. education, including experiences in 4-year colleges and nondoctoral programs; and [Notices of the American Mathematical Society is it would introduce interdisciplinary postdoctoral positions for new Ph.D.s in math­ published monthly except bimonthly in May, June, ematics. Important components that are seen as necessary to such a program are July, and August by the American Mathematical nurturing, group building, deepening understanding of mathematics and expanding Society at 201 Charles Street, Providence, Rl 02904- knowledge beyond the doctoral dissertation, providing a broad spectrum of career 2213. Second class postage paid at Providence, path opportunities, and instilling the desire for continued scholarship and learning. Rl and additional mailing offices. POSTMASTER: Such a program will need the commitment and support of the federal agencies, the Send address change notices to Notices of the American Mathematical Society, Customer Service academic community, and business and industry. Department, American Mathematical Society, P. The responsibilities and expectations on the mathematics community and the aca­ 0. Box 6248, Providence, Rl 02940-6248.] Publi­ demic departments of mathematical sciences are quite demanding. The infrastructure cation here of the Society's street address, and the of the profession needs attention. An important component of this infrastructure is the other Information in brackets above, is a technical postdoctoral experience for mathematicians and preparation for lifelong scholarship requirement of the U. S. Postal Service. All cor­ respondence should be mailed to the Post Office and professional development. Box, NOT the street address. Tel: 401-455-4000. William Jaco

386 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY After all, if you watch television prompted Mark Twain to deduce that Letters you can't help noticing that politicians "teaching is the fine art of imparting are impressed by dramatic and eloquent knowledge without possessing it." to the Editor statements. John A. Baker Maurice Machover University of Waterloo St. John's University (Received February 18, 1992) (Received March 18, 1992) Open Letter to Shafarevich The March 1992 issue of the Notices Calculus Reform of the American Mathematical Society Unrecognized Talent In Murray Protter' s article "Calculus contained the Open Letter to Shafare­ A recent issue of The New Yorker (2 Reform II," the recommendation that vich which was signed by over three Mar 92) contains an interesting and each faculty member take on an addi­ hundred mathematicians. The Open Let­ lengthy (approximately 20 pages) pop­ tional section of calculus is no doubt ter was published as an advertisement. ular article which I highly recommend sufficient to ensure that his proposals A statement that this "advertisement" as reading for AMS members. It deals will not be adopted wholesale. How­ was paid for by the Society and not mostly with the plight of two well­ ever, since the essence of the method of by the signatories was, unfortunately, known Ukrainian-born American math­ instruction he calls for-small sections omitted. ematicians who are brothers. In spite taught by faculty and graduate students In the interest of openness and ac­ of their obvious talent (I have reviewed alike-is the structure currently in place curacy in journalism, a note to this some of their papers for MR), they can't at Yale, we feel compelled to address effect should have appeared. I would find serious academic employment. The some of the assumptions that underlie like to think that the Council's decision content of the article is a microcosm his argument. to ensure that this letter appear in the of a very old problem of mathemat­ Explicitly driving the article is an Notices reflects the Society's commit­ ical culture embedded in research on emphasis on small class sizes. While ment to combating anti-semitism. mathematical objects which are not en­ we believe that lecture courses of 500 Irwin Kra tirely elusive or eccentric. I believe the or more students represent a serious SUNY at Stony Brook content of the article is mostly cor­ abdication of duty on the part of educa­ (Received March 23, 1992) rect and only occasionally exaggerated tors, who under such conditions could (surely Abel, e.g., who, in addition, Editor's Note: The omission of probably be replaced by a series of had problems of getting adequate food, any indication that the advertisement videotapes, we see nothing canonical was far worse off). This area of math­ referred to in the above letter was not about the number 30. In short, size is ematical culture needs more attention, paid for by the individuals involved important, but only to the extent that but not the kind of focus that prevents was an editorial oversight and was not the professor knows his or her students people from engaging in mathematical done with the intention of misleading and that they feel comfortable ask­ research, itself. In any case, the article anyone. The editors regret any mis­ ing questions in class. Our experience should be carefully reviewed in MR for understanding that was caused by this shows that this is possible in courses its historical and cultural value. oversight. of 50-60 students. Albert A. Mullin Huntsville, AL Letters to the Editor Pilot Assessment (Received March 3, 1992) Letters submitted for publication in the Notices of the Mathematical Sciences are reviewed by the Editorial Committee. The "Pilot Assessment of the Math­ The Notices does not ordinarily publish com­ ematical Sciences," prepared for the Who is Teaching plaints about reviews of books or articles, al­ though rebuttals and correspondence concerning House Committee on Science, Space, Precollege Mathematics? reviews in Bulletin of the American Mathemati­ and Technology (Notices, February A recent report suggests that high cal Society will be considered for publication. 1992, Vol. 39, No. 2), is certainly school students in Canada and the Letters should be typed and in legible form deficient in Mathematics or they will be returned to the sender, possibly impressive, to-the-point, and true. It is U.S.A. are resulting in a delay of publication. All published an admirable response to the question­ as compared to their peers in, for ex­ letters must include the name of the author. Let­ naire. ample, Czechoslovakia and Hungary. ters which have been, or may be, published else­ However, truth is not enough! I This should not be surprising. Outside where will be considered, but the Managing Ed­ itor of the Notices should be informed of this wish they had included some of the re­ of North America, people who teach fact when the letter is submitted. ligious fervor of the mathematician. We Mathematics in high schools are re­ The committee reserves the right to edit let­ could have used Fourier's statement on quired to have learned a substantial ters. the "Austere Beauty of Mathematics" amount of mathematics in Universi­ Letters should be mailed to the Editor of the Notices, American Mathematical Society, P. 0. or the Pythagorean Doctrine that math­ ties. In North America, teacher training Box 6248, Providence, RI 02940, or sent by ematics satisfies the soul, or even said is controlled by pedagogical institutes email to [email protected], and will be ac­ it makes mathematicians happy. having philosophies of the sort that knowledged on receipt.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 387 ...... ______...... _...... _... __ .___ ...... _.. ___ ... ___ ...... -.... -...... _.. , ... _...... Letters to the Editor

At Yale we have a system very could be put to use in a number of again a narrow focus (now sharpened much like the one Protter advocates. creative ways; their absence robs cal­ by competition among sections) on the Courses are taught in numerous small culus students of a valuable resource exams. A least-common-denominator sections, whose sizes are targeted at and graduate students of a gentle in­ approach is not therefore strictly a 30-35, but which have recently ranged troduction to teaching in an American result of large class size. from 3 to 67. Our experience is that university. In conclusion, we fail to see how within this range, the putative benefits We are unsure with what degree of Protter' s suggestions will improve cal­ of small class size are of minor sig­ sarcasm to interpret Protter' s vignettes culus instruction at research universi­ nificance in comparison to other issues of the popular and unpopular calcu­ ties. In fact, many of the problems we affecting the quality of instruction. We lus teachers. If he means to suggest experience at Yale occur precisely be­ have several instructors whose sections that speaking clearly, working illustra­ cause our system so closely resembles routinely swell beyond capacity on the tive examples, and developing a rapport the one he proposes. strength of good word-of-mouth. These with the students are irrelevant to teach­ instructors and their students generally ing well, then we strongly object. If the William Cherry do not find the size of their classes to students seem to prefer not to learn John Fischer be detrimental, and exam scores seem how to write proofs, it is because the Yale University to corroborate this feeling. curriculum is not sufficiently rigorous. (Received March 3, 1992) On the other hand, our less success­ We guarantee that if they are expected ful sections suffer from exactly those to understand proofs when examined, Thank you for Murray Protter' s can­ conditions more likely to prevail un­ the instructor who proves theorems will did article on calculus teaching in the der Protter's proposal. Since the teach­ enjoy a surge in popularity. Protter con­ January Notices. Obviously, he's been ing of calculus consumes an enormous cedes that some faculty members would around. However, I find another prob­ amount of our resources, it requires the prefer not to teach calculus at Berkeley, lem with his proposal. In my opinion, participation of graduate students, tem­ despite the reduced teaching load. This at least one-half of all mathematics porary and visiting faculty, as well as seems to indicate some combination of professors haven't the slightest clue tenured professors. As a consequence, antipathies for large classes and for cal­ as to how to teach undergraduates. In the overall level of institutional expe­ culus. To the extent that the latter plays fact, some of them aren't competent to rience with the curriculum at any time a role, we suggest that those who, de­ teach at all, and only the timidity of is low. This system requires the partic­ spite incentives to do so, would prefer docile graduate students, upon whom ipation of instructors who may actively not to teach calculus, should perhaps they propel their inscrutable wares, ac­ dislike teaching calculus, who aren't have that preference respected. Con­ counts for their continuing sustenance very good at teaching calculus, or who versely, those who for whatever reason within the collegiate entity. simply teach calculus too often to keep enjoy teaching calculus and who are Having completed four years as the subject fresh. We hasten to point successful at it, should be encouraged a T A, I have a much more radical out, however, that these individuals to continue. The argument that calcu­ proposal. I believe that all universi­ make invaluable educational contribu­ lus students would be thrilled at the ties, from the large state schools to tions to our department as advisors prospect of interacting with a tenured the Princetons, should split their facul­ to graduate students, as instructors of faculty member rings hollow to us. In ties into teaching and research faculties, graduate courses, and in many cases as our experience, they care little whether thereby creating colleges within univer­ instructors of upper-level undergraduate they're being taught by a Fields medal­ sities to handle 90% of the instruction courses. Any mathematics department ist or a struggling graduate student, but of freshmen and sophomores. Whatever at a research university will always and more about the clarity of presentation else you may think of this proposal, the indeed should always have some num­ and the accessibility of the instructor. addition of tenured, professional calcu­ ber of faculty members and graduate There remains the issue of how lus teachers to our universities could students who for one reason or another to measure successful teaching. Exam be the answer to a calamitous national will not be effective calculus instruc­ scores and student popularity cannot tell crisis. tors, and hence research departments the whole tale, but neither must they be I have heard the argument that must be organized with this in mind. entirely misleading: if an instructor is asking a world authority in projective Just as importantly, this broad partici­ focusing narrowly on routine examples planes to teach Calc I max-min prob­ pation in calculus instruction comes at that will result in high exam scores, the lems "is of mutual benefit to teacher and the cost of variety in the upper-level fault lies not only with him or her, but student." That is simply bogus public undergraduate curriculum, a considera­ also in the curriculum and in the design relations, in my opinion. In truth, most tion absent from Protter' s supply-side of exams. Moreover, in a multiple­ research mathematicians are bored to scheme. In contrast, a system that in­ section system as advocated in the tears teaching undergraduate courses, cludes teaching assistants would allow article, calls for "fairness" will lead to whether in a small class or a large for extra class time (something we as common exams, which in turn can lead lecture. How can it benefit a student to instructors have felt a need for) that to homogenization of the product and be taught by a bored teacher? So let's

388 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·············· ... LiWI!WIIIIIIlll.--11-lllllllllffill .. --ll-ll.llB.IlPil. ·111·11: ·:~••lllllll!lil•wm······· Letters to the Editor change the system so they won't have these kids attended. But at another tions. If a set of warm bodies can be to. Texas college, attended by middle and herded into the 1Oth grade and kept Ronald A. Wiener upper class students, another basic alge­ alive for three years, with none of Sarasota, Florida braic question-simplify the expression the students being knifed (and none of (Received January 23, 1992) (a - 1 + b- 1) -'-produced similar bad re­ the teachers mugged) then the mission sults: only 4 out of 25 calculus students is a success and all students gradu­ With respect to Calculus teaching, none performed the needed conversion, ad­ ate. Various exceptions are scattered of the learned AMS members under­ dition, and inversion. about the country-e.g., the Boston stands the main issues. It matters not So high school math preparation is Latin School, Pierce High School (in whether we teach a lean and lively or bad, anywhere you go. Richardson, Texas), or Beverly Hills a fat and lazy calculus. Either way, Again, the failure isn't hard to trace: High-but these are just isolated sin­ students will fail because they can't high school graduates know nothing gularities. perform the basic algebraic manipula­ about algebra for the same reason they Parents, of course, blame all this on tions required in such a course. know nothing about history, art, liter­ teachers who, they say, fail to enforce E.g., I recently asked the ten stu­ ature, or anything else. To state it in discipline. But such criticism is better dents in my first semester calculus class the most primitive terms: the kids think directed at father and mother; if chil­ (at a Texas college) to write the ex­ that ajb + cj d = (a+ c)j(b +d) for the dren don't respect their parents, they'll pansion of (a+ b)2-and received not a same reason that they think Karl Marx not respect other authority figures, like single satisfactory answer. Seven stu­ was one of the Marx Brothers or that teachers. dents wrote what was anticipated-a2 + Renoir is the name of a planet. So bad math results from bad high b2-while three others, although know­ So the generalization is: students schools, which in turn result from bad ing about cross-terms, were unaware of know nothing about algebra because parents. I'll let the AMS take it from commutativity, and so wrote them as they know nothing about anything. there. ab+ba. Now, this particular college was The general cause also seems clear. Leland Sapiro (literally and figuratively) on the wrong High schools no longer function as ed­ McNeese State University side of the tracks, so a poor score ucational institutions but as what one (Received January 27, 1992) might be blamed on the ghetto schools writer calls minimum security institu-

Series in Discrete Mathematics and Theoretical Computer Science

Discrete and Computational Geometry: Volume 6 Papers from the DIMACS Special Year Jacob E. Goodman, Richard Pollack, and William Steiger, Editors

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

to change. Free shipment by surface: for air 1991 Mathematics Subject Classijications: 03, 05, 12, 13, 14, All prices subject delivery, please add $6.50 per title. Prepayment required. 15, 32, 51, 52, 57, 68, ISBN 0-8218-6595-1, Order from: American Mathematical Society, P.O. Box 1571, 378 pages (hardcover), December 1991 Annex Station, Providence, RI 02901-1571, or call toll free 800- Individual mem. $40, List price $66,. Institutional mem. $53 321-4AMS in the continental U.S. and Canada to charge with Your ordering code is DIMACS/6NA VISA or MasterCard. Canada residents, please include 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 389 Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States

------··-.. ····-··-...... , .. _____ ...... -...... and industry. This inadequate preparation, continuing high In July 1990, the Board on Mathematical Sciences (BMS) attrition, and the declining interest of domestic students, the of the National Research Council (NRC) convened the inadequate interest of women students, and the near-absent Committee on Doctoral and Postdoctoral Study in the interest of students from underrepresented minorities in doc­ United States to conduct a study and make recommenda­ toral study are problems that transcend the current difficult tions for improvement and change in doctoral and postdoc­ job market. toral education in the mathematical sciences. The Com­ The charge to the Committee on Doctoral and Postdoc­ mittee's report, "Educating Mathematical Scientists: Doc­ toral Study in the United States was to determine what makes toral Study and the Postdoctoral Experience in the United certain programs successful in producing large numbers of States," was released in March 1992. Presented here are domestic Ph.D.s, including women and underrepresented the report's Executive Summary and Introduction, in addi­ minorities, with sufficient professional experience and ver­ tion to critiques of the report written by five members of satility to meet the research, teaching, and industrial needs the mathematical sciences community. of our technology-based society. The committee based its Reprinted with permission from "Educating Mathemati­ findings cin site visits to a diverse set of programs in 10 cal Scientists: Doctoral Study and the Postdoctoral Expe­ universities carried out in late 1990 and early 1991. These rience in the United States," 1992. Published by National programs were in both small and large, and in both public Academy Press, Washington, D.C. To order the complete and private, universities. They were also geographically book, sixty-four pages, $19, call 1-800-624-6242, or send diverse. They were all in the ''top 100" and included four a check plus $3 for shipping and handling to National departments in the "top 20." Academy Press, 2101 Constitution Avenue, N.W., P.O. The audience to which the report speaks is all U.S. Box 285, Washington, D.C. 20055. doctoral and postdoctoral programs in the mathematical Committee on Doctoral and Postdoctoral Study in the sciences, and, in particular, those programs that have limited United States: Ronald Douglas, State University of New human and financial resources. The report suggests that even York at Stony Brook, Chair, Hyman Bass, Columbia Uni­ with limited resources success can be achieved if, among versity; Avner Friedman, University of Minnesota; Peter other things, a program focuses its energies rather than trying Glynn, Stanford University; Ronald Graham, AT&T Bell to implement a "standard" or traditional program that covers Laboratories; Rhonda Hughes, Bryn Mawr College; Richard too many areas of the mathematical sciences. It also notes Jacob, Arizona State University; Patricia Langenberg, Uni­ that departments with the best faculty do not necessarily have versity of Maryland; D. J. Lewis, University of Michigan; J. the most successful doctoral and postdoctoral programs. A Scott Long, Indiana University at Bloomington; John Rice, quality faculty is necessary for a good program, but of equal University of California at San Diego; Donald Richards, importance are students and researchers that can benefit University of Virginia; Karen Uhlenbeck, University of Texas from the program. at Austin; Mary Wheeler, Rice University. In this report, a "successful" program is understood to be one that accomplishes the following two objectives. • All students, including the majority who will spend their Executive Summary careers in teaching, government laboratories, business, Although the United States is considered a world leader in and industry rather than in academic research, should mathematical sciences research and in doctoral and postdoc­ be well prepared by their doctoral and postdoctoral toral education, concern is growing about whether the needs experience for their careers. of the profession and of an increasingly technological soci­ • Larger percentages of domestic students, and, in partic­ ety are being met. Many doctoral students are not prepared ular, women and underrepresented minorities, should be to meet undergraduate teaching needs, establish productive attracted to the study of and careers in the mathematical research careers, or apply what they have learned in business sciences.

390 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY !nr m-r~q:;· Educating Mathematical Scientists

In its site visits, the Committee on Doctoral and Post­ careers in research universities, teaching universities, doctoral Study in the United States looked for features that government laboratories, business, and industry. were present in successful programs as well as for elements • Doctoral students and postdoctoral fellows should learn that were detrimental to quality education. The committee teaching skills and other communication skills appropri­ noted that successful programs possessed, in addition to ate for their future careers. the sine qua non of a quality faculty, the following three • The number of postdoctoral fellowships in the mathe­ characteristics: matical sciences should be greatly increased so that such 1. A focused, realistic mission, positions can be viewed as the logical next step after 2. A positive learning environment, completion of the doctorate for the good student, not as a 3. Relevant professional development. highly competitive prize for a select few. More postdoc­ A positive learning environment is an environment toral fellowships should have applied, interdisciplinary, that provides the assistance, encouragement, nurturing, and or pedagogical components. feedback necessary to attract and retain students and to give Changing the American doctoral and postdoctoral system them an education appropriate for their future careers. in the mathematical sciences so that it responds better to the The findings of the committee are as follows: needs of the profession, students, and the society is a task • There are several different models (missions) for pro­ that requires the cooperative efforts of faculty, departments, grams, including professional societies, and federal agencies. The departments at research universities have a special responsibility to * the standard model, which supports research in a broad raise the level and increase the knowledge of talented but range of areas, offers depth in each one, and has as underprepared entering American doctoral students. Federal its goal preparation for careers at research universities, agencies should continue their programs and also increase and their awareness of the impact of their programs on the * specialized models, such as the subdisciplinary model, doctoral and postdoctoral system. Professional societies the interdisciplinary model, the problem-based model, should be involved in monitoring change in the universities, and the college-teachers model, which were seen to al­ the agencies, and the community. But action, if it starts at all, leviate two large human resource problems, recruitment will start from the faculty. The faculty should be aware that and placement, and to be conducive to clustering of creating and maintaining a successful doctoral/postdoctoral faculty, postdoctoral associates, and students, a practice program will require additional effort and time. The long­ that helps create a positive learning environment and term benefits to the department, the students, and the society promote relevant professional development. are clearly worth the effort. • Both standard and specialized programs can be success­ ful. However, programs that do not have the human or 1. Introduction financial resources to run a successful standard program In the period since World War II, research in the mathe­ should consider whether a specialized model might better matical sciences has flourished in the United States. Large fit their needs. numbers of graduate students and researchers from around • New Ph.D.s with a broad academic background and the world have come to this country to study and to work in communication skills appropriate for their future careers pure and applied mathematics, in well-established and new are better able to find jobs. fields. The American system of doctoral and postdoctoral • Active recruiting increases the pool of quality students. study and research in the mathematical sciences is consid­ It does not just reapportion the pool. It also increases ered by many to be an unqualified success, in contrast to the the number of women and underrepresented minorities. system of pre-college and undergraduate education. Students with strong mathematical backgrounds have The current scarcity of highly qualified domestic graduate a choice of studying mathematical sciences, physical students, often attributed to mediocre pre-college education sciences, engineering, law, medicine, and other areas. and to related problems in undergraduate education, is seen More of them can be attracted to the mathematical by many as an unfortunate circumstance but not as a major sciences. problem. In the 1990-1991 academic year, only 43% (461 • Clustering faculty, postdoctoral associates, and doctoral out of the adjusted total of 1061 reported in McClure, 1991, students together in research areas is a major factor in p. 1093) of the recipients of Ph.D.s in the mathematical creating a positive learning environment. sciences from institutions in the United States were U.S. • A positive learning environment is important to all citizens (McClure, 1991), whereas during the 1960s, 82% of doctoral students but is crucial for women and underrep­ the recipients of such Ph.D.s from U.S. institutions were U.S. resented minorities. citizens (NSF [National Science Foundation], 1988). Among • All departments, including those characterized as elite the U.S. citizen recipients of Ph.D.s in the 1990-1991 and selective, need to provide a supportive learning academic year, less than a quarter were women and less than environment. a twentieth were from underrepresented minorities. American • Doctoral students and postdoctoral fellows should receive mathematical sciences departments, research laboratories, broad academic preparation appropriate for their future and industry are relying increasingly on students, faculty,

MAY/JUNE 1992, VOLUME 39, NUMBER 5 391 Educating Mathematical Scientists and professional researchers from abroad because fewer and their doctorates. The first of these two types of completion fewer American students are being attracted to study in rate is an appropriate measure of the success of highly the mathematical sciences and because the education that selective programs, while the second is appropriate for less many of those students receive leaves them ill equipped to selective programs. The committee observed a number of compete with their foreign counterparts. programs for which both rates were well above 50 percent. Noting the scarcity of highly qualified domestic students and the current tight employment market, some maintain that Purpose and Scope of This Report the chief problem in the doctoral and postdoctoral system The charge to the committee was to determine what makes is overproduction of Ph.D.s, a problem that should be certain doctoral and postdoctoral programs in the math­ solved by encouraging students to choose other disciplines ematical sciences successful in producing large numbers and by reducing the number of doctoral students. Our of domestic Ph.D.s, including women and underrepresented overreliance on academia for jobs for new Ph.D.s is often not minorities, with sufficient professional experience and versa­ considered to be a problem, nor is the matching of doctoral tility to meet the research, teaching, business, and industrial education with the positions that graduates take considered needs of our technology-based society. The mathematical to be a priority. Increasing production of Ph.D.s since sciences are considered to be pure mathematics, applied 1987, international events that have increased immigration mathematics, statistics and probability, operations research, of students and professional mathematicians to the United and scientific computing. Computer science, a separate States, and a recession in the economy have indeed combined discipline, is not included among the mathematical sciences. to produce what is now the most difficult employment The doctoral period considered in this report extends market for Ph.D. mathematicians since the 1970s. Further from the first year of graduate study through completion of complicating the current picture are the indications that the the thesis, regardless of whether or not the student obtains demand for mathematical scientists will rise as the many a master's degree. The postdoctoral period is the first five mathematical scientists hired in the 1960s start to retire over years after receipt of the Ph.D. A postdoctoral associate, the next decade (NRC [National Research Council], 1990b). postdoctoral fellow, or, in common parlance, "postdoc," The long-term growth in demand for mathematical scientists is a recent Ph.D. who has a fully funded position to do in academia, government, business, and industry and the research. Since such a small number of new Ph.D.s in the expectation that the wave of immigration of mathematical mathematical sciences enjoy postdoctoral fellowships, this talent to the United States will eventually taper off suggest report concerns not only postdoctoral fellows but also junior that the country will be best served by a positive outlook faculty working during the postdoctoral period. that emphasizes attracting more domestic students into the The purpose of this report is to present and disseminate mathematical sciences and giving those students proper information about types of mathematical sciences doctoral foundations for their future careers. and postdoctoral programs that succeed in attracting large A positive outlook that serves the interests of the numbers of domestic students, including women and under­ profession and the country can be translated into actions represented minorities, and succeed in giving their students intended to achieve the following two broad objectives: academic and professional experience that is relevant to • All students, including the majority who will spend their their future careers. There are U.S. programs that provide careers in teaching, government laboratories, business, high-quality doctoral education to student bodies that are and industry rather than in academic research, should 80% American, have nearly 50% women, or have 30% be well prepared by their doctoral and postdoctoral underrepresented minorities. This report, based on the com­ experience for their careers. mittee's insights gained in site visits to 10 universities, • Larger percentages of domestic stuqents, and, in partic­ describes characteristics of these programs. What these pro­ ular, women and underrepresented minorities, should be grams do differently and what they and others consider to attracted to the study of and careers in the mathematical be their successes and their frustrations is information that . sciences. this report seeks to make available to the community so In this report, a "successful" program is understood as to encourage doctoral/postdoctoral program models that to be one that accomplishes these two objectives. The are relevant to the needs not only of academic research needed renewal of the profession, as pointed out in the but also of teaching, government, business, and industry, ''David I" report (NRC, 1984), A Challenge of Numbers and to increase the quality and number of domestic Ph.D.s, (NRC, 1990b), and the "David II" report (NRC, 1990c), especially women and underrepresented minorities. requires larger percentages of domestic students. Although This report follows on and is complementary to a number statistics invariably oversimplify the situation, the following of studies by the National Research Council that examine the two "completion rate" statistics concerning percentages of health of U.S. mathematical sciences research and education, domestic students are useful in judging a program's success: including Renewing U.S. Mathematics: Critical Resource for (1) the percentage of students who entered the program five the Future (NRC, 1984), Everybody Counts (NRC, 1989), years earlier and who have received their doctorates, and (2) A Challenge of Numbers (NRC, 1990b), Moving Beyond the percentage of students who completed their second year Myths (NRC, 1991b), Renewing U.S. Mathematics: A Plan of graduate study four years earlier and who have received for the 1990s (NRC, 1990c), and Actions for Renewing U.S.

392 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ······························--···---·-··------Educating Mathematical Scientists

Mathematical Sciences Departments (NRC, 1990a). One National Research Council (NRC), 1984, Renewing U.S. Mathe­ includes the following pertinent summary. matics: Critical Resource for the Future ("David I" report), National Academy Press, Washington, D.C. Graduate and postdoctoral training programs offered National Research Council (NRC), 1989, Everybody Counts: ARe­ by mathematical sciences departments are key to the port to the Nation on the Future of Mathematics Education, National successful renewal of the profession and reform of Academy Press, Washington, D.C. mathematics education. Successful programs can attract National Research Council (NRC), 1990a, Actions for Renewing sciences and U.S. Mathematical Sciences Departments, National Academy Press, individuals to a career in the mathematical Washington, D.C. can develop highly qualified teachers and researchers to National Research Council (NRC), 1990b, A Challenge ofNumbers: stimulate, nurture, and train future generations. Is our People in the Mathematical Sciences, National Academy Press, Wash­ present graduate and postdoctoral educational system in ington, D.C. mathematics working well? The answer seems clearly National Research Council (NRC), 1990c, Renewing U.S. Mathe­ to be that it could be much better. The community could matics: A Plan for the 1990s, ("David If' report), National Academy attract more students to the study of the mathematical Press, Washington, D.C. National Research Council (NRC), 1991b, Moving Beyond Myths: sciences, and more students entering graduate programs Revitalizing Undergraduate Mathematics, National Academy Press, could succeed in obtaining doctorates. With nurtur­ Washington, D.C. ing and continued attention through good postdoctoral National Science Foundation (NSF), 1988, Science and Engineering programs, more of these young people could develop Doctorates: 1960-86, National Science Foundation, Washington, D.C. into good mathematicians-some as teachers, some as researchers, and many as both. (NRC, 1990a, p. 13) In order to stimulate discussion of the report, "Educating and the Postdoc­ Contents of This Report Mathematical Scientists: Doctoral Study in the United States," the Notices solicited Chapter 2 gives a brief historical perspective of the mathe­ toral Experience of the report from five members of matical sciences in America, with emphasis on doctoral and the following critiques postdoctoral training. the mathematical sciences community. Chapter 3 describes how some programs in the present system achieve success. Three characteristics of successful programs-a focused and realistic mission, a positive learn­ ing environment, and relevant professional development­ Solomon Garfunkel are introduced in this chapter. The issue of having a high­ quality faculty-a sine qua non of a successful program-is Garfunkel is Executive Director of the Consortium for acknowledged but not discussed in detail in this report. Mathematics and its Applications in Lexington, MA. The heart of the report is Chapters 4-7, which treat the three characteristics of successful programs and human First, let me begin by saying that I am pleased that this study resource issues that must be taken into account. Chapter was done and this report written. It is well past time that we 4 discusses human resource issues; in particular, those take a serious look at doctoral and postdoctoral programs related to domestic students, women, and underrepresented and how they could and should be improved. The fact that minorities are examined. A number of specialized missions this study was undertaken under the aegis of the National for doctoral/postdoctoral programs are described in Chapter Research Council (NRC) is admittedly a good news/bad 5. Chapter 6 discusses a positive learning environment. news situation. The good news is that the prestige of the Relevant professional development is described in Chapter NRC may help increase the awareness of the community 7. and encourage more people to read and take its contents Chapter 8 describes how faculty, departments, profes­ seriously. The bad news is that, as with other NRC reports, sional societies, and federal agencies can work together to the review process has a "smoothing" effect and tends to create more successful programs. take out strong and controversial positions. This is not a A guide for self-evaluation by departments forms Ap­ strong report. With one notable exception, it says nothing pendix A. Appendix B includes advice to prospective wrong and may in fact do some good. However, it manages doctoral students on how they can best choose a doctoral to miss the central point and is therefore largely irrelevant program. Appendix C is a brief discussion of master's de­ to serious debate. gree programs in the mathematical sciences, a feature that That central point is the reward system (for both faculty may form a part of a well-rounded graduate program in the and students). Nowhere in the report is there any mention of future as doctoral programs become more oriented toward reward. If faculty are only promoted or granted tenure on the wider job markets, including business and industry. basis of research, the real message to graduate students is loud and clear. Moreover, what about the graduate students References themselves? If they are "trained" to teach through courses, McClure, D.E., 1991, "1991 Annual AMS-MAA Survey (First Report)" seminars, evaluations, etc., what are their rewards? What in Notices of the American Mathematical Society, 38, 1086-1102. if they fail to demonstrate adequate teaching ability or

MAY/JUNE 1992, VOLUME 39, NUMBER 5 393 Educating Mathematical Scientists communication skills, but can write strong theses? Do we FernY. Hunt go ahead and certify them as college faculty, or do we tell prospective employers of their deficiencies? In short, (how) Hunt is associate professor of mathematics at Howard do we put our money where our mouths are? While I realize University. On leave from Howard this year, she is that these are extremely hard questions requiring a great currently a research mathematician at the Computing and deal of community debate, to completely ignore them here Applied Mathematics Laboratory at the National Institute is a dramatic failure. of Standards and Technology. If this were the only flaw in an otherwise well-intentioned report, I probably wouldn't have written this critique. In April, the Washington Post reported that an influential Unfortunately, there is another 'more serious problem, and, study of the National Science Foundation forecasting serious to be honest, one I found quite disturbing. shortages of scientists and engineers begirining in the 1990s This study's treatment of the subject of foreign students was based on faulty extrapolations and that the predicted is very poorly done. The report correctly speaks to the need may in fact be overstated. This is disappointing news issues involved in increasing enrollment and graduation indeed, as it comes in the :midst of one of the most rates of American students in general and women and unfavorable job markets for mathematicians in more than a underrepresented minorities in particular. However, in the decade. Yet, there are many in the mathematical community half page devoted to foreign students, the entire tone is who believe that the gravest risk to the future of mathematics about the problems they present to their fellow graduate in the U.S. is not the oversupply of mathematicians but the students and undergraduates they may teach. Thus; we are undersupply of future American mathematicians. This is termed "boundary value told that "foreign students often lhave a higher level of one of an array of what might be problems" arising from our failure to communicate the value mathematical experience" and therefore "when placed in the and meaning of our mathematical work to certain groups same introductory courses ... often perform better than the at the boundary of the mathematics world. In this case, American students." Moreover, "the committee believes that the group is prospective mathematicians, but one could add such a disparity can contribute to an increase in the dropout other groups, such as students and scientists working in rate among domestic students, especially among women other fields and, beyond these, the general public. and underrepresented minorities." The analysis of foreign In recognition of the problem of declining percentages students concludes with of domestic students in mathematics Ph.D. programs, the "Colleges and universities have of necessity had to rely Board on Mathematical Sciences charged the Committee on increasingly on foreign nationals to teach undergraduate Doctoral and Postdoctoral Study in the United States to pro­ mathematics. The long-term ramifications and impact duce a report that surveyed a variety of programs throughout of this practice need careful study." the country. The Committee has successfully carried out this task, defining and describing successful graduate programs This discussion is at best disingenuous. Foreign graduate that produce large numbers of domestic Ph.D.s and, more students now make up about 45% of all graduate enrollments. generally, Ph.D.s that are adequately prepared to fill our They are our students. Moreover, most of those who get research and educational needs in universities, government, Ph.D.s stay in this country, teach our undergraduates, and and industry. The Committee's most significant and ad­ work in government labs and in industry. They may very mirable achievement. was to make attracting and retaining well have· different problems than domestic students, but larger percentages of domestic students-and, in particular, they need "a positive learning environment" just as much as women and minorities-a crucial part of the definition of any other student group. Foreign students cannot be seen as a successful program. Further, in a section entitled "The a problem for American students or, worse, be pitted against Key to Action," the Committee stated that "the depart­ women and underrepresented minorities. This is dangerous ments at research universities have a special responsibility ground. to raise the level and increase the knowledge of talented but I am sure that the authors of this study were well underprepared entering American doctoral students." intentioned. However, to advance the discussion of graduate Fortunately, the Committee found that there are programs programs we must seriously address the university reward around the country that are successful by this definition and structure and take a much deeper look at the participation achieve this success with many techniques that do not seem of foreign-born students throughout the system. It is my to require a lot of money. What is required is a commitment sincere hope that the AMS or the Joint Policy Board for on the part of individual faculty and departments to seek Mathematics (JPBM) will undertake such a project in the out students and provide sustained support. In a national ethnic animosity, .the call near future spurred by this report and our reactions to it. atmosphere of growing racial and for active nurturing of minority students will not be an easy *Editor's Note: JPBM recently convened a Committee one for us to hear. It will be tempting for the community to on Professional Recognition and Rewards. Information about simply build on the recent modest increases in the number this Committee appears in the Inside the AMS column in of female Ph.D.s mainly coming from ethnic groups already this issue of the Notices. well represented in the profession. The techniques described

394 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Educating Mathematical Scientists in this report will work for many minority students, and I am productive research environment and the implicit repudiation convinced that continuing efforts to increase both women of the lamentably common competitive paradigm in which and minorities will enrich the community not only socially the adviser orchestrates a trial-by-ordeal for his (or her) but scientifically as well. inexperienced rival. In nonacademic settings, mathematicians are far likelier My own observations about recruitment of talented un­ to encounter nonmathematicians ranging from scientists who dergraduates agree with the report's: most departments, use a lot of mathematics to administrative types with very shockingly, just don't. We seem to be content to let dozens little scientific background. The report urges departments of students who enjoy mathematics go on to careers in to prepare students to operate successfully in such envi­ physics, computer science, or even law, without mention­ ronments. Mathematicians need to be able to talk about ing mathematics graduate school. The number of students mathematics to nonmathematicians in a way that doesn't pursuing bachelor's theses or other independent work is trigger unpleasant memories from their student days. The ridiculously small. training graduate students (should) receive in teaching can Hit-or-miss recruitment methods overlook students capa­ also be used to sharpen communication skills. In addition, I ble of doing mathematics, but, unfortunately, they find more would recommend that graduate faculty who aren't already than enough to fill the small number of research positions collaborating with nonmathematicians go out of their way available today. The sad truth is that with the collapse to talk with researchers in other departments at their univer­ of the academic job market last year and the even worse sities and to researchers in government laboratories or local market this year, there are already many talented research companies so that she or he can gain first-hand knowledge mathematicians at liberty, and there will soon be more. The of some of the barriers to communication and collaboration, committee attempted to address this issue by revising the many of which are not well understood by the mathematics mission of doctoral programs to include better preparation community. for "college teaching" and industry. Unfortunately, this sec­ To insure the health of the mathematical enterprise in the ond set of suggestions is vague and incoherent. To quote the twenty-first century, how must doctoral programs change if report: they must at all? The Committee has succeeded admirably in addressing this question and making the case for change, "The college-teachers model is designed to prepare and they have pointed to the characteristics of programs teachers at two- and four-year colleges. A college that are successfully meeting this challenge. The report is teachers program is to be distinguished from a program a worthy contribution, and I hope its recommendations are that confers doctor of arts or doctor of education implemented. degrees. Breadth of course work and an emphasis on professional development in pedagogy are, in addition to a research apprenticeship, parts of such a program." Andrew J. Lazarus The attempt to combine course breadth and research depth is a recipe for mediocrity-as the committee realized Lazarus received his Ph.D. from the University of Cal­ when dealing with faculty specialization, where it suggested ifornia at Berkeley in 1989. Since then, he has been a that departments, except the very best, concentrate their visiting assistant professor at U.C. Riverside and U.C. efforts. The same should hold true for graduate students. Davis. Since the research component of the college-teachers model will be diluted-it is intended for the students who will The Committee on Doctoral and Postdoctoral Study in the be furthest from the research frontier in any one field-the United States has produced a report whose suggestions fall difference between the new Ph.D. and the D.A. and Ed.D. into two categories. The first set discusses improvement of is that the latter two have poor reputations already while the doctoral programs within the framework of their current first will need time to develop one. The committee seems mission, the production of research mathematicians. Most to have assumed without proof that training in pedagogy of these proposals are meritorious and all are reasonable. I is more important for college teachers than university commend two of them specifically: research atmosphere and professors, who still teach, albeit less. Except perhaps for recruitment. faculty closely involved in precollegiate teacher training, I I believe that the training of graduate students is a fun­ don't see why this is so. damental obligation of senior faculty. Many world-famous The report also fails to articulate why graduates of this mathematicians find ways to integrate supervision of grad­ program will be more attractive to colleges. Colleges are uate students into their own research program, leaving ex­ now choosing from literally hundreds of applicants. Some amples, subcases, and analogues to the apprentices. Faculty colleges want demonstrated teaching excellence; others see and students work together in a way similar to programs the job crisis as an opportunity to hire first-rate scholars in laboratory science. In a successful program, everyone who just miss a position at a major university. None are roots for everyone else. Although I do not agree with every complaining about a lack of qualified applicants, quite the assertion in the report's chapter "Positive Learning Envi­ contrary. The positions for graduates of the college-teachers ronment," I was impressed with its suggested models for a model are chimerical. Even the report avers only that need

MAY/JUNE 1992, VOLUME 39, NUMBER 5 395 Educating Mathematical Scientists for them "could increase" by the end of the '90s. One private, top twenty and top one hundred, geographically wonders where this idea came from, since the committee diverse, etc.). contained only one member from a four-year college, an elite Unfortunately, this approach makes it impossible for institution with teaching load and publication expectations readers to decide for themselves whether they agree with similar to research universities', and no members from the conclusions of the report. Built into the definition of two-year colleges. a "successful" program is the idea that "larger percentages The suggestions about involving mathematics with indus­ of domestic students, and, in particular, women and un­ try do not appear to be any better informed. (The committee derrepresented minorities should be attracted to the study contained one member from industry, but he is from an atyp­ of and careers in the mathematical sciences." Given that ical quasi-academic think tank which has, moreover, had a this is a part of the definition of successful, one longs for hiring slowdown for years.) Only a handful of nonacademic information as to how successful these programs are in jobs are being advertised in the Notices and Employment order to compare their success with one's own department. Information in the Mathematical Sciences. If there truly Providing such information, or offering what the committee are plentiful industrial positions for mathematicians, active viewed as appropriate goals for a department, would have solicitation of ads for them would be a great service the strengthened the report. Society could perform for recent graduates. But if not, and Whether our institutions are producing enough domestic we are driving taxicabs, let us at least have earned a quality students, especially women and underrepresented minorities, degree. was one of the concerns that led to this report, and success with domestic students was built into the definition of a "successful" program. We are told that, "departments at research universities have a special responsibility to Jim Lewis raise the level and increase the knowledge of talented but underprepared entering American doctoral students." Lewis is chair of the department of mathematics and How shall we fulfill that responsibility? Each department statistics at the University of Nebraska at Lincoln. A makes decisions as to which graduate students receive member of the AMS Committee on Science Policy, he financial support. Even though active recruiting can increase chairs the Committee's task force on academic support the pool of quality students, most departments will still for mathematics and connections between mathematics be faced with choosing between a domestic student and a research and education. foreign student who appears to have better qualifications for graduate work. Should department chairs reserve a certain Almost any department chair in the mathematical sciences percentage of their resources for American students? If so, will find Educating Mathematical Scientists: Doctoral Study how much? and the Postdoctoral Experience in the United States to Another part of the definition of a "successful" program be a useful document in connection with a careful look at also concerns me: "All students, including the majority who their own department. The current job market for Ph.D.s will spend their careers in teaching, government labora­ has caused most people in doctoral granting institutions to tories, business, and industry rather than academic research, reassess the job they are doing and to look for ways to should be well prepared by their doctoral and postdoctoral improve the employment possibilities of their students. experience for their careers." This theme is repeated so often The report offers what appears to be sound advice built that one who did not know better might conclude that the around the major themes that a successful department must five areas described above are five separate but relatively have a quality faculty, a focused mission, a positive learning equal career paths for Ph.D.s in the mathematical sciences. environment, and relevant professional development. Of Are there jobs for mathematics Ph.D.s in government particular use will be the list of questions in the appendix laboratories, business, and industry that are going unfilled? A on "Doctoral and Postdoctoral Program Self-Evaluation." careful look at the 1991 AMS-MAA Survey in the November Indeed, the report will have a positive impact on graduate 1991 issue of the Notices reveals that, if one considers only programs in mathematics if enough faculty use this list to the graduates of Group I, II, and III departments and takes analyze their own departments. out the statistics students, only thirty-three individuals went The goal of the report was to determine what makes into government, business, and industry jobs. Let us all certain programs successful. The approach was to conduct wish it were not so. Let us attempt as a profession to site visits to ten programs that had been identified as open markets for our graduates in government, business, successful and report on the characteristics that made those and industry. At the same time, let us realize that currently programs successful. The committee that produced this only about 6% of new Ph.D.s outside of statistics and the report made the fundamental decision that in order to Group V departments obtain jobs in the U.S. and outside of receive the cooperation of the departments visited, no academia. program identification would be made. As readers of the Finally, I take issue with the implied distinctions between report, we are assured that the ten programs visited were careers in teaching and careers in academic research. Even both successful and diverse (small and large, public and while trying to stress that we should pay greater attention to

396 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Educating Mathematical Scientists

developing the abilities of our students to teach, the report's ogres here, or even administrators; we're talking about our repeated references to careers in teaching and careers in fellow (sic) mathematicians, who rightly demand enormous academic research as if they were separate perpetuates an respect. Why then do American students leave graduate unfortunate separation. A colleague of mine likes to say school disenchanted? Who do some of the best never ap­ that he considers himself a teacher-scholar. I think this is ply? Why so few women and minority students? I believe the correct perspective. As institutions vary, so will the graduate schools have failed the rest of the mathematics distribution of effort between research and teaching. Perhaps community when their completion rates are low and when the real point is that about two-thirds of all academic they promote a definition of future mathematician whose positions at or above the assistant professor level are in narrowness excludes most talented young people growing institutions that do not offer a Ph.D. This fact, together with up in the U.S. Perhaps even those programs that are doing a the need to open nonacademic markets for our graduates, good job along the recommended lines will deny the impor­ should influence how we prepare Ph.D.s in mathematics. tance of such issues. My own colleagues may have my head on a platter when this appears. I shudder at the thought of a senior mathematician's saying sarcastically to a young Carol S. Wood woman student, "I'm told you need a supportive environ­ ment. What does that mean?'' But the current generation Wood is chair of the department of mathematics at of students takes careful note of the graduate environment, Wesleyan University and president of the Association for regarding atmosphere and attrition rates as crucial factors Women in Mathematics. in considering graduate study. This is the impression I gain from listening to the students I meet across the country, For mathematicians, a graduate program is highly desirable, undergraduate and graduate. There is a generational/cultural particularly a doctoral program; it is one measure of serious­ gap deepening over time. Many of us over-forty mathemati­ ness of purpose, and it allows teaching at a very rewarding cians are experienced know-it-alls, fiercely competitive and level. When administering a graduate program, most of us eager to stand out as the best. My mother loved games and build on our own graduate experiences, incorporating a few hated to lose; by the time I entered a classroom I was happy modificiations which we would have liked. Novel programs to compete under "boys' rules." This played a greater role have come into existence mostly in response to external in my choice of career than I usually want to admit. In pressures. It would be surprising if a report from within the time I found an intellectual excitement in mathematics much community called for extreme upheaval, although the current deeper and more satisfying than simply beating the next guy document does put in a strong plug for professional masters to a theorem (although sometimes I wonder ... after all, my programs. Since this report has gone through NRC's editing middle name is Saunders). But our craft is still presented and stringent approval measures, it may be argued that the to students as much more a competition for stardom than is result is radical indeed, calling for significant changes in healthy or even accurate. We invite a reaction of disgust or how the U.S. mathematics doctoral community is to be discouragement: "I love mathematics but just don't belong renewed in future years, and stressing the importance of a with these people." Surely we have more imagination than to "positive learning environment." The existence of such an believe that every talented student who exits in this manner environment cannot be left to chance, but happens by design ''just doesn't have what it takes to be a mathematician!" and by intervention on the part of forceful, respected mem­ A recent NSF report from a conference of Presidential bers of the program. Nonetheless, some believe that only a Young Investigators indicates that throughout the sciences few schools matter, and that their students are well served the over-forty set is out of step with the ambitions and by the sheer excellence of the faculty and the resultant op­ views of the next leaders. A highly competitive setting has portunities to sit at the feet of these masters. It is unfortunate very limited appeal to today' s brightest students, and is in that the best schools are the least likely to heed this report; fact a downright tum-off to many women and minorities. some will point proudly to the achievements of their suc­ Their interest in hard work is hardly increased by the threat cessful students, thereby dismissing any notion that a more of having their weaker peers weeded out. The NRC report "positive learning environment" is needed. Part of me wants suggests that we take a careful look at how we recruit and to agree that nothing but the pursuit of mathematics should educate our successors and make some adjustments in our matter ... until I see the results. We're not talking about culture. We dismiss it at risk.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 397 Graduate Education in Transition The Report of a Conference Sponsored by The Conference Board of the Mathematical Sciences

DC, May 4-6, 1991. At this meeting, leaders of various This report of the Conference Board of the Mathematical segments of the mathematical sciences community were Sciences (CBMS) is based on a workshop held in June asked two key questions: what are the nation's needs and 1991 in Washington, D.C. The report first appeared in how can the community best respond? February 1992. Twenty-four individuals participated in the conference. Among them were seven current presidents and six former presidents of CBMS member societies. A complete listing of the participants is given at the end of this report. Introduction The conference began with keynote remarks by Luther Williams, Assistant Director of the National Science Foun­ Background dation, Directorate for Education and Human Resources, In the last few years, both activity and urgency of reform and by Calvin Moore, Vice-President for Academic Af­ efforts in mathematics education have increased dramati­ fairs at the University of California at Berkeley, followed cally. There is widespread agreement that the mathematics by the charge to the participants given by Ivar Stakgold, education system, from elementary school through graduate Chair of CBMS. The participants were formed into three school, needs to be greatly improved, and that the changes working groups-the Doctoral Group, the Master's Group, required to bring about this improvement will not come and the Professional Development Group--corresponding easily or quickly, but will require a continuing commitment roughly to the three types of postbaccalaureate education of time and effort. At the school and collegiate levels, the in mathematics. Throughout the working sessions and gen­ mathematical sciences community has refocused its atten­ eral discussions, the participants were asked to identify the tion on teaching and the needs of today's students. The national needs in postbaccalaureate education in the math­ Mathematical Sciences Education Board and the CBMS ematical sciences and to recommend what actions should member societies are now working to implement the vision be taken, and by whom, to make the graduate education of school mathematics presented in the National Council of enterprise more responsive to those needs. Teachers of Mathematics (NCTM) Standards. Undergradu­ This report is based on the written summaries of the ate mathematics education is the focus of major programs working groups and of the discussions which took place at in the National Science Foundation and in many of the the plenary sessions. It is organized into two main sections: mathematics professional societies. At both the school and Discussion of the Issues and Recommendations. collegiate levels, there is increasing emphasis on changing The Conference Board of the Mathematical Sciences the culture and priorities of the mathematical community to would like to express our gratitude to the Exxon Education promote the importance of teaching. Foundation for their support of this conference. In contrast to this, no comparable national effort or leadership has emerged as yet in the mathematics graduate education enterprise. Despite an apparent mismatch between Discussion of the Issues the needs of the nation and much of the current practice in graduate programs, relatively little attention has been given Introduction to postbaccalaureate education in the mathematical sciences. The amount of national attention now given to educational reform in mathematics is staggering. Can anyone recall an The CBMS Conference American president addressing a meeting of mathematics In order to promote serious discussion of the issues of educators, as George Bush did recently at the National graduate education and to. move the mathematical sci­ Summit on Mathematics Assessment? ences community to action, the Conference Board of the The report of the Federal Coordinating Council for Mathematical Sciences organized a three-day conference on Science, Education, and Technology (FCCSET) accompa­ "Graduate Education in Transition," held in Washington, nying the President's 1992 budget both deplores the present

398 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ""'111------·illtl'ill... illi! __ _...... _.... __ ... Graduate Education in Transition

state of science and mathematics education and proposes rece1vmg their degrees. Most mathematics Ph.D.'s spend objectives and pri()rities to guide future federal activities. their careers in comprehensive universities and colleges, Recommended budget increases run 28% at the precollege where the mission of the institution and the role of the level, 14% at the undergraduate level, but only 2% at the faculty is much broader than simply producing research. graduate level. The importance of all the roles of the faculty-research and Unlike the post-Sputnik reform, which was driven by graduate education, undergraduate education, service to a military needs, the present effort is driven by economic broad set of client disciplines, community outreach, service concerns. The government sees leadership in science and to the department, the university, the local community, and mathematics as a critical element to regain American com­ the profession-must be recognized, and some preparation petitiveness in the international arena. for these roles should begin in graduate school. Many reports have analyzed aspects of mathematics The success of the Ph.D. program in producing a cadre education and have proposed remedies (see, for example, of strong researchers must be balanced against weaknesses in [1], [2]). Member societies of CBMS have played important the preparation for college teaching and other careers. There parts in writing these reports and translating them into is the cost of unfulfilled obligations and missed opportunities. action. The two Boards of the National Research Council Programs in mathematics (unlike those in other mathematical (the Mathematical Sciences Education Board and the Board sciences such as statistics and operations research) often are on Mathematical Sciences) have provided both stimulus and held in splendid isolation without stressing, or sometimes coordination for many of these projects. The mathematical even mentioning, connecting strands to other sciences. community has generally participated with energy and en­ The emphasis on individual, independent research is often thusiasm in these studies and plans for action. Indeed, in a exaggerated; whether in the real world or even in academic speech delivered at the International Congress of Industrial research, there is considerable need for teamwork either and Applied Mathematics in July 1991, D. Allan Brom­ within or across disciplines. ley, Assistant to the President for Science and Technology, One unfortunate consequence of the parochialism in praised the mathematical community for its leadership in graduate mathematics education is that much of industry and educational reform. business still regards mathematicians with some suspicion. It is not surprising that relatively little is said concerning Few industries have career paths for mathematicians; con­ graduate study in most of these reports since the most tributions of a mathematical nature are often not recognized pressing needs are clearly in school education and in as such because they are made by physicists, engineers, and undergraduate education (see, however, [3], [4], [5]). Now computer scientists. that a concerted effort is being made at these levels, we An interesting case in point is given by the list of the ten submit that without reform in graduate education no lasting greatest engineering achievements of the past quarter century change in school or undergraduate education is likely. as compiled by the National Academy of Engineering: Short-term intervention programs in the schools will yield the moon landing, application satellites, microprocessors, some temporary benefits, but the attitudes and skills of computer-aided design and manufacturing, the CAT scan, school teachers are, in the long run, molded in colleges advanced composite materials, jumbo jets, lasers, fiber-optic and universities, where these teachers are instructed by the communications, and genetically engineered products. Each products of our graduate schools. One does not have to of these spectacular engineering achievements has a strong subscribe to a domino theory to see that all parts of our mathematical component identifiable (and acknowledged) by educational system are interdependent. engineers but not by the general public. There is also a more direct reason for suggesting changes We also believe that industry does not take full advantage in graduate education in the mathematical sciences. Although of the potential of mathematics. Although part of the reason our graduate programs have brought U.S. mathematics to lies with the attitude and training of some mathematicians, world leadership in research, they have been less successful equally important factors are some shortsighted business in preparing students for college teaching and for positions practices that have become prevalent in recent years. Policy in industry. makers and corporate managers are often so concerned What are the features of graduate education in the math­ with short-term profit that they do not sufficiently invest ematical sciences that need attention? The main problem is in technological development and industrial innovation (see the mismatch between graduate programs and the existing [6]). job market. The gap is even wider if we take into account In this report, we shall make a number of recommen­ potential, unexploited markets. The Ph.D. program in math­ dations to departments, scientific organizations, and funding ematics (the use of the singular is appropriate in view of agencies to help bring graduate education in the mathemat­ the considerable similarities among programs), culminating ical sciences closer to the needs of American society. For as it does in a research dissertation, is intended principally the past several years, departments of mathematical sciences to prepare students for careers on the faculty of research have faced increasing and more varied responsibilities, often universities. This narrow focus has led to a very strong without adequate resources. On some campuses, a favorable community of research mathematicians in the U.S., despite climate has made ii possible for the faculty to meet the the fact that nearly 80% of Ph.D.'s publish little after challenges of research, educational reform, and service to

MAY/JUNE 1992, VOLUME 39, NUMBER 5 399 ------·-----Graduate Education in Transition the institution and community. The time has come for other instill a professional attitude toward real-world problems. university administrations, in conjunction with the federal This means that mathematicians must be fully prepared agencies that support mathematics and science, to correct the to accept the responsibility of familiarizing themselves chronic underfunding of mathematical sciences departments with the methodology for analyzing practical problems, in order that they may achieve the goals and expectations of whether expounded by chemists, engineers, biologists, or our society as we move into the twenty-first century. economists. There are a few excellent applied mathematics programs in the U.S. and elsewhere that provide this National Needs orientation; they deserve to be publicized and could serve as The present demand for Ph.D.'s in the mathematical sci­ models (with local variations) for the education of industrial ences is generated by several different market segments: mathematicians. Goals and standards for such programs university faculty, college faculty, industry and commerce, should be promulgated by professional societies as they and government organizations and laboratories. In the five have been for teacher preparation. year period 1986-1990, 80% of the new Ph.D.'s in the At the same time, many small and medium size industries mathematical sciences employed in the U.S. took academic have been slow in adopting mathematical modeling and positions. If the field of statistics is factored out, the per­ computational mathematics. One reason is the lack of centage climbs to nearly 90% (see [7]). In the existing properly trained applied mathematicians with an interest in market, new mathematics Ph.D.'s are employed principally industrial problems. Another is industrial inertia and perhaps by academic institutions. Although some mathematical sci­ even some residual distaste for mathematics in management. entists move into industry or government after a postdoctoral The pressure on near-term corporate profits and the lack of a appointment or junior facu1ty position, little data are avail­ government industrial policy also have serious consequences able on this subject. Demographic projections show more for American economic competitiveness. Michael Schrage facu1ty retirements in the period 1995-2000 than can be has pointed out how "mathematics remains a crucial-and filled by prospective Ph.D.'s at the present rate of produc­ misapplied-key to economic edge" [6]. Believing as we do tion. Although economic strains in many states have caused in the potential effectiveness of the mathematical sciences retrenchment in hiring in 1990 and 1991, many observers in industry, we must make a concerted effort to demonstrate expect this to be temporary. this to industry. A possible approach is to organize academic­ At the Master's level, the market is more difficult industrial centers on the model of the European Consortium to pinpoint. It is clear that the industrial, business, and for Mathematics in Industry. government share of the market is much more significant The continued technological and economic health of the here than at the Ph.D. level (see [8], [9]). Two-year colleges U.S. depends on maintaining at least the present supply of and secondary schools are major employers, and there is graduate-level mathematical scientists. In recent years, half also evidence that much of precalculus teaching at colleges of our Ph.D.'s have been foreign, and most have entered the and universities is provided by Master's degree facu1ty. American job market. This ratio does not seem appropriate Recent reports have considered the preparation of for the steady state. American women and minorities, prospective teachers in schools [10], [11], in two-year who will be a large fraction of the new entrants in the colleges [12], and in four-year colleges [13]. This workshop work force by the year 2000, have traditionally not been strongly supports the recommendations in these reports. In attracted in sufficient numbers to careers in the mathematical particu1ar, we endorse the key principles of the Mathematical sciences. No doubt some are merely expressing their free Association of America Committee on Preparation for Col­ choice, but others may have been kept away for lack of lege Teaching [13], namely that doctoral programs should encouragement. We propose a number of remedies: active prepare students to meet a wide range of professional respon­ recruitment, a supportive environment, and a better balance sibilities, should not be limited to specialization in narrow between competitive and collaborative activities in graduate areas, and should give systematic attention to promoting programs. A supportive and nurturing atmosphere, which excellence in the teaching of mathematics. is helpful to all students, is essential for recruiting and The mathematical sciences have yet to find their proper retaining students from underrepresented groups. place in industry. We consider the mathematical sciences In examining present postbaccalaureate education, one as an important, if partially untapped, industrial resource. cannot help but observe the lack of postdoctoral opportuni­ A recent National Research Council report, "Mathematical ties in the mathematical sciences as compared to physics or Sciences, Technology, and Economic Competitiveness" [14], chemistry, for instance. Opportunities for later career devel­ points out some of the vital contributions that have been opment also seem to be minimal. As mathematics expands, made by the mathematical sciences to technology, but also so often does its circle of applications. There is a need to challenges the U.S. mathematical community to speed the respond to individual demand for specific courses and to transfer of new technologies to the production line. present advances in mathematics that can be expected to be Mathematics as an industrial resource needs both greater important in applications. School and college teachers will acceptance and further development. Graduate programs with also profit from "updating" their education, both to keep an industrially oriented point of view are relatively rare. them intellectually active and to enable them to incorporate To paraphrase J.R. Ockendon [15], such programs should new ideas into their teaching.

400 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Graduate Education in Transition

Design of Graduate Programs V aloes and Attitudes We strongly advocate greater diversity among graduate We must convey to students (and to the public at large) that programs to take advantage of existing and potential career mathematics is a lively, dynamic, and varied profession that opportunities as described in the previous sections. As has attracted inquisitive minds since the birth of civilization. pointed out in the Board on Mathematical Sciences report [4], It is important that both principal aspects of mathematics graduate and postdoctoral programs offered by mathematical be appreciated: its useful, indispensable role in science and sciences departments are the key to successful renewal of technology, and its continuing intellectual fascination over the profession and reform of mathematics education. There the ages. is a need for programs that are sensitive to the needs of Students entering graduate school in the mathematical individual students and that recognize broad options for sciences are presumably already interested in the subject different career paths, i.e., the personal mix of research, and exhibit some talent for it. The graduate experience teaching, outreach, service, and other professional activities should build on these advantages by further stimulating the that each student chooses. students' enthusiasm, and by both widening and deepening The first step in designing or reforming a graduate their mathematical knowledge. surfaces in reports such program is a realistic assessment of resources. What are the One important issue that always is the balance between research and teaching. Some talents and interests of the faculty? Are there prospects for as ours years ago, the scales may have tipped towards research, but regional cooperation with industry, business, government, they have begun to swing back to a proper appreciation of and colleges? Does the university possess strengths in other both aspects of the profession. Advocates of better balance areas that could lead to interdisciplinary or joint programs? urge that research be interpreted more broadly to include What is the department's track record in recruiting and other types of scholarship as well as specialized research placing students? What financial support is available for [16]. The need for educational reform has also given more research prospective students through teaching assistantships, importance to collaborative activities, to more stimulating assistantships, or internships? presentation of undergraduate courses, to the inclusion of Answering these questions, exploring opportunities, forg­ computation (symbolic, numerical, and graphical), and to ing links, and enlisting administration support will take fac­ emphasis on communication skills. These latter skills are ulty energy and dedication, but it is the best way to create a equally important in industry. In [17], Fan Chung of Bellcore viable program. Even established institutions with a strong makes that point forcefully: record of sending graduates to the faculties of research uni­ versities also place other of their graduates at comprehensive An industrial researcher interacts with a wide variety of universities, four-year colleges, and in industry. We hope people including engineers, computer scientists, physi­ to influence them to reexamine their programs and become cists, chemists, and business people. The effectiveness more aware of the diversity of their mission. For universities of one's work depends on the ability to convey the whose niche is less secure and for others contemplating new power and impact of mathematics as well as its beauty to explain mathematics programs, we urge them to strive for individuality and to try and elegance. It is quite possible terms to nonexperts. Even a good colloquium to meet some well-defined market needs. After a department in general talk involves several different levels of depth. Success­ has selected its goals, it must design a program that will ful communication not only transfers knowledge and realistically take into account the potential careers of the insight helpful to others but also brings up good prob­ students. lems, new directions, and interesting ideas. Of course, in industrial mathematics, for For a master's program not everyone is gifted with good communication skills. in addition to some core math­ example, one would include However, preparation and work can help make up the ematics, courses in modeling, in probability and statistics, difference. in computational mathematics, and in optimization. Clinics, seminars in industrial mathematics, case studies, and in­ For foreign students, it is particularly important to try ternships are all possible "practical experiences" that could as early as possible to gain proficiency in English, both be part of the program. Such a program could perhaps in speaking and writing. Although it is desirable to share some offerings with operations research or statistics preserve and cherish one's own ethnic heritage, it is programs based in other departments. essential to avoid cultural isolation and to thrive in both A Ph.D. program to prepare for college teaching would worlds when planning a career in this country. stress broadly based scholarship rather than narrowly focused Graduate students, both domestic and foreign, are sup­ research and would pay careful attention to curricular ported in large measure by teaching assistantships. Univer­ issues and to the goals of undergraduate education. The sities have the clear responsibility to carefully train and relations between the branches of mathematics and between supervise all teaching assistants, and, for foreign students, mathematics and other disciplines would be emphasized to to also make sure that they speak English well and are enable prospective college teachers to meet a wide range of sufficiently familiar with the sociology of the American professional responsibilities. classroom. Many of our universities already have such

MAY/JUNE 1992, VOLUME 39, NUMBER 5 401 Graduate Education in Transition programs in place. But, beyond this-to paraphrase the • Expand postdoctoral programs at government labora­ Mathematical Association of America report [11]- univer­ tories and help to fund postdoctoral programs in in­ sities should reward teaching assistants and junior faculty dustry and academic institutions. Establish postdoctoral who are performing well and should help those who are programs that combine research with preparation for teaching inadequately. Although university teaching is done teaching. largely by the lecture method, alternative approaches en­ couraging student initiative and collaborative learning are Industry being adopted successfully in many different settings. Such • Establish internships similar to those available in statis­ approaches can also be introduced on a limited scale in the tics. Expand summer employment programs. Provide graduate curriculum. Graduate students, being more mature appropriate postdoctoral opportunities. and motivated than the average undergraduate, do respond to • Cooperate with professional societies and universities well organized lectures presented in a challenging manner. to communicate the mathematical needs of the work­ Room can be made, however, for some problem-oriented place and to develop suitable programs in industrial seminars in which students participate actively and give mathematics. oral presentations of projects. Working in small groups • Recognize the industrial role of computational and ap­ also has benefits: it develops comradeship among students plied mathematics and help to establish industrial career and prepares them for the team approach encountered in paths for mathematical scientists. most research groups in industry, government, and even • Change managerial attitudes and financial practices to universities. take into account the long-term advantage of industrial innovation and technological development in achieving economic competitiveness. Recommendations • Cooperate with academic institutions and professional societies in the continuing professional development of Mathematical Sciences Departments employees. • Review existing and prospective graduate programs, taking into account the potential job market, faculty Professional Societies skills within and outside the department, and available • Jointly develop and disseminate career information for resources (including possible connections with local in­ graduate students. Provide an information service for dustry, school districts, and other academic institutions). currently available jobs and potential jobs. Investigate • Expose graduate students to some collaborative projects the possibility of a placement office. with oral presentations; prepare all students to become • Establish standards and goals for graduate programs. effective teachers or communicators of mathematics. Develop a list of existing programs with their special • Elevate Master's programs to professional status with features. well-defined goals related to specific market needs. • Provide a wide range of opportunities for continuing pro­ Examples include preparation for teaching in two-year fessional development, occasionally in cooperation with colleges and for industrial employment. societies in other fields, including programs for in-service • Establish a climate in which the spectrum of contribu­ teachers and programs relating to new technologies, to tions by the faculty is recognized and valued. Consider new fields of application, and to recent mathematical adopting guidelines such as those described in Boyer's developments. Involve regional chapters of professional "Scholarship Reconsidered." societies in these efforts. • Provide a supportive learning environment for all po­ • Develop and publicize a list of mathematical contribu­ tentially successful students, with the particular goal of tions in industry and government. Promote the industrial encouraging and retaining underrepresented groups. use of mathematics, mathematical models, and computa­ • Include computational mathematics as a component in tional mathematics. Develop an industrial liaison group all graduate programs. to help industry find appropriate specialists for particular problems. Universities • Organize workshops and conferences which bring to­ • Provide adequate resources to chronically underfunded gether prospective industrial employers and university mathematical sciences departments. faculty to discuss industry needs. • Establish a climate in which the spectrum of contribu­ tions by the faculty is recognized and valued. Consider References adopting guidelines such as those described in Boyer's 1. National Research Council, Everybody Counts: A Report "Scholarship Reconsidered." to the Nation on the Future of Mathematics Education, Washington, DC, National Academy Press, 1989. Government 2. National Research Council, Moving Beyond Myths: • Provide stable funding for Ph.D. students by balancing Revitalizing Undergraduate Mathematics, Washington, DC, teaching, fellowship, and research support. National Academy Press, 1991.

402 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Graduate Education in Transition

3. National Research Council, Educating Mathematical 11. Mathematical Association of America Committee Scientists: Doctoral Study and the Post-Doctoral Experience on the Mathematical Education of Teachers, A Call for in the United States, Washington, DC, National Academy Change: Recommendations for the Mathematical Prepara­ Press, 1992. tion of Teachers of Mathematics, Washington, DC, Mathe­ 4. Board on Mathematical Sciences, Actions for Renew­ matical Association of America, 1991. ing U.S. Mathematical Sciences Departments, Washington, 12. American Mathematical Association of Two-Year DC, National Research Council, 1990. Colleges Committee on Education, Guidelines for the Aca­ 5. Board on Mathematical Sciences, Renewing U.S. demic Preparation of Mathematics Faculty at Two-Year Mathematics: A Plan for the 1990s, National Research Colleges, (To appear 1992). Council, Washington, DC, National Academy Press, 1990. 13. Mathematical Association of America Committee 6. Schrage, Michael, "Mathematics Remains a Crucial­ on the Preparation for College Teaching, First Report: and Misapplied-Key to Economic Edge," The Washington "How Should Mathematicians Prepare for College Teach­ Post, 13 September 1991, page 02. ing," Notices of the American Mathematical Society, 36:10 7. McClure, Donald E., "1991 Annual AMS-MAA Sur­ (December 1989) 1344-1346. vey (First Report)," Notices of the American Mathematical 14. Glimm, James (Ed.), Mathematical Sciences, Tech­ Society, 38:9 (November 1991) 1086--1122 nology, and Economic Competitiveness, Board on Mathe­ 8. Madison, Bernard L. and Hart, Therese A., A Chal­ matical Sciences, National Research Council, Washington, lenge of Numbers: People in the Mathematical Sciences, DC, National Academy Press, 1991. Committee on Mathematical Sciences in the year 2000, 15. Ockendon, J. R., ECMI Newsletter, (March 1991). National Research Council, Washington, DC, National 16. Boyer, Ernest L., Scholarship Reconsidered: Pri­ Academy Press, 1990. orities of the Professoriate, Princeton, NJ, The Carnegie 9. Seitelman, Lee, "The Old Economic Rules No Longer Foundation for the Advancement of Teaching, 1990. Apply," SIAM News, 24:5 (September 1991) 6. 17. Chung,.Fan R. K., "Should You Prepare Differently 10. National Council of Teachers of Mathematics, Pro­ for a Non-Academic Career," Notices of the American fessional Standards for Teaching Mathematics, Reston, VA, Mathematical Society, 38:6 (June/July 1991) 560-561. National Council of Teachers of Mathematics, 1991.

~1'!-t~A.r,~.., (!u"'~'~) TRANSLATIONS OF MATHEMATICAL MONOGRAPHS ... 0 . liNDED \~ Introduction to the Classical Theory of Abelian Functions, Volume 96 A. I. Markushevich Markushevich's book presents an exposition of the fundamentals of the theoxy of Abelian functions based on the methods of the classical theoxy of functions. This theoxy includes the theoxy of elliptic functions as a special case. Among the topics covered are theta functions, Jacobians, and Picard varieties. In addition, the detailed historical introduction cultivates a deep understanding of the subject. Thorough and self­ contained, Introduction to the Classical111eory ofAbelian Functions provides readers with an excellent complement to the usual algebraic approach.

1991 Mathematics Subject Class!ftcatiDns: 14; 33 ISBN 0·8218-4542-X, 175 pages (hardcover), Feb. 1992 Indiv. member $74, Ust price $123, Inst. member $98 Your ordering code Is MMON0/96NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 403 Scientific Issues in Manufacturing Army Research Office Holds Workshop to Define Research Directions

Is manufacturing a fundamentally messy endeavor, with dies "gaps" in knowledge that need to be filled before successful forcing metal into a crude approximation of the ideal shape, knowledge transfer can be made. "house of cards" scheduling that collapses when delivery of The workshop brought together about thirty-five partic­ the right bolts is delayed, and cost considerations dictating ipants, mostly from departments of industrial or electrical quick and dirty solutions instead of careful planning? Or is engineering or statistics, though several were from mathe­ manufacturing a futuristic marvel, with visual sensors that matics or applied mathematics departments and a few from examine products for defects, robots transporting materi­ industry. Emerging from the presentations were a variety of als quickly and efficiently, engineers quickly and cheaply intriguing problems that tax scientific and technical abilities, cycling through numerous prototypes before hitting on the and a degree of disagreement on how to get at the underly­ optimal design? At a recent workshop on Scientific Issues in ing scientific problems that manufacturing poses, on whether Intelligent Manufacturing, the answer seemed to be, a little those problems can be solved in a cost-efficient way, and on of both. whether the scientific knowledge and the right mechanisms The workshop, organized by the Mathematics and Com­ are in place to get the problems solved. puter Science Division of the Army Research Office (ARO), was held March 7-8, 1992 at ARO headquarters in Re­ U.S. Industry Lagging search Triangle Park, North Carolina. A cargo train rumbled Forming the backdrop for the workshop was the declining past the skinny pines just outside the window of the ARO ability of the U.S. to compete in global markets. Part of conference room, providing a real-world counterpoint to the problem is that other countries can manufacture better much of the high-tech talk at the workshop: there are a products at lower cost and can introduce improvements lot of great ideas for making the world more efficient, but more rapidly. In addition, points out Anil Nerode of the old technology dies hard, sometimes for good reason, and Mathematical Sciences Institute at Cornell University, many sometimes for no reason at all. companies, such as General Electric, Honeywell, and Boeing, Why is the Army interested in manufacturing? Isn't there are cutting back on their long-term research staffs. Industry a whole defense industry set up to cater to its needs, from and government do not recognize the importance of both Patriot missiles to $1000 toilet seats? Not for much longer, basic and applied research to manufacturing, he says. says Jagdish Chandra, director of ARO's Mathematics and Other problems haunt U.S. industry as well. Ideas for new Computer Science Division and organizer of the workshop. industrial processes sometimes never get put into practice In addition to responding to a government-wide initiative in because of uncertainty over whether the Environmental manufacturing, Chandra explains that, in the future, it won't Protection Agency (EPA) would approve them, says Nerode. be economically feasible for the Department of Defense Countries like Taiwan, Malaysia, and the Philippines can (DoD) to rely on an industry that's dedicated to DoD needs do things that American industries cannot because those and shielded from competition. As a result, he says, the countries have fewer environmental restrictions. Nerode DoD must support a research base that will contribute to doesn't advocate neglecting environmental concerns, but he efficient, flexible manufacturing so that other companies raised questions about whether some EPA regulations really will be able to manufacture the products the DoD needs. make sense. One famous example occurred when New York In addition, the ARO has a mission to support the science City was forbidden by the EPA to put its waste into the and technology research base. He notes that mathematics land, the water, or the air, so it put its trash on barges that and computer science provide the fundamental tools in such floated out at sea for a number of years. In the future, he areas as simulation, prototyping, and control, so his division noted, it will be crucial for industry to not just model its has an interest in supporting this kind of research. The products and processes, but its waste as well. purpose of the workshop, he says, is to identify scientific Another problem is that academia-which is where much issues in mathematics and computer science that will help of the nation's basic and applied research is done-often to solve manufacturing problems, and especially to pinpoint doesn't understand the needs of industry. James Solberg is

404 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Manufacturing Workshop

in the school of industrial engineering at Purdue University the division of applied mathematics at Brown University and is director of Purdue's Engineering Research Center for described some applications of machine vision to manu­ Intelligent Manufacturing Systems, funded by the National facturing problems. Although the power of machine vision Science Foundation. Solberg says that, for example, many was initially oversold, it has become an important tool in people in academia make careers out of applying operations many industries. A tough problem for visual inspection of research ideas to scheduling problems, but this research is products is the recognition and classification of defects. "laughed at" in the manufacturing world because it simply Defects aren't always easy to identify: is it a dust particle, does not apply to the problems industry is trying to solve. or is it a scratch? Development of machine vision has not As another example, he pointed to some research he reached a point where it is easily applicable to a wide range had done in the early 1970s on flexible manufacturing of problems, McClure says. systems-that is, systems that can be easily adapted to Cheeseborough-Ponds, which manufactures vaseline, has manufacture a variety of products. Since then, many other successfully used machine vision in a controlled situation. papers have been written that cite his initial work. He made At the end of the production cycle, jars of vaseline are run some simplifications in his research, and the later papers by a machine vision system which examines each jar for became increasingly abstract and farther removed from the misalignment of the label and lids that aren't screwed on original problem. At a recent conference on research in properly. If a jar is defective, an air jet blows it off the flexible manufacturing, he says, very few of the participants conveyor belt. Because the vision requirements were very had actually seen a flexible manufacturing system in action. specific, this system was not difficult to set up, and it turns Because of this tendency toward abstraction and distance out to be far more efficient than having people inspect the from real-world problems, flexible manufacturing has be­ jars. come a "dirty word" in the real world of manufacturing, Another example McClure discussed is optical character says Solberg, and some important opportunities have been recognition which, being a two-dimensional problem, is missed. easier to handle than three-dimensional machine vision. On the other hand, Solberg points out that industry is Optical scanners that can convert a printed document into not always as open-minded as it could be. He says he's a computer text file are nowadays available for personal been working on the development of low-cost mobile robots computers. However, McClure says this problem is fairly that could move materials around in factories, which he easy to solve, since it involves standardized characters said would save money in some situations. But industry just printed in black on a white sheet of paper. A more isn't biting, because they don't see the handling of materials difficult problem is posed by silicon wafer manufacturing, as a problem. Jokingly, Solberg described the reaction this in which an eighteen-character identification code is etched way: "We can buy K-Mart wagons and hire people to move in a standardized font onto each wafer. Various steps in materials, what do we need robots for?" the processing of the wafers can deface this code so that its characters no longer conform to the standardized font. McClure says the aim here is to develop algorithms for processing the visual information that are insensitive to the variation in appearance. This approach-finding methods that are insensitive to variation-is credited to Genichi Taguchi, a Japanese indus­ trial consultant. Ramon Leon of the statistics department of the University of Tennessee at Knoxville described another example of the "Taguchi method." A Japanese tile manu­ facturer would stack tiles onto a conveyor that would pass through the oven. Because the oven heat was not uniform, and because of the way the tiles were stacked, some tiles would come out thicker than others. Two obvious-and costly-solutions are to install fans to even out the oven heat and send through fewer tiles at a time. Instead, Taguchi proposed raising the lime content from 1% to 5% in the tile Prototype of cable driven robotic hand for endoscopic surgery. Photo cour­ clay, which makes the clay less suceptible to variations in tesy of B. Smallridge, D. C. Deno, S. Sastry, J. Wendlandt, Robotics Laboratory, temperature. Because lime is cheap, this turned out to be a University of California at Berkeley. cost-effective solution. In a number of situations described during the workshop, this idea of finding and adjusting the right control parameters turned out to be an important Some Success Stories method in solving a range of manufacturing problems. Despite these problems, there have been some clear success Medicine is another area that poses intriguing problems stories in which theoretical research has helped to solve for the development of intelligent systems. Although this some important industrial problems. Donald McClure of was not a focus of the workshop, Shankar Sastry of the

MAY/JUNE 1992, VOLUME 39, NUMBER 5 405 Manufacturing Workshop

electrical engineering and computer science department at science could inspire development of analogous structures the University of California at Berkeley described some in manufacturing. For example, a computer manipulates work he had done on a robotic device to remove polyps symbols while a manufacturing system manipulates parts; from the stomach or intestine. In endoscopic surgery, the machine language in computer science is analogous to con­ physician inserts, either through the mouth or the anus, a troller language in manufacturing; the output of a computer device that feeds visual information to a television screen. program is like the product and waste from manufacturing, Watching the screen, the physician can then use the device to and so on. Nerode put up a list of perhaps twenty such grasp the polyp, cauterize its base, and remove it. Sastry and parallels between the two areas. What is needed, he says, his coworkers have built a prototype device with a "glove" is a manufacturing "Turing machine"-a generic system that gives the physician, in addition to visual information, a that could serve as a foundation for modeling manufacturing sense of feel-an important factor, partly because the polyps systems. Of course, manufacturing runs into messy problems move around and are not easy to grasp and partly because in physics, while computer science stays in the neater realm whether a polyp feels hard or soft can give an indication of symbols, but Nerode made a persuasive case for an of malignancy. To test this device, the physicians Sastry intellectual basis for the parallels between the two areas. works with set for him a "grape-plucking" test, in which the Roger W. Brockett of the division of applied science at device had to grasp a particular grape on a bunch of grapes, Harvard University brought up some similar issues in the cauterize its base, and remove the grape without breaking it. area of motion control. Is there a way to describe motion The device cleared that hurtle, and Sastry says he expects it in terms of motion "primitives"? Can a computer language to be available within the year. be developed that would manipulate geometric data in the way that computer languages can now manipulate symbolic Ambitious Research Agendas data? Agreeing on a generic representation is crucial, he Some of the participants laid out fairly ambitious research says, because if representations of motion control are not agendas. Sastry presented a position paper on "rapid pro­ device-independent, then the engineering costs for using totyping," which he believes is the key to developing high them are prohibitive. He pointed to Postscript as an analogy quality products quickly and easily. He directed his remarks for what could be developed in motion control. In wide use toward what he called "mechatronic" devices, though his for typesetting and publishing, Postscript is page descriptor ideas extend to other products as well. Mechatronic is short­ language that can be used on any output device, be it a hand for eletromechanical-that is, electronic systems that printer or a terminal, that has a Postscript interpreter. Before control mechanical devices. One example is the antilock Postscript, the way a printed document looked depended on brake mechanism option available on new cars. Even though what kind of printer was used. Although Postscript is not the mechantronic gadget used in antilock brakes only costs perfect, Brockett notes, it is simple, portable, and in wide about $150 to manufacture, Sastry says that the antilock usage. He hopes that something similar can be developed brake option typically costs the consumer between $1200 for computer representation of motion. and $1500. It took the automobile companies so long to develop and create prototypes for the mechanism that they must amortize their investment over several years of sales. Sastry's research agenda aims at a "rapid prototyping environment," a neglected area of manufacturing that falls between basic research and production. The main idea is to provide an interface between a graphics package and a three­ dimensional "printer." In this scenario, a designer could use a CAD graphics package to generate a visual design of a mechatronic device. Information about various parts of the device are then fed to a three-dimensional output device that creates a prototype out of machinable wax, and the parts are assembled by robots. At each stage, the designer can examine the parts and and see how they fit together, not just by looking at a representation on a computer screen, but by actually handling the prototype. As Sastry points out, having a three-dimensional object to examine provides H. Kazerooni with a prototype for his robotic "extender" that allows hu­ immediate intuitive information that a picture on a computer mans to lift heavy objects. Photo courtesy of H. Kazerooni, Department of screen simply cannot communicate. All of this must be done Mechanical Engineering, University of California at Berkeley. quickly and cheaply, so that the designer can modify the Such problems are difficult because of their generality, design and cycle through a number of prototypes. which makes the lack of theoretical results a major obstacle. Nerode also had some ambitious ideas for manufactur­ Sometimes if one's aims are more specific, more sophisti­ ing, though his ideas were of quite a different type. He cated results are possible. This approach is seen in the work believes that many of the theoretical structures in computer of H. Kazerooni of the department of mechanical engineer-

406 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Manufacturing Workshop ing at the University of California at Berkeley. Among a drift toward the larger, more theoretical problems. Because number of robotics projects he described, one was partic­ his work is practical, task-specific, and easy to understand, he ularly intriguing: a robotic "extender" that assists people asserts, program officers pass it over in order to fund "sexy" in lifting objects so that, for example, a 500 pound object research on universal problems, despite the uncertainty of might feel like ten or fifteen pounds. Kazerooni showed the return on investment in such theoretical areas. There is drawings depicting various designs of this device that could value in trying to tackle universal problems, he believes, but be used for different kinds of lifting-one showed a man too much money is going in that direction, especially given using the device to load baggage into the cargo hold of an today' s tough economic times. As Kazerooni hammered airplane. Kazerooni says he was motivated in part by the away at his point, uneasy laughter spread around the room, large number of back injuries in various professions because for most of the workshop participants were of a theoretical of too much heavy lifting, and he has found enthusiastic bent. interest in industry. Having a human control the extender Although many seemed to find Kazerooni's views ex­ avoids the complication of programming a computer to treme, everyone agreed that there are major cultural obstacles control the device. that need to be overcome if theoretical research is going to have an impact on manufacturing. For academics, solving nitty-gritty problems in industry is too often a thankless job: "Universal" Problems, or Usable Solutions? it's not the kind of thing that impresses a tenure committee. A late addition to the workshop program, Kazerooni brought For its part, industry often neglects the development of the up some uncomfortable points that the organizers probably theoretical research that could insure its future strength. In hadn't bargained for. His aim is to build robotic devices the end, it appears that these kinds of sociological problems to perform a specific task, and he decried the trend toward are almost as daunting as the scientific ones. trying to solve "universal" problems to the exclusion of getting the job done. He says he constantly has to redi­ Allyn Jackson rect his students to the task at hand, for they automatically Staff Writer

Mathematical World Volume 2

Fixed Points ------I I I I Yu. A. Shashkin I B, v=x: 'l

All prices subject to change. Free shipment by surface; for air delivery, 1991 Mathematics Subject Classifications: 01, 54 please add $6.50 per title. Prepayment required. Order from: ISBN 0-8218-9000-X, 77 pages (softcover), December American Mathematical Society, P.O. Box 1571, Annex Station, Providence. RI 02901-1571, or call toll free 800-321-4AMS In the 1991, Individual member $19, List price $24 continental U.S. and Canada to charge with VISA or MasterCard. To order, please specify MAWRLD/2NA Canada residents, please add 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 407 The Agency That Came in from the Cold Richard J. Shaker

When pressed to describe mathematical subjects es­ pecially useful to us, we list algebra, number theory, Richard J. Shaker is Chief of the Office of Mathematical Research every at the National Security Agency (NSA). Following are excerpts combinatorics, probability and statistics, but, in fact, from his address at the Joint Mathematics Meetings in Baltimore important subject area in core mathematics has proved valu­ on January 8, 1992. able. Our mathematicians have used both the mathematics they have known well-their area of specialization-or the mathematics with which they were merely familiar-areas I work for a wonderful agency that does marvelous things in which they had a single graduate course, or studied for we cannot tell you about. Our public affairs office is paid for the first time after coming to NSA-to solve our problems. the number of column inches that do not appear rather than When selecting mathematicians for hire, we are not overly the number that do. They were pleased when the program influenced by their area of specialization: we look for a solid listed my affiliation as the National Security Administration, record of accomplishment in core mathematics and evidence although they would have preferred Social Security Admin­ of strong problem solving ability. Besides using mathematics istration (or our most common mistranslation, the National to solve our current problems, after solving them, we use Aeronautical and Space Administration). Throughout this mathematics to understand what we have done. The abilities Baltimore area, thousands of individuals tell store clerks of mathematicians to abstract, to generalize, to characterize, or Department of Motor Vehicle officials that they work to prove theorems, are all important to us. We have several for the Defense Department-the cogniscenti among those examples where an idea or a technique used to solve one clerks say, "Oh, you mean NSA." Our Director, a charming, problem has been developed into a major internal NSA wonderfully people-oriented leader, makes but two or three subject matter, a local paradigm, used for over a decade to public appearances a year. Yet, one of Admiral Studeman's solve a number of other problems more important than the rare appearances in 1989 was to address these societies, then original problem ... convened at Phoenix. Mathematicians are now instructed It is well known that we do a great deal of computing to display the National Security Agency, rather than the on a number of state-of-the-art computers; less well known Defense Department, on their name tags when attending that our top programmers are pure mathematicians who can, professional meetings. This exception from anonymity for at a moments notice, turn off their programming skill and mathematicians and mathematics by an agency that craves work in the rarified atmosphere of pure mathematics, though anonymity was not given lightly-only after we realized their most typical mode is to do both simultaneously. The that mathematics, a vital resource for the United States-a relationship between empirical and theoretical is synergistic, resource essential not only for our industry and science but with neither driving the other out. No matter how powerful also for our security and defense-was not receiving support our computers, we need them to be more powerful. Our best commensurate with its national importance. cryptomathematicians make them more powerful with subtle Even more than in the forties, when the great math­ coding and aggressive use of leading-edge architectures. ematicians played vital roles in the dramatic successes of When needed, our mathematicians have taken the lead in cryptanalysis during World War II, mathematics is the fun­ designing special purpose computers for especially effective damental science supporting the creation and analysis of the cryptanalytic applications. To do this, they have had to learn complex algorithms that protect vital communications. Not new concepts and subject matter, but their understanding of surprisingly, the NSA has a constant requirement for mathe­ the cryptanalytic problem and the underlying mathematics maticians in our work. We need well-trained mathematicians has been indispensable. Although they have worked closely not simply because they are well trained in the deductive with engineers and computer scientists, they could not be thinking needed in cryptanalysis-we need them because replaced by them. graduate-level mathematical concepts, ideas, and theorems Clearly, we need a healthy U.S. mathematical community are needed to solve our problems ... as a source for technical staff. More subtly, we need a

408 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·················-·····-·-···------The Agency That Came in from the Cold healthy U.S. mathematical community because no matter funding in innovative and worthwhile new programs ... how skilled our staff are, and how well they are able NSA has undertaken a number of new initiatives follow­ to apply mathematical technology to cryptologic problems, ing the 1987 meetings, in addition to our grants program there are always important new developments in mathematics and increasing participation in open research and national that seem very abstract, that seem unrelated to what we meetings. We have established a formal sabbatical program are doing, but through some miracle (sometimes referred so that you can visit us, work with us for a year or two, to as the "unreasonable effectiveness of mathematics") are and continue to remain affiliated with your university and exactly what we need to solve the important problems of participate in your university's retirement program ... We the present. For our access to the cutting edge of the "new have also constructed a program for NSA mathematicians mathematics" to be most effective, we require a strong to return to academe . . . We committed, early on, to pro­ U.S. mathematical community to help keep us informed, vide core funding for the Mathematical Sciences Education and we can best learn from you if you can take the time Board (MSEB), and, better than money, sent them one of to learn what we do. We have benefitted greatly from our best and most energetic mathematicians, Kevin Colli­ visiting academic mathematicians who have worked directly gan, on a one-year, non-reimbursable detail. With mixed on our problems, in a succession of summer conferences, feelings, we said goodbye to Joan Donahue, a fine mathe­ or on their sabbaticals, or as consultants. They have solved matician, technical manager, and leader of our educational important problems and enhanced our old technology, but, reformists, who left us to become a full-time member of more importantly, they have played a vital role in exposing the MSEB staff. We built on our MSEB connection by us to new ideas and new mathematics, some of which we meeting through them and becoming involved with the have continued to use for many years ... National Council of Teachers of Mathematics, the Alliance I am going to describe 1987 as the beginning of a to Involve Minorities in Mathematics, the [Mathematical time period when, because of concern for the health of Association of America's] SUMMA committee, and other mathematics in the United States, we began to overcome national-level efforts. We have been active in outreach pro­ our introspection and circumspection and "came out of the grams to historical black colleges and universities and other cold" to become more active citizens in the mathematical minority institutions; this year, many of our mathematicians community, but we have had important interactions with will be involved in HBCU/MI (Historically Black Colleges mathematics throughout our four decades ... and Universities/Minority Institutions) support efforts. We In 1987, we opened up the NSA twice, for two days participate in a wonderful program, the National Physical each, to 100 leaders of the U.S. mathematical community, Science Consortium, where we support a number of new letting them into the "Puzzle Palace" without requiring women and minority mathematicians each year for up to them to fill out extensive forms, be fingerprinted, or take six years through their Ph.D. studies-more important than a polygraph examination. Some thought that the reason merely sending checks, we meet the fellows, expose them to for these conclaves was a dramatic announcement: that we the excitement of NSA problems, and mentor them. At the intended from our limited technology budget to provide $2- state level, we have been a key player in the early efforts $3 million annually in grant funding for undirected (by us) to establish the Maryland Mathematics Coalition, a broadly mathematical research. I was pleased to have been correct in representative group of government, industry, and education my prediction that our 100 visitors in 1987 would be more leaders promoting mathematics education reform throughout interested in us than in our money. Several of the visitors the state. commented to me that the most important thing they learned I want to discuss in more detail two NSA programs that about NSA was that it was populated by the same kind of contribute to the health of American mathematics, that play people they worked with in their universities, which they to our strength and that are new since 1987. The first is a meant neither as praise nor criticism ... cherry-picker program. It hopes that despite all that is wrong In a two hour discussion period during the first of the with our educational system, we can discover some gems two 1987 meetings, you gave us guidance on how we should near the end of the pipeline and provide that last little push administer our new grants program. Many of our visitors to get them through. It is a program where it is easy to see had a lot to say. Everyone seemed to have a pet project, accomplishments. The second is harder. It is like throwing an area, an initiative, or a niche where funding was needed, a pebble in the ocean. It is more controversial. funding which would have great benefit to the research The first intervention program [the Director's Summer community and thus to the health of American mathematics; Program (DSP)] I want to tell you about belies the notion yet funding that for some reason was not being provided that we have problems with our educational system ... by anyone else. We listened intently and constructed our We began in late 1989 to aggressively seek out top young program accordingly. We have continued to listen. Under the undergraduates who showed great promise and interest in leadership of Brent Morris, Marv Wunderlich, and Charlie mathematics and expose them to our exciting problems. Osgood, we have, for four years, been running a program that Many thought we were doing this as a long-term recruiting the David II report praised, not only for helping in dollar program. Indeed, we were recruiting, but for mathematics, terms reverse the severe downward trend of government not for NSA. Our interest and intent was to use a summer funding of mathematics in real dollars, but for providing the experience with us, preferably between the junior and senior

MAY/JUNE 1992, VOLUME 39, NUMBER 5 409 The Agency That Came in from the Cold year, to provide direct evidence that mathematics provides two were performing exceptionally well in their current, both subject matter and training for challenging careers ... demanding academic program, and, ironically, made the We had hoped for a few more, but we were still pleased that most direct contributions to the most significant bottom-line eight were able to stick it out through the processing and results of the workshop. One, according to her father, might come, because they were eight very special young people. have gone on after taking a year off or might not have. But We were hoping that we could put these eight in a she came home from the DSP with a surge of confidence, room by themselves, working on our best problems, so that applied to all the top graduate schools, and is now in a the experience would be strongly peer-interactive, but such Ph.D. program on a National Science Foundation (NSF) an aggressively structured experience could only be pulled fellowship. The other had no intention of going on. After off if our top mathematicians took on technical director two weeks, she wanted to become an NSA employee. She responsibilities. The demands on our top mathematicians are would have been a fine one, and still may well be one, but incredible. They have too much to do, they have earned we talked her out of joining us right away. A joint math, the right to do what they want, they most enjoy solving computer science major through her junior year, she took our hardest problems, they are most rewarded for the work all pure math courses her senior year and is now in graduate they do in solving our problems. Yet, the first two of our school in a Ph.D. program on a fellowship. top mathematicians that we asked to lead the 12-week DSP The 1991 DSP was also very successful. We had more not only said yes, they worked hard during the spring to time to canvass the nation systematically, which we did prepare for the students, identifying and developing the best through the good auspisces of the MAA. With the 1990 problems to present them. When one of them was asked how success, it was easy to recruit top technical directors. They he had the time to nursemaid eight students, he responded, led a larger group of participants, including some 1990 "Did you see their resumes?" returnees, to complete solutions to three problems and The first two weeks of the workshop were extremely significant results on four others ... difficult, for the technical directors and the students. The The second, broader NSA initiative we now call the students had to learn decades of NSA-developed technology NSA Mathematics Education Partnership Program (MEPP). in two weeks, as well as a myriad of details about the four Inspired by the 1987 meetings, our mathematicians, some of problems presented them. During these two weeks, some whom had been active in educational support projects earlier, learned to program for the first time. All were proficient initiated, doubled, or redoubled their efforts. NSA volunteers programmers by the end of the summer. One, who had no went to high schools to talk on mathematics, cryptology, computer science courses on his transcript, taught everyone and other exciting applications of mathematics. As they C in half a day. Another, who also had no computer science built up their courage, they dared to venture into the middle courses on his transcript, didn't like our setup and so wrote and elementary schools, where it was scarier to talk to the a special operating system for the group. By the third week, students, because they were so young and so small, but where the students knew everything there was to know about the the potential impact was greater. In response to numerous problems, had developed their own suite of programs, had requests from the schools that we visited for a list of talks we broken into overlapping groups, and knew NSA slang and were able to give, one mathematician volunteered to produce jargon so well they sounded as if they had worked for us a brochure listing all the talks all NSA mathematicians were for ten years. We had five Sun terminals connected to the willing to give. He discovered through a nightmare year CRA Y in the room for the eight students and two technical how difficult it was to prepare such a brochure. But his directors, but we had to add three more. Optimists like me effort led to a well-defined speakers' bureau with a fixed set expected the students would make substantial contributions of offerings, along with an expressed willingness to prepare to all the problems they worked on. They did. We expected customized talks at teacher's requests. The popularity of this them to come up with innovative, new ways of looking program built over the years-in 1991, NSA speakers made at our problems. They did. We did not expect them to 230 forays into the three local counties, often presenting obtain significant bottom-line results. That's where we were multiple talks. NSA was approached to find volunteers for wrong. On the fifth and tenth weeks, they obtained very coaching mathematics teams in high schools, to lead science important results substantially solving two of the problems, enrichment programs in elementary and middle schools, and convincing the last of the skeptics that this program was to provide faculty at summer mathematics camps for gifted very worthwhile. Clearly, we were rewarded for trying to do and talented students. For each program, volunteers were a good thing. But the real payoff was not the contributions identified and NSA management supported these efforts. to our product, impressive as those contributions were. The At our initiative, our mathematicians presented two three­ real payoff was to the pipeline. day workshops to middle and high school teachers on the Incredibly, before they met us, two of our DSPers, application of mathematics to real world problems ... juniors, had not been planning to go on to graduate school After four years of active volunteer activities, a thousand following their senior year. They had outstanding academic points of light, we have decided that our support of K-12 is credentials. Some of the others had been off to faster starts, important enough to institutionalize it. Last month, Admiral taking an incredible assortment of undergraduate and even Studeman formally established the MEPP after fifteen se­ graduate level courses while in high school. But these nior mathematicians representing all the NSA mathematical

410 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The Agency That Came in from the Cold elements prepared a hard-hitting, enthusiastic report urging they might never have been exposed to had we not been creation of the office. We will continue to depend on the bringing on mathematicians for cryptography and cryptanal­ spirit and enthusiasm of our hundreds of volunteers, but we ysis. They provided big breakthroughs needed for our work believe there are benefits to establishing a single contact in communications, engineering, speech research, signals point and employing a small staff of mathematicians in processing, and the design and implementation of powerful, full-time planning and coordination. At a time of austerity, specialized computers. In doing this, they worked closely when we do not have enough mathematicians to tackle the with engineers, computer scientists, physicists, and lin­ expanding number of problems we face, it takes a sense that guists. Although at times distinctions in background blurred educational support is very important to dedicate even three as scientists worked on common problems, the ability of mathematicians to the program. We are also proud of who mathematicians to understand mathematical foundations and they are--one senior and two mid-career mathematicians employ mathematical analysis has been vital. Appreciation taking two years out from successful careers breaking codes, and respect for mathematicians among NSA managers who then to be replaced by other working mathematicians ... do not have hands-on experience in cryptanalysis and cryp­ Just as in the greater mathematics community, these tography comes in part from respect for the cult of the activities began in controversy at NSA, not the result of codebreaker but, also, and significantly, in part from the concerns of lawyers or agency managers, but concerns of demonstrated usefulness of mathematicians on projects that working mathematicians that we should not get involved, managers understood quite well but had not realized math­ that we're not the right people to help solve the problem, that ematicians would be so useful on; perhaps did not realize the problems are too hard, that they're beyond our scope, they would be useful at all. that they're societal problems, that we have a job to do, that Just as the David committee understood it was naive we're being paid to break codes, that "real mathematicians to expect that the government would discover on its own don't do K-12." But as we have convinced ourselves that the need to fund research in mathematics, it is naive to our long-term health is our concern and that we do have believe we can sit back and have industry discover math­ something to offer, we have ignored those voices rather than ematics. NSA can help a little by sharing the message it argued with them, and we have really had a wonderful time. has brought here with the captains of industry-it does try The excitement of contributing to the long-term health of to do this, whenever it can, but perhaps it needs to do our profession and the satisfaction that comes from sharing this more systematically, more deliberately. Perhaps your our excitement about doing mathematics is a real reward "power structure" can lobby industry or, further up the that more than makes up for time "away from the job." pipeline, the business schools, educating them on the value In the same way that presenting twelve talks in Baltimore of mathematicians in yet another outreach program. Math­ is perhaps more important for us than it is for you, these ematicians in industry need to convince their management, outreach activities that I've described help us understand when they do a fine piece of work, that they have been the importance of belonging to a larger community and able to do it not just because they are brilliant but because continuing to contribute to our profession. they are mathematicians. National and state consortiums Now that you know we're good guys, you'll be pleased of employers of mathematicians to support education can to hear that we're not going out of business. Cryptology add "employment" to their agendas, as I understand the remains a vital mission. The world is still a dangerous Maryland state coalition has. But without waiting for others, place, a volatile place. The need for our decision-makers there is much you can begin to do at a "grass roots" level. to be as well-informed as possible has not diminished. But At a minimum, we need enhanced awareness on the part I would be less than candid if I did not admit that we of research mathematicians of how mathematics is used are facing more then a little bit of austerity. It has not yet in industry. We need top research mathematicians to take gotten to the point where we have to conduct a bake sale occasional sabbaticals in industry so that, if for no other or collect grocery receipts to buy our computers (we do reason, they can develop perspectives and contacts that help collect grocery receipts for the local schools), but although them be broader in their ability to counsel their students on NSA is a national agency with a national mission, a large employment opportunities. We need Ph.D. advisers to keep part of our mission supports Defense, so we cannot expect in touch with their graduates in industry, as well as their to be immune from the draw down taking place in Defense. graduates in academia, to learn what they're doing as well But the consistent ability of mathematicians to understand as how they're doing. We need mathematics departments and solve the difficult problems we face has encouraged to be involved in helping undergraduates find summer jobs our management, very few of whom are mathematicians, to working with mathematicians in industry that will encourage prioritize the hiring of mathematicians first and foremost ... them to remain mathematicians. We need Ph.D. advisers to As an insular NSA cryptologic mathematician, I believe care about what permanent jobs in industry their graduates cryptography is a unique subject perfectly suited for the are taking as much as they care about what faculty positions science and art of the mathematician. But can it be all they're taking. We need our mathematicians in industry to that unique? ... [O]ur mathematicians do more than classical be employed in jobs where they can make a difference, cryptology. They have proved indispensable in project areas well-mentored to maximize the probability that they will.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 411 The Graduate Student Cohort, Doctoral Department Expectations, and Teaching Preparation Bettye Anne Case and M. Annette Blackwelder

for white males, and for U.S. citizens than for noncitizens. Because graduate students will supply most of the new The following reports on a survey conducted by the Committee on Preparation for College Teaching, a joint committee of the AMS, entrants to the professoriate, efforts toward change must the Mathematical Association of America (MAA), and the Society address underrepresentation within the graduate student for Industrial and Applied Mathematics (SIAM), chaired by Bet­ population. tye Anne Case. Both authors are members of the Department of Mathematics, Florida State University. Description of the Survey and Responses The Committee's survey was designed to provide infor­ mation about the race, sex, and citizenship characteristics Introduction of the graduate student cohort and about the preparation As requested in 1987 by the presidents of the AMS, MAA, for future teaching and attitudes about teaching in graduate and SIAM, the joint Committee on Preparation for College departments. The survey, formulated with the assistance Teaching was established with the following charge: of the AMS-MAA Data Committee, has two stages. First, a questionnaire was sent to doctoral departments in May To make recommendations concerning the appropriate 1991 with the Data Committee's Annual Survey of New preparation of college teachers of mathematics, taking Doctorates; the results of that survey are presented here. into account the varieties of institutions of higher The second stage is a follow-up survey, to be conducted education, the diversity of the mathematical sciences, during Spring 1992, to collect information about retention the backgrounds and career interests of college students, in doctoral programs of the entering 1990-1991 graduate the impact of computers, and insights from research on student learning. student cohort. Doctoral departments are divided into six groups [G]. A description of the committee's early work and recom­ Groups I, II, ill, and Va fall within the purview of the mendations is found in its 1989 First Report [CT]. Finding Committee's charge and hence were included in the survey. no existing models that embodied their recommendations, The excellent response rates, shown in Table 1, lend the Committee secured funding from the Fund for the Im­ confidence to the data. provement of Postsecondary Education, U.S. Department of Education, to conduct a survey and to promote adoption of TABLE 1 its recommendations. The project currently involves devel­ Departmental response rates opment of programs in eight doctoral departments.* as well as the survey. This article presents findings from the first Group I 36 of 39 stage of the survey. Group II 41 of 43 The wider scientific community is concerned that future Group Ill 65 of 86 faculty members be representative of the various U.S. citizen 11 of 16 population groups. It is well known that women, and Blacks Group Va and Hispanics of both sexes, are underrepresented in the mathematical community relative to their proportion in the Total 153 of 184 population. Annual data continues to show the same pattern The data about New Doctorates presented in this report of underrepresentation among new doctorates [D]. Further, is derived from the Annual AMS-MAA Survey [D] and is anecdotal information suggests that persistence through presented for comparison purposes. graduate school is lower for underrepresented groups than Sex, Race, and Citizenship Data *University of Cincinnati, Clemson University, Dartmouth College, Uni­ versity of Delaware, Harvard University, Oregon State University, University The survey sought to classify students into six racial of Tennessee, and Washington University. categories: Asian, Pacific Islander; Black; American In-

412 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ••••••••• • ••••••••••••••- I 1 'li!J. • ·. -.··•-""""""""""'""-""-"'"''""""-""-""-""""""-"""""""""""-""~--·••••w-•-·-•w••••--··••--•••- Committee Survey

dian, Eskimo, Aleut; Mexican American, Puerto Rican or Doctoral Department Entrants are U.S. c1t1zens-a fairly other Hispanic; None of the Above; Unknown. There were high percentage compared to the 56% among All Graduate four classifications for citizenship: U.S.; Canada; Other; Students and the 45% among New Doctorates. Although Unknown. Each department was asked to provide this in­ these numbers may appear to promise a larger proportion of formation for women students and for men students who U.S. citizens among future crops of doctorates, the situation first entered the department's program between June 1, 1990 is not so simple. For example, anecdotal reports from some and May 31, 1991, and whose highest degree was a bach­ departments indicate that the proportion of U.S. citizens elor's. The departments also provided race and citizenship who persist to the doctorate is significantly lower than that information for students entering in that time interval with of non-citizens. Retention will be investigated in the second a master's degree, and for all full-time graduate students stage of the survey. enrolled. Findings about graduate students will provide a (It should be noted that the numbers for All Graduate baseline for retention data to be collected in the second stage Students include, for the reporting departments, their 1991 of the survey. doctoral recipients. The cohorts of lines 1 and 2 do not overlap and are combined for line 3; also, cohorts of lines 3 Academic Expectations and the Teaching Climate and 5 are included in that of line 4.) The survey included questions about the expected prepara­ tion of incoming graduate students and about preliminary and qualifying examinations. Information was also collected TABLE 3 about teaching duties assigned to graduate students in the Percentage of U.S. citizens in department, preparation for those duties, and any additional Groups I, II, Ill, and Va among: activities in preparation for a future professorial role. Ques­ tions about teaching awards and the importance of teaching 1. 199Q-1991, Doctoral Department Entrants qualifications in hiring decisions were included as indicators with Bachelor's Degree 69% of the importance attached to teaching and the teaching climate in departments. 2. 199Q-1991, Doctoral Department Entrants with Master's Degree 41% U.S. Citizen and Underrepresented Population Groups among 3. 199Q-1991, Doctoral Department Entrants with either a Bachelor's Degree or a Master's Graduate Students and New Doctorates Degree 62% Education Level of Doctoral Department Entrants 56% Most entrants-74% of the 2,805 reported by surveyed 4. 199Q-1991, All Graduate Students departments-into doctoral programs hold only the equiv­ alent of a U.S. bachelor's degree. Of the U.S. citizens 5. 1991 New Doctorates 45% entering doctoral programs, 83% (of 1,693 reported) hold only a bachelor's degree. For Group I departments, this percentage is higher still, 88%. The remainder of reported entrants hold the equivalent of a U.S. master's degree. Women among U.S. Citizens With respect to their proportion in the workforce, women TABLE2 are underrepresented among mathematical scientists of all Percentages of doctoral department entrants types. Statistical and anecdotal information about this un­ holding only a bachelor's degree derrepresentation is well known and is collected in several papers and their references in the Notices, September 1991 Non-U.S. [B, Ha, He, J, L, S], as well as in the previously cited U.S. Citizens Citizens All Entrants statistical reports [D). Group I 88% 67% 79% This underrepresentation is strongly exhibited among Group II 81% 53% 70% faculty and students in the mathematics doctoral departments Group Ill 81% 55% 73% comprising the population of this survey-Groups I, II, III, Group Va 74% 58% 68% and Va. The Annual AMS-MAA Surveys report for Groups All Dept. Groups 83% 59% 74% I-V that 24% of the U.S. citizen new doctorates are women. However, within Group IV, the analogous figure is 38%, U.S. Citizens and within Group Vb it is 44%. Removing these department The percentage of U.S. citizens among new doctorates has groups from the data results in a drop to 20%, as seen in been stable for several years around 45% [D), but nearly 70% line 4 of Table 4 (see next page). (Note that there is no of entrants to doctoral departments with only a bachelor's overlap between lines 1 and 2, and that lines 1, 2, and 4 are degree are U.S. citizens. Table 3 shows that 62% of the included in line 3.)

MAY/JUNE 1992, VOLUME 39, NUMBER 5 413 Committee Survey

TABLE4 Group Va, the percentage of "entering" Black graduate Percentage of women among U.S. citizens students is significantly higher than for "all" Black graduate Groups I, II, II, and Va students; perhaps good recruiting will lead eventually to more doctorates awarded to Blacks. 1. 1990-1991, Doctoral Department Entrants with Bachelor's Degree 35% TABLES Numbers and percentages from underrepresented 2. 1990-1991, Doctoral Department Entrants minorities among U.S. citizen graduate students with Master's Degree 31% Entering Entering All New Graduate Graduate Entering Doctorates 3. 1990-1991, All Graduate Students 31% Students Students and with with Continuing 4. 1991 New Doctorates 20% Bachelor's Master's Graduate Degree Degree Students Only

As with the citizenship data, the numbers in Table Black 4 might be taken to predict eventual increases in the Number 49 14 134 8 percentages of women among U.S. citizen doctorates and Column% 3.5% 4.7% 2.9% 2.3% faculty. But, again, anecdotal information-combined with the stability of the percentage of women U.S. citizens among American Indian, new doctorates for a number of years-invites caution. For Eskimo, Aleut 2 11 2 whatever reason, the proportion of women who persist to Number 3 Column% 0.2% 0.7% 0.2% 0.6% the doctorate is significantly lower than that of men. The second stage of the survey will address the question: "What Mexican American, percentage of the entering 1990-1991 students persisted to Puerto Rican a third year of graduate study or have received a master's or Other Hispanic degree?" For those who obtained a master's degree and Number 24 6 199 4 then left a doctoral department, the more subtle questions Column% 1.7% 2.0% 4.3% 1.2% about "intent" (to complete only a master's or to go on for the doctorate) versus leaving with the master's degree as a Total of Above "consolation prize" will not be answered. Number 76 22 344 14 Column% 5.5% 7.4% 7.4% 4.1%

Underrepresented Minority Groups Usable 146 146 143 173 Some ethnic minority groups comprise a smaller proportion Responses of 184 of 184 of 184 of 184 among mathematicians and mathematics graduate students than in the general population; this pattern remains even Reported U.S. when one looks at women only or men only. Table 5 Citizens of combines the data from departmental Groups I, II, III, and Known Race 1384 296 4677 343 Va and gives both reported numbers and percentages for three such U.S. citizen minority groups. Table 6 reports It is interesting to determine whether the proportions Groups I and II data. Even allowing for nonreporting of men and women for the minority groups follows that departments, the numbers are very small: out of a total of in each of the graduate student cohorts. For Blacks, the 4677 doctoral students in 143 departments, only 344 are breakdown of men and women is very close to that for members of these minority groups. the entire U.S. citizen cohorts, although in departmental Because the numbers are so small, one must be wary Groups I and II a larger percentage of black graduate of generalizations, but a few comments can be made. The students entering with a bachelor's degree are women- significantly higher proportion of Hispanics among "all" 50%. Also, Eskimos-Indians have a higher percentage of graduate students than among "entering" graduate students women in each of the cohorts; six men and five women stands out. (The weight of the Hispanic data in the combined were reported among All Graduate Students and three data for these minorities causes the same effect in the women and two men among Entering Graduate Students. For Totals.) This pattern-which is also found when the data is Hispanics, the proportion of women entrants holding only examined by departmental Group and is especially marked bachelor's degrees follows that predicted by the population, in Group III-does not have favorable implications about but otherwise there are proportionately fewer women among the number of Hispanics receiving doctorates in the future. Hispanics than generally. There were two Hispanics reported Another unexpected note: For the applied departments of among new doctorates, one man and one woman.

414 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______~-~~· MIIBIIR~ilnBiBfiil.lt~· Committee Survey

TABLES background are made up. Results about the categories of Underrepresented minorities among U.S. courses surveyed are indicated below. citizen graduate students in Groups I and II Real Analysis. Real Analysis I (Advanced Calculus I) is "strongly recommended" in 96% of doctoral mathematics departments overall, with 80% reporting they will admit Entering Graduate All Entering students and let them make up the course after enrolling. Students with and Continuing (The corresponding percentages for Real Analysis II are Bachelor's Degree Only Graduate Students 91% and 86%.) It is interesting that all of the Group Va (applied) departments responded that Real Analysis I is Group I Group II Group I Group II "strongly recommended," and only 70% will allow makeup after entrance to graduate school. Modern Algebra. Predictably, few Group Va departments Black "strongly recommend" Modem Algebra I, but 93% of Group Number 8 17 31 42 percentage drops to 73% Column% 2.0% 4.2% 1.9% 3.2% I, II, and III departments do. This when it comes to Modem Algebra II; makeup is allowed in American Indian, 90% of Group I, II, aild III departments combined, but by Eskimo, Aleut only 81% of Group I departments. Number 0 2 6 Probability and Statistics. For Groups I, II, and III Column% 0.0% 0.5% 0.1% 0.5% only 21% list Probability and Statistics as "strongly rec­ ommended," and in Group I only one department does so. Mexican American, However, in Group Va there is stronger positive response: Puerto Rican 64% of the departments indicate "strongly recommended." or Other Hispanic Probability and Statistics have been included repeatedly for Number 7 7 56 30 many years in professional society curriculum recommen­ Column% 1.8% 1.7% 3.5% 2.3% dations [CU] as essential in undergraduate major programs. The Committee on Preparation for College Teaching feels Total of Above that some study of Probability and Statistics at the upper Number 15 26 88 78 division undergraduate level is necessary for the broad foun­ 6.4% 5.4% 5.9% Column% 3.8% dation in mathematical topics important to undergraduate teachers [CT, p. 1346]. Usable 33 41 34 39 Responses of 39 of43 of 39 of 43 Additional Courses. Answers reflect differences between "pure" and "applied" programs. Under the category Ap­ Reported U.S. plied Mathematics, 75% of Group Va departments indicate Citizens of "strongly recommended courses"; only 23% of the other Known Race 398 404 1616 1319 departments mark this category. The Applied Mathematics courses most often listed are Numerical Analysis and Partial Differential Equations. These courses and other courses in the general area of applied mathematics were sometimes listed under Other. Entrance and Continuation Expectations and The courses listed in the Other category most frequently Characteristics Related to Teaching as "strongly recommended" are Topology and Complex One portion of the survey was devoted to questions about Variables (Complex Variables was also sometimes listed the preparation expected of entering graduate students, con­ under Applied Mathematics). Linear Algebra and Ordinary tinuation requirements for students, preparation for teaching, Differential Equations were reported by a number of depart­ and the teaching climate in departments. ments, and this confusion led to a change in the second stage of the survey, in which the ambiguous term "upper division courses" will be replaced by "courses coming after single Entrance Requirements and multivariable calculus." There will also be provision for Entrance requirements or recommendations for upper di­ a separate listing when two programs within a department vision undergraduate courses are far from universal. The have different entrance expectations. survey asked departments whether or not certain courses were "strongly recommended" as background for entering The Preliminary Examination graduate students, and whether these courses could be made As with entrance expectations, the areas examined may up in graduate school. In some cases, the "strongly rec­ differ by choice of program within a department; on the ommended" courses were actually required for entrance. examinations, there may or may not be a choice of topics Several departments indicated that graduate students are within a program. Again, responses found in this first stage accepted only as master's candidates until deficiencies in of the survey will help to clarify the questions for the second

MAY/JUNE 1992, VOLUME 39, NUMBER 5 415 Committee Survey

stage. Respondents were asked to say whether the format extent to which doctoral programs appear to encourage was oral or written, indicate when the examination needs to mathematical breadth. Answers indicate that: be completed, and describe the content of the examination. • a number of departments consider that their preliminary The usable responses on this item were high. Here are or qualifying examinations, over several areas, accomplish some interesting highlights. this goal; • Only two departments did not report a preliminary • few departments require a minor outside of the examination. (One said there was none while one did not department-even in applied mathematics only 42% do so; answer the item.) and • A "written only" examination is more common in • 80% believe "breadth" is reflected through their areas Groups I and III but in Groups II and Va both a written of required courses. and an oral examination are the more common testing requirement. Preparation and Duties of Teaching Assistants • The examination is typically taken in the second or The Committee does not consider "TA training" sufficient third graduate year. preparation for college teaching, and such training is, in fact, • Generally, on the written portion of the examination, the primary concern of another committee. Nevertheless, the at least two areas are included, with three or four areas most Committee does see T A training as an important part of the typical. total preparation. In 42% of Group Va (applied) departments, • In about 60% of the departments, some choice of graduate students are not involved in teaching at all, or else testing area is available to the students. have responsibility only for assisting professorial faculty Content of preliminary examinations vary, because they and grading in upper division courses. Various T A training appropriately reflect the research interests of the faculty. mechanisms were listed, and the most interesting findings Therefore, it is not possible to list a set of nonoverlapping concern orientation programs (Table 7), English language areas, topics, or concentrations from which departmental training (Table 8), and faculty observations of T As (Table testing areas are taken. Samples of responses indicate in 9). Data from a previously published survey [C] about some cases student choice of topic: departments in Groups I, II, and III indicates an increase in • all of complex analysis, real analysis, topology, analysis all three activities since the mid-1980s. on manifolds, linear algebra, and abstract algebra; • three from algebra, applied mathematics, complex Table 7 analysis, real analysis, or topology; Percentage of departments reporting teaching • from a department with two doctoral programs: Pure assistant orientation programs Mathematics: algebra, real and complex analysis, topology; Applied Mathematics: analysis, numerical analysis, PDE and numerical PDE, fluid dynamics, and another topic chosen Group I Group II Group Ill from research area; • two from analysis, algebra, linear algebra, combina­ 1991 94% 95% 85% torics, or probability. 1987 [C, p. 37] 79% 86% 76% 1985 [C, p. 37] 66% 88% 64% Mathematical Breadth As indicated earlier in the discussion about undergraduate Table 8 mathematical preparation, the Committee on Preparation Percentage of departments reporting English for College Teaching considers it desirable that graduate language training students become familiar with a wide range of mathematical topics at the advanced undergraduate level: Group I Group II Group Ill Graduate education should not be limited to specializa­ tion ... Breadth of knowledge forms the background for 1991 94% 90% 75% teaching a variety of courses, for advising students, and 1987 [C, p. 36] 72% 70% 71% for recognizing different kinds of talent in mathematics. 1985 [C, p. 36] 60% 71% 68% Further, the increasing interrelation of ideas at advanced levels of research makes it imprudent to be ignorant Table9 concerning major branches of mathematics. [CT, p. Percentage of departments reporting faculty 1344] observations of teaching assistants Accomplishing this goal is a joint responsibility of undergraduate and graduate departments [CU, Case 1991, Group I Group II Group Ill pp. 4, 18, 20] and may not be specifically reflected in doctoral requirements. To provide a basis for later Committee 1991 81% 83% 72% recommendations, the survey attempted to ascertain the 1987 [C, p. 38] 62% 67% 67%

416 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Committee Survey

Student evaluations are common, but other components teaching or attitude toward the importance of teaching (Ta­ of TA training and supervision are less frequently used. ble 10). One item concerned departmental teaching awards; Although peer observations by other graduate students have since there are university- or college-wide awards programs been used and considered effective for a number of years that may not have been reported in these responses, the [C, p. 36], the reported incidence is small. Overall, 28% of second stage of the survey will ask about such awards. programs reported videotaping of classes with incidence in The last item on the survey was intended to provide some Groups I and ll at 40%. Videotaping of mock classroom indication about the importance the departments attached to sessions is thought to be much higher. (For example, non­ teaching activities. The departments were asked: "In the view specific "Uses videotape" queries in 1985 and 1987 were of your department chair, how important was evidence of answered positively in Groups I, ll, and lli by over half the teaching preparation and experience during graduate school reporting departments.) in the decisions which led to appointment of entry-level assistant professors during the last three years?" Teaching Activities of Graduate Students A scale from 1 (Not important) through 5 (Very impor­ Individuals typically teach their own classes, with varying tant) was provided. The weighted mean answer was 3.5 with levels of supervision, in departments other than the Group the responses by Groups I, II, lll, and Va, respectively, 3.1, Va (applied) departments. Duties of graduate students almost 3.4, 3.8, and 2.9. universally include grading and student contact in recitation or tutorial sections, if not in classes with full responsibility. Not Va I II Ill Very Over half of the departments indicated that graduate students important important occasionally act as substitute teachers for regular faculty. II I 1 2 131 4 5 Although graduate students often teach courses in which t department-wide examinations are used, 73% (excluding All departments Group Va) nevertheless report that their graduate students gain experience in the designing of examinations. Figure 1. Importance of teaching in hiring, by department groups Additional Items Regarding Teaching The Committee recommends that all third- and fourth-year graduate students be involved in "systematic attention to References issues and excellence in the teaching of mathematics" [CT, [B] Lynne Billard, "The Past, Present, and Future of Academic p. 1345]. The grant to the Committee through the Fund for Women in the Mathematical Sciences," Notices of the AMS 38:7 (Sep­ tember 1991) pp. 707-714. the Improvement of Postsecondary Education provides for [BR] William G. Bowen and NeilL. Rudenstine, In Pursuit of the pilot programs to design "professional seminars" and other PhD, Princeton University Press, 1992. such mechanisms. These activities would target advanced [C] Bettye Anne Case, Editor, Keys to Improved Instruction by graduate students and are in addition to T A training, which Teaching Assistants and Part-Time Instructors, MAA Notes 11, 1989, focuses primarily on an immediate concern for competent Mathematical Association of America. teaching in the department. [CT] "How Should Mathematicians Prepare for College Teach­ ing?" Notices of the AMS 36:10 (December 1989) pp. 1344-1346. The survey asked departments to list additional aspects [CU] CUPM 1991: The Undergraduate Major in the Mathemat­ of their program that prepare advanced graduate students ical Sciences (Bettye Anne Case, Chair, CUPM Subcommittee). To for undergraduate teaching, and there were few responses: be included in Heeding the Call for Change, MAA, to appear 1992. 92% of departments listed nothing. Of the few responses, CUPM 1981: Recommendations for a General Mathematical Sciences involvement in seminars in their mathematical specialty Program (Alan Tucker, Chair, CUPM Panel). Washington, DC: MAA. was mentioned most frequently. Several others mentioned [D] All of the following Annual AMS-MAA Survey reports ap­ the opportunity to teach sections of classes beyond single­ pear in Notices of the AMS. Donald E. McClure: 1991 First Report, 38:9, (November 1991) pp. 1086--1122; 1990 Second Report, 38:5 variable calculus with full classroom responsibility. One (May/June 1991) pp. 411-419; 1990 First Report, 37:9 (November department responded that students are encouraged to take a 1990) pp. 1217-1250. Edward A. Connors: 1989 Second Report, 37:6 course in the Science Teaching Department. July/August 1990) pp. 658-665; 1989 First Report, 36:9 (November 1989) pp. 1155-1188. Table 10 [G] Groups I and II include the leading departments of mathemat­ Departments making teaching awards ics in the U.S. according to the 1982 Assessment of Research-Doctorate Programs conducted by the Conference Board of Associated Research Group I Group II Group Ill Group Va Councils in which departments were rated according to the quality of their graduate faculty. Group I is composed of 39 U.S. departments with scores in the 3.0-5.0 range. Group II is composed of 43 U.S. de­ TA awards 50% 66% 31% none partments with scores in the 2.0-2.9 range. Group III contains the re­ Faculty awards 17% 36% 17% 13% maining U.S. departments of mathematics reporting a doctoral program. Group IV contains U.S. departments (or programs) of statistics, bio­ statistics, and biometrics reporting a doctoral program. Group V con­ The last two items of the survey were included to pro­ tains U.S. departments (or programs) in applied mathematics/applied vide some indication of the departmental climate regarding science, operations research and management science which report a

MAY/JUNE 1992, VOLUME 39, NUMBER 5 417 Committee Survey

doctoral program. Group Va is applied mathematics/applied science; [L] D.J. Lewis, "Mathematics and Women: The Undergraduate Group Vb is operations research and management science. [These School and Pipeline," Notices of the AMS 38:7 (September 1991) pp. findings were published in An Assessment of Research-Doctorate Pro­ 721-723. grams in the United States: Mathematical and Physical Sciences, edited [S] Alice T. Schafer, "Mathematics and Women: Perspectives and by Lyle V. Jones, Gardner Lindzey, and Porter E. Coggeshall, National Pro-gress," Notices of the AMS 38:7 (September 1991) pp. 735-737. Academy Press, Washington, D.C., 1982. The information on mathe­ matics, statistics, and computer science was presented in digest form, Notices of the AMS 30:3 (April 1983) pp. 257-267, and an analysis Data Analysis and Presentation: In addition to the AMS-MAA Data of the above classifications was given in Notices 30:4 (June 1983) pp. Committee assistance, the survey forms were prepared, distributed, and 392-393. Also see Notices 35:4 (April 1988) pp. 532-533. collection coordinated by Monica Foulkes and the AMS staff. Allyn [Ha] Jenny Harrison, "The Escher Staircase," Notices of the AMS Jackson of the AMS staff provided helpful editorial assistance. Tech­ 38:7 (September 1991) pp. 730-734. nical support and other assistance was provided by the Department of [He] Claudia Henrion, "Merging and Emerging Lives: Women in Mathematics, Florida State University, and special thanks go to Melissa Mathematics," Notices of the AMS 38:7 (September 1991) pp. 724-729. E Smith, the department's Senior Art/Publication Production Specialist. [J] Allyn Jackson, "Top Producers of Women Mathematics Doc­ The research was partially supported by Pll6B00184, Comprehensive torates," Notices of the AMS 38:7 (September 1991) pp. 715-719. Fund, FIPSE.

MEMOIRS American Mathematical Society

Number 465 Number 466

Selberg Trace Formulae Vertex Algebras and Integral and Equidistribution Theorems Bases for the Enveloping for Closed Geodesics and Laplace Algebras of Affine Lie Algebras Eigenfunctions: Finite Area Shari A. Prevost Surfaces In this book, Prevost utilizes the vertex Steven Zelditch operator representations of the affine Lie algebras to give two equivalent descriptions of an integral This work concerns a pair of dual asymptotics basis for the affine Lie algebras and their problems on a fmite-area hyperbolic surface. The associated universal enveloping algebras. Prevost first problem is to determine the distribution of also examines the vertex algebra approach closed geodesics in the unit tangent bundle. The developed by Borcherds to give a (nonexplicit) second problem is to determine the distribution of description of an integral form for the enveloping eigenfunctions (in a microlocal sense) in the unit algebras for the simply-laced aftlnes. She then tangent bundle. The main result here is a proof of extends Borcherd's method to give an analogous a signed and averaged version of the mean description of an integral basis for the remaining Lindelof hypothesis for Rankin-Selberg zeta unequal root length affine Lie algebras and their functions. enveloping algebras.

1991 Mathemntics Subject Class!fications: 11, 58 1991 Mathematics Subject Classifications: 17 ISBN 0-8218-2526-7, 102 pp. (softcover), March 1992 ISBN 0-8218-2527-5, 97 pp. (softcover), March 1992 lncllv. mem. $15, Ust $25, Inst. mem. $20 Incllv. mem. $15, Ust $25, Inst. mem. $20 Your ordering code is MEM0/465NA Your ordering code is MEM0/466NA

All prices subject to change. Free shipment by surlace; for air delivecy, please add $6.50 per title. Prepayment requireci Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GSf.

418 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Support for Mathematics Departments and Federal Funding AMS Committee on Science Policy Examines Issues Confronting the Community

Picture this scenario: A large state university faces deep research needs. Mathematics research is merely "tolerated" budget cuts. Looking around for ways to save money, the on many campuses, he said. university administration concludes that the mathematics Bolstering this point, Committee member Michael C. department's main role is to teach undergraduates. So Reed of Duke University noted that mathematicians like to the administration tells the department to discontinue its talk about how valuable mathematics is to other areas of graduate program, double the teaching load of the faculty, science, but, if such claims were true, "why aren't chemistry and hire part-timers to take up any slack. Where could and physics beating on the dean's door to get more faculty the department turn for help? Are there any standards positions in mathematics?" The fact is, he said, on most for the average teaching load of mathematics faculty? Is campuses there are few intellectual connections between there a position statement on using part-time faculty? Does mathematics and other sciences. In addition, "mathematics there exist a broad "mission" for mathematics departments is not perceived to be on the cutting edge of the most that makes the case for the importance of research and interesting research opportunities in the universities," Reed scholarship to the vitality of the department? asserted. Provosts and deans see the most important science Although this is an extreme example, many departments with the best funding opportunities coming out of interdis­ are already facing these kinds of problems on a smaller ciplinary research, which has not been the strong suit of scale. The AMS may seem to be the likeliest place to seek many mathematics departments. "So I think our political assistance, but, as William James Lewis of the University of position in the universities is actually worse than we think," Nebraska notes, the Society is entirely unprepared to help he remarked, and, were it not for teaching, mathematics with these kinds of problems. Lewis made his points during departments would be much smaller than they are today. He a meeting of the AMS Committee on Science Policy (CSP), suggested the CSP recommend that departments devote 10% held April4, 1992 in Chicago. The Committee's discussions of their resources to technology transfer. for the most part were motivated by declining resources for Such a recommendation would represent a fairly radical mathematics, be they from academic institutions or from the shift in how the AMS has traditionally operated. Should federal government. Adding an urgent tone to the discussion the AMS play a leadership role in stimulating change in were such problems as the poor job market in mathematics, departments? Should it promulgate standards for department flat funding in the National Science Foundation (NSF) teaching loads, class size, faculty size, resources, equipment, mathematics, and budget request for undirected research in and so on? (For example, the Mathematical Association of academia. widespread budget crises in America has a committee that has produced a draft report on "guidelines" for undergraduate programs in mathematics.) Departmental Woes Such questions lead to the idea of accreditation, often During the discussion about academic support for mathe­ a powerful bargaining chip in negotiations with university matics, Lewis said that the 1990s will be a time for reduced administrations. One Committee member noted that when the resources for higher education. Even Yale University has had chemistry department at his university told the administration to consolidate its departments because of budget cuts, and, that the American Chemical Society required them to offer Lewis remarked, "If Yale is cutting programs, then everyone certain courses, the administration forked over the money is." In this climate, mathematics departments could be hit for the courses without a peep of protest. On the other hand, hard with reductions in numbers of faculty, increased teach­ many react negatively to the prospect of the AMS telling ing loads, and cutbacks in graduate programs. In addition, departments what to do, how to teach, or what courses mathematics departments are often seen very differently by to offer. Some on the CSP foresaw the AMS turning into nonmathematicians on campus than they are by mathemati­ "Big Brother," watching over departments to make sure they cians. For example, the size of mathematics departments complied with a generic set of standards. tends to be driven by the number of students taught, while As Lewis pointed out, a "one size fits all" approach the size of, say, chemistry departments tends to be driven by wouldn't work, given the diversity of educational institu-

MAY/JUNE 1992, VOLUME 39, NUMBER 5 419 ···-··················-··-·····--···-··········-·······························-- ·····································-······-··------.:~ Science Policy Committee tions and departments. But perhaps general agreement could doesn't work that way. In addition, he disagreed that there's be reached on broad outlines for departmental standards and a lack of communication among these groups-last year, he responsibilities in teaching, research, outreach to other disci­ was simultaneously chair of the CSP and of the Advisory plines, curriculum development, and so on. However, Lewis Committee, and also served on JPBM. He made a point of pointed out that before such matters could be addressed, insuring that the various groups knew what the others were there needs to be discussion about and consensus on just doing. So what's wrong? "We have to face the fact that who the AMS is trying to serve. Is it trying to serve its those who are funded are happy," he said, so it's hard to get current membership, or is it trying to serve the profession the community seriously discussing science policy. more broadly? Another area that Friedlander would like his task force These issues will be examined in the coming months by to look at is support for mathematics. He would like to see a CSP task force, chaired by Lewis, on academic support various levels of fixed-rate grants, perhaps senior, junior, and of mathematics and connections of mathematics research to travel awards. Such dollar-stretching tactics are especially education. This is one of four task forces recently convened appealing in light of the news that next year's budget request by the CSP to provide more focused attention to specific for the NSF contains no increase for undirected research issues growing out of the AMS strategic plan and previous in mathematics (see the Washington Outlook column in CSP discussions. this issue of the Notices and also "The National Science Foundation Budget Request for Fiscal Year 1993," the The Washington Presence Notices, April 1992, pages 286-297). However, they also One of the other task forces, chaired by Eric M. Friedlander raise the question of whether mathematicians are selling of Northwestern University, will look at federal support themselves cheap by volunteering for a pay cut. Friedlander and public awareness of mathematics. The CSP discussed a said he believes that mathematics is sufficiently different number of ideas for strengthening what's come to be known from other sciences to warrant a different mode of funding as the "Washington presence" for mathematics. One idea that allows for expanding the base of researchers supported. was to establish mechanisms by which the Society could, The pros and cons of such grant mechanisms have been on short notice, get advice on policy matters in which a debated for years, but there has been no change, partly quick response is needed. The need for such a group has because agencies like NSF are not wild about the idea and arisen a number of times in recent years, most recently this partly because no one has seriously made a persuasive case fall, when the staff of a Congressional subcommittee asked for it. This last matter was raised as the CSP discussed how the AMS for input on a discussion of priority setting in a position paper on this issue might be produced. Again, science funding. (The Society's response was a report, which such a document would represent a new way of operating appeared in the Notices, February 1992, pages 101-110). The for the AMS-typically the Society has taken a passive CSP also discussed the possibility of having an energetic attitude toward such thorny issues. person of high mathematical stature with good political connections serve as a representative for mathematics in the A National Postdoc Program federal policy scene. Another topic that generated interest at the CSP meeting A perennial problem with the Washington presence is was a proposal for the AMS to take the lead in developing getting mathematicians of high stature to work in Washing­ an expanded program of postdoctoral appointments. The ton. Would the "mathematics advocate" position be paid, idea would be to provide a variety of paths by which new or volunteer? If it's volunteer, then there's a limit to what doctorates could continue their education and professional can be expected. And if it's paid, then it's unlikely any development, whether their primary interest is mathemat­ mathematician of the proper caliber would leave research to ics research, education, technology transfer, interdisciplinary take the job. It hasn't been easy to get top mathematicians to research, or other directions. The proposal suggests a fifty­ take positions in Washington, either in the research funding fifty cost-sharing arrangement between federal agencies and agencies or in advocacy positions. academic institutions, as well as aggressive development of Another difficulty with the Washington presence is that postdoctoral research opportunities in government laborato­ several different groups are involved-the CSP, the Joint ries and industry. The role of the AMS would be primarily Policy Board for Mathematics (JPBM), the NSF's Advisory as an advocate for getting the program established. Committee for the Mathematical Sciences, the Board on The proposal grew out of dicsussions of the CSP over Mathematical Sciences (BMS), the Conference Board of the last few years and the development reports "Educating the Mathematical Sciences (CBMS), among others. These Mathematical Scientists" from the BMS and "Graduate groups don't always communicate as effectively as they Education in Transition" by the CBMS (both reports are might, so the suggestion was made that they all meet and covered in articles in this issue of the Notices). There is a exchange information about what they're doing. But would strong feeling that more structured postdoctoral training is yet another meeting be effective? Reed thinks not. ''Talk is needed to allow new doctorates to make the crucial transition not cheap," he said, pointing to the nontrivial expense of from graduate student to professional mathematician. A such a large meeting. "We all think that if we could meet number of concerns were raised about the proposal during and decide what's good, it will happen," he said, but it the CSP meeting-some feared it would strain already

420 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ···························--··-······· ------··---·----·------··-······························· ..... ··············-···-··············-·············-········· Science Policy Committee limited federal funds for research, some wondered if such a by Reed, will focus on corporate support of mathematics large number of postdoctorates is necessary, and some were and the connections of mathematics research to the uses of wary of departments using these positions to replace tenure­ mathematics. The other, chaired by Linda Preiss Rothschild track lines. In addition, some worried about the proposal's of the University of California at San Diego, will look at suggestion that departments shift funds for teaching assistants the science policy aspects of core AMS activities, such as to these kinds of postdoctoral appointments, a strategy meetings and publications, and at the Society's international that could bode ill for graduate student support in some role. The focal areas for the task forces grew out of the AMS departments. operational plan and will form the basis for a comprehensive These criticisms notwithstanding, the CSP on the whole "science policy strategy" that the CSP will be developing felt that the basic philosophy behind the proposal-providing during the coming months. a variety of paths by which new doctorates can pursue further The CSP welcomes comments and suggestions from the education and training-was commendable. There appeared mathematical sciences community. They may be sent to the to be a clear consensus that the proposal be rewritten to chair of the Committee, Frank W. Warner ill, Department take into account the concerns of the Committee. A revised of Mathematics, University of Pennsylvania, Philadelphia, version of the proposal is to be circulated at the next CSP PA 19104-6395. meeting in Washington in September. In addition to the task forces chaired by Lewis and Allyn Jackson Friedlander, the CSP has appointed two others. One, chaired Staff Writer

On-Line Algorithms Lyle A. McGeoch and Daniel D. Sleator, Editors DIMACS: Series in Discrete Mathematics and Theoretical Computer Science,

Volume 7

This volume contains the proceedings of the Workshop on On-line Algorithms held at the DIMACS Center at Rutgers University in Febru­ ruy 1991. Presenting new results in the theory of on-line algorithms, the articles discuss a broad range of problems. Most of the papers are based on competitive (worst-case) analysis of on-line algorithms, but some papers consider alternative approaches to on-line analysis. Many of the papers examine the ways randomization can be used to yield algorithms with improved performance. This book is aimed primarily at specialists in algorithm analysis, but most of the articles present clear expositions of previous work, making reading easier for nonspecialists.

1991 Mathematics Subject Classification: 05, 68, 90 ISBN 0-8218-6596-X, 179 pages (hardcover), January 1992 Individual member $19, List price $32, Institutional member $26 Your ordering code is DIMACS/7NA

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Order from American Mathematical Society", P. 0. Box 1571, Annex Station, Providence, RI 02901-1571, or cal toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please add 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 421 Doctoral Degrees Conferred 1990-1991 Supplementary List

University of California, Santa Cruz Yen, Chen-E, A factor analytic study of The following list supplements the list of thesis (1) selected factors related to mathematics titles published in the November 1991 issue of anxiety among eighth grade students in the Notices. Each entry contains the name of MATHEMATICS Taiwan, Republic of China, and comparison the recipient and the thesis title. The number in Libby, Richard, Asymptotics of determinants to a U.S. population. parentheses following the name of the univer­ and eigenvalue distributions for Toeplitz Zelle, Claire, Multivariate analysis of selected sity is the number of degrees granted by the matrices associated with certain discontinu­ department. classification data in market research. ous symbols. INDIANA COLORADO CALIFORNIA Purdue University (9) University of Colorado, Boulder (10) INDUSTRIAL ENGINEERING University of California, Berkeley MATHEMATICS Banerjee, Prashant, A manufacturing layout (13) Barnett, Janet, Effect of Cohen and random reasoning architecture based on an auto­ reals on certain combinatorial consequences mated integration of linear objective opti­ of Martin's Axiom. STATISTICS mization and non-linear qualitative analysis. Bekkalt, Mohammed, On superatomic Boolean Chandra, Jayanta, Optimization-based oppor­ Chang, Yu-Lin, Local behavior of mixtures of algebras. normal distributions. tunistic part dispatching in flexible manu­ Bricher, Stephen, Blow up patterns for semi­ facturing systems. Chow, Edmond Dean, Stochastic minimum linear heat equations via center manifold Cook, John R., Cognitive and social factors distance tests for censored data. theory. in the design of computerized jobs. Jin, Kun, Empirical smoothing parameter Caveny, Deanna, Independence results for Foley, James P., The effect of law and training selection in adaptive estimation. certain classes of U -numbers. on all-terrain vehicle riders' safety-related Kooperberg, Charles Louis, Smoothing im­ Darby, Carl, Countable Ramsey games and behaviors. partition relations. ages, curves, and densities. Heim, Joseph, Integration of distributed het­ Limber, Mark, Quasi interiors of convex sets Lee, Sang Ho, Some statistical aspects of erogeneous simulation models for design of to optimization. gradient gel electrophoresis. and applications manufacturing systems. Martin, John, A formulation of the limitation Lorentziadis, Paragotis Loudovikou, Fore­ Lee, Ching-En Charles, An integrated method­ of size theory using ideals and representing ology for the analysis and design of cellular casts in oil exploration and prospect eval­ small collections as individuals. uation for financial decisions : a semipara­ flexible assembly systems. Shulman, Bonnie Jean, Wave propagation metric approach. Lin, Alan, Automated assembly planning for inhomogeneous media with appli­ through three-dimensional mechanical products. Meester, Ludolf Erwin, Contributions to the cations to solar coronal loops. Papantonopoulos, Sotiris A., A decision model theory and applications of statistics. Sobh, Nahil, Preconditional conjugate gradi­ for cognitive task allocation. Perman, Mihail, Random discrete distributions ent and finite element methods for massively reasoning derived from subordinators. data-parallel architectures. Wang, Ming T., A geometric methodology for manufacturing feature ex­ Wyshinski, Nancy, Asymptotic properties of Pfannes, Othimar, Edgeworth expansions for traction from a 3-D CAD model. T-statistics based on expected and observed polynomials satisfying three-term recurrence information. relations. MICHIGAN Sugahara, Clyde Nobuo, Some bootstrap University of Northern Colorado (4) methods for finite state Markov chains. Western Michigan University (8) MATHEMATICS AND APPLIED STATISTICS Wang, Xiaobao, On the estimation of trigono­ Brophy, Richard, Development of aberrancy MATHEMATICS AND STATISTICS metric and related signals. indices based on pattern-response analysis. Abay Asmerom, Ghidewon, Graph products Wang, Yonghua, On efficient estimation under Teng, Pao-Sheng, A study of the sampling and covering graph imbeddings. equation constraints. distribution of the Kurtosis and confidence Craft, David L., Surgical techniques for Wu, Colin Ou, Asymptotic efficient robust limits determined using the jackknife and constructing minimal orientable imbeddings estimates in some semiparametric models. bootstrapping procedures. of joins and compositions of graphs.

422 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -~~ mm m H m ~~ Ell mmm m mm • mm•• -11ll&J WT il.lll' Annual AMS-MAA Survey

Hevia, Hector, A representation of chemical TEXAS Zhang, Roxin, Problems of hierarchical reactions by labeled graphs. optimization : nonsmoothness and analysis Jarrett, Elzbieta, Transformations of graphs Texas A&M University (4) of solutions. and digraphs. MATHEMATICS Mull, Bruce P., Enumerating the orientable Norm closed bimodules of nest 2-cell imbeddings of complete n-partite Dai, Xingde, graphs. algebras. C' quadratic finite element Nouh, Jamal, Improving network reliability. He, Tian-Xiao, Doctoral Degrees Conferred analysis and its applications. Sprague, Thomas B., Shape preserving piece­ approximation and its appli­ 1989-1990 wise cubic interpolation. Li, Xin, Hankel List cations. Supplementary Tian, Songlin, On distance in graphs and Steven J., Normalization methods digraphs. Sepanski, in the Bootstrap Central Limit Theorem. The following list supplements the list of thesis titles published in the November 1990 Notices, NEW JERSEY pages 1231-1250, the May/June 1991 Notices, WASHINGTON page 419, and the November 1991 Notices, Stevens Institute of Technology (3) pages 1121-1122. University of Washington (3) PURE AND APPLIED MATHEMATICS Berry, Kevin A., Riemann surfaces, transcen­ APPLIED MATHEMATICS dental functions and combinatorial group Pemarowski, Mark, The mathematical analy­ CANADA theory. sis of bursting electrical activity in pancre­ Kolodzieski, Scott J., Delta-pseudo orbit atic beta cells. University of Alberta (I) shadowing in a family of trapezoidal maps. Siems, Steven, Numerical simulations of MATHEMATICS Lasser, Lewis L., A degree condition for cloud-top entrainment instability and related Hamiltonian cycles in t-tough graphs with experiments. Skantharjah, M., Amenable hypergroups. t > 1.

Translations of Mathematical Monographs • Volume 97

Topology of Foliations: An Introduction !tiro Tamura Tamura's book provides historical Specific topics include: background and a complete overview of • dynamical systems on the torus and the qualitative theory of foliations and the three-sphere systems. You will differential dynamical • local and global stability theorems for appreciate this book for its highly visual foliations presentation of examples in low dimen­ existence of compact leaves on sions. Tamura focuses particularly on • the three-spheres foliations with compact leaves, covering all the important basic results. • foliated cobordisms on three-spheres

1991 Mathematics Subject Classifications: 57; 58 ISBN 0-8218-4543-8, 193 pp. (hardcover), March 1992 Indiv. member $53, List price $89, Inst. member $71 Your ordering code is MMON0/97NA

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please add 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 423 Forum

what they got. Their response surprised me again. They said The Forum section publishes short articles on issues that are of interest to the mathematical community. Articles should be between f(x) = ln(1 + x). 1000 and 2500 words long. Readers are invited to submit articles for possible inclusion in Forum to: After further talking, they realized that Notices Forum Editor American Mathematical Society d 1 -1 P.O. Box 6248 dx 1 + x = (1 + x)2 ' Providence, RI 02940 or electronically to [email protected] and then claimed that -1 Some Comments on Education f(x) = (1 + x)2 Richard Askey I responded that this was the right derivative, but that f(x) University of Wisconsin-Madison does not satisfy (1). Could they tell me what was wrong? At the joint summer meeting, Pi Mu Epsilon has a program. They said they had forgotten the constant of integration. The Undergraduate students are there to talk about their research. banquet was announced, so I did not have five minutes to In addition to these talks, there is a reception, a banquet, and help them see what was wrong and just told them. an hour talk. For ten years I have gone to the banquet and I had not expected them to see that the author had reception to talk with some of the students. Last summer at forgotten the constant of integration, but their answers Orono I had two conversations which tell a lot about the surprised and shocked me. Students doing undergraduate current situation in mathematics education. research should not have such a poor grasp of calculus. At the reception, I was talking to three students from At the banquet I sat next to two students. One was a small liberal arts college who were there to talk on their studying at Princeton and the other at Washington University. research. After listening to descriptions of their work, I After asking what they had done, they asked what I did. asked them a mathematics question. I was going to use a One had said he had spent the summer computing Kazhdan­ new calculus book in the fall semester and, as often happens, Lusztig polynomials. I said I had caught the q-disease about there was a mistake in a problem. I wanted to see how 15 years ago, and, while it was related to these polynomials, these students would react to a problem that does not have it was a complicated story and I could not outline it then. an answer, so I asked how they would attack the following They asked what the q-disease was, so I first asked if they problem. knew the binomial theorem. They responded with Find f(x) which satisfies

x 1 (2) (1) f(t)dt= -1- 1o +x

The first suggestion was to evaluate the integral. Since I and when asked said that did not know how they would do that, I asked. They said the value was (3) (n) n! f'(x)- f'(O). k = k!(n- k)! After talking about the fundamental theorem of calculus, counted the number of ways of putting k objects of one type they finally realized they should differentiate. Then I asked and n - k of another into n places.

424 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------···--·--····-··---·---··--···--·--·--········--·······-····-·········-···---······ ········-···-·--········· Forum

I responded that (2) required that yx = xy, and if this bothers me very much. If the first group of students is at all was not true, a different result is needed. When x and y are typical, and I am afraid there are many more like them, then independent, the complete symmetric function of degree n we have very serious problems which will be masked by in two variables is the result. This is an important function, the obvious ability of the second group. We need students as is (2), so it is natural to ask if anything else exists with a like the second pair, but we also need a large middle class different commutation rule. In particular, if of students who understand mathematics, are comfortable with it, and are able to use it. Since I have become worried (4) yx = qxy, qx = xq, qy = yq about this group of students, I have tried to find out what our students know when they start mathematics at college. and if [k ]q is defined by A year ago, while teaching a short section on analytic geometry in a calculus lecture, it suddenly dawned on me that their knowledge of geometry was probably even worse (5) than their knowledge of algebra, so it would be a good idea to prove the Pythagorean theorem before using it to motivate between points. Because this was not calculus could they find a formula for these coefficients? To get them the distance obvious problem started, I stated and was not in the book, there was the of encouraging them to think about the proof. My solution (6) was to ask them to give a proof for an extra 5 points, out of 600. After they turned in this quiz, I gave a proof and and told them they would get an extra 3 points if they turned in at the next lecture a correct proof different than mine. Sixty-five students turned in something for the quiz. Most tried to prove it using trigonometry. and asked if they could tell me the next case. They started with x =r cos(} (x +y)4 =x4 + (1 +q+q2 + q3)x3y + .... y = rsinO The one stating this said he did not see the pattern for the next coefficient, but the other two were obvious. I saved and them time and stated the coefficient of x 2y2 as sin2 (} + cos2 (} = 1 so and asked if they could now figure out the general case. The same student said he did not see the pattern. The other responded by saying this could be factored as Many others stated the law of cosines and then took the angle to be a right angle. One student gave a correct proof. In the fall of 1991, I was teaching an honor section of second semester calculus. All the students were in their and then together they rewrote (6) and (7) and the case first semester at a university and had had their previous n=4 as calculus in high school. The first day they were asked to tell something about their background, such as, was there a mathematics club in their high school; had they gone; and what did it do? I also gave them two problems. The first was to state and prove the theorem of Pythagoras and the second was to derive a formula for the sum of a finite geometric series. This was stated as 1 + r + · · · + rn since it was unlikely all knew what a geometric series was. and There were 22 students the first day, and the results were somewhat better than the previous year, as they should have been since this was an honor section. Only one student knew how to prove that c? = a2 + b2, but the rest knew they did not know how to prove it and did not give obviously false proofs. However, no one knew how to derive a formula for 1 + r + · · · + rn; one knew the formula but could not Then they said the general result was clear. prove it and one knew what it was when r = 2. These two That was very impressive, and I suspect I was talking questions so shocked some of the students that they changed to two people who will be good mathematicians. This split to a regular section. Only 15 were there for the second

MAY/JUNE 1992, VOLUME 39, NUMBER 5 425 Forum week and 14 took the final. They were asked the geometric This is a good high school with more National Merit series question again, and all except one knew how to derive semifinalists than any other school in Wisconsin. If the the formula. In the middle of the semester, two students teachers there do not understand what their better students talked to me separately and each said they were taking an should learn, then we have failed in teaching them what economics course. When the professor started to talk about is important and what is of secondary importance. I think the multiplier effect of money, a geometric series was used, understanding these two results is important. After all, and they were the only students in their respective lectures many of our students wear a button which says "Question who knew how to derive this formula. I then talked to a Authority." Here they can understand something, and so friend who is a professorin the economics department and do not have to take the facts from an authority. That is asked if their students should know how to sum a geometric an important message to give them, and these facts are series. He said, "Of course, but they never do, so we always important enough that they should be understood by the do it ourselves." That says something to us, as well as to better high school students. high school teachers. I gave the q-binomial theorem problem mentioned above I went to the local high school to talk to some teachers, to the students in the honor section of calculus. Two groups, to see if I had unrealistic expectations. I think our best one of two students, one of three, solved it. The students students should know how to derive a formula for the sum were not dumb; they had never been challenged sufficiently, of a geometric series. The calculus teacher said I was being and too little had been expected of them. unrealistic since these students had not seen these series for Before you try shock treatment, as I did the first day, two years. It was really one and a half years and I think consider an unintended consequence. There were six women they should have used them in calculus. When they were in the class the first day, and none were there at the end taught this in precalculus, many series were taught at the of the week. I called them over the weekend and was able same time, and the teacher did not see any reason why the to talk one into staying. The others said they did not want students should remember this one rather than some others. to work as hard as it seemed they would have to in an In fact, they did not remember any, but should have known honor section, so they stayed with the regular sections they this and a finite arithmetic series, and the best should know had transferred to. I do not believe mathematical ability is the binomial theorem. different by gender, but it seems likely that confidence is. The teacher who teaches advanced geometry said he I returned the quiz the next day and told the class how would have been surprised if the students could prove the poorly everyone had done, so they were all in the same Pythagorean theorem. It was proved in class, but the students position, but this was not enough to keep from scaring some were never tested on its proof, only on applications of it. of the students. Next time I teach a class of bright first year I said I would have asked them to give two proofs and students, I will move somewhat more slowly to show them then write an essay on which proof showed more insight, or that higher expectations are necessary if they are to profit which one they liked better and why. from their chance to get an education.

Summer in Cambridge

The American Mathematical Society joins the London Mathematical Society in welcoming mathematicians from around the world to Cambridge, England, June 29-July 1, for the frrstjoint meeting between the two societies. The AMS is pleased and honored to help foster international cooperation among mathematicians.

While you're attending the meeting at Cambridge, visit our exhibit on the second floor of the Mill Lane Lecture Room Block. See our American Mathematical Society newest publications, learn about our electronic products, and Post Office Box 6248, Providence, Rhode Island 02940 talk with us about membership services. Telephone 401-455-4000

426 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Edited by Keith Devlin

The mortals adored what was luxurious and incompre­ hensible. Tales of Gods and Heroes: The red-ucians never fought back. They adored their "The Nectar of the Gods" Gods in silence. Red-uce was a religion for the poor. Some of the red-ucians could not venerate the First God, Har-wa­ M. C. Nucci* re. They could not afford even a small altar of Har-wa-re. Few red-ucians were lucky enough to use somebody else's Once upon a time, there was one God called Har-wa-re. altar. One of his sons was Sof-wa-re. In spite of the new religions, life was still miserable One of Sof-wa-re's sons was Sym-ba-lg. for the Mat-hm-cians. Only a few mortals were aware of From him all the Gods descended. the Threefold and venerated the new religions. Most of the The Gods were living on a mountain called Csy-ple-uce, Mat-hm-cians were still working hard by using penand­ drinking nectar and eating ambrosia. The mortals down papers. on the earth venerated and feared them. They could not One day a God called Mercury, who was the patron of understand the Gods' Mysteries. the merchants, deserted the Three Horns. It is said that he Life was hard on the earth. Some mortals, called Mat­ was tired of being an immortal automaton and thought that could be more exciting. He soon hm-cians, had to work huge fields in the Land of Mat-hm-ics. life among the mortals realized that the rich mortals only could afford to be excited. Their tools were small and inadequate. They called them How could he become rich? penandpapers. Mercury had an idea. He decided to sell to the mortals Although the Gods were enjoying themselves, life was a diluted type of the Nectar of the Gods. Also, he added pretty boring. One day the Gods had a bad argument some artificial flavors and colors to appeal more to the was shaken by an about an Apple. The Mount Csy-ple-uce unsophisticated taste of the mortals. The price was very earthquake and split into three horns: Ma-csy-ma, Ma-ple, high, yet it was a commercial success. and Red-uce. Three new religions were born. The mortals liked it a lot. Everybody wanted it. They felt First was Ma-csy-ma. It was the only religion which was like Gods. After all, nobody knew the difference between allowed to use twice the holy word Ma. the real and the diluted Nectar. The mortals decided that Second was Ma-ple which was allowed to use Ma once. there was no reason to venerate the Gods anymore. Third and the most neglected was Red-uce, which was The Gods felt threatened. What could they do to reinstate not allowed to use Ma at all. The Gods of Red-uce lost the their authority? The Three Horns had a meeting. They argument and were punished by the absence of Ma. decided that the only way out was to make the real Nectar It is said that the argument started because some of available to the mortals. the Gods wanted to help the poor Mat-hm-cians, but others Unfortunately, the real Nectar was hard to sell, in spite opposed it very strongly and won. of being cheaper. The real Nectar had a very ugly taste, On the earth, the fanatics of Ma-csy-ma and Ma-ple were and none of the additives. However, some of the poorest very loud and started a holy war against the red-ucians. Mat-hm-cians bought it. Red-uce became very unpopular because of its few sacrifices The real Nectar had a strange effect on them. At first, and mysteries. they felt light-headed, wandering around, and hitting all the keys (sic) they could find. Then they spent hours looking *Maria Clara Nucci is a tenured researcher in mathematical physics at the at all the windows, cursing the Gods, and neglecting their University of Perugia in Italy. She spent three academic years at the Georgia own fields. Finally, after many drinks, they got used to it Institute of Technology as a visiting assistant professor. One of her areas of research is the solution of differential equations implemented by symbolic and began to realize how strong they were. They could take computation. She can be reached by email at: [email protected]. care of their fields without the small tools. They could use

MAY/JUNE 1992, VOLUME 39, NUMBER 5 427 Computers and Mathematics the power of the real Nectar to cultivate their fields faster and better. Unfortunately, the Gods imposed a very strict rule to go Reviews of Mathematical Software with the sale of the real Nectar. No mortal was allowed to use the newly acquired power without the Gods' help and advice. But what could one expect from a bunch of ungrateful mortals? Some of the Mat-hm-cians disobeyed. The worst Mathematica 2.0 were the Mat-hm-cians who came from a very low-class area called Ap-pli-mat. They drank the real Nectar and used Reviewed by Sha Xin Wei* the new power without the Gods' advice. Not only that, but they also dared to cultivate strange vegetables thought to be an inferior type of ambrosia. The Ap-pli-matcians made Abstract themselves hated both by the other Mat-hm-cians and by the The Mathematica computer system is reviewed from the Gods. perspective of a mathematical user. Familiarity with version The other Mat-hm-cians liked only the diluted Nectar 1.2's basic features is assumed. with its additives. They could not bear the strong taste of the real Nectar and disliked the ambrosia-like vegetables, which had a very bad smell for their delicate nostrils. At that time, the Gods had left the Three Horns and were living among the mortals. They were considered strange people, eating strange food and talking an unintel­ ligible language. They were called X-per-ts. Some of them became judges and decided to punish the Ap-pli-matcians for breaking their rules. They sentenced the guilty Ap-pli-matcians to death. The capital sentence was administered by an old device called nogrant. However, the X-per-ts were still Gods, and their punishment went beyond those sinners' death. In Hell, the souls of those bad Ap-pli-matcians were forced to go around for eternity begging for bits of cpu. Figure l: Geodesic on a Dupin torus (A. Gray). From then on, everybody lived happily on the earth.

Introduction Mathematica 2.0 is at once a programming language, a Editorial symbolic calculator, a multimedia structured editor support­ The remainder of this month's column is devoted entirely ing computed or sampled sound, graphics, animation, and a to two reviews of the new Version 2.0 of the Mathematica virtual operating system shell. It is available from Wolfram system, covering implementations for the NeXT Cube, the Research, Inc. 1 Sun Spare 1+ and Spare 2, the Macintosh Ilfx, and Windows. The computation Kernel runs on all major computers, Familiarity with the previous Version 1.2 is assumed. including Macintosh and IBM DOS machines; the multime­ One of the two reviewers also takes a look at two small, dia outline-structured Front End runs on Mac, NeXT, and related products, Mathematica Help Stack and Mathematica Windows machines.2 Prices range from a few hundred to Quick Reference Booklet, both from Variable Symbols. thousands of dollars, depending on the machine and whether The column plans to run reviews of other large scale you run Mathematica over a network. 3 This review is based mathematics systems in the corning months. on Mathematica 2.0 beta 3 on a NeXT Cube 2.0, Sun Spare 1+, Spare 2, as well as the release version 2.0 for the Editor's address: Macintosh II fx. The window/os are NeXT 2.0, X Windows, and Mac Systems 6.0.5 and 7.0. Professor Keith Devlin Department of Mathematics and Computer Science *Sha Xin Wei is a graduate student in mathematics at Stanford University, Colby College working on a dissertation in differential geometry. He serves as the mathematics Waterville, Maine 04901 and scientific simulations consultant in the Academic Software Development group at Stanford. He can be reached by email at: [email protected]. Correspondence by electronic mail is preferred, to: 'Wolfram Research, Inc., 100 Trade Center Drive, Champaign, lllinois 61820-7237, telephone: 217-398-0700, email: info.wri.com. [email protected] 2The X Notebook Front End is rumored to be coming in a year. 3 Mathematica is bundled free with the NeXT for academic purchasers.

428 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Reviewer's Perspective Having written mathematical applications in languages rang­ ing from APL to Object Pascal and NeXTStep, until Math­ ematica no commercial program seemed useful for research in my own field, differential geometry. Like many, I found existing symbolic manipulation programs (smp) much too cumbersome to learn, and too limited to use. I'll try to take the perspective of a mathematician who's familiar with programming but prefers to work in a language as high­ level as possible, so more emphasis will be placed on the expressivity and mathematical naturalness of the language than on computational time/space-efficiency.

First Look - The Interface Following Victoria Bush's suggestion,4 let's take a tour of Mathematica 2.0 on the NeXT. Upon launch, we see that version 2.0 retains the outline structure of the original Notebook Front End, with strongly typed cells (input, output, graphics, etc.) which can be rear­ ranged and hierarchically regrouped. One of Mathematica' s chief distinctions among smp's is its sophisticated interface, which integrates formatted text, and computed or sampled graphics and sound with "live" algebraic expressions. The -. • 1 •• ·> •••••· r-• rttJ. Front End supports noncontiguous selection, plus Mac-style a •> IIJI:t. 1' u"tJ, .,,.··-> l'l•t• .. ,••. Cut-Copy-Paste and limited Undo. _._. • ·~ ·~-!.'~-; C: • ... ,.,. Menu groups have been rationalized so veteran users •.••• y- ~lJ •-• tlll•t ·• •t•r "" •• 'lt•t .... th will have to re-orient themselves. Zoom and cell type popup -•--fUid;llll~ (t...... I· I"""+ --··h {a,y,at, menus have been attached to the new Front End. 5 Indeed, features such as rulers providing much better control over layout, multi-style text cells, indexing, and the luxurious Find menu enable one to prepare books entirely within Mathematica. One may view the page at an enlarged scale while printing at the finer scale on paper, thus reducing the need to change font sizes or cell types just to keep expressions contained on the screen. The Graph menu suggests one of the principal reasons to use the Front End. Special recognition should be given fdr the embedded PostScript interpreter. One can drag-expand a graphics cell to arbitrary size, read off point coordinates, copy and paste points, even translate graphics between several representations including PostScript, Mathematica Input Form, PICT, or TIFF, depending on the machine. Figure 2: Macintosh and NeXT Notebook Front Ends. Animation is quite straightforward: select a set of graphics Unfortunately, the Front Ends do not support the interac­ cells, then choose Animate Selected Graphics. VCR controls tivity common to Macintosh programs: direct manipulation, appear that allow you to vary the speed and direction or mouse-select-drag-scaling, object-oriented graphics, and the single-step through the frames. 6 Printing is also simple: select like.1 Understandably, WRI labors under the cross of lowest your graphics and choose Print Selection; Mathematica ships common denominator graphic user interface technology, by PostScript to the printer. committing to a uniform notebook interface across X and Windows, as well as Mac and NeXT systems. One would 4AMS Notices, 37, 10 (December 1991). appreciate, however, at least the ability to rotate or translate 51n two small but annoying respects, the new Front End seems less friendly than version 1.2: key equivalents for the cell types don't work until you first 7 Milo had a very elegant rectangle-select zoom feature. Theorist even click a cell's border, and on the NeXT one must dig farther into the menus in supports this on its 3D surface plots. Theorist allows you to spin a surface order to change a cell attribute (using Style Inspector). by mousing on it directly, rather than going to a separate dialog. Theorist, 6 Animation on non-NeXT unix machines requires the Animation.m package however, is overly encrosted with buttons and popup menus for my taste. Both and must be mediated by the graphics driver appropriate to the window graphics of these Mac programs support direct manipulation algebra, which should come system. WRI supplies the necessary files. into its full strength in the emerging pen-based computers.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 429 ...... -...... -······-··-······-···· .. -··········-···"""""""""""--"·····-····------llllr············-·······················----········-········-····-·········--··················································-··-···-···· Computers and Mathematics

an object by directly mousing on the graphic. 8 Despite some calls for it, the new Front End does not support '113X, relying instead on a crude but readable 0.5 fixed-width font, line-oriented format.9 Four of the most useful help commands in the Front End, besides Cut-Copy-Paste of course, are command completion -0.5 (1\k), parentheses matching (1\B), query mode (!\ ?), and template (1\i). -1

Figure 4: Plot of cos(x) superposed with cos(:z:) + •i•~;\ Mathematica takes care of myriad details such as placing tick marks, scaling axes, perspective, and color shading, most of which you can adjust via options. The almost overly rich set of plotting functions 10 draw parametrized curves and surfaces, level sets, as well as complexes of geometric primitives: points, discs, polyhedra, etc. ParametricPlot3D [ { y Sin [x] , x + Cos [y] , Sin [y] Cos[x]}, {x,0,4}, {y,-1,2}, Boxed~False, Axes~ True, AxesEdge ~ {{-1,-1},{-1,-1},{-1,-1}}, AxesLabel~{"x", "y", "z"}, ViewPoint~{-0.783, 3.228, 0.647}] ParametricPlot3D (Figure 5) for both curves and sur­ faces is now a built-in function. Following the laudable principle of unifying treatment of graphics objects and alge­ braic objects, graphics can now be nested or presented as arrays, superposed, colored according to custom functions, or projected under arbitrary maps. Graphics now can be trans­ formed (cast) from one type to another.U Unfortunately, not Figure 3: 3D View Point Selector Panel. all information survives this casting: level curve point lists in ContourGraphics cannot be extracted, for example, even after casting into general Graphics3D type. Kernel Features Over 280 objects have been added to Version 2, but this is not an unalloyed blessing. The plethora of structure operators described below might more sensibly be merged into one polymorphic structure operator; similarly with the graphics functions.

Graphics One of Mathematica' s great strengths is its integrated set Figure 5: A parametric plot. of graphics operations. The Front End set a standard with 30 perspective has been slightly generalized to allow Postscript-based script-generated graphics which could be choice of both Viewpoint (where the eye is placed) and manipulated in the same window· as the algebraic formulas ViewCenter (where the eye looks), but it's still nearly used to describe and transform them. In Mathematica, you impossible to get inside a complicated surface and view it simply type inside out, because the ViewPoint cannot be placed close Plot[ {Cos[x], Cos[x] + Sin[x- 3]/2- x}, {x, 0, to the origin. In fairness, we note that no other common 3/2 Pi}] smp has as sophisticated a rendering system. Some defaults to plot a set of curves. (Figure 4) arguably could be improved, e.g. ClipFill could default to None to avoid spuriously filling in holes on truncated 81 understand that it would be quite difficult to "invert" a mouse location surfaces. through a PostScript rule-description, but one need not have a complete inversion of mouseloc-->(point in model space), merely a way to map 10Plot, Plot3D, ParametricPlot, ParametricPlot3D, DensityPlot, ContourPlot, mousedrags to rotations, which is a much simpler matter. Mter all, that's what plus analogous functions for arrays. the ViewPoint selector does already, but in a separate window. 11 For efficiency reasons, geometric objects are represented in various 9The Kernel, however, can convert Mathematica expressions to 'lEX. C, or formats, e.g., Graphics (curves or points in the plane), SurfaceGraphics (graphs Fortran formats. 'IEXForm works best with expressions that fit on a single line. z = f(x, y)), or most generally, Graphics3D.

430 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Algebra matrix operations include Inverse, Transpose, Row-Re­ Mathematica' s Solve and sister functions work best with ra­ duce, Eigenvalues, and Eigenvectors, now supple­ tional functions; version 2 has been augmented by a general mented by Pseudoinverse, SingularValues, QRDecom­ inverse function notation that is of debatable value, especially posi ti.on, and SchurDecomposi tion for numerical matri­ when dealing with transcendental functions or functions with ces. The standard Linear Algebra packages now include no global inverse. Currently, the algebraic operators tend more matrix (column, row, block) operators and an extended to be too fine, or too coarse. 12 For polynomials, there SymbolicSum. is an extensive set of special operators-Together, Col­ One of Mathematica's most powerful features is the lect , Simplify, Expand, etc.-to factor out and collect general mechanism for dealing with array structures, using expressions, some of which work only over Q. Experience APL/LISP-like functions such as generalized inner and with smp's suggests that flexible, robust medium/fine grain outer products. Version 2.0 augments the set of structure algebraic operators such as Expand or Collect are more operators-Select, Sort, Cases, Count, etc.,-yet there useful than behemoths. To illustrate with a toy example, are gaps: Cases and Position should accept boolean tests, take the expression Q derived from a quadratic expansion of and Select should accept patterns.

2 -sm. ~t -a) about t = 0: Q = Normal[ Series [1/ (2-Sin [ t-a]) , t, 0, 4]] ; Analysis We collect terms and extract the numerator: In addition to the splendid variety of special functions, rang­ Q = Together[Q]; P = Numerator[Q]; ing from AiryAi and Erf to Riemann Zeta, a reasonable and then extract the coefficients of t2 in P : complement of basic tools are available, such as Find­ Factor[Coefficient[P, t,2]] 12 (2 + Sin[a])2 Root, FindMinimum, Series, Limit and differentiation (2 Cos[a] 2 + 2 Sin[a] + Sin[a] 2 ) D. Directional limits are useful as far as it goes, though in Most mathematicians are disappointed to discover that one of the rare lapses into "magic numbers," the notation symbolic expressions tend to mushroom under automatic +1 or -1 could have been replaced by more descriptive symbolic transforms, unlike numerical calculations, which names. One wishes for a generalization to direction vectors can be controlled slightly better. For example, algorithms for in multivariate real functions, as well as a more robust way numeric matrix inversions are of O(n2) at worst, whereas of handling singularities, perhaps. Limit and a few other symbolic inversions are O(n!). General algebraic simpli­ functions have been generalized to Reallnterval set values. fication of general expressions can be quite difficult to For example design because the computer doesn't possess a human math­ U =Limit[ Sin[x], x-> Infinity] ematician's heuristics, yet. Tensor calculations are a good returns example. We typically apply symmetries and identities in Realinterval[{-1,1}] our head and expand terms only when necessary, keeping which works in simple cases. However, although one can, other terms under control by symbolic substitution. Without for example, evaluate heuristics, an smp like Mathematica (or its siblings) finds V = 1/(U + 4) it difficult to avoid exponential blowup of symbol com­ Rea1Interval[{1/5, 1/3}] plexity. Though the authors note that there is no general evaluating any but the simplest functions reveals some finite procedure for checking symbolic identity, 13 one basic limitations: criticism of Mathematica is that it doesn't present algebraic ArcTan[V]Realinterval[{Min[ArcTan[1/5], expressions in human-readable canonical form even in some ArcTan[1/3]], Max[ArcTan[1/5], ArcTan[1/3]]}] fairly standard domains like rational functions or matrices. f [Realinterval[{a, b}]] is formally defined as the Unfortunately, Short provides too brief a structure synopsis shortest interval containing the image of the interval [a, b] while the new Shallow, which presents the top level of an under map f. The Kernel does not support set-valued maps expression tree, often fails to capture interesting features: or interval arithmetic, though the designers may be aiming Shallow [Q] (384 + Times [ «3»] + Times [ «3»] in such directions. 14 + Times [ «3»] + Times [ «3»] + Times [ «3»] + Novices will have to sort out differences between D and Times[<<3>>] + Times[<<2>>] + Times[<<3>>] + Derivative: Dis the operator on the space of differentiable Times[<<3>>] + <<20>>) I (24 Plus[<<2>>] ) 5 functions, whereas Derivative is used to denote its images. Canonical forms for certain types of objects, and some Mathematica 2.0 can now handle an appreciably extensive way to customize the structure of representation of algebraic range of indefinite integrals, but still suffers from some prob­ expressions (e.g., placement of minus signs and reciprocal lems. For example, while the positive branch of v'1 + cos(x) powers) would ameliorate this generally intractable problem. is plotted by default, the integral f07r v'1 + cos(x)dx is Linear programming problems (both equality and in­ evaluated to -2~. equality) can be solved using built-in functions. Basic Moreover, the definite integral doesn't try to look for

singularities in the integrand, hence J~ 1 ,12 dx evaluates to 12Maple's op structure operator is another example of a powerful but too complicated way to extract subexpressions. 13Wolfram, p. 270. 14There is an instructional package NumericalMath 'lntervalArithmetic.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 431 ...... _...... ················-·-····················-····--················--·.. -···-········--········------·-···-···-·······-·-······--···----···-····-·····-··-·-·-·····-·················-·-····-···-.. -·-··--·-·· Computers and Mathematics

-2. Maple and MACSYMA reportedly share these sorts of amalgam of functional, procedural, list/array-based, and rule­ defects but to a lesser degree. 15 A useful enhancement would based styles, inheriting ideas from LISP, C, APL, and older be a general change of variables user option. smp's. DSolve and especially NDSolve now provide convenient At the most fundamental level, Mathematica works by ways to study ordinary differential equations; DSolve finds replacing sequences of strings by other sequences of strings, closed solutions for linear systems and simple nonlinear hence the description, rule-based symbolic manipulation. systems for which the derivatives can be easily isolated. Ar­ Mathematica's rule-based rewrite system allows you to guably the more useful function, NDSolve uses a fairly robust quite easily teach it formal manipulations such as group adaptive mix of integrators, the Adams predictor-corrector relations or algebraic simplifications. method for non-stiff ODEs and backward differentiation As a simple example, to reduce polynomials in the ring formula/Gear method for stiff ODEs. (Figure 2) Q[a], where a is a root of an irreducible polynomial, say Cyclotomic[9, x], we generate a rule Numerical Operations, Data Analysis rule = AlgebraicRules[ Cyclo- tomic[9, x]==O] Now numeric functions can be compiled for speedier eval­ x6 -> -1 - x3 uation, especially in plotting and integration of complicated then apply it, expressions. Some control structures can be compiled, but (1-x) 12 I. rule not array structures. to obtain The built-in Fit function apparently duplicates the Lin­ -1143 + 846 x - 441 x2 - 1143 x3 earRegression function that comes with the Data Analysis + 1287 x4 - 1287 x5 packages. It's quite convenient for ''back of the enve­ Algebraic algorithms can be written naturally and with lope" data analysis, as are the new approximation functions concision. Still, rule-based symbolic rewriting, while pow­ InterpolatingFunction and InterpolatingPolynomial. erful, can be tricky to use, especially since the order of Unfortunately, these work only on one-dimensional data. application may not be precisely controlled. A rule to com­ Now data can be approximated by piecewise polynomials plete the square, for example, would be easier to write if with specified degree and boundary derivative values. there were some way to control an expression's canonical Don't expect Mathematica to find eigensystems for ordering. lOOOx 1000 matrices; there are plenty of applications plus The functional syntax allows one to compose oper­ extensive libraries of public domain code more suitable for ators on abstract objects, such as Ricci [metric] and numerical analysis.16 Unless you are a specialist, however, RiemannCurvature [metric] which can be defined without Mathematica's arbitrary precision and rational arithmetic specifying the dimension or the metric in advance. eliminate any need for a calculator program, particularly One can write, for example, a procedure which automat­ if you use its powerful array operators and functional ically generates a lattice difference scheme directly from a algebra. One should be mindful that computers treat ratios differential equation. Consider a differential equation of the of integers quite differently from decimal representations, form: and Mathematica is no exception: zeroes of functions or af 2 solutions to differential equations may be found more at = [J, D J, D f] accurately when coefficients are given in one form and not the other. where function f : Rn x R ---+ R is represented discretely Version 2.0 now handles numerical FFT's in arbitrary by an n-dimensional lattice of real values for each t, which dimension. we'll denote by f. Partial derivatives of f are represented conventionally as symbols, e.g., Language: naturalness, extensibility, expressivity ,Pf While the interface is most important as one learns a dx1dx3 ---+ f13 complex smp--and frequently determines whether or not an smp is tried at all-the most important aspect of an smp Given the dimension of the domain n the rewrite rules for experienced users, to my mind, is its scripting language. diffRel {f1 -> d0[1, f], ... ,f13 -> dD[1, First of all, names should be fully spelled out, without 3,f]' ... } cryptic letter hashes like Maple's dpoly, op or intP We themselves can be automatically generated, using string can extend Mathematica's basic functions by defining our operators, where dD is a difference operator defined on own functions in scripts using a syntax close to mathematical lattices of arbitrary dimension defined by rules like: usage, unencumbered by nonmathematical directives as in a d0[1, f_] := RotateLeft[f] - f typesetting language like 'lEX- The language is an expressive One then can translate the differential equation simply by appending the rewrite rule diffRel: 15Many examples have been posted on the sci.math.symbolic bboard. df_dt = Phi[f, Div[f], Hessian[f]] I . diffRel; 16Examples: Matlab--numerical arrays, S-statistical programming, NetLib-­ f += df_dt; (* f = f + df_dt;*) scientific computation source code. 17Using aliases or the Front End's command completion, slow typists need The second statement is a matrix transform f ---+ f + 1t not peck out long names in full. (assuming unit time step for simplicity). There are no trivial

432 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics iterate-loops and no indices. We gain tremendous flexibility, approximation, computational geometry, vector analysis, concision, and clarity by writing programs using a high-level animation, and a host of graphics functions mentioned language whose syntax is essentially standard math syntax. above. The packages vary in robustness and sophistication, but are generally well documented, with references to Operating Systems, MathLink literature where applicable; some can serve as examples of As mentioned above, Mathematica is broken into two parts: a scripts. Kernel which performs the core computations-like graphics Public domain packages are available by anonymous calculations, polynomial algebra, bignum arithmetic-and a ftp from Internet sites throughout the country, including Front End which presents the multimedia notebook interface otter.stanford.edu. As the editor of the otter archive, I en­ and deals with all human interaction. courage submissions of research or instructional applications Version 2 contains a virtual operating system which that may be useful to the mathematical community. The provides machine-invariant means to list, create, or read computer bulletin boards sci.math and sci.math.symbolic oc­ files, change directories, and execute external routines. The casionally post useful information. Also, Addison Wesley's Kernel communicates with external processes in three ways: Mathematica Journal provides an Electronic Supplement (1) by reading and writing data in ascii files, which is quite with each issue. straightforward, (2) by calling compiled code from within Mathematica, and (3) by calling Mathematica from within Remarks on Limitations your own program. WRI supplies a compiler script named I have highlighted a few design problems, though unlike mcc and files to be included in your custom code so that some earlier reviewers, I have focused on mathematical it can be invoked just as any built-in function. The most rather than computer science issues such as garbage collec­ powerful extension is to compile WRI' s MathLink methods tion, speed, internal representation of data, or the lexical in your own program to pass typed strings to the Kernel representation of some binary operators. and interpret its answers in your code. You can, in this way, write your own interface and treat Mathematica as a Correctness symbolic/graphic computation engine. Command-line "front Mathematica l.O's bugs in algebra and integration disap­ ends" have been written in emacs 18 and 'IFX; friendlier ones pointed early users. Experience with large software systems have been written on the NeXT. 19 One could perform a teaches one to take a more sanguine view of any new com­ service to the community by writing a direct manipulation plex code, expecting hosts of bugs to be reported and-if graphics front end incorporating some ideas from Live20 the authors are responsible-corrected. Version 2.0' s algebra or Theorist, or structured array front ends for matrices or and integration routines have been speeded up and made sequences of groups. more correct, modulo the branch cut problem, and now approach Maple in "accuracy" if not speed. Packages Mathematica comes with an extensive and growing set of Sets, Inequalities, Logic "packages" that contain scripts to be loaded when needed. Mathematica's chief mathematical shortcoming is the lack The DeclarePackages method prepares Mathematica to of a general typing mechanism-a way to define math­ automatically load a package when one of the package's ematical structures. For example, while one can define a functions is invoked. There's a constant tension between custom membership function which indicates which symbols keeping the kernel small for speedy launch, flexibility, explicitly belong to a class: extensibility-which requires more package juggling-and QuaternionQ[a_] := (Head[a] == Quaternion) stuffing the kernel with everything for speedy execution of there is no general mechanism to declare that a Real is a individual kernel functions-which requires a smaller pack­ Complex is a Quaternion; moreover, no type checking is age library. Mathematica's balance still needs adjustment. performed unless you redefine functions to explicitly do so. Why are some quantum mechanical functions built-in when Related to this type problem is the absence of the notion of a there are no good built-in rules to handle complex arith­ general abstract set, which was noted in the review of version metic? On Unix platforms, one may "compile" packages 1.22 Most computer programmers instinctively assume that into a custom image of Mathematica, a useful feature for all interesting sets are enumerable. Other shortcomings are experts. the absence of inequalities or logic calculus. Package topics now include recurrence equations, special One rigorous general solution might be to implement matrix forms, permutation and rotation groups, symbolic some sort of facility that installs facts, such as "if f is sums, 21 symbolic Laplace and Fourier transforms, Pade odd and integrable, then its integral over R is zero" in a knowledge system. It seems safe to say that current 18 D. Dill; D. Jacobson, Mathematica Journal, vol 2, no. I semantic reasoning systems are too cumbersome and weak 19 including T. Gray's RealTime Algebra, M. Mezzino's PhaseScope, and working mathematician's hard disc. Objective Technologies' MathPalette. to deserve space in a 20 Live is a graphics front end written by J. Friedman for Silicon Graphics. On the other hand, the utility of partial solutions should be 21 Sum[a[k] ,k,kmin,kmax], where ~ is a rational function, replaces Version l's GosperSurn. 22AMS Notices, November 1988 [3]

MAY/JUNE 1992, VOLUME 39, NUMBER 5 433 Computers and Mathematics investigated, especially if that would strengthen automatic program, not something one should expect to run on an IBM algebraic simplification. 23 PC or Mac SE with only a couple of megabytes of RAM. To appease hardware heavies, speed benchmarks have Help, Documentation been collected on a range of machines.25 A very coarse Mathematica's online help is exemplary among smp's. estimate of relative times is Some effort has been put into placing the cursor near Mac!Ifx : Sparc1 : NeXT2: Sparc2: MIPS where the parser chokes and generating meaningful error 10 9 8 5 : 2 messages. On all platforms ?foo elicits the usage statement where the numbers are average benchmark times, though for symbol foo from the Kernel's database on built-in or the relative times for individual operations can vary broadly. user-defined functions. Context, Names, Path, coupled Floating point speeds don't enter directly into most of these with wildcarding, provide ways to locate symbols defined symbolic tests, and the graphics speed depends critically on in several contexts, a useful feature when multiple packages how Postscript is rendered on a particular device. may be loaded into memory. The Front Ends provide Experience teaches that raw cpu speeds, whether mea­ additional help as mentioned in section 3.24 One defect is that sured in mips or mflops, have much less to do with how fast there's apparently no way to get a list of the acceptable values you can do mathematics with a computer than the algorithms of an option. For example, Options [Plot3D] provides implemented, the language you use to communicate with a list of Plot3D's options, including the default value the machine, and how data is presented. Order of magnitude AxesStyle-+Automatic, but ?AxesStyle doesn't retrieve differences in speed and memory can be significant, but its alternate values. Even Wolfram's reference manual does anything less is usually not. Connectivity, on the other not list the values in one location. hand, can be radically important. A Mac or Sun Spare Usage messages can be associated with any function; on a network becomes a completely different beast from even the language of the help messages can be specified. To a standalone machine. Mathematica' s designers had this in WRI' s great credit, they are committed to internationalizing mind when they decided to write the program in two parts, their system, though it's unfortunate that they cannot take and to store complete notebook structure information in ascii full advantage of Apple's internationalization support (e.g., files so they could be sent by email or ftp between any two Chinese or Arabic systems) because other operating systems machines on a network. are deeply bound to Roman languages. The most complete Since the Kernel and the Front End may sit on different non-European conversion is their Japanese edition. There's machines, one can optimize use of hardware. One arrange­ even a proximity spellchecker which can be useful for ment I recommend is to run the Front End on a Mac or novices; experts can tum it off. NeXT, hooked via Ethernet to a fast compute server, say a WRl has responded to widespread requests for recipes MIPS or Silicon Graphics with lots of memory. This way by publishing a series of Technical Reports describing the you can perform large calculations with as little as 4 M theoretical bases and usage for its graphics, integration, local memory on a cheap, friendly machine. One can even polynomial algebra, ordinary differential equations routines, run Mathematica over a network. with several instances of etc. While several Reports contain careful treatments of the the kernel collaborating on a computation. Sun Sparcstations theory (e.g., the article on definite and indefinite integrals), running X Windows work well either as servers or clients, more precise descriptions of Kernel algorithms would be but without a true Front End for non-NeXT Unix rna­ desirable. chines, viewing, transforming, or printing graphics remains relatively cumbersome. Speed, Memory, Networks What counts is the time it takes from the birth of a question Cost in your mind to comprehending the computer's response, It's a shame that WRl has been rather tight-fisted with uni­ not cpu clock speed! In one case culled from netland, versities, refusing until recently to give substantial discounts Mathematica 2.0 took about 45 seconds to solve a system of to academic clients. Some universities have been able to ODE's, where Maple V took 3 (on a Sun Spare), but adding negotiate site licenses with WRl, but only after extensive the days it took for the user to get a correct reply to a query consultation. about Maple syntax, Mathematica won hands down. In the early stages of exploration, one prefers flexibility, naturality, and expressivity over speed of execution, and often this Conclusion suffices. On the other hand, this is definitely a workstation Among the many interesting applications written in Math­ ematica, substantial systems include S. Christensen & L. 23 Maple is beginning to implement such a facility. MACSYMA had such Parker's MathTensor- tensor analysis with explicit metrics, features. ScratchPad is designed around such semantic lines, but appears to be J. Lee's DG- exterior calculus tensor analysis on bundles, somewhat labyrinthine. Schlumberger, Inc.'s Mathematica to C/Fortran translator, as 24 ~he Mac Front End even carries its own version of balloon help (Balloon Help ts a trademark of Apple Co.) which presumably will be subsumed under System 7.0's general help system. A COMMAND-? turns the cursor into a"?" 25 All machines had at least 8 M RAM. Benchmarks are available by which you touch on any window part or menu item to be described. anonymous ftp from otter.stariford.edu.

434 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics well as J. Uhl and H. Porta's Calculus&Mathematica course. so that a Windows version might be much better to These deserve independent reviews in this column. work with than the command-line oriented DOS version Mathematica's algebra and calculus, though systemati­ available before now. The marriage of the two programs, cally corrected, still suffer from significant defects. Unlike however, raises some concern. After all, both Windows other smp's, Mathematica was designed from the ground and Mathematica have a certain reputation for being prima­ up for machine-independent use, integrated graphics and donnas: they are finicky, occasionally unstable programs, algebra, and mathematical naturality. As a general purpose and they are both particularly demanding on the systems smp, geometric visualization and mathematical programming they run in. Running Mathematica under Windows seems language, it ranks among the costliest and the best. like asking for trouble. Unfortunately, these fears seem to have been entirely References fulfilled in the version under review: the main impression [1] Mathematica Journal, 1 no. 1-4 (1991), 2 no. 1 (1992). one gets is that of using an unfinished product, rather [2] Mathematica in Education, 1 (1991). than a release version of a major program costing a great [3] Jon Barwise et. al. Mathematica, AMS Notices, 35 no. 9 (1988) deal of money. This is largely a matter of problems with 1333-1349. the front end, rather than with the "kernel" (which does [4] Richard Fateman. A review of Mathematica, preprint (1991). the computations); unfortunately, the front end is our only [5] Barry Simon. Four computer mathematical environments. AMS Notices 37 no. 7 (1990) 861-868. doorway to the kernel. Since this is a review of the Windows [6] Stephen Wolfram. Mathematica-A system for doing mathemat­ implementation, rather than of the Mathematica system as ics by computer, Addison-Wesley, 2nd ed. (1991). a whole, we will largely focus on this side of things, with only a few comments relating to the Mathematica kernel. For a more complete description of that side of things, see the review by Sha Xin Wei, also in this issue. Mathematica 2.0 for Windows How good is your system? As might be expected, Mathematica makes serious demands on the computer system Reviewed by Fernando Q. Gouvea* on which it is to run. First of all, the program requires at least a 386 processor with a 387-compatible arithmetic Computer algebra systems have become part of the standard coprocessor; it would probably be happier on a 486. Next, work tools of most mathematicians. They are used as the kernel requires about 10 MB of memory to load (this research tools, allowing a much greater range of experiments is in addition to the memory used by Windows itself and and calculations on personal computers than has ever been by the "front end."). For most users, this will mean that possible before, and also as teaching devices, allowing one must create a permanent swapfile for Windows and students to look beyond the boring technical complexity use it for virtual memory. The tests we report on were of computing derivatives and integrals or row-reducing done on a 386+387 system running at 33 MHz, with 8MB matrices, so that, one hopes, the focus of our teaching may real memory and using a 15 MB permanent swapfile for go to the conceptual side of mathematics where it belongs. the program regularly and intensely, users Of the many available systems, Mathematica seems to Windows. To use their systems to at least 12 MB have achieved the greatest popularity. This is due, perhaps, should consider upgrading to its very well-designed interface, which makes using the of memory. well, considering how of­ program less tedious and more intuitive than is the case Installation went surprisingly for many of the other systems. This interface (the "front ten it is that one runs into trouble with automatic installation that every user is running a end," in Mathematica lingo) also makes the system an programs (which tend to assume with excellent teaching tool, allowing the program to show a plain-vanilla Windows with a VGA graphics driver and friendly face to students who might be intimidated by the Program Manager as the shell). The installation procedure greater complexity of interacting directly with the program copies all the relevant files to the directory you specify, kernel and also allowing instructors to create "notebooks" creates a new Program Manager group, and returns you to that function as interactive tutorials. Windows. No information is given as to which files are The incarnation of Mathematica under review brings being installed. all this to the Windows 3.0 environment, which seems to The first run: So let's try it. Double-click on the new have become the dominant graphical operating environment Program Manager icon, and . . . instant lockup. One can for MS-DOS computers. Considering the popularity of both see a dialog box on the screen asking for the usual name Mathematica and Windows, the appearance of this version and company information (and an unusual request for a is only fitting and expected. Windows, as a graphical numerical password), but the mouse is dead, keys do not environment, allows the use of the "notebook" interface to respond, and even a warm boot through the Control-Alt-Del Mathematica that is one of the most attractive features of keystroke fails to work. Reset time. the Macintosh and NeXT implementations of the program, Restart the computer, think. Since the mouse pointer froze immediately (which is not the case for most Windows *Fernando Gouvea is an Assistant Professor of Mathematics at Colby crashes), one suspects the mouse driver, which is the new College in Maine. His email address is: [email protected]. mouse driver from Microsoft (version 8.10), and includes

MAY/JUNE 1992, VOLUME 39, NUMBER 5 435 Computers and Mathematics a utility for fiddling with the color and size of the mouse as to get things to actually work.1 cursor. So let's not use that utility (which runs a separate Using the program: The most immediate thing one process of its own under Windows), but keep the new driver. has to deal with is the password business. The program Try again. would frequently ask for the password, usually on loading, This time, we get further. The dialog box pops up, but occasionally in later stages, too. My first impression asking for name, organization (why do software companies was that this was a particularly annoying form of copy­ assume that everybody belongs to some organization?), and protection. It slowly became clear, however, that this was a password to be found in a card that accompanies the not the case, as reports from other users on the internet program. Look up the password (long), type it in, and the described different symptoms. After some experimenting, I front end begins to load (as usual, the kernel is not loaded found the answer in a tip from Dan Halem at UCSC: until necessary). Before anything else can happen, however, I cured the password problem by changing my QEMM we get a UAE. setup. If you are using QEMM or something like it add Those who have never used Windows have probably "x=e000-e7ff". Then erase the password line from the never met the dreaded UAE: the Unrecoverable Application MATH.INI file in your windows directory. Then the Error message which Windows posts when some program next time you run it, reenter the information. It worked has done something naughty and needs to be killed. The on my system. WRI said they didn't know what the dialog box has an "OK" button; clicking on it will, if one problem was, but they thought it was related to QEMM, is lucky, kill the application while allowing one to exit so I started playing with it ... gracefully from Windows. (If one is unlucky, Windows gets killed too, and. one is left with either a locked-up machine This suggestion does work, and for the most part or is dumped back to DOS.) Fortunately, Microsoft has eliminates the repetitive request for the password, provided provided a little utility called "Dr. Watson," which gives one is not using the "stealth" feature in QEMM.2 However, some clue as to what is going on. In this case, "FE failed in I do still get an occasional "please enter the password" DISPLAY," which points to some evil interaction between message, especially after the system has been in a strange the Front End and the video driver. state, such as very low system resources. Very well, the video driver is known to be a little Having solved that problem (or, before it was solved, flakey (it is the "Turbo Windows" driver supplied with the having typed in the password), one can play with the Diamond SpeedS tar super-VGA card, which is very fast program. In general, it behaves very much like other but occasionally interacts badly with other programs). So, versions of Mathematica, and thus has the virtues and change the video driver, restart. defects characteristic of that system (see below for some This time, it works, but with one surprise. A dialog idiosyncratic comments). As usual, the graphics capabilities of the program are impressive, including the use of Display box pops up, asking the user to retype the long password PostScript technology that allows very detailed control of the from the license card. Once that is done, the program starts graphics output. (Doing graphics eats up memory, however, normally, and the kernel loads when requested, using up an and the Windows version does not have the "save after every alarming amount of memory. A little readout at the bottom computation" option that can be used to free up memory in right says how much memory is free; it keeps getting smaller the Macintosh version.) The program is also a competent as one works, since the kernel does not seem to be able to symbolic manipulator and very good at numerical work. clean out unused data from memory. Still, the program is For example, I computed a large number of the Fourier now usable. coefficients of several modular forms, drew pictures of the Calling for support is the next step. At the very least, platonic solids and made animations from them, used several one hopes that Wolfram Research will be able to give some of the number theory packages that come with the program, useful information on the incompatibility with the mouse all without problems. driver, which is, after all, a Microsoft product. The call There are, however, several glitches. reaches a friendly technician, who explains that he is a The most immediately noticeable is that the program is Macintosh person who really knows nothing useful about pretty much unable to print. In fact, on my computer, I have the Windows implementation and suggests that an email never issued a "print" command to Mathematica without message detailing the problems might be more effective.

Write up the message, send it out. 1The following may offer an interesting contrast: a few weeks after That was two months ago. No answer has been received, discovering the conflict between Mathematica and the new Microsoft mouse not even to my query asking for a reply. Now, of course, driver, I saw a (unrelated) posting on the Usenet by one of the Microsoft mouse programmers. I sent him a note describing the problem. He immediately my reviewer's package does include a phone number to call acknowledged it, thanked me, and a few weeks later sent me a note saying that with questions, but since a normal user sure won't have the problem has been identified, and perhaps can be solved soon. · that number, I decided to refrain from calling it. The lack 2This is a memory-management program, one of two "standard" programs of response to my request for support is quite a serious used for this on DOS machines. The interaction between Mathematica and QEMM probably stems from the fact that Mathematica directly accesses some problem, I feel. Many users of the program will lack the region of memory, and the fix amounts to telling QEMM to exclude that region expertise to figure out how to juggle their system around so from its managing.

436 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·-·······················································-········· ······················-···-··············-······--···------~-- Computers and Mathematics getting a UAE, and the fault has usually been serious enough The Mathematica kernel is the heart of the Mathematica to crash the Windows session entirely (one is left at the system, and it is not clear that any of the problems described DOS prompt at once). This is almost certainly due to some above have to do with the kernel itself. They seem to interaction between the front end and another of my drivers relate, rather, to the "front end." In fact, the Windows (the Adobe Type Manager? the video driver?). It happens implementation of the Mathematica kernel seems to be irrespective of whether I try to print to a dot matrix printer functionally equivalent to the Macintosh version (which is or try to get PostScript output to a file (and therefore is very the only one I compared it with). Notebooks transfer quite likely not a problem with the printer driver itself). I assume easily between the two platforms (they are text files, so the issue is solvable, but by now I am getting into "why no serious translation problems arise), and the output is bother" mode. essentially identical too. Similarly, not all the usual examples work. For example, The usual set of Mathematica benchmarks indicated on page 702 of the Mathematica book, there is the example that the speed of this version compares quite well with of solving the Lorenz differential equations numerically. that of the Macintosh version. To be specific, I ran the Attempting this will consistently produce a UAE. The same benchmarks under Windows and on a Macintosh Quadra is true for the examples that involve file access: as far as I 900. As expected, the Quadra is significantly faster, but not can tell, none of them work. unreasonably so. For example, Factor Integer [2~2~6+1] All these problems suggest that one should glance at the took 6.04 seconds under Windows and 4.08 seconds on the manual, and among the many bits of documentation one Quadra, and finds some "release notes" that inform us of other potential Show[Graphics3D[Stellate[Stellate[Icosahedron[] problems. For example: ]]]] took 12.02 seconds under Windows and 11.22 seconds on In the current release, you must be careful when you the Quadra. All in all, the timings seem quite respectable. Selection. Remember to select the word use Complete The virtues and defects of the kernel itself are becoming that you want to complete before you choose fragment well known, and are discussed in Xin Wei's article. As a Complete Selection. Then you must choose one of whole, I find the Mathematica system usable, but occasion­ words from the menu that appears on the completed ally rather strange. Perhaps the fact that so many of the Do not click outside this menu in the your screen. functions behave in a "natural" way underscores the few Mathematica window; if you do, you will not be that do not. For example, there are the usual annoying bugs able to dismiss the menu, and you will have to quit in the definite integration routines. My current favorite is Mathematic a. Integrate[Sqrt[1+Cos[x]],{x,O,Pi}] There are several other warnings in that vein, including which returns a negative answer. I assume this reflects the one that says that unchecking the "Group output cells with usual "branch cut problem," though doing the integral by input" option will cause the program to crash at the next hand does not seem to lead through any dangerous turnings. calculation. An experiment confirmed that the crash will While Mathematica may not be perfect, it is still quite indeed happen. What is more, the program will remember an impressive system for "doing mathematics by computer." your change in setting, and will keep on crashing until you The kernel is a powerful computational tool, and the change it again. (Why this menu choice was not "grayed graphically-oriented interface is relatively easy to learn. In out" is beyond me.) order to be useful for teaching and research, however, such A more subtle issue has to do with the Windows a program must be stable and dependable, and the current "system resources." It is my impression that Mathematica implementation of Mathematica for Windows unfortunately occasionally will fail to release the resources it no longer is anything but.4 It seems very likely that version 2.1 of requires, leading to a situation where resources are very Mathematica for Windows will soon be released, and that low and the system starts to behave strangely. This is not most of the problems will by then be corrected. Interested systematic and may be due to some strange interaction with users would do well to bide their time. other programs. All of this says "unfinished" to me. The bugs are known, and probably will be fixed. 3 However, the version being tested is not some prerelease version, but rather the shipping It a program that has 4 A recent press-release from Wolfram Research asserts that Mathematica version. seems unreasonable to release 2.0 is significantly more stable under Windows 3.1; I have not been able problems like this without correcting them. t9 test this, since version 3.1 is being released as this is written. The same document mentions a forthcoming version for Windows NT (which is still only 3Word on the internet is that version 2.1 should be out in a few months. a promise). It conspicuously fails to mention an OS/2 version.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 437 Inside the AMS

Annual Report of the Secretary • support mathematical education at all levels, • advance the status of the profession of mathematics, Robert M. Fossum encouraging and facilitating full participation of all individuals, and Strategic and Long Range Planning • foster an awareness and appreciation of mathe­ The pages of the 1991 Notices are replete with news about matics and its connections to other disciplines and the Society's planning for the future. The January 1991 everyday life. issue announces the creation of a Strategic Planning Task Force (SPTF). The complete report of the Task Force, which AMS Publications, Meetings, and Membership was approved by the Executive Committee and Board of These are the most important and visible programs for Trustees (ECBT) at its meeting in May 1991 (albeit not the Society. The publications program costs about 75% of unanimously), appears in the July/August 1991 issue of the the total Society budget and furnishes a similar amount Notices. The Task Force identified eight strategic issues that of the income. In addition to the recent downturn in the Society should address. These are: the economy, there are other issues that will affect the 1. The Mission of the AMS. publication program, such as electronic forms for delivery 2. AMS Publications, Meetings, and Membership. of published material. The major part of the publication 3. Other AMS Programs and Services. effort is expended on Mathematical Reviews. Efforts to cut 4. External Challenges Facing the AMS and the Mathe- costs while still maintaining the usefulness of the product matics Community. are under consideration. 5. Vitality of the Mathematics Profession. The Society offers two types of broad interest meetings, 6. Fragmentation of the Mathematics Community. National and Sectional Meetings. These have evolved into 7. Membership, Voluntary Leadership, and Governance. a fairly routine pattern. However, one can question whether 8. Internal Management of the AMS. the current patterns address the needs of all the members of the Society and whether these meetings should include The Mission of the AMS activities other than Special Sessions and Invited Addresses. While the original mission statement of the Society appears These questions are now under consideration by an ad hoc to be broad, it is nevertheless rather vague. The Task Force committee on Meetings. thought that it did not serve to guide the organization in And perhaps there are other areas in which the Society its role definition and decision-making. Thus a revision was can provide services to its members without significantly suggested and proposed to the Council in August 1991. increasing the cost to these members. For example, the After some discussion, the Council passed the following Society has established e-MATH, which has many electronic resolution: services. e-MATH is currently being supported by grants from the National Science Foundation. The Council of the American Mathematical Society adopts the following statement of mission: Other AMS Programs and Services The AMS, founded in 1888 to further the interests Reports from various Society committees and/or groups of mathematical research and scholarship, serves concerning these activities, as well as other issues and the national and international community through activities mentioned elsewhere in this report, will appear its publications, meetings, advocacy, and other pro­ from time-to-time in the Notices. grams, which • promote mathematical research, its communication External Challenges Facing the AMS and the Mathemat­ and uses, ics Community • encourage and promote the transmission of math­ The SPTF identified major external issues as: ematical understanding and skills, • the volatile job market for mathematicians,

438 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·~~-~---·~·----·-~·-~·-·--·-·---~~-~~--...._limmmmmmmMii&m-m·• Inside the AMS

• the renewal of the profession, Richard M. Schoen. There were eight Special Sessions and • mathematics education reform at all levels, the usual complement of sessions for contributed papers. • national public policy development in support of the Since the International Congress on Mathematical Educa­ sciences and mathematics, and tion (ICME) will take place in mid-August 1992 in Quebec • creating a more positive image of mathematics and City, Canada, the AMS-MAA Joint Meetings Committee mathematicians. decided not to hold a Summer Mathfest in 1992. The MAA These issues are being considered by various committees will hold meetings of some of its committees and Board of and task forces within the Society. Governors just before the ICME. Meetings of the Council of the AMS and other committees will be arranged. Vitality of the Mathematics Profession The AMS and MAA have agreed to meet jointly with The Committee on Science Policy and the Committee on the Canadian Mathematical Society in August 1993 at Education are addressing access, recruitment, and retention the University of British Columbia in Vancouver, British aspects of the profession. Columbia. The three organizations are planning an exciting scientific program. Fragmentation of the Mathematics Community An initial response to the problem of fragmentation has Prizes and Awards been the appointment of the joint AMS-MAA Committee A feature of Annual and Summer Meetings is the awarding on Cooperation mentioned below. of prizes. At the Annual Meeting in San Francisco in January 1991, the Society awarded the Oswald Veblen Prize Membership, Voluntary Leadership, and Governance in Geometry, the Ruth Lyttle Satter Prize in Mathematics, A principal concern in this area is to have effective and a Citation for Public Service. At the Summer Meeting Volunteer Leadership that is maintaining excellent lines of in Orono in August 1991, the Society awarded three Steele communication with the membership and staff. President Prizes. Artin asked the Committee on Committees to look into the structure of committees of the Society. The Committee on The Oswald Veblen Prize in Geometry Committees suggested that a subcommittee be appointed, The 1991 Oswald Veblen Prize in Geometry was awarded with supplemental members from outside the Committee, to Andrew J. Casson of the University of California at to consider the committee structure. This subcommittee has Berkeley and to Clifford H. Taubes of Harvard University. been active during 1991. It expects to have a report ready Casson received the prize for his work on the topology for the Fall1992 ECBT meeting. of low dimensional manifolds and Taubes received the prize for his work in Yang-Mills theory. The prize is Meetings named in the memory of Oswald Veblen (1880-1960) who The Annual Meeting of the Society in 1991 was held served as President of the Society in 1923 and 1924. It is in San Francisco, California, in January. The Colloquium funded by contributions from former students of Veblen and Lectures were delivered by Robert MacPherson and the supplemented from the Steele Prize Fund. Gibbs Lecture was given by Michael Atiyah. In honor of the 20th Anniversary of the founding of the Association Ruth Lyttle Satter Prize for Women in Mathematics, there was a joint AMS-AWM­ The first Ruth Lyttle Satter Prize was awarded to Dusa MAA Invited Address delivered by Christel Rotthaus. G.D. McDuff of the State University of New York at Stony Mostow, President of the AMS in 1987 and 1988, delivered Brook for her work on symplectic geometry. The Council his Retiring Presidential Address. There were three AMS­ established this prize to honor the memory of Ruth Lyttle MAA Invited Addresses, five Invited Addresses, sixteen Satter. It is to be awarded to a woman mathematician Special Sessions, and many sessions for contributed papers. every other year for an outstanding contribution to research The 1991 Summer Meeting of the Society was held in in mathematics during the past five years. This prize is Orono, Maine on the campus of the University of Maine endowed by a gift from Joan S. Birman. in August. The meeting marked the introduction of a new format for summer meetings: The Summer Mathfest. Under Leroy P. Steele Prizes this format, the scientific portion of the meeting is limited The Leroy P. Steele Prizes for 1991 were awarded at the to three days, with Invited Addresses and the like held in Summer Meeting of the Society held in Orono. The 1991 the morning and Special Sessions, sessions for contributed Steele Prize for Expository Writing went to Jean-Fran~ois papers, and committee meetings limited to the afternoon Treves for his book Pseudodifferential and Fourier Integral (and evening if necessary). Prizes for the AMS and MAA Operators (Volumes 1 and 2) published by Plenum Press in were awarded at a joint banquet held the evening before the 1980. The 1991 Steele Prize for a Fundamental Paper went meeting began. The Orono Mathfest featured three AMS­ to Eugenio Calabi for his fundamental work on complex MAA Invited Addresses, an AMS History of Mathematics differential geometry. The 1991 Steele Career Prize was Lecture delivered by George W. Mackey, two Progress in awarded to Armand Borel for his work in laying the Mathematics Lectures, one by H.W. Lenstra, Jr.and one by foundations of the theory of linear algebraic groups. The

MAY/JUNE 1992, VOLUME 39, NUMBER 5 439 Inside the AMS

Leroy P. Steele Prizes were established in 1970 in honor of of speakers in mathematical symposia it cosponsors with George David Birkhoff, William Fogg Osgood, and William AAAS. Casper Graustein and are endowed by a bequest from Leroy P. Steele. Science Policy The Committee on Science Policy (CSP) has been active AMS Centennial Fellowships during 1991. The Long Range Planning Committee, the AMS Centennial Fellowships were awarded in 1991 to ECBT, and the Council have recommended that the CSP Daniel Bump of Stanford University and to Karl Villonen develop long range plans for Society science policy, in of Brandeis University. These fellowships are intended to particular to address the strategies outlined by the SPTF. provide enhanced research opportunities to mathematicians The CSP is currently working with internal task forces to who are several years past the Ph.D., who have a strong develop these plans in several different areas. research record, but who have not had extensive postdoctoral The CSP has recommended that the Society and its research support in the past. They are awarded to individuals officers engage in closer cooperation with MAA. To this who have received a Ph.D. from seven to twelve years prior end, a joint AMS-MAA Committee on Cooperation has been to winning the award. The stipend in 1991 was $38,000. established. This committee has met several times and is Funds for these awards are supported by contributions from in the process of identifying areas of close cooperation and members of the Society. The Society contributes to the mutual support. program from its general fund. Education As mentioned above, the Council has established a Commit­ Sectional Meetings tee on Education. It has now met several times. Its current There were six sectional meetings of the Society in 1991 agenda is concerned mostly with developing a set of policies at which nineteen Invited Addresses were delivered and in line with the strategies mentioned above for the Society numerous Special Sessions were held. Attendance at these to follow in the education arena. sectional meetings continues to improve. The Society dis­ plays its books, journals, and its MathSci database at these sectional meetings. In addition, registration by credit card is JPBM The Joint Policy Board for Mathematics (JPBM) is a now available at most sectional meetings. cooperative venture sponsored by the Society, the MAA, and SIAM. Each of the three participating organizations have three representatives on JPBM. These nine members Other Meetings and Conferences then appoint a tenth member as the Chair. One of JPBM's Society sponsored its annual AMS Summer Research The major activities has been to direct its Office of Governmental Groups and Their Institute. In 1991 the topic was Algebraic and Public Affairs (OGPA) in Washington, DC. Ed Connors Frankel, Eric Friedlander, Representations, organized by Igor served as Director of OGPA until mid-summer. He has and Brian Parshall. William Haboush (chair), Jens Jantzen, returned to his position as Professor of Mathematics at the Institute was held at the Pennsylvania State University, The University of Massachusetts. After Connors departed, JPBM Park, PA, in July 1991. University appointed Richard Herman of the University of Maryland Conferences in the Mathe­ The Joint Summer Research as Chair of JPBM and Director of OGPA. This change took University of Washington, matical Sciences were held at the effect in the Fall of 1991. Seattle, from 22 June to 2 August 1991. These were spon­ sored by the AMS, SIAM, and the Institute for Mathematical Statistics (IMS). Topics in 1991 were: Stochastic modeling Committees and statistical inference for selected problems in biology, As part of the long range planning process, a study of the Graph minors, Theory and applications of multivariate time committee structure has commenced. A list of charges for all series analysis, Stochastic inequalities, Biojluiddynamics, committees of the Society, including the joint committees, Motives, Mathematical aspects of classical field theory, and is being assembled. A good portion of this work was Systems of coupled oscillators. finished in mid-1990. As of the end of 1991, there were 96 The twenty-fifth annual Symposium on Some Mathe­ committees listed in the 1992 Professional Directory (which matical Questions in Biology on Theoretical approaches represents the status at the end of 1991). In the middle of for predicting spatial effects in ecological systems was held 1991 there were 431 members of Society committees. These on 8 August 1991 in San Antonio, TX during the Annual represented 136 institutions from 38 of the 50 states, 5 Meeting of the Ecological Society of America. This sympo­ different institutions in Canada, and a handful of institutions sium is sponsored by the AMS, SIAM, and the Society for from outside North America. Mathematical Biology. The AMS helped to support mathematical sciences Elections and officers activities at the American Association for the Advancement The election of officers in 1991 featured a first for the of Science (AAAS) by contributing to the sponsorship Society-a contested election for the position of President-

440 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS

Elect. The Council agreed to try contested elections for this debt, and unrestricted fund balances amounted to 40% of position, with a review of the process after six years. In total assets, about 1% lower than 1990. 1991 the Council nominated Ronald Graham and Stephen Smale as candidates for President-Elect. Also, the Council II. Summary Financial Statements appointed Nominators Gian-Carlo Rota and Raoul Bott to The Treasurer this year again presents to the membership write articles for the Notices about the respective candidates. summary financial statements of the Society. A copy of the This material appeared in the September 1991 Notices, just Society's audited financial statements, as submitted to the before ballots were mailed. Trustees and the Council, will be sent from the Providence The 1991 election also marked the introduction (at Office to any member who requests it from the Treasurer. least to the Secretary) of email campaigning. At least one The Treasurer will be happy to answer any questions candidate used electronic mail to request recipients for their members may wish to put to him concerning the financial vote. Perhaps this portends the time when all campaign affairs of the Society. material will be sent out via electronic mail. Steve Armentrout had announced that he would serve SUMMARY STATEMENT OF ACTIVITY only one more term as Associate Treasurer, so a search For the Years Ended December 31, 1991 and 1990 was initiated to identify a new Associate Treasurer. The {Thousands of Dollars) search committee reported to the November 1991 ECBT, which approved the report. The January 1992 Council then Revenue 1991 1990 appointed B. A. (Al) Taylor of the University of Michigan Journals $10,227 58% $ 9,780 59% as the Associate Treasurer Designate. He will serve in this Books 2,131 12% 1,636 10% capacity during 1992 and take office as Associate Treasurer Dues 1,669 9% 1,532 9% on 1 February 1993. Membership Activities 367 2% 237 1% The results of the 1991 Election have been reported Meetings 595 3% 533 3% elsewhere in the Notices and will not be repeated here. Grants and Contracts 996 6% 1,263 8% Investment Income 690 4% 725 4% MathSci Online/Tapes Conclusion and Disc 626 3% 448 3% These are only a part of the activities of the Society during Other 469 3% 443 3% 1991. The economic downturn had its effects on the Society Total revenue $17,770 100% $16,597 100% budget. In particular, the Society noticed a marked decrease in journal subscriptions and other purchases. The financial Expense 1991 1990 situation is reported by the Treasurer in this issue of the Journals 9,720 58% $ 8,533 51% Notices. As always, the Officers and Staff of the Society $ Books 1,769 11% 1,426 9% welcome input, suggestions, and comments from you, the Marketing 474 3% 594 4% members. Membership Records 390 2% 391 2% Membership Activities 662 4% 508 3% Meetings 647 4% 712 4% Report of the Treasurer (1991) Grants and Contracts 1,036 6% 1,342 8% Franklin P. Peterson Software Development Projects 424 2% 873 6% MR Database I. Introduction Development Project 118 1% 679 4% During 1991, the Society's revenues increased 7% over MathSci Online/Tape 1990, while its expenses increased only about 1%. The and Disc 401 2% 379 2% result was an excess of revenues over expenses in 1991 Other 1,091 7% 1,173 7% of $1,038,000 compared to a small deficit in 1990. I will Total expense $16,732 100% $16,610 100% explain some of the more significant reasons for this below. Excess (Deficiency) of As I explained last year, the Society has taken several Revenues over Expenses $ 1,038 ($ 13) steps to improve its book publishing program. These steps include initiatives in acquisition, production, and marketing. These efforts have begun to pay off. Book revenues are up SUMMARY BALANCE SHEET about 30% over 1990, and the publication of new titles in December 31, 1990 and 1991 books in series is up 68%. {Thousands of Dollars) MathSci revenues have increased significantly without significant increases in expenses. These increases were Assets 1991 1990 nearly all in sales of MathSci Disc. Cash & temporary investments $ 5,125 $ 3,315 The Society's balance sheet remains healthy. As of Other short-term investments 970 833 December 1991, there was no long-term or short-term bank Investments in Treasury Notes 516

MAY/JUNE 1992, VOLUME 39, NUMBER 5 441 Inside the AMS

Receivables-members & others III. Operations (less allowance doubtful accounts) 1,299 1,325 I now turn to a more detailed discussion of the Society's Due from invested funds 26 1991 operations. Deferred prepublication costs 867 977 Journals. Journals provide the largest fraction of the Inventory of completed books & Society's revenues and expenses. In the past, journals have back volumes of journals 1,665 1,234 operated at a net loss (the net loss on MR was greater than Prepaid expenses and deposits 1,015 1,014 the combined net income of the other journals). Since 1985, Property and equipment journals (in the aggregate) have operated in the black and (less accumulated depreciation) 4,691 5,176 provided a very significant portion of the Society's surplus Total operating assets 16,174 13,874 (the excess of revenues over expenses in the summary Long-term investments financial statements above). It can be expected that the (unrestricted) 7,217 6,755 amount of surplus generated by journals will decrease over Total operating assets and the next few years. This is a result of pressure from unrestricted investments 23,391 20,629 subscribers to keep prices low, increases in costs which Long-term investments are largely outside of the control of the Society, and (restricted) 2,285 2,280 attrition in subscribers. Alternative cost saving opportunities and alternative sources of support are being sought to Total assets $25,676 $22,909 compensate for the higher expenses. MathSci Disc is a good example of the latter. Books. Included in this category are not only books Liabilities and fund balances (monographs or collections of articles) but review volumes Accounts payable $ 1,197 $ 954 and indexes to journals. In 1991 book sales increased 30% Subscriptions, dues, and other over 1990 sales. This increase reflects the publication of a revenues received in advance 10,147 8,600 record number of books. Much of the increase over prior Other miscellaneous years was in translated books, an area which the AMS has liabilities 1,655 1,713 given particular attention in 1990 and 1991. Total liabilities 12,999 11,267 Dues, Membership Activities, and Membership Unrestricted fund balances: Records. The Society has about 489 institutional mem­ Operating fund balance 3,175 2,607 bers and 27,300 individual members. Of the latter, about Unrestricted invested fund 11,800 pay no dues because they are student nominees, balances: emeritus members, or reviewers without convertible cur­ Economic Stabilization 7,065 6,594 rency. Individual member dues are two-tiered to provide Friends of Mathematics 124 124 some relief to lower paid members. Increases in dues for Other 28 37 individual members are set annually by a cost-of-living index. Total unrestricted invested Costs which can be considered to be partially covered by funds 7,217 6,755 dues include the cost of maintaining membership records, Total unrestricted fund balances 10,392 9,362 the deficits of Abstracts, Bulletin, ElMS, the Notices, and Restricted invested fund the Professional Directory, deficits from meetings, including balances: the Employment Register, and the AMS support of the Joint Endowment funds: Policy Board on Mathematics. The Endowment Fund 100 100 Meetings. Meetings has operated at an overall deficit, Robert Henderson 548 548 as a service to the mathematics community. The 1991 deficit Joseph Fels Ritt 23 23 was significantly less than. the 1990 deficit. This was the Prize funds 183 183 result of increases in registration fees and increases in the Waldemar J. Trjitzinsky 196 189 number of registrants at meetings. C. V. Newsom Fund 100 100 Grants and Contracts. Grant support is mainly for Centennial Research Fellowship 31 31 travel and subsistence for participants in research confer­ Pooled Income Fund 5 5 ences, institutes, and seminars, plus the Society's cost in Eliakim Hastings 3 3 preparing and running these conferences. The money re­ Undistributed net gains on ceived from government agencies is reimbursement only, investment transactions 1,070 1,098 with no profit to the AMS. The Society also has contracts Total restricted invested to perform services for other organizations, and this helps funds 2,259 2,280 to recover some fixed costs. The decrease in this category Due to operating funds 26 reflects a 1990 grant for travel support to ICM90. Total liabilities and fund Software Development Projects. The primary project balances $25,650 $22,909 included in this group is the development of a system for the

442 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Inside the AMS management of order fulfillment, customer and membership JPBM Committee on databases, and related functions. The costs involved include Professional Recognition and Rewards personnel costs, computer usage charges, and other indirect The Joint Policy Board for Mathematics (JPBM) Committee costs. This is intended to benefit all of the publications and on Professional Recognition and Rewards met in Baltimore membership related activities of the Society. in January and again in Washington in March. The charge software MR Database Development. This is another to the committee was sharpened and approved, the course It is a rewrite of the MR database, development project. for the committee's work was set, and plans were made to which is used for the management of the information used visit five institutions to talk to faculty and administrators in the preparation of Mathematical Reviews and related about the local recognition and rewards system. publications. Its cost also includes personnel costs, computer The committee was appointed in response to growing usage charges, and other indirect costs. awareness that the rewards structure is one of the key Other Revenues and Expenses. The principal compo­ factors supporting and inhibiting the renewal of the pro­ nents of other revenues and expenses are e-Math (the single fession, the revitalization of precollege, undergraduate, and largest item), 1}3X related products, UME Trends, Video education, and the promotion of interdisciplinary Tapes, and the AMS support of the Joint Policy Board on graduate community to reach Mathematics. work and efforts by the mathematics out to other disciplines and to industry. The problems faced by the community and the role of the rewards system are documented in a number of recent reports, particularly the National Research Council report "Renewing U.S. Math­ ematics, A Plan for the 1990s", the Carnegie Foundation IV. Assets and Liabilities for the Advancement of Teaching report by Ernest Boyer So far, this report has dealt with sources of revenue and titled "Scholarship Reconsidered, Priorities for the Profes­ applications of expense. Another aspect of the Society's soriate", and the National Science Foundation report finances is what it owns and owes, or its assets and "America's Academic Future, A Report of the Presidential liabilities, which are reported in the Summary Balance Young Investigator's Colloquium on U.S. Engineering, Sheet. The Society maintains its accounts in fund groups. Mathematics, and Science Education for the Year 2010 and The operating funds include membership and publications Beyond". activities; the invested funds include both endowment funds has accepted the following seven-point (gifts and bequests whose principal is required to be invested The Committee a dialogue on these issues within the math­ in perpetuity and whose income must be used for the purpose charge: initiate contributions that stated by the donor) and quasi-endowment funds (those ematical sciences community; identify determine how those funds set aside by the Board of Trustees for designated should be recognized and rewarded; purposes). Most of the quasi-endowment investments have involved (faculty members, department chairs, deans, math­ been reserved as an economic stabilization fund, as a hedge ematicians, and managers employed in industry) value the against future economic difficulties. various contributions and determine how the rewards system The Society's fiscal year coincides with the period cov­ works in practice; study methods of evaluation of types ered by subscriptions and dues. Since dues and subscriptions of contributions that are identified as being important; ar­ are generally received in advance, the Society reports a ticulate the ways contributions are, and can be, rewarded; large balance of cash and temporary investments on its fiscal make recommendations on the contributions that should be year-end, December 31. This amounted to about $6,611,000 recognized and rewarded and on methods to evaluate these in 1991 and $4,148,000 in 1990. The recorded liability for contributions; and produce a plan to lead the community the revenues received in advance was about $10,147,000 toward implementing the recommendations. and $8,600,000 on the same dates. The difference can be Calvin C. Moore, Associate Vice-President for Aca­ thought of as having been invested in the Society's other demic Affairs, University of California, is the chair of assets. Effectively, the Society borrows from its subscribers the committee; the other members are: Barbara T. Faires, to finance current operations and long-term investments. Westminster College; Gene H. Golub, Stanford University; This is a common practice in the publishing industry and Phillip A. Griffiths, Institute for Advanced Study; Shirley allows the Society to maintain a very low amount of bank A. Hill, University of Missouri at Kansas City; William E. debt, which was zero throughout 1991 and 1990. Kirwan, III, University of Maryland; Peter D. Lax, Courant The Society's property and equipment include land, Institute, New York University; Carolyn R. Mahoney, Cali­ buildings and improvements, and office furniture, equip­ fornia State University, San Marcos; Barry Mazur, Harvard ment and software. The Society also owns a small amount University; Gary C. McDonald, General Motors Research of transportation equipment. The land, buildings, and im­ Laboratory; Stephen B. Rodi, Austin Community College; provements include the Society's headquarters building in Richard A. Tapia, Rice University; John A. Thorpe, State Providence and the Mathematical Reviews offices in Ann University of New York, Buffalo; Andrew B. White, Jr., Los ~~or. The largest part of the Society's office equipment is Alamos National Laboratory; and CarolS. Wood, Wesleyan Its mvestment in computer facilities. University.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 443 Inside the AMS

Creating a dialogue within the mathematical sciences LAVENDER, a sophomore at Duke, received the IBM Award community is viewed as one of the most important charges for achievement in mathematics in her senior year in high to the committee. This dialogue will begin with the five site school. She is undecided about her career goals after earning visits planned for April and May 1992. Fifteen to twenty her undergraduate degree, but she is considering teaching or additional site visits will be made during the 1992-1993 an area in which mathematics is applicable. She says she academic year, mathematical sciences departments will be enjoys mathematics and hopes to put her degree to good surveyed, and panel discussions will be organized at na­ use. tional and regional meetings of the three organizations that Howard Payne University selected PAMELA Jo CHANEY. comprise JPBM: the American Mathematical Society; the Geraldine Boyd, head of the mathematics department, reports Mathematical Association of America; and the Society for that Ms. Chaney is a very capable student with great potential Industrial and Applied Mathematics. Comments and sugges­ to be successful in graduate school. Selected both for her tions from individuals are welcomed and should be brought mathematical promise and her financial need, Ms. Chaney is to the attention of the project director, William Adams, De­ a thirty-two year old wife and mother of three children. She partment of Mathematics, University of Maryland, College had dropped out of high school in her senior year. Her return Park, MD 20742 or via email to [email protected]. to school has been a great success: she has maintained a 4.0 average for her first three semesters while carrying a heavy courseload, working twenty hours per week, and caring for Transactions ofthe her family. American Mathematical Society Montana State University selected three students. MELis­ SA CocKERILL is a senior from Maryland. She will attend Temporary Policy Change graduate school in the fall and is planning on a career in The Transactions of the AMS has found that it has a backlog government or industry. DEBORAH FAGAN is a senior from of distressing dimensions. In order to reduce the backlog Montana who also plans to attend graduate school next quickly, the editors have agreed to a policy, which has year. A member of Beta Alpha Psi, a national accounting already been implemented, of sharply higher standards for honorary society, she is planning a career in industry and publication. As a consequence, many papers that formerly may continue on to a doctorate. SHERRY HEIS is a senior would have been easily accepted now cannot be accepted from Montana. Graduate school is also in her future, though at all, and those that .are accepted are still subject to the she has not fixed on a career plan. She is a member of Phi backlog. The change in policy is temporary, but will continue Kappa Phi and has received another scholarship award from until the situation is remedied. We hope it will require less the mathematics department. than a year. Updated information about the backlog is to be The University of Scranton selected THOMAS A. SHIMKUS. published in each issue of the Transactions. Gary Eichelsdorfer, chairman of the mathematics department, James E. Baumgartner reports that Mr. Shimkus is the son of a Lithuanian immi­ Managing Editor, Transactions grant who has been unemployed since the summer of 1991, with no job prospects. Mr. Shimkus graduated second in a class of 165 from Scranton Preparatory High School and Trjitzinsky Awards Made to Students currently is a junior in mathematics with a GPA of 3.9. "A The January 1992 issue of the Notices, page 22, carried an genuine love of learning motivates this young man," says announcement of four awards made through the Society's Professor Eichelsdorfer. "He approaches his studies with Waldemar J. Trjitzinsky Memorial Fund. The mathematics an eagerness and enthusiasm that makes him a welcome departments at Duke University, Howard Payne University, member of any course." In addition to tutoring students in Montana State University, and the University of Scranton a work-study program, Mr. Shimkus works as a dishwasher each received $2500 to assist needy students of mathematics. at a local restaurant and sold Christmas trees over the The departments were asked to select students to receive winter holidays. When asked what he would like to do after the awards. The Society has received word from the four graduation, he says he would like to continue his education institutions about the students receiving the awards. with the goal of becoming a college professor or an actuary. Duke University selected three students. RoBERT LANE In his spare time, Mr. Shimkus enjoys weight lifting and BASSETT competed in various mathematics contests while reading. When asked what kind of books he likes, he replied: in high school and says he finds mathematics "valuable as "Mathematics, of course." a pure, logical system of thought." He says he hopes to These four schools were selected for awards in a random find a job in applied mathematics, but is also considering drawing from the pool of AMS institutional members. The graduate school. LINIE YUNWEN CHANG attended the North recipients of the next round of Trjitzinsky awards, to be Carolina School of Science and Mathematics and is cur­ given annually, will be announced in an upcoming issue rently a junior at Duke. She says she hopes to participate of the Notices. For more information about the Trjitzinsky in a mathematics research project this summer. She plans to fund, contact Timothy J. Goggins, Development Officer, attend medical school and become a pediatrician. KARA LEE AMS, P.O. Box 6248, Providence, RI 02940-6248.

444 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook

Given the numbers above, it is evident that there was some This month's column is written by Richard Herman, flexibility within the Mathematical and Physical Sciences Chair of the Joint Policy Board for Mathematics and dean Division (within which lies the DMS). Assistant Foundation of the College of Computer, Mathematical, and Physical Director David Sanchez, the Director of the Mathematical Sciences at the University of Maryland, College Park. and Physical Sciences Division, revealed that he had $16.4 million of discretionary funds. He made a decision to provide The fiscal year 1993 budget for the National Science his discretionary resources to some disciplines that had not Foundation (NSF) poses some interesting questions for our received initiative funding, feeling that "not to do so was community. By and large, any incremental funding appears unacceptable." as "initiative" directed within the Division of Mathematical To set the consequences of this budget in perspective, it Sciences (DMS). Looking at the Foundation increase as a is useful to look not only at mathematics, but at most other whole, 88% went for specified areas, with roughly half of that disciplines. Take the biological sciences. The increment in due to initiatives such as Global Change, High Performance this area is $46.4 million or 16.9%. This large percentage Computing and Communications, etc., generated by the is entirely initiative directed and is consistent with the NSF Federal Coordinating Council on Science, Engineering, and strategy of "Strengthening the research base in areas critical Technology (FCCSET). The other NSF specified activities to enhancing the nation's education and research enterprise" include Foundation initiatives in environmental research (through support of individual investigators). This is not and manufacturing and other programs such as the Laser meant to justify actions but to indicate the process. The Interferometer Gravitational Wave Observatory and the U.S. result in mathematics is the same, of course, where we now Antarctic Program. This leaves about $54 million, or 12%, see no increment in "disciplinary research." unspecified. Does this mean that those doing disciplinary research are Before going on, let me add a few words about the out of the picture? I suppose to some extent this depends FCCSET process. Judith Sunley, Director of the DMS, points on whom you ask and what you mean by the question. out that, "The FCCSET process is very complex, with ideas It's hard to imagine that much of this incremental funding coming up through several agencies, circulating through will not be available to some (but not all) of those doing the FCCSET committees and returning to the agencies for disciplinary research. On the one hand, we see an 8.1% implementation". This is meant to avoid duplication of effort increase for DMS and, on the other, no increase for the and encourage cooperation and, in particular, would have traditional disciplines. The small relative increases afforded "NSF focus on the basic research end of an initiative." to most mathematical subdisciplines in recent years could This year, we have been presented, or, more properly, have led us to the conclusion that one day we would be so confronted, boldly with the results of the fact that the confronted. Nevertheless, the bold nature of the budget has NSF, much as any other agency, has to make appealing led some to a foreboding view. arguments for its increases. (In actual fact, dollar increases The budget divisions are unnecessarily stark. However, to the Foundation for items such as the Antarctic program I doubt that anyone imagines that cross-disciplinary work would not necessarily be available for other items.) Walter could be spoken of without acknowledging the importance Massey, Director of the NSF, pointed this out at the Joint of the disciplines. In fact, Sunley remarks that, "Interdis­ Mathematics Meetings in Baltimore in January, when he ciplinary work that is on the intellectual frontier requires remarked that, "(part of his) job is to increase the total disciplinary input that is likely to be deep, broad, and very resources flowing to NSF." imaginative. Without cutting edge results coming from the That the budget request is less than what the NSF disciplines, you don't make progress on the interdisciplinary originally requested of the Office of Management and front." This statement would seem to suggest that "dis­ Budget in the fall of 1991 is probably true. Some directives ciplinary" workers have to take a good hard look at the came from without and, quite clearly, some from within. Request For Proposals, which should be appearing soon. In

MAY/JUNE 1992, VOLUME 39, NUMBER 5 445 Washington Outlook the long run, participation in the initiatives (to which we how the fiscal year 1994 budget should more amply reflect have a great deal to offer) is likely to enhance the position the needs of the community as well as those to whom we of mathematics. answer. (While this column has been motivated to some So we are left to ask "what next?" This would seem extent by the NSF budget, it should be clear that we need to break down into short- and long-term plans. With regard to have discussions with all the agencies. For example, the to the latter, perhaps some comfort is offered by the fact aggregate mathematics budget for Department of Defense that there is only likely to be one more initiative at the agencies decreased by 1.2%.) FCCSET level. (There has already been an announcement Many different approaches to the short-term issues have of a Manufacturing Initiative in fiscal year 1994.) Moreover, already been suggested by members of the community. additional involvement should help us shape future budgets. Various meetings have taken place. One particular meeting To date, as Sunley points out, "Mathematicians have been with Walter Massey served to present concerns and helped involved only in a marginal way in FCCSET process. This to set the situation in perspective. Speaking to community changed with the recent appearance of Ed David and Phil leaders, Massey suggested that we need to be proposing Griffiths before the FCCSET committee. A sustained effort new strategies for continued growth. The Joint Policy Board is needed." Yet it is likely that the imprint of this year will for Mathematics, acting through its constituent societies, is be with us for some time (the FCCSET process requires endeavoring to help structure long-range strategies for the five-year plans). This calls for a recognition that this is not community. business as usual and that we need to be thinking now about

American Mathematical Society

Algebraic K-Theory, Commutative Algebra, and Algebraic Geometry R. Keith Dennis, Claudio Pedrini, and Michael R. Stein, Editors

This volume contains the proceedings of a U.S.-Italy joint summer seminar held in June 1989 in Santa Margherita Ligure, Italy, which focused on the connections between classical arguments in commutative algebra and Algebraic K -Theory, algebraic algebraic geometry, and the contemporaneous development of Commutative Algebra, K-theory in the United States. These connections were exemplified by the and Algebraic Geometry work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions pro­ ceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of K-theory to arithmetic and real geometry.

1991 Mathematics Subject Classifications: 19, 14, 13 ISBN 0-8218-5130-6; 230 pages (softcover), March 1992 $47 Individual member $35, List price $59, Institutional member "'--Amencan Mathematical Soc1ety Your ordering code is CONM/126NA

All prices subject to change. Free shipment by suriace; for air delivery, please add $6.50 per title. Prepayment required. Order from American Mathematical Society, P. 0. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

446 NOTICES OF THE AMERICAN MATHEMATIC.AL SOCIETY News and Announcements

Lawrence J. Corwin MacPherson Receives the Courant Institute of Mathematical 1943-1992 NAS Mathematics Prize Sciences at New York University. He Lawrence J. Corwin, professor of math­ Robert D. MacPherson of the Mas­ moved to the University of California ematics at Rutgers University, died on sachusetts Institute of Technology has at Los Angeles as an assistant professor March 19, 1992 at the age of 49. received the National Academy of Sci­ in 1976 and advanced to the rank of Born on January 20, 1943 in East ences (NAS) Award in Mathematics associate professor in 1977. In 1979, Orange, New Jersey, Professor Cor­ for "his role in the introduction and ap­ he joined the faculty of U.C. Berkeley win received his A.B. in 1964, A.M. plication of radically new approaches as a professor. Since 1984, he has been in 1965, and Ph.D. in 1968, all from to the topology of singular spaces in­ a professor at Princeton University. Harvard University. He was a C.L.E. cluding characteristic classes, intersec­ Professor Majda has held visiting Moore Instructor at the Massachusetts tion homology, perverse sheaves, and professorships at the Courant Institute, Institute of Technology (1968-1970), stratified Morse theory." The award, the College de France, the Institute a visiting member at the Courant In­ presented every four years, was estab­ for Mathematics and its Applications stitute of the Mathematical Sciences lished by the AMS in honor of its at the University of Minnesota, and (1970--1971), and an assistant profes­ Centennial in 1988. The first recipient the Mathematical Sciences . Research sor at Yale University (1971-1975). of the award was Robert Langlands. Institute in Berkeley. From 1972 to 197 4, he was a Sloan A more extensive piece on MacPher­ In 1990, Professor Majda presented Foundation Fellow. He joined the fac­ son and his work is under preparation a plenary lecture at the International of Mathematicians in Ky­ ulty of Rutgers University in 1975 and and will appear in a future issue of the Congress oto. He was an invited speaker for the advanced to the rank of professor in Notices. AMS symposium, Mathematics into the 1980. He held visiting positions at the Twenty-first Century, held during the Institute for Advanced Study at Prince­ AMS Centennial in Providence in Au­ ton (Fall 1973) and at the Institut des gust 1988. His other honors and awards Hatues Etudes Scientifiques, Biires-sur­ Majda Receives NAS include an Alfred P. Sloan Foundation Yvette (Spring 1974). Applied Mathematics Award Fellowship (1977-1979), the Medal of groups, An active researcher in Lie Andrew J. Majda of Princeton Univer­ the College de France (1982), and the harmonic representation theory, and sity has received the National Academy John von Neumann Award and Lecture analysis, Professor Corwin was the co­ of Sciences Award in Applied Mathe­ of the Society for Industrial and Ap­ author of three books and numerous ar­ matics and Numerical Analysis. The plied Mathematics (1990). In January ticles. He presented invited lectures in $10,000 prize is given every three 1984, he presented an invited address many institutions in the U.S., Canada, years. Professor Majda was cited for at the Joint Mathematics Meetings in Europe, and South America. He was "his extraordinary insight and invalu­ Louisville. Since 1987, he has been an also very active in administration at able contributions to the analysis and associate editor of the Journal of the Rutgers University, serving as chair of application of partial differential equa­ AMS. the mathematics department from 1975 tions especially to supersonic flow, to 1981 and as associate provost for the combustion, vortex motion, and tur­ mathematical and physical sciences and bulent diffusion." engineering from 1988 to 1990. Profes­ Professor Majda was born in East Bourgain Receives sor Corwin served as a member-at-large Chicago, Indiana on January 30, 1949. Ostrowski Prize of the AMS Council from January 1989 He received his B.S. in mathematics JEAN BOURGAIN of the Institut des to January 1992. in 1970 from Purdue University and Hautes Etudes Scientifiques and the He is survived by his wife, Amy his M.S. and Ph.D. in mathematics in University of illinois at Urbana­ Cohen, also on the mathematics faculty 1973, both from Stanford University. In Champaign has received the 1991 Os~ at Rutgers, and a son, Nathan. 1973, he became a Courant Instructor at trowski Prize. The prize of 50,000

MAY/JUNE 1992, VOLUME 39, NUMBER 5 447 News and Announcements

Swiss francs is to be awarded on May outstanding mathematical accomplish­ Elections to the 8, 1992 at a ceremony at the math­ ments. The first award, presented in American Academy ematical institute of the University of 1989, went to Louis de Branges. The American Academy of Arts and Basel. Sciences has announced the election of 205 new fellows in recognition of their distinguished contributions to science, Burdzy Receives Rollo Davidson scholarship, public affairs, and the arts. Prize Also named were forty Foreign Hon­ The trustees of the Rollo Davidson orary Members. Trust have awarded the 1992 Rollo The Academy was founded in 1780 Davidson Prize to K.RZYSZTOF BURDZY by John Adams and other leaders of of the University of Washington at the young republic, who chartered the Seattle. Burdzy was cited for his work learned society "to cultivate every art on the geometry of Brownian paths. and science which may tend to ad,. vance the interest, honor, dignity, and happiness of a free, independent, and Petryshyn Receives Prize virtuous people." The Academy con­ and is Elected to ducts a program of scholarly projects, Ukraine Academy studies, and publications which address W olodymyr V. Petryshyn of Rutgers issues of public interest. University was elected to full member­ Among the elections were sev­ ship in the Academy of Sciences of eral that are likely to be of inter­ Ukraine. He was cited "for the out­ est to the mathematical sciences com­ standing contribution to the growth of munity: MICHAEL ASCHBACHER, Cali­ Jean Bourgain nonlinear functional analysis and, in fornia Institute of Technology; DoN­ particular, for the development of the ALD LYMAN BURKHOLDER, University original theory of A-proper operators of lllinois at Urbana-Champaign; JoHN Bourgain was cited for his contri­ and its application to the solvability of HoRTON CoNWAY, Princeton Univer­ butions to several areas of mathemat­ ordinary and partial differential equa­ sity; DAVID DONOHO, University of ics: harmonic analysis, ergodic theory, tions." California at Berkeley; BENEDICT H. functional analysis (particularly Banach The Presidium of the Academy also GROSS, Harvard University; MELVIN space theory), complex analysis, and awarded to Professor Petryshyn, jointly HocHSTER, University of Michigan; classical convexity theory. The prize with Thor I. Skrypnik of the Institute of RoBERT MAcPHERSON, Massachusetts citation said: "In all these areas, J. Applied Mathematics and Mechanics Institute of Technology; MARINA RAT­ Bourgain solved dozens of central long in Donetsk, the Krylov Prize for 1992. NER, University of California at Berke­ standing open problems and developed This prize is the highest and most ley; and ALAN DAVID WEINSTEIN, Uni­ new powerful research tools and direc­ prestigious award the Academy bestows versity of California at Berkeley. tions. In his work he uncovered nu­ upon a scholar for original contributions Elected as Honorary Foreign Mem­ merous suprising connections between to mathematics. The prize is to be bers were: FRIEDRICH ERNST PETER these various subjects. As a result of presented in May in Kiev. HIRZEBRUCH, Max Planck Institut, Bonn; Bourgain' s achievements several large The prize honors M. M. Krylov, GREGORI MARGULIS, Yale University domains in these areas changed com­ who, during the 1920s, made funda­ and IPPA, Moscow; SHIGEFUMI MoRI, pletely." mental contributions to the theory of Research Institute of Mathematics, SCI, Among his many achievements, the constructive methods in mathematical Kyoto; DAVID RUELLE, Institut des prize citation mentions in particular his physics and, during the 1930s, founded Hautes Etudes Scientifiques, Paris; and ergodic theorem on arithmetic subse­ Gointly with his student, N. N. Bo­ JACQUES TITs, College de France, Paris. quences, the construction of A(p) sets, golyubov) the theory of nonlinear me­ his maximal function theorem in R 2, chanics. Established by the Academy and the recent restriction and multiplier in 1964, the prize is presented annually AMS Centennial Fellowships theorems. to one or two scholars for outstanding Awarded Alexander M. Ostrowski (1893- and original contributions in mathemat­ The Society has awarded three Centen­ 1986), a professor of mathematics at ics, mathematical physics, and theo­ nial Fellowships for 1992-1993. The the University of Basel, established a retical cybernetics. Previous recipients recipients are K.RZYSZTOF BURDZY of foundation for awarding an interna­ of the Krylov Prize include N. N. the University of Washington, Seattle; tional prize for higher mathematics. Bagolyubov, V. M. Glushkov, M. G. WILLIAM MENASCO of State Univer­ The Ostrowski Prize is conferred every Krein, A. P. Pagorelov, and A. V. sity of New York, Buffalo; and DAVID two years to an individual or group for Skorokhod. MORRISON of Duke University.

448 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···························---~~~rlllfft•~••m••---·••[.-··-·-----···--·~··-···~--·--·~-~·--~--·­ News and Announcements

Krzysztof Burdzy laborated with Joan Birman, Joel Hass, Morrison's research interests in­ Krzysztof Burdzy received his Ph.D. in Alan Reid, Morwen Thistlethwaite, and clude algebraic geometry over the com­ 1984 from the University of California, Abby Thompson. plex numbers and geometric mathe­ Berkeley, under Jim Pitman. He spent matical physics, particularly superstring one year at the University of California, theory. He will spend next year at the San Diego, as an S. E. Warschawski Institute for Advanced Study, where he Assistant Professor. He worked for two expects to devote much of his attention years at the Institute of Mathematics to understanding the recently discov­ of the Polish Academy of Sciences in ered phenomenon of "mirror symme­ Wroclaw and he visited Purdue Uni­ try". versity for one year. Since 1988, he Information about the competition has been at the University of Washing­ for the 1993-1994 AMS Centennial ton, Seattle, where he is currently an Fellowships will be published in the associate professor. Funding Information for the Mathemat­ ical Sciences section of the next issue of the Notices.

Guggenheim Fellowships Awarded The John Simon Guggenheim Memo­ rial Foundation has announced awards to 149 artists, scholars, and scientists in its sixty-eighth annual competition. William Menasco The awards, gleaned from 3162 appli­ cations, were made on the basis of un­ David Morrison usually distinguished past achievement David Morrison received his Ph.D. in and exceptional promise for future ac­ 1980 from Harvard University under complishment. A total of $3,925,000 the direction of Phillip Griffiths. He will be awarded this year. was on the faculty at Princeton Uni­ There were five mathematical sci­ versity from 1980 to 1986, with a entists among the awardees this year. leave during 1984-1985 at Kyoto Uni­ Their names, affiliations, and areas of versity. He was partially supported by research are: an NSF Postdoctoral Fellowship during Krzysztof Bunlzy SIMEON M. BERMAN, Courant In­ 1982-1984, and by the Japan Society stitute of Mathematical Sciences, New His research is focused on path for the Promotion of Science while in York University, stochastic models of properties of Brownian motion and Japan. Since 1986, he has been asso­ immunological variables in HIV in­ boundary problems in "classical" po­ ciate professor of mathematics at Duke fection; BRUCE HAJEK, University of tential theory. University. Illinois at Urbana-Champaign, stochas­ tic algorithms; PHILIP J. HANLON, Uni­ William Menasco versity of Michigan, studies in alge­ William Menasco received his Ph.D. in braic combinatorics; RICHARD B. MEL­ 1981 from the University of Califor­ ROSE, Massachusetts Institute of Tech­ nia at Berkeley under the direction of nology, analysis and geometry of mani­ Professor Rob Kirby. He was a Hill folds with comers; and ILYA PIATETSKI­ Assistant Professor at Rutgers Univer­ SHAPIRO, Yale University and Tel­ sity, New Brunswick, from 1981 to Aviv University, studies in automorphic 1984. He joined the faculty of the State forms. University of New York at Buffalo in 1985. In 1991 he became associate Fulbright Awards Announced professor at Buffalo. He intends to use The J. William Fulbright Scholarship the AMS Centennial Fellowship for a Board and the U.S. Foreign Scholar­ leave of absence to visit the Institut des ship Board have announced the names Hautes Etudes Scientifiques. of 950 academics, professionals, and in­ Menasco's research interests in­ dependent scholars who have received clude low dimensional topology, knot awards to lecture, consult, or conduct theory, and hyperbolic geometry. He research abroad during the 1991-1992 considers himself fortunate to have col- David Morrison academic year.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 449 ·-.. --·-·--··-·-·············----·-····--·-----·-···--.... _. _____ ...... ______...... -...... News and Announcements

A number of scholars in the math­ parment chairs and other senior schol­ The NSF-NATO awards, made an­ ematical sciences have received these ars. nually since 1959, provide recipients awards. Their names, affiliations, and Among this year's awardees are with a $2600 monthly stipend to study the country in which they will use the twenty in mathematics. Their names and conduct research in institutions and scholarships are listed below. and affiliations are: laboratories in NATO countries other RAYMOND G. 1\YOUB, Pennsylva­ BRUCE J. BAYLY, University of Ari­ than the U.S. In addition to the stipends, nia State University, Syria; SARAH A. zona; CHRISTOPHER BISHOP, State Uni­ some support is also provided to fellows DoUGLAS, University of Oregon, India; versity of New York at Stony Brook; for research-related expenses, travel ex­ STEPHEN J. GARLAND, Massachusetts SHELDON CHANG, Massachusetts In­ penses, and dependents. Institute of Technology, Israel; JA­ stitute of Technology; ETHAN S. DEV­ Forty-two men and sixteen women coB E. GOODMAN, City College of INATZ, University of Washington; RAN­ were selected to be this year's fel­ the City University of New York, Swe­ DALL DOUGHERTY, Ohio State Uni­ lows. There were four recipients in the den; DIANNE C. HANSFORD, Arizona versity; LISA J. FAUCI, Tulane Uni­ mathematical sciences. Following are State University, Germany; R. NEAL versity; GIAN MICHELE GRAF, Califor­ their names, their current institutions HART, Sam Houston State University, nia Institute of Technology; ANDREW (in parentheses), and the institutions at Oman; JOSEPH HOROWITZ, University JAMES GRANVILLE, University of Geor­ which they will hold the postdoctoral of Massachusetts at Amherst, India; gia; MANOUSSOS G. GRILLAKIS, Uni­ fellowship. SURENDER K. JAIN, Ohio University, versity of Maryland; ZHENG-Xu HE, JAMES W. ANDERSON (State Univer­ India; WILLIAM B. JoNES, University Princeton University; JUHA M. HEINON­ sity of New York at Stony Brook), Uni­ of Colorado at Boulder, Norway; SAMI EN, University of Michigan; NIGEL versity of Warwick, England; LEA R. KHURI, Wellesley College, Yugoslavia; DAVID HIGSON, Pennsylvania State Uni­ BIRMIWAL (University of Connecticut), RICHARD W. MADSEN, University of versity; NICOLAOS KAPOULEAS, Brown University of Toronto, Canada; CHRIS­ Missouri at Columbia, Malawi; AN­ University; JIAN-SHU LI, University of TIAN HoUDRE (University of Mary­ THONY N. MICHEL, University of Notre Maryland; XIAO-SONG LIN, Columbia land at College Park), University of Dame, Austria; JoHN A. NoHEL, Uni­ University; THOMAS MOUNTFORD, Uni­ Paris, France; and RACHEL A. KUSKE versity of Wisconsin at Madison, Czech versity of California at Los Angeles; (Northwestern University), University and Slovak Federal Republic; VLADIMIR ALAN NADEL, University of Chicago; of Utrecht, Netherlands. I. OLIKER, Emory University, Brazil; IGOR REIDER, University of Oklahoma; ALEXANDER G. RAMM, Kansas State NICOLAI RESHETIKHIN, University of NSF Awards University, Israel; RAE M. SHORTT, California at Berkeley; DoNNA MARIE Mathematical Sciences Wesleyan University, Germany; and TESTERMAN, Wesleyan University; Postdoctoral Research WALTER S. SIZER, Moorehead State Nominations for candidates for the Fellowships University, Ghana. next round of Sloan Fellowship awards The National Science Foundation (NSF) are due by September 15, 1992. Can­ has awarded Mathematical Sciences didates must be members of the regular Postdoctoral Research Fellowships to Sloan Fellowship Awardees faculty at a college or university in forty recent recipients of doctoral de­ Announced the U.S. or Canada and must be at an grees in the mathematical sciences. The Alfred P. Sloan Foundation has early stage of their research careers. For "As researchers in the mathemati­ awarded fellowships to ninety young further information on making nomina­ cal sciences expand their interactions scientists who are faculty members at tions, write to: Sloan Research Fel­ with other disciplines and as the inter­ fifty-three colleges and universities in lowships, Alfred P. Sloan Foundation, play increases between the various ar­ the U.S. and Canada. Suite 2550, 630 Fifth A venue, New eas of mathematics itself, opportunities The grants of $30,000 each for a York, NY 10111. for postdoctoral research and training two-year period are administered by become increasingly important," says each fellow's institution. Fellows, once Judith Sunley, director of NSF's di­ chosen, are free to pursue whatever NSF-NATO Postdocs Awarded vision of mathematical sciences. ''The lines of inquiry are of most interest to The National Science Foundation (NSF) Fellowship Program helps to provide them, and they are permitted to use the has announced the names of fifty­ these opportunities and serves to focus fellowship funds in a wide variety of eight young U.S. scientists and en­ attention on this issue throughout the ways to further their research aims. gineers who will receive 1992 NSF­ broad mathematical sciences commu­ More than 400 nominations for NATO Postdoctoral Fellowship in Sci­ nity." the 1992 awards were reviewed by ence Awards. The awards, designed to Awards are made to U.S. citizens, a panel of distinguished scholars. The foster closer collaboration in science nationals, or permanent residents based panelists in mathematics were Spencer and technology research among mem­ on their demonstrated ability and on J. Bloch, Richard B. Melrose, and bers of the North Atlantic Treaty Orga­ the significance of career improvement William P. Thurston. Candidates for nization, will enable fellows to conduct the fellowship would potentially pro­ the fellowships are nominated by de- their postdoctoral research abroad. vide. The program is designed to allow

450 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements recipients to choose research programs soN (University of Minnesota), Uni­ LORENZO SADUN (University of Texas at host institutions that will have max­ versity of Minnesota; WILLIAM Do­ at Austin), University of Texas at imum impact on their future scientific RAN (University of Michigan), Mas­ Austin; LEONARD SCHULMAN (Mas­ development. sachusetts Institute of Technology; sachusetts Institute of Technology), Uni­ A panel of mathematical scientists, DAVID FARMER (Oklahoma State Uni­ versity of California, Berkeley; MICHAEL chosen by the American Mathematical versity), Columbia University and Math­ SHAPIRO (Ohio State University), City Society, the Institute of Mathematical ematical Sciences Research Institute; University of New York Graduate Cen­ Statistics, and the Society for Industrial ELIOT FRIED (Carnegie Mellon Univer­ ter; BRIAN SPENCER (Northwestern Uni­ and Applied Mathematics, evaluated sity), Pennsylvania State University; versity), California Institute of Technol­ 130 applications. Final selections were MASAAKI FuRUSAWA (Stanford Uni­ ogy; and FREDERICK WILHELM (Uni­ made by NSF. versity), Stanford University; IRENE versity of Maryland), State University The stipend of $66,000 provides GAMBA (Trenton State University), of New York at Stony Brook. support for two nine-month academic Courant Institute of Mathematical Sci­ Information abaout the NSF Mathe­ years and three two-month summers. ences; DAVID GoLDBERG (Purdue Uni­ matical Sciences Postdoctoral Research Each awardee may choose between versity), Purdue University; DANIEL Fellowship Program for 1993 will be two options for receiving the academic GoLDSTEIN (University of California, published in the Funding Information year support: as full-time support for Santa Cruz), University of Califor­ in the Mathematical Sciences section any eighteen academic year months in nia, Santa Cruz and Harvard Uni­ of a future issue of the Notices. a three-year period, in intervals not versity; ALBERT GOODMAN (University shorter than three consecutive months of Chicago), University of Oregon; NSF Awards Minority Graduate (the Research Fellowship Option) or as WILLIAM GRAHAM (Massachusetts In­ Fellowships a combination of full-time and half­ stitute of Technology), University of The National Science Foundation (NSF) time support over a period of three Chicago; MICHELANGELO GRIGNI (Uni­ has announced the names of 120 mi­ academic years, usually one academic versity of British Columbia), Princeton nority students who have been offered year full-time and two academic years University; MATTHEW GuRSKY (Uni­ fellowships for graduate study in the half-time (the Research Instructorship versity of Chicago), University of Chi­ natural and social sciences, mathemat­ Option). cago; MARY ANN HoRN (University ics, and engineering. The 1991 recipients are listed be­ of Virginia), University of Minnesota; The NSF Minority Graduate Fel­ low (institutions in parentheses are the CHRISTIAN HouDRE (University of Mary­ lowships provide a stipend of $14,000 current institutions, those outside the land), University of Maryland; ALEXAN­ per year for three years of full-time parentheses are those at which the fel­ DER Izzo (University of Michigan), graduate study, together with an annual lowship will be held.) Partial support Brown University; PHILIP KEENAN cost-of-education allowance in lieu of for seven of the awards was provided (Rice University), Rice University; all tuition and fees at U.S. institutions. by the following disciplinary divisions T AKASHI KIMURA (University of Texas The fellowships may also be used over at the National Science Foundation: at Austin), University of North Car­ a five-year period to pem1it students to Computer and Computation Research, olina; ISAAC KLAPPER (Columbia Uni­ incorporate teaching or research assis­ Advanced Scientific Computing, Inte­ versity), University of Arizona; RACHEL tantships into their education. grative Biology and Neuroscience, and KusKE (Northwestern University), Stan­ Applications were submitted by Atmospheric Sciences. ford University; CHUN-NIP LEE (North­ 1480 minority students nationwide and DwiGHT BARKLEY (Princeton Uni­ western University), Northwestern Uni­ were evaluated by a panel assembled by versity), University of Texas at Austin; versity; EUGENE LERMAN (University the National Research Council. Awards CURTIS BENNETT (Michigan State Uni­ of Pennsylvania), University of Cali­ were made in thirty-four states, and versity), University of Illinois at Chica­ fornia, Santa Cruz; YAIR MINSKY (Yale fifty-nine went to women. go; DANIELL£ CARR (Duke University), University), University of Michigan; The eight recipients in the mathe­ Boston University and Courant Insti­ DANIEL NAKANO (Northwestern Uni­ matical sciences are listed below, to­ tute of Mathematical Sciences; DER­ versity), Northwestern University; RA­ gether with their baccalaureate insti­ CHEN CHANG (University of Mary­ FAIL 0STROVSKY (Massachusetts Insti­ tutions (in parentheses) and the insti­ land), Princeton University and Uni­ tute of Technology), University of tutions where they will pursue their versity of Maryland; PETER CHOLAK California, Berkeley and Intemational graduate studies. [Editor's Note: The (University of Michigan and University Computer Science Institute; ToNIANN institution of graduate study listed for of Victoria), University of Michigan PITASSI (University of Toronto), Uni­ each recipient is from the original ap­ and Cornell University; DAVID CHOPP versity of California, San Diego; CHRIS­ plication form and, in many cases, may (University of California, Los Angeles), TOPHER RAPHAEL (Brown University), change before study actually begins.] University of California, Los Angeles; Stanford University; AL YSON REEVES KAREN MARIE APODACA (New Mex­ MARIE DILLON DAHLEH (University of (Cornell University), Brandeis Univer­ ico State University), New Mexico California, Los Angeles), University of sity; VICTOR REINER (University of State University; MARIA F. BASTERRA California, Los Angeles; DAVID DoB- Minnesota), University of Minnesota; (University of Texas at Austin), Univer-

MAY/JUNE 1992, VOLUME 39, NUMBER 5 451 ...... ···············-·-···------···················--·---············-·-·····························-·-··---·-· News and Announcements sity of California at Berkeley; JosEPH sity), University of California at Berke­ SCOTT RAYMOND (California Institute CooK (Baldwin-Wallace College), Uni­ ley; HUBERT LEWIS BRAY (Rice Uni­ of Technology), University of Arizona; versity of California at Berkeley; Eu­ versity), Princeton University; HowARD MICHAEL SEAN RICHMAN (Brown Uni­ GENE ANDRES HOUSEMAN (University ANDREW CHAMBLIN (Rice University), versity), Princeton University; KATHY of California at Berkeley), University University of Oxford; WILLIAM CHEN ELIZABETH RUSSELL (Rice University), of Wisconsin at Madison; KATHRYN (Washington University), University of Texas A&M University; WILLIAM ALAN MARIE LEWIS (University of Kentucky), California at Berkeley; ELAINE CHEW SCHNEEBERGER (Duke University), Purdue University; CASSANDRA MooRE (Stanford University), Stanford Univer­ Princeton University; KEITH GOODWIN (Southwestern University), Rice Uni­ sity; MARK THOMAS CHRISMAN (Uni­ SOLLERS (University of California at versity; JOHN ANTHONY QUINTANILLA versity of California at Davis), Univer­ Davis), Cornell University; ERic JoEL (Stanford University), University of sity of California at Berkeley; MICHAEL STOLLNITZ (Swarthmore College), Cal­ Maryland; and DORN VERNESSA VER­ CoLE (Hofstra University), University ifornia Institute of Technology; CATHER­ NON (Howard University), Howard Uni­ of Chicago; BRIAN DAVID CONRAD (Har­ INE ANN SUGAR (Pomona College), versity. vard University), Princeton University; Princeton University; STEVE C. WANG KEITH CONRAD (Princeton University), (Cornell University), University of Chi­ NSF Graduate Fellowships Harvard University; KAREN ELIZABETH cago; ERIC KARL WEPSIC (Harvard Uni­ Awarded EDWARDS (University of California at versity), University of California at The National Science Foundation (NSF) Berkeley), University of California at Berkeley; THOMAS PETER WITELSKI has announced the names of 740 stu­ Berkeley; AVROM IRWIN FADERMAN (Cooper Union), California Institute dents who have been offered fellow­ (University of California at Los Ange­ of Technology; and MICHAEL ERNEST ships for graduate study in the natural les), University of California at Berke­ ZIEVE (Harvard University), University and social sciences, mathematics, and ley; LISA KAREN FLEISCHER (Harvard of California at Berkeley. engineering. University), Cornell University; KEviN The NSF Graduate Fellowships pro­ BRUCE FOLTINEK (University of Cal­ Modeling Contest Winners vide a stipend of $14,000 per year gary), Duke University; FRANCIS YEIN Announced for three years of full-time graduate CHEI FUNG (Kansas State University), A national panel of judges, including study, together with an annual cost­ Princeton University; MICHAEL GIDEON representatives from the Operations Re­ of-education allowance in lieu of all GREENBLATT (California Institute of search Society of America and the So­ tuition and fees at U.S. institutions. Technology), University of Chicago; ciety for Industrial and Applied Mathe­ The fellowships may also be used over DAVID GREGG GUPTA (Georgia Insti­ matics, is pleased to announce the win­ a five-year period to permit students to tute of Technology), Massachusetts In­ ners of the 1992 Mathematical Contest incorporate teaching or research assis­ stitute of Technology; DAVID JOHN in Modeling. They are: Pomona Col­ tantships into their education. HAROLDSEN (Utah State University), lege, University of Colorado at Bou1- Applications were submitted by University of Arizona; BRENDAN En­ der, North Carolina School of Science 7723 individuals nationwide and were WARD HASSETT (Yale University), Har­ and Mathematics (a high school), Okla­ evaluated by a panel assembled by vard University; RONALD JAMES How­ homa State University, and Washington the National Research Council. Awards ARD (University of Chicago), Princeton University. were made in all fifty states, and 290 University; ALAN JAFFRAY (California The yearly contest presents two went to women. State University at Sonoma), University open-ended problems to teams of three The awards include forty-two in the of Chicago; JEREMY ADAM KAHN (Har­ undergraduates, who choose one of the mathematical sciences and thirty-two vard University), University of Califor­ problems to solve. This year, the first in computer science. The recipients in nia at Berkeley; JOHN ALLEN KUCHEN­ problem was to determine the power to the mathematical sciences are listed be­ BROD (Transylvania University), Har­ be radiated by an air traffic control radar low, together with their baccalaureate vard University; GREGORY DAVID LAND­ at a major metropolitan airport; the sec­ institutions (in parentheses) and the in­ WEBER (Princeton University), Harvard ond problem was to arrive at an optimal stitutions where they will pursue their University; LEWIS Kuo-WEI LEE (Stan­ prioritized scheduling system for an graduate studies. [Editor's Note: The ford University), Harvard University; emergency power restoration system. institution of graduate study listed for LUCY LIFSCHITZ (University of Califor­ The contest drew 292 teams represent­ each recipient is from the original ap­ nia at Los Angeles), Yale University; ing 189 schools in six countries-the plication form and, in many cases, may BRADLEY WILLIAM MANN (Princeton U.S., Canada, China, Ireland, Lithuania, change before study actually begins.] University), Harvard University; WIN­ and Hong Kong. Teams were given four DANIEL JONATHAN ALLCOCK (Uni­ STON CHIH-WEI Ou (Princeton Uni­ days, from Friday February 21 through versity of Texas at Austin), Univer­ versity), University of Chicago; DAVID Monday February 24, to research the sity of California at Berkeley; MARTIN MICHAEL PATRICK (Carnegie-Mellon topic and come up with a solution. ZDENEK BAZANT (University of Ari­ University), Princeton University; NICH­ Contestants may not seek help from zona), University of Arizona; WALTER OLAS PHAT (Princeton University), anyone, but they may use inanimate JOHN BOSCARDIN, JR. (Brown Univer- Harvard University; CHRISTOPHER sources to support their solutions.

452 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

This contest differs from others in NSF support has been awarded to the Meeting on March 3, 1992 at the that it is the only national contest in eighteen EPSCoR -eligible states and National Academy of Sciences in Wash­ which the teams of students work to­ Puerto Rico. Previous awards were ington, the group of more than 120 gether to find a solution; other contests made in 1980, 1985, 1987, and 1989. scientists and engineers drafted a let­ either have the students work alone or ter to D. Allan Bromley, assistant to have the individual team members work New NSF Assistant Director President Bush for science and technol­ alone and combine scores for a team to­ Named ogy. Bromley requested the meeting to tal. In addition, the problems call upon William Harris has been named As­ obtain advice on what the U.S. govern­ a variety of skills and talents, including sistant Director for Mathematical and ment might do to preserve science in writing skills, organizational skills, as Physical Sciences (MPS) of the Na­ the FSU. A number of representatives well as mathematical knowledge. tional Science Foundation (NSF). He of the AMS and the mathematical sci­ The two teams judged outstanding replaces David A. Sanchez, who fin­ ences community attended the meeting. in their solution of the air traffic con­ ished a two-year tour of duty at the "Achieving U.S. goals of shrink­ trol problem were Pomona College and NSF and has returned to Lehigh Uni­ ing and redirecting the FSU military the University of Colorado at Boulder. versity, where he is vice president and [research and development] effort and For the power system problem, three provost. developing the science and technology teams were judged to be outstanding: As the head of the MPS direc­ component of the civilian economy North Carolina School of Science and torate, Harris will oversee the Division will require providing opportunities for Mathematics, Oklahoma State Univer­ of Mathematical Sciences, as well as both FSU weapon scientists and non­ sity, and Washington University. More research divisions in astronomy, chem­ weapon scientists," the letter says. "The than forty teams were cited for mer­ istry, materials research, and physics. U.S. can play a leadership role among itorious solutions, and nearly seventy The total budget of this directorate Western countries in revitalizing for­ received honorable mentions. exceeded $623 million in fiscal year mer Soviet science and technology if The Consortium for Mathematics 1992. we act quickly." The group also noted and its Applications administers the Harris, formerly assistant to the di­ that collaborations with world-class re­ contest. For more information, write to: rector for science and technology, pro­ search groups in the FSU can benefit COMAP, Suite 210, 57 Bedford Street, vided advice to NSF director Walter American science and business. Lexington, MA 02173. Massey on a broad range of scien­ Among its many recommendations, tific and policy matters, including long­ the group suggested that: EPSCoR Awards Announced range planning and cross-directorate ac­ • funding from the existing $400 mil­ The National Science Foundation (NSF) tivities. Previously, he was director of lion in the Department of Defense announced awards totaling more than the NSF's Office of Science and Tech­ budget for FSU weapons disman­ $13.7 million in fiscal year 1992 to nology Infrastructure, where he over­ tlement should be used this year eleven states and one territory through saw the Science and Technology Cen­ for immediate support of new re­ the Experimental Program to Stimulate ters, Research Facilities, and Academic search opportunities for critical FSU Competitive Research (EPSCoR). Research Instrumentation programs. weapon scientists and the most Alabama, Arkansas, Kentucky, A chemist, Harris first came to the highly qualified nonweapon scien­ Louisiana, Maine, Mississippi, North NSF in 1977 as a program director in tists. Dakota, Oklahoma, Puerto Rico, South physical chemistry. Previously, he was • in addition to funding support of Carolina, South Dakota, and Wyoming at Furman University in Greenville, $25 million for weapon scientists will each receive from $1 million to South Carolina. He was an undergradu­ Inter­ $1.3 million per year over three years ate at the College of William and Mary through the newly proposed national Science and Technology to strengthen academic departments and and received his Ph.D. in chemistry million or support improved research activities. In from the University of South Carolina Center in Moscow, $25 be made addition to NSF support, the recipi­ in 1970. He did postdoctoral work at more this fiscal year should programs ents will provide nearly $93 million to the National Institutes of Health. available for cooperative outside the support the improvements. for non weapon scientists EPSCoR is designed to help gov­ Group Recommends Action center. ernments and their academic institu­ to Stem Soviet "Brain Drain" • a special fund of $50 million to tions improve the quality of science The U.S. government should act "im­ $100 million should be established and engineering research, increase the mediately and aggressively" to help to help replenish and refurbish equip­ number of scientists and engineers that reorient the basic scientific and techno­ ment, journals, and books used in are able to compete successfully for logical capabilities of the former Soviet laboratories of special importance. federal grants, and foster long-term im­ Union (FSU) and stem the "brain drain" The U.S. should take the lead in provements in research and education. as many Soviet scientists look beyond obtaining the necessary funds from Since the program's inception in their borders for lucrative jobs, says a bilateral and multilateral assistance 1978, approximately $66 million in group of U.S. scientists and engineers. agencies for this purpose.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 453 News and Announcements

The meeting divided into working have completed their junior year. This Jumelage 92, the third annual meet­ groups that developed separate rec­ Institute is designed to give participants ing of the logic and computer science ommendations on four topics, one of insight into research areas of the Center community, will meet at MSI Octo­ them being basic research. The group faculty, and also to acquaint them with ber 15-17, 1992. Anil Nerode will emphasized that U.S. cooperative ac­ the rigors of advanced mathematics. organize this discussion of the mod­ tivities should not ignore those Soviet Both Hampton and Carnegie Mellon em lambda calculus, functional pro­ scientists who chose not to participate faculty will be involved in the Institute. gramming, and the implementation of in the military-industrial complex. To For more information about activi­ constru«tive logic systems. address short-term emergency needs, ties of the Center for Nonlinear Anal­ In addition, Cornell's M. Stillman the group suggested that $5 million ysis, contact the Center at the Depart­ and B. Sturmfels are organizers for to $10 million of the $25 million for ment of Mathematics, Carnegie Mellon the Regional Institute in Geometry and nonweapon scientists should be pro­ University, Pittsburgh, PA 15213-3890; Computational Algebraic Geometry to vided over the next six months to the Fax: 412-268-6380; email: enOs@ meet at Amherst College from July 6- extramural research programs of U.S. andrew .cmu.edu. 13, 1992; A. Nerode is program chair agencies for supplements to Ameri­ for the symposium on Logical Foun­ can grantees. These supplements would dations of Computer Science to meet "expand or initiate collaborative ac­ News from the at Tver University, Russia from July tivities with former Soviet scientists" Mathematical Sciences Institute 20-24, 1992; M. Sweedler is an orga­ in areas of direct interest to the U.S. Cornell University nizer for the International Symposium In addition, the group recommended The Mathematical Sciences Institute on Symbolic and Algebraic Computa­ considering a binational foundation for (MSI) will host five workshops at Cor­ tion (ISSAC) to meet in Berkeley from support. Emphasizing that it did not call nell University in the coming months July 27-29, 1992; C. Mueller will orga­ for "a welfare system for [FSU] sci­ and will cosponsor five others through­ nize a workshop on Stochastic Partial entists," the group urged expansion of out the country and abroad. Differential Equations to meet at the "mutually advantageous binational col­ J. Remmel of UCSD and P. Clote University of Rochester from July 17- laboration with well-known scientists of Boston College are the organizers of 18, 1992; and A. Brown, Jr. and H. and high-quality research groups based Feasible Mathematics II on May 28-30, Blair are organizers for a workshop on on evaluations by American scientists." 1992. Invited speakers include: M.L. Documents, Computation, and Prefer­ The summary of recommendations Bonet-Carbonell, S.R. Buss, D. Cenzer, ence to meet in Washington, DC from from the March 3 meeting is available B. Kapron, P. Kolaitis, J. Krajicek, T. October 21-23, 1992. MSI researchers free from: Office of Central Europe Pitassi, A. Razborov, and G. Takeuti. will participate in the Tenth U.S. Army and Eurasia, National Academy of Sci­ Logical Methods in Mathematics Mathematics Conference, organized by ences, 2101 Constitution Avenue, NW, and Computer Science, a workshop the U.S. Army Research Office and Washington, DC 20418; telephone 202- to honor MSI Director Anil Nerode's meeting at West Point, NY from June 334-2644. 60th birthday, is being organized by R. 16-19, 1992. Shore, J.N. Crossley, J. Remmel, and For information about any of these News from the M. Sweedler. It will meet at Cornell events, contact J. Chiment at the Math­ Center for Nonlinear Analysis from June 1-3, 1992. J. Hartmanis, D. ematical Sciences Institute, 409 College 607-255-8005, Carnegie Mellon/Hampton Kozen, V. Lifschitz, S. MacLane, G. Ave., Ithaca, NY 14850, Universities Metakides, J. Remmel, G. Sacks, D. [email protected]. A workshop on Computational Meth­ Scott, and R. Soare will give invited ods in Materials Science will be held talks. They will be joined by more than News from the September 16-18, 1992 at Carnegie twenty other speakers. Institute for Mathematics Mellon. The organizers are R.A. Nico­ J. Guckenheimer of Cornell will· and its Applications laides and D. Kinderlehrer. Topics will host an extended workshop on Patch University of Minnesota include the numerical treatment of liq­ Dynamics to meet in Ithaca, NY from The Institute for Mathematics and its uid crystals, phase transitions, interfa­ June 22-July 17, 1992. Applications (IMA) Postdoctorates in cial phenomena, and superconductivity. M. Cranston from the University of Industrial Mathematics program, initi­ Diffusion approximations of dis­ Rochester will organize a workshop on ated in fall 1990 with four positions crete stochastic systems will be the Stochastic Analysis to be held Septem­ has now grown to seven one-to-two subject of a workshop to be held in the ber 13-15, 1992. The workshop will year positions. These appointments are fall of 1993 and organized by T. Kurtz focus on the interplay of analysis and in addition to the regular IMA postdoc­ of the University of Wisconsin and S. probability. Invited speakers include: toral program and are funded jointly Shreve of CMU. R. Banuelos, C. Bishop, K. Burdzy, D. by the National Science Foundation In June, the Center is sponsoring Burkholder, E. Carlen, M. Freidlin, E. (NSF) and IMA and by the partic­ a four-week Summer Mathematics In­ Hsu, N. Krylov, P. March, M. Pinsky, ipating industries. They are designed stitute for undergraduate students who T. Salisbury, and Z. Zhao. to prepare mathematicians for research

454 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ···························································------News and Announcements careers involving ongoing academia­ D. Week 4: Global climate model­ tion for the Advancement of Science industry interaction. Familiarity with ing. (AAAS), in collaboration with its affil­ PDE and/or numerical analysis is de­ The overlap in each segment of iated organizations, would like to rec­ sired, but no knowledge in engineering the program is intended to increase ognize such contributions through the is required. Postdoctorates spend 50% interaction among scientists and math­ AAAS Award for International Scien­ effort working with industrial scien­ ematicians working in specified areas. tific Cooperation. tists from a sponsoring industry and The 1992-1993 academic year pro­ This monetary prize of $2500 in­ 50% effort in their personal research gram at the IMA will be Control cludes a certificate of citation and and in the regular IMA program. For Theory and its Applications. The Co­ travel expenses to the AAAS meet­ fall 1992, positions have been filled ordinators for this program are H.J. ing. The award is open to any living in the following research areas: Air Sussmann (Chairman), W.H. Fleming, individual (or individuals) in the in­ Quality Modeling (Ford); Diffractive P.P. Khargonekar, P.R. Kumar, D.L. ternational scientific and engineering Optics (Honeywell); Imaging Analy­ Russell, and S.E. Shreve. The year is community. Contributions worthy of sis (Siemens, Princeton); Micromagnet­ divided into three parts (corresponding the award include but are not limited ics (3M); Near-Infrared Imaging (3M); to fall, winter, and spring quarters) al­ to: promotion of innovative interna­ Robust Control (Honeywell); and Semi­ though it is expected that there will tional research, teaching, publications, conductors (Siemens, Munich). be considerable fluidity between the program or project administration, de­ The IMA 1992 summer program various parts. velopment, technology transfer, scien­ will be Environmental Studies: Math­ (1) Fall: September 8-December tific standards, or networking activities. ematical, Computational and Statis­ 30, 1992, Linear and distributed pa­ Nominations for the award should tical Analysis, July 6-31. The Organiz­ rameter systems be submitted by September 15, 1992. ing Committee is M. Wheeler (Chair), (2) Winter: January 2-March 30, For more information on the nomina­ J. Chang, M. Ghil, D. McTigue, J. 1993, Nonlinear systems and optimal tion procedure and the award, contact: Seinfeld and P. Switzer. This summer control Elizabeth J. Kirk, CAIP Coordinator, program is designed to provide a much (3) Spring: April 1-June 30, 1993, American Association for the Advance­ needed interdisciplinary forum for joint Stochastic and adaptive systems ment of Science, 1333 H Street, NW, exploration of recent advances in the Fall quarter highlights are a Tu­ Washington, DC 20005; telephone 202- formulation and application of (A) en­ torial, (September 8-11, 1992, orga­ 326-6650. vironmental models, (B) environmental nized by P.P. Khargonekar and D.L. data and data assimilation, (C) stochas­ Russell; a workshop on Robust Con­ Call for Nominations tic modeling and optimization, and (D) trol Theory, September 21-25, 1992, for Fermat Prize Global climate modeling. These four organized by B.A. Francis and P .P. The Fermat Prize recognizes the work conceptual frameworks provide com­ Khargonekar; a workshop on Control of a research mathematician in the ar­ mon themes among a broad spectrum Systems Design for Advanced Engi­ eas in which Pierre de Fermat worked, of specific technical topics at this work­ neering Systems: Complexity, Uncer­ specifically: principles of variational shop. The program will bring forth a tainty, Information, and Organiza­ theory, foundations of the calculus mix of physical concepts and processes tion, October 12-16, 1992, organized of probabilities and analytic geome­ such as chemical kinetics, atmospheric by D. Enns, M. Morari, and C.N. Nett; try, and number theory. The prize is dynamics, cloud physics and dynamics, a workshop on Control and Optimal given by Universire Paul Sabatier and flow in porous media, remote sensing, Design of Distributed Parameter Sys­ Matra Marconi Space. climate statistics, stochastic processes, tems, November 9-13, 1992, organized Within these parameters, the spirit parameter identification, model perfor­ by J.E. Lagnese, D.L. Russell, and L. of the prize is to recognize those results mance evaluation, aerosol physics and White; and a period of concentration that are accessible to the largest number chemistry, and data sampling together on Flow Control, November 16-20, of professional mathematicians. with mathematical concepts in stiff dif­ 1992, organized by M. Gunzburger. The prize includes 100,000 FF, do­ ferential systems, advective-diffusive­ For more information about IMA nated by Matra Marconi Space, and is reactive PDE's, inverse scattering the­ activities, see the Meetings and Con­ awarded every two years in Toulouse. ory, time series analysis, particle dy­ ferences section of this issue or contact The third award will be made in spring namics, stochastic equations, optimal the IMA ([email protected]). 1993. The first award, in 1989, went control, and others. The program con­ to Abbas Bahri and Kenneth Ribet; sists of four parts: Call for Nominations the second award, in 1991, went to A. Weeks 1 and 2: Environmental for the AAAS Award for Jean-Louis Colliot-Thelene. models International Cooperation For more information on the prize B. Weeks 2 and 3: Environmental Many scientists and engineers con­ rules and on how to nominate can­ data and assimilation tribute their time to conduct research didates, write to: Prix FERMAT de C. Weeks 3 and 4: Stochastic mod­ and develop programs of an interna­ Recherche in Mathematiques, Service eling and optimization. tional nature. The American Associa- des Relations Publiques, Universite Paul

MAY/JUNE 1992, VOLUME 39, NUMBER 5 455 ····"--·--·----··-···············-····-·-·------News and Announcements

Sabatier, 118 route de Narbonne, 31062 Birkhauser Verlag's series, "Progress standards after January 1, 1987, but not Toulouse Cedex, France. The deadline in Mathematics," subject to the usual later than the deadline of this announce­ for submitting nominations is Decem­ regulations concerning copyright and ment. The following documents must ber 19, 1992. author's rights. The committee will also be enclosed: short curriculum vitae of recommend publication of those non­ the applicant; brief description of the Ferran Sunyer I Balaguer Prize winning monographs which are judged research conducted; list of publications The Institut d'Estudis Catalans an­ to be of high scientific value. presented; off-prints of the publications nounces the Ferran Sunyer i Bala­ Monographs, preferably typeset in presented (a typescript can be accepted guer Prize, an international mathemati­ 'lEX. must be submitted before De­ only if accompanied by a formal let­ cal research prize competition open to cember 31, 1992 to: Fundaci6 Ferran ter of acceptance for publication in a all mathematicians. The prize honors Sunyer i Balaguer, Institut d'Estudis journal, signed by the editor). the memory of Ferran Sunyer i Bala­ Catalans, Carme, 47, 08001, Barcelona, Applications will be examined by guer (1912-1967), a self-taught Catalan Spain; email: [email protected]. a committe of three members, two of mathematician who, in spite of a seri­ Preliminary versions, in a form suitable whom will be chosen by members of ous physical disability, was very active to be refereed, will also be considered. the Class of Mathematical, Physical, in research in classical analysis and Submission of a monograph implies and Natural Sciences at the Istituto achieved international recognition. acceptance of all conditions of the Lombardo from among members of The prize will be awarded for a competition. the Class. The third member will be mathematical monograph of an expos­ chosen by the Landriani family. In itory nature presenting, at the level Giovanni Sacchi Landriani case the latter were to resign, the third of graduate students or nonspecialists, Prize member would be chosen by the head of the latest developments in an active In honor of the memory of Giovanni the Department of Mathematics of the area of research in mathematics, based Sacchi Landriani, who tragically died University of Pavia, where Landriani mainly on the applicant's own work. while at the height of his scientific worked as a CNR researcher. The prize The monograph must be in English and activity, a competition for a prize of 10 cannot be awarded to more than one run at least 150 pages. The winner million Italian Liras is sponsored by the individual. In case the prize is not will be chosen by a committee consist­ Istituto Lombardo of the Accademia di awarded, the prize funds will be used ing of Gerhard Frey, Universitat Essen; Scienze e Lettere· in Milan, Italy. for a subsequent competition. Joan Girbau, Universitat Autonoma de The prize recognizes original im­ The deadline for admission to the Barcelona; Paul Malliavin, Universite portant contributions to the field of competition is November 14, 1992. de Paris VI; Joseph Oesterle, Univer­ numerical methods for partial differ­ Applications received after this date site de Paris VI; and Alan Weinstein, ential equations. Last year's recipient will not be considered, regardless of University of California at Berkeley. of the prize was Douglas Arnold of the reason for delay. Application ma­ The prizewinner will be announced in Pennsylvania State University. terials should be sent to: Presidente Barcelona on April22, 1993. In order to be considered for the dell'Istituto Lombardo, Palazzo de Br­ The prize carries a monetary award competition, papers submitted by ap­ era, via Borgonuovo 25, 20121 Milano, of 12,000 ECU. In addition, the win­ plicants should have been accepted for Italy. ning monograph will be published in publication in a journal of international

Meeting of NSF Advisory Committee for OMS

As this issue of the Notice! was going to 0% increase for Disciplinary Research at the junior and senior levels and, in the printer, the Advisory Committee for in the DMS 1993 budget is a terri­ each category, the award size should the National Science Foundation's Di­ ble mistake. It sends a very negative only vary moderately from the mean. vision of Mathematical Sciences (DMS) message about the value placed on dis­ Support for budget items such as grad­ concluded a three-day meeting. A re­ ciplinary mathematical sciences. Dis­ uate students, postdocs, and equipment port on this meeting is being prepared ciplinary research in the mathematical should be either based on justification for a future issue. However, the Advi­ sciences is and must remain the central for the items within the proposal and sory Committee passed, unanimously, part of the DMS program. awarded independently of the tier sys­ several resolutions, two of which are • In order to implement our resolu­ tem or based on a separate proposal. particularly important to the mathemat­ tion of unlinking award sizes to salaries, One of the intentions of this res­ ical community. These resolutions are the Advisory Committee recommends olution is to significantly increase the reported below. that the DMS consider a two-tier award number of principal investigators sup­ • The Advisory Committee feels system. These tier awards should be ported. that the decision by the NSF to request

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

DoE Announces workshops, conferences, and special re­ paramount in making decisions among New Postdoc Program search years have an opportunity to otherwise equally meritorious propos­ The Department of Energy (DoE) has contribute to this effort. Conferences als. Proposals that have an impact on announced a new program that will will be supported only if equivalent the nation's science personnel base, provide postdoctoral research opportu­ results cannot be obtained at regular especially with regard to doctoral re­ nities at the DoE national laboratories meetings of the professional scientific cipients, graduate students, women, mi­ for scientists and engineers. societies. Requests should follow the norities, and persons with disabilities, The fellowships, which include a general format of "Grants for Research will be given a higher priority than oth­ $52,800 stipend, will be awarded to and Education in Science and Engi­ erwise equally meritorious proposals those who have earned doctorates in the neering" (NSF 90-77). Activities of an which do not. physical, engineering, or computational annual, semiannual, or recurring na­ Additional information about sup­ sciences, areas most critical to DoE. ture in a specific research area should port for these kinds of activities, in­ Up to ten fellowships will be awarded be submitted to the appropriate disci­ cluding format and evaluation criteria, each year and may be extended for plinary research program for consider­ is available in the program announce­ up to two additional years. Selection ation rather than the Office of Special ment, "Conferences, Workshops, and of awards will be made by panels of Projects. Special Years in the Mathematical Sci­ experts within the discipline, including For conferences, there will be two ences" (NSF 91-91). This publication DoE laboratory scientists and others. submission deadlines each year: Novem­ also contains information about special Applications may be requested from: ber 1 for conferences to be held research conference activities supported Science/Engineering Education Divi­ the following June through Novem­ by the NSF through the AMS, the So­ sion, Oak Ridge Institute for Science ber; and May 1 for conferences to be ciety for Industrial and Applied Math­ and Education, P.O Box 117, Oak held the following December through ematics, and the Conference Board on Ridge, TN 37831-0117; or call 615- May. For a special academic year or the Mathematical Sciences. In addition, 576-9934. fall semester/quarter, the deadline is "Opportunities in the Mathematical Sci­ November 1 of the previous year. For ences 1992" (NSF 91-143) contains ad­ Information from the a spring semester/quarter, the deadline ditional information about programs of Office of Special Projects is May 1 of the previous year. These interest to the mathematical sciences Among the various programs within the deadlines apply to conference proposals community. Division of Mathematical Sciences at originating with academic institutions. Both publications may be requested the National Science Foundation (NSF) Requests for international travel by from: Office of Special Projects, Di­ is the Office of Special Projects, which groups of mathematical scientists ordi­ vision of Mathematical Sciences, Na­ supports research, education, and in­ narily originate with educational institu­ tional Science Foundation, Room 339, frastructure in a variety of modes dif­ tions or professional scientific societies. 1800 G Street NW, Washington, DC ferent from the usual disciplinary re­ The Office of Special Projects will not 20550; telephone 202-357-3453. Elec­ search projects. In particular, it provides consider individual requests for interna­ tronic versions may be obtained through support for several types of research tional travel. Proposals should be sub­ STIS, the NSF's online publication sys­ conferences, including symposia, work­ mitted one year before the requested tem. For an electronic copy of an infor­ shops, regional conferences, and special travel is to occur. mation flyer on STIS (NSF 91-10), send research years. For conference, special year, or in­ an email message to [email protected] The NSF is committed to enlarging ternational travel proposals, the crite­ (Internet) or stisfly@nsf (Bitnet). In­ and enhancing the science personnel rion of overall impact on the U.S. math­ structions for using STIS appear in the base of the U.S. Organizers of research ematical sciences community will be Notices, September 1991, page 796.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 457 For Your Information

Calculus Reform nity for discussion of issues related to calculus reform and Study Group Formed improvement. More details will appear in the Meetings At the Joint Mathematics Meetings in Baltimore in January section of future issues of the Notices. 1992, a new group on improvement of calculus instruction The poster session is co-sponsored by the AMS and by took shape. The Calculus Reform Study Group, chaired the Committee on Calculus Reform And the First Two Years by Marcelle Bessman of Frostburg State University, is a (CRAFTY) of the Mathematical Association of America. network of people working on calculus reform projects, CRAFTY has been at the forefront of calculus reform and has with or without outside funding. The Study Group seeks to for several years sponsored panel discussions and sessions provide a forum for ongoing reports, dialogue, and debate for contributed papers and posters at national meetings. The about all aspects of calculus teaching. Society's co-sponsorship of the poster session reflects the To further this goal, the Study Group is sponsoring the concern with improved mathematical instruction at all levels, following activity at the Joint Mathematics Meetings in San which is articulated in the mission statement appearing in Antonio in January 1993: the AMS strategic plan. The session will feature displays of information about and materials from current calculus • A panel discussion, "Calculus Reform and the AP­ reform projects of all types. It will bring those interested in Calculus Program," organized by Howard Lewis Penn of working on calculus reform together with project directors the U.S. Naval Academy and George M. Rosenstein, Jr. who have already gone through the start-up process. Those of Franklin and Marshall College. More information will interested in displaying materials at the poster session should appear in the Meetings sections of future issues of the contact, as early as possible, James F. Hurley, University of Notices. Connecticut, Department of Mathematics, U-9, Storrs, CT • A poster session for calculus reform projects. This 06269-3009 (electronic mail: [email protected]), session is being organized by James F. Hurley of the or Paul Zorn, Department of Mathematics, St. Olaf College, University of Connecticut and Paul Zorn of St. Olaf College. Northfield, MN 55057 (electronic mail: [email protected]). A • An informal open forum for those involved in calcu­ brief abstract of 150-300 words should indicate how long lus reform or interested in becoming involved. Organized the project has been under way, the nature of the activity, by Marcelle Bessman, this forum will provide an opportu- and how many students will participate during 1992-1993.

Open Letter to the Mathematical Community from the New Assistant Director at NSF As incoming Assistant Director for the Mathematical and suggestions from all sources, made to either myself, Dr. Physical Sciences Directorate [MPS], I feel it is very Sunley, or Dr. Jerry Bona, Chair of the Advisory Committee. important to put a strong team in position quickly. I William C. Harris, Assistant Director Designate have asked Judy Sunley, currently Division Director for Mathematical and Physical Sciences the Mathematical Sciences [DMS], to join that team as Executive Officer for MPS. In this position, Dr. Sunley Editor's Note: Addresses for contacting the above individuals are: will have the opportunity to bring to bear on all of MPS Dr. William C. Harris or Dr. Judith S. Sunley the many skills that have characterized her exemplary and Mathematical and Physical Sciences, Room 512 effective service as Division Director for DMS. National Science Foundation 1800 G Street, N.W., Washington, DC 20550 Initially, Dr. M. Kent Wilson, a capable and experienced Telephone: 202-357-9742 NSF executive, will serve as Acting Division Director. We email: [email protected] or [email protected] will be recruiting someone from the mathematical sciences Professor Jerry L. Bona community to serve as Dr. Sunley' s replacement during Department of Mathematics the period of her MPS assignment (up to two years). The Pennsylvania State University Advisory Committee for the Mathematical Sciences will 215 McAllister Avenue, University Park, PA 16802-6401 play a major role in the recruitment process. We welcome email: [email protected]

458 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1992 AMS Elections

Council Nominations President's Candidates Vice President, Members-at-Large, Trustee Nominating Committee for 1992 and 1993 One vice-president, five members-at-large of the Council, Three members of the Nominating Committee are to be and one trustee will be elected by the Society in a contested elected in the fall of 1992. Continuing members are: election in the fall of 1992. Michael Aschbacher, Daniel M. Burns, Jr., Jerry L. Kazdan, The vice-president will serve for a term of three years Joseph Lipman, Walter David Neumann, Carol S. Wood. effective February 1, 1993. The Council has nominated two President Michael Artin will name six candidates for the candidates for the position, namely: three positions. Melvin Hochster Anil Nerode The five members-at-large will serve for a term of three Editorial Boards Committee ye_ars. The Council nominated ten candidates, namely: Two members of the Editorial Boards omrnittee are to be James H. Curry Peter Li elected in the· fall of 1992. Continuing members are: Richard Gloria C. Hewitt Kenneth A. Ribet James Milgram, Bhama Srinivasan, Nolan R. Wallach, Svetlana R. Katok Philip D. Wagreich Robert J. Zimmer. President Michael Artin will name four Steven George Krantz Jonathan M. Wahl candidates for the other two places. James I. Lepowsky Susan Gayle Williams The trustee will serve for a term of five years. The Robert M. Fossum Council nominated two candidates, namely: Secretary Roy L. Adler Richard W. Beals Urbana, illinois

Oscillation and Dynamics in Delay Equations John R. Graef and Jack K. Hale, Editors

Containing frontier contributions by leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January, 1991. With special emphasis on delay equations, the papers cover a broad range of topics in Oscillation and Dynamics ordinary, partial, and difference equations and include applications to problems in in Delay Equations commodity prices, biological modeling, and number theory. This book will interest graduate students and researchers in mathematics and those in other fields who have an interest in delay equations and their applications.

1991 Mathematics Subject Classifications: 11, 34, 35, 39, 45, 58 ISBN 0-8218-5140-3,263 pp. (softcover), June 1992 lndiv. mem. $22, List $36, Ins!. mem. $29 Your ordering code is CONM/129NA

1'-- All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Amerrcan Mathematrcal Socrcty Order from: American Mathematical Society, P.O. Box 1571 , Annex Station, Providence, Rl 02901-1571 , or call toll free 800·321·4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 459 J ml Xll. 'It Me

J1ULXll.

Dear Colleagues:

The American Mathematical Society and the London Mathematical Society have joined forces for the first joint meeting in Cambridge, England, from Monday, June 29 to Wednesday, July 1, 1992. A Joint Program Committee consisting of members of both societies has worked diligently to create an excellent scientific program consisting of five Invited Addresses and ten Special Sessions. There will also be sessions for shorter contributed papers.

It is the first time that the two societies have collaborated in this way and we trust the event will be a model for future similar joint meetings. We hope this meeting will encourage cooperation between members of the two societies and among mathematicians throughout the world.

The Joint Meeting is being held at a propitious time for the UK mathematical community. The first symposia at the Isaac Newton Institute for Mathematical Sciences recently established in Cambridge, will start immediately after the meeting. We hope that participants will take the opportunity to visit the Institute during their stay in Cambridge.

We hope this will be a mathematical feast that will most certainly be memorable. We are pleased that our societies are working together to offer our members a meeting of this nature and we are sure that it will be a rewarding experience for all.

Sincerely yours,

Michael Artin President American Mathematical Society Joint Meeting of the American and London Mathematical Societies Cambridge, England June 29-July 1, 1992

King's College Chapel The first joint meeting of the American Mathematical John M. Ball, Heriot-Watt University, Edinburgh, En­ Society (AMS) and the London Mathematical Society (LMS) ergy minimization and microstructure. will be held at the University of Cambridge, England, from Lawrence Craig Evans, University of California, Berke­ Monday June 29 to Wednesday July 1, 1992. ley, Harmonic maps and Hardy spaces. Benedict H. Gross, Harvard University, Langlands pa­ Joint Program Committee rameters in representation theory and number theory. Nigel J. Hitchin, University of Warwick, Einstein met­ The members of the Joint Program Committee are William rics and algebraic geometry. Michael Atiyah, Hyman Bass, Robert M. Abikoff, Sir Edward Witten, School of Natural Science, Institute Fossum, and Sir John Kingman. for Advanced Study, Princeton University, Localization and gauge theories. Local Organizing Committee The members of the Local Organizing Committee are Special Sessions Professor J. H. Coates (chair), Dr. W. B. R. Lickorish, Mrs. By invitation of the same committee, there will be ten S. Lowe, Miss S. M. Oakes, Dr. A. R. Pears, Dr. N. I. special sessions of selected twenty-minute papers. The the and Dr. R. L. Taylor. Shepherd-Barron, names and affiliations of the organizers, are as follows: Discrete group actions, Alan Beardon, University of Invited Addresses Cambridge, William J. Harvey, King's College London, Caroline. M. Series, University of Warwick. By invitation of the Joint Program Committee, there will Probabilistic combinatorics, Bela Bollobas, University be five invited one-hour addresses. The speakers, their of Cambridge, and Ronald L. Graham, AT&T Bell Labo­ affiliations, and the titles of their talks are: ratories.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 461 Meetings

Number theory, John H. Coates, University of Cam­ The Isaac Newton Institute for Mathematical Sciences bridge. The Isaac Newton Institute for Mathematical Sciences Discrete geometry and convexity, Jacob E. Goodman, has been established in Cambridge as a British national CUNY, City College, New York, and David Lannan, research institute with Sir Michael Atiyah as Director. Its University College, London. activities will encompass pure mathematics, applied mathe­ The microstructure of crystals, Richard D. James, matics, statistics, engineering, computer science, theoretical University of Minnesota, Minneapolis. physics, and all the other sciences in which mathematics Operator algebras, Vaughan F. R. Jones, University is applied. Construction of a purpose-designed building for of California, Berkeley, E. Christopher Lance, University the Institute will be completed shortly before the meeting. of Leeds, and Antony J. Wassermann, University of There is an "Open Day" on Thursday, July 2, from 10:00 Cambridge, a.m. until 3:00 p.m. Current trends in numerical analysis of nonlinear prob­ Registration lems, Rangachary Kannan, University of Texas at Arling­ ton. No provision has been made for on-site registration. Groups: finite and algebraic, William M. Kantor, Uni­ Registered participants should pick up their badge, program versity of Oregon, and Jan Saxl, University of Cambridge. and tickets (where applicable) at the Registration Desk. Par­ Geometric topology in low dimensions, W. B. R. Lick­ ticipants who wish to obtain a guest badge for their guest(s) orish, University of Cambridge. should do so at the Registration Desk. The Registration desk Classical analysis, Cora S. Sadosky, Howard University. will be located at Robinson College on Monday, June 29, from 10:00 a.m. to 5:00p.m., and at the Mill Lane Lecture Contributed Papers Room Block on Tuesday, June 30, from 9:00 a.m. to 5:00 p.m. There will also be sessions for contributed ten-minute papers. Social Events Activities of Other Organizations The LMS is providing a complimentary reception for all Materials of the Association for Women in Mathematics registered participants in the Dining Hall of Robinson (AWM) and the European Women in Mathematics (EWM) College at 9:15 p.m. on Monday, June 29. are on display in the exhibit area. An infonnal lunch is · A Conference Dinner for all participants resident at being arranged; details will be posted at the display table in Robinson College and a limited number of non-residents the exhibit area and available from Bettye Anne Case, Cora (based on availability) will be held in the Dining Room in Sadosky or Caroline Series. Robinson College at 7:30p.m. on Tuesday, June 30. Registered participants who purchased tickets to the Other Events of Interest Conference Dinner should pick up their tickets along with their badge and program at the Registration Desk. It is Book Exhibits and Exhibits regretted that tickets cannot be purchased at the meeting. All meeting participants are invited to visit the Book Exhibits in the Mill Lane Lecture Room Block (MLLRB). Abstracts Books published by the two Societies together with publi­ cations of Cambridge University Press, Oxford University Participants desiring a personal copy of the booklet contain­ Press, and several other publishers are on display. Books ing the AMS and LMS abstracts presented at this meeting will be sold at discounted prices. The Book Exhibit is open may request a copy at the Registration Desk. from 9:00a.m. to 5:00p.m. on Tuesday and Wednesday. The book, educational media and software exhibits Message Board are open from 9:00 a.m. to 5:00 p.m. on Tuesday and There will be a personal message board set up in the Wednesday. Their exact location will be announced at the Registration Area on Tuesday, June 30, at the Mill Lane meeting. Lecture Room Block. Sculpture Exhibit An exhibition of sculpture is being presented by Gabriella Accommodation Bollobas on Monday, June 29, from 6:00p.m. until 11:00 p.m., at Robinson College. The exhibition features bronze Reservations for Robinson College, the University Arms busts and full size plaster cast figures of mathematicians and Hotel, and the Holiday Inn Hotel can be obtained through physicists, including Sir Isaac Newton, P. A.M. Dirac, G. H. the Mathematics Meetings Service Bureau (MMSB) through Hardy, J. E. Littlewood and Stephen Hawking, and bronze May 29, 1992. Mter this date, participants who are interested plaques of Euler, Gauss, Hilbert, Ramanujan, and others. In in obtaining accommodation at the University Arms Hotel addition, there are numerous drawings and photographs of or the Holiday Inn Hotel should call these facilities directly. contemporary mathematicians. The MMSB can no longer guarantee availability of rooms

462 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings or special convention rates. No provision has been made providing bed and breakfast. It should be noted that the for on-site reservations at Robinson College. City of Cambridge is a great tourist attraction. Meeting participants who are interested in making accommodations Robinson College of this type are forewarned that it is usually necessary to Participants who reserved a room during preregistration make a reservation long in advance of the date of the at Robinson College should check in at the Porters' Lodge, meeting. which is open 24 hours a day. Here, they will be given a room key, a map of the college and a leaflet about Robinson Travel and Local Information College. They will then be directed to their accommodation and to the meeting's Registration Desk. TRA VCON, INC,. the official travel management firm for Robinson College is Cambridge University's newest the meeting, has arranged for special discounts aboard college. It is set on several acres of wooded gardens, and Northwest Airlines (Northwest Airlines' London airport is only a ten-minute walk from the Mill Lane Lecture Room Gatwick). If Northwest Airlines does not provide convenient Block and the Babbage Lecture Theatre, where all the service from your area, TRA VCON will be happy to inform meeting activities will take place. you of the most convenient flights and lowest available A room and board package at a cost of $424.08/£228.00 airfare on other airlines. Each participant will receive will include a bed for the nights of Monday, Tuesday, and $100,000 flight insurance with each ticket purchased through Wednesday; a buffet meal on Monday evening; breakfast, TRAVCON aboard any airline. For further information lunch, and dinner on Tuesday and Wednesday; and breakfast regarding these special airfares, contact TRAVCON, Inc at on Thursday. A limited number of rooms will be available 1-800-999-9780 or 203-232-9939. Participants arriving at for Sunday, June 28, at an extra charge of $81.84/£44.00 Gatwick, Heathrow, or Stansted airports are recommended and includes breakfast on Monday. It is regretted that to travel to Cambridge on Cambridge Coach Service #78 accommodation at Robinson College is not available outside and 79. Coaches leave at hourly intervals. Alternatively, this period. The MMSB can provide further information on there is frequent train service from London King's Cross Robinson College before the meeting. and Liverpool Street stations. If travelling from the airports by car, follow motorways M25 then M11. Parking space in University Arms Hotel Cambridge is very limited. The University Arms has been Cambridge's leading Participants in the meeting will have an opportunity hotel since 1834. It has been extensively modernized, but to explore the historic city of Cambridge. The University still retains the elegance of former times. Single, twin, or consists of over thirty self-governing colleges spread around double en suite bedrooms are available at a nightly rate the city centre in beautiful surroundings. King's College of $159.96/£86.00 for a single room and $195.30/£105.00 Chapel, the Great Court of Trinity College, and the Bridge for a twin or double room. For further information and of Sighs at St. John's College will perhaps be well-known to reservations, please call 022-335-1241 or fax at 022-331- everyone but there are many other buildings both medieval 5256. and modem that must be seen. There are many museums Holiday Inn Cambridge and galleries of which the most notable is the Fitzwilliam The Holiday Inn is Cambridge's newest hotel, having Museum. The Tourist Information Centre on Wheeler Street opened in 1991. Its facilities include an indoor swimming publishes a Two Hour Guide to Cambridge which describes pool. Single, twin, or double en suite bedrooms are available a walking tour of the main sights. For those with more time at a nightly rate of $130.20/£70.00 for a single room and to spare, the Tourist Centre has much more information on $204.60/£110.00 for a twin or double room. For further places to visit and things to see. information and reservations, please call 022-346-4466 or fax at 022-346-4440. Other Conferences and Meetings Please note that the dollar rates listed above for accom­ The European Congress of Mathematics (ECM) will be held modation are subject to market fluctuation and may be more from July 6-10, 1992, in Paris, France. This is the first or less at the time of the meeting than shown above. Congress of the European Mathematical Society (EMS). Other Hotels and Guest Houses There will be forty-one conferences on pure and applied Information about other accommodation in Cambridge mathematics and fifteen round tables on the general theme can be obtained from the Cambridge Tourist Information Mathematics and Society. For further information write to: Centre, Wheeler Street, Cambridge CB2 3BQ, United ECM, College de France, 3 rue d'Ulm, F75005, Paris, Kingdom. The Information Centre publishes a booklet titled France. A list of meetings and conferences being held in Accommodation for Visitors in and around Cambridge which Europe after this meeting will be provided upon request. gives details of hotels, guest houses, and establishments

MAY/JUNE 1992, VOLUME 39, NUMBER 5 463

~ ~

! !

i i

1 1

I I

Theater Theater

Hotel Hotel

I I

Footpath Footpath

Footpath Footpath

Institute Institute

Park Park

Arms Arms

~etre~ ~etre~

College College

yards yards

Lecture Lecture

Lecture Lecture

I I

Inn Inn

Private Private

River River

Public Public

Pedestrian Pedestrian

Car Car

Block Block

Newton Newton

SCALE SCALE

300 300

3oo 3oo

Lane Lane

I I

Robinson Robinson

Babbage Babbage

Mill Mill

Holiday Holiday

University University

Room Room

Isaac Isaac

......

~ ~

IJfil IJfil

1 - 1

4 4 -

5 5 -

3 3 -

2 2 - 1 1

I I

6 6 -

Sfj Sfj

--

n... n...

Depts.) Depts.)

(Univeristy (Univeristy

SidgwickSite SidgwickSite

--

Archaeology Archaeology

MuseumofCJassical MuseumofCJassical

~ ~

-

• •

School School

Univeuity Univeuity

-

Music Music

~ ~

Rugby Rugby

Hall Hall

University University

Ground Ground

Clare Clare

~ ~

,.... ,....

~ ~

z z

m m ~ ~

m m

m m

3: 3:

m m ~ ~

lJ lJ

"TI "TI

fJl fJl ~ ~

> >

z z

0 0

3: 3:

g g

3: 3:

:t :t

~ ~

0 0 : : Presenters of Papers

Numbers following the names indicate the speakers' positions on the program. • Invited Lecturer * Special Session Speaker

Al-Bassam, M. A., 95 * Frohlich, J .. 7 4 *Luczak, T., 12 * Sadosky, C., 133 *Anderson, J. M., 135 * Gabai, D., 112 *Luks, E. M., 180 Sagle, A., 92 * Aschbacher, M., 83 * Geiges, H., 127 Lundelius, R., 106 *Schneider, R., 176 *Avellaneda, M., 13 *Gillespie, T. A., 87 * Lutwak, E., 116 * Scholl, A. J., 60 *Barany, I., 63 *Gilman, J., 6 *Lyons, R., 85 * SeppaHi, M., 110 * Babai, L., 181 * Glowinski, R., 79 *Ma, L., 69 *Shephard, G. C., 177 Bachelis, G. F., 200 *Goddard, P., 75 * Macbeath, A. M., 108 * Shor, P. W., 10 • Ball, J. M., 1 * Goffman, C., 193 *Maclachlan, C., 109 Sibner, R. J., 100 Baum, P., 143 Golomb, S. W., 149 Maher, P. J., 203 Sine, R., 201 * Bellow, A., 86 Gompa, R. R., 212 * Mani-Levitska, P., 117 Somer, L., 45 Ben-El-Mechaiekh, H., 197 Gompa, V. L., 140 * Maskit, B., 2 Sorenson, J., 153 *Berenstein, C. A., 191 * Goodman, J. E., 113 *Mathieu, Y. E., 32 *S6s, V. T., 169 Berger, R. I., 53 * Gordon, C., 34 *Matos, J. P., 70 Spain, P. G., 40 Berman, R., 35 * Gorenstein, D., 84 * McDiarmid, C., 11 * Spector, S., 118 *Bhattacharya, K., 14 * Graham, R., 168 *McMullen, P., 174 *Spencer, J., 166 *Bien, F., 183 Graham, S. W., 49 *Melvin, P., 186 * Sreenivasan, K. R., 24 * Blackadar, B., 17 * Gritzmann, P., 114 *Morton, K. W., 156 Sritharan, S. S., 204 *Bleiler, S., 31 • Gross, B. H., 54 Moussa, N., 210 *Stein, E. M., 91 * Bollobas, B., 55 * Gunzburger, M.D., 159 *Miiller, S., 71 *Stem, R. J., 128 *Bona, J., 157 * Guralnick, R. M., 29 Muses, C.,43 * Sverak, V., 123 * Borcherds, R., 18 *Hayman, W. K., 194 Neuberger, J. W., 41 Tattersall, J. J., 145 *Boston, N., 154 *Heath-Brown, D. R., 173 *Neumann, P. M., 179 * Tavare, S., 8 *Brandt, A., 80 * Helson, H., 192 *Nicolaides, R. A., 22 *Taylor, M., 171 Brodzki, J., 139 *Hildebrand, M. V., 7 *Nicolaides, R., 68 *Taylor, R., 61 *Bullett, S., 165 Hiremath, G. R., 101 * Nikolskii, N., 88 * Temam, R., 77 Burke, M. R., 148 • Hitchin, N. J., 107 Nouri-Moghadam, M., 207 Tesser, S. B., 137 * Cameron, P. J., 27 * Hooley, C., 172 * Olson, T., 72 *Testerman, D. M., 81 * Carbery, A., 90 Hoyt, W. L., 51 *Osher, S., 23 Trench, W. F., 93 *Chang, D.-C., 89 Huang, M. L., 39 * Pach, J., 175 Tsui, S.-K., 198 * Chipot, M., 15 *Ivanov, A. A., 182 *Papadopoulos, A., 164 Tubbs, R., 46 * Chiswell, I. M., 161 Izzo, A. J., 37 *Parry, G. P., 119 Turquette, A., 146 * Choi, S., 130 danson, S., 57 * Paulin, F., 162 Van Buskirk, J. M., 102 *Chung, F. R., 167 Jensen, D. W., 52 * Pedregal, P., 120 Venables, H. A., 97 *Cohen, A. M., 184 Joyner, D., 48 *Peller, V. V., 132 Vernon, M. H., 99 * Connes, A., 19 *Kahn, J., 58 Percus, J. K., 42 * Voiculescu, D., 125 Corduneanu, C., 98 Kalia, R.N., 205 Plymen, R., 141 Voutier, P.M., 47 Cotter. C. S., 50 Kannappan, P., 206 * Popa, S ., 124 *Wassermann, A., 126 * Coxeter, H. S., 64 *Kauffman, L. H., 187 *Powell, M. J., 20 *Weiss, G., 136 Cross, R., 202 *Kawauchi, A., 188 * Praeger, C. E., 25 *Welsh, D. J., 59 * Cuntz, J ., 73 *Keen, L., 4 * Pyber, L., 82 Wenocur, R., 150 Dahiya, R. S., 96 Khalil, R., 196 Quine, J. R., 36 *Wheeler, M., 76 *Danzer, L., 65 King, J. P., 94 Quinn, F., 104 White, A. T., 151 Dilworth, S. J., 199 *Kleinschmidt, P., 115 * Raviart, P. A., 21 *Whitten, W., 30 *Dyer,M., 66 * Kolchin, V. F., 9 * Ribet, K. A., 62 Wigley, N. M., 144 *Earle, C. J., 5 * K6mer, T. W., 190 Rieders, E., 208 *Wills, J. M., 178 *Epstein, D. B., 111 * Kotschick, D., 129 *Riley, R., 33 *Winkler, P., 56 * Erdos, P., 170 * Kra, I., 3 * Rochberg, R., 134 Wise, G. L., 38 •Evans, L. C., 214 *Kulkarni, R. S., 163 Rogers, A., 105 • Witten, E., 160 * Fenn, R., 185 Lehman, J. L., 44 *Rogers, R. C., 122 Wood, J. A., 103 Ferenbaugh, C. R., 142 Leng, W. S., 147 *Rose, D. J., 78 Xu, J.-J., 213 Fine, D. S., 211 * Lichtenbaum, S., 155 Rotman, J., 138 *Young, N. J., 131 *Fine,J., 67 * Liebeck, M. W., 26 * Ruberrnan, D., 189 Zayed, A. I., 209 * Firoozye, N. B., 16 Lindgren, W., 152 *Rybka, P., 121 *Fix, G. J., 158 * Lubotzky, A., 28 Saccoman, J. J., 195

MAY/JUNE 1992, VOLUME 39, NUMBER 5 465 Program of the Sessions

The time limit for each contributed paper in the sessions is ten minutes. In the special sessions, the time limit varies from session to session and within sessions. To maintain the schedule, time limits will be strictly enforced. Abstracts of papers presented in the sessions at this meeting will be found in the June 1992 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the numbers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting .

....------,------"~--·---~--~-----

Monday, June 29 Special Session on Probabilistic Combinatorics, I

08:45-11:15 Room 2, Mill Lane Lecture Room Invited Address Block

08:45 Random walks supported on random points ofZjnZ. 19:45 -20:45 Babbage Lecture Theatre, New (7) Martin V. Hildebrand, University of Michigan, Ann Museum Site Arbor (875-60-59) 09:10 Independent process approximations for random (1) Energy minimization and microstructure. (8) combinatorial structures. John M. Ball, Heriot-Watt University, United Kingdom R. Arratla and S. Tavare*, University of California, (875-73-112) Los Angeles (875-05-170) (Sponsored by Bela Bollobas) 09:35 Cycles in random graphs and hypergraphs. (9) V. F. Kolchin, Academy of Sciences of the USSR Tuesday, June 30 (875-05-202) (Sponsored by Bela Bollobas) 10:00 Keller's cube-tiling conjecture is false. (10) Jeffrey C. Lagarlas and Peter W. Shor*, AT&T Bell Laboratories, Murray Hill, New Jersey (875-52-134) Special Session on Discrete Group Actions, I 10:30 Almost evel}' graph can be covered by rA/21 linear ( 11 ) forests. Colin McDiarmid*, University of Oxford, 08:45-11:05 Room 4, Mill Lane Lecture Room England, and Bruce Reed, Rheinische Block Friedrich-Wilhelms-Universitat, Germany (875-05-195) 10:55 The size of the last cycle in the random graph 08:45 Some inequalities for Kleinian groups. (12) process. Preliminary report. (2) Bernard Masklt, State University of New York, Stony Svante Janson, Uppsala University, Sweden, and Brook (875-99-212) Tomasz Luczak*, Adam Mickiewicz University, Poland 09:15 Holomorphic motions and Teichmiiller spaces. (875-05-131) (Sponsored by Bela Bollobas) (3) Preliminary report. Clifford J. Earle, Cornell University, Irwin Kra*, State University of New York, Stony Brook, and Samuel L. Krushkal, Bar llan University, Israel (875-32-38) Special Session on Microstructure of Crystals, I 09:45 Pleating coordinates for deformation spaces of (4) Kleinian groups. Preliminary report. 08:45-10:35 Room 6, Mill Lane Lecture Room Linda Keen*, Herbert H. Lehman College, City Block University of New York, and Caroline Series, Warwick University, United Kingdom (875-30-108) 08:45 Piezoelectricity in composite materials. (13) Marco Avellaneda, Courant Institute of Mathematical 10:15 Geodesics in infinite dimensional Teichmiiller spaces. Sciences, New York University (875-49-151) (5) Preliminary report. Clifford J. Earle*, Cornell University, Irwin Kra, State 09:15 Some problems in polycl}'stalline materials that University of New York, Stony Brook, and Samuel L. (14) undergo the Martensitic phase transformation. Krushkal, Bar llan University, Israel (875-32-50) Kaushik Bhattacharya, Courant Institute of Mathematical Sciences, New York University 10:45 Some examples of discrete two-generator subgroups (875-49-152) (6) of PSL(2, C). Preliminary report. Jane Gilman, Institute for Advanced Study 09:45 Approximated convex envelope of a function. (875-35-31) (15) M. Chipot, University of Metz, France (875-49-153)

466 ------r······ ...... Program of the Sessions

10:15 An investigation into small parameter limits of lattice 09:45 Questions provoked by a theorem on latin squares. {16) convolutions and stored energies in magnetic (27) Peter J. Cameron, Queen Mary and Westfield materials. College, University of London, United Kingdom Nikan B. Firoozye, Heriot-Watt University, United (875-20-192) (Sponsored by William M. Kantor) Kingdom and University of Minnesota, Minneapolis 10:15 Counting congruence subgroups. Preliminary report. (875-73-169) (28) Alex Lubotzky, Hebrew University, Israel (875-20-55) (Sponsored by William M. Kantor) 10:45 Transitive permutation modules. Preliminary report. Special Session on Operator Algebras, I (29) Robert M. Guralnick, University of Southern California (875-20-43) 08:45-11:15 Room 3, Mill Lane Lecture Room Block Special Session on Geometric 08:45 Approximately homogeneous C* -algebras. Dimensions, I (17) Bruce Blackadar, University of Nevada, Reno Topology in Low (875-99-208) 09:35 Lie superalgebras and product formulas for Siegel 08:45 -11 :05 Room 9, Mill Lane Lecture Room (18) modular forms. Block Richard Borcherds, University of Cambridge, United Kingdom (875-81-197) (Sponsored by Vaughan F. 08:45 Recognizing nonorientable Seifert bundles. Jones) (30) Wilbur Whitten, University of Southwestern Louisiana 10:30 Non-commutative geometry. (875-57 -11) (19) Alain Connes, IHES, Buras-sur-Yvette, France 09:15 Exceptional Dehn fillings. (875-46-200) (Sponsored by Vaughan F. Jones) (31) Steven Bleiler*, Portland State University, and Craig Hodgson, University of Melbourne, Australia (875-57 -12) Special Session on Current Trends in Numerical 09:45 Title to be announced. I (32) Yves E. Mathieu, University of Provence, France Analysis of Nonlinear Problems, (875-99-217) 10: 15 Representations of the groups of skew triple unions of 08:45 -11 :05 Room 7, Mill Lane Lecture Room (33) knots. Block Robert Riley, State University of New York, Binghamton (875-57-88) 08:45 Augmented Lagrangian methods for constrained (20) optimization calculations. 10:45 When is an incompressible torus created by Dehn Michael J. D. Powell, University of Cambridge, United (34) surgery on a knot? Kingdom (875-65-179) Cameron Gordon* and John Luecke, University of Texas, Austin (875-57-95) 09: 15 Numerical approximation of the Vlasov-Maxwell (21) equations. P. A. Raviart, Ecole Polytechnique, France (875-65-186) (Sponsored by Rangachary Kannan) Session on Analysis and Probability 09:45 Covolume methods for viscous flows. {22) Roy A. Nicolaides, Carnegie Mellon University (875-65-185) (Sponsored by Rangachary Kannan) 08:45 -10:40 Room 8, Mill Lane Lecture Room Block 10:15 Numerically capturing subscale behavior. (23) Stanley Osher, University of California, Los Angeles 08:45 Some mapping properties of the radial-limit function of and Cognitech, Inc., Santa Monica, California (35) an inner function. Preliminary report. (875-65-189) Robert Berman* and Togo Nishiura, Wayne State 10:45 Wavelets and turbulence. University (875-30-1 01) (24) Katepalli R. Sreenivasan, Yale University 09:00 The determinant of the Laplacian on moduli space. (875-65-201) (36) J. R. Quine* and Mark Hughes, Florida State University (875-30-121) 09:15 Uniform algebras generated by holomorphic and Special Session on Groups: (37) pluriharmonic functions. Preliminary report. Finite and Algebraic, I Alexander J. lzzo, University of Michigan, Ann Arbor {875-32-57) 09:30 Mutual independence. 08:45 -11:05 Room 1, Mill Lane Lecture Room (38) Gary L. Wise*, University of Texas, Austin, and Eric Block B. Hall, Southern Methodist University (875-6Q-168) 08:45 lmprimitive group actions on graphs and designs. 09:45 R numbers and queues. Preliminary report. (25) Cheryl E. Praeger, University of Western Australia, {39) Mei Ling Huang*, Brock University, and Percy Brill, Australia (875-20-13) University of Windsor (875-62-143) 09:15 Linear algebraic groups with finitely many orbits. 10:00 From sample-values to zeros and poles. (26) M. W. Llebeck, Imperial College, United Kingdom (40) Philip G. Spain, University of Glasgow, United (875-20-174) (Sponsored by William M. Kantor) Kingdom (875-65-130)

467 Program of the Sessions

Tuesday, June 30 (cont'd) Invited Address

11:30 -12:30 Babbage Lecture Theatre, New Museum Site 10:15 Sobolev gradients and differential equations. in representation theory and (41) J. W. Neuberger, University of North Texas (54) Langlands parameters (875-65-17) number theory. Benedict H. Gross, Harvard University (875-11-25) 10:30 An expanded set of correlation tests for random (42) number generators. Ora Engelberg Percus and J. K. Percus*, Courant Institute of Mathematical Sciences, New York Special Session on Probabilistic Combinatorics, II University (875-65-99) 14:00-16:20 Room 2, Mill Lane Lecture Room Block Session on Number Theory 14:00 Percolation in the cube. (55) Bela Bollobas, University of Cambridge, United Kingdom (875-05-172) 08:45-11:25 Seminar Room A, Department of 14:30 Collisions among random walks on a graph. Applied Mathematics and Theoretical Physics (56) Don Coppersmith, IBM T. J. Watson Research Center, Yorktown Heights, New York, Prasad Tetali, 08:45 The use of infinite numbers to make explicit the poles Rutgers University, Piscataway, and Peter Winkler*, (43) of the factorial function. Bellcore, Morristown, New Jersey (875-05-135) C. Muses, Mathematics and Morphology Research 15:00 Limit theorems using associated variables. Centre (875-11-111) (57) Svante Janson, Uppsala University, Sweden 09:00 Heeke operators on ternary cusp forms. (875-99-205) (44) J. Larry Lehman, Mary Washington College 15:30 Asymptotically good list-colorings. (875-11-145) (58) Jeff Kahn, Rutgers University, New Brunswick (875-05-87) 09:15 Upper bounds for frequencies of elements in (45) second-order recurrences over a finite field. 16:00 The Potts model. Lawrence Somer, Catholic University of America (59) D. J. A. Welsh, Merton College, United Kingdom (875-11-16) (875-05-98) 09:30 Gelfand's theorem for Drinfeld modules. (46) Paul Georg Becker, Math lnstitut der Universitat, Germany, W. Dale Brownawell, Pennsylvania State Special Session on Number Theory, I University, University Park, and Robert Tubbs*, University of Colorado, Boulder (875-11-175) 14:00 -16:30 Room 4, Mill Lane Lecture Room 09:45 Primitive divisors of Lucas and Lehmer sequences. Block (47) Paul M. Voutier, University of Colorado, Boulder 14:00 £-functions and extensions of motives. (875-11-193) (60) Anthony J. Scholl, University of Durham, United 10:00 On the stable Shimura correspondence for SL(2). Kingdom (875-11-176) (48) David Joyner, United States Naval Academy 14:50 Representations of Galois groups associated to (875-11-21) (61) automorphic forms. Richard Taylor, University of Cambridge, United 10:15 On u o q)(n). Preliminary report. Kingdom (875-11-03) (49) S. W. Graham*, Michigan Technical University, M. Filaseta and C. Nicol, University of South Carolina, 15:45 More on Serre's conjectures. Columbia (875-11-26) (62) Kenneth A. Ribet, University of California, Berkeley (875-11-138) 10:30 The computational dynamics of Pollard's rho method. (50) Preliminary report. Christopher S. Cotter, University of Northern Colorado (875-11-42) Special Session on Discrete Geometry and Convexity, I 10:45 Configurations of lines which determine modular (51) families of K3 surfaces. Preliminary report. W. L. Hoyt*, Rutgers University, New Brunswick, and 14:00-16:20 Room 1, Mill Lane Lecture Room C. F. Schwartz, Rider College (875-11-53) Block 11 :00 Dihedral perfect numbers. 14:00 On the number of convex lattice polytopes. Preliminary (52) David W. Jensen* and Eric R. Bussian, United (63) report. States Air Force Academy (875-11-93) lmre Barany, Mathematical Institute, Hungary 11 :15 Ideal class group structure. (875-52-78) (53) Ruth I. Berger, Memphis State University 14:30 Two aspects of the regular 24-ce/1 in four dimensions. (875-11-218) (64) H. S. M. Coxeter, University of Toronto (875-52-73)

468 ·············-··············· ············································································································· ·····························m------.-·-··············-····--·-~-----····-··-·········---- Program of the Sessions

15:00 Strategies for the generation of Penrose tilings with (65) defects, which (hopefully) will not lead to dead ends. Special Session on Current Trends in Numerical L. Danzer, Universitii.t Dortmund, Germany Analysis of Nonlinear Problems, II (875-52-66) (Sponsored by Jacob E. Goodman)

15:30 A class of convex programs with applications to 14:00-16:20 Room 7, Mill Lane Lecture Room (66) computational geometry. Block Martin Dyer, University of Leeds, United Kingdom (875-90-67) (Sponsored by Jacob E. Goodman) 14:00 A mixed-characteristic method for contaminant (76) transport. 16:00 Betti numbers for convex polytopes. Mary Wheeler, Rice University (875-65-183) (67) Jonathan Fine, Cambridge, United Kingdom (875-52-39) 14:30 Applications of inertial manifolds to scientific (77) computing. Roger Temam, University of Paris XI, France (875-65-190) Special Session on Microstructure of Crystals, II 15:00 Numerical analysis for ULSI simulation. (78) Donald J. Rose, Duke University (875-65-182) 15:30 Application of decomposition methods to some class 14:00 -16:20 Room 6, Mill Lane Lecture Room (79) of nonlinear partial differential equations. Block Roland Glowinski, University of Houston, University Park (875-65-181)

14:00 Numerical methods for computing microstructure. 16:00 Multi-scale computational methods. (68) Roy Nicolaides, Carnegie Mellon University (80) Achi Brandt, Weizmann Institute of Science, Israel (875-49-159) (875-65-188) (Sponsored by Rangachary Kannan)

14:30 Numerical computation for a variational problem in (69) micromagnetics. Special Session on Groups: Mitchell Luskin, University of Minnesota, Minneapolis, and Ling Ma*, Carnegie Mellon University (875-65-44) Finite and Algebraic, II

15:00 Young measures supported on a given set. (70) Joio P. Matos, lnstituto Superior Tecico, Portugal 14:00-16:20 Room 9, Mill Lane Lecture Room (875-49-157) Block 14:00 A1 type subgroups in semisimple algebraic groups and 15:30 Surface energy and microstructure in coherent phase (81) the finite groups of Lie type. Preliminary report. (71) transitions. Donna M. Testerman, Wesleyan University Stefan Muller, lnstitut fOr Angewandte Mathematik, (875-20-204) Germany (875-49-156) 14:30 Large subgroups of finite groups. Preliminary report. 16:00 Piezoelectric polycrystals: Effective medium (82) Laszlo Pyber, Rutgers University, Piscataway (72) approximation and bounds. (875-20-94) (Sponsored by William M. Kantor) Tamara Olson, Yale University (875-49-160) 15:00 Quasithin groups. (83) Michael Aschbacher, California Institute of Technology (875-20-100) Special Session on Operator Algebras, II 15:30 Revising the classification of the finite simple groups. (84) Daniel Gorenstein* and Richard Lyons, Rutgers University, New Brunswick (875-20-118) 16:00 A local characterization of sporadic groups. 14:00-16:30 Room 3, Mill Lane Lecture Room (85) Richard Lyons* and Daniel Gorenstein, Rutgers Block University, New Brunswick (875-20-1 02)

14:00 Quantized differential forms in non-commutative (73) geometry. Joachim Cuntz, University of Heidelberg, Germany Special Session on Classical Analysis, I (875-99-213) Cockcroft Lecture Theatre, New 14:50 Operator algebras tensor categories and conformal 14:00-16:30 (74) field theory. Preliminary report. Museum Site Jorg Frohlich, Eidgen Technological Hochschule, 14:00 A solution to an old problem of Hopf in ergodic theory. Switzerland (875-99-214) (Sponsored by Vaughan F. Jones) (86) Alexandra Bellow*, Northwestern University, and A. P. Calderon, University of Chicago (875-46-203) 15:45 Vertex operator algebras. 14:25 Analogues of classical IJ' inequalities. Preliminary (75) Peter Goddard, University of Cambrige, United (87) report. Kingdom (875-81-196) (Sponsored by Vaughan F. T. A. Gillespie, University of Edinburgh, United Jones) Kingdom (875-42-82)

469 ---· ······-·-·-·----.. -----·-·"·"-·--·-- Program of the Sessions

14:15 Monopoles on 3-manifo/ds with ends. (cont'd) (100) L. M. Sibner, Polytechnic Institute of New York, and Tuesday, June 30 R. J. Slbner*, Brooklyn College, City University of New York (875-53-178) 14:30 New diagonal properties and metrization II. Preliminary (101) report. 14:50 Stieltjes operator measures, evolution equations and G. R. Hiremath, Talladega College (875-54-146) (88) univalent functions. N. Nikolskll*, University of Bordeaux I, France and 14:45 A census of positive knots. Steklov Mathematics Institute, USSR, and V. (102) James M. Van Buskirk, University of Oregon Vasyunln, Steklov Mathematics Institute, USSR (875-57-150) (875-47-81) 15:00 Morse flows on SO(n) and spin(n). Preliminary report. (103) Jay A. Wood, Purdue University, Calumet Campus 15:20 spaces and elliptic boundary value problems. HP (875-57-194) (89) Der.Chen Chang*, University of Maryland, College Park, Eli Stein, Princeton University, and Steven 15:15 A topological quantum theory approach to the Krantz, Washington University (875-42-80) (1 04) Andrews-Curtis conjecture. Frank Quinn, Virginia Polytechnic Institute and State 15:45 Restriction implies Bochner-Riesz for paraboloids. University (875-57-47) (90) Anthony Carbery, University of Sussex, United Stochastic calculus on supermanifold,s and the Kingdom (875-42-123) 15:30 (105) Atiyah-Singer index theorem. 16:1 0 Oscillatory integrals and radon transforms. Alice Rogers, King's College, United Kingdom (91) Elias M. Stein, Princeton University (875-42-124) (875-58-164) 15:45 Continuity of hyperbolic spectral theory for (1 06) degenerating Riemann surfaces of finite volume. Session on Differential Equations Jay Jorgenson, Yale University, and Rolf Lundelius*, University of Southern California (875-58-48) 14:00 -15:40 Room 8, Mill Lane Lecture Room Block Invited Address 14:00 Critical elements of quadratic systems. (92) Arthur Sagle*, University of Hawaii, Hilo, and Michael Kinyon, University of Utah (875-34-04) 16:45-17:45 Babbage Lecture Theatre, New 14:15 Asymptotic behavior of solutions of functionally Museum Site nonoscillatory second order differential (93) perturbed (107) Einstein metrics and algebraic geometry. equations. Nigel J. Hltchin, University of Warwick, United Trench, Trinity University (875-34-08) William F. Kingdom (875-53-90) 14:30 A deterministic model for arms growth. Preliminary (94) report. Carey B. Joynt and Jerry P. King*, Lehigh University (875-34-19) 14:45 Extension of Riemann P-function. Wednesday, July 1 (95) M. A. AI-Bassam, University of Cambridge, United Kingdom (875-34-37) 15:00 Nonlinear neutral delay differential equations of a Special Session on Discrete Group Actions, II (96) higher order. R. S. Dahlya* and A. Zafer, Iowa State University (875-34-51) 08:45 -11 :05 Room 1, Mill Lane Lecture Room Block 15:15 Schroedinger conditions. Preliminary report. (97) Ji, A. Venables, Portsmouth Polytechnic, United 08:45 Nilpotent groups of automorphisms of Riemann Kingdom (875-35-136) (1 08) surfaces. A. M. Macbeath, Tayport, United Kingdom 15:30 Abstract Volterra equations: Stability and (875-20-56) (98) boundedness. Preliminary report. C. Corduneanu, University of Texas, Arlington 09:15 p-groups of symmetries of surfaces. (875-45-92) (1 09) Colin Maclachlan* and Yasemln Talu, Aberdeen University, United Kingdom (875-57-40) 09:45 Computation of a period matrix of a compact and (11 0) symmetric Riemann surface. Session on Geometry Mika Seppala, University of Helsinki, Finland (875-32-122) 14:00-15:55 Seminar Room A, Department of 10:15 Certain Seifert 3-manifold groups are automatic. Applied Mathematics and Theoretical Physics (111) D. B. A. Epstein, University of Warwick, United Kingdom (875-99-209) 14:00 Calculating the extrinsic geometry of a tube. 10:45 Convergence groups are FiJchsian groups. (99) Michael H. Vernon, Lewis-Clark State College (112) David Gabai, California Institute of Technology (875-53-144) (875-30-129)

470 ------····"""''''"""""""""""""""""""""''""'"""""""""Program of the Sessions

Special Session on Discrete Special Session on Operator Algebras, Ill Geometry and Convexity, II 08:45-11:15 Room 3, Mill Lane Lecture Room Block 08:45-11:05 Room 4, Mill Lane Lecture Room 08:45 The structure of subfactors. Block (124) Sorin Popa, University of California Los Angeles (875-99-215) (Sponsored by Vaughan F. Jones) 08:45 Arrangements, spreads, and topological planes. 09:35 Gaussian random matrices and free product operator (113) Jacob E. Goodman*, City College, City University of (125) algebras. Preliminary report. New York, Richard Pollack, Courant Institute of Dan Voiculescu, University of California, Berkeley Mathematical Sciences, New York University, Rephael (875-46-1 09) Wenger, Ohio State University, Columbus, and Tudor 10:30 Operator algebras and conformal field theory. Zamfirescu, Universitat Dortmund, Germany (126) Antony Wassermann, University of Cambridge, (875-52-69) United Kingdom (875-46-198) (Sponsored by Vaughan 09:15 Deciding uniqueness in norm-maximization. F. Jones) (114) Preliminary report. Peter Grltzmann*, University of Trier, Germany, and Victor Klee, University of Washington (875-52-76) Special Session on Geometric 09:45 Paths on polyhedra and their importance in Topology in Low Dimensions, II (115) optimization. Preliminary report. Peter Kleinschmidt, Universitat Passau, Germany 08:45 -10:35 Room 9, Mill Lane Lecture Room (875-52-77) (Sponsored by Jacob E. Goodman) Block 10:15 On a conjecture of Firey. Preliminary report. 08:45 Symplectic structures on 'J'Z-bundles overT2 • (116) Erwin Lutwak, Polytechnic Institute of New York (127) Hansjorg Geiges, University of Cambridge, United (875-52-79) Kingdom (875-53-22) (Sponsored by W. B. Lickerish) 10:45 Between combinatorial and smooth manifolds. 09:15 Surgery on cusp fibers. (117) Preliminary report. (128) Ronald Fintushel, Michigan State University, and Peter Mani-Levitska, University of Bern, Switzerland Ronald J. Stern*, University of California, Irvine (875-52-75) (Sponsored by Jacob E. Goodman) (875-57-58) 09:45 On the fundamental groups of manifolds with (129) distributions. N. A'Campo, University of Basel, Switzerland, and D. Special Session on Microstructure of Crystals, Ill Kotschlck*, University of Basel, Switzerland and Queen's College, United Kingdom (875-58-91) 10:15 Convex real projective structures on closed surfaces 08:45-11:15 Room 6, Mill Lane Lecture Room (130) are closed. Block Suhyoung Chol*, Kyungpook National University, Korea, and William M. Goldman, University of Maryland, College Park (875-51-18) 08:45 An existence theory for nonlinear elasticity that allows (118) for cavitation. Preliminary report. Stefan Muller, lnstitut fur Angewandte Mathematik der Universitat Bonn, Germany, and Scott Spector*, Special Session on Classical Analysis, II Southern Illinois University (875-73-96)

09:10 The kinematics of continuously defective crystals. 08:45-11:15 Cockcroft Lecture Theatre, New (119) G. P. Parry, University of Bath, United Kingdom Museum Site (875-49-161) 08:45 Superoptimal approximation by analytic functions. 09:35 Extreme measures for the two-well problem. (131) N.J. Young* and V. V. Peller, Lancaster University, (120) Pablo Pedregal, Carnegie Mellon University United Kingdom (875-30-65) (875-49-162) 09:1 0 Spectral properties of selfadjoint Hankel operators. (132) A. V. Megretskii, Royal Institute of Technology, 10:00 Relaxation of multiple integrals in the space of Sweden, V. V. Peller*, University of Lancaster, United· (121) functions of bounded variation. Kingdom, and S. R. Treil, Michigan State University Irene Fonseca, Carnegie Mellon University, and Piotr (875-47-127) Rybka*, Warsaw University, Poland (875-49-163) 09:35 lnterplolation of analytic functions in the polydisk. 10:30 Nonlocal penalties on microstructure. (133) Mischa Cotlar, Universidad Central de Venezuela, (122) Robert C. Rogers, Virginia Polytechnic Institute and Venezuela, and Cora Sadosky*, Howard University State University (875-49-158) (875-42-177) 10:00 Weighted norm estimates for potential operators and 10:55 Microstructures and regularity for variational integrals. (134) eigenvalue estimates for Schrodinger operators. (123) Vladimir Sverak, Heriot-Watt University, United Richard Rochberg, Washington University Kingdom (875-49-154) (875-46-23)

471 ...... ______···--·---·········-·-·············----·················-·····-·····-·-······---····-····--.. ·---·-·····----·---··-·---··-- Program of the Sessions

09:30 Liftings for Lebesgue measure. Wednesday, July 1 (cont'd) (148) Maxim R. Burke, University of Prince Edward Island (875-04-165) 09:45 Correlation of sequences from cyclic difference sets. (149) Solomon W. Golomb, University of Southern California (875-05-113) 10:30 On tangents to curves. Preliminary report. (135) J. M. Anderson*, University College, United Kingdom, 10:00 Probabilistic proofs of hypergeometric identities. and F. D. Lesley, San Diego State University (150) Roberta Wenocur, West Chester University (875-99-207) (875-05-20) 10:55 Besov and Triebei-Lysorkin spaces on spaces of 10:15 Genus imbeddings of (3m, 6) -cages. Preliminary (136) homogeneous type. (151) report. Yongsheng Han, University of Windsor, and Guido John B. Fink, Kalamazoo College, and Arthur T. Weiss*, Washington University (875-42-46) White*, Western Michigan University (875-05-60) 10:30 A theory of quasi-uniformities for completely regular (152) frames. Preliminary report. Session on Algebra Peter Fletcher, Virginia Polytechnic Institute, Worthen Hunsaker, Southern Illinois University, Carbondale, and William Lindgren*, Slippery Rock University of 08:45-10:40 Room 8, Mill Lane Lecture Room Pennsylvania (875-06-107) (Sponsored by Michael E. Block Detlefsen) 08:45 The stabilizer of a Schubert variety. 10:45 Countable games and monotone cores. (137) Steven B. Tesser, Indiana State University (153) John Sorenson, Valparaiso University (875-90-126) (875-16-167) 09:00 Simple Lie algebras in characteristic 2, graphs, and (138) Fisher's theorem. Preliminary report. Special Session on Number Theory, II Joseph Rotman* and Paul Weichsel, University of Illinois, Urbana-Champaign (875-17-10) 09:15 Semidirect products, derivations and reduced cyclic 09:00-10:45 Room 2, Mill Lane Lecture Room (139) cohomology. Block Jacek Brodzki, University of Texas, Austin and Mathematical Institute, United Kingdom (875-18-29) 09:00 Deformation spaces of Galois representations. 09:30 Universal algebras having canonical function spaces. (154) Nigel Boston, University of Illinois, (140) Vijaya L. Gompa, Ball State University (875-18-62) Urbana-Champaign (875-11-133) 09:45 Operator K -theory and p-adic algebraic groups. 10:00 Zeta-functions of orders. (141) Preliminary report. (155) Stephen Lichtenbaum, Brown University Roger Plymen, University of Manchester, United (875-11-106) Kingdom (875-19-34) 10:00 Some new proofs of the "Monstrous Moonshine' (142) conjectures. Charles R. Ferenbaugh, Princeton University Special Session on Current Trends in Numerical (875-20-09) Analysis of Nonlinear Problems, Ill 10:15 Universal example for proper actions. (143) Paul Baum, Pennsylvania State University, University 09:15-11:05 Room 7, Mill Lane Lecture Room Park (875-20-28) Block 10:30 Direct product ring representations of digital signal (144) processing algorithm. 09:15 Numerical modelling of the compressible Neil M. Wigley, University of Windsor (875-94-116) (156) Navier-Stokes equations. (Sponsored by Tim Traynor) K. W. Morton, University of Oxford, United Kingdom (875-65-184) 09:45 Instability of solitary waves. Session on Graphs and Combinatorics (157) Jerry Bona*, Pennsylvania State University, University Park, Vassilios Dougalis, National Technical University of Athens, Greece, Ohannes 08:45-10:55 Seminar Room A, Department of Karakashian, University of Tennessee, Knoxville, and Applied Mathematics and Theoretical Physics William McKinney, North Carolina State University 08:45 Saunderson's algorithm. (875-65-139) (145) J. J. Tattersall, Providence College (875-01-15) 10:15 Geometric algorithms for eye/ides, developables, and 09:00 An intuitive and minimal axiomatic system for (158) related surfaces. (146) m-valued logic. Preliminary report. George J. Fix, University of Texas, Arlington Atwell Turquette, University of Illinois, (875-65-187) Urbana-Champaign (875-03-30) 10:45 Analysis and approximation of control problems for 09:15 The non-linear universal wave-function, and complete (159) nonlinear partial differential equations. (147) multifold ordered universe. Max D. Gunzburger, Virginia Polytechnic Institute and W. S. Leng, Birkbeck College, Univeristy of London, State University (875-65-180) (Sponsored by United Kingdom (875-03-52) Rangachary Kannan)

472 Program of the Sessions

Invited Address Special Session on Number Theory, Ill

11:30 -12:30 Babbage Lecture Theatre, New 14:00-16:30 Room 4, Mill Lane Lecture Room Museum Site Block

(160) Localization and Gauge Theories. 14:00 Galois module structure of principal homogeneous Edward Witten, Institute for Advanced Study (171) spaces. (875-81-85) Martin Taylor, University of Manchester, United Kingdom (875-11-137) 14:50 An almost pure sieve and its applications. Special Session on Discrete Group Actions, Ill (172) C. Hooley, Wales University, United Kingdom (875-99-216) 15:45 The size of Selmer groups for the congruent number 14:00 -16:20 Room 1, Mill Lane Lecture Room (173) problem. Block D. R. Heath-Brown, Magdalen College, United Kingdom (875-99-206) 14:00 The growth series of a graph product. (161) I. M. Chiswell, Queen Mary and Westfield College, University of London, United Kingdom (875-20-125) Special Session on Discrete 14:30 Pseudogroups of isometries and Rips' theorem on free (162) actions on R-trees. Geometry and Convexity, Ill Frederic Paulin, Ecole Normale Super de Lyon, France (875-99-211) 14:00 -16:20 Room 6, Mill Lane Lecture Room 15:00 Uniform tree lattices. Block (163) Ravi S. Kulkarni, Graduate School and University Center, City University of New York (875-30-141) 14:00 On simple polytopes. Preliminary report. 15:30 On the ergodicity of the geodesic flow associated to a (174) Peter McMullen, University College of London, United (164) discrete group of isometries of a tree. Kingdom (875-52-72) Athanase Papadopoulos, University Louis Pasteur, 14:30 Towards a geometric graph theory. France (875-99-21 0) (175) Janos Pach, Mathematical Institute Hungarian 16:00 Limit sets of correspondences. Preliminary report. Academy, Hungary and Courant Institute of (165) Shaun Bullett* and Christopher Penrose, Queen Mathematical Sciences, New York University Mary and Westfield College, University of London, (875-52-68) (Sponsored by Jacob E. Goodman) United Kingdom (875-30-97) (Sponsored by Alan F. 15:00 Stability results for convex bodies. Preliminary report. Beardon) (176) Rolf Schneider, Albert-Ludwigs-Universitat, Germany (875-52-70) (Sponsored by Jacob E. Goodman) 15:30 Pick's theorem for lattice polygons. Special Session on Probabilistic (177) G. C. Shephard*, University of East Anglia, United Kingdom, and B. Grunbaum, University of Combinatorics, Ill Washington (875-52-74) (Sponsored by Jacob E. Goodman) 14:00 -16:20 Room 2, Mill Lane Lecture Room 16:00 Quermassintegra/s, successive minima, and minimal Block (178) determinants. Jorg M. Wills, University of Siegen, Germany 14:00 Random liars. (875-52-71) (166) Joel Spencer, Courant Institute of Mathematical Sciences, New York University (875-05-02) 14:30 Laplacian and vibrational spectra for homogeneous Special Session on Groups: (167) graphs. Fan R. K. Chung*, Bellcore, Morristown, New Jersey Finite and Algebraic, Ill and Harvard University, and Shlomo Sternberg, Harvard University (875-05-1 05) 14:00 -16:30 Room 3, Mill Lane Lecture Room 15:00 An affine walk on the hypercube. Preliminary report. Block (168) Persi Diaconis, Harvard University, and Ron Graham*, AT&T Bell Laboratories, Murray Hill, New 14:00 A proof of a conjecture of Garrett Birkhoff and Philip Jersey (875-05-103) (179) Hall. Peter M. Neumann, Queen's University, United 15:30 Random Ramsey problems. (169) Vera T. Sos, Hungarian Academy of Science, Kingdom (875-20-07) Hungary (875-05-171) (Sponsored by Bela Bollobas) 14:25 Computing in solvable linear groups. (180) Eugene M. Luks, University of Oregon (875-20-120) 16:00 Problems in probabilistic number theory and (170) combinatorics. 14:50 Topics in asymptotic group theory. Paul Erdos, Hungarian Academy of Sciences, (181) Laszlo Babai, University of Chicago and Eotvos Hungary (875-05-1 04) University, Hungary (875-20-191)

473 Program of the Sessions

Wednesday, July 1 (cont'd) Session on Function Algebras

14:00-16:25 Seminar Room A, Department of Applied Mathematics and Theoretical Physics 15:20 On Y -presentations for the monster and related (182) groups. 14:00 On the extension of linear operators. A. A. Ivanov, Institute for System Studies, Russia (195) John J. Saccoman, Seton Hall University (875-46-01) (875-20-119) 14:15 Smooth points of unit balls of operator and function 15:45 Epimorphic subgroups of affine algebraic groups. (196) spaces. (183) Frederic Bien, Princeton University (875-20-173) Roshdi Khalil, Bahrain University, Bahrain (875-46-05) (Sponsored by Robert M. Fossum) 17:10 Standard· bases related to minuscule weight modules. (184) Arjeh M. Cohen*, CWI, The Netherlands, and 14:30 Continuous approximation of set-valued maps and Richard H. Cushman, University of Utrecht, The (197) coincidence theorems. Netherlands (875-14-132) Hichem Ben-EI-Mechaiekh, Brock University (875-46-114) (Sponsored by Mei L. Huang) 14:45 On extreme normal completely positive linear maps. (198) Preliminary report. Special Session on Geometric Sze-Kai Tsui, Oakland University (875-46-115) Topology in Low Dimensions, Ill 15:00 New convexity and fixed point properties in Hardy and (199) Lebesque-Bochner spaces. M. Besbes, University of Paris, France, S. J. 14:00 -16:20 Room 9, Mill Lane Lecture Room Dilworth*, University of South Carolina, Columbia, P. Block N. Dowling, Miami University, and C. J. Lennard, University of Pittsburgh, Pittsburgh (875-46-14) 14:00 Racks and links in codimension two: Abstract. (185) Roger Fenn, Sussex University, United kingdom 15:15 A quantitative generalization of a theorem of Hille. (875-57-63) (200) Gregory F. Bachelis*, Wayne State University, and Sadahiro Saeki, Kansas State University (875-46-148) 14:30 Signature defects and quantum invariants. (186) Paul Melvin, Bryn Mawr College (875-57-27) 15:30 Convergence of random products of operators. (201) Preliminary report. 15:00 Temperley-Lieb recoupling and 3-manifold invariants. Robert Sine, University of Rhode Island (875-46-64) (187) Preliminary report. 15:45 Relatively open operators and the ubiquitous concept. Louis H. Kauffman, University of Illinois, Chicago (202) Ronald Cross, University of Cape Town, Republic of (875-55-128) South Africa (875-47-06) 15:30 Topological imitations of 3-manifolds and the quantum 16:00 Commutator approximants. (188) invariants. Preliminary report. (203) P. J. Maher, Middlesex Polytechnic, United Kingdom Akio Kawauchi, Osaka City University, Japan (875-47-54) (875-57-33) (Sponsored by W. B. Lickerish) 16:15 Young measures as optimal controls for Navier-Stokes 16:00 On the homotopy invariance of Casson's invariant. (204) equations. (189) Preliminary report. S. S. Sritharan, University of Colorado Boulder Daniel Ruberman, Brandeis University (875-57-140) (875-49-32)

Special Session on Classical Analysis, Ill Session on Special Functions and Applied Mathematics 14:00 -16:20 Cockcroft Lecture Theatre, New Museum Site 14:00 -16:10 Room 8, Mill Lane Lecture Room 14:00 The collapse of the inverse function theorem. Block (190) Thomas William Korner, University of Cambridge, 14:00 The generalized Leibniz rule and its consequences. United Kingdom (875-26-84) (205) R. N. Kalia, Saint Cloud State University (875-26-142) 14:30 The Pompeiu problem in the Heisenberg group. 14:15 Rotation invariant separable functions are Gaussian. (191) Carlos A. Berenstein, University of Maryland, College (206) PI Kannappan, University of Waterloo (875-39-45) Park (875-42-89) 14:30 Approximation of control and optimal control problems 15:00 Large analytic functions. (207) using neural nets. (192) Henry Helson, University of California, Berkeley M. Nouri-Moghadam* and M. Ermish, Pennsylvania (875-30-83) State University, Lehman (875-41-11 0) 15:30 Two remarks on porous sets. 14:45 A generalization of the Cantor-Lebesgue theorem. (193) Casper Goffman, Purdue University, West Lafayette (208) J. Marshall Ash, DePaul University, Robert P. (875-26-35) Kaufman, University of Illinois, Urbana-Champaign, 16:00 An inequality for bounded Fourier series, related to an and Eric Rieders*, DePaul University (875-42-117) (194) isoperimetric problem. 15:00 Wavelet transform of periodic generalized functions. W. K. Hayman, University of York, United Kingdom (209) Ahmed I. Zayed, University of Central Florida (875-42-149) (875-42-147)

474 ···········-····-········-··························································-································-···------·································································································································································· Program of the Sessions

15:15 Construction of numerical solutions of permanent (21 0) capillar-heavy waves of two liquids. Invited Address Nabll Moussa, American University in Cairo, Egypt (875-76-199) 16:45 -17:45 Babbage Lecture Theatre, New 15:30 Chem-Simons theory via path integrals. Museum Site (211) Dana S. Fine, University of Massachusetts, Dartmouth (875-81-41) (214) Harmonic maps and Hardy spaces. Lawrence C. Evans, University of California, Berkeley 15:45 Quasiperiodic perturbations and normal forms. (875-35-86) (212) Raghu R. Gompa, Indiana University, Kokomo (875-81-61) (Sponsored by Vijaya L. Gompa) 16:00 Global interfacial instability and micro-structure (213) formation in dendritic crystal growth. Jian-Jun Xu, McGill University (875-82-24)

American Mathematical Society TRANSLATIONS Series 2 • Volumes 148 & 150

Algebra and Analysis Spectral Theory of Operators A. D. Aleksandrov, S. G. Gindikin, Editor 0. V. Belegradek, I. A. Bokut, and Yu. L. Ershov, Editors This volume focuses on the spectral theory of differential operators. The emphasis is on This collection consists of lectures estimates of the number of negative delivered at the First Siberian Winter eigenvalues of elliptic School, "Algebra and Analysis," held differential operators and on in March 1987 at a retreat near the analysis of asymptotical Kemerovo. The school was organized distribution of eigenvalues. by Kemerovo State University and the This collection provides an Institute of Mathematics of the excellent overview of prob­ Siberian Branch of the Academy of lems in the field, for Gindikin Sciences of the USSR. The conference ranks among the leading drew more than 100 participants from Soviet specialists in this area of Novosibirsk, Kemerovo, Omsk, research. Moscow, St. Petersburg, and other 1991 Mathematics Subject Classifications: cities. 34, 47; 58, ISBN 0-8218-7500-0, 176 pages The papers concern current research on the (hardcover), March 1992 interface of algebra and analysis. Indiv. mem. $67, List $112, Inst. mem. $90, Your ordering code is TRANS2/150NA 1991 Mathematics Subject Classifications: 05, 14, 15, 16, 17, 22, 28, 34, 51, 53, ISBN 0-8218-3700-1, 112 pages (hardcover), February 1991, Indiv. mem. $38, List $63, Inst. mem. $50. Your ordering code is TRANS2/148NA

All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

475 Invited Addresses and Special Sessions

Invited Addresses Organizers and Topics at AMS Meetings of Special Sessions The individuals listed below have accepted invitations to The list below contains all the information about Special address the Society at the times and places indicated. For Sessions at meetings of the Society available at the time some meetings, the list of speakers is incomplete. this issue of Notices went to the printer. The section below entitled Information for Organizers describes the timetable Dayton, OH, October 1992 for announcing the existence of Special Sessions. Martin Golubitsky Louis H. Kauffman Jonathan I. Hall J. T. Stafford October 1992 Meeting in Dayton, Ohio Central Section Associate Secretary: Andy R. Magid Los Angeles, CA, November 1992 Deadline for organizers: Expired Robert K. Lazarsfeld Thomas C. Sideris Deadline for consideration: July 13, 1992 Tomasz S. Mrowka Colin C. Adams and Ara S. Basmajian, Hyperbolic manifolds Carolyn A. Dean, Timothy J. Hodges, and J. Toby Stafford, Quantum groups and regular algebras San Antonio, TX, January 1993 Joanne M. Dombrowski and Richard Mercer, Operator Richard A. Brualdi Carolyn S. Gordon theory and operator algebras (AMS-MAA) Wu-Yi Hsiang Anthony B. Evans and Terry A. McKee, Combinatorics and Luis A. Caffarelli Bernd Sturmfels graph theory (Colloquium Lectures) Leon Takhtajan Daniel E. Frohardt, Groups and geometries Subrahamanyan Chandrasekhar Alexander V archenko Lop Fat Ho, Srdjan D. Stojanovic and Thomas Svobody, (AMS-MAA) Mary F. Wheeler Control theory and partial differential equations James Douglas, Jr. (AMS-MAA) Muhammud N. Islam and Lawrence Turyn, Differential and integral equations Knoxville, TN, March 1993 Louis H. Kauffman, Knots and topological quantum field Paul R. Blanchard Richard A. Tapia theory Olav Kallenberg Michelle L. Wachs Hendrik J. Kuiper and Tapas Mazumdar, Ricatti equations and transport theory Washington, DC, April1993 Anatoly S. Libgober and Stephen Sperber, Topology of affine Fan R. K. Chung Joel Sprock hypersuifaces and related number theory Leopold Flatto A. Zamolodchikov Joe D. Mashburn, Set-theoretic topology C. David Minda, Function theory

Vancouver, British Columbia, Canada November 1992 Meeting in Los Angeles, California August 1993 Western Section Associate Secretary: Lance W. Small Louis Nirenberg (AMS-CMS) Jill Pipher (AMS-CMS) Deadline for organizers: Expired Deadline for consideration: July 13, 1992 Invited addresses at Sectional Meetings are selected by Michael Aschbacher, Robert M. Guralnic.k, and David B. the Section Program Committee, usually twelve to eighteen Wales, Finite and algebraic groups months in advance of a meeting. Members wishing to nomi­ Francis Bonahon and Robert L. Meyer, Hyperbolic geometry nate candidates for invited addresses should send the relevant Robert Brooks and Peter A. Perry, Spectral geometry information to the Associate Secretary for the Section who Lawrence Bin, Algebraic and complex geometry will forward it to the Section Program Committee. Eugene Gutkin and Nicolai T. A. Haydn, Dynamical systems

476 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Robert C. Penner and Edward Witten, Topics in geometry Alexandre S. Freire, Variational problems in geometry and physics Don B. Hinton and Kenneth Shaw, Sturm-Liouville opera- tors, applications, and extensions January 1993 Meeting in San Antonio, Texas Tim Kelley, Numerical methods in optimization Associate Secretary: W. Wistar Comfort John C. Mayer, Continua theory and dynamical systems Deadline for organizers: April 13, 1992 Balram S. Rajput and Jan Rosinski, Stochastic processes Deadline for consideration: September 17, 1992 Michelle L. Wachs, Algebraic combinatorics Kathleen T. Alligood and Judy A. Kennedy, Continuum theory and dynamical systems April1993 Meeting in Salt Lake City, Utah Thomas Archibald and Victor Katz, History of mathematics Western Section Alvaro Arias, Banach space theory Associate Secretary: Lance W. Small Charles E. Aull, History of general topology Deadline for organizers: July 9, 1992 Deadline for consideration: January 6, 1993 Melvyn S. Berger, Small divisor problems in analysis Scott T. Chapman, Commutative algebra April1993 Meeting in Washington, DC William J. Coles and B. A. Fusaro, Environmental modeling Eastern Section David Cox and Bernd Sturmfels, Combinatorial methods in Associate Secretary: computational algebraic geometry W. Wistar Comfort (until 1131193) Raul Curto and David R. Larson, Operator theory and Lesley M. Sibner (after 1131193) triangular operator algebras Deadline for organizers: July 17, 1992 Deadline for consideration: January 6, Michael R. Darnel, Ordered algebraic structures 1993 John J. Benedetto and Rodney B. Kerby, Waveletes in Robert S. Doran, C*-algebras: 1943-1993 (a 50-year cele­ sampling theory and signal processing bration) Kevin G. Hockett and E. Arthur Robinson, Ergodic theory, K. L. Duggal, Differential geometry dynamical systems and applications Saber N. Elaydi, John R. Graef, and William F. Trench, Joel Sprock, Nonlinear elliptic problems in geometry and Stability and asymptotic behavior of difference equations physics Dennis R. Estes and Donald James, Quadratic forms Naomi Fisher, Harvey B. Keynes, and Philip D. Wagreich, Research in undergraduate education May 1993 Meeting in DeKalb, Illinois Robin Forman and John E. Luecke, Topology and geometry Central Section Dennis DeTurck and Carolyn S. Gordon, Eigenvalues in Associate Secretary: Andy R. Magid Deadline for organizers: August 21, 1992 Riemannian geometry Deadline for consideration: February 3, 1993 Morris W. Hirsch and Halbert White, Dynamics and com­ Michael A. Filaseta, Number theory putation in neural networks Zoltan Furedi, Combinatorics Hans A. Koch, Rafael de la Llave, and Charles Radin, Andrew J. Granville, Analytic number theory Infinitely many degrees of freedom Frank Harary, Graph theory Xinzhi Liu and Seenith Sivasundaram, Integro-differential Steffen Lempp, Recursion theory equations: stability and control Mohsen Pourahmadi, Stochastic processes David E. Marker and Philip H. Scowcroft, Model theory and Linda R. Sons, Function theory algebra Joel H. Spencer, Probabilistic methods John E. McCarthy, Holomorphic spaces Peter Weaterman, Discrete groups Alec Norton and Mary Lou Zeeman, Low dimensional geometric dynamical systems August 1993 Meeting in Vancouver, L. Alayne Parson and Mark Sheingorn, Modular forms and British Columbia, Canada related topics Associate Secretary: Lance W. Small Nikolay Reshetikhin, Leon Takhtajan, and Alexander V ar­ Deadline for organizers: November 11, 1992 chenko,, Quantum groups Deadline for consideration: April 27, 1993

October 1993 Meeting March 1993 Meeting in Knoxville, Tennessee in College Station, Texas Central Section Southeastern Section Associate Secretary: Andy R. Magid Associate Secretary: Deadline for organizers: January 22, 1993 Joseph A. Cima (until 1131/93) Deadline for consideration: July 14, 1993 Robert J. Daverman (after 1/31193) Deadline for organizers: June 26, 1992 Deadline for consideration: December 15, 1992 January 1994 Meeting in Cincinnati, Ohio David F. Anderson and David E. Dobbs, Commutative ring Associate Secretary: theory Joseph A. Cima (until 1131193) Robert J. Daverman (after 1131193) Ben G. Fitzpatrick and Suzanne M. Lenhart, Optimal control Deadline for organizers: April 5, 1993 and applic,ations Deadline for consideration: September 23. 1993

MAY/JUNE 1992, VOLUME 39, NUMBER 5 -----··-·------Invited Addresses and Special Sessions

March 1994 Meeting in Lexington, Kentucky be in the hands of the PCNM at least nine months prior to Southeastern Section the meeting at which the Special Session is to be held in Associate Secretary: order that the committee may consider all the proposals for Joseph A. Cima (untill/31/93) Special Sessions simultaneously. Proposals that are sent to Robert J. Daverman (after 1/31/93) Deadline for organizers: June 18, 1993 the Providence office of the Society, to Notices, or directed Deadline for consideration: To be announced to anyone other than the Associate Secretary will have to be forwarded and may not be received in time to be considered March 1994 Meeting in Manhattan, Kansas for acceptance. Central Section It should be noted that Special Sessions must be an­ Associate Secretary: Andy R. Magid Notices Deadline for organizers: June 25, 1993 nounced in in such a timely fashion that any member Deadline for consideration: To be announced of the Society who so wishes may submit an abstract for consideration for presentation in the Special Session before June 1994 Meeting in Eugene, Oregon the deadline for such consideration. This deadline is usually Western Section three weeks before the deadline for abstracts for the meeting Associate Secretary: Lance W. Small in question. Deadline for organizers: September 7, 1993 Deadline for consideration: To be announced Special Sessions are very effective at Sectional Meetings and can usually be accommodated. The processing of January 1995 Meeting in Denver, Colorado proposals for Special Sessions for Sectional Meetings is Associate Secretary: Andy R. Magid handled in essentially the same manner as for Annual Deadline for organizers: April 20, 1994 and Summer Meetings by the Section Program Committee. Deadline for consideration: To be announced Again, no Special Session at a Sectional Meeting may be approved so late that its announcement appears past the March 1995 Meeting in Chicago, Illinois deadline after which members can no longer send abstracts Central Section for consideration for presentation in that Special Session. Associate Secretary: Andy R. Magid The Society reserves the right of first refusal for the Deadline for organizers: June 24, 1994 Deadline for consideration: To be announced publication of proceedings of any Special Session. These proceedings appear in the book series Contemporary Math­ January 1996 Meeting in Orlando, Florida ematics. Associate Secretary: Lance W. Small More precise details concerning proposals for and orga­ Deadline for organizers: April 12, 1995 nizing of Special Sessions may be found in the "Rules for Deadline for consideration: To be announced Special Sessions" or may be obtained from any Associate Secretary. Information for Organizers Special Sessions at Annual and Summer Meetings are held under the supervision of the Program Committee for National Meetings (PCNM). They are administered by the Associate Proposals for Special Sessions to the Secretary in charge of that meeting with staff assistance from Associate Secretaries the Meetings Department in the Society office in Providence. The programs of Sectional Meetings are arranged by the According to the "Rules for Special Sessions" of the Associate Secretary for the section in question: Society, Special Sessions are selected by the PCNM from Western Section a list of proposed Special Sessions in essentially the same Lance W. Small, Associate Secretary Department of Mathematics manner as individuals are selected to give Invited Addresses. University of California, San Diego The number of Special Sessions at a Summer or Annual La Jolla, CA 92093 Meeting is limited. The algorithm that determines the number Electronic mail: [email protected] of Special Sessions allowed at a given meeting, while (Telephone 619-534-3590) simple, is not repeated here, but can be found in "Rules for Central Section Andy R. Magid, Associate Secretary Special Sessions" on page 614 in the April 1988 issue of Department of Mathematics Notices. University of Oklahoma Each person selected to give an Invited Address is 601 Elm PHSC 423 Norman, OK 73019 invited to generate a Special Session, either by personally Electronic mail: [email protected] organizing one or by having a Special Session organized (Telephone 405-325-6711) by others. Proposals to organize a Special Session are Eastern Section sometimes requested either by the PCNM or by the Associate W. Wistar Comfort, Assoc~ate Secretary (until January 31, 1993) Secretary. Other proposals to organize a Special Session may Department of Mathematics be submitted to the Associate Secretary in charge of that Wesleyan University Middletown, CT 06457 meeting (who is an ex-officio member of the committee and Electronic mail: [email protected] whose address may be found below). These proposals must (Telephone 203-347-9411)

478 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 00 00 ······-·······································m··---·······-···-·····-·- •m- - -m••••oo•••••o•o• """" """"000000•000-00JillB--Mi*~---······-·------Invited Addresses and Special Sessions

Lesley M. Sibner, Associate Secretary (beginning February I, 1993) Electronic submission of abstracts is available to those Department of Mathematics who use the 1l3X typesetting system. Requests to obtain Polytech University of New York Brooklyn, NY ll201-2990 the package of files may be sent electronically via the (Telephone 718-260-3505) Internet to [email protected]. Requesting the Southeastern Section files electronically will likely be the fastest and most Joseph A. Cima, Associate Secretary (until January 31, 1993) convenient way, but users may also obtain the package Department of Mathematics on ffiM or Macintosh diskettes, available free of charge University of North Carolina, Chapel Hill by writing to: Electronic Abstracts, American Mathe~atical Chapel Hill, NC 27599-3902 Electronic mail: [email protected] Society, Meetings Department, P.O. Box 6887, Providence, (Telephone 919-962-1050) RI 02940, USA. When requesting the abstracts package, Robert J. Daverman, Associate Secretary (beginning February 1, 1993) users should be sure to specify whether they want the plain Department of Mathematics 1l3X, ~-'lEX, or the IDEX package. University of Tennessee Knoxville, TN 37996-1300 Number of Papers Presented (Telephone 615-974-6577) ]oint Authorship As a general rule, members who anticipate organizing Special Sessions at AMS meetings are advised to seek approval at least nine months prior to the Although an individual may present only one ten-minute scheduled date of the meeting. No Special Sessions can be approved too late contributed paper at a meeting, any combination of joint to provide adequate advance notice to members who wish to participate. authorship may be accepted, provided no individual speaks more than once. An author can speak by invitation in more Information for Speakers than one Special Session at the same meeting. A great many of the papers presented in Special Sessions at An individual may contribute only one abstract by title meetings of the Society are invited papers, but any member in any one issue of Abstracts, but joint authors are treated of the Society who wishes to do so may submit an abstract as a separate category. Thus, in addition to abstracts from for consideration for presentation in a Special Session, two individual authors, one joint abstract by them may also provided it is received in Providence prior to the special be accepted for an issue. early deadline announced above and in the announcements of the meeting at which the Special Session has been scheduled. Contributors should know that there is a limitation in size Site Selection for Sectional Meetings of a single Special Session, so that it is sometimes true that Sectional Meeting sites are recommended by the Associate all places are filled by invitation. Papers not accepted for Secretary for the Section and approved by the Committee a Special Session are considered as ten-minute contributed of Associate Secretaries and Secretary. Recommendations papers. are usually made eighteen to twenty-four months in ad­ Abstracts of papers submitted for consideration for pre­ vance. Host departments supply local information, ten to sentation at a Special Session must be received by the twelve rooms with overhead projectors for contributed pa­ Providence office (Meetings Department, American Mathe­ per sessions and Special Sessions, an auditorium w~th t~in matical Society, P. 0. Box 6887, Providence, RI 02940) by overhead projectors for invited addresses, and regtstrati.on the special deadline for Special Sessions, which is usually clerks. The Society partially reimburses for the rental of three weeks earlier than the deadline for contributed papers facilities and equipment, and for staffing the registration for the same meeting. The Council has decreed that no desk. Most host departments volunteer; to do so, or for more paper, whether invited or contributed, may be listed in the information, contact the Associate Secretary for the Section. program of a meeting of the Society unless an abstract of. the paper has been received in Providence prior to the deadline.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 479 Call For Topics For 1994 Conferences

Suggestions are invited from mathematicians, either singly or understandings embodied in the von Neumann proceedings, in groups, for topics for the various conferences that will be will, it is hoped, reflect exceptional mathematical leadership. organized by the Society in 1994. The deadlines for receipt of Deadline For Suggestions: September 1, 1992 these suggestions are given below, as well as some relevant information about each of the conferences. An application form to be used when submitting suggested topic(s) for any 1994 AMS Summer Research Institute of these conferences (except the Short Course Series) may be Summer Institutes are intended to provide an understandable obtained by writing to the Meetings Department, American presentation of the state of the art in an active field of Mathematical Society, P.O. Box 6887, Providence, RI 02940; research in pure mathematics and usually extend over a or by telephone: 401-455-4146; FAX 401-455-4004; email: three-week period. Dates for a Summer Institute must not MEET®MATH.AMS.COM. overlap those of the Society's summer meeting, which is Individuals willing to serve as organizers should be scheduled for August. There should be a period of at least aware that the professional meetings staff in the Society's two weeks between them. Proceedings are published by the Providence office will provide full support and assistance AMS as volumes in the series Proceedings of Symposia in before, during, and after each of these conferences, thereby Pure Mathematics. relieving the organizers of most of the administrative detail. Current and recent topics: Organizers should also note that for all conferences, except 1989-Several complex variables and complex geometry, Summer Research Conferences, it is required that the organized by Steven G. Krantz of Washington University. proceedings be published by the AMS and that proceedings 1990-Differential geometry, organized by Robert E. Greene of Summer Research Conferences are frequently published. of the University of California, Los Angeles, and Shing­ A member of the Organizing Committee must be willing to Tung Yau of Harvard University. serve as editor of the proceedings. 1991-Algebraic groups and their generalizations, William All suggestions must include (1) the names and affilia­ Haboush, University of Illinois, Urbana-Champaign. tions of proposed members and the chair of the Organizing 1992-Quadratic forms and division algebras: Connections Committee; (2) a one- to two-page description addressing with algebraic K- theory and algebraic geometry, William the focus of the topic, including the imp()rtance and time­ Jacob and Alex Rosenberg, University of California, Santa liness of the topic, and estimated attendance; (3) a list of Barbara. the recent conferences in the same or closely related areas; 1993-Stochastic analysis, Michael Cranston, University (4) a tentative list of names and affiliations of the proposed of Rochester; Richard T. Durrett, Cornell University; and principal speakers; and (5) a list of likely candidates who Mark A. Pinsky, Northwestern University. would be invited to participate and their current affiliations. Deadline For Suggestions: September 1, 1992 Individuals submitting conference suggestions are requested to recommend sites or geographic areas which would assist the Meetings staff in their selection of an appropriate site. 1994 AMS-SIAM-SMB Symposium Some Mathematical Questions in Biology This one-day symposium, sponsored jointly by the AMS, the Society for Industrial and Applied Mathematics (SIAM), 1994 von Neumann Symposium and the Society for Mathematical Biology (SMB), is usually Through a bequest from Carroll V. Newson to memorialize held in conjunction with the annual meeting of a biological the late John von Neumarin and his accomplishments, the society closely associated with the topic. Papers from the Society has established a new quadrennial symposium called symposia are published by the AMS as volumes in the series the von Newmann Symposium. This new conference series Lectures on Mathematics in the Life Sciences. will focus on concepts in the forefront of mathematics, and it Current and recent topics: is intended that they occupy a position of importance in the 1989-Sex allocation and sex change: Experiments and evolution of mathematical thought. Subjects of these one­ models, organized by Marc Mangel of the University of week symposia are to be topics of emerging significance, California, Davis. expected to underlie future mathematical development. Ideas 1990-Neural networks, organized by Jack D. Cowan of expressed and shared at these Symposia, and the new the University of Chicago. ·

480 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ••••m m m•m m m mm mm•m••••••• m•••mmmmm • jlf}!---~~IJ'BIIIilil ----~-- Call for Topics

1991-Theoretical approaches for predicting spatial effects to subjects in which there is important interdisciplinary ac­ in ecological systems, organized by Robert H. Gardner, tivity at present. A one-week or two-week conference may Oak Ridge National Laboratories. be proposed. Topics for the eleventh series of one-week 1992-Mathematica/ models in cell biology, organized by conferences being held in 1992 are: Conformal field theory, Byron Goldstein, Los Alamos National Laboratory, and topological field theory, and quantum groups; Cohomol­ Carla Wofsy, University of New Mexico. ogy, representations, and actions of finite groups; Nielsen 1993 -Proposal not yet selected. theory and dynamical systems; The Penrose transform and Deadline For Suggestions: September 1, 1992 analytic cohomology in representation theory; Wavelets and applications; Commutative algebra: syzygies, multiplicities and birational algebra; Change-point problems; Control and 1994 AMS-SIAM Summer Seminar identification of partial differential equations; and Adaptive in Applied Mathematics designs. The goal of the Summer Seminar, sponsored jointly by the If proceedings are published by the AMS, they appear AMS and the Society for Industrial and Applied Mathematics as volumes in the series Contemporary Mathematics. (SIAM), is to provide an environment and program in applied Deadline For Suggestions: February 1, 1993 mathematics in which experts can exchange the latest ideas and newcomers can learn about the field. Proceedings are published by the AMS as volumes in the series Lectures in Call for Topics for Applied Mathematics. 1994 AMS Short Course Series Current and recent topics: The AMS Short Courses consist of a series of introductory 1989-The mathematics of random media, organized by survey lectures and discussions which take place over a Werner Kohler of Virginia Polytechnic Institute and State period of two days prior to and during the Joint Mathematics University and Benjamin White of Exxon Research & Meetings held in January and August each year. Each theme Engineering Company. is a specific area of applied mathematics or mathematics 1990-Vortex dynamics and vortex methods, organized by used in the study of a specific subject or collection of Claude Greengard of IBM T. J. Watson Research Cen­ problems in one of the physical, biological, or social ter and Christopher R. Anderson of the University of sciences, technology, or business. California, Los Angeles. Current and recent topics: 1991-No seminar held. Wavelets and applications (January 1993), New scientific 1992-Exploiting symmetry in applied and numerical anal­ applications of geometry and topology (January 1992), Un­ ysis, organized by Eugene L. Allgower, Kurt Georg, and reasonable effectiveness of number theory (August 1991), Rick Miranda, Colorado State University. Probabilistic combinatorics and its applications (January 1993 -Proposal not yet selected. 1991), Combinatorial games (August 1990), Mathematical Deadline For Suggestions: September 1, 1992 questions in robotics (January 1990), Cryptology and com­ putational number theory (August 1989), and Matrix theory and applications (January 1989). Proceedings are published 1994 AMS-IMS-SIAM Joint Summer by the Society as volumes in the series Proceedings of Research Conferences in the Symposia in Applied Mathematics, with the approval of the Mathematical Sciences Editorial Committee. These conferences, jointly sponsored by the AMS, the Insti­ Deadline for Suggestions: Suggestions should be submit­ tute for Mathematical Statistics (IMS), and the Society for ted by December 1, 1992. Industrial and Applied Mathematics (SIAM), emulate the scientific structure of those held at Oberwolfach and repre­ Submit suggestions to: AMS Meetings Department, P.O. sent diverse areas of mathematical activity' with emphasis Box 6887, Providence, RI 02940; FAX: 401-455-4004; on areas currently especially active. Careful attention is paid email: [email protected].

MAY/JUNE 1992, VOLUME 39, NUMBER 5 481 Joint Mathematics Meetings in San Antonio AMS Special Sessions and Contributed Papers MAA Contributed Papers

The Joint Mathematics Meetings in San Antonio will be held venient way, but users may also obtain the package on IDM January 6-9 (Wednesday-Saturday), 1993. The first full or Macintosh diskettes, available free of charge by writing announcement of the meetings will appear in the October to: Director of Meetings, American Mathematical Society, 1992 issues of Notices and FOCUS. This preliminary P.O. Box 6887, Providence, RI 02940. When requesting the announcement is made to encourage member participation abstracts package, users should be sure to specify whether and to provide lead time for submission of abstracts for they want the plain 'J.EX, ~-'lEX, or the rn.t;X package. consideration for presentation in AMS Special Sessions and Only abstracts should be sent to [email protected]. for submission of abstracts for AMS and MAA Contributed · Questions regarding an abstract should be addressed to abs­ Paper Sessions. [email protected]. Questions regarding meetings should be addressed to [email protected]. AMS Special Sessions A list of Special Sessions for this meeting can be found in the Invited Addresses and Special Sessions section of this MAA Contributed Papers issue. Contributed papers are being accepted on several topics in Most of the papers to be presented at these Special collegiate mathematics for presentation in contributed paper Sessions will be by invitation; however, anyone contributing sessions at the meeting. The organizers listed below solicit an abstract for the meeting who feels that his or her paper contributed papers pertinent to their sessions' interests and would be particularly appropriate for one of these sessions concerns; material should be sent to the organizer whose should indicate this clearly on the abstract, and should name is followed by an asterisk (*). Please note that any submit it by September 18, 1992, three weeks earlier days scheduled for any session are tentative. The topics, than the normal deadline for contributed papers, in order organizers, and their affiliations are: that it be considered for inclusion. • Assessment programs for the undergraduate major, Fri­ Abstracts should be prepared on the standard AMS day morning and Saturday afternoon form available from the AMS office in Providence or in departments of mathematics and should be sent to Abstracts, Charles F. Peltier* Meetings Department, American Mathematical Society, Post Department of Mathematics Office Box 6887, Providence, RI 02940. A charge of $16 is Saint Mary's College imposed for retyping abstracts that are not in camera-ready Notre Dame, IN 46556 form. email: [email protected] fax: 219-284-4492 James W. Stepp, University of Houston AMS Contributed Paper Sessions Abstracts should be prepared on the standard AMS form This session sponsored by the CUPM Subcommittee on available from the AMS office in Providence or in de­ Assessment, seeks papers on use of assessment of student partments of mathematics and should be sent to Abstracts, achievement in evaluation of undergraduate programs in Meetings Department, American Mathematical Society, Post mathematics. Contributors may address program evaluation Office Box 6887, Providence, RI 02940, so as to arrive (as related to assessment of student achievement), methods of by the abstract deadline of October 8, 1992. A charge assessment of individual student achievement, development of $16 is imposed for retyping abstracts that are not in of goals and criteria for assessment, or the effects of camera-ready form. Late papers will not be accepted. assessment on the development of programs. Contributions addressing methods of assessment or describing experience with programs for assessment are particularly encouraged. Electronic Submission of AMS Abstracts This service is available to those who use the 1.EX typeset­ • "Capstone" courses for senior mathematics majors, ting system and can be used for abstracts of papers to be Wednesday and Thursday mornings presented at this meeting in AMS sessions only. Requests to Christopher E. Barat and Pamela Crawford* obtain the package of files may be sent by electronic mail on Department of Mathematics the Internet to [email protected]. Requesting the Randolph-Macon College files electronically will likely be the fastest and most con- Ashland, VA 23005

482 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY --- · - · · --- ·11. ill! 1 &l££i£11IRWJJ,%ii11'!B Joint Mathematics Meetings in San Antonio

In recent years, there has been a dramatic increase in • Interactive learning environments, Wednesday and Thurs­ the number and variety of "capstone" courses designed to day mornings provide senior mathematics majors with a "summation" of Katherine Pedersen* their undergraduate experiences and to sharpen fundamental NSF Statewide Systemic Initiative skills such as reading and writing mathematics, problem 435 S. Chapelle solving, and research techniques. This session welcomes Pierre, SD 57501 papers describing courses of this type, as well as those discussing how such courses might be developed. Topics Sandra Z. Keith, St. Cloud State University may include the choice of a "capstone" theme, course Interactive learning environments in undergraduate math­ organization, innovative student assignments, evaluation of ematics have been a topic of growing interest in the last student performance, and the integration of "capstone" few years. Interactive modes of teaching include collabo­ courses into existing major sequences. rative learning and cooperative learning as well as teach­ ing/learning • Empowering the mathematical community, Wednesday strategies that enable students to interact not morning and Thursday afternoon only with each other and the instructor but with materials and technology. Typically, the student interactions are struc­ Gloria F. Gilmer* tured by the instructor for maximum benefit to the students. Math-Tech, Inc. Technology often plays a role as group study and group 9155 N. 70 St. assignments have been a natural outgrowth of environments Milwaukee, WI 53223 that use computers and calculators. Papers for this session, Marilyn Frankenstein, University of Massachusetts, Boston sponsored by the Committee on Computers in Mathematics Patricia C. Kenschaft, Montclair State College Education, will not be limited to those using technology. Alvin M. White, Harvey Mudd College Preference will be given to papers describing, with ap­ This session is organizer by the Joint AMS-MAA­ propriate data, the author's own experiences in promoting AAAS Committee on Opportunities in Mathematics for interactive learning environments, especially collaborative Underrepresented Minorities (COMUM) in cooperation with learning and cooperative learning. the MAA Committee on the Participation of Women, The Cricical Math Network, and the Humanistic Math Network. • Linear algebra, Wednesday and Friday afternoons, and Student empowerment refers to an internal state in which Thursday evening students see themselves as responsible for, in control of, or Donald R. LaTorre* the source of their own learning. When students control few Department of Mathematical Sciences elements in the learning environment, their empowerment Clemson University is low; when they control many elements, it is high. Clemson, SC 29634-1907 Mathematically powerful students think and communicate, Steven J. Leon, University of Massachusetts, Dartmouth drawing on mathematical ideas and using mathematical tools A. Duane Porter (for the LACSG), University of Wyoming and techniques. Mathematically powerful work is purposeful. Thus, papers are sought which respond to questions such This session invites papers on innovations in teaching as the following: What are we doing to empower students? linear algebra, including: (1) the use of computer algebra What must the profession do to empower others at all systems, supercalculators, or computer software; (2) experi­ educational levels and interests? What must the profession ences with materials from the A TLAST summer workshops; do to empower others at all educational levels and interests? (3) experiences with the Core Curriculum recommended Why are some instructional models more empowering for by the Linear Algebra Curriculum Study Group; and (4) students than others? "Gems" of exposition in linear algebra; and (5) other innovative teaching or curriculum ideas in linear algebra. • Impact of non-traditional instructional methods on test­ ing and evaluation, Wednesday and Thursday afternoons • Mathematics and the arts, Thursday afternoon and Sat­ Linda H. Boyd* urday morning Mathematics Department JoAnne S. Growney* DeKalb College Department of Mathematics and Computer Science 555 North Indian Creek Dr. Bloomsburg University Clarkston, GA 30021 Bloomsburg, PA 17815 Elizabeth Teles, Montgomery College, Maryland This session invites submissions on the follwing themes: The session is organized by the Committee on Two­ (1) Application of mathematical methods of thought and Year Colleges. Papers are requested describing the impact design to another art form. (2) Examination of art­ of non-traditional methods of instruction on testing and works/artforms in which mathematics is included in the evaluation. These methods include but are not limited to content or in the construction. (3) Strategies/examples for laboratory exercises or experiments, group projects, and teaching and learning mathematics by exploring its links student presentations. with other arts.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 483 Joint------··················································· Mathematics Meetings in San Antonio ... ··············•·•···············• ......

• Recreational mathemagical computing, Friday morning Demographic changes have meant that educators are and Saturday afternoon now required to teach mathematics to students from a wide Dr. Michael W. Ecker* variety of multicultural and multilingual backgrounds. This Editor/Publisher session welcomes papers which describe research on student Recreational & Educational Computing learning as well as methods of teaching mathematics to these 909 Violet Terrace students. Descriptions of courses taught should address how Clarks Summit, PA 18411 these students learn mathematics, teaching methods used, This session plans to present diverse recreations in which and the effectiveness of these methods. computer programming plays a supplementary but essential • Use of visualization in the teaching of mathematics, role. Though the computer languages and topics are open, Friday morning and Saturday afternoon some preference will be given to recreations and/or recre­ Howard Lewis Penn* ational problem-solving with widest appeal for maximum Mathematics Department accessibility. Thus papers at a more elementary or interme­ diate level are particularly sought, perhaps using BASIC, 572 Holloway Rd. QuickBASIC, or Pascal. Papers presenting recreations off United States Naval Academy the beaten path or that unify seemingly diverse themes are Annapolis, MD 21402-5002 also most welcome. Utility software for aiding such inves­ email: [email protected] .mil tigations will be welcome, but more so to the extent that it James R. King, University of Washington is connected to particular problems. Since it is impossible This session, organized by the Committee on Computers to anticipate the range of topics and papers of interest, all in Mathematics Education, invites presentations that illustrate proposals and suggestions are encouraged and will be given the use of visualization in mathematics teaching. Authors serious consideration. should send an abstract which includes a description of how • Recruitment and retention of women in mathematics visualization will be used in the presentation. In particular, revisited, Saturday morning and afternoon if the use of computers or other technology is contemplated, include a very precise description of what is needed (it Marcelle Bessman* is expected that a Macintosh and an MS-DOS-PC with 328 Braddock, #212 overhead projection panels will be available). Frostberg, MD 21532 email: [email protected] • Using data and computers in teaching statistics, Wednes­ fax: 813-872-9342 day morning and Thursday afternoon (May 10-Aug. 20, mailing address will be 644 Geneva Mary Parker* Place, Tampa, FL 33606) Department of Mathematics This session, sponsored by the Committee on Partici­ Austin Community College pation of Women in Mathematics, is a sequel to the 1987 11928 Stonehollow Drive contributed paper session ''Recruitment and Retention of Austin, TX 78758-3101 Women in Mathematics", which focused on the factors George Cobb, Mount Holyoke College affecting the participation of women in mathematics. Since that time the Committee on Participation of Women in The MANASA Joint Committee on Undergraduate Mathematics was formed to assess the problem and develop Statistics organized this session to explore the use of or encourage projects designed to improve recruitment and data and computers in undergraduate statistics courses. retention of women. One such project is the recent commit­ Contributions are specifically invited which discuss how the tee publication "Winning Women into Mathematics." The use of data and/or computer simulations can be used to purpose of this session is to learn about projects under­ strengthen the teaching of important concepts, to emphasize taken at educational institutions and agencies that employ statistical thinking, and to foster active learning. Papers on mathematicians to encourage participation of women in upper division mathematical statistics courses are welcome mathematics. Of particular interest are presentations that as well as papers on more elementary courses. describe such a project, the obstacles encountered, proposed or accomplished solutions, and projections for the future. Presentations are normally limited to ten minutes, al­ though selected contributors may be given up to twenty • Teaching mathematics to multicultural and multilingual minutes. Individuals wishing to submit a paper for any of students, Friday morning and afternoon these sessions should note the following NEW PROCE­ Richard O'Lander* DURES: The name(s) and address(es) of the author(s) and Division of Computer Science, Mathematics & Science a one-page summary of the paper should be sent directly St. John's University to the organizer whose address is given. The purpose of St. Vincent's College this summary is to enable the organizer(s) to evaluate the Grand Central & Utopia Parkways appropriateness of the paper for the session, so this summary Jamaica, NY 11439 should be as detailed and informative as possible within the

484 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ······-····----.. -················-········-·· ··--·····~----.. ·------··--·-··-···------···--·························-···-····-···------Joint Mathematics Meetings in San Antonio

one-page limitation. This summary must reach the organizer obtained in advance from either the AMS office or the MAA by September 10, 1992. Summaries should NOT be sent Washington office and the abstract may be submitted along to the MAA Washington office. with the summary. The organizer will acknowledge receipt of the summary. Rooms where MAA contributed paper sessions will be If the paper is accepted for presentation, the organizer will held are equipped with an overhead projector and screen. send the author(s) a standardized abstract form. to be used Blackboards are not available. Persons having other equip­ to prepare a brief abstract, which will be published in the ment needs should contact the MAA Associate Secretary journal Abstracts (copies will be available in the registration (Kenneth A. Ross, Department of Mathematics, Univer­ area). sity of Oregon, Eugene, OR 97403-1222; electronic mail: Completed abstract forms must be returned to the or­ [email protected]) as soon as possible, but in any ganizer promptly and no later than September 24. Do case prior to November 9. Upon request, the following will not send the abstracts to the AMS, and do not submit be made available: one additional overhead projector/screen, them electronically. Abstracts not received by that date 35mm carousel slide projector, or I/2'' or 3/4'' VHS video cannot be published. If desired, an abstract form may be cassette recorder with one color monitor.

1992 Symposium on Some Mathematical Questions in Biology Cell Biology Denver, Colorado, November 1992

The twenty-sixth annual Symposium on Some Mathematical through the aggregation of cell suiface receptors; Jennifer Questions in Biology, focusing on Cell Biology, will be Linderman (University of Michigan, Ann Arbor), Cell-cell held during the annual meeting of the American Society interactions and the activation of T cells in an immune re­ for Cell Biology, November 15-19, 1992, at the Colorado sponse; George Oster (University of California, Berkeley), Convention Center in Denver, Colorado. The symposium The dynamics of single-motor molecules; and Michael Reed is sponsored by the American Mathematical Society, the (Duke University), The transport of organelles in axons. Society for Industrial and Applied Mathematics (SIAM), Proceedings of the symposium will be published by the and the Society for Mathematical Biology (SMB). AMS in the series Lectures on Mathematics in the Life The AMS-SIAM-SMB Committee on Mathematics in Sciences. · the Life Sciences serves as the Organizing Committee for The SMB has funds for partial support of graduate the symposium. The committee members are Jack D. Cowan, students attending the symposium. To request support, James W. Curren, Marcus W. Feldman, Eric S. Lander, Marc contact John Rinzel, Chief, Mathematical Research Branch, Mangel (Chair), and James D. Murray. Byron Goldstein and NIADDKD, Bldg. 31, Room 4B-54, NIH, Bethesda, MD Carla Wofsy serve as organizers. 20892, by June 15, 1992. The application should include a There will be two afternoon sessions, each including one-page research summary and one letter from a faculty three invited lectures on mathematical and biophysical ap­ sponsor. proaches to problems in cell biology. The dates will appear Discount airfares are available from United Airlines for and in the next issue of the Notices. The speakers and their travel November 12-22, 1992. Call 1-800-521-4041 topics are: Micah Dembo (Los Alamos National Labora­ refer to file number 524YM. For further information on the symposium, contact the tory), Modeling cell adhesion; Elliot Elson (Washington Symposium Conference Coordinator, AMS, P.O. Box 6887, University School of Medicine, St. Louis), Interpretation Providence, R1 02940, or [email protected] by of measurements of cellular deformability; Byron Gold­ electronic mail. stein (Los Alamos National Laboratory), Cell activation

MAY/JUNE 1992, VOLUME 39, NUMBER 5 485 Mathematical Sciences 1-3. Logical Analysis and Computer Sci­ ence in Honor of the 60th Birthday of MSI Director A. Nerode, Mathematical Sciences Meetings and Conferences Institute, Ithaca, NY. (Apr. 1992, p. 343) 1-5. Seventh International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, Western Michigan Univer­ sity, Kalamazoo, MI. (May/Jun. 1991, p. 476) 1-5. IMA Workshop on Linear Algebra for Control Theory, University of Minnesota, Minneapolis, MN. (Oct. 1990, p. 1141) 1-5. Third International Conference on Mathematical Population Dynamics, Uni­ versity of Pau, France. (Dec. 1991, p. 1336) THIS SECTION contains announcements of meetings and conferences of interest to some 1-5. Calcul Formel et Equations Differen­ segment of the mathematical public, including ad hoc, local, or regional meetings, and tielles, Marseille, France. (Jan. 1992, p. 49) meetings or symposia devoted to specialized topics, as well as announcements of regularly 1-5. NSF-CBMS Regional Research Con­ scheduled meetings of national or international mathematical organizations. (Information on ferences in the Mathematical Sciences: meetings· of the Society, and on meetings sponsored by the Society, will be found inside the Number Theory and Dynamical Systems, front cover.) AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers, California State University, Fresno, Cali­ and specifies the place, date, subject (when applicable), and the speakers; a second fornia. (Jan. 1992, p. 49) announcement will be published only if there are changes or necessary additional information. 4-6. AT LAST: An NSF-ILAS Project to Once an announcement has appeared, the event will be briefly noted in each issue until Augment the Teaching of Linear Algebra it has been held and a reference will be given in parentheses to the month, year, and through the use of Software Tools, West page of the issue in which the complete information appeared. Asterisks (*) mark those Valley College, Saratoga, CA. (Feb. 1992, announcements containing new or revised information. p. 142) IN GENERAL, announcements of meetings and conferences held in North America carry only date, title of meeting, place of meeting, names of speakers (or sometimes a general *4-11. DI Week on Algebra and Algebraic statement on the program), deadlines for abstracts or contributed papers, and source of Geometry, Puerto de Ia Cruz (Tenerife). further information. Meetings held outside the North American area may carry more detailed information. In any case, if there is any application deadline with respect to participation in INVITED SPEAKERS: Tentative: A. Bak (U. the meeting, this fact should be noted. All communications on meetings and conferences in Bielefeld), G. Elencwajg (U. Nice), A. the mathematical sciences should be sent to the Editor of the Notices, care of the American Facchini, A. Frohlich (Queen's College), Mathematical Society in Providence. Hermann (U. KOln), M. Knus, Lipman DEADLINES for entries in this section are listed on the inside front cover of each issue. In (Purdue U.), M.P. Malliavin (U. Paris order to allow participants to arrange their travel plans, organizers of meetings are urged VI), McConnell (U. Leeds), Robiano (U. to submit information for these listings early enough to allow them to appear in more than Genova), Spivakosky (Hravard U.), Villa­ one issue of the Notices prior to the meeting in question. To achieve this, listings should be mayor (Buenos Aires). received in Providence SIX MONTHS prior to the scheduled date of the meeting. INFORMATION: Victoria Reyes Sanchez, 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, Dept. de Matematica Fundamental, Univ. only meetings and conferences for the twelve-month period following the month of that issue de La Laguna, 38206, La Laguna, Tener­ will appear. As new information is received for meetings and conferences that will occur ife, Canary Island, Spain. later than the twelve-month period, it will be announced at the end of the listing in the next possible issue. That information will not be repeated until the date of the meeting or 7-11. International Joint Conference on conference falls within the twelve-month period. Neural Networks "IJCNN '92", Baltimore, MD. (Dec. 1991, p. 1337) 7-13. Computational Group Theory, Ober­ wolfach, Federal Republic of Germany. (Feb. Lafayette, IN. (May/Jun. 1991, p. 475) 1991, p. 147) Spring 1992. DIMACS Workshop on Ex­ 1992 8-11. Sixth SIAM Conference on Discrete pander Graphs: Theory and Applications, Mathematics, University of British Columbia, 1992. IMACS Symposium on Symbolic Center for Discrete Mathematics, Rutgers, Vancouver, Canada. (May/Jun. 1991, p. 476) Computation in Engineering Design, IDN, The State University of New Jersey, New Lille, France. (Jul./Aug. 1990, p. 746) Brunswick, NJ. (Oct. 1991, p. 1007) 8-12. Seminaire Sud-Rhodanien de Geome­ trie, Marseille, France. (Jan. 1992, p. 49) 1992. IMACS International Conference on Computational Physics, University of Col­ 8-12. NSF Undergraduate Faculty En­ orado, Boulder, CO. (Oct. 1990, hancement Workshop: Algorithmic Num­ p. 1141) June 1992 ber Theory, California State University, Spring 1992. International Conference on June 1992. IMACS Symposium on Numer­ Fresno, CA. (Jan. 1992, p. 50) Finite Elements and Boundary Elements ical Computing and Mathematical Mod­ 8-12. Gordon Research Conferences "Fron­ in Geophysics, Monteray, CA. (Oct. 1990, elling, Bangalore, India. (Oct. 1990, p. 1141) tiers of Science", Tilton, NH. (Apr. 1992, p. 1141) June 1992. Continuum Models for the Mi­ p. 344) Spring 1992. Third IMACS International crostructure of Crystals, International Centre 8-13. Zero-dimensional Schemes, Ravello, Conference on Expert Systems in Numer­ for Mathematical Sciences, Edinburgh, Scot­ Italy. (Sep. 1991, p. 837) ical Computing, Purdue University, West land. (Oct. 1991, p. 1009) 8-13. Continuum Models for the Mi-

486 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ~·~--~··~··~··~~·~···~-~~=·m·~·~~··~~~~~·~-~·-·-...... ~-··-...... ~·~· .. -··~· ... -..... ···~-T,IT'W-f~fi.~jii~'t€£·~-...... Meetings and Conferences

crostructure of Crystals, Edinburgh, Scot­ 15-19. :Fourth Conference on Formal Technology, Delph, The Netherlands. (Jan. land. (Jan. 1992, p. 50) Power Series and Algebraic Combinatorics, 1992, p. 50) 8-19. Dirichlet Forms, Villa Monastero, Universite du Quebec a Montreal. (Sep. 1991, * 16-19. Tenth U.S. Army Mathematics Varenna, Italy. (Dec. 1991, p. 1337) p. 837) Conference, West Point, NY. 15-19. Sixth International Conference on 8-19. Workshop on Dynamical Systems, ORGANIZER: U.S. Army Research Office. Domain Decomposition Methods in Science International Centre for Theoretical Physics, INFORMATION: J. Chiment, Mathemati­ and Engineering, Como, Italy. (Nov. 1991, Trieste, Italy. (Jan. 1992, p. 50) cal Sciences Institute, 409 College Ave., p. 1169) 9-11. International Conference on Art Ithaca, NY 14850; 607-255-8005; Fax: and Mathematics, SUNY Albany, NY. (Feb. 15-19. Tire a Preciser, Marseille, France. 607-255-9003; jjc @cornellc.cit.cornell.edu. 1992, p. 142) (Jan. 1992, p. 50) 9-14. International Conference on Dif­ * 15-19. Logic and Computer Science, Centre 17-20. Fourth International Conference ferential Geometry and Global Analysis, International de Recontres Mathematiques, on Computers and Learning, ICCAL '92, Munster, Federal Republic of Germany. (Apr. Luminy, France. Acadia University, Nova Scotia, Canada. (Feb. 1991, p. 147) 1992, p. 344) ORGANIZER: M.R. Donnadieu. 17-20. Second Geoffrey Butler Memo­ 10-16. Geometric Topology Workshop, CONFERENCE TOPICS: A-calculus, func­ J. rial Conference on Differential Equations Technion, Haifa, Israel. (Nov. 1991, p. 1168) tional programming, nonclassical logics, and Population Biology, University of Al­ 11-13. AT LAST: An NSF-ILAS Project proof theory, logic programming, categor­ berta, Edmonton, Alberta, Canada. (Feb. 1992, to Augment the Teaching of Linear Alge­ ical logic. p. 143) bra through the use of Software Tools, INVITED SPEAKERS: S. Abramsky (Lon­ Auburn University, Auburn, AL. (Feb. 1992, don), S. Artemov (Moscou), M. Bezem 18-20. Eighteenth International Workshop p. 142) (Utrecht), E. Borger (Pise), V. Danos on Graph-Theoretic Concepts in Computer Science "WG '92", Wiesbaden-Naurod, Fed­ 11-13. Ninth Annual Western Workshop in (Paris VII), R. Dyckhoff (St. Andrew), eral Republic of Germany. (Jan. 1992, p. 50) Geometric Topology, Colorado College, Col­ J.Y. Girard (CNRS Paris), K. Mac Aloon orado Springs, Colorado. (Mar. 1992, p. 244) (NY), F. Montagna (Siene), H. Ono (Hi­ 18-20. Problem Solving Across the Cur­ riculum, Wells College, Aurora, NY. (Jan. 11-13. Logical Methods in Mathematics roshima), M. Parigot (Paris), V. Ribakov 1992, p. 50) and Computer Science, Cornell University, (Krasnoyarsk), K. Segerberg (Uppsala), Ithaca, NY. (Mar. 1992, p. 244) J. Smith (Goteberg), P. Aczel (Manch­ 18-20. AT LAST: An NSF-ILAS Project ester), H.P. Barendregt (Nijmegen), G. 12-13. Conference on the Teaching of Cal­ to Augment the Teaching of Linear Al­ Boolos (MIT), B. Courcelle (Bordeaux), gebra through the use of Software Tools, culus, Harvard University, Cambridge, MA. J.P. Delahaye (Lille), Y. Gurevich (Ann (Apr. 1992, p. 344) University of Wisconsin, Madison, WI. (Feb. Arbor), G. Japaridze (Tbilissi), I. Moerdijk 1992, p. 143) 12-14. Canadian Mathematical Society (Utrecht), Y. Moschovakis (Los Angeles), 18-20. Eighth Summer Conference on Summer Meeting, York University, North E. Palmgren (Uppsala), A.M. Pitts (Cam­ York, Ontario, Canada. (Nov. 1990, p. 1289) General Topology and Applications, Queens bridge), U. Schmerl (Munich), Ph. Scott College, CUNY, New York City. (Mar. 1992, 12-20. D-moduli and Representation The­ (Edimbourg), S. Solovev (St. Petersburg). p. 245) ory, Ca' Foscari, Venezia, Italy. (Dec. 1991, INFORMATION: M.R. Donnadieu, Dept. de p. 1337) Math.-Informatique, Faculte des Sciences 19-23. International Conference on Com­ de Luminy, Case 901, 13288 MAR­ plex Analysis, Nankai Institute of Mathemat­ 13-16. Conference in Geometric Group ics, Tianjin, China. (Feb. 1992, p. 143) Theory, Ohio State University, Columbus, SEILLE Cedex 9, Tel: 91 26 90 47 OH. (Nov. 1991, p. 1168) or 91 26 90 80; Fax: 91 26 90 38; email: 21-27. Porous Media, Oberwolfach, Federal Republic of Germany. (Feb. 1991, p. 147) 13-18. Inverse Problems in Engineering: [email protected]. Theory and Practice, Palm Coast, FL. (Mar. 21-July 10. Summer Geometry Institute, 15-20. International Conference and Sum­ Park City, Utah. (Nov. 1991, p. 1169) 1992, p. 244) mer School on the Theory and Applications 14-17. Third Symposium on "Chaotic Dy­ of Dynamical Systems, Huddinge (Stock­ 22-24. Seventh IMACS International Con­ ference on Computer Methods for Partial namical Systems", Conference Center "Woud­ holm), Sweden. (Mar. 1992, p. 245) schoten", The Netherlands. (Mar. 1992, p. 244) Differential Equations, Rutgers University, 15-20. Fourier Analysis and Partial Dif­ New Brunswick, NJ. (Dec. 1991, p. 1337) 14-20. Fifth International Symposium on ferential Equations, Miraflores de la Sierra, Statistical Decision Theory and Related near Madrid, Spain. (Mar. 1992, p. 245) 22-25. Seventh Annual IEEE Symposium Topics, Purdue University, West Lafayette, on Logic in Computer Science, Santa Cruz, * 15-20. Interactive Mathematics Text Project: CA. (Sep. 1991, p. 838) IN. (Sep. 1990, p. 938) Mathcad 3.1, University of Pennsylvania. 14-20. Freiformkurven und Freiform­ 22-25. Seventh Annual Conference on ftachen, Oberwolfach, Federal Republic of INSTRUCTOR: L. Senechal. Structure in Complexity Theory, Boston Germany. (Feb. 1991, p. 147) CosT: $500. University, Boston, MA. (Nov. 1991, p. 1169) INFORMATION: E. Deeba, Dept. of Ap­ 15-18. Wave Phenomena II: Modem The­ 22-26. Fifth International Meeting on plied Math. Sciences, Univ. of Houston­ ory and Applications, Edmonton, Alberta, Statistical Climatology (SIMSC), Toronto, Downtown, One Main St., Houston, TX Canada. (Nov. 1991, p. 1169) Canada. (Nov. 1991, p. 1169) 77002; 713-221-8550. 15-18. Computer Vision and Pattern 22-26. Twelfth Conference on Probability Recognition, Champaign, IL. (Dec. 1991, 15-27. Nonequilibrium problems in many­ and Statistics in the Atmospheric Sciences, p. 1337) particle systems, Montecatini Terme, Italy. Toronto, Canada. (Nov. 1991, p. 1169) 15-19. Twenty-first International Confer­ (Dec. 1991, p. 1337) 22-26. The Twelfth Dundee Conference ence on Stochastic Processes and their Ap­ 16-18. 1992 IFAC/IFIPIIMACS Interna­ on Ordinary and Partial Differential Equa­ plications, Toronto, Canada. (May/Jun. 1990, tional Symposium on Artificial Intelligence tions, Dundee, Scotland. (Nov. 1991, p. 1170) p. 613) in Real-Time Control, Delph University of 22-26. International Conference on Spec-

MAY/JUNE 1992, VOLUME 39, NUMBER 5 487 ...... _...... ______-·---·------..-·------Meetings and Conferences

tral and High Order Methods, Montpellier, C&O, Univ. of Waterloo, Waterloo, On­ Equipe de Logique, UFR de Mathema­ France. (Jan. 1992, p. 50) tario, Canada N2L 3Gl; 519-885-1211; tiques, Universite de Paris VII, 2, Place 22-26. Convergences en Analyse Multi­ Fax: 519-746-6530; email: combot@ Jussieu, 75251 Paris Cedex 05, France; voque et Optimisation, Marseille, France. math.uwaterloo.ca. email: [email protected]. (Jan. 1992, p. 50) 22-July 17. Patch Dynamics D, Mathemati­ 5-11. Mathematische Modellierung und 22-26. International Conference on Non­ cal Sciences Institute, Ithaca, NY. (Apr. 1992, Simulation Elektrischer Schaltungen, Ober­ linear Evolution Problems, Rome, Italy. p. 345) wolfach, Germany. (Jul./Aug. 1991, p. 645) (Jan. 1992, p. 50) 23-27. Workshop on Computational Ge­ 5-August 1. NSF Regional Geometry Insti­ 22-26. Convergences en Analyse Multi­ ometry, Turin, Italy. (Dec. 1991, p. 1338) tute: Computational Algebraic Geometry, voque et Unilaterale, CIRM, Luminy, France. 25-27. AT LAST: An NSF-ILAS Project Amherst College, Amherst, MA. (Oct. 1991, (Mar. 1992, p. 245) to Augment the Teaching of Linear Al­ p. 1010) * 22-26. Coxeter Groups and Algorithmic gebra through the use of Software Tools, 6--10. European Congress of Mathematics, Representation Theory, Lyon, France. University of Wyoming, Laramie, WY. (Feb. Paris, France. (Apr. 1992, p. 345) 1992, p. 143) PRoGRAM: The conference will focus on 6--10. Mathematical Conferences in Perth, the algorithmic aspects of coxeter groups 28-July 4. Hyperbolic Systems of Conser­ University of Western Australia. (Sep. 1991, and Heeke algebras, with a view towards vation Laws, Oberwolfach, Federal Republic p. 838) in representation theory of Germany. (Feb. 1991, p. 147) their applications 6--10. Eighteenth Australasian Conference Lie groups and in geometry. of reductive 29-30. International Conference on the on Combinatorial Mathematics and Com­ Contributions of a computer science nature Development of Mathematics from 1900 to binatorial Computing, Perth, Western Aus­ from users of the theory and reports 1950, Luxembourg. (Mar. 1992, p. 245) tralia. (Nov. 199l,p. 1170) working in other fields are also invited. 29-July 1. Joint Meeting with the London 6-10. Thirty-Sixth Annual Meeting of ORGANIZING COMMITTEE: F. Bien (Prince­ Mathematical Society, Cambridge, England. ton U.), Fokko du Cloux and T. Fack (U. the Australian Mathematical Society, Perth, Claude Bernard, Lyon). INFORMATION: H. Daly, American Math­ Western Australia. (Nov. 1991, p. 1170) INVITED SPEAKERS: J. Carrell, W. Cassel­ ematical Society, Post Office Box 6887, 6--10. Strange Attractors and Knots, Dy­ man, A. Cohen, V. Deodhar, F. Digne, M. Providence, Rhode Island 02940. namical Systems Institute, Boston University, T. Springer, J. Boston, MA. (Feb. 1992, p. 144) Dyer, A. Garsia, Lehrer, 29-July 3. International Conference on Tits, N. Wallach. K-Theory, Strasbourg, France. (Dec. 1991, * 6--10. Fourth Workshop on Stochastic INFORMATION: F. du Cloux, lnst. de p. 1338) Analysis, Oslo, Norway. (Please note change Math et Informatique, Universite Claude of place and time from Jul./Aug. 1991, p. 645) Bernard, F-69622 Villeurbanne Cedex, 29-July 3. Workshop on Data Analysis and France; [email protected]; Fax: Robustness, Ascona, Switzerland. (Jan. 1992, ORGANIZING COMMITTEE: A.S. Ustunel +33-72.44.80.65. p. 51) (Paris), M. Zakai (Haifa), T. Lindstrom 29-July 3. Greco Calcul Formel, Marseille, and B. Oksendal (Oslo). * 22-26. Waterloo '92: An International France. (Jan. 1992, p. 51) INFORMATION: A.S. Ustunel, ENST, Dept. Conference on Combinatorics and Opti­ 29-July 5. Nineteenth International Collo­ Reseaux, 46, rue Barrault, 75634 Paris mization, University of Waterloo, Waterloo, quium on "Group Theoretical Methods in Cedex 13, France; Fax: 33-1-45891664; Ontario, Canada. Physics", Salamance, Spain. (May/Jun. 1991, email: [email protected] or T. Lindstrom PLENARY SPEAKERS: G. Andrews (Penn p. 476) and B. Oksendal, Dept. of Math., Univ. of State), V. Chaval (Rutgers), T. Cole­ Oslo, Box 1053 Blindern, N-0316 Oslo, man (Cornell), W. Cook (Bellcore), J. Norway; Fax: 47-2-854349; email: lind­ Dennis (Rice), L. Lovasz (Eotvos, Hun­ [email protected] or [email protected]. July 1992 gary), P. Seymour (Bellcore), D. Stin­ 6-11. RICA '92: RISC-LINZ Summer L. Teirlinck (Auburn), C. son (Nebraska), 1-4. Algebres d'Operateurs 1992 (a satel­ School in Computer Algebra 1992, Johannes Thomassen (Technical U., Denmark). lite conference of the European Congress of Kepler University, Linz, Austria. (Feb. 1992, SPECIAL SESSIONs/WORKSHOPS: Algebraic Mathematics), University of Orleans, France. p. 144) combinatorics: D. de Caen, H. Barcelo, (Jan. 1992, p. 51) A. Brouwer, M. Conder, S. Fomin, C. * 6--11. Interactive Mathematics Text Project: * 2-4. Banach Space Theory, Miniconfer- Mathematica for Windows, University of Greene, M. Haiman, J. Hall, P. Hanlon, ence, Perth, Western Australia. D. Leonard, I. Macdonald, .P. Terwilliger, Pennsylvania. INFORMATION: S.P. Fitzpatrick, Dept. of T. Visentin, R. Weiss; Codes, designs, INSTRUCTOR: J. Manfredi. Math., Univ. of Western Australia, WA and cryptography: I. Blake, D. Jung­ ·CosT: $650. 6009, Australia. nickel, K. Heinrich, C. Lindner, B. Mills, INFORMATION: M. Hoft, Dept. of Math., A. Rosa, G. Simmons, N. Sloane, R. 2-4. Conference in Mathematical Logic, Univ. of Michigan-Dearborn, Dearborn, Wilson; Combina­ * Stanton, A. Street, R. Paris, ·France. MI 48128; 313-593-5175. torial optimization: R. Kannan, B. Korte, J. Orlin, W. Pulleyblank, A. Schrijver, PROGRAM: The talks will give a survey * 6-11. Interactive Mathematics Text Project: E. Tardos, K. Truemper; Graph the­ of recent research in mathematical logic Mathcad 3.1, University of Pennsylvania. ory: N. Alon, R. Haggkvist, F. Jaeger, which will be acccessible to a general C.St.J.A. Nash-Williams; Nonlinear opti­ mathematical audience. INSTRUCTOR: J. Goebel. mization: J. Birge, A. Conn, A. Dontchev, INVITED SPEAKERS: T. Coquand, A. Lou­ CosT: $500. C. Lemarechal, P. Loewen, B. Mor­ veau, A. Prstel, P. Pudlak, A. Wilkie, and INFORMATION: H. Gore, Dept. of Math., dukhovich, M. Overton, D. Shanno. B. Zilber. Morehouse College, Atlanta, GA 30314; INFORMATION: Waterloo '92, Dept. of INFORMATION: Colloque de Logique, 404-215-2614.

488 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1';-;M)-~·····················-···· Meetings and Conferences

6-13. Regional Institute in Geometry Platen, School of Math. Sci., The Aus­ fornia. (Feb. 1991, p. 147) and Computational Algebraic Geometry, tralian National Univ., Canberra, ACT 19-24. Neural and Stochastic Methods in Amherst College, MA. (Apr. 1992, p. 345) 2601, Australia. Image and Signal Processing, San Diego, 6-17. Conference on Contemporary Topics CA. (Feb. 1992, p. 145) 13-18. Interactive Mathematics Text Proj- in Combinatorics, University of Wyoming, * ect: Mathcad 3.1, University of Pennsylvania. * 19-24. International Society for Optical Laramie, WY. (Feb. 1992, p. 144) Engineering (SPIE) Annual Symposium, 6-31. IMA Summer Program on Environ­ INSTRUCTOR: D. Royster. San Diego, CA. CosT: $500. mental Studies: Mathematical, Computa­ INFORMATION: Tel: 206-676-3290. tional, and Statistical Analysis, Institute for INFORMA noN: J. Morrison, Dept. of Math., Mathematics and its Applications, University Towson State University, Towson, MD 19-25. Lower-Dimensional Theories and of Minnesota. (Sep. 1991, p. 838) 21204; 410-830-3595. Domain Decomposition Methods in Me­ 6-August 14. Summer Program in Math­ * 13-18. Interactive Mathematics Text Proj­ chanics, Oberwolfach, Federal Republic of ematical Physiology, Mathematical Sciences ect: Mathematica for Windows, University Germany. (Feb. 1991, p. 147) Research Institute, Berkeley, CA. (Sep. 1991, of Pennsylvania. 19-25. Applications of Nonstandard-Analy­ p. 838) sis to Analysis, Functional Analysis, and INSTRUCTOR: B. Davis. 7,.August 7. Workshop on Stochastic Par­ Probability Theory, Heinrich Fabri-Institut tial Differential Equations, Mathematical CosT: $650. der Universitiit Tiibingen, Blaubeuren (Uim), INFORMATION: T. McCutcheon, Dept. of Sciences Institute, Ithaca, NY. (Apr. 1992, Federal Republic of Germany. (Jul./Aug. p. 345) Math., Los Angeles Pierce College, 6201 1991, p. 645) Winnetka Ave., Woodland Hills, CA 91371; 8-25. Twenty-second Summer Ecole d'ete 818-347-0551, ext. 468. 19-31. SERC Numerical Analysis Sum­ de Calcul des Probabilites, Saint-Flour (Can­ mer School, Lancaster University, Lancaster, tal). (Apr. 1992, p. 345) * 13-18. Interactive Mathematics Text Project: England. (Dec. 1991, p. 1338) 10-12. Annual Meeting for the Aus­ Mathematica for Windows, University of 20-24. The Fifth International Conference tralasian Association for Logic, Australian Pennsylvania. on Fibonacci Numbers and their Applica­ National University, Canberra, Australia. (Mar. INSTRUCTOR: H. Porta. tions, University of St. Andrews, St. Andrews, 1992, p. 246) CosT: $650. Scotland. (May/Jun. 1991, p. 476) 11-18. St. Andrews Colloquium, University INFORMATION: H. Gore, Dept. of Math., 20-24. Second Symposium on Logical of St. Andrews, Scotland. (Jul./Aug. 1991, Morehouse College, Atlanta, GA 30314; Foundations of Computer Science (SCFS p. 645) 404-215-2614. '92), Tver University, Tver, USSR. (Dec. 12-16. Dynamics of Annulus Maps, Dy­ 1991, p. 1339) namical Systems Institute, Boston University, 13-24. SMS-NATO ASI: Bifurcations and 20-24. Titre a Preciser, Marseille, France. Boston, MA. (Feb. 1992, p. 144) Periodic Orbits of Vector Fields, Univ. (Jan. 1992, p. 51) de Montreal, Montreal, Canada. (Dec. 1991, 20-24. SIAM Fortieth Anniversary Meet­ 12-17. International Colloquium on p. 1338) Automata, Languages and Programming, ing, Los Angeles, CA. (Mar. 1992, p. 246) 13-31. Miniworkshop on Nonlinearity and Vienna, Austria. (Jul./Aug. 1991, p. 645) 20-24. Third International Conference Chaos, Trieste, Italy. (Jan. 1992, p. 51) * 12-18. Arithmetic Algebraic Geometry, on Algorithms for Approximation, Oxford, Oberwolfach, Federal Republic of Germany. * 13-August 7. 1992 CRM Summer School England. on Control Theory, Montreal, Canada. (Feb.l991,p.147) INFORMATION: E. Smith, Applied and 13-15. Third Annual Gottingen Workshop INFORMATION: S. Chenevert, CRM, Univ. Computational Math. Group, RMCS (Cran­ on the History of Modern Mathematics, de Montreal, C.P. 6128-A, Montreal, Que­ field), Shrivenham, Swindon, Wilts, SN6 Mathematischen Institut der Georg-August­ bec H3C 3J7, Canada. 8LA, England. Universitiit Gottingen. (Mar. 1992, p. 246) 15-17. Premieres Journees Marocaines de * 13-15. Mathematics and Computers in * 20-25. Interactive Mathematics Text Proj- Mathematiques Appliquees, Rabat, Maroc. ect: Mathcad 3.1, University of Pennsylvania. Sports., Bond University, Gold Coast, Queens­ (Jan. 1992, p. 51) land. * 17-18. Stochastic Partial Differential Equa- INSTRUCTOR: C. Alexander. INFORMATION: N. de Mestre, School of tions, University of Rochester. CosT: $500. Information and Computer Science, Bond INFORMATION: M. Hoft, Dept. of Math., University, Gold Coast, Queensland 4229, ORGANIZER: C. Mueller. Univ. of Michigan-Dearborn, Dearborn, Australia; email: neville_de_mestre@ INFORMATION: J. Chiment, Mathemati­ MI 48128; 313-593-5175. cal Sciences Institute, 409 College Ave., macmail.bu.zo.au. Ithaca, NY 14850; 607-255-8005; Fax: * 20-25. Interactive Mathematics Text Proj­ 13-17. Titre a Preciser, Marseille, France. 607-255-9003; email: jjc@ ect: Maple for Windows, University of Penn­ (Jan. 1992, p. 51) cornellc.cit.cornell.edu. sylvania. 13-17. RISC-LINZ Summer Course on 19-23. Sixth ACM International Confer­ INSTRUCTOR: J. Stan Devitt. Quantifier Elimination, Johannes Kepler Uni­ ence on Supercomputing, Washington, DC. CosT: $500. versitiit, Linz, Austria. (Feb. 1992, p. 144) (Dec. 1991, p. 1338) INFORMATION: E. Deeba, Dept. of Ap­ plied Math. Sciences, Univ. of Houston­ * 13-17. Instructional Workshop on Nu­ 19-23. Complexity and Computability Downtown, One Main St., Houston, TX merical Methods for Stochastic Differential over the Reals, Dynamical Systems Insti­ 77002; 713-221-8550. Equations, Geelong, Victoria, Australia. tute, Boston University, Boston, MA. (Feb. INFORMATION: P.E. Kloeden, Dept. of 1992, p. 144) 20-26. International Conference on Alge­ Computing and Math., Deakin Univ., 19-24. SIAM Annual Meeting (SIAM's braic Geometry, Universite Paris-Sud. (Jan. Geelong, Victoria 3217, Australia; or E. 40th Anniversary), Los Angeles, Cali- 1992, p. 52)

MAY/JUNE 1992, VOLUME 39, NUMBER 5 489 Meetings and Conferences

21-25. Rademacher Centenary Confer­ * 27-29. International Symposium on Sym­ [email protected] or ence, Pennsylvania State University, Univer­ bolic and Algebraic Computation, Berkeley, [email protected]. sity Park, PA. (Jan. 1992, p. 52) CA. (Please note updated information from 2-8. Algebraische Zahlentheorie, Oberwol­ 22-25. AT LAST: An NSF-ILAS Project Jan. 1992, p. 52) fach, Federal Republic of Germany. (Feb. to Augment the Teaching of Linear Al­ KEYNOTE SPEAKERS: J.R. Rice, Purdue 1991, p. 147) gebra through the use of Software Tools, U.-What is an answer?; and W.M. Ka­ University of Maryland, College Park, MD. * 2-8. Conference on Algebra and its Appli- han, U. of California, Berkeley-A fear of cations, Middlesbrough, UK. (Feb. 1992, p. 145) constants. Last week of July. The Ninth Latin Amer­ INFORMATION: K. Yelick, ATTN: ISSAC INFORMATION: A. Oswald, School of Com­ ican Symposium of Mathematical Logic, U92, 571 Evans Hall, Comp. Sci. Division, puting and Math., Teesside Polytechnic, Universidad Nacional del Sur, Bahia Blanca, Univ. of California, Berkeley, CA 94720; Middlesbrough, Cleveland TS 1 3BA, UK; Argentina. (Mar. 1992, p. 246) email: [email protected]. email: [email protected]. * 24-25. Workshop on Matrix Theory, Uni- 27-31. Mathematical Physics of Disordered 3-6. Conference on Artificial Intelligence versity Bielefeld, Germany. Systems, Marseille, France. (Jan. 1992, p. 52) and Symbolic Mathematical Computations, INVITED SPEAKERS: R. Brualdi, S. Fried­ 27-31. Algorithms for Approximation, Karlsruhe, Germany. (Mar. 1992, p. 247) land, C. He, G. Krause, N. Mehrmann, R. Cranfield Institute of Technology, Oxford. 3-7. Sixth Workshop on Lie-Admissible Nabben, A. Pothen, H. Schneider (tenta­ (Feb. 1992, p. 145) Formulations, Clearwater, FL. (Mar. 1991, tive). 27-August 1. Workshop on Computational p. 244) INFORMATION: V. Mehrmann, Fakultaet Linear Algebra in Algebraic and Related 3-7. Fifth International Meeting of Statis­ fuer Mathematik, Universitaet Bielefeld, Problems, Essen, Federal Republic of Ger­ tics in the Basque Country, San Sebastin, Postfach 8640, D-4800 Bielefeld 1, FRG; many. (Jan. 1992, p. 52) Spain. (Jul./Aug. 1991, p. 646) tel: 0521-106-4798; email: Mehrmann@ * 27-August 1. Interactive Mathematics Text 3-7. Second Meeting of the International math1.mathematik.uni-bielefeld.de. Project: Maple for Windows, University of Linear Algebra Society (ILAS), University 26-30. Dynamics, Competition, and Neu­ Pennsylvania. of Lisbon, Portugal. (Mar. 1992, p. 247) ral Networks, Dynamical Systems Institute, INSTRUCTOR: C. Scheftic. 3-8. Ninth Latin American Symposium Boston University, Boston, MA. (Feb. 1992, CosT: $400. on Mathematical Logic, Bahia Blanca, Ar­ p. 145) INFORMATION: M. Pepe, Dept. of Math., gentina. (Jan. 1992, p. 52) 26-31. Eighteenth International Sympo­ Seattle Central Community College, 1701 * 3-8. Twelfth Brazilian Algebra Meeting, sium on Rarefied Gas Dynamics (RGD18), Broadway, Seattle, WA 98122; 206-587- Diamantina, Minas Gerais, Brazil. University of British Columbia, Vancouver, 4073. ORGANIZING COMMITTEE: D. Avritzer, H. Canada. (May/Jun. 1991, p. 477) 30--August 1. The State of Matter: Confer­ Merklen, F.C.P. Milies, I. Vaisencher, and 26-August 1. Variationsrechnung, Ober­ ence on Mathematical Physics, Celebrating P.H.V. Barros. wolfach, Germany. (Feb. 1991, p. 147) the Sixtieth Birthday of E.H. Lieb., Copen­ INVITED SPEAKERS: E. Becker, A. Prestel, 26-August 1. AMS-SIAM Summer Semi­ hagen, Denmark. (Dec. 1991, p. 1339) C. Peskine, A. Shokrollahi, H. Yamaki, nar on Exploiting Symmetry in Applied and T.L. Smith, R. Miranda, N. Vonessen, M. Numerical Analysis, Colorado State Univer­ Marshall, A. Sirois, D. Levcovitz, S.C. sity, Fort Collins, CO. Coutinho, H. Goodinho, F. Coelho, and August 1992 N.R. Rocco. INFORMATION: D.L. Salter, AMS, P.O. August 1992. The International Confer­ INFORMATION: M. Spira, Dept. de Matem­ Box 6887, Providence, RI 02940. ence Lobachevsky and Modern Geom­ atica, ICEx-UFMG, Caixa Postal 702, 30.161 * 26-August 15. SIMS Tutorial: Mathemat­ etry devoted to the 200th Anniversary Belo Horizonte MG, Brazil; Fax: 55-31- ical Sciences in Genomic Analysis, Rutgers of Lobachevsky's birthday, Kazan, USSR. 4481559; email: [email protected]. University. (Feb. 1991, p. 147) August 1992. Kinetics of Phase Transi­ PRoGRAM: The tutorial is intended for * 3-8. Forty-fourth International Meeting tions, International Centre for Mathematical advanced undergraduate and graduate stu­ of the ICSIMT, University of illinois at Sciences, Edinburgh, Scotland. (Oct. 1991, dents and postdoctorals in the biological Chicago, illinois. p. 1010) and mathematical sciences who have a PRoGRAM: Meeting theme: the student *August 1992-May 1993. Special Year in keen interest in the application of quanti­ confronted by Mathematics. The meeting Nonlinear PDEs and Dynamical Systems, tative methodologies to genomic analysis will focus on the following questions: Brigham Young University, Provo, UT. and who have had some experience in l(a) What is the nature of the knowledge their application to other scientific fields. PRoGRAM: Throughout the year, long- and and understanding of mathematics that stu­ TuTORIAL TOPICS: Fragment assembly, short-term visitors will be in residence. dents have?, 1(b) What mathematics do we informatics, pattern analysis of molecular The long-term visitors will include P. Hess want students to develop?, 2(a) What out­ sequences, DNA and protein structure (Zurich), N. Dancer (Armidale), J. Mallet­ of-school mathematics do students bring to predictions. Paret (Providence), G. Fusco (Rome), X.­ the classroom?, 2(b) How can we exploit TUTORIAL FACULTY: C.J. Benham, C. Y. Chen (Atlanta), and X. Chen (Pitts­ this?, 3(a) What are the obstacles to devel­ DeLisi, M. Farach, G. Hamm, B.S. Lander, burgh). The program will include weekly oping concepts and learning mathematics A. Lapedes, G. Myers, M. Noordewier, W. seminars in PDEs and dynamical systems (language, symbolism, abstraction, formal­ Sofer, M.S. Waterman. and will conclude with a conference. ism, students' and teachers' conception of INFORMATION: SIMS, 97 Parish Road INFORMATION: P. Bates, Dept. of Math., mathematics)?, 3(b) How do students de­ South, New Canaan, CT 06840; 203- Brigham Young Univ., Provo, UT 84602; velop mathematical concepts and how can 966-1008; Fax: 203-972-6069. 801-378-4156; Fax: 801-378-2800; email: this be stimulated?, 4(a) How can students

490 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -····----.. ---·~-----.... ~ .. ·-~·~--~·····-··---~-~-~--- .,,..,,,,., ..,,.,_.,,.,,_,..,.~~-~--: ------···· "' Meetings and Conferences

be involved in doing mathematics?, 4(b) 10-15. A Workshop on Numerical Ranges * 17-22. Interactive Mathematics Text Proj- How can this involvement lead to the and Numerical Radii, The College of William ect: Mathcad 3.1, University of Pennsylvania. development of mathematical knowledge? and Mary, Williamsburg, VA. (Apr. 1992, INSTRUCTOR: B. Levy. INFORMATION: ICSIMT 44, c/o A.I. Wein­ p. 347) CosT: $500. zweig, Univ. of lllinois at Chicago, * 10-15. Interactive Mathematics Text Proj- INFORMATION: T. McCutcheon, Dept. of Dept. of Math., Stats., and Comp. Sci., ect: Mathcad 3.1, University of Pennsylvania. Math., Los Angeles Pierce College, 6201 m/c 249, Box 4348, Chicago, IL 60680; INSTRUCTOR: B. Levy. Winnetka Ave., Woodland Hills, CA 91371; 312-996-8612; Fax: 312~996-1491; email: 818-347-0551, ext 468. u14818@uicvm. CosT: $400. INFORMATION: M. Pepe, Dept. of Math., * 3-8. Interactive Mathematics Text Project: Seattle Central Community College, 1701 17-23. Seventh International Congress on Maple for Windows, University of Pennsyl­ Broadway, Seattle, WA 98122; 206-587- Mathematical Education (ICME-7), Uni­ vania. 4073. versite Laval, Quebec, Canada. (Sep. 1991, p. 839) INSTRUCTOR: D. Schwalbe. * 10-18. Canadian Mathematical Society CosT: $500. Annual Seminar on Representations of Al­ * 17-28. Fourth European Summer School in Logic, Language, and Information, Uni­ INFORMATION: J. Morrison, Dept. of Math., gebras and Related Topics, Carleton Univer­ versity of Essex, Colchester, England. Towson State University, Towson, MD sity, Ottawa, Canada. (Please note additional 21204; 410-830-3595. information to Dec. 1991, p. 1339) SECTIONS: Language, logic, computation, LECTURERs: M. Broue (Paris), W. Crawley­ language and logic, logic and computation, 3-14. NATO Advanced Study Institute: Boevy (Oxford), C.W. Curtis (Oregon), M. computation and language. Linear Algebra for Large Scale and Real­ Dyer (Notre Dame), R. Dipper (Stuttgart), INFORMATION: D. Arnold or L. Sadler, Time Applications, Leuven, Belgium. (Feb. Yu. A. Drozd (Kiev), K. Erdmann (Ox­ Dept. of Language and Linguistics, Uni­ 1992, p. 145) ford), I.M. Gelfand (Rutgers), D. Han­ versity of Essex, Wivenhoe Park, Colch­ 3-28. IMA Summer Program for Graduate delman (Ottawa), D. Happel (Bielefeld), ester C04 3SQ, UK; or from A. de Roeck, Students: Mathematical Modeling, Univer­ B. Keller (Paris), H. Lenzing (Paderborn), Dept. of Comp. Science, University of Es­ sity of Minnesota, Minneapolis, MN. (Dec. J. McKay (Concordia), R.V. Moody (Al­ sex; email: [email protected]. 1991, p. 1339) berta), T. Okuyama (Osaka), B.J. Parshall 4-7. Chaos and its Applications, Trieste, (Virginia), J.A. de Ia Pena (Mexico), I. 18-22. Third Colloquium on Differential Italy. (Jan. 1992, p. 52) Reiten (Trondheim), K.W. Roggenkamp Equations, Plovdiv, Bulgaria. (Oct. 1991, 5-9. Topology, University of Georgia, (Stuttgart), A.N. Rudakov (Moscow), L.L. p. 1011) Athens, GA. (Apr. 1992, p. 346) Scott (Virginia), S.P. Smith (Washington), * 19-22. Sixth International Conference on W. Soergel (Bonn), 0. Solberg (Brandeis), * 7-10. Twelfth International Symposium Representations of Algebras (ICRA VI), A. Skowronski (Torun), D.-N. Verma Carleton University, Ottawa, Canada. (Please on Forecasting (ISF-92), Wellington, New (Bombay), T. Wakamatsu (Saitama), A. Zealand. note additional information to Dec. 1991, Weiss (Alberta). p. 1340) INFORMATION: L. Fraser Jackson, ISF- 11-15. The Seventh KAIST Mathematics LECTURERS: M. Broue (Paris), W. Crawley­ 92, P.O. Box 10-277, Wellington, New Workshop, Korea Advanced Institute of Sci­ Zealand; email: [email protected]. Boevy (Oxford), C.W. Curtis (Oregon), M. ence and Technology, Taejon, Korea. (Feb. Dyer (Notre Dame), R. Dipper (Stuttgart), 9-12. The Twelfth Annual International 1992, p. 146) Yu. A. Drozd (Kiev), K. Erdmann (Ox­ Conference on Critical Thinking and Ed­ 13-17. First Colloquium on Numeri­ ford), I.M. Gelfand (Rutgers), D. Han­ ucational Reform, Sonoma State University, cal Analysis, Plovdiv, Bulgaria. (Oct. 1991, delman (Ottawa), D. Happel (Bielefeld), California. (Mar. 1992, p. 247) p. lOll) B. Keller (Paris), H. Lenzing (Paderborn), J. McKay (Concordia), R.V. Moody (Al­ * 9-13. Joint Statistical Meetings, Boston, 15-19. International Conference on As­ MA. sociative Rings, Irkutsk, USSR. (Feb. 1992, berta), T. Okuyama (Osaka), B.J. Parshall p. 146) (Virginia), J.A. de Ia Pena (Mexico), I. INFORMATION: American Statistical Asso­ Reiten (Trondheim), K.W. Roggenkamp ciation, 1429 Duke St., Alexandria, VA 16-20. CRYPTO '92, University of Califor­ (Stuttgart), A.N. Rudakov (Moscow), L.L. nia, Santa Barbara. (Mar. 1992, p. 248) 22314-3402. Scott (Virginia), S.P. Smith (Washington), 16-22. Reelle Analysis, Oberwolfach, Ger­ W. Soergel (Bonn), 0. Solberg (Brandeis), 9-15. Jordan-Algebren, Oberwolfach, Fed­ many. (Jul./Aug. 1991, p. 646) A. Skowronski (Torun), D.-N. Verma eral Republic of Germany. (Feb. 1991, p. 147) 16-29. 1992 NATO Advanced Study In­ (Bombay), T. Wakamatsu (Saitama), A. 9-16. 1992 ASL European Summer Meet­ stitute: Wavelets and their Applications, Weiss (Alberta). ing (Logic Colloquium '92), Budapest, Hun­ Tuscany, Italy. (Feb. 1992, p. 146) gary. (Mar. 1992, p. 247) 17-19. Algebraic Computing in Geometry, 19-26. World Congress of Nonlinear Ana­ 10-14. Kinetics of Phase Transitions, Ed~ Linz, Austria. (Feb. 1992, p. 146) lysts, Melbourne, FL. (Nov. 1991, p. 1171) inburgh, Scotland. (Jan. 1992, p. 52) 17-21. The Sixth International Confer­ 22-28. Eighteenth International Congress 10-14. Summer School in the Model The­ ence on Boundary and Interior Layers­ of Theoretical and Applied Mechanics, ory of Fields-the Field of Real Numbers Computational and Asymptotic Methods Technion-Israel Institute of Technology, Haifa, with Exponentiation, University of Crete, (BAIL VI), Summit County, Colorado. (Nov. Israel. (Jan. 1991, p. 52) Greece. (Mar. 1992, p. 247) 1991, p. 1170) 23-29. Mathematical Finance, Oberwol­ 10-14. NSF-CBMS Regional Conference: 17-21. The Alan Day Conference on fach, Federal Republic of Germany. (Feb. Hopf Algebras and Their Actions on Rings, Lattices and Algebras, McMaster Univer­ 1991, p. 147) DePaul University, Chicago, IL. (Mar. 1992, sity, Hamilton, Ontario, Canada. (Nov. 1991, 23-29. Web Geometry, Oberwolfach, Fed­ p. 247) p. 1171) eral Republic of Germany. (Jan. 1992, p. 53)

MAY/JUNE 1992, VOLUME 39, NUMBER 5 491 ...... ······-································-····...... _. __ .______·-··-···-----··-·--··------:-- Meetings and Conferences

* 24-28. Tenth Symposium on Computa­ Theory, Centre de Recherches Mathematiques, * 13-15. MSI Workshop on Stochastic Anal- tional Statistics (COMPSTAT), Neuchatel, Universite de Montreal, Montreal Quebec, ysis, Cornell University. Switzerland. Canada. (Apr. 1992, p. 347) PROGRAM: The workshop will focus on INFORMATION: COMPSTAT Secretariat, *Academic Year 1992-1993. Real Closed the interplay of analysis and probability. Groupe de Statistique, Univ. de Neucha­ Fields, Cornell University, Ithaca, NY. INVITED SPEAKERS: R. Banuelos, C. tel, Pierre-a-Maze! 7, CH-2000 Neuchatel, PRoGRAM: ACSyAM, the MSI center for Bishop, K. Burdzy, D. Burkholder, E. Switzerland. Symbolic Methods in ALgorithmic Math­ Carlen, M. Freidlin, E. Hsu, N. Krylov, ematics at Cornell University, Will em­ P. March, M. Pinsky, T. Salisbury, and Z. 25-29. Sixth School of Algebra and Anal­ Zhao. ysis, Irkutsk, USSR. (Feb. 1992, p. 146) phasize Real Closed Fields for 1992-1993. INFORMATION: J. Chiment, Mathemati­ INFORMATION: M. Sweedler, jc5@ * 25-29. Third Islamic Countries Conference cal Sciences Institute, 409 College Ave., cornella.bitnet, MSI, 409 College Ave., on Statistical Sciences, Rabat, Morocco. Ithaca, NY 14850; 607-255-8005; Fax: Ithaca, NY 607-255-8005. INFORMATION: Secretary, Executive Board, 607 -255-9003; jjc @cornellc.cit.cornell.edu. Islamic Society of Statistical Sciences, 2-4. Ninth IFAC Workshop on Control 122-F, Liberty Plaza, Gulberg-IIl, Lahore, Applications of Optimization, Munich, Ger­ * 13-18. Sixth International Conference on Pakistan; or M. Benyaklef, Conference many. (Apr. 1992, p. 348) Stochastic Programming, Udine, Italy. Chairman, I.N.S.E.A. BP 6217, Rabat, 4-9. Homotopy Theory, Lake of Garda, INFORMATION: G. Andreatta, Dept. of Pure Morocco. Italy. (Apr. 1992, p. 348) and Applied Math., Via Belzoni, No. 7, 26-28. IMACS RM2S '92 Kobe, Kobe Uni­ 6-12. Topologie, Oberwolfach, Federal Re­ 35131 Padova, Italy. versity, Kobi, Japan. (May/Jun. 1991, p. 477) public of Germany. (Feb. 1991, p. 148) 30-September 5. Komplexe Analysis, Ober­ 7-11. Reseaux, Marseille, France. (Jan. 1992, 13-19. 4-Dimensional Manifolds, Oberwol­ wolfach, Federal Republic of Germany. (Feb. p. 53) fach, Federal Republic of Germany. (Feb. 1991, p. 147) 1991, p. 148) 7-14. IMACS Conference on Innovative 30-September 5. Seventy-five Years of Methods in Numerical Analysis, Padova 13-19. DMV-Jahrestagung, Berlin, Federal Radon Transform, Universitaet Wien, Wien, University at Bressanone, Italy. (Jan. 1992, Republic of Germany. (Jan. 1992, p. 53) Austria. (Apr. 1992, p. 347) p. 53) 13-19. Symposium on Analytic and Geo­ 30-September 5. International Congress on metric Aspects of Hyperbolic Geometry: In­ 8-11. IMA Tutorial: Introduction to Lin­ Nonlinear Analysis; Variational and Topo­ structional Conference, University of War­ ear Multivariable Control, Optimal De­ logical Methods, Xalapa, Veracruz, Mexico. wick, Coventry, UK. (Mar. 1992, p. 248) sign, and Parameter Estimation, Institute (Apr. 1992, p. 347) for Mathematics and its Applications, Univer­ 14-18. Twentieth European Meeting of 31-September 2. Fourth International Work­ sity of Minnesota (Sep. 1991, p. 839) Statisticians, Bath, UK. (Nov. 1991, p. 1171) shop on Generalized Convexity, Pees, Hun­ 14-18. Second Atelier International de gary. (Jan. 1992, p. 53) * 9-10. Symposium on High Performance Distributed Computing, HPDC-1, Syracuse, Theorie des Ensembles, Marseille, France. 31-September 4. Large Scale Scientific NY. (Jan. 1992, p. 53) Computation, Universitlit Bielefeld. (Feb. 14-25. Algebra (Advanced Workshop), 1992, p. 146) PROGRAM: The theme of HPDC-1 is to in­ Trieste, Italy. (Jan. 1992, p. 53) vestigate software techniques and architec­ * 31-September 4. International Symposium 16-18~ Second SIAM Conference on Con­ on Numerical Analysis-ISNA '92, Prague, tural support for application of parallel and trol in the 90s, Minneapolis, MN. (Feb. 1991, Czechoslovakia. distributed computing for solving compu­ p. 148) tationally intensive applications across a PRINCIPLE LECTURERS: J. Albrecht (Claus­ network of high-performance computers. 16-20. IMACS/SICE International Sympo­ thai), 0. Xelsson (Nijmegen), J. Douglas sium on Robotics, Mechatronics and Man­ CONFERENCE TOPICS: Parallel and dis­ (Purdue), Yu. Kuznetsov (Moscow), R. ufacturing Systems, Kobe, Japan. (Jan. 1992, tributed algorithms to solve computation­ Rannacher (Heidelberg), J.R. Whiteman p. 53) ally intensive problems across a LAN, (Brunei), T. Yamamoto (Matsuyama). MAN, or WAN; architectural support for 17-19. International Conference on Group INFORMATION: The Secretary ofiSNA '92, high-speed communications or intercon­ Theory, University of Timisoara, Romania. MFF University Karlovy, Malostranske nection networks; gigabit network archi­ (Jul./Aug. 1991, p. 646) namesti 25, 118 00 Praha 1, Czechoslo­ tectures; networking for multimedia data; 17-19. SIAM Conference on Control and vakia; email: [email protected]; Fax: high-speed communication transport pro­ its Applications, Minneapolis, MN. (Mar. 422 532742. tocols to achieve Gigabit/sec application­ 1992, p. 248) 31-September 11. Arithmetic Algebraic to-application transfer rates; performance 20-26. Funktionalgeichungen, Oberwol­ Geometry (Advanced Workshop), Trieste, evaluation of experimental systems to fach, Federal Republic of Germany. (Feb. Italy. (Jan. 1992, p. 53) solve supercomputing applications across 1991, p. 148) a network of computers. 21-23. Seventh International Conference INFORMATION: Syracuse University, 111 on Multivariate Analysis in Memory of September 1992 Link Hall, Syracuse, NY 13244; 315- Ronald A. Fisher, Barcelona, Spain. (Jan. 443-4282; G. Fox (General Chair), 315- 1992, p. 53) September 1992. IMACS 2nd Interna­ 443-4741, [email protected]; or G. tional Conference on System Simulation Craig (Local Chair), 315-443-4389, 21-23. Workshop on Algebraic Cycles, and Scientific Computing-BICSC '92, Bei­ [email protected]. Mathematical Sciences Research Institute, jing, China. (May/Jun. 1991, p. 477) Berkeley, CA. (Jan. 1992, p. 53) September 1992. Workshop on Topics 9-11. Royal Statistical Society Full Con­ 21-25. IMA Workshop on Robust Control in Probability and Lie Groups-Boundary ference, Sheffield, UK. (Nov. 1991, p. 1171) Theory, Institute for Mathematics and its

492 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ---· -- -- mm m II!IERRERBR~-- •mm -·· --·· ·-...wu R?NB Meetings and Conferences

Applications, University of Minnesota. (Sep. 12-16. International Conference on Poly­ Computational Methods in Mathematical 1991, p. 839) nomial Automorphisms and Related Top­ Physics, Acireale (Catania), Italy. ics, CIRM, Lurniny, France. (Jan. 1992, p. 54) *26-27. Thirty-second Midwest Partial Dif­ CONFERENCE TOPICS: Classical Lie groups, ferential Equations Seminar, Purdue Uni­ 14-20. First African Conference on Re­ exact solutions, conservation theorems; versity, West Lafayette, IN. search in Computer Science, Yaounde, perturbation methods in group analysis; Cameroon. (Feb. 1992, p. 147) INFORMATION: D. Phillips, Purdue Univer­ conditional (partial) symmetries; Backlund sity, Dept. of Math., West Lafayette, IN 15-17. Jumelage 92, Mathematical Sciences transformations, nonlocal symmetries; 47907. Institute, Ithaca, NY. (Apr. 1992, p. 348) group analysis of finite-difference equa­ 15-19. SIAM Conference on Applications tions; software packages; and problems of 27-0ctober 3. Darstellungstheorie Endlicher of Dynamical Systems, Salt Lake City, UT. group classification. Gruppen, Oberwolfach, Federal Republic of (Mar. 1992, p. 249) INVITED SPEAKERS: W.F. Ames, R.L. An­ Germany. (Feb. 1991, p. 148) derson, G.W. Bluman, 0. Bogoyavlenski, 17. Three Decades of Numerical Lin­ C. Cercignani, Y. Choquet-Bruhat, A. Do­ 3D-October 2. Thirtieth Annual Allerton ear Algebra at Berkeley: A Conference in nato, V.A. Dorodnitsyn, D. Fusco, W. Conference on Communication, Control, Honor of the Sixtieth Birthdays of Beres­ Fushchich, A. Greco, N.H. lbragimov, and Computing, University of Illinois, IL. ford Parlett and William Kahan, University P.G.L. Leach, F. MAgri, A. Morro, P.J. (Feb. 1992, p. 147) of California, Berkeley. (Mar. 1992, p. 249) 31-0ctober 4. Third International Con­ Olver, L.V. Ovsiannikov, C. Rogers, A.A. 18-24. Geometrie, Oberwolfach, Federal Samarskii, F. Swarz, and E.S. Suhubi. ference on Function Spaces, Institute of Republic of Germany. (Feb. 1991, p. 148) Mathematics, Adam Mickiewicz University, CALL FOR PAPERS: Abstracts (of up to 2 Poznan, Poland. (Feb. 1992, p. 147) 19-21. The Fourth Symposium on the pages) for a 20 minute presentation are to Frontiers of Massively Parallel Computa­ be received by June 15, 1992. tion, McLean, VA. (Dec. 1991, p. 1340) INFORMATION: A. Valenti, Dept. of Math., October 1992 19-23. Modeles Arch et Applications a Ia Univ. of Catania, Viale A. Doria, 6, 95125 October 1992. Workshop on Superpro­ Finance, Marseille, France. (Jan. 1992, p. 54) Catania, Italy; Fax: 95 330094; Tel: 95- 339052; email: [email protected]. cesses and Interacting Systems, Centre de 19-23. Fourth International Symposium Recherches Mathematiques, Universite de on Orthogonal Polynomials and their Ap­ 30-November 1. Central Section, Wright Montreal, Montreal, Quebec, Canada. (Apr. plications, Evian, France. (Feb. 1992, p. 148) State University, Dayton, OH. 1992, p. 348) 20-23. Second Beijing International Con­ INFORMATION: W. Drady, American Math­ 2-3. Fourth Midwest Conference on the ference on System Simulation and Scientific ematical Society, P.O. Box 6887, Povi­ History of Mathematics, Miami University, Computing-BICSC '92, Beijing, China. (Jan. dence, RI 02940. Oxford, OH. (Mar. 1992, p. 249) 1992, p. 54) 4-10. Funktionalanalysis, Oberwolfach, Fed­ 20-25. Workshop on Conservative Systems * 31. Differential Geometry Day, Eastern Germany. (Feb. 1991, p. 148) eral Republic of and Quantum Chaos, Fields Institute for Illinois University, Charleston, IL. * 9-10. Developments from the Stone Age, Sciences, Waterloo, Research in Mathematical PRINCIPLE SPEAKERS: S. Alexander, U. University of Chicago, Chicago, IL. p. 349) Ontario. (Apr. 1992, of Illinois; K. Burns, Northwestern U.; PRoGRAM: The basic idea of the confer­ 21-23. Documents, Computation, and Pref­ L. Conlon, Washington U.; H.R. Hughes, ence is to trace the development of some of erence, Washington, DC. (Apr. 1992, p. 349) Southern lllinois D.-Carbondale; J. Kamink­ the major areas in mathematics from their * 22-25. Semi-Annual Regional Workshop er, Indiana D.-Purdue U. at Indianapolis. state when Marshall Stone led the math in Dynamical Systems and Related Topics, INFORMATION: P. Coulton, Dept. of Math., dept. of the U. of Chicago through their Penn State University, State College, PA. Eastern Illinois Univ., Charleston, IL current situation to their future prospects. 61920; 217-581-5902; email: cfprc@ The program will include: The Stone Age: PROGRAM: A regular meeting dedicated to ux l.cts.eiu.edu. faculty and students (S. Mac Lane); ge­ recent results in the theory of smooth dy­ ometry and physics (1. Singer); Hilbert namical systems, ergodic theory, symbolic space and functional analysis (R. Kadi­ dynamics, topological dynamics, Hamilto­ son); Analysis (A. Calderon); topology (P. nian mechanics and related areas in differ­ May); Algebra (I. Kaplansky). ential geometry, differential equations and November 1992 Lie theory. 15-20 one hour and 45 minute INFORMATION: K. Swanson, Dept. of Math., November 1992. The International Lie­ talks are expected. 5734 University Avenue, Chicago, IL Lobachevsky Colloquium Dedicated to the ORGANIZERS: A. Katok and H. Weiss. 60637. Anniversaries of Sophus Lie's 150 birthday INFORMATION: A. Katok, 814-865-2266; and Nikolai Lobachevski's 200 birthday, ll-17. Arbeitsgemeinschaft mit Aktuellem [email protected] or R. Man­ Tartu (Estonia). (Feb. 1992, p. 148) Thema, Oberwolfach, Federal Republic of ning, 814-865-7527, Dept. of Math., Penn Germany. (Feb. 1991, p. 148) State Univ., University Park, PA 16802. November 1992. Workshop on Stochastic 12-16. IMA Workshop on Control Systems Control, Centre de Recherches Mathematiques, Quebec, Design for Advanced Engineering Systems: 22-30. Forty-sixth Conference and ·con­ Universite de Montreal, Montreal Complexity, Uncertainty, Information, and gress of the International Federation for Canada. (Apr. 1992, p. 349) Organization, Institute for Mathematics and Information and Documentation, Madrid, 1-6. The First Pan American Conference its Applications, University of Minnesota. Spain. (May/Jun. 1991, p. 477) on Pre-Columbia Mathematics, Astronomy, (Sep. 1991, p. 840) 25-31. Stochastische Analysis, Oberwol­ and Modes of Thought, Univ. Francisco 12-16. Workshop on Visualization of Ge­ fach, Federal Republic of Germany. (Feb. Marroquin, Guatamala City and Tikal. (Dec. ometric Structures, Mathematical Sciences 1991' p. 148) 1991, p. 1340) Research Institute, Berkeley, CA. (Jan. 1992, * 27-31. International Workshop on Modern 1-7. Kombinatorik, Oberwolfach, Federal p. 54) Group Analysis: Advanced Analytic and Republic of Germany. (Feb. 1991, p. 148)

MAY/JUNE 1992, VOLUME 39, NUMBER 5 493 Meetings and Conferences

2-6. Workshop on Symbolic Dynamics, Time and Technology will be the theme. Warwick, England. (Feb. 1992, p. 149) Mathematical Sciences Research Institute, L. Smarr (National Center for Supercom­ 27-31. Holiday Symposium on Lie Group Berkeley, CA. (Jan. 1992, p. 54) puting Application) will give the keynote Representations and Combinatorics, New * 7-11. Mathematics and Molecular Biology address "Grand Challenges". Special ses­ Mexico State University, Las Cruces, NM. ID: Computational Approaches to Nucleic sions on massively parallel vs "tradi­ (Sep. 1991, p. 840) Acid Structure and Function, Santa Fe, NM. tional" supercomputers, visualization, and machine clustering will be offered. Also, SESSIONS: Structural correlates of RNA special sessions dedicated to pharmaceu­ function, simulations of DNA structure, tical and medical issues relating to super­ 1993 simplified models of DNA, computation computers. 1992-1993. Mittag-Lemer Institute's Aca­ of DNA structures, measures of molecular INFORMATION: P. Sarnide, SC92 Confer­ demic Program for 1992-1993: Special evolution, RNA conformations, structural ence Office, SCD/NCAR, P.O. Box 3000, Problems in Mathematical Physics, Djur­ theory, and graphics programs. Boulder, CO 80307; 303-497-1808; Fax: sholm, Sweden. (Nov. 1991, p. 1171) CALL FOR PAPERS: Abstract deadline: 303-497-1298; [email protected]. Spring 1993. IMACS Symposium on Math­ September 15, 1992. 16-22. Workshop on Normal Forms, Ho­ ematical Modelling, Wiener Neustadt, Ger­ INFORMATION: PMMB, 103 Donner Lab­ many. (Jan. 1992, p. 54) oratory, U. of California, Berkeley, CA moclinic Bifurcations and Chaos, Fields In­ 94720; Fax: 510-642-4071; sylviaj@ stitute for Research in Mathematical Sciences, 1993. Second IMACS International Con­ violet. berkeley .edu. Waterloo, Ontario. (Apr. 1992, p. 350) ference on Computational Physics, Univ. of * 20-22. Academic Knowledge and Power, Colorado, Boulder, CO. (Jan. 1992, p. 55) 8-14. Numerische Integration, Ober­ University of Maryland, College Park, MD. wolfach, Federal Republic of Germany. (February 1991, p. 148) INFORMATION: R. Harvey, Dept. of Sociol­ January 1993 ogy, UMCP, 2112 Art Sociology Building, 8-14. Third Austrian Symposium on the College Park, MD 20742; 301-405-6392. 3-7. International Conference on Scientific History of Mathematics, Neuhofen an der Computation and Differential Equations, Ybbs (Lower Austria). (Mar. 1992, p. 249) 23-25. European Symposium on Research Auckland, New Zealand. (May/Jun. 1991, 9-13. IMA Workshop on Control and in Computer Security, Toulouse, France. p. 477) (Feb. 1992, p. 148) Optimal Design of Distributed Parameter 3-9. Grundlagen der Geometrie, Ober­ Systems, Institute for Mathematics and its 23-27. Seminaire Sud-Rhodanien de Ge­ wolfach, Federal Republic of Germany. (Jan. Applications, University of Minnesota. (Nov. ometric, Marseille, France. (Jan. 1992, p. 54) 1992, p. 55) 1991, p. 1171) 29-December 5. Theory of Large De­ 3-9. Extensions of Buildings and Ge­ 13-15. Second Joint Meeting of the Mid­ viations, Oberwolfach, Federal Republic of ometries, Oberwolfach, Federal Republic of west Conference on Ordinary Differential Germany. (Feb. 1991, p. 148) Germany. (Jan. 1992, p. 55) Equations and the Southeastern-Atlantic Regional Conference on Differential Equa­ 4-9. Advances in Computational Mathe­ matics, India International Center, New Delhi, tions, University of Kentucky, Lexington, December 1992 KY. (Apr. 1992, p. 349) India. (Feb. 1992, p. 149) 14-16. The Third Biennial Conference 2-4. Workshop on Curves, Abelian Vari­ * 10-15. First Panamerican Workshop in of the Allahabad Mathematical Society, eties, and their Moduli, Mathematical Sci­ Applied and Computational Mathematics, Allahabad, India. (May/Jun. 1991, p. 477) ences Research Institute, Berkeley, CA. (Jan. Simon Bolivar University, Caracas, Venezuela. 1992, p. 54) 15-20. An Applications Symposium on Op­ ORGANIZING COMMITTEE: (U.S.A. and tics, Electro-Optics, and Lasers in Industry, 4-5. International Workshop on Matrix Canada): P. Boggs, Vice Chairman (Na­ Boston, MA. (Feb. 1992, p. 148) Methods for Statistics, University of Auck­ tional Institute of Standards and Tech­ land, Auckland, New Zealand. (Feb. 1992, 15-21. Komplexitatstheorie, Oberwolfach, nology); J. Castillo, Chairman (San Diego p. 148) State U.); J. Dennis (Rice U.); R. O'Malley Federal Republic of Germany. (Feb. 1991, p. 148) 6-12. Theory and Numerical Methods for (U. of Washington); R. Russel (Simon Initial-Boundary Value Problems, Oberwol­ Fraser U.); S. Steinberg (U. of New Mex­ 16-18. Workshop on Higher Dimensional fach, Federal Republic of Germany. (Feb. ico); R. Tapia (Rice U.). Geometry, Mathematical Sciences Research 1991, p. 148) WORKSHOPS: Matrix analysis and com­ Institute, Berkeley, CA. (Jan. 1992, p. 54) 7-11. IMACS Symposium on Scientific putation; optimization; mathematical oil 16-20. International Congress on Numer­ Computing and Mathematical Modelling, recovery; network modelling; mathemat­ ical Methods in Engineering and Applied Bangalore, India. (May/Jun. 1991, p. 477) ics in industry; applied probability and Sciences, University of Concepcion, Con­ 8-11. International Conference on Com­ statistics; scientific computing; numerical cepcion, Chile. (Jul./Aug. 1991, p. 646) puter Science and Control, Paris, France. methods; numerical differential equations; 16-20. IMA Period of Concentration: Flow (Apr. 1992, p. 350) solving partial differential equations in Control, Institute for Mathematics and its irregular regions; applied sciences and 11-16. Workshop on Generalized Inverses­ engineering; and mathematical ecology. Applications, University of Minnesota. (Sep. Computational Techniques and Applica­ 1991, p. 840) INVITED TALKS: G. Ponce, J. Nocedal, tions, Indian Statistical Institute, Delhi, India. B. O'Malley, V. Pereyra, C. Grebogi, B. * 16-20. The Fifth Annual High Per- (Mar. 1992, p. 249) Cockburn, J. Koiller, H. Keller, D. Tapia, formance Computing and Communication 13-19. Asymptotische Statistik, Oberwol­ Conference-Supercomputing 92, Minneapo­ H. Simon. fach, Federal Republic of Germany. (Feb. SHORT CouRSES: P. Boggs and H. Simon. lis, MN. (Please note updated information to 1991, p. 148) Apr. 1992, p. 349) CALL FOR PAPERS: Send a one page ex­ 15-17. Third IMA Conference on Math­ tended abstract to the appropriate work­ PROGRAM: Voyages of Discovery through ematics Signal Processing, University of shop organizer by June 30, 1992.

494 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··························-.:~······ Meetings and Conferences

10-16. Computational Methods for Non­ 21-27. Curves, Images, Massive Com­ [email protected]. linear Phenomena, Oberwolfach, Federal Re­ putation, Oberwolfach, Federal Republic of public of Germany. (Jan. 1992, p. 55) Germany. (Jan. 1992, p. 55) 21-24. Sixth SIAM Conference on Par­ allel Processing for Scientific Computing, 13-16. Joint Mathematics Meetings, San 22-28. Workshop on Pattern Formation Norfolk, VA. (Mar. 1992, p. 250) Antonio, TX. (including the annual meetings and Symmetry Breaking, Fields Institute for of the AMS, AWM, MAA, and NAM) Research in Mathematical Sciences, Waterloo, 21-27. Analysis auf Lokalsymmetrischen Ontario. (Apr. 1992, p. 351) Raumen, Oberwolfach, Federal Republic of INFORMATION: H. Daly, AMS, P.O. Box Germany. (Jan. 1992, p. 55) 6887, Providence, RI 02940. * 25-March 1. A Conference on Numerical Analysis with Automatic Result Verifica­ 22-28. Workshop on Pattern Forma­ * 15-16. 1992-1993 ASL Winter Meeting, tion, Lafayette, LA. (Please note additional tion in Earth Sciences and Biology, Fields San Antonio, TX. information to Jan. 1992, p. 55) Institute for Research in Mathematical Sciences, Waterloo, Ontario. (Apr. 1992, PROGRAM: This meeting will be held in INVITED SPEAKERs: Partial List: F. Al­ p. 351) conjunction with the annual meeting of varado (Wisconsin), E. Hansen (Los Al­ 24-25. Central Section, DePaul University, the AMS. tos), A. Neumaier (U. Freiburg), M. Plum Chicago, IL. CALL FOR PAPERS: Deadline for abstracts: (U. Ki:iln), and S. Rump (U. Hamburg). October 1992. CALL FOR PAPERS: Abstracts due by Au­ INFORMATION: W. Drady, AMS, P.O. Box gust I, 1992. 6887, Providence, RI 02940. 17-22. 1993 IEEE International Sympo­ sium on Information Theory, San Antonio, 28-March 6. Medical Statistics: Statistical 28-April 3. Combinatorial Convexity and TX. (Feb. 1992, p. 149) Methods for Risk Assessment, Oberwolfach. Algebraic Geometry, Oberwolfach, Federal 17-23. Combinatorial Optimization, Ober­ Federal Republic of Germany. (Jan. 1992, Republic of Germany. (Jan. 1992, p. 56) wolfach, Federal Republic of Germany. (Jan. p. 55) * 29-April 2. Workshop on Diophantine 1992, p. 55) Geometry, Mathematical Sciences Research 24-30. Optimale Steuerung Partieller Dif­ Institute, Berkeley, CA. ferentialgleichungen, Oberwolfach, Federal March 1993 PRoGRAM: This workshop is part of the Republic of Germany. (Jan. 1992, p. 55) MSRI program on Transcendance and 7-13. Mathematische Stochastik, Oberwol­ *25-27. Fourth ACM-SIAM Symposium on Diophantine problems taking place during fach, Federal Republic of Germany. (Jan. Discrete Algorithms., Austin, Texas. (Please the second half of 1992-1993. 1992, p. 55) note update to Mar. 1992, p. 250) ORGANIZER: P. Vojta. 14-20. Gewohnliche Differentialgleichun­ 25-29. IMA Workshop on Robotics, In­ INFORMATION: I. Kaplansky, Director, Math­ gen, Oberwolfach, Federal Republic of Ger­ stitute for Mathematics and its Applications, ematical Sciences Research Institute, 1000 many. (Jan. 1992, p. 55) University of Minnesota, Minneapolis, MN. Centennial Dr., Berkeley, CA 94720. (Nov. 1991, p. 1171) 15-19. IMA Workshop on Systems and Control Theory for Power Systems, Insti­ 31-February 6. Asymptotics and Adaptivity tute for Mathematics and its Applications, in Computational Mechanics, Oberwolfach, University of Minnesota, Minneapolis, MN. April1993 Federal Republic of Germany. (Jan. 1992, (Nov. 1991, p. 1 172) p. 55) 4-10. Topics in Pseudo-Differential Op­ * 17-20. Pure and Applied Linear Algebra: erators, Oberwolfach, Federal Republic of The New Generation, University of West Germany. (Jan. 1992, p. 56) Florida, Pensacola, FL. 5-9. IMA Tutorial: Design and Analysis of February 1993 INVITED SPEAKERS: R. Bapat (Indian Sta­ Adaptive Systems, Institute for Mathematics 1-3. IMA Minisymposium on Biological tistical lust.), J. Cohen (The Rockefeller and its Applications, University of Minnesota, Control of Movement, Institute for Math­ U.), G. Cybenko (U. of Illinois), B. de Minneapolis, MN. (Nov. 1991, p. 1172) ematics and its Applications, University of Moor (Katholieke U. Leuven), R. Gural­ 9-10. Western Section, University of Utah, Minnesota, Minneapolis, MN. (Nov. 1991, nick (U. of Southern California), D. Her­ Salt Lake City, Utah. p. 1172) shkowitz (Technion-Israel lust. of Tech.), C.K. Li (College of William and Mary), R. INFORMATION: W. Drady, AMS, P.O. Box 7-13. Partielle Differentialgleichungen, 6887, Providence, RI 02940. Oberwo1fach, Federal Republic of Germany. Mathias (College of William and Mary), (Jan. 1992, p. 55) V. Mehrmann (U. Bielefeld), D. O'Leary I 1-17. Arbeitsgemeinschaft mit Aktuellem (U. of Maryland), A. Ran (U. Amster­ 8-17. IMA Workshop on Nonsmooth Anal­ Thema. Oberwolfach, Federal Republic of dam), H. Shapiro (Swarthmore College), Germany. (Jan. 1992, p. 56) ysis and Geometric Methods in Determin­ I. Zaballa (U. Del Pois Vasco). istic Optimal Control, Institute for Math­ BANQUET SPEAKER: P. Halmos (Santa 12-16. IMA Workshop on Adaptive Con­ ematics and its Applications, University of Clara U.). trol, Filtering, and Signal Processing, In­ Minnesota, Minneapolis, MN. (Mar. 1992, CALL FOR PAPERS: Participants are invited stitute for Mathematics and its Applications, p. 250) to present 10 to 15 minute talks on topics University of Minnesota, Minneapolis, MN. 14-20. Applicable Algebra, Oberwolfach, in linear algebra. Send an abstract, camera (Nov. 1991, p. 1172) Federal Republic of Germany. (Jan. 1992, ready, 7.5 inches wide by 5 inches long 14-16. Seventh SEFI European Seminar p. 55) with at most 4 lines per inch by January on Mathematics in Engineering Education, 16--25. IMA Workshop on Nonsmooth 20, 1993. Eindhoven University of Technology, The Analysis and Geometric Methods in Con­ INFORMATION: J.R. Weaver, Dept. of Netherlands. (Feb. 1992, p. 149) trol, Institute for Mathematics and its Applica­ Math. and Stats., 1000 University Park­ 15-22. Symposium on Analytic and Ge­ tions, University of Minnesota, Minneapolis, way, Univ. of West Florida, Pensacola, ometric Aspects of Hyperbolic Geometry: MN. (Nov. 1991, p. 1172) FL 32514-5751; 904-474-2283; email: Research Level Workshop, University of

MAY/JUNE 1992, VOLUME 39, NUMBER 5 495 ····················--···--····· "lli!d!!!Wlmllllll£1i!MII--Uml!il!l!~i!UBIIMIIII!I!I!IIi!l!l!l!l!lli!llli~R····-- ············-··-···-··-··-·-... ·... ···---········- ··········-··········--··­ Meetings and Conferences

Warwick, Coventry, UK. (Mar. 1992, p. 250) 6-9. Annual Meeting of the Statistical Probability, Ohio State University, Colum­ 18-24. The Arithmetik of Fields, Ober­ Society of Canada, Wolfville, Nova Scotia, bus, OH. Canada. (Feb. 1992, p. 149) wolfach, Federal Republic of Germany. (Jan. INFORMATION: J. Rosenblatt, Math. Dept., 1992, p. 56) 6-12. Analysis auf Kompakten Varietiiten, Ohio State University, 100 Mathematics 18-24. Mathematische Grundlagen und Oberwolfach, Federal Republic of Germany. Building, 231 West 18th Ave., Columbus, Numerische Verfahren bei Transsonischen (Jan. 1992, p. 56) OH 43210-1174; 614-292-4975. Stri:imungen, Oberwolfach, Federal Republic 7-II. IMA Tutorial: Mathematical Theory of Germany. (Jan. 1992, p. 56) which Has become an Integral Part of 27-July 3. Algebraische K-Theorie, Ober­ 25-May 1. Low Dimensional Dynamics, Modern Financial Economics, Institute for wolfach, Federal Republic of Germany. (Jan. Oberwolfach, Federal Republic of Germany. Mathematics and its Applications, University 1992, p. 57) (Jan. 1992, p. 56) of Minnesota, Minneapolis, MN. (Nov. 1991, p. 1172) 7-13. Workshop on Pattern Formation July 1993 May 1993 and Cellular Automata, Fields Institute for Research in Mathematical Sciences, Waterloo, * 6-9. European Multigrid Conference '93, 3-7. IMA Tutorial: Verification Issues in Ontario. (Apr. 1992, p. 352) Amsterdam, The Netherlands. Discrete Event Systems, as well as Per­ PRoGRAM: The conference aims at pro­ formance and Control, Institute for Math­ 13-19. Differential-Algebraic Equations: ematics and its Applications, University of Theory and Applications in Technical Sim­ viding a forum for the presentation and discussion of recent research in the general Minnesota, Minneapolis, MN. (Nov. 1991, ulation, Oberwolfach, Federal Republic of p. 1172) Germany. (Jan. 1992, p. 56) area of multilevel methods. The confer­ ence will consist of 10 invited lectures in 3-9. Workshop on Ecological Systems, * 14-17. The Fifth Asian Logic Conference, National University of Singapore, Singapore. plenary sessions and selected presentations Fields Institute for Research in Mathemati­ in two parallel sessions. cal Sciences, Waterloo, Ontario. (Apr. 1992, PROGRAM: The conference will cover all CONFERENCE THEMES: Computational fluid p. 352) major areas of mathematical logic, as well dynamics, reservoir engineering, semicon­ 9-15 ..Reelle Algebraische Geometrie, Ober­ as related areas in computer science. There ductor device modeling, statistical physics, wolfach, Federal Republic of Germany. (Jan. will be sessions for contributed papers. parallel computing, adaptive computing, 1992, p. 56) INVITED SPEAKERS: H.P. Barendregt, L. and numerical analysis of multigrid meth­ 10-12. IMACS Symposium on Signal Pro­ Blum, H.J. Keisler, W.J. Mitchell, T.A. ods. cessing and Neural Networks-SPANN '93, Slaman, L. van der Dries, and H. Woodin. CALL FOR PAPERS: Send three copies of Universite du Quebec at Montreal, Canada. CALL FOR PAPERS: Abstracts due by April an extended abstract of no more than 2 (Jan. 1992, p. 56) 1993. pages by December 15, 1992. 10-14. IMA Workshop on Discrete Event INFORMATION: Fifth Asian Logic Confer­ INFORMATION: EMG '93, European Multi­ Systems, Manufacturing Systems, and Com­ ence, Dept. of Math., National Univ. of grid Conference 1993, c/o CWI, Simone munication Networks, Institute for Mathe­ Singapore, Singapore 0511; email: mat­ van der Wolff, P.O. Box 4079, 1009 matics and its Applications, University of· [email protected]. AB Amsterdam, The Netherlands, tel: Minnesota, Minneapolis, MN. (Nov. 1991, 020-5929333; Fax: 020-5924199; email: p. 1172) 14-18. IMA Workshop on Mathematical [email protected]. Finance, Institute for Mathematics and its 16-22. Mathematical Problems in Vis­ Applications, University of Minnesota, Min­ * 12-23. Conference on Universal Algebra coelastic Flows, Oberwolfach, Federal Re­ neapolis, MN. (Nov. 1991, p. 1172) and Category Theory, Mathematical Sci­ public of Germany. (Jan. 1992, p. 56) * 14-18. Linear Logic Workshop, Mathe­ ences Research Institute, Berkeley, CA. 20-23. International Conference on Ap­ matical Sciences Institute, Cornell University, PRoGRAM: The aim of this conference is to proximation Probability and Related Fields, Ithaca, NY. bring together workers in the two fields in University of California, Santa Barbara, CA. (May/Jun. 1991, p. 477) PRoGRAM: The workshop will be held at question. In addition to research reports, Cornell and sponsored by MSI. Presen­ there will be tutorial lectures and time for 21-22. Central Section, Northern lllinois informal contacts. University, DeKalb, IL. tations will be by invitation only, but attendance will be open to anyone inter­ ORGANIZING COMMITTEE: F. Linton, S. INFORMATION: W.S. Drady, AMS, P.O. ested in the subject. MSI will be able Mac Lane (cochair), R. Mckenzie (cochair), G. McNulty, W. Taylor, and C. Wells. · Box 6887, Providence, RI 02940. to provide partial support for a limited number of participants. INFORMATION: I. Kaplansky, Director, Math­ 23-29. Differentialgeometrie im Grossen, ematical Sciences Research Institute, 1000 INFORMATION: J. Chiment, Mathemati­ Oberwolfach, Federal Republic of Germany. Centennial Dr., Berkeley, CA 94720. (Jan. 1992, p. 56) cal Sciences Institute, 409 College Ave., Ithaca, NY 14850; 607-255-8005; Fax: 30-June 5. Funktionalanalysis und Nicht­ 607-255-9003; email: jjc@ lineare Partielle Differentialgleichungen, cornellc.cit.cornell.edu. Oberwolfach, Federal Republic of Germany. August 1993 (Jan. 1992, p. 56) 15-18. Third IMACS International Work­ * 1-14. Groups 93 Galway/St. Andrews, shop on Qualitative Reasoning and Decision Galway, Ireland. (Please note additional in­ Technologies-QR&DT-3, Polytechnique of formation to Jan. 1992, p. 57) June 1993 Barcelona, Spain. (Jan. 1992, p. 56) ORGANIZERS: C.M. Campbell, T.C. Hur­ June 1993. Fourth IMACS International 20-26. Konvexgeometrie, Oberwolfach, Fed­ ley, E.F. Robertson, S. Tobin, J.J. Ward. Symposium on Computational Acoustics, eral Republic of Germany. (Jan. 1992, p. 56) INVITED SPEAKERS: J.L. Alperin, M. Broue, Cambridge, England. (Jan. 1992, p. 56) * 23-26. Convergence in Ergodic Theory and P.H. Kropholler, E.l. Zel'manov.

496 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY •••••••••••••-Y-~·~--·~···~~~oooooooooooooooooooooo••o•••••~•••oo••••• Meetings and Conferences

GAP WoRKSHOP: J. Neubiiser and M. INFORMATION: B. Goldsmith, Dublin lnst. ORGANIZING COMMITTEE: A. Donato (Mes­ Schonert. of Tech., Kevin Street, Dublin 8, Dept. sina), B. Engquist (UCLA), J. Glimm, INFORMATION: Groups 93, Mathematical of Math., Stats., and Comp. Sci., Tel: Chair (Stony Brook), B. Keyfitz (U. Hous­ Institute, St. Andrews, KY16 9SS, Fife, 757541; Fax: 780282; [email protected]. ton), P. Lax (NYU), T.-P. Liu (Stanford), Scotland; groups93 @st-andrews.ac.uk. D. Serre (Lyons). 22-29. Twenty-ninth International Con­ INFORMATION: T. Mills, Dept. of Applied * 2-6. Second Gauss Symposium, Munich, gress of History of Science, Zaragoza, Spain. Math., Univ. at Stony Brook, Stony Brook, Germany. (Apr. 1992, p. 352) NY 11794-3600; 516-632-9125; Fax: 516- 632-8490; [email protected]. PROGRAM: The theme of the symposium is the direct and indirect thrust of Gaus­ The following new announcements will not sian works in all areas of mathematical be repeated until the criteria in the last sciences. paragraph in the box at the beginning of CALL FOR PAPERS: One page abstract to this section are met. be submitted by January 31, 1993. August 1994 INFORMATION: Second Gauss Symposium, P.O. Box 56, McMaster University, Hamil­ September 1993 *'1-5. Third World Congress on Compu­ ton, Ontario, Canada L8S ICO; Fax: 416- tational Mechanics (WCCM Ill), Chiba, 332-4460. * 5-12. First World Conference on Branch- Japan. ing Processes, Varna, Bulgaria. PROGRAM: 1). An ambitious program will * 2-13. Georgia International Topology Con- INFORMATION: N.M. Yanev, Dept. of be planned to cover challenging topics ference, University of Georgia, Athens, GA. Probability and Statistics, Institute of in basic sciences and technologies. 2). PRoGRAM: The conference will cover a Mathematics, Bulgarian Academy of Sci­ A number of best papers will be given wide range of topics with emphasis on 3- ences, 8, G. Bontchev Str., Sofia 1113, awards through recommendations of an and 4-dimensional topology. There will be Bulgaria; Telex: 22628 BAN BG; Fax: international paper reviewing committee. about 20 invited lectures. + 359-2-752078. 3). Promising young researchers from all INFORMATION: W. Kazez, Math. Dept., over the world will be encouraged to * 13-18. Different Aspects of Differentiabil- attend. The WCCM III is expected to be Univ. of Georgia, Athens, GA 30602; ity, Warsaw, Poland. email: [email protected]; 404-542- a forum to communicate ideas and new 2544. CONFERENCE TOPICS: Algebraic analysis; developments from a wide range of views. operational calculi; generalized functions; Researchers and engineers interested in the * 17-20. The Mathematical Heritage of Sir related convergence problems; structures field are welcome. William Rowan Hamilton, Dublin, Ireland. with derivation; subdifferentials, their gen­ CONGRESS THEMES: Mathematical mod­ eralizations and applications to optimiza­ eling and numerical methods; solid and PRoGRAM: October 16, 1993 marks the tion. structural mechanics; fluid dynamics; non­ sesquicentennial of the discovery of the ORGANIZERS: P. Antosik and D. Przeworska­ linear dynamics; material science; CAD/ quatemions by Hamilton. This event marks Rolewicz. CAM/CAE, AI, expert system, CG; smart the final break between algebra and arith­ INFORMATION: D-A-D, Inst. of Math., Pol­ algorithms and adaptive methods; paral­ metic. To celebrate this occasion, an in­ ish Academy of Sciences, Sniadseckich 8, lel computing; computational physics; and ternational conference on algebra, combi­ 00-950 Warszawa, Poland; Fax: 0048-22- industrial applications. natorics, and dynamical systems has been 293997; [email protected]. INFORMATION: T. Kawai, WCCM Ill Of­ organized by the Royal Irish Academy in fice, Dept. of Electrical Engineering, Sci­ Trinity College, Dublin. ence U. of Tokyo, 1-3 Kagurazaka, Shijuku­ INVITED SPEAKERS: N.L. Biggs (L.S.E., June 1994 ku, Tokyo 162, Japan; tel: +81-3-3235- London), J.K. Moser (ETH, Zurich), P.M. 5630; Fax: +81-3-3260-8236. Neumann (Queens College, Oxford), A.C. * 13-17. Fifth International Conference on Newell (Tucson, AZ), C. Procesi (La Hyperbolic Problems Theory, Numerical 3-11. The International Congress of Math­ Sapienza, Roma), G.-C. Rota (MIT, Cam­ Methods, and Applications, Stony Brook, ematicans 1994, Ziirich, Switzerland. (Mar. bridge). NY. 1992, p. 249)

MAY/JUNE 1992, VOLUME 39, NUMBER 5 497 New Publications Offered by the AMS

A.'df.RICAN MATHF~'dATICAL SUClElY CF::-rrENNJAL Pl.liJUCATIONS Mathematics into the lnt~n;~tl~nal Proceedings of the 'Ji>flllllrll Congress of Twenty-first Century Mathematicians International Congress of Matliematics into tlie 'Iwentyfirst Century Felix E. Browder, Editor Mathematicians, Kyoto, ~ In the summer of 1988 in 1990 Providence, the AMS celebrated its Vo\umcsl,ll lchiro Satake, Editor Centennial with a wide range of mathematical activities. Among those Held every four years, was a symposium, "Mathematics the International Congress of lMMa!bematiCI!SodetyofJapan Mathematicians features the frontier into the Twenty-first Century," which Sprinpr-Vcrlllll "'J~·· brought together a number of the top mathematics of the day. Each Congress research mathematicians who will likely is a historic event: a time for taking have a significant impact on the mathematics of the next century. stock of current results in the development of the field, a time for This book contains the lectures presented by sixteen of the eighteen lauding the mathematical stars of the day, and a time for camaraderie individuals who spoke during the symposium. Written by some of within the international mathematical community. the m_ajor international figures in mathematical research, this group Published by Springer-Verlag, this two-volume set captures the of articles covers a panorama of the vital areas of mathematics in the spirit of ICM-90, featuring the official record of the Congress, photos present epoch and will give the general mathematical reader a broad from the opening ceremonies and other events, reports on the works perspective on some of the major trends in research today. of Fields Medalists and the Nevanlinna Prize Winner, the Plenary Addresses, and the Invited Addresses. If you were at ICM-90, you'll Contents want this special publication as a memento. And if you missed F. E. Browder, Introduction; M. Aschbacher, Representations offinite groups ICM-90, you'll want it to stay informed about one of the most as permutation groups; L. A. Caffarelli, Regularity of solutions and level important conferences in mathematics. surfaces of elliptic equations; P. Diaconis, Sufficiency as statistical symmetry; (The AMS also offers a series of videotapes featuring several C. FetTerman, Atoms and analytic number theory; M. H. Freedman, Working ICM-90 lectures, suitable for viewing in class and at home. Call for a and playing with the 2-disk; H. Friedman, The incompleteness phenomena; free brochure.) B. H. Gross, Elliptic curves and modular forms; J, Harris, Developments Contents in algebraic geometry; R. Howe, A century of Lie theory; V. F. R. Jones, Vol. 2: The work of the Fields Medalists and the RolfNevanlinna Prize Winner; From quantum theory to knot theory and back: a von Neumann algebra Invited one-hour addresses at the plenary sessions; Invited forty-five minute excursion; V. G. Kac, Modular invariance in mathematics and physics; addresses at the section meetings; 1. Mathematical logic and foundations; A. J,_ Majda, Mathematical fluid dynamics: the interaction of nonlinear 2. Algebra; 3. Number theory; 4. Geometry; 5. Topology; 6. Algebraic analysis and modem applied mathematics; C. S. Peskin, Two examples of geometry; 1. Lie groups and representations; 8. Real and complex analysis; mathematics and computing in the biological sciences: Blood flow in the heart 9. Operator algebras and functional analysis; 10. Probability and mathematical and molecular dynamics; D. Sullivan, Bounds, quadratic differentials, and statistics; 11. Partial differential equaitons; 12. Ordinary differential equations renormalization conjectures; K. Uhlenbeck, Instantons and their relatives; and dynamical systems; 13. Mathematical physics; 14. Combinatorics; E. Witten, Geometry and quantum field theory. 15. Mathematical aspects of computer science; 16. Computational methods; 1991 Mathematics Subject Classifications: 00-02, OOA69, OOB10, OOB20 17. Applications of mathematics to the- sciences; 18. History, teaching, and the ISBN 0-8218-0167-8, LC 91-22093 nature of mathematics. 491 pages (hardcover), May 1992 Individual member $99, List price $165, Institutional member $132 1991 Mathematics Subject Classifications: 00 To order, please specify HMBROWDERIN ISBN 4-431-70047-1, LC 91-4972 1684 pages (hardcover), 1991 List price $160 To order, please specify PICM/90N

*The AMS distributes this book in the United States, Canada, and Mexico. O~rs from other countri~s should be sent to Springer-Verlag, 49-6221-4870, Ttergartenstr. 17, 6900 Hetdelberg, Germany.

Use the order form in the back of this issue or call 800-321-4AMS (800-321-4267) in the U.S. and Canada to use VISA or MasterCard.

498 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ______11111111111111' New Publications Offered by the AMS

L___A_ov_A_N_c_E_s_I_N_s_o_v_IE_T_M_A_T_H_E_M_A_TI_c_s_l Ll __c_o_N_T_E_M_P_o_R_A_Rv_M_A_T_HE_M_A_T_Ic_s _ _....J

Representation Theory New Approaches in and Dynamical Systems Spectral Decomposition A. M. Vershik, Editor Ridgley Lange and Volume 9 Shengwang Wang Spectral"-"'""""""'-"' DecomiiO'IIIon This volume presents research Volume 128 conducted between 1989 and 1991 by Aimed at a general mathematical the participants in the Leningrad Seminar audience, this book provides a careful on representation theory, dynamical exposition of recent developments in systems, and their applications, headed • the theory of spectral decomposition. by A. M. Vershik. The primary areas Bringing the reader from the basics up covered here are mathematical physics, to the level of current research in the area, Lange and Wang present a Lie groups and their representations, infinite-dimensional groups, readable account of the techniques used in the theory and applications topology, and dynamical systems. The book contains a number of of decomposable operators and related classes of operators. The book useful introductory surveys; for example, one paper by Vaksman and begins with a discussion of criteria for decomposable and related types Solbelman provides a systematic description of the theory of quantum of operators, and an analysis that relates and distinguishes among groups in the spirit of representation theory-a new and popular area them. Perturbation theory of decomposable and other operators, for which there are few introductory surveys. A portion of the book applications to classical Hilbert space operators, quasisimilarity, and a is devoted to adic transformations and substitutions, a new area of new class of weakly decomposable operators are also discussed. The ergodic theory. With a balance of survey papers and frontier research book closes with an exposition of some classical theories on invariant results, this book will appeal to graduate students and researchers subspaces for subdecomposable and hyponormal operators, and a alike. presentation of the parallel spectral theory of commuting systems. Contents Contents Part I. Quantum Groups, Representations of Groups and Algebras Foundations; Perturbation theory; Weakly decomposable operators and Ya. S. Soibelman and L. L. Vaksman, On some problems in the theory of automatic continuity; Invariant subspaces for subdecomposable operators; quantum groups; E. Ye. Vaysleb, Representations of quantum *-algebras Multivariate theory. slt(N + l,JR); S. V. Kerov, Generalized Hall-Littlewood symmetric functions and orthogonal polynomials; A.M. Vershik and B. S. Tsirelson, 1991 Mathematics Subject Classifications: 47Al0, 47Al3, 47Al5, 47A55, Formulation of Bell type problems and "noncommutative" convex geometry; 47B20, 47B40; 46El0, 46E35, 46F05, 46JI5, 46M20, 46M40, 47A53, 47A60, 47BIO, 47B15,47B66, 47F05 M. L. Nazarov, Projective representations of the infinite symmetric group; ISBN 0-8218-5139-X, LC 92-6183, ISSN 0271-4132 V. L. Ostrovskii and Yu. S. Samonenko, Structure theorems for a pair 273 pages (softcover), June 1992 of unbounded selfadjoint operators satisfying a quadratic relation; L. I. Individual member $26, List price $44, Institutional member $35 Vainerman, Relations between compact quantum groups· and Kac algebras; To order, please specify CONM/128N A. I. Barvinok, Combinatorial complexity of orbits in representations of the symmetric group; Part II. Dynamical Systems and Approximations Oscillation and Dynamics A.M. Vershik and A. N. Livshits, Adic models of ergodic transformations, spectral theory, substitutions, and related topics; D. Yu. Burago, Periodic in Delay Equations metrics; D. Yu. Burago, Flows with positive entropy; B. Solomyak, On the John R. Graef spectral theory of adic transformations; M. Solomyak, On simultaneous and Jack K. Hale, action of Markov shift and adic transformation; A. N. Livshits, About a Editors certain weakly mixing substitution; V. N. Berestovskii and A.M. Vershik, Manifolds with intrinsic metric, and nonholonomic spaces. Volume 129 1991 Mathematics Subject Classifications: 03015, 05A99, 20C30, 20C32, 28005, 46K10, 46L55, 53C20, 58A30, 58B30, 58F17, 81R50; 05A20, 20C30, Oscillation theory and dynamical • systems have long been rich and active 22A30, 22025, 330, 46L05, 53C20, 68Q14, 70F25 ISBN 0-8218-4108-4, LC 91-640741, ISSN 1051-8037 areas of research. Containing frontier 267 pages (hardcover), June 1992 contributions by some of the leaders in the field, this book brings Individual member $70, List price $116, Institutional member $93 together papers based on presentations at the AMS meeting in To order, please specify ADVSOV/9N San Francisco in January, 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modeling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications. Contents S. J. Bilchev, M. K. Grammatikopoulos, and I. P. Stavroulakis, Oscillations of second-order neutral differential equations with deviating arguments;

MAY/JUNE 1992, VOLUME 39, NUMBER 5 499 New Publications Offered by the AMS

T. A. Burton, J, Terjeki, and B. Zhang, A wave equation viewed as an and primitive ideals in enveloping algebras of solvable Lie superalgebras; ordinary differential equation; Y. Cao, The oscillation and exponential W. May, Endomorphism algebras of not necessarily cotorsion-free modules; decay rate of solutions of differential delay equations; S.-N. Chow and J, C. McConnell and R. B. Warfield, Jr., Direct sum decompositions of W. Huang, Transition layers for a singularly perturbed 2-dimensional system vector spaces equipped with linear and bilinear forms; G. 0. Michler, of differential-difference equations; H. G. Diamond and H. Halberstam, Maximal orders and deformations of modular group algebras; R. Mines and Differential difference equations in analytic number theory; A. M. Farahani C. Vinsonhaler, Butler groups and Bext: A constructive view; B. J. Miiller, and E. A. Grove, A simple model for price fluctuations in a single commodity Goldie-prime serial rings; J, Osterburg, D. S. Passman, and D. Quinn, A market; J. R. Graef, M. K. Grammatikopoulos, and P. W. Spikes, Some Connes spectrum for Hopf algebras; R. S Pierce, Minimal regular rings; results on the asymptotic behavior of the solutions of a second order nonlinear C. E. Praeger and P. Schultz, The Loewy length of the Jacobson radical of neutral delay equation; G. Ladas and C. Qian, Linearized oscillations for a bounded endomorphism ring; J. D. Reid, Warfield duality and irreducible nonautonomous delay difference equations; S.M. Verduyn Lunel, Small groups; F. Richman, The constructive theory of countably generated Warfield solutions and completeness for linear junctional differential equations; H. L. modules; D. J, Saltman, A note on generic division algebras. Smith and Y. Kuang, Periodic solutions of differential delay equations with 1991 Mathematics Subject Classifications: 16-06, 20-06, 16Pxx, 16Sxx, threshold-type delays; H.-0. Walther, Unstable manifolds of periodic orbits 20Kxx; 16Dxx, 16Exx of a differential delay equation; J. Wiener and L. Debnath, The Fourier ISBN 0-8218-5142-x, LC 92-13697, ISSN 0271-4132 method for partial differential equations with piecewise continuous delay. 394 pages (softcover), June 1992 1991 Mathematics Subject Classifications: 34-06, 34K05, 34Kl0, 34K15, Individual member $29, List price $49, Institutional member $39 To order, please specify CONM/130N 34K25, 34K30, 34K40, 34A05, 34Cl0, 34Cll, 34C15, 34E05, 34E10, 11N25, 35B05, 35B25, 35B40, 35Ll0, 39Al2,45El0, 58F09 ISBN 0-8218-5140-3, LC 92-12229, ISSN 0271-4132 263 pages (softcover), June 1992 Individual member $22, List price $36, Institutional member $29 Proceedings of the To order, please specify CONM/129N International Con­ ference on Algebra Abelian Groups and Dedicated to the Memory Proceedings of the Noncommutative Rings: International Conference on Algebra Dedicated of A. I. Mal' cev A Collection of Papers to the Memory of A. I. Mal'cev L.A. Bokut', Yu. L. Ershov, in Memory of Robert B. Abelian Groups and A. I. Kostrikin, Editors and Noncommutatlve Ring•: Warfield, Jr. A Collection of Papers In Memory Volume 131 of Robert B. Warfield, Jr. L. Fuchs, K. R. Goodearl, J. T. Stafford, and In August 1989, more than 700 Soviet algebraists and more than 200 C. Vinsonhaler, Editors foreign mathematicians convened in Novosibirsk in the former Soviet Volume 130 Union for the International Conference on Algebra. Dedicated to the memory of A. I. Mru'cev, the great Russian algebraist and logician, This collection of research papers is the conference marked the first time since dedicated to the memory of the distinguished algebraist Robert B. the International Congress of Mathematicians was held in Warfield, Jr. Focusing on abelian group theory and noncommutative Moscow in 1966 that Soviet algebraists could meet with a large number of ring theory, the book covers a wide range of topics reflecting their foreign colleagues. This volume contains the proceedings from Warfield's interests and includes two articles surveying his this historic conference. Some of the Soviet contributions to this volume contributions to mathematics. Because the articles have been refereed are not easily available from other sources. to high standards and will not appear elsewhere, this volume is Some of the major figures in the field, including indispensable to any researcher in noncommutative ring theory or P. M. Cohn, P. Gabriel, N. Jacobson, E. R. Kolchin, and V. abelian group theory. With papers by some of the major leaders in the Platonov, contributed to this volume. The papers span a broad range field, this book will also be important to anyone interested in these of areas including groups, Lie algebras, associative areas, as it provides an overview of current research directions. and nonassociative rings, fields and skew fields, differential algebra, universal algebra, categories, Contents combinatorics, logic, algebraic geometry, geometry, topology, and Robert Breckenridge Warfield, Jr.; C. Vinsonhaler, The abelian group papers mathematical physics. of Robert B. Warfield, Jr.; K. R. Goodearl and J, T. Stafford, Warfield in Contents ring theory; U. Albrecht, Endomorphism rings, tensor products, and Fuchs' Section 1: Groups; Section 2: Geometry; Section 3: Lie algebras; problem 47; R. Behler, R. GObel, and R. Mines, Endomorphism rings of Section 4: Rings; Section 5: Fields and skew fields/differential algebras; p-groups having length cojinal with w; A. D. Bell, Skew differential operators Section 6: Nonassociative rings; Section 7: Universal algebra, categories, on commutative rings; G. M. Bergman, Isomorphisms from top to bottom; and combinatorics; Section 8: Algebraic geometry; Section 9: Logic. A. Braun, Power intersection in Noetherian P.l. rings; K. A. Brown and M. Lorenz, Colimits of functors and Grothendieck groups of infinite group 1991 Mathematics Subject Classifications: 00, 03, 06, 08, 12, 13, 14, 16, 17, algebras; P. M. Cohn, Modules over hereditary rings; A. van den Essen 18, 20, 22, 51; 05, 11, 15, 19, 53 ISBN (Set) 0-8218-5134-9; ISBN (Part 1) 0-8218-5136-5; ISBN (Part 2) and A. H. M. Levelt, An explicit description of all simple k[[x]][8]-modules; 0-8218-5137-3; ISBN (Part 3) 0-8218-5138-1, LC 92-9983, ISSN 0271-4132; L. Fuchs and C. Metelli, Countable Butler groups; K. R. Goodearl, An 712 pages (Part 1); 704 pages (Part 2); 666 pages (Part 3) (softcover), unbounded localizable clique; I. Herzog, The Auslander-Reiten translate; May 1992 Set: B. Zimmermann Huisgen, On the abundance of N1-separable modules; Individual member $124, List price $206, Institutional member $165 R. S. Irving, Graded BGG algebras; D. A. Jordan, Krull and global Part 1: Individual member $48, List price $80, Institutional member $64 Part 2: Individual member $47, List price $79, Institutional member $63 dimension of certain iterated skew polynomial rings; G. Krause, Prime factor Part 3: Individual member $42, List price $70, Institutional member $56 series of modules over a Noetherian algebra; T. H. Lenagan, Enveloping To order, please specify CONM/131N (Set), CONM/131.1N (Part 1), algebras of solvable Lie superalgebras are catenary; E. S. Letzter, Prime CONM/131.2N (Part 2), CONM/131.3N (Part 3)

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

Laplacian in Euclidean spaces, elementary solutions, smoothness TRANSLATIONS OF MATHEMATICAL of solutions, Vishik-Sobolev problems, the Schauder theory, and MONOGRAPHS degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers Complements of will appreciate this book for the way it brings together a variety of Discriminants of techniques that have arisen in different branches of mathematics. Smooth Maps: Topology Contents and Applications Partial differential operators of elliptic type; The Laplacian in Euclidean V. A. Vassiliev spaces; Constructions and estimates of elementary solutions; Smoothness Volume 98 of solutions; Vishik-Sobolev problems; General boundary value problems; Schauder estimates and applications; Degenerate elliptic operators. This book examines a wide class of topological spaces, including many 1991 Mathematics Subject Classifications: 35-02; 35A, 35B, 35J that play important roles in differential ISBN 0-8218-4556-X, LC 92-2953, ISSN 0065-9282 and homotopy topology, algebraic 288 pages (hardcover), May 1992 geometry, and catastrophe theory. Among these are spaces of Morse Individual member $79, List price $132, Institutional member $106 To order, please specify MMON0/99N and generalized Morse functions, iterated loop spaces of spheres, classifying spaces of braid groups, and spaces of knots. Vassiliev develops a general method for investigating such spaces topologically, providing new proofs and generalizations of many results. One of the book's main results is a system of knot invariants which is stronger than all known polynomial invariants. In addition, an important Groups, Generators, relationship between topology and complexity theory is used to obtain Syzygies, and Orbits the best known estimates for the numbers of branchings of algorithms in Invariant Theory solving polynomial equations. A major contribution to the field of algebraic topology, this V. L. Popov book provides the first comprehensive report on these developments. Volume 100 Vassiliev, whose results have proved especially fruitful in recent research in knot theory, is a major leader in the field. This book will The history of invariant theory spans interest mathematicians in differential and homotopy topology and nearly a century and a half, with roots complexity theory, as well as physicists interested in string theory in certain problems from number theory, and Feynman diagrams. It is also suitable as a textbook for graduate algebra, and geometry appearing in courses in topology, catastrophe theory, and, to a more limited extent, the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the complexity theory. connection between invariants and. orbits was essentially discovered Contents in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant Cohomology of braid groups and configuration spaces; Applications: theory was in fact subsumed by a general theory of algebraic groups. complexity of algorithms, and superpositions of algebraic functions; Written by one of the major leaders in the field, this book Topology of spaces of real functions without complicated singularities; provides an excellent, comprehensive exposition of invariant theory. Stable cohomology of complements of discriminants and caustics of isolated Its point of view is unique in that it combines both modem and singularities of holomorphic functions; Cohomology of the space of knots; classical approaches to the subject. The introductory chapter sets the Appendix 1: Classifying spaces and universal bundles. Join; Appendix 2: Hopf historical stage for the subject, helping to make the book accessible algebras and H-spaces; Appendix 3: Loop spaces; Appendix 4: Germs, jets, to nonspecialists. and transversality theorems; Appendix 5: Homology of local systems. 1991 Mathematics Subject Classifications: 55P53, 57M25, 57R45 Contents ISBN 0-8218-4555-1, LC 92-8176, ISSN 0065-9282 The role of reductive groups in invariant theory; Constructive invariant 208 pages (hardcover), June 1992 theory; The degree of the Poincare series of the algebra of invariants and Individual member $98, List price $164, Institutional member $131 a finiteness theorem for representations with free algebra of invariants; To order, please specify MMON0/98N Syzygies in invariant theory; Representations with free modules of covariants; A classification of normal affine quasihomogeneous varieties of SL:!; Quasihomogeneous curves, surfaces, and solids. Partial Differential 1991 Mathematics Subject Classifications: l4D25, 14L30; 14Jl0, 20G20 Operators of Elliptic Type ISBN 0-8218-4557-8, LC 92-10604, ISSN 0065-9282 Norio Shimakura 245 pages (hardcover), June 1992 Volume 99 Individual member $109, List price $181, Institutional member $145 To order, please specify MMON0/100N This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the

MAY/JUNE 1992, VOLUME 39, NUMBER 5 501 .. ·························-·······-----...... _.. _._ ...... _. ------····-·------··························---····New Publications Offered by the AMS

Qualitative Theory of Contents Differential Equations The geometry of Neumann systems; A Neumann system for the AKNS problem; Zhang Zhi-fen, Ding The divisor map; Hamiltonian formalism; The Neumann system; Bibliography. Tong-ren, Huang Wen­ 1991 Mathematics Subject Classifications: 58F07; 35Q20, 58F05, 58Fl9, 17B65, 14H40 zao, and Dong Zhen-xi ISBN 0-8218-2537-2, LC 92-6951, ISSN 0065-9266 (Translated from the 59 pages (softcover), May 1992 Individual member $14, List price $23, Institutional member $18 Chinese by Anthony To order, please specify MEM0/467N Wing-Kwok Leung) Volume 101 This book provides an introduction - l\']1 \]\ l'l<"' Intersections of Thick to and a comprehensive study of the qualitative theory of ordinary Cantor Sets differential equations. It begins with fundamental theorems on ~ Roger Kraft existence, uniqueness, and initial conditions, and discusses basic principles in dynamical systems and Poincare-Bendixson theory. Number 468 The authors present a careful analysis of solutions near critical Problems in dynamical systems points of linear and nonlinear planar systems and discuss indices involving homoclinic tangencies, of planar critical points. A very thorough study of limit cycles homoclinic bifurcations, and the is given, including many results on quadratic systems and recent creation of horseshoes have led to the developments in China. Other topics included are: the critical point problem of analyzing the difference sets at infinity, harmonic solutions for periodic differential equations, {tlr n (r' + t) i 0} of Cantor sets r systems of ordinary differential equations on the torus, and structural and r' embedded in the real line. In this stability for systems on two-dimensional manifolds. This book would work, the author proves two theorems about difference sets of Cantor be accessible to graduate students and advanced undergraduates and sets, both of which involve the concept of the thickness of a Cantor would also be of interest to researchers in this area. Exercises are set. The first gives conditions on the thicknesses of two Cantor sets included at the end of each chapter. that determine if the intersection of the two Cantor sets must contain a Cantor set or if the intersection may, in a nontrivial way, be as Contents small as one point. The second theorem states that if the product of Fundamental theorems; Critical points on the plane; Indices of planar the thicknesses of two Cantor sets is strictly greater than one, then for critical points; Limit cycles; Critical points at infinity; Harmonic solutions for a generic point t in their difference set, r n (r' + t) contains a Cantor two-dimensional periodic systems; Systems of ordinary differential equations set. on the torus; Structural stability. Contents 1991 Mathematics Subject Classifications: 34; 34A, 34C, 34D ISBN 0-8218-4551-9, LC 91-23961, ISSN 0065-9282 Theorems and examples; Cantor sets and thickness; Proof of Theorem 1.2; 461 pages (hardcover), May 1992 Third kind of overlapped point; Second Kind of overlapped point; First kind of Individual member $173, List price $288, Institutional member $230 overlapped point; The dynamics of lT! rr'; Results about the geometric process; To order, please specify MMON0/101N Proof of Theorem 6.2(1); The boundary between A1 and A2 ; Proof of Theorem 1.1. MEMOIRS OF THE AMS 1991 Mathematics Subject Classifications: 58Fl4, 34C37, 54F50, 28A80 ISBN 0-8218-2528-3, LC 92-6942, ISSN 0065-9266 119 pages (softcover), May 1992 Individual member $16, List price $26, Institutional member $21 - To order, please specify MEM0/468N \~1! \:; )l l,ic.~, Neumann Systems for the ~ - Algebraic AKNS Problem \Jl\](1!-- Eigenvalues of the Randolph J. Schilling Laplacian for Heeke Number 467 - Triangle Groups The Neumann system, an algebraically completely integrable Dennis A. Hejhal Hamiltonian system, consists of Number469 harmonic oscillators constrained to This work is concerned with move on the unit sphere in configuration • computational aspects of the Selberg • space. Any finite gap potential of Hill's ,_ trace formalism. In this area, equation may be expressed in terms of i computing the discrete spectrum of the a solution to the Neumann problem. The present work is concerned ' non-Euclidean Laplacian is especially with an algebraically completely integrable Hamiltonian system important. Heeke triangle groups represent one of the simplest whose solutions may be used to describe the finite gap solutions possible cofinite settings for this type of problem. In addition to of the AKNS spectral problem, a first order two-by-two matrix considering the usual type of eigenfunction, the author discusses an linear system. Trace formulas, constraints, Lax pairs, and constants updated analysis of pseudo cusp forms and their residual effects. The of motion are obtained using Krichever' s algebraic inverse spectral actual computer code, run on a Cray supercomputer, is included in transform. Computations are carried out explicitly over the class of the appendices. Possibilities for further work, both theoretical and spectral problems with square matrix coefficients. computational, are examined.

502 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Contents 1991 Mathematics Subject Classification: 05 Eigenvalues of the Laplacian for Heeke triangle groups; (Reprint of) ISBN 0-8218-8064-0 Eigenvalues of the Laplacian for P S L(2, Z) : Some new results and NTSC format on l/2" VHS videotape; approx. one hour, May 1992 computational techniques. Individual member $29.95, List price $49.95, Institutional member $39.95 To order, please specify VIDE0/68N 1991 Mathematics Subject Classifications: 1 IF30, I IF72, 30F35, 35P05, 65N35 ISBN 0-8218-2529-l, LC 92-6943, ISSN 0065-9266 The Theory and 165 pages (softcover), May 1992 Individual member $19, List price $29, Institutional member $23 Applications of Harmonic To order, please specify MEM0/469N Mappings between Riemannian Manifolds VIDEOTAPES Richard M. Schoen Over the last fifteen years, there have been numerous results in harmonic maps, making it an important area Compound Soap Bubbles, having ramifications in other branches Shortest Networks, of mathematics. Richard Schoen, one of the major figures in the field, provides an excellent introduction to the and Minimal Surfaces field in this expository lecture. He discusses existence, uniqueness, Frank Morgan and regularity questions, as well as various applications of the theory. The study of soap bubbles has long In addition, he explains the great differences in the theory depending fascinated mathematicians and children on the sign of the curvature of the target manifold or space. The alike. In this polished and engaging Bochner method and the application to rigidity questions for discrete videotaped lecture, Frank Morgan shares groups is also covered. Requiring little background in harmonic his passion for soap bubbles and related maps, the lecture is aimed at the level of advanced undergraduates or topics. The lecture balances intuitive graduate students. enjoyment and mathematical rigor, indicating the daunting technical 1991 Mathematics Subject Classifications: 35, 49, 53, 58 challenges the subject poses. Morgan sprinkles enough open questions ISBN 0-8218-8065-9 throughout the lecture to intrigue anyone--for example, it is unknown NTSC format on l/2" VHS videotape; approx. one hour and a half, May 1992 whether the common triple bubble succeeds in minimizing surface Individual member $29.95, List price $49.95, Institutional member $39.95 area, or whether there is some as yet undiscovered configuration that To order, please specify VIDE0/69N encloses the same three volumes with less area. In an entertaining twist, Morgan has the audience vote on which configurations comprise the least area-and the answers are often surprising. Combining Algorithms in Algebraic intuitive pictures, personal touches, challenging open questions, and Number Theory humor, this lecture will spark the interest of students and researchers alike. It would be accessible to undergraduate mathematics majors. H. W. Lenstra, Jr. Algorithms in algebraic number 1991 Mathematics Subject Classifications: 53, 49 theory are as old as the field itself. ISBN 0-8218-8063-2 Traditionally, the users of such NTSC format on l/2" VHS videotape; approx. one hour, May 1992 Individual member $29.95, List price $49.95, Institutional member $39.95 algorithms were number theorists To order, please specify VIDE0/67N needing to do computations in algebraic number fields. However, recent applications, such as factoring large Laplacians of Graphs integers, have changed this situation. In this videotape, Lenstra presents a clear, well-paced, and fascinating and Hypergraphs lecture on some of the fundamental questions arising in this area. He Fan R. K. Chung formulates the basic problems of algorithmic algebraic number theory "Can you hear the shape of a in rigorous terms, explaining what advances have been made and graph?" may sound like a nonsensical where work still needs to be done. The main topic of the lecture is twist on the famous drum problem, but the investigation of the multiplicative structure of rings of algebraic in fact it captures an intriguing analogy integers, the principal tool being a group that simultaneously describes between manifolds and graphs. In this the class group and the group of units of such a ring. Lenstra shows clear and well-paced lecture, the noted that the study of algorithms not only increases understanding of graph theorist Fan Chung exploits this algebraic number fields, but also stimulates curiosity about them. For analogy to produce some interesting and this reason, the lecture would be an excellent addition to a course useful results. She starts with a historical perspective on graphs, their touching on these topics. It is accessible to advanced undergraduates uses in computer science, and their inherent mathematical interest. and graduate students with backgrounds in algebra and number theory. She discusses Laplacians of graphs and hypergraphs from both the 1991 Mathematics Subject Classifications: 11Y40, 11YI6, 11R65 homological and graph theoretical viewpoints. The eigenvalues of ISBN 0-8218-8066-7 the Laplacians can be related to various properties of hypergraphs NTSC format on l/2" VHS videotape; approx. one hour and a half, May 1992 and used to strengthen and imply previous graph-theoretic results. A Individual member $29.95, List price $49.95, Institutional member $39.95 variety of applications to extremal combinatorics and computational To order, please specify VIDE0/70N complexity are discussed, in addition to a number of open problems.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 503 New Publications Offered by the AMS

Mathematics under Bertrand, Nombres de Perron et problemes de rationalite; M. Car, Le Hardship Conditions probleme de Waring pour les corps de fonctions; J. Cherly, Resolution du probleme de Waring pour les cubes dans F2 [X]; P. Cohen and J. Wolfart, in the Third World Monodromie des fonctions d'Appell, varietes abeliennes, et prolongement Neal I. Koblitz modulaire; E. Dubois and R. P.-Le Roux, Sur la longueur du developpement en fraction continue de ..J!(iiJ; W. Duke, Sums over Primes of the Fourier What is the situation for mathematics N. Distribution of in the Third World? In this lively coefficients of Half-integral weight cusp forms; Elkies, work on the square root and controversial videotaped lecture, supersingular primes; B. Erez, A survey of recent D. R. Heath-Brown, The number of abelian groups Koblitz examines such questions as of the inverse different; after bombieri and why mathematics research flourishes of order at most x; M. N. Huxley, Exponential sums R 1 ; J. F. Jaulent, in Vietuam, while other countries lwaniec; D.-O. Jaquet, Classification des reseaux dans absolues; M. Laurent, Sur quelques resultats contend with "brain drain" to the U.S. and Europe. He also looks at Noyau universe[ et valeurs R. Massy, Surles Bases normales d'entiers mathematics education in Central America, where the "New Math" recents de transcendance; On recurrences for some hypergeometric type craze took hold, sometimes with disastrous results. Some of the stories relatives; T. Matala-Aho, Elliptic curves, primality proving, and some he relates show the deprivation and nearly overwhelming problems, polynomials; F. Morain, titanic primes; L. Murata, On the magnitude of the least primitive root; while other stories describe people of great tenacity, resourcefulness, Wagner, Duffin-Schaeffer theorem on diophantine and heroism. At the end of his lecture, he suggests specific actions B. Nakada and G. numbers; J. Pas, Some applications of uniform that individuals and mathematics organizations can take to help keep approximation for complex p-adic cell decomposition; R. Queme, On diophantine approximation by mathematics alive and growing in the Third World. Anyone with an a given number field; P. Rambour, Elements fixes du interest in international issues of mathematics research and education algebraic numbers of separable sous !'action de son groupe de Galois; will enjoy this eye-opening lecture. complete d'une cloture P. Satge, Quelques problemes de rationalite lies au theoreme de Poncelet; 1991 Mathematics Subject Classifications: 01, 00 N. Schappacher, Les conjectures de beilinson pour les courbes elliptiques; ISBN 0-8218-8067-5 B. P. Schlickewei, Resultats quantitatifs en approximation diophantienne; NTSC format on 1/2" VHS videotape; approx. one hour, May 1992 J.-P. Serre, Motifs; J.-P. Serre, Lettre a M. Tsjasman; C. Soule, Geometrie Individual member $29.95, List price $49.95, Institutional member $39.95 d'Arakelov et theorie des nombres transcendants; M. Tsfasman, Global fields, To order, please specify VIDEOn1N codes, amf sphere packings; W. Veys, Relations between numerical data of an imbedded resolution. 1991 Mathematics Subject Classifications: 11, 12, 14 ISSN 0303-1179 405 pages (softcover), 1992 SOCIETE MATHEMATIQUE DE FRANCE, ASTERISQUE Individual AMS or SMF member $41, List price $58 To order, please specify AST/198/200N

The AMS distributes Asterisque only in the U.S., Canada, and Mexico. Orders from other countries should be sent to the Maison de la SMF, Case 916, Luminy, 13288 Marseille Cedex 9, France or to OFF!Lm, 48 rue Gay-Lussac, 75240 Paris Cedex 05, France. Individual members of either AMS or SMF are entitled to the member price. (ISSN 0303-1179) Seminaire Bourbaki Number 201-202-203 ASTERISQUE This volume grew out ot the Bourbaki Seminar and consists of fifteen survey lectures on a variety of current research topics. In particular, there are expositions of recent results on the Journees Arithmetiques geometry of Brownian motion in the de Luminy, 17-21 Juillet plane, the Riemann-Roch theorem in 1989 Arakelov geometry, the determination ~-~iQIJU of indecomposable knots by the .. J.VMINY G. Lachaud, Editor fundamental group of their complement, Floer homology, Igusa's 11·11 J1JlldAT 1l8t Number 198-199-200 zeta function, the combinatorics of resultants, and representations of Every two years, the "Journees quantum groups. Arithmetiques" present a wide panorama Contents on the state of the art in number theory. This book contains five reports on recent G. B. Arous, Geometrie de la courbe brownienne plane; J.-B. Bost, Theorie progress in a variety of areas, including de !'intersection et theoreme de Riemann-Roch arithmetiques; A. Gramain, Rapport sur la theorie classique des noeuds (2eme partie); J.-C. Sikorav, tra~sendence; the Beilinson conjectures for elliptic curves; motives (w1th three texts by A. Grothendieck); Arakelov geometry and Homologie associee a une fonctionnelle [d'apres A. Floer]; J.-C. Yoccoz, transcendental number theory; and global fields, codes, and sphere Polynomes quadratiques et attracteur de Henon; F. Comets, Limites packings. The volume contains more than twenty-six papers presented hydrodynamiques; G. Benniart, Representations des groupes reductifs by the conference participants. p-adiques; J. Le Potier, Fibres de Higgs et systemes locaux; P. Pansu, Le jlot geodesique des varietes riemanniennes a courbure negative; G. Skandalis, Contents Approche de la conjecture de Novikov par Ia cohomologie cyclique [d'apres J, P. Allouche, Sur la transcendance de la serie formelle IT; A. M. Berge A. Connes, M. Gromov et H. Moscovic1]; J.-P. Bourguignon, Stabilite and J. Martinet, Reseaux extremes pour un groupe d'automorphismes; A. par deformation non-lineaire de Ia metrique de Minkowski [d'apres D.

504 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY '!Ill b! m; #llfilf""""" ...... _ ...... New Publications Offered by the AMS

Christadaulau et S. Klainennan]; J. Denef, Report an lgusa's local zeta 1991 Mathematics Subject Classification: 00 function; F. Loeser, Polytopes secondaires et discriminants; 0. Mathieu, ISSN 0303-1179 Bases des representations des graupes simples complexes [d'apres Kashiwara, 512 pages (softcover), 1992 Lusztig, Ringel et al.]; M. Rosso, Representations des groupes quantiques; Individual AMS or SMF member $50, List price $73 G. Henniart, Erratum a l'expase 711. To order, please specify AST/201/203N

Proceedings of the International Congress of Mathematicians Kyoto, 1990 Ichiro Satake, Editor

Held every four years, the ICM features the frontier mathematics of the day. Each Congress is a historic event: a time for taking stock of current results in the development of the field, a time for lauding the mathematical stars of the day, and a time for camaraderie within the international mathematical community. This two-volume set, published by Springer-Verlag, captures the spirit of ICM-90, featuring the official record of the Congress, photos from the opening ceremonies and other events, reports on the works of Fields Medalists and the Nevanlinna Prize Winner, the Plenary Addresses, and the Invited Addresses. If you were at ICM-90, you'll want this special publication as a memento. If you missed ICM-90, you'll want it to stay informed about one of the most important confer­ ences in mathematics.

1991 Mathematics Subject Classifications: 00 ISBN 0-387-70047-1, 1684 pp. (hardcover), 1991 List price $160. Your ordering code is PICM/90NA

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. The AMS distributes this book in the United States, Canada, and Mexico. Write to American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST. Orders from other countries should be sent to Springer-Verlag, 49-6221-4870, Tiergartenstr. 17, 6900 Heidelberg, Germany.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 505 Selected books from AMS warehouse overstock. 70% Discount on most titles!

Discount applies only to the books on the following pages. DIRECT SALES ONLY. NOT AVAILABLE TO BOOKSTORES OR AGENTS. Orders must be sent on the special Warehouse Sale form (or facsimile). For telephone orders, please specify Warehouse Sale to ensure proper discount. Sale ends July 16, 1992.

Code List Sale Code List Sale Code List Sale

Ten lectures on operator algebras, Automated theorem proving: After 25 years, CBMS Regional Conference William Arveson, reprinted 1988, 93 pp. edited by W. W. Bledsoe and D. W. Loveland, CBMS/55WS $21 $6 reprinted 1985, 360 pp. Series in Mathematics CONM/29WS $40 $12 Prescribing the curvature of a Riemannian manifold, Jerry L. Kazdan, reprinted 1988, 55 pp. Four-manifold theory, edited by Cameron Gordon Algebraic and analytic aspects of operator CBMS/57WS $18 $5 and Robion C. Kirby, reprinted 1988,528 pp. algebras, I. Kaplansky, reprinted 1980,20 pp. CONM/35WS $54 $16 CBMS/1WS $16 $5 Barish-Chandra homomorphisms for P·adic groups, Roger Howe, 1985, 76 pp. Combinatorial methods in topology and algebraic Twisted honeycombs, H.S.M. Coxeter, 1970, 47 pp. CBMS/59WS $18 $5 geometry, edited by John R. Harper and CBMS/4WS $15 $5 Richard Mandelbaum, reprinted 1988, 349 pp. Factorization of linear operators and geometry of CONM/44WS $42 $13 Holomorphic vector fields on compact Kahler Banach spaces, Gilles Pisier, reprinted 1987, 154 pp. manifolds, Y. Matsushima, 1971, 38 pp. CBMS/60WS $24 $7 Random matrices and their applications, CBMS/7WS $15 $5 edited by J. E. Cohen, H. Kesten, Minimax methods in critical point theory with and C. M. Newman, reprinted 1988, 358 pp. Notes from a ring theory conference, applications to differential equations, Paul H. CONM/50WS $41 $12 I. N. Herstein, 1971, 38 pp. Rabinowitz, reprinted 1988, 110 pp. CBMS/9WS $15 $5 CBMS/65WS $22 $7 Logic and combinatorics, edited by Stephen G. Simpson, reprinted 1990, 394 pp. Automata on infinite objects and Church's CONM/65WS $44 $13 problem, M. Rabin, reprinted 1982, 22 pp. Colloquium Publications CBMS/13WS $17 $5 Statistical inference from stochastic processes, edited by N. U. Prabhu, 1988, 386 pp. CONM/80WS $42 $13 Lectures on linear groups, 0. T. O'Meara, Structure and representations of Jordan algebras, third printing 1988, 87 pp. N. Jacobson, 1968, 453 pp. CBMsnzws $18 $5 COLL/39WS $50 $15 Index of Mathematical Papers Approximation with rational functions, D. J. Newman, reprinted 1981, 52 pp. CBMS/41WS $18 $5 Contemporary Mathematics Index of Mathematical Papers, Mathematical Reviews Indexes, July-December 1970. Special functions and linear representations of IMP/1 WS $89 $27 Lie groups, Jean Dieudonne, reprinted 1982,59 pp. Proceedings of the conference on integration, CBMS/42WS $17 $5 topology, and geometry in linear spaces, edited by William H. Graves, 1980, 269 pp. Rudiments of Ramsey theory, Ronald L. Graham, CONM/2WS $26 $8 Lectures reprinted 1983, 65 pp. in Applied Mathematics CBMS/45WS $14 $4 Problems of elastic stability and vibrations, edited by Vadim Komkov, 1981, 137 pp. CONM/4WS $16 $5 Topics in dynamic bifurcation theory, Jack K. Lectures in statistical mechanics, G. E. Uh1enbeck, Hale, reprinted 1983, 84 pp. G. W. Ford, and E. W. Montroll, reprinted 1986, CBMS/47WS $14 $4 Plane ellipticity and related problems, edited by Robert P. Gilbert, 1982,245 pp. 181 pp. LAM/1WS $43 $13 Brown-Peterson homology: an introduction and CONM/llWS $32 $10 sampler, W. Stephen Wilson, reprinted 1988, 86 pp. Space mathematics, Part 2, edited by J. B. Rosser, CBMS/48WS $17 $5 Proceedings of the Northwestern homotopy theory conference, edited by Haynes R. Miller reprinted 1974,258 pp. LAM/6WS $43 $13 Structure of factors and automorphism groups, and Stewart B. Priddy, 1983, 454 pp. CONM/19WS $40 $12 Masamichi Takesaki, 1983, 107 pp. Mathematical problems in the geophysical CBMS/51WS $25 $8 Value distribution theory and its applications, sciences. 1. Geophysical fluid dynamics, edited by Chung-Chun Yang, 1984, 253 pp. edited by W. H. Reid, 1971, 383 pp. CONM/25WS $38 $11 LAM/13WS $63 $19

506 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... _ .... _•.. _. __ ...... ------··------AMS Warehouse Sale

Code List Sale Code List Sale Code List Sale

Mathematical problems in the geophysical Twisted polynomial hyperalgebras, E. Halpern, Hitting probabilities of single points for processes sciences. 2. Inverse problems, dynamo theory, reprinted 1972,61 pp. with stationary independent increments, and tides, edited by W. H. Reid, 1971, 370 pp. MEM0/29WS $18 $5 lf, Kesten, 1969, 129 pp. LAM/14WS $60 $18 MEM0/93WS $16 $5 Isoclinic n-planes in Euclidean 2n-space, Clifford Mathematical aspects of physiology, parallels in elliptic (2n-1) -space, and the Hurwitz Equivariant maps of spheres into the classical edited by Frank C. Hoppensteadt, 1981,394 pp. matrix equations, Y.-C. Wong, reprinted 1971, groups, J. Folkman, 1971, 42 pp. LAM/19WS $58 $17 112pp. MEM0/95WS $15 $5 MEM0/41WS $17 $5 Fluid dynamics in astrophysics and geophysics, Intrinsic measures on complex manifolds edited by Norman R. Lebovitz, 1983, 269 pp. Foundations of relative homological algebra, and holomorphic mappings, D. A. Eisenman, 1970, LAM/20WS $67 $20 S. Eilenberg and J. C. Moore, reprinted 1966, 39 pp. 80pp. MEM0/55WS $15 $5 MEM0/96WS $15 $5 Lectures on Mathematics Torsion in SU-bordism, P. E. Conner Isometric embeddings of Riemannian and pseudo­ and E. E. Floyd, reprinted 1969,72 pp. Riemannian manifolds, R. E. Green, 1970, 63 pp. in the Life Sciences MEM0/60WS $16 $5 MEM0/97WS $15 $5 Projections onto translation-invariant subspaces Similarity of automorphisms of the torus, Some mathematical questions in biology. II, of U (G), H. P. Rosenthal, 1966, 84 pp. R. L. Adler and B. Weiss, 1970,43 pp. edited by J.D. Cowan, 1972, 121 pp. MEM0/63WS $15 $5 MEM0/98WS $15 $5 LLSCI/3WS $26 $8 Deformation theory of pseudogroup structures, Properties of planar graphs with uniform vertex Some mathematical questions in biology. III, V. Guillemin and S. Sternberg, 1966, 80 pp. and face structure, J. Malkevitch, 1970, 116 pp. edited by J.D. Cowan, 1972, 151 pp. MEM0/64WS $15 $5 MEM0/99WS $15 $5 LLSCI/4WS $30 $9 On the enumeration of non-planar maps, Unoriented bordism and actions of finite groups, Some mathematical questions in biology. IV, W. G. Brown, 1966, 42 pp. R. E. Stong, 1970, 80 pp. edited by J. D. Cowan, 1973, 150 pp. MEM0/65WS $15 $5 MEM0/103WS $15 $5 LLSCIISWS $37 $11 The undecidability of the domino problem, Octonion planes defined by quadratic Jordan Some mathematical questions in biology. V, R. Berger, 1966, 72 pp. algebras, J. R. Faulkner, 1970,71 pp. edited by J. D. Cowan, 1974, 141 pp. MEM0/66WS $15 $5 MEM0/104WS $15 $5 LLSCI/6WS $29 $9 The modified algorithm of Jacobi-Perron, Compactly covered reflections, extension Some mathematical questions in biology. IX, L. Bernstein, 1966,44 pp. of uniform dualities and generalized almost edited by Simon A. Levin, 1978, 244 pp. MEM0/67WS $15 $5 periodicity, M. H. Powell, 1970,235 pp. LLSCI/10WS $35 $11 MEM0/105WS $16 $5 The metastable homotopy of S", M. Mahowald, Some mathematical questions in biology. X, 1967,81 pp. Numbers with small prime factors, and the least edited by Simon A. Levin, 1979, 179 pp. MEMOn2WS $15 $5 kth power non-residue, K. K. Norton, 1971, 106 pp. LLSCI/11 WS $26 $8 MEM0/106 $15 $5 Two papers on similarity of certain Volterra Some mathematical questions in biology, integral operators, S. J. Osher, 1967, 47 pp. Cellular decompositions of 3-manifolds that yield edited by Simon A. Levin, 1979,218 pp. MEMOn3WS $15 $5 3-manifolds, S. Armentrout, 1971,72 pp. LLSCI/12WS $33 $10 MEM0/107WS $15 $5 A class of functional equations of neutral type, Some mathematical questions in biology, J. K. Hale and K. R. Meyer, 1967, 65 pp. Asymptotic behavior of solutions and adjunction edited by George F. Oster, 1980,274 pp. MEMOn6WS $15 $5 fields for nonlinear first order differential equa­ LLSCI/13WS $36 $11 tions, W. Strodt and R. K. Wright, 1971,284 pp. Measurable, continuous, and smooth vectors MEM0/109WS $16 $5 Some mathematical questions in biology­ for semigroups and group representations, Neurobiology, edited by Robert M. Miura, 1982, R. T. Moore, 1968, 80 pp. On the mixed problem for a hyperbolic equation, 122 pp. MEMonsws $15 $5 T. Balaban, 1971, 117 pp. LLSCI/15WS $29 $9 MEM0/112WS $15 $5 Denjoy integration in abstract spaces, D. W. Solomon, 1969, 69 pp. Structures in topology, D. Harris, 1971,96 pp. Memoirs of the American MEM0/85WS $15 $5 MEMOI115WS $15 $5 Mathematical Society Souslinoid and analytic sets in a general setting, Constructive measure theory, E. Bishop A. H. Kruse, 1969, 127 pp. and H. Cheng, 1972, 85 pp. MEM0/86WS $15 $5 MEMOI116WS $15 $5 The decomposition of Walsh and Fourier series, I. I. Hirschman, fourth printing 1983, 65 pp. An extension of Mackey's method to Banach Extensions of positive-definite functions, MEM0/15WS $20 $6 *-algebraic bundles, J.M.G. Fell, 1969, 168 pp. J. R. McMullen, 1972,71 pp. MEM0/90WS $16 $5 MEMOI117WS $15 $5 Produits tensoriels topologiques et espaces nucl&ires, A. Grothendieck, sixth printing 1979, 336 pp. A conformal mapping technique for infinitely The Cauchy-Goursat problem, P. DuChateau, MEM0/16WS $25 $8 connected regions, M.G. Arsove and G. Johnson, 1972, 60pp. Jr., 1970, 56 pp. MEM0/118WS $15 $5 The generalized Pontrjagin cohomology MEM0/91WS $15 $5 operations and rings with divided powers, On A.-nuclearity, E. Dubinsky and M. S. Ramanujan, Emery Thomas, reprinted 1968, 82 pp. Doubly timelike surfaces, J. K. Beem 1972, 101 pp. MEM0/27WS $16 $5 and P. Y. Woo,_1969, 115 pp. MEM0/128WS $16 $5 MEM0/92WS $15 $5 Cohomology groups and genera of higher­ On summability methods for conjugate Fourier­ dimensional fields, E. Snapper, third printing 1971 , Stieltjes integrals in several variables and 100pp. generalizations, T. Walsh, 1973, 103 pp. MEM0/28WS $16 $5 MEM0/131WS $18 $5

MAY/JUNE 1992, VOLUME 39, NUMBER 5 507 ------·-·-······----·--""""-"'-""---·-··-AMS Warehouse Sale .. -·_ .... ,._... __ .... __ ~

Code List Sale Code List Sale Code List Sale

Extension theory of formally normal The fundamental principle for systems and symmetric subspaces, E. A. Coddington, 1973, of convolution equations, Daniele Carlo Struppa, · Translations of Mathematical 80pp. 1982, 167 pp. MEM0/134WS $16 $5 MEM0/273WS $18 $5 Monographs Canonical differential operatorS and lower-order P,homotopy equivalences have a-cross sections, symbols, R. J. V. Jackson, 1973,235 pp. Luis Montejano, 1982, 37 pp. Harmonic analysis of functions of several complex MEM0/135WS $18 $5 MEM0/274WS $15 $5 variables in the classical domains, L. K. Hua, translated by L. Ebner and A. Koninyi, Unitary representations on partially holomorphic Algebraic K-theory ;.nd localised stable homotopy fourth printing 1986, 186 pp. cohomology spaces, J. A. Wolf, 1974, 152 pp. theory, Victor P. Snaith, 1983, 102 pp. MMON0/6WS $37 $11 MEM0/138WS $17 $5 MEM0/280WS $18 $5 Additive theory of prime numbers, L. K. Hua, Derivations and automorphisms of Banach Intersection calculus on surfaces with applications translated by N. H. Ng, 1965, 190 pp. algebras of power series, S. Grabiner, 1974, 124 pp. to 3-manifolds, John Hempel, 1983,48 pp. MMON0/13WS $40 $12 MEM0/146WS $17 $5 MEM0/282WS $15 $5 Intrinsic geometry of surfaces, A. D. Aleksandrov Uniform simplification in a full neighborhood Geometrical methods in congruence modular and V. A. Zalgaller; translated by J. M. Danskin, ofa transition point, Y. Sibuya, 1974, 106 pp. algebras, H. Peter Gumm, 1983, 79 pp. 1967,327 pp. MEM0/149WS $16 $5 MEM0/286WS $14 $4 MMON0/15WS $42 $13 Equilibrium states on thin energy shells, Irreducible triangular algebras, Baruch Solei, Expansions in eigenfunctions of selfadjoint R. L. Thompson, 1974, 110 pp. 1984,87 pp. operators, Ju. M. Berezanskll; translated by MEM0/150WS $17 $5 MEM0/290WS $15 $5 R. Bolstein, J. M. Danskin, J. Rovnyak, and L. Shulman, 1968, 809 pp. Sur les sections analytiques de Ia courbe Nonmodular lattice varieties, Henry Rose, 1984, MMON0/17WS $88 $26 universelle de Teichmiiller, J. H. Hubbard, 1976, 76pp. 137pp. MEM0/292WS $15 $5 The operator of translation along the trajectories MEM0/166WS $21 $6 of differential equations, M. A. Krasnosel 'skir; Maximal functions measuring smoothness, Ronald translated by Scripta Technica, 1968, 294 pp. Parametrized knot theory, S. Ocken, 1976, 114 pp. A. DeVore and Robert C. Sharpley, 1984, 116 pp. MMON0/19WS $49 $15 MEM0/170WS $21 $6 MEM0/293WS $17 $5 Statistical problems with nuisance parameters, Local surgery and the exact sequence Theoremes d'indices Gevrey pour les equations Ju. V. Linnik; translated by Scripta Technica, 1968, of a localization for Wall groups, William Pardon, ditTerentielles ordinaires, Jean-Pierre Ramis, 1984, 258pp. 1977, 171 pp. 95pp. MMON0/20WS $42 $13 MEM0/196WS $21 $6 MEM0/296WS $16 $5 Constructive real numbers and function spaces, Boundary-interior layer interactions in nonlinear Essays in the history of mathematics, George B. N. A. ~anin; translated by E. Mendelson, 1968, singular perturbation theory, F. A. Howes, Dantzig, Lars Garding, Frank C. Hoppensteadt, Kurt 325 pp. reprinted 1982, 108 pp. Kreith, Jerzy Neyman, Ralph Price, and Wolfgang MMON0/21WS $56 $17 MEM0/203WS $20 $6 Wasow, edited by Arthur Schlissel, reprinted 1987, 74pp. Mahler's problem in metric number theory, V. G. Symmetric structures in Banach spaces, MEM0/298WS $15 $5 Sprind!uk; translated by B. Volkmann, 1969, 192 pp. W. B. Johnson, B. Maurey, G. Schechtman, MMON0/25WS $34 $10 and L. Tzafriri, reprinted 1980, 298 pp. The structure of shock waves in magnetohydrody­ MEM0/217WS $21 $6 namics, Mahmud Hesaaraki, 1984, 96 pp. The Stefan problem, L. I. Rubin~teln; translated MEM0/302WS $16 $5 by A. Solomon, 1971, 419 pp. Primary homotopy theory, Joseph Neisendorfer, MMON0/27WS $74 $22 reprinted 1983, 67 pp. Multipliers of radical Banach algebras of power MEM0/232WS $15 $5 series, W. G. Bade, H. G. Dales, and K. B. Laursen, The functional method and its applications, 1984, 84 pp. ' E. V. Voronovskaja; translated by R. P. Boas, 1970, The degenerate principal series for Sp(2n), MEM0/303WS $16 $5 203 pp. Robert Gustafson, 1981, 81 pp. MMON0/28WS $53 $16 MEM0/248WS $15 $5 Dimensions of spaces of Siegel cusp forms of degree two and three, Minking Eie, 1984, 184 pp. Differential equations of the second order with On Villamayor and Zelinsky's long exact MEM0/304WS $16 $5 retarded argument. Some problems of the theory sequence, Mitsuhiro Takeuchi, 1981, 178 pp. of vibrations of systems with retardation, MEM0/249WS $18 $5 The lattice of interpretability types of varieties, S. B. Norkin; translated by L. J. Grimm 0. C. Garcia and W. Taylor, 1984, 125 pp. and K. Schmitt, 1972, 285 pp. Global structural stability of flows on open MEM0/305WS $18 $5 MMON0/31WS $53 $16 surfaces, Janina Kotus, Michal Krych, and Zbigniew Nitecki, reprinted 1983, 109 pp. The unfolding and determinacy theorems for Triangular and Jordan representations of linear MEM0/261WS $18 $5 subgroups of sil and 'X, James Damon, 1984, 88 pp. operators, M.S. Brodskll; translated MEM0/306WS $16 $5 by J. M. Danskin, 1972, 246 pp. The cohomology of Chevalley groups of excep­ MMON0/32WS $45 $14 tional Lie type, Samuel N. Kleinerman, 1982, 82 pp. Attractors representing turbulent flows, MEM0/268WS $15 $5 PeterS. Constantin, Ciprian Foias, Operators, oscillations, waves, M. S. Liv§ic; and Roger Temam, reprinted 1988, 67 pp. translated by Scripta Technica Ltd., 1973,274 pp. C*-bundles and compact transformation groups, MEM0/314WS $17 $5 MMON0/34WS $63 $19 Broce D. Evans, 1982,63 pp. MEM0/269WS $15 $5 Nonlinear stability of shock waves for viscous Theory of convex programming, E. G. Gol'~tern; conservation laws, Tai-Ping Lui, reprinted 1988, translated by K. Makowski; translation edited The symplectic cobordism ring n. 109 pp. by R. T. Rockafellar, 1972,57 pp. Stanley 0. Kochman, 1982, 170 pp. MEM0/328WS $20 $6 MMON0/36WS $34 $10 MEM0/271WS $18 $5

508 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Code List Sale Code List Sale Code List Sale

Projection-iterative methods for solution Mathematical developments arising from lfilbert of operator equations; trans!. by Israel Program for problems, edited by F. E. Browder, SIAM-AMS Proceedings Scientific Translations; trans!. edited by R. G. third printing 1976, 628 pp. Douglas, N. S. Kurpel', 1976, 196 pp. PSPUM/28WS $43 $13 MMON0/46WS $58 $17 Transport theory, edited by I. K. Aub-Shumays, Automorphic forms, representations R. Bellman, and G. Birkhoff, 1969, 327 pp. Differential forms orthogonal to holomorphic and L-functions, Part 1, edited by A. Borel SIAMS/lWS $40 $12 functions or forms, and their properties, and W. Casselman, third printing 1990, 322 pp. L.A. Alzenberg and Sh. A. Dautov, 1983, 165 pp. PSPUM/33.1 WS $35 $11 Numerical solution of field problems MMON0/56WS $50 $15 in continuum physics, edited by G. Birkhoff Automorphic forms, representations, and R. S. Varga, 1970, 280 pp. and L-functions, Part 2, edited by A. Borel SIAMS/2WS $37 $11 Proceedings of Symposia in and W. Casselman, third printing 1990, 382 pp. PSPUM/33.2WS $35 $11 Mathematical aspects of electrical network Applied Mathematics analysis, edited by F. Harary and H. S. Wilf, 1971, Harmonic analysis in Euclidean spaces, Part 1, 206pp. edited by Guido Weiss and Stephen Wainger, SIAMS/3WS $36 $11 Wave motion and vibration theory, reprinted 1981, 460 pp. edited by A. E. Heins, 1954, 169 pp. PSPUM/35.1WS $45 $14 Mathematical aspects of statistical mechanics, PSAPM/5WS $34 $10 edited by J.C.T. Pool, 1972, 89 pp. Harmonic analysis in Euclidean spaces, Part 1, SIAMS/5WS $32 $10 Numerical analysis, edited by Gene H. Golub edited by Guido Weiss and Stephen Wainger, and Joseph Oliger, third printing 1985, 135 pp. reprinted 1981,438 pp. Stochastic differential equations, edited PSAPM/22WS $20 $6 PSPUM/35.2WS $42 $13 by J. B. Keller and H. P. McKean, 1973, 209 pp. SIAMS/6WS $53 $16 Modem statistics: methods and applications, Geometry of the Laplace operator, edited by Robert V. Hogg, 1980, 110 pp. edited by Robert Osserman and Alan Weinstein, Mathematical aspects of chemical and PSAPM/23WS $22 $7 reprinted 1982, 323 pp. biochemical problems and quantum chemistry, PSPUM/36WS $40 $12 edited by D. S. Cohen, 1974, 153 pp. Game theory and its applications, edited SIAMS/8WS $43 $13 by William F. Lucas, reprinted 1983, 136 pp. Operator algebras and applications, Part 1, PSAPM/24WS $21 $6 edited by Richard V. Kadison, 1982, 632 pp. Nonlinear programming, edited by R. W. Cottle PSPUM/38.1WS $64 $19 and C. E. Lemke, reprinted 1980, 200 pp. Operations research mathematics and models, SIAMS/9WS $26 $8 edited by Saul I. Gass, reprinted 1983, 198 pp. Operator algebras and applications, Part 2, PSAPM/25WS $18 $5 edited by Richard V. Kadison, 1982,625 pp. Fracture mechanics, edited by Robert Burridge, PSPUM/38.2WS $64 $19 1979, 169 pp. The mathematics of networks, edited by Stefan A. SIAMS/12WS $29 $9 Burr, reprinted 1984, 142 pp. The mathematical heritage of Henri Poincare, PSAPM/26WS $24 $7 Parts I and 2 as a set, edited by Felix E. Browder, reprinted 1984, 905 pp. Selected Translations Computed tomography, edited by Lawrence A. PSPUM/39WS $104 $31 Shepp, reprinted 1986, 86 pp. in Mathematical Statistics PSAPM/27WS $22 $7 Singularities, Part I, edited by Peter Orlik, 1983, 676pp. and Probability Applied cryptology, cryptographic protocols, and PSPUM/40.IWS $77 $23 computer security models, edited by Richard A. DeMilio, George I. Davida, David P. Dobkin, Singularities, Part 2, edited by Peter Orlik, 1983, Twenty-five papers on statistics and probability, Michael A. Harrison, and Richard J. Lipton, 680pp. 1961, 306 pp. reprinted 1985, 192 pp. PSPUM/40.2WS $77 $23 STAPRO/lWS $49 $15 PSAPM/29WS $33 $10 Complex analysis of several variables, Twenty-two papers on statistics and probability, Population biology, edited by Simon A. Levin, edited by Yum-Tong Siu, 1984,297 pp. 1966, 274 pp. 1984, 101 pp. PSPUM/41WS $67 $20 STAPR0/6WS $47 $14 PSAPM/30WS $30 $9 Recursion theory, edited by Ani! Nerode Eleven papers from the fourth Prague conference Environmental and natural resources mathemat­ and Richard A. Shore, 1985, 528 pp. on information theory, statistical decision ics, edited by Robert W. McKelvey, 1985, 143 pp. PSPUM/42WS $79 $24 functions, and random processes, 1970, 221 pp. PSAPM/32WS $38 $11 STAPR0/8WS $40 $12 Pseudodifferential operators and applications, Fair allocation, edited by H. Peyton Young, 1985, edited by Franr,:ois Treves, 1985,301 pp. Twenty-two papers on statistics and probability, 170 pp. PSPUM/43WS $58 $17 1973, 279 pp. PSAPM/33WS $30 $9 STAPR0/11WS $43 $13 Geometric measure theory and the calculus of variations, edited by William K. Allard Twenty papers on statistics and probability, 1973, Proceedings of Symposia and Frederick J. Almgren, Jr., 1986, 464 pp. 312 pp. PSPUM/44WS $72 $22 STAPR0/12WS $60 $18 in Pure Mathematics Twenty papers on statistics and probability, 1973, Reviews 298 pp. Differential geometry, Part 1, edited by S. S. Chern ST APR0/13WS $72 $22 and R. Osserman, reprinted 1982,451 pp. PSPUM/27.1WS $63 $19 Reviews of Papers in Alg!lbraic and Differential Topology, Topological Groups, and Homological Differential geometry, Part 2, edited by S. S. Chern Algebra, 1940-(;7, edited by Norman E. Steenrod, and R. Osserman, reprinted 1982,443 pp. 1969, 1448 pp. PSPUM/27.2WS $70 $21 REVTOP/WS $91 $27

MAY/JUNE 1992, VOLUME 39, NUMBER 5 509 ...... ·-······-···-······· .. ···-·"·······················"'""""""-····--·········"""""""""""""""""""""" ______AMS Warehouse Sale

Code List Sale Code List Sale Code List Sale

Theory of numbers, mathematical analysis, two types of error structures, K. B. Stewart, Proceedings of the Steklov and their applications (1976), edited reprinted 1973,403 pp. by S.M. Nikol'skll, 1979,289 pp. TABLES/1WS $34 $10 Institute of Mathematics STEKL0/142WS $109 $33 Four sets of tables. Probability integral of the Algebra, theory of numbers and their applications doubly noncentral t-distribution with degrees of Approximation of functions in the mean (1967), (1978), edited by S.M. Niko1'skll, 1980,283 pp. freedom n and noncentrality parameters oand Jl, edited by S. B. Ste~kin, 1969, 138 pp. STEKLO/l48WS $132 $40 W. G. Bulgren; Doubly noncentral F distribution­ STEKL0/88WS $56 $17 Tables and applications, M. L. Tiku; Tables of Limits of indeterminacy in measure ofT-means expected sample size for curtailed f'JXed sample The Milne problem with anisotropic scattering of subseries of a trigonometric series (1978), size tests of a Bernoulli parameter, C. R. Blyth and (1968), M. V. Maslennikov, 1969, 161 pp. D. E. Men'{ov, 1981, 56 pp. D. Hutchinson; Zonal polynomials of order 1 STEKL0/97WS $57 $17 STEKLO/l49WS $33 $10 through 12, A.M. Parkhurst and A. T. James, 1974, 388pp. Parametric normed spaces and normed massives Multiple trigonometric sums (1980), G. I. Arhipov, TABLES/2WS $40 $12 (1969), K. K. Go1ovkin, 1972, 121 pp. A. A. Karacuba, and V. N. tubarikov, 1982, 126 pp. STEKL0/106WS $53 $16 STEKL0/151WS $64 $19 The distribution of the size of the maximum cluster of points on a line, Norman D. Neff Equations in free semigroups (1971), The geometry of positive quadratic forms (1980), and Joseph I. Naus, 1980, 207 pp. Ju. I. Hmelevskir, 1976, 270 pp. edited by S. S. Ry~kov, 1982, 258 pp. TABLES/6WS $26 $8 STEKL0/107WS $118 $35 STEKL0/152WS $114 $34 The product of two normally distributed random Collection of articles. I (1971), edited by I. G. Spectral theory of automorphic functions (1981), variables, William Q. Meeker, Jr., Larry W. Petrovskir and S.M. Niko1'skll, 1973,399 pp. A. B. Venkov, 1983, 163 pp. Cornwell, and Leo A. Aroian, 1981,256 pp. STEKL0/112WS $103 $31 STEKLO/l53WS $88 $26 TABLEsnws $33 $10 Problems in the constructive trend Theory of numbers, mathematical analysis, in mathematics. V (1970), edited by V. P Orevkov and their applications (1981), edited by N. N. Bog­ AMS Translations-Series 2 and N. A. Sanin, 1972, 287 pp. olyubov and K. K. Mardzhanishvili, 1983, 248 pp. STEKL0/113WS $63 $19 STEKL0/157WS $92 $28 Eleven papers on analysis, 1963, 412 pp. Theory and applications of differentiable Analytic number theory, mathematical analysis, TRANS2/34WS $43 $13 functions of several variables. IV (1972), and their applications (1981), edited by N. N. Bog­ edited by S.M. Nikol'skll, 1974,403 pp. olyubov and K. K. Mardzhanishvili, 1984, 247 pp. Nine papers on logic and group theory, 1967, STEKL0/117WS $104 $31 STEKL0/158WS $97 $29 256pp. TRANS2/64WS $45 $14 On integral functionals with variable domain of integration (1972), edited by I. I. Daniljuk, 1976, Sixteen papers on number theory and algebra, 144pp. Mathematical Surveys 1969,264 pp. STEKL0/118WS $53 $16 and Monographs TRANS2/82WS $47 $14 Difference methods of solving problems Twelve papers on algebra, algebraic geometry, of mathematical physics. n (1973), and topology, 1969, 275 pp. Geometric asymptotics, V. Guillemin $48 $14 edited by N. N. Janenko, 1975, 99 pp. and S. Sternberg, reprinted 1977, 474 pp. TRANS2/84WS STEKL0/122WS $53 $16 $76 $23 SURV/l4WS Sixteen papers on logic and algebra, 1970, 276 pp. $43 $13 Regular Dirichlet·Voronol partitions Symplectic groups, 0. Timothy O'Meara, TRANS2/94WS for the second triclinic group (1973), M. I. Stogrin, reprinted 1982, 122 pp. Ten papers on algebra and functional analysis, 1975, 116 pp. SURV/16WS $47 $14 STEKL0/123WS $53 $16 1970, 254 pp. TRANS2/96WS $42 $13 Partially ordered abelian groups with interpola· Boundary value problems of mathematical 1986, 336 pp. tion, Kenneth R. Goodearl, Five papers on logic and foundations, 1971, physics. IX (1975), edited by 0. A. Lady~henskaja, SURV/20WS $82 $25 1977, 179 pp. 288 pp. $47 $14 STEKL0/127WS $57 $17 Basic hypergeometric series and applications, TRANS2/98WS 1989, 124 pp. Nathan J. Fine, reprinted Five papers on logic and foundations, 1972, Collection of articles. IT (1972), SURV/27WS $47 $14 edited by S.M. Nikol'skir, 1974,303 pp. 275 pp. STEKL0/128WS $88 $26 TRANS2/99WS $43 $13 Problems in the constructive trend Selected Tables Six papers in analysis, 1973, 250 pp. in mathematics. VI (1973), edited by V. P. Orevkov TRANS2/101WS $57 $17 and N. A. Sanin, 1976, 272 pp. in Mathematical Statistics STEKL0/129WS $130 $39 Ten papers in analysis, 1973,252 pp. TRANS2/102WS $56 $17 International conference on mathematical Five sets of tables. Tables of the cumulative problems of quantum field theory and quantum noncentral chi-square distribution, G. E. Hayman, Some problems of mathematics and mechanics, statistics. II, Fields and particles. Mathematical Z. Govindarajulu, and F. C. Leone; Tables of the 1976,265 pp. questions of quantum statistics (1975), exact sampling distribution of the two-sample TRANS2/104WS $72 $22 edited by V. S. V1adimirov, reprinted 1982,450 pp. Kolmogorov-Smirnov criterion D (m s n), STEKL0/136WS $120 $36 P. J. Kim and R.I. Jennrich; Criti~· values and Twelve papers in logic and algebra, 1979, 250 pp. probability levels for the Wilcoxon rank sum test TRANS2/113WS $47 $14 C-types of n-dimensionallattices and 5-dimen­ and the Wilcoxon signed rank test, F. Wilcoxon, sional primitive parallelohedra (with application S. K. Katti, and R. A. Wilcox; The null distribution Twelve papers in analysis, I. S. Belov, E. R. to the theory of coverings) (1976), S. S. Ry~kov of the first three product-moment statistics for Cekanovskil, E. M. Dyn'kin, V. M. Falvy~evskil, and E. P. Baranovskir, 1978, 140 pp. exponential, half-gamma, and normal scores, V. P. Glu~ko, G. M. Henkin, S. V. Hru§l!ev, STEKL0/137WS $80 $24 P.A.W. Lewis and A. S. Goodman; Tables to M. M. Malamud, B. S~ Mitjagin, T.V. Pdkova, facilitate the use of orthogonal polynomials for

510 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Code List Sale Code List Sale Code List Sale

B.S. Pavlov, M.A. Pekker, 0. M. Smeljanskil, A. Four papers on ordinary differential equations, Volume 5: Index to Statistics and Probability: E. Tumanov, and S. A. Vinogradov, 1980,202 pp. M.G. Krein and V. A. Jakubovic, 1983, 168 pp. Locations and Authors, Ian C. Ross TRANS2/115WS $55 $17 TRANS2/120WS $47 $14 andJohnW. Tukey,l973,1092pp. TUKEY/5WS $111 $33 Sixteen papers on differential equations, Ju. V. Egorov, A. V. Fursikov, D. M. Galin, Tukey Citation Index Volume 7: The Library and Information Science Ju. S. II'j~enko, T. F. Kalugina, V. Ju. Kiselev, Cumlndex, Frederick G. Kilgour, 1973, 722 pp. A. I. Komel!, A. A. Lok§in, N. 0. Maksimova, TUKEYnws $61 $18 0. A. Oleinik, V. M. Petk:ov, P.R. Popivanov, Volume 1: The Statistics Cumlndex, E. V. Radkevi~. C. V. Ray.gelov, D. A. Silaev, James L. Dolby and John W. Tukey, 1973,498 pp. A. N. So§itaisvili, M. A. Subin, A. I. Suslov, TUKEY/IWS $55 $17 and M. I. Vi§ik, 1982, 339 pp. Vestnik of the Leningrad TRANS2/118WS $97 $29 Volume 2: Index to Statistics and Probability: University (Mathematics) The Citation Index, John W. Tukey, 1973, 1269 pp. Twelve papers in algebra, V. A. Dem'janenko, TUKEY/2WS $124 $37 Journal A. I. Mal'cev, A. Ju. Ol'~anskil, Sx A. Ovsienko, B. I. Plotkin, A. V. Rolter, B. M. :sain, Volumes 3 and 4: Index to Statistics and Hsieh Shengkang, A. I. Sir§ov,l. S. Slavutskii, Probability: Permuted Titles, Ian C. Ross Volumes 1-16 (1974-1984), per volume A. A. ~melev, and Wang Yuan, 1983, 139 pp. and John W. Tukey, 1975,2384 pp. VEST/1, 2, 3, 4, 5, 6, 7, 8, 16/WS TRANS2/119WS $43 $13 TUKEY/3/4WS $141 $42 $237 $71 ---Hurry, Sale Ends July 16, 1992!

Send VISA and MasterCard orders to: Send orders with remittance to: Charge by phone in the U.S. and Canada American Mathematical Society American Mathematical Society 800-321-4AMS (321-4267) P.O. Box 6248 Annex Station, P.O. Box 1571 Please specify Warehouse Sale Providence, RI 02940-6248 Providence, RI 02901-1571 to ensure proper discount.

Q Check enclosed Q VISA

Mail to Q MasterCard Ordered by: (if different) ______Card Number ------

Expiration Date------Signature ______

Customer code: ______

Order Code Sale Price Qty Item Total Order Code Sale Price Qty Item Total

All orders must be prepaid. Canada residents, please add 7% GST. Free Book Total ,p 0 shipment by surface. For air delivery, please add $6.50 per title. Discount ~ Q Air Delivery '1. ...~ applies only to the books on the previous pages. DIRECT SALES ONLY. lw~ ~ NOT AVAILABLE TO BOOKSTORES OR AGENTS. Orders must be Total ·... ~'" sent on th1s Warehouse Sale form (or facsmule).

MAY/JUNE 1992, VOLUME 39, NUMBER 5 511 AMS Reports and Communications

Recent Appointments For election to the posttlon of this activity shall continue only Vice-President: Avner Friedman, Linda as long as access to and use of Committee members' terms of of­ Keen, and Robert Osserman. the facility is provided on a com­ fice on standing committees expire For election to the position of pletely non-discriminatory basis. Member-at-Large of the Council: Ruth on January 31 following the year Both resolutions were passed by the M. Charney, Carl C. Cowan, Jacob Eli given in parentheses following their Council. Goodman, Alfred W. Hales, Rebecca names, unless otherwise specified. Finally, the Council passed the fol- A. Herb, Joshua A. Leslie, Elliott H. lowing resolution: The following have been discharged by Lieb, De Witt L. Sumners, and Gunther the Council with thanks: ad hoc Sigma A. Uhlmann. The Council of the AMS requests Xi Committee and the Committee on For election to the position of a report from the Executive Direc­ Cooperative Symposia. Trustee: Maria M. Klawe and Charles tor, to be delivered at the August John B. Friedlander (1994) and C. Sims. 91 Council meeting, on the imple­ James B. Serrin (1994) have been ap­ The Council heard the Annual Re­ mentation of the policies decided pointed to the Progress in Mathematics port from the Executive Director, Wil­ by the membership in the January Committee by President Michael Artin. liam H. Jaco, and Ramesh Gangolli re­ 1988 referendum. Continuing members of the committee ported to the Council on the activities As usual, the Council discussed are Hyman Bass (1992), chair, Peter of the Strategic Planning Task Force. the job crisis for young people in W. K. Li (1993), and Haynes R. Miller President Artin announced that he had mathematics before adjourning at about (1993). asked the Committee on Committees 11 p.m. Joseph L. Taylor has been ap­ to study the committee structure of the pointed chair of the ad hoc Committee Society in order to rationalize that part Robert M. Fossum on Prizes and Awards by President of the governance of the Society. Secretary Michael Artin. Continuing members of The Council considered a report Urbana, Illinois the committee are Joan S. Birman, from its ad hoc Committee on Relations Frederick W. Gehring, Ronald L. Gra­ with Russian Mathematicians. There The Business Meeting in Orono ham, Joseph J. Kohn, and Gian Carlo were two resolutions contained in this The Business Meeting of 8 August Rota. report which were accepted by the 1991 began about 12:25 p.m. President Council. Artin presided. The Council Meeting in Tampa This Council establishes a stand­ The Secretary presented a brief re­ The Council of the American Mathe­ ing committee to consider current port on the meeting of the Council that matical Society met at 7:00 p.m. on problems in mathematical life and had taken place on 7 August 1991 (and Thursday, 21 March 1991, in the Board mathematical institutions in East­ reported on previous to this report). Room of the Holiday Inn, Busch Gar­ em Europe. The committee would The meeting adjourned at about dens, Tampa, Florida. President Artin be concerned both with discrimi­ 12:45 p.m. presided. There were 18 members nation issues particular to Eastern present. Europe and with studying whether Robert M. Fossum The main business of the spring to engage in cooperative ventures. Secretary meeting of the Council is to receive the Urbana, Illinois report of its Nominating Committee and The Council accepts in princi­ to make nominations for the elections ple the recommendation to es­ The Council Meeting in Orono that are to take place in the fall. tablish an AMS Library/Resource The Council of the American Math­ The Council made the following Room in the Soviet Union and ematical Society met at 2:00 p.m. nominations: asks the Executive Committee to on Tuesday, 7 August 1991, at the For election to the position of recommend to the Council when Black Bear Inn, Orono, Maine. Pres­ President-Elect: Ronald L. Graham and and where, with the understand­ ident Artin presided. There were 20 Stephen Smale. ing that AMS cooperation with members present.

512 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY mm . mmm•••••••• -~-= m···-·•m••• AMS Reports and Communications

The Executive Director (ED) re­ ences (BMS) and the Mathematical been provided for support of e-MATH, ported on the implementation of the Sciences Education Board (MSEB) to travel to international conferences, and policies adopted by the membership in have AMS representation at the BMS support of mathematicians in develop­ the January 1988 referendum. In the and the MSEB meetings. Conversely, ing countries. Through recent efforts report, the ED recalled the statements both of these organizations will have of the new AMS Development Office, of the resolutions. He then went on to representatives at Executive Commit­ corporate and private foundation funds say: tee and Board of Trustees (ECBT) have been received for support of So­ "Most of the AMS effort of direct meetings to report to the Society. A ciety activities. The new Development advocacy for mathematics research has representative of the AMS attends (and Office is a major step in the Society's been conducted in coordination with often participates at) meetings of the efforts to increase funding for support the Office of Governmental and Pub­ Advisory Board of the Division of of mathematics research. Increased de­ lic Affairs (OGPA) of the Joint Policy Mathematics at the NSF. Representa­ velopment activity is expected. Board for Mathematics (JPBM). Re­ tives of the AMS meet with principals "A report has recently been de­ cently, JPBM has been restructured to of the DAVID II Report to discuss livered to the Society by its Strate­ have, in addition to the three represen­ possible AMS activities that could be gic Planning Task Force (SPTF). This tatives from each of the three partic­ taken to assist in attaining the recom­ report recommends a strategic direc­ ipating organizations, a tenth member mendations of the DAVID II Report. tion for the Society and a number of to serve as Chair of JPBM. This struc­ These discussions are continuing. goals that the Society should attain over ture is hoped to bring to JPBM more "The AMS, through its representa­ the next 3-5 years. One such goal is efficient organization and to allow for tives, participates in two major groups to "articulate and advocate an agenda continuity and more sustained efforts that advocate support for mathematics that promotes the vitality and quality on behalf of JPBM and its oversight of research. One is the Council of Sci­ of mathematics and its development OGPA. entific Society Presidents (CSSP). This through mathematics research." Flow­ "Since 1988, OGPA has undergone group monitors administrative actions ing from this goal will be various objec­ changes of directors, having had two and legislation that might affect the tives and strategies that will provide the directors and an acting director. Cur­ science community. They work with Society with an action plan designed rently, OGPA is without a director. representatives from federal agencies to increase the fraction of nonmilitary However, there continue to be major and with legislative staff, offering ad­ funding for mathematics research and efforts on behalf of the public aware­ vice and advocating for science. The increase total research support." ness/information activity of JPBM to President of the Society is the AMS Ex-President Browder also reported promote the value of mathematics re­ representative and this contact has been to the Council on this issue. His re­ search and its importance to applica­ valuable and in keeping with the spirit marks were: tions of mathematics and to mathemat­ of the 1988 Referendum. The other "This report is in response to the ics education. In addition, OGPA now group is the Coalition for National request of the Council for a report on has a full-time staff person acting as Science Funding (CNSF). This is a the effects of the referenda, and the a liaison with the legislative branch of coalition of a number of professional actions taken by the officers of the government. This activity has been pri­ organizations and other organizations Society in response to them. marily a channel for information, both that work to sustain federal support of "The first referendum called for in­ to and from the legislative branch of science and engineering. They particu­ action (with respect to solicitation for government. Through this activity, the larly advocate for support of the NSF "star wars" research) and the inaction Presidents of the JPBM participating budget and its doubling over the near called for has been carried out. No offi­ organizations have provided written tes­ term. The math community is repre­ cers of the Society have been involved timony for support of National Science sented on the board of directors of in soliciting funds for research on "star Foundation (NSF) funding. The pub­ CNSF and the President has provided wars" projects. lic information and legislative activities written testimony on behalf of mathe­ "The second referendum asserted of JPBM/OGPA have been funded to matics through this group's efforts. possible deleterious effects of military continue through June 1992 and are be­ "In addition to serving as an advo­ funding of research and asked the of­ ing supervised by the Chair of JPBM. cate for increased support for mathe­ ficers to work toward increasing the Liaison with the legislative branch of matics research, the AMS seeks federal, nonmilitary fraction of mathematical government is continuing in coopera­ corporate, foundation, and private fund­ research funding, as well as increasing tion with the activities of OGP A. ing for activities it undertakes in sup­ the total funding available. "Direct liaisons have been estab­ port of mathematics research. Federal "Representations have been made to lished with certain boards in Wash­ funding is obtained for support of the increase NSF funding of mathematics ington in order to keep the Society AMS Summer Research Conferences, in personal contacts between officers of informed and to have channels for Summer Institutes, Summer Seminars, the Society and of NSF. The AMS has communication. The AMS has arranged and Symposia on Mathematical Biol­ joined the Coalition for National Sci­ with the Board on Mathematical Sci- ogy. In addition, federal funds have ence Funding, a broad based organiza-

MAY/JUNE 1992, VOLUME 39, NUMBER 5 513 ...... ·-··-·····-··--·"····--·--········-······-···-············-·-·.. ·············---····--·····"·····-"·············------AMS Reports and Communications tion which advocates increased NSF ap­ Referendum 2, and resigned from the to the Third Pan-African Congress of propriations from Congress. Lisa Thomp­ AMS in protest. the African Mathematical Union to be son of the OGPA sits on the board of "Some bafflement was expressed held in Nairobi in August 1991. The directors, representing JPBM. Such an also by high officials of NSF, that it Council is pleased that an officer of increase of NSF funding might tend to seemed as though AMS was rejecting the Society can deliver these greetings increase the non-DOD fraction of math the military agencies' participation in personally. It looks forward to future research funding, unless of course, the carrying out the recommendations of cooperation with the Union in further­ DOD support of mathematics increased the first David Report to increase math­ ing the mathematical sciences." faster. ematical research funding, and AMS The Council agreed to the establish­ "In Spring 1990, an ad hoc con­ expected NSF to carry the burden alone. ment of a series called Mathematical sortium, including ACM, IEEE, APS, "Referenda 3-5, being directed to World to be copublished with MAA. and others was formed, to advocate the outside world, enunciating generally While the series is being dominated the channeling of funds liberated from agreed on goals, will not be discussed by translations from Russian, the sub­ military projects by the end of the here." committee of the Russian Translation Cold War, into supporting scientific Among other items of information Committee will remain as editors, rep­ research, (the "peace dividend"). The received by the Council were several resenting AMS. MAA will select two AMS participated in the initial meeting involving Society activities with re­ editors to make a total editorial com­ of this group, and Ed Connors became a gard to Eastern European and Soviet mittee of four. member of the steering committee. The Union mathematicians. The Committee The Council discussed the signifi­ onset of the Gulf Crisis two months on Science Policy (CSP) had recom­ cant backlog of the Transactions, but later sent this project into suspended mended appointment of an ad hoc com­ took no action while it awaited results animation. However, it is not clear how mittee to investigate issues associated of further discussions and analysis of the activities of this group might have with needed assistance in the Eastern the problem. It did pass the following agreed with the ''fraction" goal of ref­ European and Soviet Union mathemat­ resolution concerning backlog: erendum 2, if the political process had ical sciences community. Appointment "This Council recommends to the produced more funds for basic research of this Committee was delayed until ECBT that each journal should publish inside the military agencies. the report of the ad hoc Committee in its "information to authors" page a "In fact, appropriations and funding on Relations with Russian Mathemati­ definition of backlog and a report of decisions in DOD and non-DOD areas cians was delivered. That report was the backlog as that issue went to press. are made by different agencies and by presented to the March 1991 Council. In addition, the backlogs of the AMS different committees of Congress. The Professor Deborah Raimo, Presi­ journals should be regularly published budget agreement in Congress in Fall dent of the Mathematical Association in the Notices." 1990 stipulates that for the next few of America (MAA), reported to the The Council approved a restructur­ years funds saved in defense cannot Council on activities of MAA and joint ing of the Proceedings Editorial Com­ be shifted to nondefense areas, funds activities that were of interest to the mittee. There is a small number of saved in each category can only be Council. coordinating editors who comprise the used to reduce the deficit. The Council noted the founding Proceedings Editorial Committee. In "On the agency level, the mathe­ of the European Mathematical Society turn, there is a larger number of as­ matical research program officers work (EMS) bypassing the following resolu­ sociate editors who are appointed by to convince their superiors of the value tion: the Editorial Boards Committee. These of mathematical research for these "The Council of the American Math­ individuals will still be listed as editors agencies, and to increase mathematics' ematical Society sends congratulations on the masthead of the journal. share of the budget. to the European Mathematical Society The Council approved several ap­ "There is a perception that some of on the occasion of its founding on 29 pointments to various editorial boards. the program officers in the DOD agen­ October 1990. The Council is pleased These appointments have been noted in · cies have felt that their jobs have been to note that the aims of the European the Notices. It also approved the Nom­ made more difficult by Referendum 2 Mathematical Society are very close to inating Committee's recommendations and that their work was unappreciated those of the AMS. It looks forward to for appointment to the Committee to and rejected by the membership of the cooperation with the EMS in activities Monitor Problems in Communications. AMS. There seemed to be a noticeable within the mathematical sciences that It then corisidered the report of coldness in relations between AMS and will further these aims." the Strategic Planning Task Force. The many of these program officers after And it noted that the African Mathe­ Executive Committee and Board of the referenda were adopted. matical Union was sponsoring the Third Trustees had asked the Council to "A similar unhappiness was mani­ Pan-African Congress in August 1991 discuss the report and to act on the fested among a substantial number of by passing the following resolution: statement of mission. Members of the AMS members, mostly members of "The Council of the American Math­ Council did discuss the report. Trustee SIAM, who felt personally offended by ematical Society sends congratulations Paul Sally was granted the privilege of

514 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications -----~---··········~-········ .... the floor to announce that, contrary to then turned its attention to the method · This Committee should consult published statements, the SPTF report by which working officers of the Soci­ the Secretary concerning this ap­ was not unanimously endorsed by the ety are to be appointed. It adopted the pointment. ECBT but that in fact he had abstained following method: during the vote on endorsement. Sally "3. Secretary: When considering "A standing committee of the EC wished that his abstention be put on the the Secretary, this Committee is and BT, to be called the ECBT record. As the report of the SPTF has augmented by the Treasurer. This Nominating Committee, will be appeared in the Notices, it will not be Committee would evaluate the created. It would consist of the discussed here. current Secretary and receive rec­ fifth-year elected member of the The current Mission Statement, ommendations for this position. BT, the fourth-year and second­ found in the Society's Articles of In­ It would report on its recommen­ year elected members of the ~~· corporation (1923), re~ds as follo~s: dations to the May ECBT for and the Chair of the Council s "The particular busmess and obJects forwarding to the August Council Nominating Committee. The Ex­ of the Society are the furtherance of ~e meeting. When it is expected that ecutive Director would be a non­ interests of mathematical scholarship a sitting Secretary will not serve voting member of the Committee. and research." again, this Committee should at­ The SPTF Report recommended a tempt to nominate a replacement "1. Associate Secretaries: This revised version of the Mission State­ at least one year in advance of ment. The statement was endorsed Committee would evaluate cur­ the end of the term so that the by the ECBT and recommended f~r rent Associate Secretaries and re­ replacement can serve a break­ adoption by the Council. The Council ceive recommendations for this in period of about one year. amended the SPTF statement slightly position. It would report on its This Committee should consult and adopted the following resolution: recommendations to the May the President concerning this ap­ ECBT for forwarding to the Au­ "The Council of the American pointment. gust Council meeting in the ~e~ Mathematical Society adopts the when the term expires. When 1t 1s following statement of mission: "4. Treasurer: When considering expected that a sitting Associ~te the Treasurer, this Committee is Secretary will not serve agam, augmented by the Secretary. This "The AMS, founded in 1888 to this Committee should attempt to Committee would evaluate the further the interests of mathe­ nominate a replacement at least current Treasurer and receive rec­ matical research and scholarship, one year in advance of the end ommendations for this position. serves the national and interna­ of the term so that the replace­ It would report on its recommen­ tional community through its pub­ ment can serve a break-in period dations to the May ECBT for lications, meetings, advocacy, and of about one year. This Commit­ forwarding to the August Council other programs, which tee should consult the Secretary meeting. When it is expected that concerning these appointments. • promote mathematical research, a sitting Treasurer will not serve its communication and uses, again, this Committee should at­ "2. Associate Treasurer: When tempt to nominate a replacement considering the Associate Trea­ at least one year in advance of • encourage and promote the surer position, the Committee is transmission of mathematical un­ the end of the term so that the augmented by the Treasurer. This derstanding and skills, replacement can serve a bre~­ Committee would evaluate the in period of about one year. This current Associate Treasurer and Committee should consult the As­ • support mathematical education receive recommendations for this at all levels, sociate Treasurer concerning this position. It would report on its appointment. recommendations to the May • advance the status of the profes­ ECBT for forwarding to the Au­ sion of mathematics, encouraging "When considering the report and gust Council meeting in the ~ear and facilitating full participation making further recommendations when the term of office exprres. of all individuals, to the Council the EC and BT When it is expected that a sitting will consist of one Committee Associate Treasurer will not serve and voting will be by majority • foster an awareness and ap­ again, this Committee should at­ (i.e., the EC and BT will tog~ther preciation of mathemati~s ~~ its tempt to nominate a replacement connections to other disciplines form the nominating committee at least one year in advance of and everyday life." for these positions)." the end of the term so that the Several committee reports were re­ replacement can serve a break­ The Council approved a revision in ceived by the Council. The Council in period of about one year. its policy regarding petition tables at

MAY/JUNE 1992, VOLUME 39, NUMBER 5 515 ------!iiir""''''"""'''''''''''''''''""''''"'''''''''''"'''''"'''''''''''''''''''' AMS Reports and Communications sectional meetings so that petition ta­ (2) Students for whom English is tending their last Council meeting, the bles will be made available at sectional a second language are frequently Executive Director, William Jaco, made meetings as the need arises. put at an unfair disadvantage be­ remarks on the Society's Operational The Council gave unanimous con­ cause of unfamiliar phrasing of Plan. President Artin commented on sent to consider a resolution proposed the questions on a departmental the activities of the Joint Policy Board by the Society's Committee on Human examination. for Mathematics' Committee on Profes­ Rights of Mathematicians concerning sional Recognition and Rewards and the the closing of Birzeit University in the (3) Because of different emphases, pilot Assessment of the Mathematical West Bank. The resolution was tabled levels of preparation, styles of in­ Sciences prepared for the House Com­ by the Council. struction, etc., departmental ex­ mittee on Science, Space, and Technol­ The Council adjourned at about aminations do not fulfill the goal ogy. (This pilot assessment appears in 6:30p.m. of a uniform measure of ability the February 1992 issue of the Notices.) for different sections of the same The Council approved participation Robert M. Fossum course. of the Institute for Mathematical Statis­ Secretary tics in the Annual Survey and concomi­ Urbana, illinois (4) Any individual who is re­ tant membership on the AMS-MAA garded as sufficiently competent Data Committee. The Business Meeting to be entrusted with the day-to­ Reports from many committees were in Baltimore day teaching of a course should a received. Appointments to several ed­ The Business Meeting of 9 January fortiori be considered capable of itorial committees were made. The 1992 began about 4:25 p.m. President creating appropriate examinations Council reappointed R. Andy Magid Artin presided. and grading systems. and Lance Small to two-year terms as Before the meeting was called to Associate Secretaries, the terms to be­ Be it resolved that: order, the floor was given to Vice­ gin on 1 February 1992. It appointed President Blum who reported that the the American Mathematical So­ Robert Daverman and Lesley Sibner Council had approved publishing an ciety considers it a principle of to two-year terms as Associate Sec­ open letter to I. R. Shafarevich along academic freedom that all indi­ retaries, these terms to begin on 1 with signatures as an advertisement viduals teaching university math­ February 1993. And it appointed B. A. in the Notices. (This complimentary ematics courses shall have the Taylor to a two-year term as Asso­ advertisement appeared on page 264 of right to prepare their own ex­ ciate Treasurer, the term beginning on the March 1992 issue of the Notices.) aminations and to set their own 1 February 1993. She read the open letter and notified the grading scales. The Council approved the establish­ membership that it was still possible to ment of an AMS-MAA Joint Archives The Committee on the Agenda for add signatures to the letter. Committee and it approved a standing Business Meetings proposed that the The Secretary announced the results Committee on Electronic Publication resolution be referred to the Society's of the election of 1991. These have with the charge to include responsibil­ Committee on Education. This motion been publi&hed on page 152 of the ity for oversight of the scientific scope passed and the resolution has been for­ February 1992 issue of the Notices. and content of e-MATH, examination warded to the Committee on Education. The Secretary presented a brief re­ with staff and the Executive Committee The meeting adjourned at about port on the meeting of the Council that and Board of Trustees of ways in which 5:15p.m. had taken place on 7 January 1992. the Society can best stay abreast of de­ A motion for the Business meeting Robert M. Fossum velopments in the area of electronic proposing a Resolution on Departmen­ publication, and study of those features tal Examinations, proposed by Robert Secretary Urbana, illinois which might best serve the profession. 0. Stanton, that had been submitted A resolution concerning Birzeit Uni­ to the Committee on the Agenda for versity in the West Bank Submitted by Business Meetings, was presented at The Council Meeting in Baltimore the Committee on Human Rights of the meeting. The resolution reads as The Council of the American Math­ Mathematicians failed to gain a major­ follows: ematical Society met at 2:00 p.m. ity. on Tuesday, 14 January 1992, in the A resolution asking that an objec­ A Resolution on Departmental Exam­ Yosemite Room C of the San Francisco tive "to strive to increase the compo­ inations Hilton on Hilton Square, San Francisco, nent of support coming from nonmili­ Whereas: CA. President Browder presided. There tary sources" be added to the report of (1) Departmental examinations can were 32 members present. the Strategic Planning Task Force was discourage innovative teaching After the results of the 1991 Elec­ tabled. techniques and impede. advances tion were announced and the Council After hearing from Vice-President in education. thanked those members who were at- Blum about the Third Pan-African

516 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Congress, the Council agreed to en­ "If (now or at a future time) the Sylvia Wiegand, chair of the sub­ courage the AMS to pursue cooperative NEC feels it appropriate, this commit­ committee of the Committee on Com­ projects with the African Mathemati­ tee will concur with the publication mittees that is considering the structure cal Union, and it directed the Long in the Notices of this quote from our of committees of the Society, discussed Range Planning Committee to study report: "this ad hoc committee be­ the progress-to-date of the committee. relations with the international mathe­ lieves that NEC acted thoughtfully and Her remarks were preceded by com­ matical community. responsibly in its decision not to pub­ ments from President Artin. The Council then considered a mo­ lish the letter and that this decision The motion by the Secretary to tion to instruct the Notices Editorial was made in accord with NEC's edi­ conduct elections to the Nominating Committee (NEC) to publish an open torial policies," provided there is also Committee and the Editorial Boards letter to Shaferevich. This motion was included a statement like the first sen­ Committee by the method of approval substituted by the last section, amended, tence of these Recommendations. voting was passed. Elections to these of the report of an ad hoc committee "We consider this an unusual event, committees will be conducted by the that had been appointed by the Pres­ and do not propose that our recommen­ approval method in the future. ident to consider publication of the dations be construed as setting any It was noted that Ed Connors, who letter. This section reads as follows: general policy." served as Director of OGPA since 1 "III. Recommendations. This com­ This motion was then passed by the July 1990, left at the end of his term mittee feels that there are very valid Council. on 30 June 1991. Richard Herman has concerns raised by the [Kra/Blum] let­ The Council considered general pol­ replaced him as Director of OGP A. In ter. We think that these concerns would icy concerning letters to the editor pub­ addition, Herman has been elected as be best served by a factual, reasoned, lished in the Notices. It then passed the Chair of JPBM. and hopefully impartial article on the following resolution: The Council adjourned at about 7 subject, written by someone who knows p.m. the details. "The existence of political or so­ "As an additional compromise, the cial content is, in itself, not suf­ Committee recommends that the letter ficient reason to reject a letter Robert M. Fossum and its list of signatories be published as submitted for publication in the Secretary an unpaid advertisement in the Notices Notices." Urbana, Illinois as soon as possible.

Journal of the American Mathematical Society

When the Journal of the Americ,an Mathematical Society first appeared in 1988, it gained instant respect for its careful selection of relevant, important, and timely research. The editors are devoted to publishing research articles of the highest quality in all areas of pure and applied mathematics. Editors of this journal include: H. Blaine Lawson, Jr., Robert D. MacPherson, Richard Melrose, Andrew Odlyzko, and Wilfried Schmid.

1992 Subscription Prices List $136*, Institutional member $109*, Individual member $82* (ISSN 0894-0347) Back volumes are also available. Call AMS Customer Services for prices.

*Add for postage: Surface delivery to destinations outside the U.S. and India- $8; to India- $18. Expedited delivery to destinations in North America- $13; elsewhere- $36. All prices subject to change. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 517 Miscellaneous

Personals Rene De Vogelaere, of the Uni­ William Nelson, of the Mitre Cor­ Alexander V. Arhangelskii, of Mos­ versity of California, Berkeley, died on poration, died on April12, 1992, at the cow State University, has accepted the December 14, 1991, at the age of 65. age of 54. He was a member of the position of Professor of Mathematics at He was a member of the Society for 21 Society for 25 years. Ohio University starting with the 1992- years. Kaj L. Nielsen, Professor Emeritus 1993 academic year. He will teach win­ Ralph M. Ford, of Auburn Uni­ of Butler University, died on February ter and spring quarters and maintain his versity, died on December 6, 1991. He 21, 1992, at the age of 77. He was a position at Moscow State University. was a member of the Society for 5 member of the Society for 53 years. Dusan Repovs, of the University of years. John T. O'Bryan, of the Rose­ Ljubljana, has been appointed Research Lawrence F. Guseman, Jr., of Hulman Institute of Technology, died Dean of the Faculty of Education at that Texas A&M University, died on Novem­ on December 18, 1991, at the age of institution. ber 5, 1991, at the age of 53. He was a 21. He was a member of the Society member of the Society for 24 years. for 1 year. Ben Johnson, of Ft. Mohave, Ari­ Mary K. Peabody, of North Manch­ Deaths zona, died on December 19, 1991, at ester, Indiana, died on December 20, Leon W. Cohen, Professor Emeritus the age of 72. He was a member of the 1991, at the age of 74. She was a of the University of Maryland, died on Society for 28 years. member of the Society for 49 years. February 21, 1992, at the age of 88. Joseph D. E. Konhauser, of Mac­ Richard S. Pierce, a Professor He was a member of the Society for 67 alester College, died on February 28, Emeritus from Tucson, Arizona, died years. 1992, at the age of 67. He was a on March 15, 1992, at the age of 65. Lawrence J, Corwin, of Rutgers member of the Society for 42 years. He was a member of the Society for 41 University, died on March 19, 1992, at Jurgen Kraft, of the University of years. the age of 49. He was a member of the Puerto Rico, died on Januaty 18, 1992, William R. Scott, a Professor Emer­ Society for 26 years. (See the News at the age of 38. He was a member of itus from Salt Lake City, Utah, died on and Announcements section, p. 447.) the Society for 11 years. February 15, 1992, at the age of 72. Sammy Daghir, a teaching fellow Kenneth D. Lerche, of Ellicott He was a member of the Society for 52 at SUNY at Albany, died in October City, Maryland, died on July 8, 1991, years. 1991, at the age of 26. He was a at the age of 54. He was a member of Jan Tryba, of the University of member of the Society for 3 years. the Society for 30 years. Gdansk, died on January 27, 1992, at Mahlon M. Day, Professor Emer­ Deane Montgomery, Professor the age of 35. He was a member of the itus of the University of Illinois, died Emeritus at the Institute for Advanced Society for 4 years. on March 18, 1992, at the age of 79. Study, died on March 15, 1992, at the Hubertus J, Weinitschke, of the He was a member of the Society for 54 age of 92. He was a member of the University of Erlangen-Numberg, died years. Society for 59 years and was President on December 5, 1991, at the age of 72. Piero L. de Mottoni, of the Uni­ in 1961 and 1962. A tribute to Profes­ He was a member of the Society for 33 versity of Rome, died on November sor Montgomery is being prepared and years. 25, 1990, at the age of 47. He was a will be appearing in a future issue of member of the Society for 12 years. the Notices.

518 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Visiting Mathematicians (Supplementary List)

The list of visiting mathematicians includes both foreign mathematicians visiting in the United States and Canada, and Americans visiting abroad. Note that there are two separate lists.

American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of Special Interest Period of Visit Chan, Tony (U.S.A.) Chinese University of Hong Kong Applied Mathematics 9/92- 6/93 Chen, S. Y. (U.S.A.) Chinese University of Hong Kong Differential Geometry 9/92- 6/93 Dennis, Stanley C.R. (Canada) Laboratoire de Mechanique des Flow of Fluids 5/92- 9/92 Fluides, France Greene, Robert (U.S.A.) Danish Technical University, Denmark Differential Geometry 9/92- 12/92 Hahn, Alexander (U.S.A.) University of Innsbruck, Austria Algebra 8/92- 5/93 Mattson, H.F., Jr. (U.S.A.) INRIA Rocquencourt Discrete Mathematics 4/92- 7/92 Pierce, Donald A. (U.S.A.) Radiation Effects Research Cancer Research and Mathematical 9/92- 9/93 Foundation, Japan Statistics Pillay, Anand (U.S.A.) University of Freiburg, Germany Logic 8/92- 1/93 Protter, Philip (U.S.A.) University of Paris VI, France Stochastic Analysis 5/93- 7/93 Rogawski, Jonathan (U.S.A.) Hebrew University of Jerusalem, Number Theory 9/92- 6/93 Israel Sommese, Andrew (U.S.A.) University of Bayreuth, Germany; Algebraic Geometry 9/92- 10/92 Max Planck Institute, Germany Takesaki, Masamichi (U.S.A.) University of Tokyo, Japan Operator Algebras 9/92- 12/92

Visiting Foreign Mathematicians Abramovici, Flavian (Israel) University of Calgary Geophysics 7/92- 6/93 Aleman, Alexandru (Germany) University of Tennessee Complex analysis/Operator Theory 8/92- 12/92 Badr, Hassan (Saudi Arabia) University of Western Ontario Flow of Fluids 11/91 - 8/92 Baik, Seung 11 (Korea) Memphis State University Boolean Algebra and Theory of 1/92- 1/93 Semi-rings Bakir, Saad (Jordan) Virginia Polytechnic Institute and Quality Control 7/92- 9/92 State University Barbu, Viorel (Romania) Ohio University Differential Equations 1/93- 6/93 Bolondi, Giorgio (Italy) University of Notre Dame Algebraic Geometry 8/92- 1/93 Castillo, Rafael Rene del Rio University of Tennessee Differential Equations 8/92 - 12/92 (Mexico) Cho, Yong Hwan (Korea) University of Missouri-Columbia Dynamical Systems 8/92- 8/93 Cushman, Richard (The University of Calgary Hamiltonian Systems 5/92- 8/92 Netherlands) Dancer, Edward N. (Australia) Brigham Young University Partial Differential Equations 9/92- 12/92 Elsner, Ludwig (Germany) University of Calgary Matrix Theory 8/92 Exel, Ruy (Brazil) University of New Mexico Operator Algebras 8/92- 6/93 Ezhov, Vladimir (Russia) Oklahoma State University Several Complex Variables 8/92- 5/94 Feldvoss, Jorg (Germany) University of Wisconsin-Milwaukee Representation Theory 8/92- 12/92 Feng, Keqin (China) Universite Laval Number Theory 1/92 - 8/92 Franca, Leopolda (Brazil) Purdue University Applied Mathematics 1/93 - 5/93 Galeeva, Roza (Russia) University of Wisconsin-Milwaukee Dynamical Systems 8/92- 12/92

MAY/JUNE 1992, VOLUME 39, NUMBER 5 519 ______...... - ...... - ...... -...... Visiting Mathematicians

...... ~

Name and Home Coung-y Host Institution Field of S);!ecial Interest Period of Visit Guofang, Wei (China) University of California, Santa Differential Geometry 7/92- 7/94 Barbara Gupta, Ramesh Chandra Memphis State University Fluid Flows 7/92- 7/93 (Singapore) Heintze, Ernst Friedrich University of Notre Dame Differential Geometry 8/92- 2/93 (Germany) Henderson, LeRoy (Australia) State University of New York at High Speed Aero-Dynamics 9/91 - 7/92 Stony Brook Herzog, Jurgen (Germany) Purdue University Commutative Algebra 1/93- 5193 Hess, Peter (Switzerland) Brigham Young University Partial Differential Equations 9/92- 12/92 Isaza, Pedro (Columbia) Syracuse University Partial Differential Equations 5/92- 9/92 Kang, Soon Ja (Korea) Louisiana State University Probability Theory 1/92- 12/92 Kapitanskii, Lev (Russia) Brown University Differential Equations 9/92- 7/93 Kawamura, K. (Japan) University of Saskatchewan Topology 9/92- 8/93 Kim, Hee Sik (Korea) University of Alabama Partially Ordered Sets, Semirings 12/91 - 12/92 Kim, Seon Jeong (Korea) Louisiana State University Algebraic Geometry 1/92- 12/92 Knarr, Norbert (Germany) University of Notre Dame Differential Geometry, Finite Group 8/92- 5193 Theory Koyama, A. University of Saskatchewan Topology 5/92- 8/92 Kucery, Radan Universite Laval Number Theory 10/91 - 3/93 (Czechoslovakia) Kurylev, Yaroslav (Ukraine) Purdue University Applied Mathematics 8/92- 5193 Ladyzhenskaya, Olga (Russia) Case Western Reserve University Partial Differential Equations 1/93- 6/93 Latushkin, Yuri (Russia) University of Missouri-Columbia Differential Equations, Dynamical 8/92- 8/93 Systems Lee, Youngjo (Korea) Oregon State University Mixed Linear Models and 7/92- 9/92 Mathematical Statistics Leme, Paulo Paes (Brazil) Purdue University Applied Mathematics 8/92 - 12/92 Li, Gang (China) State University of New York at Numerical Analysis and Scientific 7/91 - 7/93 Stony Brook Computing Liverani, Carlangelo (Italy) State University of New York, Stony Dynamical Systems 9/92- 1/93 Brook Lobb, Lawson (Australia) University of California, Santa Calculus, Linear Algebra 10/92 Barbara Markus, A.S. (Israel) University of Calgary Functional Analysis 9/92- 10/92 Mejfa Jorge (Columbia) Syracuse University Partial Differential Equations 5/92- 9/92 Merklen, Hector (Brazil) Syracuse University Representations of Finite-Dimensional 9/92- 12/92 Algebras Mishchenko, Aleksander Brown University Topology 7/92- 12/92 (Russia) Moore, Derek, W. (England) California Institute of Technology Theoretical and Computational Fluid 4/92- 9/92 Mechanics Morimoto, Mitsuo (Japan) University of New Mexico Functional Analysis 1/93- 6/93 Munkholm, Hans Jorgen University of Notre Dame Topology 8/92- 5193 (Denmark) Nash-Williams, C.ST.J.A. West Virginia University Graph Theory, Combinatorics 8/92- 5/93 (England) Ostrovskii, Iosif (Ukraine) Purdue University Complex Analysis 9/92- 11/92 Park, Byung-Gu (Korea) University of Wisconsin-Madison Statistics 1/92- 2/93 Perelman, Grigori (Russia) State University of New York, Stony Differential Geometry 1/92- 6/93 Brook Pitteloud, Yves (Switzerland) Brandeis University Homological Algebra 9/92- 5193 Rolski, Tomasz (Poland) University of North Carolina-Chapel Stochastic Processes 7/92- 7/93 Hill

520 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------·-·····--·~···-···"···················-··Visiting Mathematicians

Name and Home Country Host Institution Field of Special Interest Period of Visit Sahab, Salem (Saudi Arabia) Idaho State University Approximation Theory 6/92- 9/92 Saito, Kimiaki (Japan) Louisiana State University Probability Theory 4/92- 4/93 Serre, Jean-Pierre (France) Harvard University Number Theory 9/92- 12/92 Shi, Jian-Yi (China) University of Notre Dame Algebraic Groups, Representation 8/92- 5/93 Theory Shokranian, Salahoddin Purdue University Automorphic Forms 8/92- 12/92 (Iran/Brazil) Steinberg, David M. (Israel) University of Wisconsin-Madison Statistics 8/92- 7/93 Szekeley, Laszlo (Hungary) University of New Mexico Graph Theory 8/92- 6/93 Tafel, Jacek (Poland) University of Calgary Mathematical Physics 8/92- 10/92 Tempelman, Arkady (Lithuania) Pennsylvania State University Probability-Ergodic Theory 7/92- 6/93 Thandapani, E. (India) University of Saskatchewan Difference Equations 6/92- 7/92 Vahidi-Asl, Mohammad Q. The Johns Hopkins University Probability 9/92- 6/93 (Iran) Wang, Feng (China) State University of New York at Computational Mathematics and 7/92- 6/93 Stony Brook Applied Mathematics Werner, Dirk (Germany) University of Missouri-Columbia Functional Analysis l/93- 8/93 Yan, Keren (China) State University of New York, Stony Operator Theory 9/92- 1193 Brook Yang, Yumin (China) State University of New York at Computational Fluid Dynamics 8/91 - 8/92 Stony Brook Zeng, Yanni (China) Brown University Linear Partial Differential Equations 9/92- 7/93

Differential Geometry, Global Analysis, and Topology A. Nicas and W. F. Shadwick, Editors

This book contains the proceedings of a special session held at the Summer Meeting of the Canadian Mathematical Society in June 1990, at Dalhousie University. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay between geometry, global analysis, and topology. Some topics include applications to: • low dimensional manifolds • control theory • integrable systems • Lie algebras of operators • algebraic geometry

You will appreciate the insight Differential Geometry, Global Analysis, and Topology provides into recent trends in these areas.

1991 Mathematics Subject Classifications: 14, 53, 57,58 ISBN 0·8218·6017·8, 185 pp. (softcover), March 1992 Individual member $30, List price $50, Institutional member $40 CMS individual members can order at the Individual member price. Your ordering code is CMSAMS/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.0. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free B00·321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 521 New Members of the AMS

ORDINARY MEMBERS Thomas Ezra Love, Univ of Xiaohua Xing, Univ of California Polytech State University M M Abu-Jaudeh, Saint Paul's Pennsylvania, Philadelphia Massachusetts, Amherst Philip Laurence Banks College, Lawrenceville, VA Joseph F Lucke, Allentown, PA Ming Wei Xu, Academia Sinica, Matthew W Williams Laurence Thomas Maloney, New Beijing, People's Republic of Mario Bonk, Braunschweig, California State University Hayward Germany York Univ, NY China George Zweig, Los Alamos, NM Jane E Brecha Howard Edward Brandt, Adelphi, Joseph M Martel, Orem, UT Isaak E Mayzlin, Providence, RI Yvonne Y Fok MD Johnson Chua Lim Bela Brindza, Kossuth Lajos Univ, Christine A McMillan, Univ of Patrick E Serpa Debrecen, Hungary Virginia, Charlottesville Wayne H Meyer, Milan, IL Cheryl L Vega Maurizio Carlucci, Rome, Italy RECIPROCITY MEMBERS Martha Ayers Alvey Carter, John M Miller, The Woodlands, TX California State University Beavercreek, OH David John Naples, Saint Edward's Asociaci6n Materruitica Espanola Northridge Uuiv, Austin, TX Zhaolin Cheng, Shandong Univ, Delors Herbera Sheri L Berger David Scott Obrosky, Univ of Jinan, People's Republic of Deutsche Mathematiker-Vereinigung Karen Jean Boydston China Pittsburgh, PA T Offermann, Honolulu, HI e. V. Henry Nelson Browne Donna Lee Copenhaf\)r, Brentwood, Hans-Dietrich 0 F Gronau Marshall Copelan 1N Yun Peng, Johns Hopkins Univ, Baltimore, MD Viktor M H Schroeder William J Drumm Thomas G Davis, West Palm Beach, Hermes Augusto Puyau, Buenos Barbara J Jones FL Thomas Helmut Sonar Aires, Argentina Scott Allan Kelley Alan Davison, Altamonte Springs, Manfred Tasche Buddhavarapu Sailesh Ramarnurtie, FL Irish Mathematical Society Michael Jay King Georgia State Univ, Atlanta Christopher V Devol, Aiken, SC Steven K Knight Chris Larson Rasmussen, College Gerard John Murphy Harvey Dubner, Ridgewood, NJ Donal P O'Donovan Rebecca Lynn Levi Park, MD Janette M Marquand Anita Louise Fagerman, West Igor Reider, Univ of Oklahoma, Mathematical Society of Japan Lafayette, IN Kobina Biney Mends Norman Masafumi Murai Craig Alan Feinstein, Silver Spring, Allen Arthur Pinero Claudiu Cristian Remsing, Rhodes Societe Mathematique Suisse MD Univ, Graharnstown, Republic Bamdad Samii Martin Flucher Robert G Flower, Alburtis, PA of South Africa Michael John Semenoff Dennis S Friday, National Institute David L Rodgers, Mathematical Sociedade Portuguesa de Materruitica Karen Lee Irvine Tait of Standards & Technology, Reviews, Ann Arbor, MI Mohammad Rostami llmar Arno Yitsut Boulder, CO Matthew David Rotelli, Blacksburg, Wiskundig Genootschap Kathleen J Young Zoltan Furedi, Univ of Illinois, VA Abraham Broer Cleveland State University Urbana,IL Kristin A Schleich, Univ of British Jack Chia-Chieh Chen CarlL Gardner, Duke Univ, Columbia, Vancouver, Canada Durham, NC William A Schneeberger, Durham, Robert S Clark Kalpana A Godbole, Michigan NC Constance Jeanne Gardner Technological Univ, Houghton Margaret Seebohm, Livermore, CA NOMINEE MEMBERS Laura Jane Urbanski Adnan M Haider, Alexandria, VA Gregory M Sobko, Santee, CA College of Charleston Leonard B Hearne, Washington, DC Warren G Staley, Tucson, AZ American University Dorothea M Broome Lisa Claire Jeffrey, Institute for Joyce B Higginbotham Yoel Steinberg, Brooklyn, NY Brenda Chapman Advanced Study, Princeton, NJ Andrew Peter Termena, New Arizona State University Marcus Cheung Eric S Klein, City College (CUNY), Carlisle, OH Weiqiang Xie Michelle L Eleazer New York, NY Ami E Trahanovsky-Orletsky, Alfred G Kohler, Fresh Meadows, Hampton, VA Auburn University Douglas R Holmes NY Dietrich A Uhlenbrock, Univ of Edwin H Smith Erin K McNelis Saisankar Kolli, Univ of Louisville, Wisconsin, Madison Buwling Green State University Shannon Moore KY Panagiotis Vezyreas, Willimantic, Michael Steven Dugan College of William & Mary Alexander Kozhevnikov, Univ of CT Heather D DeSimone Haifa, Israel Brigham Young University Marlos A G Viana, Univ of lllinois Maria Sally Frances Relova Brian Andrew LaMacchia, at Chicago Elizabeth A Newman James Eric Tyson Cambridge, MA Song Wang, Dublin, Republic of David LeGrande Smith Melissa L Young Steven E Levy, Washington, DC Ireland Merrill Teemant Edward Kirby Lewis, New York, Senny Widjaja, Corvallis, OR Julie K Thompson Cornell University NY Jody Stegall Williams, Atlanta, GA Tana Jo Wilson Richard A Levine

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

Dartmouth College Mokhtar Boucheikhchoukh SUNY at Albany Mohamed Lemine El Hadrami Gabriele Maria Germann Rebecca A Crabb Michael D Romero Hiroshi Hamada Duke University Hassan Daghigh SUNY at Stony Brook Xiaoyong Han Po-Jen Cheng Tim R Hammond Paul David Friedman Greg Holinberg Anne-Marie Filip Olga G Kharlampovich Steven J Kraseski Li Liu Joel Stephen Foisy Yin Li James G Kuczmarski Kamlesh M Patel Kevin Bruce Foltinek Nilani Liyanage Patrick A Lezark Amy F Rabb-Liu Alexandre I Kabanov Charles Martin Peng Lu Chunwoo Yang Kevin Jay Kesseler Robert Milson SUNY, College at Brockport University of California, Irvine Christopher Thomas Michael Konstantinan Vasilakos William Carl Frank Frank Dell Kronewitter Ioannis Vlassopoulos Jiabin Zhao James Richard Gears University of California, Los Angeles East Carolina University McMaster University Christa L Miller Jonathan Foster Binkley Egloff Charles Wavley Pearson Daniel SUNY, College at Geneseo Alexander Frederic Brown George Mason University Memphis State University Theresa Girardi Daniel K Clegg James Turtora Jiannong Wang Phuonghang Thi Huynh Janet Cowden Christopher P Custer Grand Valley State University Mississippi State University San Diego State University Thomas Martin Kieft Marion Beroujon Harris Paul Martin Lannen Giulio DellaRocca Eknath P Ghate Oktay Kurbanov Naval Postgraduate School Simon Fraser University Angela R Granger Joel R Meulenberg Annette P Cornett Janez Ales Michael W Hardt Haverford College Nicholls State University Antonio Cabal-Rodriguez Abdellah Hssaine Eugenie Lee Hunsicker Courtney L Adams Tai-Yu Chen Myungjoo Kang David A Hebert Roger R Coroas Hofstra University Deborah L Kilb Laura A Lavigne Guanghua Deng Micheline A Schreiber Jah Shiu Liu Catherine L Melancon Shahriar J Fariborz Indiana State University David Richard Nowicki Jennifer Austin Rodriguez Pavol Gvozdjak Bing W Lau Oswaldo R B Oliveira Timothy G Waldrip Susan Marshall Fort Greg C Steele Indiana-Purdue University, Maureen D Watson Raphael A Okojie Wayne Timothy J Surenoonk North Carolina State University Darren Stanley Joni E Davis Michael Alan Zeitzew Alan Douglas Hoffler Jingdong Yu Sharon M Hathaway University of Hawaii North Georgia College Southern Methodist University Inst for Advanced Study Son Yong Kim Tisha Rochell McConnell Robert Roy Ferdinand Ann S Almgren University of Houston Andy 0 Miller Randy C Taylor Leticia Barchini Mazy Jane Ferguson Frank Douglas Nicoletti Analee Witt Max J Bezard Sarah Helen Ferguson Wendy Leigh Roper Southern Oregon State College Gilles D Courtois Lorenzo Hector Juarez Sonya E Smith Mary Ann Agnes Eder Evia Toshiyuki Kobayashi Xuewn Li University Jun Murakami Northeastern University Southwest Missouri State Scott F Powers Jean M Andress Page Starr Min Chen Francisco Javier Sanchez David R McWilliams Nanhua Xi Northern Michigan University Jurgen Kurt Singer Tamara L Smithee Johns Hopkins University, Baltimore Katie L Davidson Cornell Leroy Wooten Lowell E Abrams Stacy Jo Sanders St Olaf College Dexuan Xie Dena S Cowen Oakland University Karen M Brown Canfang Zhai Hung Ding Carol L Lang Patrick T Haertel Zhuangzhi Zhang Kristen E Nelson Erik E Endres Ohio State University, Columbus University of Illinois at Eric Juergen Rawdon Saundra G Hampson Bogdan Bucicovschi Urbana-Champaign Robert D Rosell Masanari Kida Yuqing Chen Jenna Caldwell Deborah E Moyer Kan Yuk Andy Lau Texas Christian University Heng Huat Chan Zoran Z Petrovic Tony J Marie Monroe B Harden Geurnlan Choi Damian A Smiroldo Mark C McClure Trenton State College Brian Thomas Habing Lillian Sorak Linghua Peng Karen Consalvi Meesoon Han Louisiana Tech University Xiaofeng Peng University of Akron Joanna Y Lee Keith M Fletcher Tibor Szabo Doreen E Maxwell Jennifer Ruth Martin Penny J Hix Irina A V aindiner University of Alabama-Birmingham Scott Raymond Meeth Marshall University Dmitry A Vompe Margaret Shull Bierwirth Steven Theodore V ahl Patricia Lynn Coulter Carla C van de Sande Louis Hucon Ephraim Kathleen Mary Vrba Kathryn J Freidel Oregon State University Patresa Darlene Goode Jennjung Wu David James French Dave Carsen Plaehn Kiwon Kim Lee Mingqing Xiao D Shane Jonas Portland State University William D McRae Taeil Yi Mary A Sengewalt Hun Bak Ramya Ramaswamy University of Kansas Mathematics Sciences Res lnst Yanbing Lu Mohammed Reza Riasati Michael Davidson Nimish A Shah James Dale McGlothin University of Arizona University of Laval McGill University Matei Perussi Ahmad Alkhatib Youssef ElFrom Sami Emmanuel Alajaji Purdue University, Calumet Martha T Case Mohammed Elhakimi Phuc V Bi James Calabrese Cheryl L DeLorme Francois Grondin

MAY/JUNE 1992, VOLUME 39, NUMBER 5 523 ······················································································------~·~--··························································································································· New Members of the AMS

Osvaldo Pio Hossian David E Harrelson Welf G Schneider University of Wise, Madison University of Maryland, College Park Dubravko Ivansic Min Shao John Stuart Jordan Paul Robert Harris Caryn L Latham Tianning Shi University of Wise, Stevens Point Georgia A Martin Hong Li Sabine B Spranger Donald R Sruith Yong Li David Austin Pierce University of Southwestern Louisiana University of Wyoming Valentino Zocca Muhammad A Sharif Jose Chong Laila M Bakir Jagat K Sheth University of Michigan Zhaoyun Xing Damian William Betebenner Mustafa Uzel Charles A Pehlivanian University of Texas at Austin Lingxia Li Stanislav M Vasilev Michael Alan Carlisle Brian Joseph Suchomel University of Missouri, Columbia Xiangdong Xie Cristina Dejong Grieg Apostol Todorov Vassilev Wilhelm Michael Sticka Fushen Zhang Valerie Josiane Ventura Nicholas R Visser University of Montana Bingjun Zhou Nikki Rochelle Ash University of Texas at San Antonio Gregg Waterman University of Ottawa Chunyu Chai Cynthia R Aranda William Spencer Weber Yuexiu Zhang Roslyn Marie Denny Karen Rebecca Baker Page Darren White Douglas Edward Galarus University of Pittsburgh, Pittsburgh Gabriel Cano University of the South Weizhong He Frederick K Douglas Stephanie Lopez Cano Saurabh Dutta-Chowdhury Zhigang Zhang Tina Maria Fagan Anastasios Liakos University of the West Indies Weixin Zhou Joseph Herman Magnotta Donna Marie Fazzini Samuel Eric Hairston Robin M Antoine University of N C at Chapel Hill Becky Ann Skerkoski Jodi Jean Healy Lisa Maria McShine Deidre D Goodwin Thamban IlJath V alappil Margaret Bmce Huddleston Karim David Rahaman Jennifer L Laveglia University of Regina Conrad Douglas Krueger Leslie Roy Robinson David William Lyons Suqin Ao Genevieve M Marsh VPI & SU Mir Zia Mahmood Paula L McKenna Tina R Burrell John R Peach University of Rhode Island Dina Lynne Meyer Anthony V Zangara Natalie M Priebe Christos John Schinas Fermin Duenez Ortiz Virginia Commonwealth University Christine Scharlach University of Southern California Ricardo Jose Pina Danny J Turner II Kathleen L Ambmso Juergen K Amendinger Sandra Kay Steitle University of N C at Greensboro Ioana B Boca Elizabeth Anne Tanner Wake Forest University Manuel J Sanders III Di Chen Antoinette Willis J Keith Yarbrough Steven G Wicker Chung-Kuang Chu Frank Zamarripa Washington & Lee University University of Nebraska at Omaha Zhaohui Hao University of Tulsa Brad David Martin Patrick W Prince Insook Kim Karen S Cullison Wellesley College Young Mee Koh University of New Mexico University of Utah Anne Marie Morse Chen-Yao G Lao Changhui Dong Traci Lee Bell Excelsis San Diego Magno Wichita State University University of North Texas Steven Christopher Morrell Kyunghee Moon Angela Diane Zimmerman Jesse William Byrne Robert F Murphy University of Washington University of Notre Dame Katherine C Caplan Xavier University Chiu Yeung Ngo Gregory Otis Cron Meeyoung Kim Susan P O'Hara Barry John Jacobson University of Oklahoma Horia Calin Pop Angela A Pasquale Yeshiva University Paul Andrew Buckelew VandaPop University of Western Ontario Michael Tzvi Segal Cary Evan Crawford Ziwei Qin Serge John David D' Alessio Youngstown State University Rita A Freeman Poomima C Raghu University of Windsor Michele DePinto Jay L Hall Alejandro J Ruiz Shuxin Zhang John Walter Lewis

524 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

for SUGGESTED USES for classified advertising are positions available, books or lecture notes ommendation, including one which addresses sale, books being sought, exchange or rental of houses, and typing services. teaching, to be sent directly to John Randall, from THE 1992 RATE IS $60 per inch on a single column (one-inch minimum), calculated Acting Chair, Department of Mathematics and the top of the type; $30 for each additional 16. inch or fraction thereof. No discounts for multiple Computer Science, Rutgers University, Newark, can ads or the same ad in consecutive issues. For an additional $1 0 charge, announcements NJ 07102. be placed anonymously. Correspondence will be forwarded. Rutgers University is an equal opportu­ Advertisements in the "Positions Available" classified section will be set with a minimum nity/affirmative action employer. one-line headline, consisting of the institution name above body copy, unless additional headline copy is specified by the advertiser. Advertisements in other sections of the classified pages will be set according to the advertisement insertion. Headlines will be centered in boldface at no extra charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, including lines and spaces within. Any fractional text will be charged at the next 16. inch rate. Ads will appear in the language in which they are submitted. JOHN JAY COLLEGE OF Prepayment is required of individuals but not of institutions. There are no member discounts CRIMINAL JUSTICE for classified ads. Dictation over the telephone will not be accepted for classified advertising. THE CITY UNIVERSITY OF NEW YORK AMS DEADLINES are listed on the inside front cover or may be obtained from the Department of Mathematics Advertising Department. U.S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, Assistant Professor, tenure-track position, Sep­ religion or national origin. "Positions Available" advertisements from institutions outside the U. S. tember, 1992. Requirements: Ph.D. Mathe­ cannot be published unless they are accompanied by a statement that the institution does not matics; or expected to have it completed by discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific September 1 , 1992; demonstrated potential for wording may be found near the Classified Advertisements in the January and July/August issues research; strong commitment to teaching. Com­ of the Notices. puter science, numerical analysis or operations SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians research background preferred. John Jay Col­ are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS lege of Criminal Justice, located in Manhattan, (321-4267) in the U.S. and Canada for further information. is a senior college in CUNY. Send resume, SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, graduate transcript, relevant reprints, disser­ Rhode Island 02940. AMS location for express delivery packages is 201 Charles Street, tation abstract and three letters of reference Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are to Sydney Samuel, Chairperson, Department not required to do so. AMS FAX 401-455~4004. of Mathematics, John Jay College of Criminal Justice, 445 West 59 Street, New York, NY 10019 by May 15, 1992. Minorities and women are encouraged to apply. AAIEOE Employer. POSITIONS AVA INDIANA HANOVER COLLEGE UNIVERSITY OF ROCHESTER Department of Mathematics Department of Biostatistics Assistant professor (entry level position) start­ The Department of Biostatistics at the Univer­ ILLINOIS ing September 1992. Responsibilities in general sity of Rochester invites applications for NIH undergraduate mathematics, including intro­ funded postdoctoral positions, beginning Sept. ductory statistics. The successful applicant will 1, 1992. Postdoctoral fellows will participate SOUTHERN ILLINOIS UNIVERSITY demonstrate a dedication to superior teaching in the design and analysis of cancer studies, AT CARBONDALE within the context of the liberal arts. Ph.D. as well as conduct their own independent Temporary Positions required. AAIEOE. Please send letter of ap­ research. The program requires U.S. citizen­ 1992-1993 plic!ltion, vita, transcripts, and at least three ship or permanent residence. Applicants must Department of Mathematics letters of reference to Christine Wilcox, Sec­ possess a Ph.D. or equivalent. Applications retary to the Mathematics Search Committee, from women and minorities are encouraged. Temporary positions are anticipated starting Hanover College, Hanover, IN 47243 .. Contact: Martin A. Tanner, Department of on August 16, 1992 as Lecturer. Masters de­ Biostatistics, Box 630, University of Rochester gree in mathematics or admission to candidacy Medical Center, 601 Elmwood Ave., Rochester, required; Ph.D. preferred. Applicants should NY 14642. AAIEOE. provide evidence of excellence in teaching and foreign applicants must provide evidence of -~NEW JERSEY ability to teach in English effectively. Prefer­ ence given to applicants with research interests RUTGERS-NEWARK ,OHIO compatible with those of the faculty. The du­ Department of Mathematics ties will consist of 12 hours of undergraduate and Computer Science INSTITUT DE CALCUL MATHEMATIQUE mathematics instruction each semester. Clos­ KENT STATE UNIVERSITY one or two Moses Newall Combs ing date May 15, 1992 or until positions are We anticipate Professorships beginning Septem­ B. Beauzamy, P. Enflo, and P. Wang wish to filled. Send applications (including transcripts) Assistant ber 1992, contingent on funding. These are develop their research group on Quantitative to: term appointments. estimates for polynomials in one or several Temporary Positions three-year, non-renewable have recently received the variables and they encourage applications for c/o Ronald Kirk, Chair Candidates should Ph.D., show outstanding promise for research Ph.D. studies (These) in this direction. Department of Mathematics and demonstrate a commit­ The topic has direct applications to Analysis Southern Illinois University at in mathematics, ment to effective teaching. Preference will be (Fourier Analysis, Harmonic Analysis), to Num­ Carbondale given to candidates with research interests ber Theory, and Computer Science (Symbolic Carbondale, Illinois 62901. within representation theory, number theory, Computation, Massively Parallel Programming). SI.UC is an Equal Opportunity/Affirmative Action topology, or geometry. The teaching load will It is supported by the National Science Foun- Employer. be two courses per semester. . dation (U.S.A.), the C.N.R.S. (France), the Applicants should send a curriculum vitae Ministry of Defense (France), and DIGITAL Eq. and arrange for at least three letters of rec- Corp.

MAY/JUNE 1992, VOLUME 39, NUMBER 5 525 -·-·---·-···-··--··-··-··-·--·---·-·····-····-·-···------.------·······-·········-···-···--·······-····-·····-···············-·····-···-················-... ··---······ ··················-·····--·-············ Classified Advertisements

The applicants should be citizens either of all fields of mathematics. Applicants must have from the Swedish Natural Science Research the U.S. or of one of the countries of the a Ph.D. in Mathematics earned or anticipated Institute is available. If such funding is received, European Community. They will have to work by 9/1/92. These positions are available for a the teaching load is reduced to six hours a either in Paris or in Kent, and may have to one-year period. Applicants should send a vita, week. travel between both places. list of publications, a statement describing cur­ The salary is negotiable, with a lower Please write to: Prof. Bernard Beauzamy, rent and planned research, and ask two people starting level of about USD 40,000. lnstitut de Calcul Mathematique, Universite de to send letters of recommendation by July The University of Uppsala is one of the Paris 7, 2 Place Jussieu, 75251 Paris Cedex 31, 1992. All communications should be ad­ oldest in Europe and has a college town at­ 05, France, or to Prof. Per Enflo, Prof. Paul dressed to: Search Committee, Global Analysis mosphere comparable to those of Oxford and Wang, Department of Mathematical Sciences, Research Center, Department of Mathemat­ Cambridge. Uppsala is located 65 km north Kent State University, Kent, Ohio 44242, U.S.A. ics, Seoul National University, Seoul, 151-742, of Stockholm, about a 25 minute drive away Republic of Korea. from the international airport and about 55 min­ utes away from the Mittag-Leffler Mathematical Institute. GUAM Applications, including a curriculum vitae MEXICO and a list of publications, should be sent by UNIVERSITY OF GUAM September 1 , 1992, to UNIVERSIDAD AUTONOMA Division of Mathematical Sciences Chairman METROPOLITANA-IZTAPALAPA CAMPUS Department of Mathematics The University of Guam solicits applications Uppsala University The Department of Mathematics invites ap­ to establish a list of eligibles for the following Box 480 plications for four tenure-track positions at a non-tenure or tenure track, full-time position S-751 06 Uppsala senior level to start at any time after January (one-, two-, or three-year appointment): SWEDEN 1 , 1993. For two of these positions, preference Instructor to Associate Professor (Computer will be given to specialists in any branch of Science) theoretical and applied statistics. Qualifications: Applications will be accepted until the po­ Ph.D. and demonstrated strong research record sition is filled and review of applications will and teaching experience. It is expected that the begin on May 20, 1992. candidate will be able to teach in Spanish after Candidates with an earned Ph.D. in com­ one year's residence in Mexico. We offer com­ puter science will be given preference. Candi­ petitive salaries to suitably qualified applicants. research, Ph.D., dates must have at least a Master's Degree Professor/lecturer, teaching and The university will arrange Mexican visas and also broad in Computer Science with teaching experience specialities, Topology, Algebra, work permits for those hired. in English. at the tertiary level. The successful candidate competence in other. fields, Fluent To apply, send curriculum vitae and arrange undergraduate must have a strong commitment to qualify Long teaching experience at for at least three letters of reference to be sent thesis teaching of both students in mathematics and and graduate levels including supervising to Professor Richard G. Wilson. available imme­ computer science, and a demonstrated interest research, location immaterial, Departamento de Matematicas upon request. in the implementation of a degree program in diately, references and resume Av. Michoacan Y La Purisima S/N computer science. Applicant must be a U.S. Respond to Applicant Code 48, AMS Notices, APDO. Postal 55-534 02940-6248. citizen or permanent resident prior to employ­ P. 0. Box 6248, Providence, Rl C.P. 09340 Mexico, D.F. Mexico ment. This status is necessary for both tenure The Universidad Autonoma Metropolitana or non-tenure track appointments. Rank and lstapalopa Campus is a publicly funded insti­ salary will be commensurate with qualifications tution located in the south-east of Mexico City and experience. with a student body of 15,000 and a mathemat­ Requests for official application forms and PUBLICATIONS FOR SALE ics department of 50 full-time tenured faculty. other information may be directed to the Per­ Normal teaching load is 3-4 trimester courses sonnel Services Division, UOG Station, Mangi­ per year. FERMATICA, a newsletter for Fermat's Last lao, Guam 96923. Send completed application Theorem enthusiasts, issue No 3, ''The Cubic form, updated resume or curriculum vitae, of­ Challenge." Please send $1.95 to Fermatica, ficial graduate transcripts (sent directly from P.O. Box HH24, LEEDS, Yorks, LS8 3TB, awarding institution/s), copies of undergradu­ SWEDEN England to receive your copy. ate transcripts, and three letters of reference or placement file to: UPPSALA UNIVERSITY University of Guam Department of Mathematics Prof. Tower Chen, Chair Computer Science Search Committee The Department invites applications for three MATH SCI PRESS, 53 Jordan Rd., Brook­ c/o Personnel Services Division to five expected tenure positions as lecturers. line, MA 02146, 617-738-0307. Geometric UOG Station, Mangilao, Guam 96923 The starting dates for the appointments are Structures and Nonlinear Physics, $95. Ge­ For more information, call (671) 734-91 09/9535 negotiable within the interval fall semester ometric Computing Science, $85, both by or call Dr. John Rider toll free at 1-800-821- 1992 to fall 1993. We seek candidates in R. Hermann. To appear: Lie Theory and 9233. UOG is an Equal Opportunity Affirmative all areas of Mathematics, but in particular in Generalized Function Algebras. Action Employer. areas that are complementary to those of the current faculty. The traditional strength of our Department is Analysis where our Faculty has the highest international standard. We thus KOREA encourage mathematicians whose interest lie, PUBLICATIONS WANTED for instance, in algebra, geometry, topology, and logic to apply. Should we receive many SEOUL NATIONAL UNIVERSITY Wanted: Mathematical books, journals, reprints, Global Analysis Research Center excellent applications in a certain area, we will make every effort to create a research group in ephemera. Contact R. K. Dennis, Math. Dept., Postdoctoral Positions U., Ithaca, NY 14853-7901. that particular field. White Hall, Cornell Tel: 607-255-4027, FAX: 607-255-7149. email: The Global Analysis Research Center expects The lecturer position entails a 12 hour a dennis@ mssun7.msi.cornell.edu to have several postdoctoral positions begin­ week teaching duty. However, for mathemati­ ning Fall 1992. Applications are welcome in cians actively involved in research, funding

526 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY UMETRENDS News and Reports on Undergraduate l\lathematics Education

UME TRENDS is an 8-page newsletter filled with the most recent developments in mathematical education. You will find valuable and often controversial articles on

timely subjects such as: ~zz~ lVotewort]) YBooks .A Media Vie 8JJ.d Such: • Ws and R. . ~~V eviews Educational developments in mathematics departments • Descriptions and evaluations of innovative educational programs • Minorities and mathematics • Reports on research in undergraduate mathematics education • Capsule reviews of noteworthy educational articles • Current information on activities at the National Science Foundation

Learning Software Exchange on Teaching Innovations ~ EDITED BY DAVID A. SMITH

Ifyou are concerned with bringing the problems of mathematics education to the attention of mathematicians involved with research, teaching, and industry, subscribe today!

The subscription fee for Volume 4 (six issues) is $12 ($20 outside the U.S.). Prepayment is required. Call toll-free (800)321-4AMS in the continental U.S. and Canada to charge to VISA or MasterCard or send your prepaid order to American Mathematical Society P.O. Box 1571 Annex Station Providence, RI 02901-1571. ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• NATIONAL UNIVERSITY OF Sl NGAPORE

. ' ; . DEPARTMENT OF MATHEMATICS

Applications are invited forteaching appointments studentenrolmentofsome 15,000. All departments attheLecturerorSenior Lecturerlevelfromcandi­ are well-equipped with a wide rangeoffacilitiesfor dates who are able to teach in one or more of the teaching and research. following areas: All academic staff have access to the following Pure Mathematics computer and telecommunication resources: an Applied Mathematics individual microcomputer(an IBMAT-compatible Operations Research or Apple Macintosh); an IBM mainframe computer Statistics with 16 MIPS of computing power; an NEC SX supercomputer with 650 MFLOPS of computing Candidates should possess a PhD degree in Math­ power; departmental laser printers; a wide spectrum ematics ora relevant field and have a strong commit­ of mainframe and microcomputer software; voice­ ment to teaching and research. mail. A campus-wide network, which is based on the high speed optical fibre based FDDI technology, Gross annual emoluments range as follows: links up all the academic staff and student micro­ computers, UN IX workstations and provides access Lecturer S$50,390 64,200 to the mainframe computer, the supercomputer, Senior Lecturer S$58,680 100,310 UNIX hosts, the on-line I ibrary catalogue, Internet (US$1.00=S$1 .61 approximately) and BITNET.

The commencing salary will depend on the candidate's qualifications, experience and the level Application forms and further information on terms of appointment offered. and conditions of service may be obtained from:

Leave and medical benefits will be provided. De­ pending on the type of contract offered, other ben­ The Director efits may include: provident fund benefits or an end­ Personnel Department of-contractgratuity, asettling-in allowanceofS$1 ,000 National UniversityofSingapore or S$2,000, subsidised housing at nominal rentals 10 Kent Ridge Crescent ranging from S$1 OOtoS$216 p.m., education allow­ Singapore0511 ance for up to three children subject to a maxim urn ofS$16,425 per annum per child, passage assistance The Director and baggage allowance for the transportation of North America Office personal effects to Singapore. Staff members may National UniversityofSingapore undertake consultation work, subject to the ap­ 55 East 59th Street proval of the University, and retain consultation fees New York; NY 10022, U.S.A. up to a maximum of 60% of their gross annual Tel:(212)751-0331 emoluments in a calendar year.

The Department of Mathematics is a department in Enquiries may also be sentth rough B ITN ETto: the Faculty of Science. There are eight faculties in PERPL@ NUS3090,orthroughTelefax: the National UniversityofSingaporewith a current (65) 7783948 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• NANYANG TECHNOLOGICAL UNIVERSITY NATIONAL INSTITUTE OF EDUCATION

ACADEMIC APPOINTMENTS IN MATHEMATICS & MATHEMATICS EDUCATION The Nanyang Technological University (NTU) is a full and comprehensive university. Courses that are offered currently at NTU include Accountancy, Arts, Business, ComputerTechnology, Education, Engineering (Civil, Electrical & Mechanical) and Science. The National Institute of Education (NIE) as part oft he University is responsible for the training ofteachers of all subjects at pre-school, primary, secondary and pre-university levels. It aims to achieve excellence in teacher training and research in arts, science, education and physical education. It offers courses that range from diploma to degree and post-graduate levels. Applications are invited for Faculty appointments in the Division of Mathematics of the School of Science from candidates who must possess a relevant PhD degree. Preference will be given to those who are able to teach in more than one of the areas listed and with proven ability in research. Candidates for Mathematics Education positions should also have a professional teaching qualification and at least 2 years of relevant qualified teaching experience.

Algebra • Analysis Geometry • Operations Research Teaching of Primary/Secondary Mathematics

Salary and Conditions of Service Gross Annual Emoluments range as follows:

Professor : S$1 08,870 - S$146,970 Associate Professor : S$ 88,650 - S$122,870 Senior Lecturer : S$ 58,680 - S$1 00,31 0 Lecturer : S$ 39,350- S$ 64,200

The commencing salary will depend on the candidate's qualifications, experience, and the level of appointment offered. Leave, medical and provident fund benefits will be provided. Candidates wishing to be considered should write or fax to:

Director of Personnel NANV ANG TECHNOLOGICAL UNIVERSITY Nanyang Avenue Singapore 2263 Fax: 791 9340 giving their Curriculum Vitae and the names and addresses of Three Referees. MATHEMATICAL SciENCES RESEARCH INSTITUTE 1000 CENTENNIAL DRNE, BERKELEY, CALIFORNIA 94720

The Institute solicits applications for membership during the 1993-94 year, which begins on September?, 1993. In 1993-94 two programs will be featured. Although these areas will be emphasized, applications from candidates in all fields will be welcome.

DIFFERENTIAL GEOMETRY. A full-year program with greater activity in the Fall term. The following two areas will be emphasized:

Riemannian Geometry/Geometric Structures. (Main Area) Topics will include: 1. Curvature and topology; 2. Minimal submanifolds and harmonic maps; 3. Spectral geometry (including analytic torsion and Quillen metrics); 4. Spaces of Riemannian manifolds (compactness, collapse, F-structures, etc.); 5. Geometric inequalities (including isoperimetric and isosystolic inequalities, filling radius, simplicial volume, etc.); 6. Spaces of non-positive curvature (structure at infinity, rigidity, buildings, etc.); 7. Einstein spaces and reduced holonomy; moduli; 8. Conformal, affine, and symplectic geometry; Thurston geometries.

Geometry and Physics. (Secondary Area) Topics will include: 1. Gauge field theory, Donaldson theory, Floer homology, the Chem-Simons functional, monopoles, elliptic cohomology; 2. Gravity and twistor theory; 3. Riemannian geometry in infinite dimensions; quantum field theory. The program committee consists of" W. BaUmann, R. Bott, R. Bryant, C. Gordon, M. Gromov, K. Grove, B. Lawson (chairman), R. Schoen.

DYNAMICAL SYSTEMS AND PRoBABILISTIC METHODS FOR PDE's. The aim of the 1994 program will be to bring together mathematicians, applied mathematicians, physicists, numerical analysts and experimentalists working in related areas, to explore common interests. The program will include workshops devoted to specific scientific areas, such as water waves and nonlinear optics. Topics in the program will include: 1. The emergence of statistical methods, as well as dynamical systems methods, in the analysis and numerical study of evolutionary POE's; 2. Recent developments in infinite dimensional KAM problems, in the stability, scattering and long-time asymptotics of nonlinear waves, and in the use ofrenormalization methods for evolutionary POE's; 3. Fundamental successes,. such as the theory of completely integrable soliton equations and the theory of inertial manifolds. · The program committee consists of· P. Delft (co-chairman), P. Holmes, J. Hyman, D. Levermore, D. McLaughlin (co­ chairman), C. Wayne.

PosTDOCTORAL FELLOWSHIPS We anticipate making approximately 20 awards of postdoctoral fellowships. The stipend for 1992-93 is $30,000 and it will be at least that for 1993-94. In addition there is an award for round trip travel. The candidate's Ph.D. should be 1988 or later. Candidates are asked to solicit three letters of recommendation. Most awards are for a year, but a shorter period is possible. The deadline for applications is November 30, 1992.

RESEARCH PROFESSORSHIPS These awards are intended for midcareer mathematicians; the applicant's Ph.D. should be 1987 or earlier. There is an earlier deadline for applications: September 30, 1992. Please see the separate announcement of these awards elsewhere in this issue of theNotices. Candidates may apply for both a General Membership and a Research Professorship (but only one award will be made per candidate). GENERAL MEMBERSHIPS Applications are invited for part or all of 1993-94. Letters of recommendation are encouraged but not required. It is generally expected that members at this level will come with partial or full support from other sources. The deadline for applications is November 30, 1992. FURTHER REMARKS Starting with applications for 1993-94, MSRI is introducing application forms. If you are interested in applying, you should request an application form. Write to: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley CA 94720, or send email to: info@msri. org with the message: get program app. ascii (or app. TeX, if you prefer). Women and minority candidates are especially encouraged to apply.

Candidates are asked to make sure that their application materials and letters of reference arrive by the deadline (September 30, 1992 for Research Professorships and November 30, 1992 for the others). Late applications cannot be assured a complete consideration. Awards will be announced by early December, 1992 for Research Professorships and by mid-February, 1993 for the others.

In 1994-95 MSRI will feature two programs: Automorphic Forms, and Low Dimensional Dynamical Systems. 'The Institute is committea to tfie princip{es of'Equa[ Opportunity ana .9Lffirmative Ylction. RESEARCH PROFESSORSHIPS at the MATHEMATICAL SCIENCES RESEARCH INSTITUTE 1000 CENTENNIAL DRIVE, BERKELEY, CALIFORNIA 94720

The Mathematical Sciences Research Institute (MSRI) announces the availability of Research Professorships for the 1993-94 year.

These awards are intended for midcareer mathematicians; the applicant's Ph.D. should be 1987 or earlier. An award for a full academic year will be limited to a ceiling of $30,000 and normally will not exceed half the applicant's salary. Appointments can be made for a portion of the year; the $30,000 ceiling and half salary limit would then be prorated. It is anticipated that between six and ten awards will be made. In addition to the basic stipend, there will be an award for round trip travel to MSRI.

In 1993-94 MSRI will feature two programs: Differential Geometry, and Dynamical Systems and Probabilistic Methods for POE's. Please consult the general MSRI announcement for 1993-94 elsewhere in this issue of the Notices. Research Professorships are directed to applicants in all fields of the mathematical sciences. There are also General Memberships, which normally offer smaller awards. An applicant may apply for both (but only one award will be made per applicant). Women and minority candidates are especially encouraged to apply. Beginning with applications for 1993-94, MSRI is introducing application forms. If you are interested in applying, you should request an application form. Write to: MathematicalSciencesResearchlnstitute, 1000 Centennial Drive, Berkeley CA 94720, or send email to: info@msri. org with the message: get program app. ascii (or app. TeX,ifyou prefer). Candidates are asked to make sure that their application materials and letters of reference arrive by the deadline of September 30, 1992 for Research Professorships. Late applications cannot be assured a complete consideration. Awards will be announced in early December, 1992. Send applications to the address shown above.

?Jie Institute is committed to tlie principfes of'Equal Opportunity and~ffirmative ~ction .

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• UNIVERSITY OF CAMBRIDGE • • Isaac Newton Institute for Mathematical Sciences •

ROSENBAUM VISITING FELLOWSHIPS • Applications are invited for Rosenbaum Visiting Fellowships The stipend of a Fellow will be $17,500 for the six-month at the Isaac Newton Institute for Mathematical Sciences. tenure and travel expenses may be provided. To be eligible, Four Fellowships of six-months duration will be awarded candidates must have a Ph.D. and be U.S. citizens or annually out of funds generously provided by the Paul and permanent residents or have resided in the U.S. for a mini­ Gabriella Rosenbaum Foundation. There will be one Fel­ mum of four years. lowship associated with each of the four scientific programmes run by the Institute. The programmes planned for 1993-94 Applications, including a curriculum vitae, list of publica­ are: tions and the names of two referees, should be sent by 30 September 1992 (in the case ofthe july to December 1993 Computer Vision programmes) or 31 March 1993 (in the case of the january to (July to December 1993) june 1994 programmes) to: Random Spatial Processes (july to December 1993) Deputy Director, Dr. Peter Goddard Geometry and Gravity Isaac Newton Institute for Mathematical Sciences (January to june 1994) 20 Clarkson Road Cellular Automata, Aggregation and Growth Cambridge CB3 OEH, U.K. (January to june 1994) (from whom further details of the programmes can be obtained) ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Proceedings of Symposia in PURE MATHEMATICS SYDNEY, AUSTRALIA Equality of employment opportunity Is Unfverslty policy Complex Geometry SCHOOL OF MATHEMATICS-~ and Lie Theory PROFESSOR OF James A. Carlson, PURE MATHEMATICS CHAIR OF C. Herbert Clemens, Applications are invited for the Chair of Pure Mathematics PURE MATHEMATICS David R. Morrison, Editors which becomes vacant following the appointment of the present incumbent, Professor G. Brown as Deputy Vice­ Reference No: 13/01 Chancellor (Research) at the University of Adelaide. The other Applications and expressions of interest are invHed for Chair of Pure Mathematics is held by Professor M.G. Cowling. appointment to a Chair of Pure Mathematics within the This volume contains thirteen pa­ Applicants should have a distinguished record of research and School of Mathematics and Statistics which fell vacant scholarship in a branch of Pure Mathematics, and the ability to on 1 January 1991 on the retirement of Professor pers presented during the Sympo­ provide academic leadership to the Department and School. G.E.Wall, FAA. sium on Complex GeometJ:y and Lie The School of Mathematics is one of the largest in Australia, The University is seeking applicants with a capacity for Theory held in Sundance, Utah, in and has a record of excellence in research, as well as a leadership who can make a major contribution to the commitment to excellence in teaching at all undergraduate and School's excellence in research and teaching. May 1989. The symposium reviewed postgraduate levels. Within the School, the Department of Established areas of research in Pure Mathematics twenty years of interaction between Pure Mathematics, with an academic staff of around 25, has include category theory, algebraic groups and their active research groups in functional analysis, operator representations, computational algebra and number these two fields, concentrating on algebras, harmonic analysis, ergodic theory, partial differential theory, dynamical systems, singularity theory, group their links with Hodge theory. equations, mathematical physics, relativity, discrete theory, geometric topology, number theory and Complex Geometry and Lie Theory mathematics, group theory, number theory and combinatorics. combinatorics. While preference may be given to The Department encourages both basic and applied research, applicants with expertise in one of the above areas, is a valuable resource for graduate and collaborative interaction with other Departments and suitably qualified persons from any branch of Pure students and other researchers who In Mathematics are Invited to apply. Schools within the University and with external bodies. wish to learn about the field. addition, the School of Mathematics is currently building It is·anticipated that interviews for the Chair will be held strength in the areas of mathematical computer science, and within three months of the closing date. computational science and engineering. Salary will be at the rate of A$73 800 - A$77 900 per 1991 Mathematics Subject Classifications: The appointee will be expected to serve as Head of annum (top of salary range will not be available until 23 32; 14, 22, 58, ISBN 0-8218-1492-3, Department or Head of School for a term or terms if so July 1992). Provision is also made for limited private 348 pp. (hardcover). December 1991 requested. consulting in accordance with the University's Indiv. mem. $44, List $73, lnst. mem. $58 Further information may be obtained from Professor I.H. regulations. Assistance with relocation expenses to Your ordering code is PSPUM/53NA Sloan, Head of School, (telephone: international number Sydney will be provided. +61 2 697 2957; facsimile: international number Enquiries about the School and the Chair should be +61 2 662 6445). directed to the Head of School In writing, Salary: AUS $73,800 per annum, rising to AUS $77,900 per by telephoning 61 2 692 4533 or by faxing to annum after July 23, 1992. 61 2 692 4534. Subject to consent by the University, Professors may The University reserves the right not to proceed with undertake a limited amount of higher consultative work. any appointment for financial or other reasons. The University reserves the right to fill any chair by invitation. Membership of a superanuation scheme may be a condition of employment for new appointees. Ref Applications close: Friday July 31, 1992. 92/1511. Method of Application for Academic positions: All prices subject to change. Free shipment by Four copies of the application, quoting reference no., surface; for air delivery, please add $6.50 per including curriculum vitae, list of publications and the title. Prepaymentrequired. Orderfrom:Ameri­ Details of the position, together with conditions of names, addresses and fax nos., of no more than frve can Mathematical Society, P.O. Box 1571, appoinlment, ate available from Ms Margaret Aillerr, referees, to be lodged by the above closing dates Annex Station, Providence, RI 02901-1571, or Senior Appointments Unit, UNSW, PO Box 1, All applications to be sent to: the Assistant Registrar call toll free 800-321-4AMS (321-4267) in the Kensington, NSW 2033, Australia, (telephone: (Appointments), Staff Office (K07), The University of continental U.S. and Canada to charge with Sydney, N.S.W. 2006, AUSTRALIA. Facsimile VISA or MasterCard. Canada residents, please international number +61 2 697 2728; facsimile: 61 2 692 4316 by 11 June 1992. intemalional number +61 2 313 6561}. People from include 7o/o GST. Equal employment opportunity and targeted EEO groups ate encouraged to apply. no smokmg m the wotkpluce are Untvetstty poltctes 86117 THE SWISS FEDERAL INSTITUTE OF TECHNOLOGY LAUSANNE L'ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE (EPFL)

invites applications for a position of an

ASSISTANT PROFESSOR IN DIFFERENTIAL GEOMETRY for its Department of Mathematics LECTURER • FIXED TERM •••••••••••••••••••••••••• School of Mathematics and Statistics Reference No: 817/14 Applications are invited for appointment to the position of Lecturer in the School of The new professor should be a young and active researcher whose Mathematics & Statistics. The School has active research groups in the following areas: Algebra, Analysis, Nonlinear Analysis, Applied Mathematical and Computational research area is in Riemannian geometry or Riemann surface Modelling, Statistics, Topology and Geometry, Category Theory and Combinatorics, theory. He will participate in the teach"ing Computational and Discrete Mathematics. program of the Strong preference will be given to candidates whose research interests are in the areas Mathematics Department. The position is limited to three years, of Algebra, Analysis and Topology and whose appointment would strengthen existing research groups in the School. Candidates must have a PhD, a strong research reoord a prolongation to six years is not excluded. and a demonstrated commHment to excellence in teaching. Courses in mathematics are given at all undergraduate and postgraduate levels and include computer-based courses. Both research and teaching are supported by a large network of worf

UNIVERSITY OF CAPE TOWN Dept of WEB DEVELOPMENT CORPORATION WEB Development Corporation invites applications for the Mathematics: position of: Professor1 Associate Professor1 RESEARCH ASSOCIATE Senior Lecturer /Lecturer An ideal candidate should have experience in pattern Applications are inv~ed for two vacant posts in the Deportment of Mathematlcs. recognition, signal processing or related fields, as well as Candidates in all fields of Mathematics are invited to apply. For the Chair. extensive programming expertise. the University seeks to secure the services of a mathematician of interna­ tional repute, whose presence and activ~ies will also be of benefit to mathematicians or other scientists outside of his/her immediate speciality. A Ph.D. degree in Mathematics, Computer Science or The ranks of the successful applicants will be decided upon the basis of qualifications and experience. Electrical Engineering is required. The remuneration packages include attractive statt benefits such as non­ contributory medical aid, a housing subsidy in certain circumstances, and a pension scheme. Further details are available on request. WEB Development is a small research laboratory near Further information may be obtained from CSIRIS, Su~e 350, 4801 Philadelphia whose current activities span computer sci­ Massachusetts Avenue, NW Washington DC 20016. ence, cognitive science, optics and physical chemistry. Applicants should subm~ a full curriculum v~ae and the names, addresses and telephone numbers of three referees nat later than 30 June 1992 to the Appointments Officer, University of Cape Town, Rondebosch 7700, Republic of South Alrica; telephone (21) 650-2192; fax (21) 650-2138. (Late Please send resume with two references to: applications will be considered.) Candidates should indicate in their letters of application for which post Is they wish to be considered. Dr. Mahmut Guner The policy and practlce of the Univers~ of Cape Town are to oppose dis­ criminatlon on grounds of gerder, race or creed in any sphere of univers~ WEB Development Corporation rne. UCT has consistently protested, and conftnues to protest. against aport­ held laws and practices and ~ committed to working towards a just future Longwood Corporate Center South for our country. lnformafton on this is available on request. 415 McFarlan Road C73006/1660-0 Kennett Square, PA 19348 TOPICS IN APPLIED MATHEMATICS New! JOURNAL OF NONPARAMETRIC STATISTICS Editor in Chief: I.A. Ahmad, Division of Statistics and Statistical Consulting Laboratory, Northern Illinois University, De Kalb, Illinois, USA This journal covers all theoretical and applied aspects of nonparametric statistics, including model (distribution)-free methods, rank procedures, parameter-free methods, functions-functional estimation and inference, inference of stochastic processes, nonparametric Bayes methods and decision procedures, and semiparametrlc techniques. 4 issues per volume • ISSN: 1048-5252 • Current subscription: Volume 1 (1992) New! OPTIMIZATION METHODS AND SOFTWARE Editor in Chief: Yu.G. Evtushenko, Computing Center, Russian Academy of Sciences, Moscow, Russia Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. 4 issues per volume • ISSN: 1055-6788 • Current subscription: Volume 1 (1992) OPTIMIZATION A Journal of Mathematical Programming and Operations Research Previously published by Akademie Verlag, Berlin, Germany Editor in Chief: K.·H. Elster, TU Delft Faculty of Technical Mathematics and Information, Delft, The Netherlands The journal publishes theoretical and applied papers related to the fields of linear, nonlinear, stochastic, parametric, discrete and dynamic programming; control theory; game theory; mathematical modelling of economic and technological processes; inventory; queueing theory; reliability; renewal theory; and network methods. 4 issues per volume • ISSN: 0233-1934 • Current subscription: Volumes 23-26 (1992) SYSTEMS ANALYSIS-MODELLING-SIMULATION Journal of Mathematical Modelling and Simulation in Systems Analysts Previously published by Akademie Verlag, Berlin, Germany Editor in Chief: A. Sydow, GMD-Research Institute for Innovative Computer Systems and Technologies, Berlin, Germany Published are articles on systems analysis and systems theory, modelllng and simulation in environmental protection, macroeconomics, agricultural production, regional planning, biosciences, traffic control, large engineering systems, resources distribution, and management systems. 4 issues per volume • ISSN: 0232-9298 • Current subscription: Volumes 9-11 (1992) STATISTICS A Journal of Theoretical and AppDed Statistics Previously published by Akademie Verlag, Berlin, Germany Editor in Chief: 0. Bunke, Humboldt Universitiit zu Berlin, Germany This journal publishes theoretical and applied papers related to the different fields of statistics, including regression and variance analysis, design of experiments, foundations of statistical inference, statistical decision theory, testing hypotheses, parameter estimation, nonparametric methods, sequential procedures, time series and statistical prob­ lems for stochastic processes, and statistical data analysis. 4 issues per volume • ISSN: 0233-1888 • Current subscription: Volumes 23-24 (1992) -Send for a free sample copy!- For pricing information or to obtain a free sample copy of any journal, please contact the publisher For Faster Semce In the US: Call (800) 545-8398 • Fax (212) 645-2459 In all other countries, contact the UK office: Call (0734) 568316 • Fax (0734) 568211 The Unified Computation Probability and Random Advances in Numerical Laboratory Processes Analysis Modelling, Specifications, and Tools Problems and Solutions Volume I: Nonlinear Partial Differ­ EDITED BY CHARLES RAITRAY AND GEOFFREY GRIMME1T AND ential Equations and Dynamical RoBERT G. CLARK DAVID STIRZAKER Systems This book is concerned with the theory This book contains 675 problems in EDITED BY WILL LIGHT and techniques required in the con­ probability and random processes, 1991 224 pp.; 29 illus. struction and implementation of together with their solutions 853438-8 $52.00 complex software. April 1992 376 pp.; 1 illus. (The Institute ofMathematics and its 853448-5 paper $18.95 Volume II: Wavelets, Subdivision Applications Conference Series, New Series) Algorithms, and Radial Basis June 1992 480 pp.; 68 illus. Patterns and Waves Functions 853684-4 $85.00 The Theory and Applications of EDITED BY WILL LIGHT May 1992 224 pp.; 5 illus. Reaction-Diffusion Equations 853439-6 $55.00 PETER GRINDROD Reliable Numerical This textbook introduces the theory of Computation certain classes of nonlinear partial Algebraic Computing EDITED BY M.G. Cox AND differential equations known collectively S.IiAMMARuNG as reaction-diffusion equations. with REDUCE This essential reference for all numerical (Oxford Applied Mathematics and Comput­ MALcoLM A.H. MAcCALLUM AND analysts is completely up-to-date witli ing Science Series) FRANCIS J. WRIGHT the latest developments on the Lancws 1991 256 pp.; 69 illus. This book provides a comprehensive algorithm, QR-factorizations, error 859692-8 paper $39.95 introduction to the versatile REDUCE propagation models, parameter estima­ 859676-6 cloth $75.00 software. tion problems, sparse systems, and September 1991 320 pp. Oscillation Theory of Delay 853443-4 paper $24.95 shape-preserving splines. 853444-2 cloth $65.00 1991 368 pp.; 33 illus. Differential Equations 853564-3 $75.00 With Applications I. GYORI AND G. LADAS Cryptography and Coding II Introducing Einstein's This monograph on delay differential EDITED BY CHRIS MITCHELL Relativity equations includes applications to a This conference proceedings covers RA. D'INvERNo variety of scientific problems. both cryptography and coding theory . The objectives of this book are to (Oxford Mathematical Monographs) (The Institute ofMathematics and its familiarize students with the basic ideas September 1991 384 pp. Applications Conference Series, New Series 853582-1 $85.00 and equations of Einstein's theory, and 33) to cover three main topics: black holes 1992 320 pp.; 73 illus. gravitational waves, and cosmology. ' 853393-4 $87.00 1992 400 pp.; 213 illus. The Mathematical Revolution 859653-7 cloth $75.00 Inspired by Computing 859686-3 paper $39.95 EDITED BY J.H. JoHNSON AND M.J. LoOMES This conference volume examines the Disorder in Physical Systems Variational Methods in impact of computers on mathematics. Mechanics A Volume in Honour of John (The Institute ofMathematics and its Hammersley Applications Conference Series, New Series 30) TosHio MuRA AND TATSUHITO KoYA EDITED BY G.R GRIMMETT AND 1991 344 pp.; illus. The recent success and popularity of D.J.A. WELSH 853658-5 $55.00 the finite-element method, crucial to This volume surveys the current state of solving mathematical problems in research in random phenomena. Integral Equations many branches of engineering today, is 1990 392 pp.; 26 illus. JIRO KoNDO based on the variational methods 853215-6 $75.00 All the main classes of integral equations discussed in this textbook. March 1992 336 pp.; 73 illus. including Volterra, Fredholm, and 506830-0 $39.95 Probability and Random nonlinear integral equations are covered Processes in this textbook. Second Edition (Oxford Applied Mathematics and Comput­ GEOFFREY GRIMMETT AND ing Science Series) DAVID STIRZAKER October 1991 464 pp.; 31 illus. Linear Algebra 859691-X paper $35.00 STERLING K BERBERIAN From revie1vs of the first edition: "This 859681-2 cloth $80.00 new textbook on probability and This textbook provides a rigorous introduction to the main concepts of stochastic processes should quickly linear algebra, including the basic become established as one of the best theory of vector spaces and linear maps texts available." -The Times Higher and more advanced topics. Education Supplement. 1992 376 pp.; 48 illus. March 1992 416 pp.; 19 illus. 853436-1 $39.95 853665-8 paper $35.00 853666-6 cloth $67.50 NOTICE TO NATURALIZED CITIZENS FROM, OR WHO HAVE RESIDED FOR A SIGNIFICANT PERIOD OF TIME IN, THE FOLLOWING COUNTRIES: Afghanistan, Albania, Angola, East Berlin, Bulgaria, Cambodia (Kampuchea), Cuba, Czechoslovakia, Estonia, Ethiopia, German Democratic Republic (East Germany), Hungarian People's Republic (Hungary), Iran, Iraq, Democratic People'sRepublic of Korea (North Korea), Laos, Latvia, Libyan Arab Republic, Mongolian People's Republic (Outer Mongolia), Nicaragua, People's Republic of China, Poland, Rumania, Southern Yemen, Syria, Union of Soviet Socialist Republics, Democratic Republic of Vietnam (North Vietnam), South Vietnam, Yugoslavia, the Kurile Islands and South Sakhalin (Karafuto). YOU MAY HAVE BEEN THE VICTIM OF UNCONSTITUTIONAL DISCRIMINATION BASED ON YOUR NATIONAL ORIGIN If you are a naturalized United States citizen nently enjoined the DoD from enforcing it. and your country of origin is included Huynh v. Cheney, 87~3436 TFH (D.D.C. above, or you resided in one of these coun~ March 14, 1991). tries for a significant period of your life, the If you are a naturalized citizen and you Department of Defense (DoD) or a DoD believe you have been adversely affected by contractor may have unlawfully denied you a the enforcement of the regulation on or security clearance or employment, promo~ after January 2, 1987, you may have certain tion, fellowship or scholarship that required legal rights. For further information, you a security clearance, or asked you to apply should contact the United States for a Limited Access Authorization, as a Department of Justice Office of Special result of DoD's enforcement of a regulation Counsel for Immigration Related Unfair which denied security clearances to newly Employment Practices (OSC), by calling naturalized United States. citizens from these 1~800~255~ 7688 or (202) 653~8121; 1~800~ countries or who resided in these countries 237~2515 or (202) 296~0168 (TDDdevice for a significant period. for the hearing impaired); or by writing to The DoD and DoD contractors acted OSC, P.O. Box 65490, Washington, D.C. pursuant to a regulation that became effec~ 20035~5490. The OSC will provide infor~ tiveonJanuary 2, 1987. Although DoD mation and help you process a claim free of rescinded the regulation on February 12, charge. The opportunity to pursue these 1988, it may have been applied after that rights is subject to certain time limits, so if date. The United States District Court for you believe the regulation was applied to the District of Columbia has declared the you, contact the Office of Special Counsel regulation unconstitutional and perma~ as soon as possible. Klaus Doerk, University ofMainz, Germany Trevor Hawkes, University ofWarwick, Coventry, England Finite Soluble Groups 1992. xiv + 891 pages. Cloth $148.00 ISBN 3-11-012892-6 de Gruyter Expositions in Mathematics, Vol. 4 Editors: 0. H. Kegel, V. P. Maslov, W. D. Neumann, andR. 0. Wells, Jr.

This book presents an overall picture of the theory of ftnite soluble groups as it has developed over the past thirty years. Emphasis is on those parts of the subject where a coherent and unifted body of knowledge has emerged: the theory of Schunck classes and formations with their associated projectors and normalizers; and the dual theory of Fitting classes with their injectors and radicals. The book is essentially self-contained and includes all the basic and prerequisite results from group theory and representation theory to make it accessible to the student who is familiar with the basic methods of modem algebra. As a standard reference the book should provide a stimulus to further research in a subject area that has shown itself capable of a vigorous new life. Contents: Prerequisites-General Group Theory • Prerequisites-Representation Theory • Introduction to Soluble Groups • Classes of Groups and Closure Operations • Projectors and Schunck Classes • The Theory of Formations • Normalizers • Further Theory of Schunck Classes • Further Theory of Formations • Injectors and Fitting Sets • Fitting Classes-Examples and Properties Related to Injectors • Fitting Classes-The Lockett Section • Fitting Classes-Their Behaviour as Classes of Groups • Appendix a: A Theorem ofOates and Powell • Appendix {3: Frattini Extensions.

Anvarbek M. Meirmanov, University ofBonn, Germany The Stefan Problem Translated from the Russian by Marek Niezg6dka and Anna Crowley 1992. ix + 245 pages. Cloth $89.00 ISBN 3-11-0114 79-8 de Gruyter Expositions in Mathematics, Vol. 3 Editors: 0. H. Kegel, V. P. Maslov, W. D. Neumann, andR. 0. Wells, Jr.

This monograph offers an exposition of most recent results on evolutionary problems with free boundaries of Stefan type. The central part of the book is devoted to the author's famous results on the existence of classical solutions to the multidimensional Stefan problem. Topics covered include: local and global existence of solutions of one- and two-phase problems, use of Lagrange variables in multidimensional problems, classical solutions of one-dimensional problems (including the problem of filtration), properties of generalized solutions (mushy regions), approximate models and crystallization problems. This book is intended for advanced students and research mathematicians, in particular applied mathematicians and engineers.

Contents: Preliminaries • Classical Solution of the Multidimensional Stefan Problem • Existence of the Classical Solution to the Multidimensional Stefan Problem on an Arbitrary Time Interval• Lagrange Variables in the Multidimensional One-Phase Stefan Problem • Classical Solution of the One-Dimensional Stefan Problem for the Homogeneous Heat Equation • Structure of the Generalized Solution to the One-Dimensional Stefan Problem. Existence of a Mushy Region • Time-Periodic Solutions of the One-Dimensional Stefan Problem • Approximate Approaches to the Two-Phase Stefan Problem • Appendix:/. G. Gotz, A. M. Meirmanov: Modelling of Binary Alloy Crystallization. Prices are subject to change.

For North America: Walter de Gruyter Walter de Gruyter, Inc. 200 Saw Mill River Road Berlin • New York Hawthorne, NY 10532 A NEW PUBUCATION GROUPES LINEAIRES REPRESENTATIONS OF ALGEBRIQUES REAL REDUCTIVE GROUPS R.Bedard A.W.Knapp Ces notes constituent une in­ Lecture notes. Contents: Com­ THE ZETA FUNCTIONS OF troduction a la theorie des pactgroups; General theory for groupes algebriques affines et noncompact groups; Classes of PICARD MODULAR sont accessibles au lecteur representations; Appendix A: possedant les notions de base Exercises; Appendix B: Sup­ SURFACES ae la topologie generale et de plementary lectures; Index. l'algebre commutative. 1990 . 257 pp., Spiralbound 1991 . 149 pp., Spiralbound ISBN 2-921120-09-7 ISBN 2-921120-12-7 $29 CON /$26 US An integrated account edited by RobertP. Langlands $23 CON /$21 US (IAS,Princeton) & DinakarRamakrishnan (California A SURVEY OF THE HODGE Institute of Technology) AUTOMORPHIC FORMS CONJECTURE AND ANALYTIC NUMBER J.D. Lewis Although they are central objects in the theory of diophantine THEORY These lecture notes serve as an equations, the zeta-functions of Hasse-Weil are not well Ram Murty (Editor) introduction to topics in trans­ understood. One large class of varieties whose zeta-functions are Contents: A. Adophson and S. cendental algebraic geometry perhaps within reach are those attached to discrete groups, and Sperber, Exponential Sums on centered around the general called generically Shimura varieties. The techniques involved are (F *)"; E. Bombieri, On Hodge conjecture. . difficult: representation theory and harmonic analysis; the trace Vl'nogradov's Mean Value 1991 . 400 pp., Softcover formula and endoscopy; intersection cohomology and L1- Theorem and Weyl Sums; D. ISBN 2-921120-11-9 cohomology; and abelian varieties with complex multiplication. Bump, S. Friedberg and J. $37 CON /$34 US Hoffstein, On Walaspurger's The simplest Shimura varieties for which all attendant problems Theorem; W. Duke and H. TABLES OF occur are those attached to unitary groups in three variables over Iwaniec, An Estimate for Coeffi­ REPRESENTATIONS OF imaginary quadratic fields, referred to in the present volume as cients of L-Functions; P. Delmer SIMPLE LIE ALGEBRAS Picard modular surfaces. In an attempt to render this very new and J.-M. Deshouillers, domain accessible to mathematicians in related fields and to Simplexes II Coordonnees Entre­ W.G. Mcl

1992. 492 pages, Hardcover ~------ISBN 2-921120-08-9 1------$37 CDN/$34 US l..eeL!'ostal Code: ..... _j

Credit card orders by phone (514) 343-7501, by fax (514) 343-2254 or E-mail: [email protected] •• NEW FROM BIRKHAUSER

RIEMANNIAN FUNDAMENTALS OF GROUP THEORETICAL GEOMETRY THE THEORY OF METHODS AND THEIR M. DO CARMO, Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil OPERATOR ALGEBRAS APPLICATIONS Translated from the Portuguese by F. VOLUME III: Elementary Theory­ ALBERT FASSLER, Ingenieurschule Biel, FLAHERTY, Oregon State University, An Exercise Approach Switzerland and the late EDUARD STIEFEL Corvallis and The book is written at a level appropriate to "It is the best text for a beginning graduate course VOLUME IV- SPECIAL TOPICS: scientists wishing to apply the concepts to in differential geometry that I have ever seen, in Advanced Theory -An Exercise symmetry problems or to familiarize them­ any language whatsoever. The text itself is Approach selves with group theory in an applied setting. alive ... good clear, engaging writing ... delightful to illustrated with over 50 figures, the book R. KADISON, University of Pennsylvania, and presents theory, examples, and applications, read." J.R. RINGROSE, University of Newcastle -Herman Gluck, University of Pennsylvania interacting with each other in a didactically "It is an exceptionally interesting book, nicely The many readers of the highly acclaimed refreshing and unconventional way, while organized, clearly written, and very well treatise on which these volumes are based maintaining mathematical integrity and translated." will enthusiastically welcome the authors' accuracy. The applications are written with -William Firey, Oregon State University decision to share with them their detailed the non-expert in mind. The book is highly "Finally a translation of do Carma's Brazilian solutions to the stimulating and penetrating recommended to a wide variety of practicing classic. The style is pedagogically ideal. Concepts exercises that appeared in the first two scientists. Its use of algorithmic concepts in are motivated and there are ubiquitous examples volumes. With clarity, thoroughness, and many instances will make it particularly and exercises. I believe this to be the best depth, these solutions supplement the basic valuable to students of any field in which introductory text on Riemannian geometry." theory and provide an invaluable tool for symmetry problems play an important role. -Robert Gardner, University ofNorth Carolina students and researchers in mathematics and 1992 296 pp. 57 illus. Hardcover CONTENTS: theoretical physics and engineering. They ISBN 0-8176-3527-0 $49.50 Differential Manifolds • Riemannian Metrics • Affine provide models which test understanding Connections/Riemannian Connections • Geodesics/ Convex Neighborhoods • Curvature • Jacobi Fields • and suggest alternate methods and styles for Isometric Immersions • Complete Manifolds/Hopf-Rinow producing further solutions and extending INTRODUCTION and Hadamard Theorems • Spaces of Constant Curvature knowledge in such areas as functional • Variations of Energy • The Rauch Comparison Theorem analysis and quantum physics. • The Morse Index Theorem • The Fundamental Group of TO THE GALOIS Manifolds of Negative Curvature • The Sphere Theorem • VOLUME III: 1991 278 pp. Hardcover References • Index. ISBN 0-8176-3497-5 $34.50 CORRESPONDENCE 1991 300 pp. Hardcover VOLUME IV: 1992 594 pp. (approx.) M. FENRICK, Mankato State University, ISBN 0-8176-3490·8 $39.50 Hardcover ISBN 0·8176-3497-3 $49.50 (tent.) Minnesota Mathematics: Theory and Applications This textbook is intended to serve as an intro­ ADVENTURES duction to the study of the Galois correspon­ INFINITE dence. The book is self contained in that it is IN STOCHASTIC only assumed that the student has a certain DIMENSIONAL level of mathematical sophistication and has PROCESSES studied some elementary linear algebra. The MORSE THEORY necessary background theory of groups and by SIDNEY RESNICK, Cornell University rings is covered in the first chapter, thus pro­ AND MULTIPLE viding a firm foundation for the study of the Accessible to beginners, this serious approach Galois correspondence itself. At each stage of SOLUTION PROBLEMS to applied probability features the basic development concrete examples have been by KUNG-CHING CHANG, Peking stochastic processes that are necessary given, and many of these examples include University, Beijing ingredients for building models of a wide exercises which involve verifying facts, thus variety of phenomena exhibiting time giving the student the chance to confirm This research level monograph is the first varying randomness. Ideally suited as a first book to present various critical point understanding of the example. In addition, year graduate text. there are numerous exercises, of varying theorems in a unified framework. The author CONTENTS: employs Morse theory as a tool to study Preliminaries: Discrete Index Sets and/or Discrete State degrees of difficulty, at the end of each section. multiple solutions to differential equations Spaces • Markov Chains • Renewal Theory • Point 1991 189 pp. Hardcover Prooesses • Continuous Time Markov Chains • Brownian ISBN 0-8176-3522-X $49.50 arising in the calculus of variations. Motion • The General Random Walk • References • Critical groups for isolated critical points Indexes or orbits, which exceed the information 1992 500 pp. (approx.) Hardcover provided by the Leray-schauder index, are ISBN 0-8176-3591-2 $64.50 (tent.) introduced. CONTENTS: Three Easy Ways to Order! Introduction • Infinite Dimensional Morse Theory • Call: Toll-Free 1-800-777-4643. Critical Point Theory • Applications to Semilinear Elliptic In NJ call (201) 348-4033. Your reference number is Y592. Boundary Value Problems • Multiple Periodic Solutions of Hamiltonian Systems • Applications to Harmonic Maps Write: Birkhauser, Order Fulfillment -Dept. and Minimal Surfaces • Appendix • Indexes Y592, P.O. Box 2485, Secaucus, NJ 07096-2491. 1992 450 pp. (approx.) Hardcover ISBN 0-8176-3451-7 $69.50 (tent.) Visit: Your Local Technic~ Bookstore or urge your librarian to order for your department. Oj) Birkhiiuser Payment can be made by check, purchase order or credit card. Please enclose $2.50 for shipping ($1.00 for each additional book) and add appropriate sales tax if you reside LL(}» Boston Basel Berlin in NY, NJ, MA, VT, or CA. Canadian nesidents please add 7% GST. Prices subject to change without notice. ,... ~nB~~~~~~~~~~~~~

Jerrold E. Marsden, Elementary Classi.::al Anao/sif, W. H. page 234, proof ofTheorem 2. Defmethe function G:A c R" x R•--. R• x R" by is of class C!. and the identity mapping is of class C"', m:cr:o.•• (!'. The matrix of partial derivatives of G (Jacobian I 0 · 0 I

0 I 0 ··· 0· OF, OF1 OF1 OF, ax,· ... ox. ~ ... i!Ym

niCally .;.\' .., It's a breeze.

Scientific Word is a front end to TEX. It includes a Windows version of 1.1\TEX and a Windows previewer. It stores files It will have you typing mathematics in in ASCII 1.1\TEX format and imports most minutes. It's so easy, you can compose existing 1.1\TEX documents. and edit directly on the screen without being forced to think in TEX. So chill out! Let Scientific Word make your life a breeze. All you need is a PC And it gets even better! With Windows with Windows 3.0 or higher, running in 3.0, you simply use the mouse to click standard or enhanced mode... and on symbols and objects such as Scientific Word. fractions, brackets, etc., and they appear in your document. Or, you can enter the same symbols with keyboard shortcuts. . Call 800-874-2383 to order your copy today. Ask about our 30 day money-back guarantee and our educational discount. ... .It's that easy.

1190 Foster Road • Las Cruces, NM 88001 TEL: (505} 522-4600 • FAX: (505) 522-0116 TELEX: 317629 SOFTWARE RESEARCH, INC. Scientific Word is a registered trademark of TCI Software Research Inc T EX is a trademark of the American Mathematical Society Windows is a trademark

An Extension of lntrodudion to Casson's Invariant Princeton Algebraic and Kevin Walker Construdive This book describes an invariant, A, of ori­ Combinatorics of ented rational homology 3-spheres which is Train Tracks Quantum Field a generalization of work of Andrew Casson in the integer homology sphere case. Let R. C. Penner with J. L. Harer Theory R(X) denote the space of conjugacy classes Measured geodesic laminations are a natu­ John C. Baez, Irving E. of representations of n; (X) into SU(2). Let ral generalization of simple closed curves in 1 Segal, 0N1,W2,F) be a Heegaard splitting of a surfaces, and they play a decisive role in vari­ and Zhengfang Zhou rational homology sphere M. Then A(M) is ous developments in two-and three-dimen­ The authors present a rigorous treatment declared to be an appropriately defined sional topology, geometry, and dynamical of the first principles of the algebraic and analytic core of quantum field theory. Their intersection number of R0N1) and R0N2) systems. This book presents a comprehen­ inside R(F). sive treatment of the rich combinatorial aim is to correlate modern mathematical the­ A formula describing how A transforms structure of the space of measured geodesic ory with the explanation of the observed under Dehn surgery is proved. The formula laminations in a fixed surface. Families are process of particle production and of parti­ involves Alexander polynomials and Dede­ described by specifying a train track in the cle-wave duality that heuristic quantum field theory provides. Many topics are treated kind sums, and can be used to give a rather surface, and the space of measured geo­ here in book form for the first time, from elementary proof of the existence of A. It is desic laminations is analyzed by studying properties of train tracks in the the origins of complex structures to the also shown that when M is a Z2-homology sphere, A(M) determines the Rochlin invari­ surface. quantization of tachyons and domains of ant of M. Annals of Mathematics Studies, 125 dependence for quantized wave equations. Princeton Series in Physics Annals of Mathematics Studies. 126 Paper: $22.50 ISBN 0-691-02531-2 $59.50 ISBN 0-691-08546-3 Paper: $16.50 ISBN 0-691-02532-0 Cloth: $55.00 ISBN 0-691-08764-4 Cloth: $39.50 ISBN 0-691-08766-0 Princeton University Press 41 WILUAM ST. • PRINCETON, NJ 08540 • ORDERS: 800-777-4726 • OR FROM YOUR LOCAL BOOKSTORE SYMPOSIA GAUSSIANA Series A: Mathematics and Theoretical Physics. A SELECTION OF PAPERS IN VOLUME 1: P. Ribenbolm: Gauss and the Class Number Problem; E. Knobloch: The Hypothetical Nature of Mathematical Proofs- Gauss and the Development of Error Theory; A.S. Wightman: The Present State of Quantum Field Theory; P. Lelong: Analyse Complexe et Geometrie Algebrique - Role des Objets Analytiques Souples; Y.l • Petunln: Gauss Problem for Unimodal Distributions and Construction of Confidence Limits; A. Mlcall: Progres Recants dans Ia Theorie des Algebras de Clifford; C.DeWitt-Morette and S. Gwo: One Spin Group- Two Pin groups; S.W. MacDowell and 0. Tornkvlst: Instability and Phase Transition of the Electro-Weak Vacuum in a Strong Uniform Magnetic Field; R. Thom: Geometrical Invariants of Plane or Spherical Stationary Flows. JOURNAL OF COMPUTING AND INFORMATION Honorary Editor: R.W. Hamming A SELECTION OF PAPERS IN VOLUMES 1 AND 2: J. Aczel: Merging Relative Scores - Our Correct Ways and a Wrong Way; R.G. Stanton: An Algorithm for Non-Isomorphic Coverings; Klas Forsberg and lan F.Biake: The Enumeration of Constrained Sequences; Prabir Bhattacharya and Kal Qlan: Binary Image Processing by Polynomial Approach; Siegfried Heller:Robest Estimation of Arma Models; S. Thomaier: Error Correcting Polyhedral Codes; S. Gulasu: On Projection Pursuit; R.G. Lintz: Non-Deterministic Dynamical Systems-1 & II; M. Akahlra and K. Takeuchi: A Definition of Information Amount Applicable to Non-Regular Cases.

To order and for information: Fax: (416) 332-4460 Write: PO Box 56, McMaster Universit , Hamilton, Ontorio, Canada LSS 1CO

Essential Mathematics from Cambridge

Computational Learning Theory Boundary Integral and M.H.G. Anthony and N. Biggs Singularity Methods for Cambridge Tracts in Theoretical Computer Science 30 Linearized Viscous Flow 1992 200 pp. 41603-5 Hardcover $36.95 C. Pozrikidis Cambridge Texts in Applied Mathe!fllltics 8 The Design and Analysis of 1992 269 pp. 40502-5 Hardcover $69.50 Research Studies 40693-5 Paper $27.95 Bryan F.J. Manly 1992 370 pp. 41453-9 Hardcover $89.95 Now in paperback ... 42580-8 Paper $37.95 Algebraic Number Theory A. Frohlich and M.J. Taylor Stopping Times and Directed Cambridge Studies in Advanced Mathematics 27 Processes 355 pp. 43834-9 Paper about $29.95 G.A. Edgar and Louis Sucheston Encyclopedia ofMathematics and its Applications 47 Available in bookstores or write: 1992 400 pp. 35023-9 Hardcover $54.95

General Orthogonal Polynomials CAMBRIDGE Herbert Stahl and Vilmos Totik UNIVERSITY PRESS Encyclopedia ofMathematics and its Applications 43 40 West.20th Street, New York, NY 10011-4211. 1992 320 pp. 41534-9 Hardcover $59.95 Call toll-free 800-872-7423. MasterCardNISA accepted. Prices subject to change. AN INTRODUCTION RANDOM FATIGUE TO WAVELETS From Data to Theory APPLY Charles K. Chui K. Sobczyk and B.F. Spencer, Jr. January1992, 264pp., $49.95 January1992, 266pp., $49.95 ISBN: 0-12-174584-8 ISBN: 0-12-654225-2

YouRSELF WAVELETS STABILITY AND A Tutorial in Theory and T IME-0PTIMALCONTROL Applications OF HEREDITARYSYSTEMS edited by Charles K. Chui E.N.Chukwu April1992, 528pp., $59.95 January1992, 723 pp., $69.95 ISBN: 0-12-174560-0 ISBN: 0-12-174590-2

CoNVEX FuNCTIONs, PARTIAL FRACTAL ATTRACTION™ A Fractal Design System ORDERINGS, AND STATISTICAL for the Macintosh® APPLICATIONS Kevin D. Lee and YosefCohen Josip E. Pecaric, Frank Proschan, January1992, $49.95 and Y.L. Tong ISBN: 0-12-440740-4 May 1992,448 pp., $84.00 Includes 80-page manual and one floppy disk. ISBN: 0-12-549250-2 Macintosh is a registered trademark of Apple Computer, Inc.

Order from your local bookseller or directly from CALL TOLL FREE A ACADEMIC PRESS HarcourtBraceJovanovich, Publishers 1·800·321·5068 V Book Marketing Department #20052, 1250 Sixth Avenue, San Diego, CA 92101 Quote this reference number for free postage and handling on your prepaid order ,. 20052 FAX 1·800·235·0256 Prices subject to change without notice.© 1992 by Academic Press, Inc. All Rights Reserved. SUABISS- 20052.

COMBINATORIC$

CONFERENCE BOARD 01= THE MATHEMATICAL SCIENCES AND PARTIALLY Subfactors and Knots ORDERED SETS Vaughan F. R. Jones Dimension Theory William T. Trotter Subfactors and Knots provides an extensive introduction to the theory of von Neumann algebras and to knot theory and William Trotter has written the first research-level mathematics book concentrating on combinatorial topics for finite partially braid groups. The presentation follows the historical develop­ ordered sets. With dimension theory serving as a unifying ment of the theory of subfactors and the ensuing applications to theme, research on partially ordered sets, or posets, is linked to knot theory, including full proofs of some of the major results. more traditional topics in combinatorial mathematics-including Jones treats in detail the Homfly and Kauffman polynomials, graph theory, ramsey theory, probabilistic methods, hypergraphs, introduces statistical mechanical methods on knot diagrams, and algorithms, and computational geometry. This book should attempts an analogy with conformal field theory. serve as a catalyst for the continuing development of combinatorial theory for the evolution of random partially 1991 Mathematics Subject Classifications: 46, 57; 16, 22, 81, 82 ordered sets and related structures. With many examples, ISBN 0-8218-0729-3, 113 pages (softcover), November 1991 exercises, and research problems, it will foster research activity All individuals $26, List price $43 in combinatorial mathematics for years to come. To order, please specify CBMS/80NA Johns Hopkins Series in the Mathematical Sciences

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 $45.00 hardcover per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. The Johns Hopkins University Press Canada residents, please add 7%GST. 701 West 40th Street, Suite 275, Baltimore, Maryland 21211 To order, call1-800-537-5487. American Mathematical Society New Titles! Translations of Mathematical Monographs

Complements of Discriminants of Smooth Maps: Topology and Applications Volume 98 V. A. Vassiliev A major contribution to the field of algebraic topology, this book provides the first comprehensive report on recent developments. Vassiliev, whose results have proved especially fruitful in recent research in knot theory, is a major leader in the field. This book will interest mathematicians in differen­ tial and homotopy topology and complexity theory, as well as physicists interested in string theory and Feynman diagrams. It makes a great textbook for graduate courses in topology, catastrophe theory, and, to a more limited extent, complexity theory.

1991 Mathematics Subject Class!fications: 55, 57 ISBN 0-8~18-4555-1, 208 pp. (hardcover), June 1992 Individual member $98, List price $164, Institutional member $131 Your ordering code is MMON0/98NA

Partial Differential Operators of Elliptic Type, Volume 99 Norio Shimakura Shimakura's book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses: · • the Laplacian in Euclidean spaces • elementary solutions • smoothness of solutions • Vishik-Soboloev problems • the Schauder theory • degenerate elliptic operators.

Originally in Japanese, Shimakura's book is written for an undergraduate course or first-year graduate course in partial differential equations and is of interest to researchers as well.

1991 Mathematics Subject Class!fications: 35 ISBN 0-8218-4556-X, 288 pp. (hardcover), June 1992 Individual member $79, List price $132, Institutional member $106 Your ordering code is MMON0/99NA

All prices subject to change. Free shipment by surface; for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please Include 7% GST. Application for Membership 1992 AMERICAN MATHEMATICAL SOCIETY (January-December) Date ...... 19 ......

Please read the reverse side of this form to determine what member­ Fields of Interest ship category you are eligible for. Then fill out this application and If you wish to be on the mailing lists to receive informa­ retum it as soon as possible. tion about publications in fields of mathematics in which Subscriptions to the Notices and the Bulletin (New Series) are in­ you have an interest, please consult the list of major cluded as part of your membership. headings of the 1991 Mathematics Subject Classifica­ tion below. Select no more than five category num­ bers and fill in the numbers where indicated on the left. These categories will be added to your computer record Fim Mldd!. so that you will be informed of new publications or spe­ Please indicate below the way your name should appear in the Combined cial sales in the fields you have indicated. Membership List. 00 General 01 History and biography Fim Mldd!. or lniti•l 03 Mathematical logic and foundations 04 Set theory Place of Birth ..•.••••••....•.....•...•.•...•....•••....••.••••• 05 Combinatoric& City St•tfl Country 06 Order, lattices, ordered algebraic structures Date of Birth ..••...... •...•...••••...•..•..••...... ••••.•..... 08 General algebraic systems 11 Number theory Oily Month Yur 12 Field theory and polynomials If formerly a member of AMS, please indicate dates •...••...•....•••. 13 Commutative rings and algebras 14 Algebraic geometry Check here if you are now a member of either MAA D or SIAM D 15 Linear and multilinear algebra; matrix theory Degrees, with institutions and dates ....•..••..•...•....•••.••..... 16 Associative rings and algebras 17 Nonassociative rings and algebras 18 Category theory, homological algebra 19 K-theory 20 Group theory and generalizations 22 Topological groups, Lie groups 26 Real functions Present position .....••...... •...... ••.•••...•.•..••.. 28 Measure and int_egration 30 Functions of a complex variable 31 Potential theory Firm or institution ...... •.•.•...... •....•...... •.•..••. 32 Several complex variables and analytic spaces 33 Special functions 34 Ordinary differential equations Zip/Country 35 Partial differential equations 39 Finite differences and functional equations Primary Fields of Interest (choose five from the list at right) 40 Sequences, series, summability 41 Approximations and expansions 42 Fourier analysis 43 Abstract harmonic analysis Secondary Fields of Interest (choose from the list at right) 44 Integral transforms, operational calculus 45 Integral equations 46 Functional analysis 4 7 Operator theory Address for all mail 49 Calculus of variations and optimal control; optimization 51 Geometry 52 Convex and discrete geometry 53 Differential geometry 54 General topology 55 Algebraic topology 57 Manifolds and cell complexes Telephone number(s) .•...... •...... ••..•...... ••••• 58 Global analysis, analysis on manifolds 60 Probability theory and stochastic processes Electronic address .••..•.•••...•.•...... •.....•...... ••••••••. 62 Statistics 65 Numerical analysis 68 Computer science 70 Mechanics of particles and systems Signlltute 73 Mechanics of solids 76 Fluid mechanics 78 Optics, electromagnetic theory Prepayment Methods and Mailing Addresses 80 Classical thermodynamics, heat transfer All payments must be in U.S. Funds. 81 Quantum theory Send checks, money orders, UNESCO coupons to American Mathemat­ 82 Statistical mechanics, structure of matter ical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571 83 Relativity and gravitational theory 85 Astronomy and astrophysics To use VISA or MasterCard, fill in information requested and mail to 86 Geophysics American Mathematical Society, P.O. Box 6248, Providence, Rl 02940- 90 Economics, operations research, programming, 6248 or call (401) 455-4000 or 1-800-321-4AMS. games 92 Biology and other natural sciences, behavioral For Foreign Bank Transfers: The name and address of the AMS bank is sciences Rhode Island Hospital Trust National Bank, Account #000-753-111, One 93 Systems theory; control Hospital Trust Plaza, Providence, Rl 02903, U.S.A. 94 Information and communication, circuits VISA D MasterCard D ...... At:COUnt number Expltetlon d8tfl M2NO Membership Categories Reciprocating Societies

Please read the following to determine what membership category you D Allahabad Mathematical Society are eligible for, and then indicate below the category for which you are D Asociaci6n Matematica Espanola applying. D Australian Mathematical Society For ordinary members whose annual professional income is below $45,000, D Berliner Mathematische Gessellschaft e.V. the dues are $78, for those whose annual professional income is $45,000 or D Calcutta Mathematical Society more, the dues are $104. D Dansk Matematisk Forening The CMS Cooperative Rate applies to ordinary members of the AMS who D Deutsche Mathematiker-Vereinigung e.V. are also members of the Canadian Mathematical Society and reside outside of D Edinburgh Mathematical Society the U.S. For members whose annual professional income is $45,000 or less, D Gesellschaft fur Angewandte the dues are $66 and for those whose annual professional income is above Mathematik und Mechanik $45,000, the dues are $88. D Glasgow Mathematical Association For a joint family membership, one pays ordinary dues, based on his or her income, and the other pays ordinary dues based on his or her income, D Indian Mathematical Society less $20. (Only the member paying full dues will receive the Notices and the D Iranian Mathematical Society Bulletin as a privilege of membership, but both members will be accorded all D Irish Mathematical Society other privileges of membership.) D fslenzka Staer6frae6aMiagi6 Minimum dues for contributing members are $156. D Israel Mathematical Union For either students or unemployed individuals, dues are $26, and annual D Janos Bolyai Mathematical Society verification is required. D Korean Mathematical Society The annual dues for reciprocity members who reside outside the U.S. and D London Mathematical Society Canada are $52. To be eligible for this classification, members must belong to D Malaysian Mathematical Society one of those foreign societies with which the AMS has established a reciprocity D Mathematical Society of Japan agreement, and annual verification is required. Reciprocity members who reside in the U.S. or Canada must pay ordinary member dues ($78 or $104). D Mathematical Society of the Philippines The annual dues for external members, those who reside in developing D Mathematical Society of the Republic of China countries which do not have any mathematical society, are $55. D New Zealand Mathematical Society Members can purchase a multi-year membership by prepaying their cur­ D Nigerian Mathematical Society rent dues rate for either two, three, four or five years. This option is not D Norsk Matematisk Forening available to either unemployed or student members. D Osterreichische Mathematische Gesellschaft D Polskie Towarzystwo Matematyczne 1992 Dues Schedule (January through December) D Punjab Mathematical Society For any category of membership where more than one dues level is given, D Ramanujan Mathematical Society see the above for descriptions of Members' Categories. D Real Sociedad Matematica Espanola D Sociedad Colombiana de Matematica Ordinary member .••..•.•••••••••••••.•.•••.•.••••• $78 $104 D D D Sociedad de Matematica de Chile CMS Cooperative rate ...... D $66 D $88 D Sociedad Matematica de Ia Republica Dominicana Joint family member (full rate) ••••••.••.••••.••..•..•• D $78 D $104 D Sociedad Matematica Mexicana D Sociedade Brasileira Matematica Joint family member (reduced rate) ..••••••.•...••••••. D $58 D $84 D Sociedade Brasileira de Matematica Contributing member (minimum $156) .••••..•.•••.•••••••••••.•• D Aplicada e Computacional D Sociedade Paranaense de Matematica Student member (please verify) 1 •••••••••••••••••••••••••••• D $26 D Sociedade Portuguese de Matematica D Societat Catalans de Matematiques Unemployed member (please verify)2 •••••••••••••••••••••••• D $26 D Societe de Mathematiques Appliquees Reciprocity member (please verify)3 •••••••••••. D $52 D $78 D $104 et lndustrielles D Societe Mathematique de Belgique External member ••..•.•••.••••••••.•••••.•..•••••••••.•••• D $55 D Societe Mathematique de France D Societe Mathematique Suisse Multi-year membership ••••••••••.•••••••.•• $ ...... for ..•••. years D Southeast Asian Mathematical Society 1 Student VerHication (sign below) D Suomen Matemaattinen Yhdistys D Svenska Matematikersamfundet I am a full-time student at • •••.••.•..•••••••...•..••.••••...•..••.• D Union Mathematics Argentina ••.••••••••••••.••••••.•••••...•• currently working toward a degree. D Unione Matematica ltaliana D Vijnana Parishad of India 2 Unemployed Verification (sign below) I am currently unemployed and D Wiskundig Genootschap actively seeking employment. My unemployment status is not a result of voluntary resignation or of retirement from my last position.

3 Reciprocity Membership VerHication (sign below) I am currently a mem­ ber of the society indicated on the right and am therefore eligible for reciprocity membership.

SignBtul'8 I Order Form I For VISA or MasterCard orders, send to: For orders with remittances, send to: American Mathematical Society American Mathematical Society P.O. Box 6248 P.O. Box 1571. Annex Station Providence. Rhode Island 02940-6248 Providence. Rhode Island 02901-1571 (800) 321-4AMS (321-4267) (401) 455-4000 Ordered by:------Mail to (if different): ------

QTY CODE AUTHOR and TITLE PRICE $

D Air Delivery

Total due (All orders must be prepaid in U.S. funds) $

Charge by phone in the continental U.S. and Canada 800-321-4AMS (321-4267) D Check or Money Order DVISA D MasterCard

Card Expiration Date Signature------

Shipping and Handling Prices are subject to change without notice. Book• are sent via surface mail (UPS to U.S. addresses and printed matter elsewhere) unless air delivery is requested. The shipping and handling charges for air delivery book orders are shown in the table. Free shipment by surface: for air delivery, Journal back numbere, Mathematical Reviews indexes and review volumes are sent via surface mail to any destination 1,1nless air deliv­ please add $6.50 per book. ery is requested. Postage for surface mail is paid by the AMS. Air delivery rates, which will be quoted upon request, must be paid by the purchaser. Software: Nonindividual customers need not prepay provided a Purchase Order number is given with the order. Soft­ ware/books are sent via UPS to U.S. addresses and via U.S. postal NOT I service air parcel post to addresses outside the U.S. Add shipping and handling for Software/Books: SB per order in the U.S. and Canada; S35 per order air delivery outside the U.S. and Canada; please add Please send information about 7% GST to all orders totalling over S40 shipped to Canada. D AMS individual membership Customers in these areas should request price information from and direct their orders to the following distributors: D AMS institutional membership Japan: Maruzen Co. Ltd., P.O. Box 5050, Tokyo Interna­ D AMS corporate membership tional 100-31, Japan. Tel. Tokyo 272-7211, Telex J26516 D AMS institutional associate India: Allied Publishers Pvt. Ltd., 15, J. N. Herdia Marg., Ballard Estate, Bombay 400038, India Staple here

Fold here

NO POSTAGE NECESSARY IF MAILED IN THE UNITED STATES BUSINESS REPLY MAIL FIRST-CLASS MAIL PERMIT NO. 554B PROVIDENCE, RI

POSTAGE WILL BE PAID BY ADDRESSEE

Customer Services AMERICAN MATHEMATICAL SOCIETY P. 0. Box 6248 Providence, RI 02940-9943

111 ••••• 1.11.1 ••• 1•• 111 ••• 1.1 •• 1.1 ••• 1•• 1•• 11.11 ••• 1

Fold here Change of Address

Members of the Society who move or who change po­ of members' honors, awards, and information on Society sitions are urged to notify the Providence Office as soon service. Information of the latter kind appears regularly as possible. in Notices. Journal mailing lists must be printed four to six weeks When changing their addresses, members are urged to before the issue date. Therefore, in order to avoid dis­ cooperate by supplying the information requested below. ruption of service, members are requested to provide the The Society's records are of value only to the extent that required notice well in advance. they are current and accurate. Besides mailing addresses for members, the Society's If your address has changed or will change within the records contain information about members' positions next two or three months, please fill out this form, supply and their employers (for publication in the Combined any other information appropriate for the AMS records, Membership List). In addition, the AMS maintains records and mail to the address given below.

Name:------Customer code:------

Change effective as of:------

Old mailing address:------

NEW mailing address:------

New position:------

If mailing address is not that of your employer, please supply the following information:

New employer:------

Location of employer:------City State/Province Country Zip Code

Telephone number(s): ------

Electronic address(es): ------

Recenthonorsandawards=------

Personal items for publication in Notices: ------

Mail completed form to: Customer Services, AMS, P.O. Box 6248, Providence, RI 02940 or send the above information by email to: [email protected] or [email protected]. Staple here

Fold here

NO POSTAGE NECESSARY IF MAILED IN THE UNITED STATES BUSINESS REPLY MAIL FIRST-CLASS MAIL PERMIT NO. 554B PROVIDENCE, RI

POSTAGE WILL BE PAID BY ADDRESSEE

Customer Services AMERICAN MATHEMATICAL SOCIETY P.O. Box 6248 Providence, RI 02940-9943

Fold here American Mathematical w Society

The American Mathematical Society has an expand­ ing collection of videotaped lectures that help to pre­ a... serve a portrait of today's distinguished mathematicians while capturing the interest and enthusiasm of the speakers as they present material in their fields of expertise. You will find these expository lectures useful in courses, seminars, and general assemblies for students with an upper-level mathematics background. These inexpensive videotapes are also perfect for your school library. All videotapes belong to one of these exciting series:

AMS-MAA Joint Selected Lectures Lecture Series

Progress Science Television ICM Series in Mathematics Productions w For your FREE videotape brochure call AMS Customer Services at 800·321·4AMS (321·4267) in the continental U.S. and Canada and 401·455·4000 elsewhere.

All videotapes are NTSC format on half-inch VHS videotape and are approximately 1 hour long. Videotapes in the Progress in Mathematics series are approximately 90 minutes long. The Americ.an Mathematical Society Announces Two New Titles in its Contemporary Mathematics Series

Geometry and Nonlinear Partial Differential Equations Vladimir Oliker and Andrejs Treibergs, Editors Volume 127 This volume contains the proceedings of an AMS Special Session on Geometry, Physics, and Nonlinear PDEs, held in March 1990 at the AMS meeting in Fayetteville. The conference brought together specialists in Mange-Ampere equations, prescribed curvature problems, mean curvature, harmonic maps, evolution with curvature-dependent speed, isospectral manifolds, and general relativity. The book provides an excellent overview of the frontiers of research in these areas. 1991 Mathematics Subject Classification: 35, 53, ISBN 0-8218-5135-7, 154 pages (softcover), April1992 Individual member $22, List price $36, Institutional member $29 Your ordering code is CONM/127NA New Approaches in Spectral Decomposition Ridgley Lange and Shengwang Wang Volume 128 The book begins with a discussion of criteria for decomposable and related types of operators and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilbert space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.

1991 Mathematics Subject Classification: 47; 46 ISBN 0-8218-5139-X 272 pages (softcover), May 1992 Individual member $26, List price $44 Institutional member $35 Your ordering code is CONM/128NA MathSci Disc

MathSci Dlsc®-the mathematics reference col­ lection from the American MathematicaJ Society­ now comes tQ you on three compact discs. • Tne··first .disc-updated every six months­ provide$ y<>uwif'tMSthematical Reviews and Cur­ rent~Publk:stionscoveragefrom 1988 tothe,p~. • The ~ diSc includes everything in· MR from 1010 to 198"1. • The fhitQd._.,MR1ftlleXC1M0-1t7t), is new for 1Q92.·.MRJtMJt•~.youanindexto Math· ematlcatRe~f*blishidfrQm 194Q-79. SPRINGER FOR MATHEMATICS ~

W.A. Adkins and S.H. Weintraub, both of T.-Y. LAM, University of California, Berkeley S. ROMAN , California State University, Louisiana State University, Baton Rouge A FIRST COURSE IN Fullerton, CA ALGEBRA NONCOMMUTATlVE RINGS CODING AND An Approach via Module Theory INFORMA110N THEORY Intended for a one-semester course in Designed for a first-year graduate­ basic ring theory. Includes the An introduction to the subjects of level course in algebra. Beginning Wedderbum-Artin theory of information and coding theory at the with an introduction to group theory semisimple rings, Jacobson's theory graduate or advanced undergraduate and ring theory, the book develops of the radical, representation theory level. Assumes a basic knowledge of the basics of module theory. It then of groups and algebras, prime and probability and linear algebra. The uses module theory to investigate semiprime rings, primitive and first quarter is devoted to the basics bilinear, sesquilinear and quadratic semiprimitive rings, division rings; of information theory, including a forms. Finally, a discussion of ring ordered rings, local and semilocal proof of Shannon's famous Noisy theory and multilinear forms leads to rings, and perfect and semi perfect Coding Theorem. The remainder of a chapter on group representations, rings. Also includes numerous the book is devoted to coding theory using module theory to powerful exercises testing the understanding of and has a decidedly algebraic flavor. effect. the general theory in the text are also An appendix reviews relevant topics 1992/APP. 534 PP., 2 ILLUS./HARDCOVER included. from modem algebra. $39.95(TENT.)/ISBN 0-387-97839·9 1992/ 496 PP ., 31 ILLUS./HARDCOVER GRADUATE TEXTS IN MATHEMATICS, 1991/ 397 PP. / HARDCOVER/ $49.00 $49.95/ ISBN 0-387-97812-7 VOLUME 137 ISBN 0-387-97523-3 GRADUATE TEXTS IN MATHEMATICS , GRADUATE TEXTS IN MATHEMATICS , VOLUME 131 VOLUME 134 H.T. CROFT, Cambridge University, England; K.J. FALCONER, Bristol University, England; H..FRACTALS FOR UNSOLVED PROBLEMS MATHEMA11CS IN IN GEOMETRY THE CLASSROOM MEDICINE AND THE Part 1: Introduction to Fractals Presents a collection of geometrical LIFE SCIENCES and Chaos problems that are easy to state and Part II: Complex Systems understand, but are as yet unsolved. Introduces the subject of mathemati­ and Mandelbrot Set The problems cover a wide variety cal modeling in the life sciences to of topics including chapters on students of mathematics, the physical PART 1: 1992/ 450 PP., 289 ILLUS./ HARD­ convex sets, polyhedra, packing and sciences, and engineering who are COVER/ $29.00/ ISBN 0-387-97041-X covering, tiling, and combinatorial curious about biology. Also useful to PART II: 1992/ APP. 384 PP., 1411LLUS./ HARDCOVER/$29.00/ ISBN 0-387-97722-8 problems. The 148 sections each students in life sciences and medicine describe a problem or group of who seek an understanding of bio­ iii·MMIMMM·i; related problems along with a discus­ logical mechanisms and dynamics .,~t)' ; sion of its background and a list of through the use of mathematics. references. Particularly useful to premedical ~- ...;;;;:.;;II~I:Wiiii.lil'"' "·-)~ 0· .- --, students, as it introduces them to an 1991/198 PP., 66 ILLUS./HARDCOVER Three Easy Ways to Order. $39.95/ISBN 0-387-97506-3 assortment of phenomena involving PROBLEM BOOKS IN MATHEMATICS genetics, epidemics, and the physiol­ Call Toll Free 1-800-SPRINGER (NJ call UNSOLVED PROBLEMS IN INTUITIVE ogy of the heart, lung and kidney. 201-348-4033) or FAX 201-348-4505. MATHEMATICS II 1992/ 252 PP. , 73 ILLUS. / HARDCOVER Please mention S213 when ordering $39.95/ ISBN 0-387-97639-6 by phone. J.H. SILVERMAN, Brown University, TEXTS IN APPLIED MATHEMATICS, VOLUME 10 Write to Springer-Verlag New York, Providence, Rl; J. TATE, University of Texas, Inc., Dept. #S213, P.O. Box 2485, Austin, TX Secaucus, NJ 07096-2491. RA110NAL POINTS ON Visit your local scientific bookstore or urge your librarian to order for your ELLIPTlC CURVES department. Emphasizes the number-theoretic Payment can be made by aspects of elliptic curves. The first check, purchase order, or credit part proves the fundamental theo­ card. Please enclose $2.50 for ship­ rems of the field: The Nagell-Lutz ping ($1.00 additional books) & add theorem, Mordell's theorem, and appropriate sales tax if you reside Hasse's theorem. The remainder of ~a~ in NY, NJ, MA, VT, or CA. Canadian the book discusses special topics and ~ residents please add 7% GST. newer developments. Remember ... your 30-day return Springer -¥erlag priviledge is always guaranteed! 1992/250 PP., 35 ILLUS./HARDCOVER NEW YORK 5 / 92 REFERENCE #: 5213 $29.95/ISBN 0-387-97825-9